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Materials
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Characterizations, Mechanical Properties and Constitutive Modeling of Advanced Materials
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Characterizations, Mechanical Properties and Constitutive Modeling of Advanced Materials

A special issue of Materials (ISSN 1996-1944). This special issue belongs to the section "Mechanics of Materials".

Deadline for manuscript submissions: closed (20 June 2024) | Viewed by 18589

Printed Edition Available!
A printed edition of this Special Issue is available here.

Special Issue Editors

Dr. Madhav Baral

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Guest Editor
Department of Mechanical and Aerospace Engineering, University of Kentucky, Lexington, 40506, KY, USA
Interests: plasticity; constitutive modeling; ductile fracture; experimental and numerical methods; sheet metal and tube forming; material characterization; manufacturing processes
Special Issues, Collections and Topics in MDPI journals
Prof. Dr. Charles Lu

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Guest Editor
Department of Mechanical Engineering, University of Kentucky, Lexington, KY, USA
Interests: composites; advanced materials; mechanics; finite element modeling
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

Characterizations, mechanical properties, and constitutive modeling are three key areas of focus in the field of materials science and engineering. Characterization is the process of identifying and understanding the properties of materials, while mechanical properties refer to the behavior of materials under various mechanical loads, such as tension, compression, and bending. Constitutive modeling aims to develop mathematical descriptions of how materials respond to these loads.

This Special Issue aims to explore the latest developments in these areas, with a focus on both experimental and theoretical approaches. The Issue will cover a broad range of topics, including the characterization of advanced materials such as nanomaterials and biomaterials, the investigation of their mechanical properties under different loading conditions, and the development of constitutive models to describe their behavior.

Researchers from academia, industry, and government organizations are invited to submit their original research articles, reviews, and perspectives on these topics. The Issue will provide a valuable platform for the exchange of knowledge and ideas and shall contribute to the advancement of the field of materials science and engineering.

Topics of interest for this Special Issue include, but are not limited to:

  • Advanced materials characterization techniques;
  • Mechanical properties of advanced materials;
  • Constitutive modeling of materials;
  • Biomaterials and their mechanical properties;
  • Nanomaterials and their mechanical properties;
  • Fatigue and fracture mechanics of materials;
  • Mechanical behavior of composites and hybrid materials.

Dr. Madhav Baral
Prof. Dr. Charles Lu
Guest Editors

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Published Papers (16 papers)

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Research

19 pages, 7217 KiB  
Article
Study on the Shear Strength and Erosion Resistance of Sand Solidified by Enzyme-Induced Calcium Carbonate Precipitation (EICP)
by Gang Li, Qinchen Zhu, Jia Liu, Cong Liu and Jinli Zhang
Materials 2024, 17(15), 3642; https://doi.org/10.3390/ma17153642 - 24 Jul 2024
Cited by 1 | Viewed by 892
Abstract
Sand solidification of earth-rock dams is the key to flood discharge capacity and collapse prevention of earth-rock dams. It is urgent to find an economical, environmentally friendly, and durable sand solidification technology. However, the traditional grouting reinforcement method has some problems, such as [...] Read more.
Sand solidification of earth-rock dams is the key to flood discharge capacity and collapse prevention of earth-rock dams. It is urgent to find an economical, environmentally friendly, and durable sand solidification technology. However, the traditional grouting reinforcement method has some problems, such as high costs, complex operations, and environmental pollution. Enzyme-induced calcium carbonate precipitation (EICP) is an anti-seepage reinforcement technology emerging in recent years with the characteristics of economy, environmental protection, and durability. The erosion resistance and shear strength of earth-rock dams solidified by EICP need further verification. In this paper, EICP-solidified standard sand is taken as the research object, and EICP-cemented standard sand is carried out by a consolidated undrained triaxial test. A two-stage pouring method is adopted to pour samples, and the effects of dry density, cementation times, standing time, and confining pressure on the shear strength of cemented standard sand are emphatically analyzed. The relationship between cohesion, internal friction angle, and CaCO3 formation was analyzed. After the optimal curing conditions are obtained through the triaxial shear strength test, the erosion resistance model test is carried out. The effects of erosion angle, erosion flow rate, and erosion time on the erosion resistance of EICP-solidified sand were analyzed through an erosion model test. The results of triaxial tests show that the standard sand solidified by EICP exhibits strain softening, and the peak strength increases with the increase in initial dry density, cementation times, standing time, and confining pressure. When the content of CaCO3 increases from 2.84 g to 12.61 g, the cohesive force and internal friction angle change to 23.13 times and 1.18 times, and the determination coefficients reach 0.93 and 0.94, respectively. Erosion model test results indicate that the EICP-solidified sand dam has good erosion resistance. As the increase in erosion angle, erosion flow rate, and erosion time, the breach of solidified samples gradually becomes larger. Due to the deep solidification of sand by EICP, the development of breaches is relatively slow. Under different erosion conditions, the solidified samples did not collapse and the dam broke. The research results have important reference value and scientific significance for the practice of sand consolidation engineering in earth-rock dams. Full article
(This article belongs to the Special Issue Characterizations, Mechanical Properties and Constitutive Modeling of Advanced Materials)
►▼ Show Figures

Figure 1

Figure 1
<p>Sand particle size distribution curve.</p> Full article ">Figure 2
<p>Separation and extraction process of soybean urease: (<b>a</b>) crushed; (<b>b</b>) stirring sample powder; (<b>c</b>) centrifugation of sample; (<b>d</b>) urease.</p> Full article ">Figure 3
<p>Erosion resistance model test chamber.</p> Full article ">Figure 4
<p>Effect of dry density on stress–strain curve of EICP-cemented standard sand: (<b>a</b>) <span class="html-italic">t</span><sub>1</sub> = 1 d, <span class="html-italic">n</span> = 2; (<b>b</b>) <span class="html-italic">t</span><sub>1</sub> = 1 d, <span class="html-italic">n</span> = 4; (<b>c</b>) <span class="html-italic">t</span><sub>1</sub> = 1 d, <span class="html-italic">n</span> = 6.</p> Full article ">Figure 5
<p>Effect of cementation times on stress–strain curve of EICP-cemented standard sand (<span class="html-italic">σ</span><sub>3</sub> = 25 kPa): (<b>a</b>) <span class="html-italic">ρ</span><sub>d</sub> = 1.65 g/cm<sup>3</sup>, <span class="html-italic">t</span><sub>1</sub> = 1 d; (<b>b</b>) <span class="html-italic">ρ</span><sub>d</sub> = 1.65 g/cm<sup>3</sup>, <span class="html-italic">t</span><sub>1</sub> = 3 d; (<b>c</b>) <span class="html-italic">ρ</span><sub>d</sub> = 1.65 g/cm<sup>3</sup>, <span class="html-italic">t</span><sub>1</sub> = 5 d.</p> Full article ">Figure 6
<p>Effect of standing time on stress–strain curve of EICP–cemented standard sand (<span class="html-italic">n</span> = 6): (<b>a</b>) <span class="html-italic">ρ</span><sub>d</sub> = 1.65 g/cm<sup>3</sup>, <span class="html-italic">σ</span><sub>3</sub> = 25 kPa; (<b>b</b>) <span class="html-italic">ρ</span><sub>d</sub> = 1.65 g/cm<sup>3</sup>, <span class="html-italic">σ</span><sub>3</sub> = 50 kPa; (<b>c</b>) <span class="html-italic">ρ</span><sub>d</sub> = 1.65 g/cm<sup>3</sup>, <span class="html-italic">σ</span><sub>3</sub> = 100 kPa.</p> Full article ">Figure 7
<p>Effect of confining pressure on stress–strain curve of EICP-cemented standard sand (<span class="html-italic">n</span> = 6): (<b>a</b>) <span class="html-italic">ρ</span><sub>d</sub> = 1.55 g/cm<sup>3</sup>, <span class="html-italic">t</span><sub>1</sub> = 1 d; (<b>b</b>) <span class="html-italic">ρ</span><sub>d</sub> = 1.60 g/cm<sup>3</sup>, <span class="html-italic">t</span><sub>1</sub> = 1 d; (<b>c</b>) <span class="html-italic">ρ</span><sub>d</sub> = 1.65 g/cm<sup>3</sup>, <span class="html-italic">t</span><sub>1</sub> = 1 d.</p> Full article ">Figure 8
<p>Failure modes of EICP-cemented specimens under different cementation times and different confining pressures: (<b>a</b>) <span class="html-italic">n</span> = 2, <span class="html-italic">σ</span><sub>3</sub> = 25 kPa; (<b>b</b>) <span class="html-italic">n</span> = 4, <span class="html-italic">σ</span><sub>3</sub> = 50 kPa; (<b>c</b>) <span class="html-italic">n</span> = 6, <span class="html-italic">σ</span><sub>3</sub> = 25 kPa; (<b>d</b>) <span class="html-italic">n</span> = 6, <span class="html-italic">σ</span><sub>3</sub> = 100 kPa.</p> Full article ">Figure 9
<p>Relationship between cohesion and internal friction angle and calcium carbonate production: (<b>a</b>) cohesion; (<b>b</b>) angle of internal friction.</p> Full article ">Figure 10
<p>Model test of standard sand dam: (<b>a</b>) uncemented specimen; (<b>b</b>) the water flow reaches the dam crest; (<b>c</b>) water erosion; (<b>d</b>) end of erosion.</p> Full article ">Figure 11
<p>Influence of erosion angle on the top depth and widening of dam central axis breach: (<b>a</b>) <span class="html-italic">Q</span> = 5 L/min, breach width; (<b>b</b>) <span class="html-italic">Q</span> = 5 L/min, breach depth; (<b>c</b>) <span class="html-italic">Q</span> = 7 L/min, breach width; (<b>d</b>) <span class="html-italic">Q</span> = 7 L/min, breach depth.</p> Full article ">Figure 12
<p>Influence of erosion discharge on the top depth and widening of dam central axis breach: (<b>a</b>) <span class="html-italic">α</span> = 15°, breach width; (<b>b</b>) <span class="html-italic">α</span> = 15°, breach depth; (<b>c</b>) <span class="html-italic">α</span> = 30°, breach width; (<b>d</b>) <span class="html-italic">α</span> = 30°, breach depth; (<b>e</b>) <span class="html-italic">α</span> = 45°, breach width; (<b>f</b>) <span class="html-italic">α</span> = 45°, breach depth.</p> Full article ">Figure 13
<p>Influence of erosion time on the top depth and widening of dam central axis breach: (<b>a</b>) <span class="html-italic">α</span> = 15°, breach width; (<b>b</b>) <span class="html-italic">α</span> = 15°, breach depth; (<b>c</b>) <span class="html-italic">α</span> = 30°, breach width; (<b>d</b>) <span class="html-italic">α</span> = 30°, breach depth; (<b>e</b>) <span class="html-italic">α</span> = 45°, breach width; (<b>f</b>) <span class="html-italic">α</span> = 45°, breach depth.</p> Full article ">Figure 14
<p>Failure process of dam overtopping: (<b>a</b>) rise of water level in reservoir area; (<b>b</b>) overflow of dam; (<b>c</b>) discharge of water on slope; (<b>d</b>) scarp erosion; (<b>e</b>) traceability of water; (<b>f</b>) dam failure; (<b>g</b>) dam shrinkage; (<b>h</b>) further erosion; (<b>i</b>) stability phase.</p> Full article ">Figure 15
<p>Erosion failure mode: (<b>a</b>) <span class="html-italic">α</span> = 15°; (<b>b</b>) <span class="html-italic">α</span> = 30°; (<b>c</b>) <span class="html-italic">α</span> = 45°.</p> Full article ">
14 pages, 5220 KiB  
Article
An Algorithm for Modeling Thermoplastic Spherulite Growth Using Crystallization Kinetics
by Jamal F. Husseini, Evan J. Pineda and Scott E. Stapleton
Materials 2024, 17(14), 3411; https://doi.org/10.3390/ma17143411 - 10 Jul 2024
Viewed by 951
Abstract
Crystallization kinetics were used to develop a spherulite growth model, which can determine local crystalline distributions through an optimization algorithm. Kinetics were used to simulate spherulite homogeneous nucleation, growth, and heterogeneous nucleation in a domain discretized into voxels. From this, an overall crystallinity [...] Read more.
Crystallization kinetics were used to develop a spherulite growth model, which can determine local crystalline distributions through an optimization algorithm. Kinetics were used to simulate spherulite homogeneous nucleation, growth, and heterogeneous nucleation in a domain discretized into voxels. From this, an overall crystallinity was found, and an algorithm was used to find crystallinities of individual spherulites based on volume. Then, local crystallinities within the spherulites were found based on distance relative to the nucleus. Results show validation of this model to differential scanning calorimetry data for polyether ether ketone at different cooldown rates, and to experimental microscopic images of spherulite morphologies. Application of this model to various cooldown rates and the effect on crystalline distributions are also shown. This model serves as a tool for predicting the resulting semi-crystalline microstructures of polymers for different manufacturing methods. These can then be directly converted into a multiscale thermomechanical model. Full article
(This article belongs to the Special Issue Characterizations, Mechanical Properties and Constitutive Modeling of Advanced Materials)
►▼ Show Figures

Figure 1

Figure 1
<p>Flow chart describing process of thermoplastic spherulite growth simulation.</p> Full article ">Figure 2
<p>2D Representation of how crystallinity decreases radially from the spherulite nucleus where <math display="inline"><semantics> <mrow> <msubsup> <mstyle mathvariant="bold" mathsize="normal"> <mi>n</mi> </mstyle> <mrow> <mi>s</mi> <mi>u</mi> <mi>b</mi> </mrow> <mi>i</mi> </msubsup> </mrow> </semantics></math> is a vector containing the number of subcells assigned a specific crystallinity.</p> Full article ">Figure 3
<p>Relative crystallinity, <math display="inline"><semantics> <mrow> <msub> <mi>χ</mi> <mi>V</mi> </msub> </mrow> </semantics></math>, versus temperature for a simulation with a 10 °C/min cooldown for (<b>a</b>) increasing subcell refinement and (<b>b</b>) increasing domain size.</p> Full article ">Figure 4
<p>Validation of crystallization kinetic model with experimental DSC results [<a href="#B10-materials-17-03411" class="html-bibr">10</a>] for thermal cooldowns of 2(+), 5(×), 10(◊), 20(□), and 50(o) <math display="inline"><semantics> <mrow> <mo>°</mo> <mi mathvariant="normal">C</mi> <mo>/</mo> <mi>min</mi> </mrow> </semantics></math>.</p> Full article ">Figure 5
<p>(<b>a</b>) Sensitivity of relative crystallinity, <math display="inline"><semantics> <mrow> <msub> <mi>χ</mi> <mi>V</mi> </msub> </mrow> </semantics></math>, based on reported equilibrium melting temperatures, <math display="inline"><semantics> <mrow> <msubsup> <mi>T</mi> <mi>m</mi> <mn>0</mn> </msubsup> </mrow> </semantics></math>, and (<b>b</b>) adjusted with respect to <math display="inline"><semantics> <mrow> <msubsup> <mi>T</mi> <mi>m</mi> <mn>0</mn> </msubsup> </mrow> </semantics></math> for PEEK.</p> Full article ">Figure 6
<p>Spherulite morphologic comparison between a thin PEEK sample cooled at <math display="inline"><semantics> <mrow> <mn>20</mn> <mo> </mo> <mo>°</mo> <mi mathvariant="normal">C</mi> <mo>/</mo> <mi>min</mi> </mrow> </semantics></math> [<a href="#B5-materials-17-03411" class="html-bibr">5</a>] and simulation.</p> Full article ">Figure 7
<p>(<b>a</b>) Spherulite morphology from a sample cooled at <math display="inline"><semantics> <mrow> <mn>20</mn> <mo> </mo> <mo>°</mo> <mi mathvariant="normal">C</mi> <mo>/</mo> <mi>min</mi> </mrow> </semantics></math> with the largest spherulite diameter labelled, (<b>b</b>) the corresponding local crystallinity distribution, and (<b>c</b>) a probability density function (PDF) of spherulite volumes.</p> Full article ">Figure 8
<p>Spherulite nucleation, growth, and crystallinity for cooldown rates of <math display="inline"><semantics> <mrow> <mn>20</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <mn>200</mn> </mrow> </semantics></math>, 500, and <math display="inline"><semantics> <mrow> <mn>2000</mn> <mo> </mo> <mo>°</mo> <mi mathvariant="normal">C</mi> <mo>/</mo> <mi>min</mi> </mrow> </semantics></math> compared at the initial time step, halfway through the simulation, and the final time step, along with the final subcell crystallinity distribution. The spherulite colors in the first three columns represent spherulite numbers.</p> Full article ">Figure 9
<p>Number of spherulites versus relative volume for simulations of three different cooldown rates.</p> Full article ">Figure 10
<p>(<b>a</b>) Temperature versus time, (<b>b</b>) nuclei growth radius, and (<b>c</b>) nucleation rate for four different simulations with increasing thermal cooldown rates.</p> Full article ">Figure 11
<p>Nucleation versus temperature for three different thermal cooldowns.</p> Full article ">
18 pages, 5241 KiB  
Article
Thermo-Chemo-Mechanical Modeling of Residual Stress in Unidirectional Carbon Fiber-Reinforced Polymers during Manufacture
by Rui Bao, Junpeng Liu, Zhongmin Xiao and Sunil C. Joshi
Materials 2024, 17(12), 3040; https://doi.org/10.3390/ma17123040 - 20 Jun 2024
Cited by 1 | Viewed by 956
Abstract
The application of carbon fiber-reinforced composite materials in marine engineering is growing steadily. The mechanical properties of unbonded flexible risers using composite tensile armor wire are highly valued. However, the curing process generates a certain amount of internal residual stress. We present a [...] Read more.
The application of carbon fiber-reinforced composite materials in marine engineering is growing steadily. The mechanical properties of unbonded flexible risers using composite tensile armor wire are highly valued. However, the curing process generates a certain amount of internal residual stress. We present a detailed analysis of epoxy resin laminates to assess the impact of thermal, chemical, and mechanical effects on the curing stress and strain. An empirical model that correlates temperature and degree of cure was developed to precisely fit the elastic modulus data of the curing resin. The chemical kinetics of the epoxy resin system was characterized using differential scanning calorimetry (DSC), while the tensile relaxation modulus was determined through a dynamic mechanical analysis. The viscoelastic model was calibrated using the elastic modulus data of the cured resin combining temperature and degree of the curing (thermochemical kinetics) responses. Based on the principle of time–temperature superposition, the displacement factor and relaxation behavior of the material were also accurately captured by employing the same principle of time–temperature superposition. Utilizing the empirical model for degree of cure and modulus, we predicted micro-curing-induced strains in cured composite materials, which were then validated with experimental observations. Full article
(This article belongs to the Special Issue Characterizations, Mechanical Properties and Constitutive Modeling of Advanced Materials)
►▼ Show Figures

Figure 1

Figure 1
<p>Structure of unbounded flexible risers in deep water.</p> Full article ">Figure 2
<p>Location of FBG sensors and thermocouple for strain measurement.</p> Full article ">Figure 3
<p>The geometry and mesh of the finite element model.</p> Full article ">Figure 4
<p>Development of the degree of cure in the central point of the laminate. During the curing process of thick laminates, the curing speed is different between the interior and the surface of the material. The temperature gradients cause inconsistent thermal expansion and contraction. This inconsistency can result in residual stress within the laminate, potentially causing warping, deformation, and even cracking of the laminate, thereby compromising its dimensional stability and structural integrity. Additionally, different degrees of cure between the inner and the outer layers can result in uneven crosslinking density, leading to disparities in the mechanical properties (such as strength and toughness) in different locations, thus reducing the overall performance and reliability of the material. Furthermore, uneven solidification during the curing process can introduce defects such as uncured areas or bubbles, increasing the risk of material failure during service. An optimized curing process is necessary to overcome these challenges, requiring real-time monitoring systems to ensure uniform curing and high-quality laminate performance.</p> Full article ">Figure 5
<p>Heat flux based on the temperature at different heating rates.</p> Full article ">Figure 6
<p>Fit relationship diagram for the Nth-order reaction kinetics model.</p> Full article ">Figure 7
<p>Relationship between activation energy and degree of cure for the curing process.</p> Full article ">Figure 8
<p>Comparison of the cure rate profiles at different heating rates.</p> Full article ">Figure 9
<p>Degree of cure at different heating rates.</p> Full article ">Figure 10
<p>Relaxation modulus for the epoxy system and its master curve.</p> Full article ">Figure 11
<p>Shift factors for the relaxation modulus.</p> Full article ">Figure 12
<p>(<b>a</b>) Elastic modulus of the cured resin at different frequencies; (<b>b</b>) loss factor at different frequencies.</p> Full article ">Figure 13
<p>Development of longitudinal stress during the cure cycles in the examined laminates.</p> Full article ">Figure 14
<p>Development of transverse stress during the cure cycles in the examined laminates.</p> Full article ">Figure 15
<p>Longitudinal curing strain during the manufacturing process.</p> Full article ">Figure 16
<p>Transverse curing strain during the manufacturing process.</p> Full article ">
27 pages, 4593 KiB  
Article
A Multiphysics Thermoelastoviscoplastic Damage Internal State Variable Constitutive Model including Magnetism
by M. Malki, M. F. Horstemeyer, H. E. Cho, L. A. Peterson, D. Dickel, L. Capolungo and M. I. Baskes
Materials 2024, 17(10), 2412; https://doi.org/10.3390/ma17102412 - 17 May 2024
Cited by 2 | Viewed by 990
Abstract
We present a macroscale constitutive model that couples magnetism with thermal, elastic, plastic, and damage effects in an Internal State Variable (ISV) theory. Previous constitutive models did not include an interdependence between the internal magnetic (magnetostriction and magnetic flux) and mechanical fields. Although [...] Read more.
We present a macroscale constitutive model that couples magnetism with thermal, elastic, plastic, and damage effects in an Internal State Variable (ISV) theory. Previous constitutive models did not include an interdependence between the internal magnetic (magnetostriction and magnetic flux) and mechanical fields. Although constitutive models explaining the mechanisms behind mechanical deformations caused by magnetization changes have been presented in the literature, they mainly focus on nanoscale structure–property relations. A fully coupled multiphysics macroscale ISV model presented herein admits lower length scale information from the nanoscale and microscale descriptions of the multiphysics behavior, thus capturing the effects of magnetic field forces with isotropic and anisotropic magnetization terms and moments under thermomechanical deformations. For the first time, this ISV modeling framework internally coheres to the kinematic, thermodynamic, and kinetic relationships of deformation using the evolving ISV histories. For the kinematics, a multiplicative decomposition of deformation gradient is employed including a magnetization term; hence, the Jacobian represents the conservation of mass and conservation of momentum including magnetism. The first and second laws of thermodynamics are used to constrain the appropriate constitutive relations through the Clausius–Duhem inequality. The kinetic framework employs a stress–strain relationship with a flow rule that couples the thermal, mechanical, and magnetic terms. Experimental data from the literature for three different materials (iron, nickel, and cobalt) are used to compare with the model’s results showing good correlations. Full article
(This article belongs to the Special Issue Characterizations, Mechanical Properties and Constitutive Modeling of Advanced Materials)
►▼ Show Figures

Figure 1

Figure 1
<p>A nine-atom lattice showing the effect of an external magnetic field (<math display="inline"><semantics> <mrow> <mover accent="true"> <mrow> <mi>H</mi> </mrow> <mo>→</mo> </mover> </mrow> </semantics></math>) on the atom for which <math display="inline"><semantics> <mrow> <mover accent="true"> <mrow> <mi>m</mi> </mrow> <mo>→</mo> </mover> </mrow> </semantics></math> is the magnetic moment. (<b>a</b>) Magnetic moments when no external magnetic field is applied, and (<b>b</b>) magnetic moments when subjected to a vertical external magnetic field. Two strain components appear: a parallel strain (<math display="inline"><semantics> <mrow> <msub> <mrow> <mi>λ</mi> </mrow> <mrow> <mi mathvariant="sans-serif">ǁ</mi> </mrow> </msub> </mrow> </semantics></math>) and a perpendicular one (<math display="inline"><semantics> <mrow> <msub> <mrow> <mi>λ</mi> </mrow> <mrow> <mi mathvariant="sans-serif">⟘</mi> </mrow> </msub> </mrow> </semantics></math>).</p> Full article ">Figure 2
<p>A nine-atom lattice showing the effect of a compressive uniformly distributed stress (<math display="inline"><semantics> <mrow> <mover accent="true"> <mrow> <mi>σ</mi> </mrow> <mo>→</mo> </mover> </mrow> </semantics></math>) on the magnetic properties of the atoms presented as the magnetic moment (<math display="inline"><semantics> <mrow> <mover accent="true"> <mrow> <mi>m</mi> </mrow> <mo>→</mo> </mover> </mrow> </semantics></math>). (<b>a</b>) Non-presence of stress illustrates a horizontal orientation of the magnetic moment. (<b>b</b>) The presence of compressive stress (<math display="inline"><semantics> <mrow> <mover accent="true"> <mrow> <mi>σ</mi> </mrow> <mo>→</mo> </mover> </mrow> </semantics></math>) results in a direction change in the magnetic moment (<math display="inline"><semantics> <mrow> <mover accent="true"> <mrow> <mi>m</mi> </mrow> <mo>→</mo> </mover> </mrow> </semantics></math>) (magnetic moments pointing up).</p> Full article ">Figure 3
<p>(<b>a</b>) Polycrystalline structure showing the magnetic domains and their appropriate magnetization (<math display="inline"><semantics> <mrow> <mover accent="true"> <mrow> <mi>m</mi> </mrow> <mo>→</mo> </mover> </mrow> </semantics></math>) direction when no external magnetic field (<math display="inline"><semantics> <mrow> <mover accent="true"> <mrow> <mi mathvariant="bold-italic">H</mi> </mrow> <mo>→</mo> </mover> </mrow> </semantics></math>) is applied. (<b>b</b>) Magnified region of the polycrystalline structure, with no external magnetic field applied, and (<b>c</b>) magnified region when an external magnetic field (<math display="inline"><semantics> <mrow> <mover accent="true"> <mrow> <mi mathvariant="bold-italic">H</mi> </mrow> <mo>→</mo> </mover> </mrow> </semantics></math>) is applied. The magnetic domain’s direction aligns with the external magnetic field direction.</p> Full article ">Figure 4
<p>Multiplicative decomposition of the deformation gradient into the plastic (<span class="html-italic">p</span>), magnetic (<span class="html-italic">H</span>), damage (<math display="inline"><semantics> <mrow> <mi>φ</mi> </mrow> </semantics></math>), thermal (<span class="html-italic">θ</span>), and elastic parts (<span class="html-italic">e</span>).</p> Full article ">Figure 5
<p>The Michelson Interferometer setup used to measure the magnetostriction in this study. The iron (Fe), nickel (Ni), and cobalt (Co) specimens were placed in the magnetic coil.</p> Full article ">Figure 6
<p>Magnetostriction variation (<math display="inline"><semantics> <mrow> <msup> <mi mathvariant="bold-italic">ε</mi> <mi>H</mi> </msup> </mrow> </semantics></math>) with respect to the external magnetic field <span class="html-italic">H</span> (kA/m) for soft magnets: (<b>a</b>) cobalt (Co) and (<b>b</b>) nickel (Ni). Symbols are experimental data obtained in the part of the present study and lines are for the model.</p> Full article ">Figure 7
<p>Magnetization variation <span class="html-italic">M</span> (kA/m) with respect to the external magnetic field <span class="html-italic">H</span> (kA/m), for soft magnets: (<b>a</b>) iron (Fe), (<b>b</b>) nickel (Ni), and (<b>c</b>) cobalt (Co). Symbols are experimental data [<a href="#B108-materials-17-02412" class="html-bibr">108</a>] and lines are for the model.</p> Full article ">
11 pages, 10290 KiB  
Article
A Study on the Critical Saturation Response Characteristics of Simple and Sandwich Cylindrical Shells under Long-Duration Blast Loading
by Mao Yang, Jun Zhang, Yunfei Mu, Hanjun Huang, Bin Han and Yongjian Mao
Materials 2024, 17(9), 1990; https://doi.org/10.3390/ma17091990 - 25 Apr 2024
Viewed by 717
Abstract
Experimental research and numerical simulations of the structural response to shock waves with pulse durations of hundreds of milliseconds, or even seconds, are extremely challenging. This paper takes typical single-layer and sandwich cylindrical shells as the research objects. The response rules of cylindrical [...] Read more.
Experimental research and numerical simulations of the structural response to shock waves with pulse durations of hundreds of milliseconds, or even seconds, are extremely challenging. This paper takes typical single-layer and sandwich cylindrical shells as the research objects. The response rules of cylindrical shells under long-duration blast loadings were studied. The results show that when the pulse duration is greater than or equal to 4~5 times the first-order period of the structure, the maximum response of the structure tends to be consistent, that is, the maximum response of the cylindrical shells with different vibration shapes shows a saturation effect as the pulse duration increases. This study established the relationship between the saturation loading time and the inherent characteristics of the structure. It was found that the saturation effect was applicable under the following conditions, including different load waveforms, elastic–plastic deformation of the structure, and the loading object being a sandwich shell. This will help transform the long-duration explosion wave problem into a finite pulse-duration shock wave problem that can be realized by both experiments and numerical simulations. Full article
(This article belongs to the Special Issue Characterizations, Mechanical Properties and Constitutive Modeling of Advanced Materials)
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<p>Geometric schematic diagram of corrugated sandwich cylindrical shell.</p> Full article ">Figure 2
<p>Finite element model of S1.</p> Full article ">Figure 3
<p>The first-order vibration shapes of the structures of S1 and S2.</p> Full article ">Figure 4
<p>The pressure–time curves of dynamic loads with different pulse widths when <span class="html-italic">t</span><sub>d</sub> = 5.9 ms. (<b>a</b>) Rectangular waves; (<b>b</b>) sawtooth waves.</p> Full article ">Figure 5
<p>The maximum strain and its occurrence time.</p> Full article ">Figure 5 Cont.
<p>The maximum strain and its occurrence time.</p> Full article ">Figure 6
<p>The first-order vibration shapes of the structures of S1, S3 and S4S..</p> Full article ">Figure 7
<p>Maximum strain of the structures under different loading pulse durations and different loading waveforms.</p> Full article ">Figure 8
<p>Maximum strain of structure under different load amplitudes.</p> Full article ">Figure 9
<p>Deformation modes of the structure under different pulse durations when the amplitude is 10 MPa.</p> Full article ">Figure 10
<p>Maximum strain and deformation modes of corrugated sandwich cylindrical shells under different load amplitudes.</p> Full article ">
15 pages, 4324 KiB  
Article
Study of Dynamic Failure Behavior of a Type of PC/ABS Composite
by Jiayu Zhou, Zhaodong Xia, Dongfang Ma and Huanran Wang
Materials 2024, 17(8), 1728; https://doi.org/10.3390/ma17081728 - 10 Apr 2024
Viewed by 1182
Abstract
PC/ABS composites are commonly used in airbag covers. In this paper, uniaxial tensile experiments of a PC/ABS composite at different temperatures and strain rates were conducted. The results showed that the temperature and loading rate affect the mechanical properties of the PC/ABS composite. [...] Read more.
PC/ABS composites are commonly used in airbag covers. In this paper, uniaxial tensile experiments of a PC/ABS composite at different temperatures and strain rates were conducted. The results showed that the temperature and loading rate affect the mechanical properties of the PC/ABS composite. As the temperature increases, the yield stress decreases and the strain at the moment of fracture increases, but the strain rate at the same temperature has a relatively small effect on the mechanical properties, which are similar to ductile materials. The experimental results were applied to the Abaqus model which considered thermal effects and the exact Johnson–Cook constitutive parameters were calculated by applying the inverse method. Based on the constitutive model and the failure analysis findings acquired by DIC, the uniaxial tensile test at the room temperature and varied strain rates were simulated and compared to the test results, which accurately reproduced the test process. The experiment on target plate intrusion of the PC/ABS composite was designed, and a finite-element model was established to simulate the experimental process. The results were compared with the experiments, which showed that the constitutive and the failure fracture strains were valid. Full article
(This article belongs to the Special Issue Characterizations, Mechanical Properties and Constitutive Modeling of Advanced Materials)
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<p>Design of uniaxial tensile experiment: (<b>a</b>) MTS-810 dynamic and static materials testing machine; (<b>b</b>) Size of test material (unit: mm); (<b>c</b>) ZwickRoell-5020 high-speed hydraulic tensile testing machine system.</p> Full article ">Figure 2
<p>Ballistic impact test experimental design diagrams: (<b>a</b>) Design dimensions of target plate and bullet (unit: mm); (<b>b</b>) Layout of penetration test device.</p> Full article ">Figure 3
<p>Three times quasi static test results of the PC/ABS composite under 273.15 K and a strain rate of 0.01 s<sup>−1</sup>.</p> Full article ">Figure 4
<p>Effect of a single variable for the failure behavior of the PC/ABS composite: (<b>a</b>) Force–displacement curve of the PC/ABS composite under the same strain rate (1 s<sup>−1</sup>) and different temperatures; (<b>b</b>) Force–displacement curve of the PC/ABS composite under different strain rates at room temperature.</p> Full article ">Figure 5
<p>Comparison of yield stress under different experimental conditions: (<b>a</b>) Yield stress temperature curve; (<b>b</b>) Yield stress strain rate (logarithmic) curve.</p> Full article ">Figure 6
<p>Penetration process under different angles of view of the experiment: (<b>a</b>) Penetration process under the side angle of view of the experiment; (<b>b</b>) Penetration process from the experimental back view.</p> Full article ">Figure 7
<p>Process of determining parameters by the inversion method.</p> Full article ">Figure 8
<p>Comparison between numerical simulation and experiment after modification by inversion method: (<b>a</b>) Test results with strain rate of 0.01 s<sup>−1</sup>; (<b>b</b>) Test results with strain rate of 1 s<sup>−1</sup>; (<b>c</b>) Test results with strain rate of 10 s<sup>−1</sup>.</p> Full article ">Figure 9
<p>Experiments and simulations at high strain rates validate the accuracy of the constitutive model: (<b>a</b>) Comparison of results under different temperatures with strain rate of 100 s<sup>−1</sup>; (<b>b</b>) Comparison of results under different temperatures with strain rate of 1000 s<sup>−1</sup>.</p> Full article ">Figure 10
<p>Comparison between the deformation process of numerical simulation specimen at different times and the record of the high-speed camera.</p> Full article ">Figure 11
<p>Comparison between uniaxial tensile test results and numerical simulation of the PC/ABS composite at room temperature and different strain rates.</p> Full article ">Figure 12
<p>Comparison of the penetration failure process of the target plate in simulation and experiment.</p> Full article ">Figure 12 Cont.
<p>Comparison of the penetration failure process of the target plate in simulation and experiment.</p> Full article ">Figure 13
<p>Comparison between the failure shape of the target recovered in the penetration experiment and the simulation results: (<b>a</b>) Comparison between the experiment on the back of the target and the simulation results; (<b>b</b>) Comparison of simulation results of the frontal experiment of the target plate.</p> Full article ">
23 pages, 28117 KiB  
Article
Crashworthiness of 3D Lattice Topologies under Dynamic Loading: A Comprehensive Study
by Autumn R. Bernard and Mostafa S. A. ElSayed
Materials 2024, 17(7), 1597; https://doi.org/10.3390/ma17071597 - 31 Mar 2024
Cited by 2 | Viewed by 1109
Abstract
Periodic truss-based lattice materials, a particular subset of cellular solids that generally have superior specific properties as compared to monolithic materials, offer regularity and predictability that irregular foams do not. Significant advancements in alternative technologies—such as additive manufacturing—have allowed for the fabrication of [...] Read more.
Periodic truss-based lattice materials, a particular subset of cellular solids that generally have superior specific properties as compared to monolithic materials, offer regularity and predictability that irregular foams do not. Significant advancements in alternative technologies—such as additive manufacturing—have allowed for the fabrication of these uniquely complex materials, thus boosting their research and development within industries and scientific communities. However, there have been limitations in the comparison of results for these materials between different studies reported in the literature due to differences in analysis approaches, parent materials, and boundary and initial conditions considered. Further hindering the comparison ability was that the literature generally only focused on one or a select few topologies. With a particular focus on the crashworthiness of lattice topologies, this paper presents a comprehensive study of the impact performance of 24 topologies under dynamic impact loading. Using steel alloy parent material (manufactured using Selective Laser Melting), a numerical study of the impact performance was conducted with 16 different impact energy–speed pairs. It was possible to observe the overarching trends in crashworthiness parameters, including plateau stress, densification strain, impact efficiency, and absorbed energy for a wide range of 3D lattice topologies at three relative densities. While there was no observed distinct division between the results of bending and stretching topologies, the presence of struts aligned in the impact direction did have a significant effect on the energy absorption efficiency of the lattice; topologies with struts aligned in that direction had lower efficiencies as compared to topologies without. Full article
(This article belongs to the Special Issue Characterizations, Mechanical Properties and Constitutive Modeling of Advanced Materials)
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Graphical abstract

Graphical abstract
Full article ">Figure 1
<p>Relative density versus the ratio of radius to unit cell height. Line types distinguish between stretching (solid), bending (dotted), and mixed (dashed) deformation modes, discussed in <a href="#sec3dot1-materials-17-01597" class="html-sec">Section 3.1</a>. Line opacity indicates whether there is at least one strut aligned in the loading direction: opaque—no, semi-translucent—yes.</p> Full article ">Figure 2
<p>Stress–strain and efficiency–strain results for the quasi-static experiments (from Cao et al. [<a href="#B17-materials-17-01597" class="html-bibr">17</a>]) and the corresponding numerical model as designed for this work. Select deformation behavior illustrated in <a href="#materials-17-01597-f003" class="html-fig">Figure 3</a>.</p> Full article ">Figure 3
<p>Deformation behavior of rhombic dodecahedron cluster from experiments (half-image on the right, from Cao et al. [<a href="#B17-materials-17-01597" class="html-bibr">17</a>]) and corresponding numerical model for this work (half-images on the left) for given strain values. Corresponding stress and efficiency results are provided in <a href="#materials-17-01597-f002" class="html-fig">Figure 2</a>.</p> Full article ">Figure 4
<p>General finite element model components, using a BCC-Z unit cell (orange) for illustrative purposes. Base plate (grey) is fixed and not permitted to translate or rotate. Impactor (green) is given an initial velocity in the downward y-direction as indicated by the black arrow.</p> Full article ">Figure 5
<p>(<b>Left</b>) Unit cell internal energy over compression of lattice. (<b>Right</b>) Interface force over compression of lattice. Lettered displacement locations (A, B, C, D, E, and F) correspond to images in <a href="#materials-17-01597-f006" class="html-fig">Figure 6</a> for the two single-unit cells and the 3 × 3 layer.</p> Full article ">Figure 6
<p>Deformation behavior of two unit cells with different boundary conditions applied to the sides (fixed in top row and free in bottom row), as compared to the middle unit cell of a single-layer 3 × 3 lattice cluster (middle row). Color contour is of plastic strain, units [mm/mm]. Letters correspond to displacement locations in <a href="#materials-17-01597-f005" class="html-fig">Figure 5</a>.</p> Full article ">Figure 7
<p>Internal energy over compression displacement for AFCC topology at three relative densities, four speeds, and four initial kinetic energies. Top graphs are for initial KE of 50 J and 100 J, and bottom graphs are for initial KE of 1 J and 5 J (identified by line type per legend). Variations in initial impact speeds are distinguished using the line color specified in legend. From left to right: relative density 10%, 20%, 30%; images of unit cell provided for reference. Grey lines are used to help compare relative densities.</p> Full article ">Figure 8
<p>Stress over strain for AFCC topology at three relative densities, four speeds, and four initial kinetic energies. Top graphs are for initial KE of 50 J and 100 J, and bottom graphs are for initial KE of 1 J and 5 J (identified by line type per legend). Variations in initial impact speeds are distinguished using the line color specified in legend. From left to right: relative density 10%, 20%, 30%; images of unit cell provided for reference. Grey lines are used to help compare relative densities.</p> Full article ">Figure 9
<p>Internal energy over compression displacement for AFCC topology at a relative density of 10%. Variations in initial KE are 50 J and 100 J (distinguished by line type). Variations in initial impact speeds are 100 m/s and 1000 m/s (distinguished by line color). Color contour for images of compression of unit cells is for plastic strain [mm/mm].</p> Full article ">Figure 10
<p>(<b>Left</b>) static homogenized Young’s modulus (i.e., in compression direction) versus strut radius and (<b>right</b>) plateau stress versus strut radius (impact energy 100 J, speed 10 m/s). Legend as shown in <a href="#materials-17-01597-f001" class="html-fig">Figure 1</a>. Line types distinguish stretching (solid), bending (dotted), and mixed (dashed) deformation modes, discussed in <a href="#sec3dot1-materials-17-01597" class="html-sec">Section 3.1</a>. Line opacity indicates whether there is at least one strut aligned in the loading direction: opaque—no, semi-translucent—yes (see <a href="#materials-17-01597-t006" class="html-table">Table 6</a> for clear classification on whether strut(s) are aligned in loading direction or not). The arrow at the end of the line indicates increasing relative density.</p> Full article ">Figure 11
<p>(<b>Left</b>) homogenized Poisson’s ratio (in compression direction) versus strut radius and (<b>right</b>) densification strain versus strut radius (impact energy 100 J, speed 10 m/s). Legend as shown in <a href="#materials-17-01597-f001" class="html-fig">Figure 1</a>. Line types distinguish stretching (solid), bending (dotted), and mixed (dashed) deformation modes. Line opacity indicates whether there is at least one strut aligned in the loading direction: opaque—no, semi-translucent—yes (see <a href="#materials-17-01597-t006" class="html-table">Table 6</a> for clear classification on whether strut(s) are aligned in the loading direction or not). The arrow at the end of the line indicates increasing relative density.</p> Full article ">Figure 12
<p>(<b>Left</b>) plateau stress versus IE at densification strain and (<b>right</b>) plateau stress versus densification strain. Both sets of data are for an impact energy of 100 J, speed of 10 m/s. Legend as shown in <a href="#materials-17-01597-f001" class="html-fig">Figure 1</a>. Line types distinguish stretching (solid), bending (dotted), and mixed (dashed) deformation modes. Line opacity indicates whether there is at least one strut aligned in the loading direction: opaque—no, semi-translucent—yes (see <a href="#materials-17-01597-t006" class="html-table">Table 6</a> for clear classification on whether strut(s) are aligned in the loading direction or not). The arrow at the end of the line indicates increasing relative density.</p> Full article ">Figure 13
<p>EA efficiency versus strut radius (impact energy 100 J, speed 10 m/s)—left: struts in loading direction; right—no struts in loading direction (see <a href="#materials-17-01597-t006" class="html-table">Table 6</a> for clear classification on whether strut(s) are aligned in loading direction or not). Legend as shown in <a href="#materials-17-01597-f001" class="html-fig">Figure 1</a>. Line types distinguish stretching (solid), bending (dotted), and mixed (dashed) deformation modes. The arrow at the end of the line indicates increasing relative density. Grey lines are for ease of comparison between the data in the two plots (grey data is found as color data in the other plot).</p> Full article ">
13 pages, 6340 KiB  
Article
Experimental Study on the Wind Erosion Resistance of Aeolian Sand Solidified by Microbially Induced Calcite Precipitation (MICP)
by Jing Qu, Gang Li, Bin Ma, Jia Liu, Jinli Zhang, Xing Liu and Yijia Zhang
Materials 2024, 17(6), 1270; https://doi.org/10.3390/ma17061270 - 9 Mar 2024
Cited by 2 | Viewed by 1211
Abstract
Microbially induced calcite precipitation (MICP) is an emerging solidification method characterized by high economic efficiency, environmental friendliness, and durability. This study validated the reliability of the MICP sand solidification method by conducting a small-scale wind tunnel model test using aeolian sand solidified by [...] Read more.
Microbially induced calcite precipitation (MICP) is an emerging solidification method characterized by high economic efficiency, environmental friendliness, and durability. This study validated the reliability of the MICP sand solidification method by conducting a small-scale wind tunnel model test using aeolian sand solidified by MICP and analyzing the effects of wind velocity (7 m/s, 10 m/s, and 13 m/s), deflation angle (0°, 15°, 30°, and 45°), wind erosion cycle (1, 3, and 5), and other related factors on the mass loss rate of solidified aeolian sand. The microstructure of aeolian sand was constructed by performing mesoscopic and microscopic testing based on X-ray diffraction analysis (XRD), Fourier-transform infrared spectroscopy (FTIR), and scanning electron microscopy (SEM). According to the test results, the mass loss rate of solidified aeolian sand gradually increases with the increase in wind velocity, deflation angle, and wind erosion cycle. When the wind velocity was 13 m/s, the mass loss rate of the aeolian sand was only 63.6%, indicating that aeolian sand has excellent wind erosion resistance. CaCO3 crystals generated by MICP were mostly distributed on sand particle surfaces, in sand particle pores, and between sand particles to realize the covering, filling, and cementing effects. Full article
(This article belongs to the Special Issue Characterizations, Mechanical Properties and Constitutive Modeling of Advanced Materials)
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<p>Aeolian sand taken from Mu Us Desert in Yulin, Shaanxi, China.</p> Full article ">Figure 2
<p>Sand table device.</p> Full article ">Figure 3
<p>Wind tunnel testing equipment: (<b>a</b>) wind tunnel testing machine; (<b>b</b>) anemometer.</p> Full article ">Figure 4
<p>Curve of mass loss rate variation in aeolian sand with wind velocity: (<b>a</b>) <span class="html-italic">α</span> = 0°; (<b>b</b>) <span class="html-italic">α</span> = 15°; (<b>c</b>) <span class="html-italic">α</span> = 30°; (<b>d</b>) <span class="html-italic">α</span> = 45°.</p> Full article ">Figure 5
<p>Curve of mass loss rate variation inaeolian sand with wind velocity: (<b>a</b>) <span class="html-italic">v</span> = 7 m/s; (<b>b</b>) <span class="html-italic">v</span> = 10 m/s; (<b>c</b>) <span class="html-italic">v</span> = 13 m/s.</p> Full article ">Figure 6
<p>Curve of mass loss rate variation in aeolian sand with the number of wind erosion cycles: (<b>a</b>) <span class="html-italic">v</span> = 7 m/s; (<b>b</b>) <span class="html-italic">v</span> = 10 m/s; (<b>c</b>) <span class="html-italic">v</span> = 13 m/s.</p> Full article ">Figure 7
<p>Wind erosion morphology of loose aeolian sand (The arrow indicate the dispersion direction of the aeolian sand): (<b>a</b>) <span class="html-italic">v</span> = 7 m/s, <span class="html-italic">α</span> = 15°, <span class="html-italic">n</span> = 1; (<b>b</b>) <span class="html-italic">v</span> = 10 m/s, <span class="html-italic">α</span> = 30°, <span class="html-italic">n</span> = 1; (<b>c</b>) <span class="html-italic">v</span> = 10 m/s, <span class="html-italic">α</span> = 30°, <span class="html-italic">n</span> = 3; (<b>d</b>) <span class="html-italic">v</span> = 13 m/s, <span class="html-italic">α</span> = 15°, <span class="html-italic">n</span> = 1.</p> Full article ">Figure 8
<p>Wind erosion morphology of aeolian sand solidified by MICP (The arrow indicate the dispersion direction of the aeolian sand): (<b>a</b>) <span class="html-italic">v</span> = 7 m/s, <span class="html-italic">α</span> = 30°, <span class="html-italic">n</span> = 3; (<b>b</b>) <span class="html-italic">v</span> = 10 m/s, <span class="html-italic">α</span> = 30°, <span class="html-italic">n</span> = 3; (<b>c</b>) <span class="html-italic">v</span> = 10 m/s, <span class="html-italic">α</span> = 45°, <span class="html-italic">n</span> = 1; (<b>d</b>) <span class="html-italic">v</span> = 13 m/s, <span class="html-italic">α</span> = 30°, <span class="html-italic">n</span> = 3.</p> Full article ">Figure 9
<p>XRD spectrum: (<b>a</b>) loose aeolian sand; (<b>b</b>) MICP-solidified aeolian sand.</p> Full article ">Figure 10
<p>FTIR spectrum.</p> Full article ">Figure 11
<p>SEM image: (<b>a</b>) covering effect; (<b>b</b>) filling effect; (<b>c</b>) cementing effect; (<b>d</b>) calcite.</p> Full article ">
15 pages, 6232 KiB  
Article
Anisotropic Hardening and Plastic Evolution Characterization on the Pressure-Coupled Drucker Yield Function of ZK61M Magnesium Alloy
by Jianwei You, Jiangnan Liu, Can Zhou, Wei Gao and Yuhong Yao
Materials 2024, 17(5), 1150; https://doi.org/10.3390/ma17051150 - 1 Mar 2024
Viewed by 954
Abstract
This paper studies the plastic behavior of the ZK61M magnesium alloy through a combination method of experiments and theoretical models. Based on a dog-bone specimen under different loading directions, mechanical tests under uniaxial tension were carried out, and the hardening behavior was characterized [...] Read more.
This paper studies the plastic behavior of the ZK61M magnesium alloy through a combination method of experiments and theoretical models. Based on a dog-bone specimen under different loading directions, mechanical tests under uniaxial tension were carried out, and the hardening behavior was characterized by the Swift–Voce hardening law. The von Mises yield function and the pressure-coupled Drucker yield function were used to predict the load–displacement curves of the ZK61M magnesium alloy under various conditions, respectively, where the material parameters were calibrated by using inverse engineering. The experimental results show that the hardening behavior of the ZK61M magnesium alloy has obvious anisotropy, but the effect of the stress state is more important on the strain hardening behavior of the alloy. Compared with the von Mises yield function, the pressure-coupled Drucker yield function is more accurate when characterizing the plastic behavior and strain hardening in different stress states of shear, uniaxial tension, and plane strain tension for the ZK61M alloy. Full article
(This article belongs to the Special Issue Characterizations, Mechanical Properties and Constitutive Modeling of Advanced Materials)
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<p>Size structure of (<b>a</b>) dog-bone specimen; (<b>b</b>) R20 notched specimen; (<b>c</b>) R5 notched specimen; and (<b>d</b>) shear specimen. (Unit: mm).</p> Full article ">Figure 2
<p>Universal mechanical experimental machine and XTOP digital image correlation system.</p> Full article ">Figure 3
<p>Load–displacement curves of four different samples of ZK61M: (<b>a</b>) dog-bone specimen; (<b>b</b>) R20 notched specimen; (<b>c</b>) R5 notched specimen; (<b>d</b>) shear specimen.</p> Full article ">Figure 4
<p>Longitudinal strain–width strain curves of the dog-bone specimen for the ZK61M magnesium alloy.</p> Full article ">Figure 5
<p>Comparison of the fitting hardening curves based on Swift and Voce hardening laws with the experimental true stress–true plastic strain curve of the dog-bone specimen along RD.</p> Full article ">Figure 6
<p>Effect of the third stress invariant on the yield surface under biaxial loading.</p> Full article ">Figure 7
<p>A typical yield surface of the pressure-coupled Drucker yield function with <span class="html-italic">b</span> = 0.05 and <span class="html-italic">c</span> = 2 in (<math display="inline"><semantics> <mrow> <mi>η</mi> </mrow> </semantics></math>,<math display="inline"><semantics> <mrow> <mo> </mo> <mi>ξ</mi> </mrow> </semantics></math>,<math display="inline"><semantics> <mrow> <msub> <mrow> <mo> </mo> <mover accent="true"> <mrow> <mi>σ</mi> </mrow> <mo>̄</mo> </mover> </mrow> <mrow> <mi>V</mi> <mi>M</mi> </mrow> </msub> </mrow> </semantics></math>) space.</p> Full article ">Figure 8
<p>Flow chart of the inverse engineering method.</p> Full article ">Figure 9
<p>Finite element models with different mesh sizes for R20 notched specimen with different element numbers: (<b>a</b>) model #1: 220 elements; (<b>b</b>) model #2: 440 elements; (<b>c</b>) model #3: 660 elements; (<b>d</b>) model #4: 880 elements; (<b>e</b>) model #5: 1100 elements; and (<b>f</b>) model #6: 4400 elements.</p> Full article ">Figure 10
<p>Comparison between the predicted load–displacement curves of six finite element models with different element sizes with the experimental results for the R20 notched specimen.</p> Full article ">Figure 11
<p>Comparison of the von Mises load–displacement curves and the experimental results for the (<b>a</b>) R5 notched specimen; (<b>b</b>) R20 notched specimen; (<b>c</b>) shear sample; and (<b>d</b>) prediction error.</p> Full article ">Figure 12
<p>Comparison of the von Mises load–displacement curves with the inverse engineering method and the experimental results for the (<b>a</b>) R5 notched specimen; (<b>b</b>) R20 notched specimen; (<b>c</b>) shear sample; and (<b>d</b>) prediction error.</p> Full article ">Figure 13
<p>The pressure-coupled Drucker yield surface in (<math display="inline"><semantics> <mrow> <mi>η</mi> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <mi>ξ</mi> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <msub> <mrow> <mover accent="true"> <mrow> <mi>σ</mi> </mrow> <mo>̄</mo> </mover> </mrow> <mrow> <mi>V</mi> <mi>M</mi> </mrow> </msub> </mrow> </semantics></math>) space.</p> Full article ">Figure 14
<p>Comparison of the pressure-coupled Drucker load–displacement curves and the experimental results for the (<b>a</b>) R5 notched specimen; (<b>b</b>) R20 notched specimen; (<b>c</b>) shear sample; and (<b>d</b>) prediction error.</p> Full article ">
16 pages, 4515 KiB  
Article
A Modified DF2016 Criterion for the Fracture Modeling from Shear to Equibiaxial Tension
by Xiaona Xu, Ruqiang Yan and Xucheng Fang
Materials 2024, 17(4), 958; https://doi.org/10.3390/ma17040958 - 19 Feb 2024
Cited by 1 | Viewed by 947
Abstract
This study introduces a modified DF2016 criterion to model a ductile fracture of sheet metals from shear to equibiaxial tension. The DF2016 criterion is modified so that a material constant is equal to the fracture strain at equibiaxial tension, which can be easily [...] Read more.
This study introduces a modified DF2016 criterion to model a ductile fracture of sheet metals from shear to equibiaxial tension. The DF2016 criterion is modified so that a material constant is equal to the fracture strain at equibiaxial tension, which can be easily measured by the bulging experiments. To evaluate the performance of the modified DF2016 criterion, experiments are conducted for QP980 with five different specimens with stress states from shear to equibiaxial tension. The plasticity of the steel is characterized by the Swift–Voce hardening law and the pDrucker function, which is calibrated with the inverse engineering approach. A fracture strain is measured by the XTOP digital image correlation system for all the specimens, including the bulging test. The modified DF2016 criterion is also calibrated with the inverse engineering approach. The predicted force–stroke curves are compared with experimental results to evaluate the performance of the modified DF2016 criterion on the fracture prediction from shear to equibiaxial tension. The comparison shows that the modified DF2016 criterion can model the onset of the ductile fracture with high accuracy in wide stress states from shear to plane strain tension. Moreover, the calibration of the modified DF2016 criterion is comparatively easier than the original DF2016 criterion. Full article
(This article belongs to the Special Issue Characterizations, Mechanical Properties and Constitutive Modeling of Advanced Materials)
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<p>Four types of specimens [<a href="#B61-materials-17-00958" class="html-bibr">61</a>]: (<b>I</b>) dogbone specimens; (<b>II</b>) specimens with central hole; (<b>III</b>) notched specimens; (<b>IV</b>) in-plane shear specimens; and (<b>V</b>) bulging specimens.</p> Full article ">Figure 2
<p>Universal mechanical testing system and the XTOP digital image correlation [<a href="#B62-materials-17-00958" class="html-bibr">62</a>].</p> Full article ">Figure 3
<p>Load–stroke curves of QP980 for dogbone specimens.</p> Full article ">Figure 4
<p>Relations between axial and width strain evolution of QP980 for dogbone specimens.</p> Full article ">Figure 5
<p>Load–stroke curves of QP980 for hole specimens.</p> Full article ">Figure 6
<p>Load–stroke curves of QP980 for notched R5 specimens.</p> Full article ">Figure 7
<p>Load–stroke curves of QP980 for shear specimens.</p> Full article ">Figure 8
<p>Bulging experimental results of QP980.</p> Full article ">Figure 9
<p>Comparison of the fitted hardening laws with experimental results for QP980.</p> Full article ">Figure 10
<p>Comparison of the predicted load–stroke curves via von Mises function with experimental results for (<b>a</b>) specimens with a central hole; (<b>b</b>) notched specimens; and (<b>c</b>) shear specimens.</p> Full article ">Figure 10 Cont.
<p>Comparison of the predicted load–stroke curves via von Mises function with experimental results for (<b>a</b>) specimens with a central hole; (<b>b</b>) notched specimens; and (<b>c</b>) shear specimens.</p> Full article ">Figure 11
<p>Comparison of the predicted load–stroke curves via the pDrucker function with experimental results for (<b>a</b>) specimens with a central hole; (<b>b</b>) notched specimens; and (<b>c</b>) shear specimens.</p> Full article ">Figure 11 Cont.
<p>Comparison of the predicted load–stroke curves via the pDrucker function with experimental results for (<b>a</b>) specimens with a central hole; (<b>b</b>) notched specimens; and (<b>c</b>) shear specimens.</p> Full article ">Figure 12
<p>Comparison of the von Mises and pDrucker yield surfaces.</p> Full article ">Figure 13
<p>Comparison of the predicted load–stroke curves with the onset of ductile fracture via the modified DF2016 criterion with experimental results for (<b>a</b>) specimens with a central hole; (<b>b</b>) notched specimens; and (<b>c</b>) shear specimens.</p> Full article ">
15 pages, 9316 KiB  
Article
Identification of Apple Fruit-Skin Constitutive Laws by Full-Field Methods Using Uniaxial Tensile Loading
by Teresa Campos, Rafael Araújo, José Xavier, Quyền Nguyễn, Nuno Dourado, José Morais and Fábio Pereira
Materials 2024, 17(3), 700; https://doi.org/10.3390/ma17030700 - 1 Feb 2024
Cited by 2 | Viewed by 1193
Abstract
The protective and preservative role of apple skin in maintaining the integrity of the fruit is well-known, with its mechanical behaviour playing a pivotal role in determining fruit storage capacity. This study employs a combination of experimental and numerical methodologies, specifically utilising the [...] Read more.
The protective and preservative role of apple skin in maintaining the integrity of the fruit is well-known, with its mechanical behaviour playing a pivotal role in determining fruit storage capacity. This study employs a combination of experimental and numerical methodologies, specifically utilising the digital image correlation (DIC) technique. A specially devised inverse strategy is applied to evaluate the mechanical behaviour of apple skin under uniaxial tensile loading. Three apple cultivars were tested in this work: Malus domestica Starking Delicious, Malus pumila Rennet, and Malus domestica Golden Delicious. Stress–strain curves were reconstructed, revealing distinct variations in the mechanical responses among these cultivars. Yeoh’s hyperelastic model was fitted to the experimental data to identify the coefficients capable of reproducing the non-linear deformation. The results suggest that apple skin varies significantly in composition and structure among the tested cultivars, as evidenced by differences in elastic properties and non-linear behaviour. These differences can significantly affect how fruit is handled, stored, and transported. Thus, the insights resulting from this research enable the development of mathematical models based on the mechanical behaviour of apple tissue, constituting important data for improvements in the economics of the agri-food industry. Full article
(This article belongs to the Special Issue Characterizations, Mechanical Properties and Constitutive Modeling of Advanced Materials)
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<p>Apple cultivars: (<b>a</b>), Malus pumila Rennet; (<b>b</b>) Malus domestica Golden Delicious; and (<b>c</b>) Malus domestica Starking Delicious.</p> Full article ">Figure 2
<p>Specimen orientation (<math display="inline"><semantics> <mrow> <mi>L</mi> <mo>=</mo> <mn>60</mn> <mo> </mo> <mi>mm</mi> <mo> </mo> <mo>,</mo> <mo> </mo> <mo> </mo> <mi>B</mi> <mo>=</mo> <mn>20</mn> <mo> </mo> <mi>mm</mi> </mrow> </semantics></math>).</p> Full article ">Figure 3
<p>(<b>a</b>) Detail of the uniaxial tensile test; (<b>b</b>) Experimental setup showing DIC acquisition system; (<b>c</b>) DIC pattern with the corresponding histogram.</p> Full article ">Figure 4
<p>Evaluation of <math display="inline"><semantics> <mrow> <msub> <mi mathvariant="bold-italic">ε</mi> <mrow> <mi>x</mi> <mi>x</mi> </mrow> </msub> </mrow> </semantics></math> as a function of the coordinate <span class="html-italic">x</span> for several Virtual Strain Gauge (VVSG) values for both tension and compression tests.</p> Full article ">Figure 5
<p>Numerical results: (<b>a</b>) FE mesh showing the strain field along the loading direction; and (<b>b</b>) the attained stress–strain agreement of FE and MCalibration.</p> Full article ">Figure 6
<p>Load–unloading cycles in: (<b>a</b>) Malus domestica Starking Delicious; (<b>b</b>) Malus pumila Rennet; and (<b>c</b>) Malus domestica Golden Delicious.</p> Full article ">Figure 7
<p>Typical load–displacement curves under tensile loading. Points A, B, and C identify the following stages: within the elastic response, the occurrence of relevant strain gradients (lenticels identification), and the crack onset of apple skin, respectively.</p> Full article ">Figure 8
<p>Strain cartographies of Starking Delicious, Rennet, and Golden Delicious in the x direction for longitudinal loading (<math display="inline"><semantics> <mrow> <msub> <mi mathvariant="bold-italic">ε</mi> <mrow> <mi>x</mi> <mi>x</mi> </mrow> </msub> </mrow> </semantics></math>), obtained in three load phases according to <a href="#materials-17-00700-f007" class="html-fig">Figure 7</a> in points: (<b>a</b>) A<sub>S</sub>; (<b>b</b>) B<sub>S</sub>; (<b>c</b>) C<sub>S</sub>; (<b>d</b>) A<sub>R</sub>; (<b>e</b>) B<sub>R</sub>; (<b>f</b>) C<sub>R</sub>; (<b>g</b>) A<sub>G</sub>; (<b>h</b>) B<sub>G</sub>; and (<b>i</b>) C<sub>G</sub>.</p> Full article ">Figure 8 Cont.
<p>Strain cartographies of Starking Delicious, Rennet, and Golden Delicious in the x direction for longitudinal loading (<math display="inline"><semantics> <mrow> <msub> <mi mathvariant="bold-italic">ε</mi> <mrow> <mi>x</mi> <mi>x</mi> </mrow> </msub> </mrow> </semantics></math>), obtained in three load phases according to <a href="#materials-17-00700-f007" class="html-fig">Figure 7</a> in points: (<b>a</b>) A<sub>S</sub>; (<b>b</b>) B<sub>S</sub>; (<b>c</b>) C<sub>S</sub>; (<b>d</b>) A<sub>R</sub>; (<b>e</b>) B<sub>R</sub>; (<b>f</b>) C<sub>R</sub>; (<b>g</b>) A<sub>G</sub>; (<b>h</b>) B<sub>G</sub>; and (<b>i</b>) C<sub>G</sub>.</p> Full article ">Figure 9
<p>True stress–strain curves of apple cultivars: (<b>a</b>) Malus domestica Starking Delicious; (<b>b</b>) Malus pumila Rennet; (<b>c</b>) Malus domestica Golden Delicious; and (<b>d</b>) corresponding average curves.</p> Full article ">Figure 10
<p>Lenticels schematic illustration.</p> Full article ">Figure 11
<p>True stress–strain curve showing the obtained numerical agreement: (<b>a</b>) Malus domestica Starking Delicious; (<b>b</b>) Malus pumila Rennet; and (<b>c</b>) Malus domestica Golden Delicious.</p> Full article ">Figure 11 Cont.
<p>True stress–strain curve showing the obtained numerical agreement: (<b>a</b>) Malus domestica Starking Delicious; (<b>b</b>) Malus pumila Rennet; and (<b>c</b>) Malus domestica Golden Delicious.</p> Full article ">Figure 12
<p>Average of three cultivars.</p> Full article ">
29 pages, 26002 KiB  
Article
Effective Mechanical Properties of Periodic Cellular Solids with Generic Bravais Lattice Symmetry via Asymptotic Homogenization
by Padmassun Rajakareyar, Mostafa S. A. ElSayed, Hamza Abo El Ella and Edgar Matida
Materials 2023, 16(24), 7562; https://doi.org/10.3390/ma16247562 - 8 Dec 2023
Cited by 1 | Viewed by 1246
Abstract
In this paper, the scope of discrete asymptotic homogenization employing voxel (cartesian) mesh discretization is expanded to estimate high fidelity effective properties of any periodic heterogeneous media with arbitrary Bravais’s lattice symmetry, including those with non-orthogonal periodic bases. A framework was developed in [...] Read more.
In this paper, the scope of discrete asymptotic homogenization employing voxel (cartesian) mesh discretization is expanded to estimate high fidelity effective properties of any periodic heterogeneous media with arbitrary Bravais’s lattice symmetry, including those with non-orthogonal periodic bases. A framework was developed in Python with a proposed fast–nearest neighbour algorithm to accurately estimate the periodic boundary conditions of the discretized representative volume element of the lattice unit cell. Convergence studies are performed, and numerical errors caused by both voxel meshing and periodic boundary condition approximation processes are discussed in detail. It is found that the numerical error in periodicity approximation is cyclically dependent on the number of divisions performed during the meshing process and, thus, is minimized with a refined voxel mesh. Validation studies are performed by comparing the elastic properties of 2D hexagon lattices with orthogonal and non-orthogonal bases. The developed methodology was also applied to derive the effective properties of several lattice topologies, and variation of their anisotropic macroscopic properties with relative densities is presented as material selection charts. Full article
(This article belongs to the Special Issue Characterizations, Mechanical Properties and Constitutive Modeling of Advanced Materials)
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<p>Iso-parametric hexahedral voxel element, with the global coordinate system (<math display="inline"><semantics> <mrow> <mi>x</mi> <mo>,</mo> <mi>y</mi> <mo>,</mo> <mi>z</mi> </mrow> </semantics></math>), local coordinate system (<math display="inline"><semantics> <mrow> <mi>ξ</mi> <mo>,</mo> <mi>ζ</mi> <mo>,</mo> <mi>η</mi> </mrow> </semantics></math>), and voxel edges aligned with a global cartesian coordinate system with lengths (<math display="inline"><semantics> <mrow> <msub> <mrow> <mi>l</mi> </mrow> <mrow> <mi>x</mi> </mrow> </msub> <mo>,</mo> <msub> <mrow> <mi>l</mi> </mrow> <mrow> <mi>y</mi> </mrow> </msub> <mo>,</mo> <msub> <mrow> <mi>l</mi> </mrow> <mrow> <mi>z</mi> </mrow> </msub> </mrow> </semantics></math>), respectively.</p> Full article ">Figure 2
<p>Primitive Bravais lattices. <math display="inline"><semantics> <mrow> <mi>α</mi> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <mi>β</mi> </mrow> </semantics></math>, and <math display="inline"><semantics> <mrow> <mi>γ</mi> </mrow> </semantics></math> are angles (<math display="inline"><semantics> <mrow> <mi>α</mi> <mo>≠</mo> <mi>β</mi> <mo>≠</mo> <mi>γ</mi> </mrow> </semantics></math>), whereas <math display="inline"><semantics> <mrow> <mi>p</mi> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <mi>q</mi> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <mi>r</mi> </mrow> </semantics></math> are lengths (<math display="inline"><semantics> <mrow> <mi>p</mi> <mo>≠</mo> <mi>q</mi> <mo>≠</mo> <mi>r</mi> </mrow> </semantics></math>).</p> Full article ">Figure 3
<p>(<b>a</b>) Honeycomb lattice RVE with multiple cell envelope definitions. Periodic bases are shown with red and green arrows for the three proposed envelopes. (<b>b</b>) Visualization of the 2D Open Hexagon RVE, RVE’s envelope, voxels, and periodic basis. Voxels’ shape is not to scale.</p> Full article ">Figure 4
<p>Cell envelope definition for filtering voxels with zero and non-zero volume. Red voxel centers are considered to be inside the cell envelope, whereas blue-coloured voxel centers are outside the cell envelope based on the normal direction of the cell envelope (orange arrow).</p> Full article ">Figure 5
<p>Determination of a periodic node pair for node <math display="inline"><semantics> <mrow> <mi>i</mi> </mrow> </semantics></math> located at (<math display="inline"><semantics> <mrow> <msubsup> <mrow> <mi>x</mi> </mrow> <mrow> <mn>1</mn> </mrow> <mrow> <mi>i</mi> </mrow> </msubsup> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <msubsup> <mrow> <mi>x</mi> </mrow> <mrow> <mn>2</mn> </mrow> <mrow> <mi>i</mi> </mrow> </msubsup> </mrow> </semantics></math>) with its periodic pair <math display="inline"><semantics> <mrow> <mi>i</mi> <mo>′</mo> </mrow> </semantics></math> at <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>N</mi> </mrow> <mrow> <mi>i</mi> </mrow> </msub> <mover accent="true"> <mrow> <msub> <mrow> <mi mathvariant="bold-italic">Y</mi> </mrow> <mrow> <mi mathvariant="bold-italic">i</mi> </mrow> </msub> </mrow> <mo>→</mo> </mover> </mrow> </semantics></math> and the search radius <math display="inline"><semantics> <mrow> <mover accent="true"> <mrow> <mi>R</mi> </mrow> <mo>→</mo> </mover> </mrow> </semantics></math> (green arrow) required to search the approximate periodic node pair due to the difference between the voxel element basis and RVE’s periodic basis. This search radius can be used with a KD-Tree algorithm [<a href="#B56-materials-16-07562" class="html-bibr">56</a>] to query the closest point.</p> Full article ">Figure 6
<p>Grid convergence study.</p> Full article ">Figure 7
<p>Numerical error analysis of a closed hexagon with voxel aspect ratios of unity. (<b>a</b>) The large non-zero elastic constants. For a constant truss radius, the volume fraction changes due to the voxel meshing process, and the volume fraction converges for a smaller voxel mesh. (<b>b</b>) The homogenized effective properties of the hexagon lattice, where the fluctuations are caused by the voxel meshing process and approximating the periodic boundary conditions. (<b>c</b>) The residual terms in a log plot, where the residuals fluctuate between a high and a low value, corresponds to the error caused by approximating the periodic boundary conditions. (compare colored circles in (<b>d</b>,<b>e</b>)) The periodic boundary conditions for the voxelized hexagon lattice are marked in (<b>c</b>). (<b>d</b>) Large error (AR <math display="inline"><semantics> <mrow> <mo>≈</mo> </mrow> </semantics></math> 1) for 46 by 39 divisions, VF = 0.263. This voxelized hexagon corresponds to the upper red arrow shown in (<b>c</b>). (<b>e</b>) Small error (AR <math display="inline"><semantics> <mrow> <mo>≈</mo> </mrow> </semantics></math> 1) for 47 by 40 divisions, VF = 0.262. This voxelized hexagon corresponds to the lower red arrow shown in (<b>c</b>).</p> Full article ">Figure 7 Cont.
<p>Numerical error analysis of a closed hexagon with voxel aspect ratios of unity. (<b>a</b>) The large non-zero elastic constants. For a constant truss radius, the volume fraction changes due to the voxel meshing process, and the volume fraction converges for a smaller voxel mesh. (<b>b</b>) The homogenized effective properties of the hexagon lattice, where the fluctuations are caused by the voxel meshing process and approximating the periodic boundary conditions. (<b>c</b>) The residual terms in a log plot, where the residuals fluctuate between a high and a low value, corresponds to the error caused by approximating the periodic boundary conditions. (compare colored circles in (<b>d</b>,<b>e</b>)) The periodic boundary conditions for the voxelized hexagon lattice are marked in (<b>c</b>). (<b>d</b>) Large error (AR <math display="inline"><semantics> <mrow> <mo>≈</mo> </mrow> </semantics></math> 1) for 46 by 39 divisions, VF = 0.263. This voxelized hexagon corresponds to the upper red arrow shown in (<b>c</b>). (<b>e</b>) Small error (AR <math display="inline"><semantics> <mrow> <mo>≈</mo> </mrow> </semantics></math> 1) for 47 by 40 divisions, VF = 0.262. This voxelized hexagon corresponds to the lower red arrow shown in (<b>c</b>).</p> Full article ">Figure 8
<p>Variation of volume fraction due to increasing the number of voxel divisions in the y-direction while maintaining an aspect ratio of unity. The voxel’s center coordinate has been represented as smaller voxels. The periodic basis is plotted as a bold green line.</p> Full article ">Figure 9
<p>Visualization of mismatched periodicity (black circles) and its effect on lattice symmetry. The periodic node pairs are connected using randomly colored lines.</p> Full article ">Figure 10
<p>Comparison of normalized <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>E</mi> </mrow> <mrow> <mn>11</mn> </mrow> </msub> </mrow> </semantics></math> anisotropy plot at multiple volume fractions for (<b>a</b>) voxelized grid with ANSYS’ cubic lattice model, and (<b>b</b>) voxelized hexagon with non-orthogonal periodic basis and ANSYS’ Honeycomb lattice cell with orthogonal periodic basis. (<b>c</b>) Voxelized grid and ANSYS’ cubic lattice model. (<b>d</b>) Voxelized hexagon with non-orthogonal periodic basis and ANSYS’ Honeycomb model with orthogonal periodic basis.</p> Full article ">Figure 11
<p>Comparison of the [<a href="#B4-materials-16-07562" class="html-bibr">4</a>,<a href="#B1-materials-16-07562" class="html-bibr">1</a>] term of the homogenized elastic tensor for (<b>a</b>) hexagon lattice and (<b>b</b>) grid lattice with the [<a href="#B1-materials-16-07562" class="html-bibr">1</a>,<a href="#B1-materials-16-07562" class="html-bibr">1</a>] term for a material of <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>E</mi> </mrow> <mrow> <mi>i</mi> <mi>s</mi> <mi>o</mi> </mrow> </msub> </mrow> </semantics></math> = 2 <math display="inline"><semantics> <mrow> <mo>×</mo> <mtext> </mtext> <msup> <mrow> <mn>10</mn> </mrow> <mrow> <mn>11</mn> </mrow> </msup> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <mi>n</mi> <msub> <mrow> <mi>u</mi> </mrow> <mrow> <mi>i</mi> <mi>s</mi> <mi>o</mi> </mrow> </msub> </mrow> </semantics></math> = 0.3. The CH and D labels correspond to the data from the voxelization and ANSYS material modeller, respectively.</p> Full article ">Figure 12
<p>Anisotropy plot of the Youngs Modulus Elastic property of a 3D primitive cubic lattice cell, where the red circles mark the <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>E</mi> </mrow> <mrow> <mn>11</mn> </mrow> </msub> </mrow> </semantics></math> values at multiple rotation cell angles similar to the rotated cells shown in <a href="#materials-16-07562-f013" class="html-fig">Figure 13</a>. The dashed <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>E</mi> </mrow> <mrow> <mn>11</mn> </mrow> </msub> </mrow> </semantics></math> values are overlapped with the <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>E</mi> </mrow> <mrow> <mn>22</mn> </mrow> </msub> </mrow> </semantics></math> values due to geometrical symmetry.</p> Full article ">Figure 13
<p>A grid lattice cell discretized by 30 voxels along the x, y, and z axis, where the unit cell rotated at 0°, 22°, 45°, and 68° along the z-axis.</p> Full article ">Figure 14
<p>Visualization of the integral in Equation (18) for individual voxel elements, a hexagon with <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>l</mi> </mrow> <mrow> <mi>x</mi> </mrow> </msub> <mo>/</mo> <msub> <mrow> <mi>l</mi> </mrow> <mrow> <mi>y</mi> </mrow> </msub> <mo>=</mo> <mn>1.155</mn> </mrow> </semantics></math> and a voxel shape of (<b>a</b>) <math display="inline"><semantics> <mrow> <mn>30</mn> <mo>×</mo> <mn>30</mn> <mo>×</mo> <mn>1</mn> </mrow> </semantics></math> and (<b>b</b>) <math display="inline"><semantics> <mrow> <mn>150</mn> <mo>×</mo> <mn>150</mn> <mo>×</mo> <mn>1</mn> </mrow> </semantics></math>. Each of the individual hexagon visualizations were normalized by the value of the <math display="inline"><semantics> <mrow> <msubsup> <mrow> <mi>C</mi> </mrow> <mrow> <mi>i</mi> <mi>j</mi> </mrow> <mrow> <mi>H</mi> </mrow> </msubsup> </mrow> </semantics></math> term.</p> Full article ">Figure 15
<p>Visualization of the periodicity node pairs. Each line of a random colour represents a coupling of the degrees of freedom for that node pair. The periodic basis has been highlighted as thick green lines. The approximated periodic boundary condition can be observed while comparing how the periodic boundary condition is applied at (<b>a</b>) between regions a<sub>1</sub> to a<sub>5</sub> and a<sub>2</sub> to a<sub>4</sub>. Due to the finer mesh size, the approximation of the periodic boundary condition at (<b>b</b>) is not affected.</p> Full article ">Figure 16
<p>Convergence of error terms for the hexagon lattice with non-unity aspect ratio. The datum shown above is a reduced subset of <a href="#materials-16-07562-f007" class="html-fig">Figure 7</a>c to emphasize the decreasing residual errors (thick red line).</p> Full article ">Figure 17
<p>Comparison of normalized <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>E</mi> </mrow> <mrow> <mn>11</mn> </mrow> </msub> </mrow> </semantics></math> for the hexagon lattice at multiple volume fractions across multiple homogenization schemes present in the literature [<a href="#B26-materials-16-07562" class="html-bibr">26</a>,<a href="#B36-materials-16-07562" class="html-bibr">36</a>].</p> Full article ">Figure 18
<p>Multiple representations of the Honeycomb hexagon lattice with different representative volume elements with their corresponding periodic basis. The representative volume element of the unit cell is shown as red voxels.</p> Full article ">Figure 19
<p>Elastic properties of the 2D hexagon lattice with a relative density of 0.25 made from isotropic material with Young’s modulus of 2 × 10<sup>11</sup> Pa and Poisson’s ratio of 0.3. Two-dimensional anisotropic diagram of elastic properties for the hexagon with a volume fraction of 0.2 due to the variation of the hexagon cell angle.</p> Full article ">Figure 19 Cont.
<p>Elastic properties of the 2D hexagon lattice with a relative density of 0.25 made from isotropic material with Young’s modulus of 2 × 10<sup>11</sup> Pa and Poisson’s ratio of 0.3. Two-dimensional anisotropic diagram of elastic properties for the hexagon with a volume fraction of 0.2 due to the variation of the hexagon cell angle.</p> Full article ">Figure 20
<p>Comparison of homogenized elastic properties of a square lattice with varying cell angles between 2D MATLAB voxel and 3D voxel code.</p> Full article ">Figure 21
<p>Discretized triclinic Bravais grid lattice. The Voxel center is represented as a small sphere for a volume fraction of 0.3. The planes that represent the cell envelope definition and its normal have also been plotted.</p> Full article ">Figure 22
<p>Base lattice definition for monoclinic and triclinic Bravais lattice.</p> Full article ">Figure 23
<p>Geometric definitions for the monoclinic and triclinic grid lattice are used in this paper.</p> Full article ">Figure 24
<p>Two-dimensional and three-dimensional anisotropy plots for triclinic Bravais grid lattice (3D). Three-dimensional anisotropy plots are not to scale.</p> Full article ">Figure 25
<p>Two-dimensional and three-dimensional anisotropy plots for monoclinic Bravais grid lattice (3D). Three-dimensional anisotropy plots are not to scale.</p> Full article ">Figure 26
<p>3.4.6.4 lattice cells with a non-orthogonal periodic basis. The representative volume element of the unit cell is shown as red voxels. Evolution of selected 2D latices as the volume fraction increases.</p> Full article ">Figure 27
<p>Two-dimensional and three-dimensional anisotropy plots for 3.4.6.4 lattice.</p> Full article ">Figure 28
<p>Two-dimensional and three-dimensional anisotropy plots for X lattice in a sandwich panel (3D).</p> Full article ">
15 pages, 6233 KiB  
Article
Using the Radial Shear Rolling Method for Fast and Deep Processing Technology of a Steel Ingot Cast Structure
by Alexandr Arbuz, Anna Kawalek, Alexandr Panichkin, Kirill Ozhmegov, Fedor Popov and Nikita Lutchenko
Materials 2023, 16(24), 7547; https://doi.org/10.3390/ma16247547 - 7 Dec 2023
Cited by 3 | Viewed by 1394
Abstract
In advancing special materials, seamless integration into existing production chains is paramount. Beyond creating improved alloy compositions, precision in processing methods is crucial to preserve desired properties without drawbacks. The synergy between alloy formulation and processing techniques is pivotal for maximizing the benefits [...] Read more.
In advancing special materials, seamless integration into existing production chains is paramount. Beyond creating improved alloy compositions, precision in processing methods is crucial to preserve desired properties without drawbacks. The synergy between alloy formulation and processing techniques is pivotal for maximizing the benefits of innovative materials. By focusing on advanced deep processing technology for small ingots of modified 12% Cr stainless steel, this paper delves into the transformation of cast ingot steel structures using radial shear rolling (RSR) processing. Through a series of nine passes, rolling ingots from a 32 mm to a 13 mm diameter with a total elongation factor of 6.02, a notable shift occurred. This single-operation process effectuated a substantial change in sample structure, transitioning from a coarse-grained cast structure (0.5–1.5 mm) to an equiaxed fine-grained structure with peripheral grain sizes of 1–4 μm and an elongated rolling texture in the axial part of the bar. The complete transformation of the initial cast dendritic structure validates the implementation of the RSR method for the deep processing of ingots. Full article
(This article belongs to the Special Issue Characterizations, Mechanical Properties and Constitutive Modeling of Advanced Materials)
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Figure 1

Figure 1
<p>Scheme showing various SPD processes.</p> Full article ">Figure 2
<p>Initial 32 mm diameter ingots.</p> Full article ">Figure 3
<p>Gleeble 3800 testing machine (<b>left</b>) and a photo showing the testing of cast ODS-steel specimens in ISO-T model dies with mounted extensometers for longitudinal and transverse measurements of specimens during testing (<b>right</b>).</p> Full article ">Figure 4
<p>Experimental rolling and the RSR-10/30 radial shear rolling mill.</p> Full article ">Figure 5
<p>The rolled bar cutting scheme.</p> Full article ">Figure 6
<p>Scheme for calculating grain size parameters.</p> Full article ">Figure 7
<p>Material flow curves obtained at 600 °C: solid markers—indicate experimental data and transparent markers—–indicate approximation results.</p> Full article ">Figure 8
<p>Material flow curves obtained at 800 °C: solid markers—indicate experimental data and transparent markers—indicate approximation results.</p> Full article ">Figure 9
<p>Material flow curves obtained at 1000 °C: solid markers—indicate experimental data and transparent markers—indicate approximation results.</p> Full article ">Figure 10
<p>Material flow curves obtained at 1200 °C: solid markers—indicate experimental data and transparent markers—indicate approximation results.</p> Full article ">Figure 11
<p>Computer simulation of RSR ingot processing.</p> Full article ">Figure 12
<p>SEM (BSE) scale images of original ingot dendritic structures.</p> Full article ">Figure 13
<p>EBSD map of the axial zone (<b>left</b>) and peripheral zone (<b>right</b>) of a longitude bar section after final rolling.</p> Full article ">Figure 14
<p>EBSD study of the gradient microstructures of rolled bar longitudinal sections.</p> Full article ">Figure 15
<p>Fine structure of fine-grained zones in the peripheral bar part after final rolling.</p> Full article ">
15 pages, 33182 KiB  
Article
Numerical and Experimental Study into Paper Compression Test
by Leszek Czechowski, Paweł Pełczyński, Maria Bieńkowska and Włodzimierz Szewczyk
Materials 2023, 16(24), 7513; https://doi.org/10.3390/ma16247513 - 5 Dec 2023
Viewed by 1096
Abstract
The study aims to present the results of paper compression under an axial load. Different heights of samples subjected to compression were taken into account. The main goal of the analysis was to determine experimentally the maximum compression load. In addition, numerical models [...] Read more.
The study aims to present the results of paper compression under an axial load. Different heights of samples subjected to compression were taken into account. The main goal of the analysis was to determine experimentally the maximum compression load. In addition, numerical models based on the finite element method (FEM) were validated to refer to empirical results. The performed numerical simulations were founded on Green–Lagrangian nonlinear equations for large displacements and strains. The progressive failure of the compressed orthotropic material after exceeding maximum stresses was based on Hill’s anisotropy theory. Nonlinear calculations were conducted by using a typical Newton–Raphson algorithm for achieving a sequence convergence. The accuracy of the developed model was confirmed experimentally in compression tests. The technique of analysing the shape of the compressed paper sample on the basis of images recorded during the measurement was used. The obtained test results are directly applicable in practice, especially in the calculation of the mechanical properties of corrugated cardboard and in determining the load capacity of cardboard packaging. Knowing the maximum compressive stress that packaging paper can withstand allows packaging to be properly designed and its strength assessed in the context of the transport and storage of goods. Full article
(This article belongs to the Special Issue Characterizations, Mechanical Properties and Constitutive Modeling of Advanced Materials)
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Figure 1

Figure 1
<p>The measurement setup composed of UTM and DSLR camera (<b>a</b>) and UTM handles with chessboard patterns glued to them and a paper sample under test (<b>b</b>).</p> Full article ">Figure 2
<p>The shape (<b>a</b>) of the filter mask to emphasize the edges in the image; (<b>b</b>) the shape of the filter mask to emphasize the corners of the chessboard.</p> Full article ">Figure 3
<p>The result of the image filtering of the paper sample (<b>a</b>); the image of the sample with the edges detected (<b>b</b>); and the shape of the right edge of the tested sample obtained in subsequent images of the analysed sequence (<b>c</b>).</p> Full article ">Figure 4
<p>Model FE (<b>a</b>) and view of master node connected with outer nodes (<b>b</b>).</p> Full article ">Figure 5
<p>The shape of the paper sample and the corresponding point on the force-shortening curve for a clamping height of 3 mm at the beginning of buckling (<b>a</b>); at maximum force (<b>b</b>); at the end of the sine wave shape (<b>c</b>).</p> Full article ">Figure 6
<p>The shape of the paper sample and the corresponding point on the force-shortening curve for a clamping height of 4 mm at the beginning of buckling (<b>a</b>); at maximum force (<b>b</b>); at the end of the sine wave shape (<b>c</b>).</p> Full article ">Figure 7
<p>The shape of the paper sample and the corresponding point on the force-shortening curve for a clamping height of 5 mm at the beginning of buckling (<b>a</b>); at maximum force (<b>b</b>); at the end of the sine wave shape (<b>c</b>).</p> Full article ">Figure 8
<p>Shortening (<span class="html-italic">s</span>) vs. compression force (<span class="html-italic">F<sub>comp</sub></span>) for height of 0.7 mm (<b>a</b>) and 1.3 mm (<b>b</b>).</p> Full article ">Figure 9
<p>Shortening (<span class="html-italic">s</span>) vs. compression force (<span class="html-italic">F<sub>comp</sub></span>) for height of 2 mm (<b>a</b>) and 2.5 mm (<b>b</b>).</p> Full article ">Figure 10
<p>Shortening (<span class="html-italic">s</span>) vs. compression force (<span class="html-italic">F<sub>comp</sub></span>) for height of 3 mm (<b>a</b>) and 3.5 mm (<b>b</b>).</p> Full article ">Figure 11
<p>Shortening (<span class="html-italic">s</span>) vs. compression force (<span class="html-italic">F<sub>comp</sub></span>) for height of 4 mm (<b>a</b>) and 4.5 mm (<b>b</b>).</p> Full article ">Figure 12
<p>Shortening (<span class="html-italic">s</span>) vs. compression force (<span class="html-italic">F<sub>comp</sub></span>) for height of 5 mm.</p> Full article ">Figure 13
<p>Deflection (<span class="html-italic">w</span>) vs. distance between jaws for height of 2.5 mm (<b>a</b>) and 3 mm (<b>b</b>).</p> Full article ">Figure 14
<p>Deflection (<span class="html-italic">w</span>) vs. distance between jaws for height of 4 mm (<b>a</b>) and 5 mm (<b>b</b>).</p> Full article ">
26 pages, 12118 KiB  
Article
Crashworthiness of Foam-Filled Cylindrical Sandwich Shells with Corrugated Cores
by Pengbo Su, Bin Han, Yiming Wang, Hui Wang, Bo Gao and Tian Jian Lu
Materials 2023, 16(19), 6605; https://doi.org/10.3390/ma16196605 - 9 Oct 2023
Viewed by 1172
Abstract
Inspired by material hybrid design, novel hybrid sandwich shells were developed by filling a corrugated cylindrical structure with aluminum foam to achieve higher energy absorption performance. The crushing behavior of the foam-filled corrugated sandwich cylindrical shells (FFCSCSs) was investigated using theoretical and numerical [...] Read more.
Inspired by material hybrid design, novel hybrid sandwich shells were developed by filling a corrugated cylindrical structure with aluminum foam to achieve higher energy absorption performance. The crushing behavior of the foam-filled corrugated sandwich cylindrical shells (FFCSCSs) was investigated using theoretical and numerical methods. Numerical results revealed a significant enhancement in the energy absorption of FFCSCSs under axial compression, showcasing a maximum specific energy absorption of 60 kJ/kg. The coupling strengthening effect is highly pronounced, with a maximum value of F¯c/F¯ reaching up to 40%. The mechanism underlying this phenomenon can be approached from two perspectives. Firstly, the intrusion of folds into the foam insertions allows for more effective foam compression, maximizing its energy absorption capacity. Secondly, foam causes the folds to bend upwards, intensifying the mutual compression between the folds. This coupling mechanism was further investigated with a focus on analyzing the influence of parameters such as the relative density of the foam, the wall thickness of the sandwich shell, and the material properties. Moreover, a theoretical model was developed to accurately predict the mean crushing force of the FFCSCSs. Based on this model, the influence of various variables on the crushing behavior of the structure was thoroughly investigated through parametric studies. Full article
(This article belongs to the Special Issue Characterizations, Mechanical Properties and Constitutive Modeling of Advanced Materials)
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Figure 1

Figure 1
<p>The FFCSCS is under crushing process.</p> Full article ">Figure 2
<p>Geometric schematic of foam-filled corrugated sandwich cylindrical shells.</p> Full article ">Figure 3
<p>The finite element model of the FFCSCS under axial compression condition.</p> Full article ">Figure 4
<p>Material properties and corresponding power-hardening model of parent materials for corrugated cores and face sheets: (<b>a</b>) 6063 Al [<a href="#B54-materials-16-06605" class="html-bibr">54</a>]; (<b>b</b>) 6061Al [<a href="#B54-materials-16-06605" class="html-bibr">54</a>]; (<b>c</b>) 304L stainless steel [<a href="#B67-materials-16-06605" class="html-bibr">67</a>].</p> Full article ">Figure 5
<p>Material properties of the filled foams with different relative densities (<math display="inline"><semantics> <mrow> <msub> <mover accent="true"> <mi>ρ</mi> <mo>¯</mo> </mover> <mi mathvariant="normal">f</mi> </msub> </mrow> </semantics></math>).</p> Full article ">Figure 6
<p>Comparison between experiments [<a href="#B53-materials-16-06605" class="html-bibr">53</a>] and FE results of PMI foam-filled 1060 Al sandwich cylindrical shell: (<b>a</b>) force–displacement curves; (<b>b</b>) final collapse mode.</p> Full article ">Figure 7
<p>Crushing process and energy absorption of FFCSCS 6063-08-01: (<b>a</b>) force–displacement curves; (<b>b</b>) energy absorption–displacement curves; (<b>c</b>) collapse configurations with labels corresponding to those marked in the force–displacement curves.</p> Full article ">Figure 8
<p>Coupling enhancement effect in FFCSCS 6063-08-01: (<b>a</b>) force–displacement; (<b>b</b>) mean crushing force–displacement curves.</p> Full article ">Figure 9
<p>Collapse configuration of the FFCSCS 6063-08-01.</p> Full article ">Figure 10
<p>The formation process of folds (enclosed by the red dash circle) in FFCSCS (6063-08-01): (<b>a</b>) initial stage; (<b>b</b>) beginning of formation; (<b>c</b>) bending upwards; (<b>d</b>) compressing each other; (<b>e</b>) partially enlarged view of (<b>c</b>); (<b>f</b>) partially enlarged view of (<b>d</b>).</p> Full article ">Figure 11
<p>Crushing response of FFSCSCs with different relative foam density <math display="inline"><semantics> <mrow> <msub> <mover accent="true"> <mi>ρ</mi> <mo>¯</mo> </mover> <mi mathvariant="normal">f</mi> </msub> </mrow> </semantics></math>: (<b>a</b>) force–displacement curves for <math display="inline"><semantics> <mrow> <msub> <mover accent="true"> <mi>ρ</mi> <mo>¯</mo> </mover> <mi mathvariant="normal">f</mi> </msub> </mrow> </semantics></math> = 0.06~0.14; (<b>b</b>) force–displacement curves for <math display="inline"><semantics> <mrow> <msub> <mover accent="true"> <mi>ρ</mi> <mo>¯</mo> </mover> <mi mathvariant="normal">f</mi> </msub> </mrow> </semantics></math> = 0.16~0.19; (<b>c</b>) mean crushing force–displacement curves for <math display="inline"><semantics> <mrow> <msub> <mover accent="true"> <mi>ρ</mi> <mo>¯</mo> </mover> <mi mathvariant="normal">f</mi> </msub> </mrow> </semantics></math> = 0.06~0.14; (<b>d</b>) mean crushing force–displacement curves for <math display="inline"><semantics> <mrow> <msub> <mover accent="true"> <mi>ρ</mi> <mo>¯</mo> </mover> <mi mathvariant="normal">f</mi> </msub> </mrow> </semantics></math> = 0.16~0.19.</p> Full article ">Figure 12
<p>Collapse configuration of FFSCSCs with <math display="inline"><semantics> <mrow> <msub> <mover accent="true"> <mi>ρ</mi> <mo>¯</mo> </mover> <mi mathvariant="normal">f</mi> </msub> </mrow> </semantics></math> values ranging from 0.08 to 0.19: (<b>a</b>) 0.08; (<b>b</b>) 0.10; (<b>c</b>) 0.12; (<b>d</b>) 0.14; (<b>e</b>) 0.16; (<b>f</b>) 0.19.</p> Full article ">Figure 13
<p>Composition of the mean crushing force (<math display="inline"><semantics> <mrow> <mover accent="true"> <mrow> <mi>F</mi> </mrow> <mo>¯</mo> </mover> </mrow> </semantics></math>) for FFCSCSs with <math display="inline"><semantics> <mrow> <msub> <mover accent="true"> <mi>ρ</mi> <mo>¯</mo> </mover> <mi mathvariant="normal">f</mi> </msub> </mrow> </semantics></math> = 0.06~0.19: (<b>a</b>) absolute value; (<b>b</b>) proportion in <math display="inline"><semantics> <mrow> <mover accent="true"> <mrow> <mi>F</mi> </mrow> <mo>¯</mo> </mover> </mrow> </semantics></math>.</p> Full article ">Figure 14
<p>Influence of wall thickness and relative density of foam on the crushing properties of FFCSCSs: (<b>a</b>) mean crushing force, <math display="inline"><semantics> <mrow> <mover accent="true"> <mrow> <mi>F</mi> </mrow> <mo>¯</mo> </mover> </mrow> </semantics></math> (<b>b</b>) coupling mean crushing force, <math display="inline"><semantics> <mrow> <msub> <mrow> <mover accent="true"> <mrow> <mi>F</mi> </mrow> <mo>¯</mo> </mover> </mrow> <mrow> <mi mathvariant="normal">c</mi> </mrow> </msub> </mrow> </semantics></math>; (<b>c</b>) crushing force efficiency, <span class="html-italic">A</span><sub>E</sub>; (<b>d</b>) specific energy absorption, SEA.</p> Full article ">Figure 15
<p>Composition of the mean crushing force for FFSCSCs with different wall thicknesses and relative densities of foam: (<b>a</b>) absolute value; (<b>b</b>) proportion in <math display="inline"><semantics> <mrow> <mover accent="true"> <mrow> <mi>F</mi> </mrow> <mo>¯</mo> </mover> </mrow> </semantics></math>.</p> Full article ">Figure 16
<p>Influence of wall material and relative density of foam on the crushing properties of FFCSCs: (<b>a</b>) mean crushing force, <math display="inline"><semantics> <mrow> <mover accent="true"> <mrow> <mi>F</mi> </mrow> <mo>¯</mo> </mover> </mrow> </semantics></math>; (<b>b</b>) coupling mean crushing force, <math display="inline"><semantics> <mrow> <mover accent="true"> <mrow> <mi>F</mi> </mrow> <mo>¯</mo> </mover> </mrow> </semantics></math>; (<b>c</b>) crushing force efficiency, <span class="html-italic">A</span><sub>E</sub>; (<b>d</b>) specific energy absorption, SEA.</p> Full article ">Figure 17
<p>Composition of the mean crushing force for FFSCSCs with different wall materials and relative densities of foam: (<b>a</b>) absolute value; (<b>b</b>) proportion in <math display="inline"><semantics> <mrow> <mover accent="true"> <mrow> <mi>F</mi> </mrow> <mo>¯</mo> </mover> </mrow> </semantics></math>.</p> Full article ">Figure 18
<p>Comparison of theoretical predicated and finite element results: (<b>a</b>) coupling mean crushing force, <math display="inline"><semantics> <mrow> <msub> <mrow> <mover accent="true"> <mrow> <mi>F</mi> </mrow> <mo>¯</mo> </mover> </mrow> <mrow> <mi mathvariant="normal">c</mi> </mrow> </msub> </mrow> </semantics></math>; (<b>b</b>) mean crushing force, <math display="inline"><semantics> <mrow> <mover accent="true"> <mrow> <mi>F</mi> </mrow> <mo>¯</mo> </mover> </mrow> </semantics></math>.</p> Full article ">Figure 19
<p>Theoretical predictions of mean crushing force of FFCSCSs with equal mass: (<b>a</b>) 1060 Al face sheets with different <math display="inline"><semantics> <mrow> <msub> <mover accent="true"> <mi>ρ</mi> <mo>¯</mo> </mover> <mi mathvariant="normal">f</mi> </msub> </mrow> </semantics></math>; (<b>b</b>) 6063 Al face sheets with different <math display="inline"><semantics> <mrow> <msub> <mover accent="true"> <mi>ρ</mi> <mo>¯</mo> </mover> <mi mathvariant="normal">f</mi> </msub> </mrow> </semantics></math>; (<b>c</b>) 6061 Al face sheets with different <math display="inline"><semantics> <mrow> <msub> <mover accent="true"> <mi>ρ</mi> <mo>¯</mo> </mover> <mi mathvariant="normal">f</mi> </msub> </mrow> </semantics></math>; (<b>d</b>) 304L stainless steel face sheets with different <math display="inline"><semantics> <mrow> <msub> <mover accent="true"> <mi>ρ</mi> <mo>¯</mo> </mover> <mi mathvariant="normal">f</mi> </msub> </mrow> </semantics></math>.</p> Full article ">Figure 20
<p>Proportion of mean crushing force of FFSCSCs: (<b>a</b>) <math display="inline"><semantics> <mrow> <msub> <mrow> <mover accent="true"> <mrow> <mi>F</mi> </mrow> <mo>¯</mo> </mover> </mrow> <mrow> <mi mathvariant="normal">s</mi> </mrow> </msub> </mrow> </semantics></math>; (<b>b</b>) <math display="inline"><semantics> <mrow> <msub> <mrow> <mover accent="true"> <mrow> <mi>F</mi> </mrow> <mo>¯</mo> </mover> </mrow> <mrow> <mi mathvariant="normal">f</mi> </mrow> </msub> </mrow> </semantics></math>; (<b>c</b>) <math display="inline"><semantics> <mrow> <msub> <mrow> <mover accent="true"> <mrow> <mi>F</mi> </mrow> <mo>¯</mo> </mover> </mrow> <mrow> <mi mathvariant="normal">c</mi> </mrow> </msub> </mrow> </semantics></math>.</p> Full article ">
23 pages, 5117 KiB  
Article
Modeling of Eyld2000-2d Anisotropic Yield Criterion Considering Strength Differential Effect and Analysis of Optimal Calibration Strategy
by Kai Du, Li Dong, Hao Zhang, Zhenkai Mu, Hongrui Dong, Haibo Wang, Yanqiang Ren, Liang Sun, Liang Zhang and Xiaoguang Yuan
Materials 2023, 16(19), 6445; https://doi.org/10.3390/ma16196445 - 27 Sep 2023
Cited by 2 | Viewed by 1322
Abstract
Sheet metals usually experience various loading paths such as uniaxial tension, uniaxial compression, biaxial tension, and simple shear during the forming process. However, the existing constitutive models cannot always accurately describe blanks’ anisotropic yield and plastic flow behavior of blanks under all typical [...] Read more.
Sheet metals usually experience various loading paths such as uniaxial tension, uniaxial compression, biaxial tension, and simple shear during the forming process. However, the existing constitutive models cannot always accurately describe blanks’ anisotropic yield and plastic flow behavior of blanks under all typical stress states. Given this, this paper improves the Eyld2000-2d yield criterion by introducing hydrostatic pressure to the A-Eyld2000-2d yield criterion that can describe the strength differential effect of materials. Meanwhile, to control the curvature of the yield surface more effectively, the near-plane strain yield stresses were added in the parameter identification process to calibrate the exponent m, so that the exponent is no longer considered as a constant value. Taking the widely used AA6016-T4, AA5754-O, DP980, and QP980 blanks in the automotive stamping industry as an example, the effectiveness of the new model and different parameter identification methods was verified by predicting experimental data under various simple and complex loading paths. Subsequently, the new model employing the optimal parameter identification strategy was compared with four widely used asymmetric yield criteria under associated and non-associated flow rules, including CPB06, LHY2013, S-Y2004, and Hu & Yoon2021, to further verify the accuracy of the proposed constitutive model. The results indicate that parameter identification strategy with variable exponent can significantly improve the flexibility of the yield criterion in describing the plastic anisotropy of blanks. Compared to the other yield criteria examined in this work, the new model provides the best prediction accuracy for the yield stresses and plastic flows of all blanks, especially in the near-plane strain and simple shear stress states. Modeling under the concept of anisotropic hardening can more accurately capture the evolving plastic behavior of blanks than isotropic hardening. Full article
(This article belongs to the Special Issue Characterizations, Mechanical Properties and Constitutive Modeling of Advanced Materials)
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Figure 1

Figure 1
<p>Normalized yield loci of the A-Eyld2000-2d yield criterion calculated using (<b>a</b>) isotropic mechanical properties and (<b>b</b>) a specific set of anisotropic parameters at different exponents <span class="html-italic">m</span>.</p> Full article ">Figure 2
<p>Normalized yield loci of (<b>a</b>) AA6016-T4, (<b>b</b>) AA5754-O, (<b>c</b>) DP980, and (<b>d</b>) QP980 blanks predicted by A-Eyld2000-2d yield criterion with different parameter identification strategies.</p> Full article ">Figure 3
<p>Prediction errors of normalized yield loci of AA6016-T4, AA5754-O, DP980, and QP980 blanks calculated by the A-Eyld2000-2d yield criterion with different parameter identification strategies.</p> Full article ">Figure 4
<p>Normalized UT yield stresses of (<b>a</b>) AA6016-T4, (<b>b</b>) AA5754-O, (<b>c</b>) DP980, and (<b>d</b>) QP980 blanks predicted by the A-Eyld2000-2d yield criterion with different parameter identification strategies.</p> Full article ">Figure 5
<p><span class="html-italic">r</span>-values of (<b>a</b>) AA6016-T4, (<b>b</b>) AA5754-O, (<b>c</b>) DP980, and (<b>d</b>) QP980 blanks predicted by the A-Eyld2000-2d yield criterion with different parameter identification strategies.</p> Full article ">Figure 6
<p>Normalized yield loci of (<b>a</b>) AA6016-T4, (<b>b</b>) AA5754-O, (<b>c</b>) DP980, and (<b>d</b>) QP980 blanks predicted by several asymmetric yield criteria.</p> Full article ">Figure 7
<p>Prediction errors of normalized yield loci of AA6016-T4, AA5754-O, DP980, and QP980 calculated by several asymmetric yield criteria.</p> Full article ">Figure 8
<p>Normalized UT yield stresses of (<b>a</b>) AA6016-T4, (<b>b</b>) AA5754-O, (<b>c</b>) DP980, and (<b>d</b>) QP980 predicted by several asymmetric yield criteria.</p> Full article ">Figure 9
<p><span class="html-italic">r</span>-values of (<b>a</b>) AA6016-T4, (<b>b</b>) AA5754-O, (<b>c</b>) DP980, and (<b>d</b>) QP980 predicted by several asymmetric yield criteria.</p> Full article ">Figure 9 Cont.
<p><span class="html-italic">r</span>-values of (<b>a</b>) AA6016-T4, (<b>b</b>) AA5754-O, (<b>c</b>) DP980, and (<b>d</b>) QP980 predicted by several asymmetric yield criteria.</p> Full article ">Figure 10
<p>Yield loci of (<b>a</b>) AA6016-T4, (<b>b</b>) AA5754-O, (<b>c</b>) DP980, and (<b>d</b>) QP980 blanks predicted by IH and AH concepts at various EPSs.</p> Full article ">Figure 11
<p>UT yield stresses of (<b>a</b>) AA6016-T4, (<b>b</b>) AA5754-O, (<b>c</b>) DP980, and (<b>d</b>) QP980 predicted by IH and AH concepts at various EPSs.</p> Full article ">Figure 12
<p><span class="html-italic">r</span>-values of (<b>a</b>) AA6016-T4, (<b>b</b>) AA5754-O, (<b>c</b>) DP980, and (<b>d</b>) QP980 blanks predicted by IH and AH concepts at various EPSs.</p> Full article ">
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