Open AccessArticle

Relationship Between Fracture Fractal and Mechanical Properties of 5083 Aluminum Alloy Sheet Prepared by Alternate Ring-Groove Pressing and Torsion

Chunhui Zhang

¹,

Yu Wang

¹,

Mingxin Wang

¹,

Wenhao Li

¹,

Chunxiang Zhang

² and

Junting Luo

^1,2,*

Key Laboratory of Advanced Forging & Stamping Technology and Science, Ministry of Education of China, School of Mechanical Engineering, Yanshan University, Qinhuangdao 066004, China

State Key Laboratory of Metastable Materials Science and Technology, Yanshan University, Qinhuangdao 066004, China

Author to whom correspondence should be addressed.

Metals 2024, 14(12), 1382; https://doi.org/10.3390/met14121382

Submission received: 31 October 2024 / Revised: 27 November 2024 / Accepted: 28 November 2024 / Published: 2 December 2024

(This article belongs to the Special Issue Metal Plastic Deformation and Forming)

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Figure 1
Metallographic structure of 5083 aluminum alloy original sheet: (a) are low-magnification images; (b) are high-magnification images. "> Figure 2
Waveform position relationship of two ring wave molds. "> Figure 3
Flowchart of severe plastic deformation in the ARPT-TF-R process. Reprinted from Ref. [<a href="#B19-metals-14-01382" class="html-bibr">19</a>]. (a–f) is the strengthening process of alternating pressing-torsion deformation and leveling of the plate through two sets of ring wave molds and torsion flat molds. 1—First ring wave mold die upper die; 2—First ring wave die lower die; 3—Twist flat die upper die; 4—Twist flat lower die; 5—Second ring wave die upper die; 6—Second ring wave die lower die. "> Figure 4
Metallographic structure of ring wave repeated compression torsion–room temperature torsion flat treatment plate: (a) One-pass processing; (b) two-pass processing. "> Figure 5
SEM micro-morphology of tensile fracture of sheet processed by one pass of torsional flattening at room temperature: (a,b) are low-magnification images, and (c,d) are high-magnification images. "> Figure 6
SEM micro-morphology of tensile fracture of sheet processed by two pass of torsional flattening at room temperature: (a,b) are low-magnification images, and (c,d) are high-magnification images. "> Figure 7
Pretreatment and fitting plot of tensile fracture morphology of the original sheet at room temperature: (a) original; (b) grayscale adjustment; (c) histogram equalization; (d) binarization; (e) fitting plot. "> Figure 8
Pretreatment of low-magnification fracture morphology and fitting curve of sheet processed by one-pass torsional flattening at room temperature: (a) original picture; (b) grayscale adjustment; (c) histogram equalization; (d) binarization; and (e) fitting curve. "> Figure 9
Pretreatment of high-magnification tensile fracture morphology and fitting curve of sheet processed by one-pass torsional flattening at room temperature: (a) original picture; (b) grayscale adjustment; (c) histogram equalization; (d) binarization; and (e) fitting curve. "> Figure 10
Pretreatment of low-magnification tensile fracture morphology and fitting curve of sheet processed by two-pass torsional flattening at room temperature: (a) original picture; (b) grayscale adjustment; (c) histogram equalization; (d) binarization; and (e) fitting curve. "> Figure 11
Pretreatment of high-magnification tensile fracture morphology and fitting curve of sheet processed by torsional flattening at room temperature: (a) original picture; (b) grayscale adjustment; (c) histogram equalization; (d) binarization; and (e) fitting curve. "> Figure 12
Stress-strain curve of sheet processed by ARPT-TF-R. "> Figure 13
Fitting curve of the relationship between tensile elongation and fractal dimension of sheet processed by torsional flattening at room temperature: (a) yield strength; (b) tensile strength; and (c) elongation. "> Figure 14
Comparison of hardnesses between original sheet and sheet subjected to ARPT-TF-R. "> Figure 15
Fitting curve of relationship between hardness and fractal dimension of sheet subjected to torsional flattening at room temperature. ">

Versions Notes

Abstract

In this study, the tensile fracture morphology of a 5083 aluminum alloy sheet prepared by alternate ring-groove pressing torsion and torsional flattening at room temperature (ARPT-TF-R) under different numbers of torsional flattening passes was analyzed. The box dimension method was used to calculate the fractal dimension, and formulas for the quantitative relationships between the tensile properties and Vickers hardness of 5083 aluminum alloy sheet under different process conditions and the fractal dimension were established. The results indicated that the fracture mode of the sheet prepared by one pass was microporous aggregation fracture, and the number of large-sized dimples was small. The plate prepared by two passes had a greater number of micropores, and the dimple size was relatively small. The fractal dimension of the aluminum alloy sheet prepared by ARPT-TF-R at room temperature was 1.77–1.84. As the number of torsional flattening passes increased, the yield strength, tensile strength, Vickers hardness, and fractal dimension of the aluminum alloy sheet increased.

Keywords:

5083 aluminum alloy; alternate ring-groove pressing torsion and torsional flattening at room temperature (ARPT-TF-R); fracture morphology; box dimension method; fractal dimension

1. Introduction

5083 aluminum alloy is a medium-strength Al-Mg aluminum alloy, which generally contains an Al₃Mg₂ phase and a Mg₂Si phase. It has good toughness and corrosion resistance, as well as good machinability and weldability. Therefore, it is used extensively in aerospace, marine manufacturing, and the transportation industry. Aluminum alloy is the most ideal alloy material for manufacturing aircraft parts. At present, the mass percentage of aluminum alloy material in aircraft parts exceeds 20% [1,2,3,4].

Severe plastic deformation can greatly improve the mechanical properties of aluminum alloy [5,6,7]. Pouraliakbar et al. [8,9,10,11] performed restrictive molding processing of Al-Mn-Si specimens with stress relief. They reported that it would be better to process cold-rolled specimens with a strain of 0.8 for 2 passes, followed by annealing at 350 °C. The maximum uniform elongation of the specimens was 22.96%, but their strength decreased greatly owing to the subsequent annealing. Hesam Pouraliakbar et al. [12] studied and analyzed the microstructural evolution and the related mechanisms of aluminum alloy under deformation and subsequent annealing conditions, such as recovery, recrystallization, and strain-induced grain boundary migration. As an important index of inhomogeneous grain growth, strain-induced grain boundary migration is tracked in terms of the transformation of the grain length-to-grain width ratio. Moradpour M et al. [13] performed two passes of constrained compression deformation along the rolling direction and transverse direction of AA 5052 alloy at room temperature. The results indicated that a sub-grain/unit cell ultrafine grain structure with grain sizes of 300–500 nm was formed. Compared to those of the annealed alloy, the microhardness and tensile strength of the alloy improved significantly, reaching 75% and 105%, respectively, and the alloy exhibited uniformity and isotropy.

Our team proposed alternate ring-groove pressing torsion and torsional flattening at room temperature (ARPT-TF-R) as a strong deformation process for aluminum alloy plates, and we have retained the intellectual property rights for this process [14,15]. However, after processing, a quantitative relationship between the mechanical properties of the processed plate and those of the original plate could not be established. When the aluminum alloy sheet is broken, the propagation path of the crack is usually very complex, and the dimples on the fracture surface are distributed in a combined form with a self-similar structure. Through the fractal of aluminum alloy fracture, it can help to quantify the complexity of the fracture surface and evaluate the mechanical properties of the material, establish a relationship with the mechanical properties of the material, and then determine the microscopic mechanism of material failure and performance. It is the main research direction in the field of fracture science.

The fractal dimension of material fracture is an important analysis parameter, and its fractal means can be divided into two kinds: two-dimensional fractal and three-dimensional fractal [16,17]. The two-dimensional fractal and three-dimensional fractal vary with different materials and fracture conditions. In two-dimensional image analysis, the two-dimensional fractal dimension value is generally less than 2. The three-dimensional fractal dimension is between 2.2 and 2.4. The three-dimensional fractal is closer to the actual situation, but it is necessary to obtain the three-dimensional morphology of the fracture, and the process is more complicated Benoit B. MANDELBROT [18] completed a large number of three-dimensional fractals of the fracture surface. It is also common to generate two-dimensional fractals by binarizing the gray image, and the two-dimensional fracture morphology is the most commonly used experimental method to obtain the fracture by SEM observation. Therefore, in this study, two-dimensional fractal technology was used to fractal the tensile fracture morphology of 5083 aluminum alloy sheet prepared by ring wave compression torsion-normal temperature torsion leveling under different process conditions, calculate the fractal dimension, and determine the relationship between tensile deformation performance and fractal dimension under different process conditions. Finally, a quantitative relationship was established.

2. Process and Test Methods

2.1. Materials

The original 5083 aluminum alloy plate (Produced by Henan Mingtai Aluminum Industry Co., Ltd., Zhengzhou, China) used in the experiment was a rolled plate with a thickness of 0.63 mm. The main chemical composition is shown in Table 1. The plate was subjected to multi-pass rolling and intermediate annealing and final recrystallization annealing heat treatment. The metallographic structure is shown in Figure 1. The grains are discontinuously equiaxed, and the grain size is significantly different, mainly concentrated between 20 and 30 μm. The average grain size is about 25 μm. A large number of granular β (Al₃Mg₂) phase particles were uniformly distributed on the matrix, and a small amount of black Mg₂Si phase and gray Al₆Mn phase was observed.

2.2. Process Method

The mold of the ARPT-TF-R process includes two sets of ring wave molds and a set of flattening molds. The two sets of ring wave molds are composed of the upper mold and the lower mold, which are axisymmetric cylindrical structures. The surface shape of the mold is a ring wave of several turns, and the concave and convex positions of the upper and lower molds correspond to each other, as shown in points 1–11 in Figure 2. The concave and convex positions of the two sets of molds are staggered. The waveform position relationship between upper mold A and the ower mold B is shown in Figure 2, and C is a 5083 aluminum alloy plate.

A process flow diagram of ARPT-TF-R is shown in Figure 3. The process abbreviation definitions are shown in Table 2. The specific forming steps are as follows [19].

The circular plate is placed on the lower die of the first set of ring wave pressure torsion dies, so that the center of the plate is aligned with the center of the lower die. Make the upper die of the first set of ring wave pressure torsion die go down according to the predetermined speed, make the upper and lower die close, and the plate produces ring wave drawing and bulging deformation, as shown in Figure 3a.

Under the condition that the first set of ring wave pressure torsion die is kept closed, the upper die is twisted around the axis, as shown in Figure 3b.

The first set of ring wave pressure torsion dies back to the mold, the ring wave drawing and bulging deformation of the sheet with a torsion flat die leveling, as shown in Figure 3c.

The plate after leveling is turned over and placed in the second set of ring wave pressure torsion dies, and the ring wave drawing and bulging deformation are carried out again, as shown in Figure 3d.

Under the condition that the second set of ring wave pressure torsion dies is kept closed, the upper die is twisted around the axis, as shown in Figure 3e.

The second set of ring wave pressure torsion dies return to the mold, again with ring wave drawing and bulging deformation after the plate and torsion flat die leveling, completing a process pass, as shown in Figure 3f.

Repeating the above steps, multi-pass forming can be carried out.

2.3. Test Method

In this study, ARPT-TF-R was used to process the sheet for one pass and two passes, and then the tensile test was carried out on a Hegewald & Peschke INSPEKT Table electronic universal testing machine manufactured by Germany Hegewald & Peschke Company, Nossen, Germany. The mechanical properties of the material were tested, and the tensile fracture specimens were obtained. The tensile fracture morphology of 5083 aluminum alloy plates treated by different processes was analyzed with a Hitachi-TM3030 scanning electron microscope manufactured by Hitachi, Tokyo, Japan. The Vickers hardness of the treated 5083 aluminum alloy was tested with an MVS-1000D1 automatic turret digital microhardness tester manufactured by China Mingx M Instrument Company, Shanghai, China. The test force was 1 kgf, and the holding pressure was 10 s.

3. Microstructure Analysis

3.1. Metallographic Structure Analysis of Plate After Processing

Figure 4 shows the metallographic structure of the plate treated by cyclic wave repeated molding torsion–room temperature torsion. It can be seen that the plate is plasticized by cyclic wave repeated molding, and its microstructure is obviously refined. After one pass of severe plastic deformation treatment, the grains of the plate were fragmented, and the larger equiaxed original grains basically disappeared, resulting in discontinuous sub-grain boundaries, which further extended and developed into independent sub-grain structures, dividing the larger original grains; the average grain size gradually decreased to 13.5 μm. After two passes of severe plastic deformation treatment, the “broken crystal” trend of the plate was enhanced, the number of sub-grains was greatly increased, the sub-micron fine grains were further increased, the grain size was more uniform and fine, and the average grain size was about 10 μm.

3.2. Tensile Fracture Morphology Analysis

Figure 5 illustrates the scanning electron microscopy (SEM) micro-morphology of tensile fracture of the sheet prepared by one pass of ARPT-TF-R. According to Figure 5a,b, no obvious necking occurs in the macroscopic morphology, and the angle between the tensile fracture and the tension direction is approximately 45°. Many dimples can be observed on the torsional flat tensile fracture at 25 °C at room temperature, and white tearing edges are present near the dimples. The fracture mode corresponds to microporous aggregation fracture, that is, dimple fracture, but the number of large-sized dimples is small.

Figure 5c,d depict the presence of a second phase at the fracture dimple, such as the white block at the bottom of the dimple in the figure. However, not every dimple has a second phase because the phase may have been eliminated during the stretching process or be at the bottom of another fracture dimple. It is inferred that in the fracture process under tension, the dislocation movement encounters the second-phase particles in the aluminum alloy matrix. Owing to the pinning effect of the second-phase particles, dislocations form dislocation loops in regions close to the second-phase particles, and large numbers of such dislocation loops aggregate to form micropores. Meanwhile, under tensile stress, the dislocation loops continue to aggregate at the micropores, which causes the micropores to grow, and these growing micropores aggregate to form larger dimples. The aluminum alloy matrix has good plasticity and can deform under increasing tensile stress. In contrast, the second-phase particles have poor plasticity and do not deform easily. The deformation of the matrix and the particles is not coordinated. The internal stress resulting from this uncoordinated deformation affects the second-phase particles. This internal stress increases as the tension force proceeds, and the interface is pulled apart, resulting in the formation of micropores. Under further tension, the micropore size continues to increase, resulting in dimple formation.

Figure 6 illustrates the SEM micro-morphology of tensile fracture of the sheet prepared by two passes of ARPT-TF-R. In general, the larger and deeper the dimple, the better the plasticity of the material. According to Figure 6a,b, at room temperature (25 °C), more micropores are present at the fracture location, and their sizes are smaller, resulting in smaller dimple sizes. According to Figure 6c,d, the dimples at the fracture location are shallow at room temperature, and the directions of the tearing edges tend to be consistent. Second-phase particles can be observed in the dimples.

4. Calculation of Fractal Dimension of Tensile Fracture Morphology

The fractal dimension D is calculated by the box dimension method, and the fracture morphology image after binarization is segmented by a square grid with a side length of r. During the measurement, a coordinate grid composed of a series of boxes of different scales is used to cover the fractal structure to be studied. For each scale r, the total number of boxes containing fractal graphics C (r) is calculated, and the relationship between the total number of boxes and the scale r is shown in Formula (1). The logarithm of the two ends of the relationship between the total number of boxes and the scale r in Formula (1) is taken, and the limit value of the fractal dimension D is obtained when r gradually approaches 0, as shown in Formula (2). In order to facilitate the analysis of the distribution characteristics of the data points of the fitting curve and the calculation of the fractal dimension according to Formula (2), the box size is set in the order of

L n (\frac{1}{r})

= 1,2,3,4,…, and the specific value of the box size is

r = \frac{1}{e}, \frac{1}{e^{2}}, \frac{1}{e^{3}}

… gradually decreasing until it approaches 0.

C (r) = α r^{- D}

(1)

D = \lim_{r \to 0} \frac{L n C (r)}{L n (\frac{1}{r})}

(2)

First, the SEM images of tensile fracture of 5083 aluminum alloy plates treated by different processes were binarized by MATLAB 2016 version software, then the fractal dimension calculation program written by the box dimension method was used to fractal it, and, finally, the fractal dimension of tensile fracture morphology was obtained [20,21,22,23]. Pretreatment with different process treatments of 5083 aluminum alloy sheet with different-magnification fracture morphology pictures is shown in Figure 7, Figure 8, Figure 9, Figure 10 and Figure 11. Subfigure (e) in Figure 7, Figure 8, Figure 9, Figure 10 and Figure 11 shows the fitting curve of fractal dimension calculation for different fractures. The two groups of logarithms in Formula (2) are taken as variables X and Y. Each group (X, Y) constitutes the data points for curve fitting, and linear regression is performed on each set of lnr-lnN with the functional relationship of y = kx. The negative number of the slope of the straight line obtained by regression fitting is the fractal dimension D of the graph.

Table 3 lists the fractal dimensions of tensile fracture of the plate prepared by ARPT-TF-R. The fractal dimension of the aluminum alloy processed by torsional flattening at room temperature ranged from 1.77 to 1.84. Under the condition of the same multiple, the fractal dimension of the plate subjected to two-pass torsional flattening was greater than that of the plate subjected to one-pass torsional flattening; under the same deformation process conditions, the higher the multiple, the greater the fractal dimension in the SEM images.

5. Relationship Between Tensile Mechanical Properties and Fractal Dimension

Three groups of tensile tests were carried out for each plate under the same test conditions. The stability of the experimental data was tested by standard deviation calculation to avoid the error caused by the contingency of the test. The mean value of each set of data is used for fractal dimension fitting, as shown in Supplementary Material Table S1. Figure 12 illustrates the tensile stress-strain curves of the original plate and the plate prepared by ARPT-TF-R. Table 4 lists the tensile properties and fractal dimension of the plate prepared by ARPT-TF-R. The variations of yield strength and tensile strength were consistent with the fractal dimension, and both quantities increased as the number of deformation passes increased. Elongation decreased as the number of deformation passes increased.

The yield strength of the original sheet was 110 MPa, tensile strength was 311MPa, elongation at break was 16.9%, and fractal dimension was 1.7899. After one pass of deformation, work hardening and fine-grain strengthening of the material were significant. The yield strength of the material increased sharply to 245 MPa, tensile strength increased significantly to 340 MPa, fracture elongation decreased to 15.6%, and fractal dimension increased to 1.7956. Therefore, under the process conditions of ARPT-TF-R, strain accumulation hardening of the material was severe, material grain was refined to a certain level, effect of fine grain strengthening was obvious, and the complexity of fracture morphology increased. After two deformation passes, the yield strength of the material increased to 275 MPa, tensile strength increased to 345 MPa, fracture elongation decreased significantly to 12.2%, and fractal dimension increased to 1.8012. Therefore, the effect of grain refinement improved gradually; consequently, the strength of the material continued to increase, and the complexity of the fracture morphology increased. However, owing to the generation of a large number of sub-grain boundaries and defects, the plasticity of the material decreased.

The relationship between tensile yield strength, tensile strength, elongation, and fractal dimension of 5083 aluminum alloy sheet under different passes of torsion leveling treatment at room temperature was analyzed in detail by MATLAB software. By using the “Curve Fitting” toolbox in MATLAB, the mechanical performance parameters were fitted with the fractal dimension, the corresponding fitting curve was generated (as shown in Figure 13), and the relevant parameters of the fitting curve were obtained. The specific results are shown in Table 5. Through the fitting analysis of the fractal dimension, the correlation between the complexity of material microstructure and macroscopic mechanical properties is revealed. The effect of fractal dimension on the tensile yield strength, tensile strength, and elongation of aluminum alloy under different passes of ARPT-TF-R shows that the fractal characteristics of the microstructure of the material can effectively characterize the change trend of its mechanical properties, which provides theoretical support and experimental basis for further understanding the performance regulation of aluminum alloy under different processing conditions.

In this regard, the relationship between the tensile properties of the material at room temperature and the tensile properties of the original sheet at room temperature for different numbers of torsional flattening passes at room temperature can be obtained as follows:

σ_{s R} = 0.4988 σ_{s N R} + 8.746 (D_{R} - D_{N R}) σ_{s N R}

(3)

where

σ_{s R}

is tensile yield strength of original material at room temperature;

σ_{s N R}

is tensile yield strength of material processed by torsional flattening at room temperature;

D_{R}

is tensile fractal dimension of original material at room temperature;

D_{N R}

is tensile fractal dimension of material processed by torsional flattening at room temperature;

R_{m R} = 0.9282 R_{m N R} + 2.367 (D_{R} - D_{N R}) R_{m N R}

(4)

where

R_{m R}

is tensile strength of original material at room temperature;

R_{m N R}

is tensile strength of material processed by torsional flattening at room temperature; and

δ_{R} = 0.776 δ_{N R} - 53.91 (D_{R} - D_{N R}) δ_{N R}

(5)

where

δ_{R}

is tensile elongation of original material at room temperature and

δ_{N R}

is tensile elongation of material processed by torsional flattening at room temperature.

6. Relationship Between Hardness and Fractal Dimension

The hardness of a metal is determined by its yield strength and work hardening rate. Hardness is an important parameter that reflects the ability of a metal to resist plastic deformation, and it is related to grain boundary strength and dislocation density. An MVS-1000D1 automatic micro-hardness tester was used to test the Vickers hardness of the original sheet and the sheet prepared by ARPT-TF-R, in which the load was 200 gf and the holding time was 10 s. Six positions from the center of the sheet along the radial direction were considered in sequence for measurement, and they were labeled 1–6.

Five sets of Vickers hardness tests were performed near the circumferential direction at six positions selected for each plate, and the mean value of each set of data was used for fractal dimension fitting, as shown in Supplementary Material Table S2. Figure 14 presents a hardness comparison between the original plate and the plate prepared by ARPT-TF-R. The hardness of the plate improved remarkably after ARPT-TF-R. The process related to the hardness value calculation is shown in Supplementary Material S3. The average hardness of the plate subjected to two passes was higher than that of the plate subjected to one pass, mainly owing to increased strain accumulation with increasing number of deformation passes, and the effect of strain strengthening improved. In addition, from the center of the sheet toward its edges, hardness increased slightly, by 5–10 HV. This was mainly attributed to optimization of the mold structure in the process of alternate ring-groove pressing to control the deformation in each area of the sheet, which was performed to offset the deformation effect and the radial inhomogeneity due to the torsion process against each other to achieve uniform sheet deformation.

Table 6 lists the average hardness and fractal dimension of the original sheet and the sheet subjected to ARPT-TF-R. As the number of deformation passes increased, the average Vickers hardness of the material increased, but the increase was relatively small. In addition, the fractal dimension exhibited a consistent change pattern; that is, it increased as the number of deformation passes increased, and it was 1.7899, 1.7956, and 1.8012.

The fitting curve of the relationship between the hardness and fractal dimension of the 5083 aluminum alloy sheet at room temperature was obtained using the curve-fitting toolbox “Curve Fitting” in MATLAB, as illustrated in Figure 15. The parameters of the fitting formula were a = 0.9388 and b = 4.708.

In this regard, the relationship between the hardness of the material at room temperature and the hardness of the original sheet at room temperature under different numbers of passes of torsional flattening at room temperature was obtained as follows:

H_{V R} = 0.9388 H_{V N R} + 4.708 (D_{R} - D_{N R}) H_{V N R}

(6)

where

H_{V R}

is hardness of original material and

H_{V N R}

is hardness of material after torsional flattening.

7. Conclusions

(1): The tensile fracture of the plate treated by ARPT-TF-R process was fractal, and the quantitative relationship between the tensile properties and Vickers hardness of the plate prepared by cyclic wave repeated molding torsion–room temperature torsion and flattening under different torsion and flattening passes was established.
(2): The angle between the tensile fracture and tensile direction of the sheet prepared by one pass of ARPT-TF-R was approximately 45°. Many dimples were present on the fracture surface, and white tearing edges were formed near the dimples. The fracture mode was microporous aggregation fracture, that is, dimple fracture, but the number of large-sized dimples was small. The fracture of the plate prepared by two passes had more micropores, and the pore and dimple sizes were smaller.
(3): The fractal dimension of the aluminum alloy sheet prepared by ARPT-TF-R was 1.77–1.84, which was significantly larger than the fractal dimension of tensile fracture of the original sheet at room temperature. Under the condition of the same multiple, the fractal dimension of the plate prepared by two-pass torsional flattening was greater than that of the plate prepared by one-pass torsional flattening; under the same deformation process conditions, the higher the multiple, the greater the fractal dimension observed in the SEM images.
(4): The yield strength and tensile strength of 5083 aluminum alloy sheet increased with the increase of deformation passes, which is consistent with the change of fractal dimension. The yield strength increased by 12.2%, the tensile strength increased by 1.4%, and the elongation decreased by 21.8%. The average hardness of the two-pass sheet is 2.9% higher than that of the one-pass sheet after the ring wave repeated molding torsion–normal temperature torsion deformation treatment.
(5): Constructing a mathematical model between fractal dimension and mechanical properties of materials can further realize the predictive ability of fractal dimension and provide theoretical support for optimizing the processing technology and properties of materials.

Supplementary Materials

The following supporting information can be downloaded at: https://www.mdpi.com/article/10.3390/met14121382/s1, Table S1: Tensile properties of sheet metal and fractal dimension of fracture surface; Table S2: Hardness value of sheet metal; Supplementary S3: Hardness value calculation process.

Author Contributions

Conceptualization, C.Z. (Chunhui Zhang) and J.L.; methodology, J.L., C.Z. (Chunxiang Zhang) and M.W.; software, Y.W. and W.L.; validation, C.Z. (Chunxiang Zhang), M.W. and W.L.; formal analysis, C.Z. (Chunhui Zhang) and C.Z. (Chunxiang Zhang); investigation, Y.W. and M.W.; resources, J.L.; data curation, C.Z. (Chunhui Zhang); writing—original draft preparation, C.Z. (Chunhui Zhang); writing—review and editing, C.Z. (Chunhui Zhang); visualization, J.L. and W.L.; supervision, J.L.; project administration, J.L. All authors have read and agreed to the published version of the manuscript.

Funding

This research received no external funding.

Data Availability Statement

The original contributions presented in this study are included in the article/supplementary material. Further inquiries can be directed to the corresponding author.

Conflicts of Interest

The authors declare no conflict of interest.

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Figure 1. Metallographic structure of 5083 aluminum alloy original sheet: (a) are low-magnification images; (b) are high-magnification images.

Figure 2. Waveform position relationship of two ring wave molds.

Figure 3. Flowchart of severe plastic deformation in the ARPT-TF-R process. Reprinted from Ref. [19]. (a–f) is the strengthening process of alternating pressing-torsion deformation and leveling of the plate through two sets of ring wave molds and torsion flat molds. 1—First ring wave mold die upper die; 2—First ring wave die lower die; 3—Twist flat die upper die; 4—Twist flat lower die; 5—Second ring wave die upper die; 6—Second ring wave die lower die.

Figure 4. Metallographic structure of ring wave repeated compression torsion–room temperature torsion flat treatment plate: (a) One-pass processing; (b) two-pass processing.

Figure 5. SEM micro-morphology of tensile fracture of sheet processed by one pass of torsional flattening at room temperature: (a,b) are low-magnification images, and (c,d) are high-magnification images.

Figure 6. SEM micro-morphology of tensile fracture of sheet processed by two pass of torsional flattening at room temperature: (a,b) are low-magnification images, and (c,d) are high-magnification images.

Figure 7. Pretreatment and fitting plot of tensile fracture morphology of the original sheet at room temperature: (a) original; (b) grayscale adjustment; (c) histogram equalization; (d) binarization; (e) fitting plot.

Figure 8. Pretreatment of low-magnification fracture morphology and fitting curve of sheet processed by one-pass torsional flattening at room temperature: (a) original picture; (b) grayscale adjustment; (c) histogram equalization; (d) binarization; and (e) fitting curve.

Figure 9. Pretreatment of high-magnification tensile fracture morphology and fitting curve of sheet processed by one-pass torsional flattening at room temperature: (a) original picture; (b) grayscale adjustment; (c) histogram equalization; (d) binarization; and (e) fitting curve.

Figure 10. Pretreatment of low-magnification tensile fracture morphology and fitting curve of sheet processed by two-pass torsional flattening at room temperature: (a) original picture; (b) grayscale adjustment; (c) histogram equalization; (d) binarization; and (e) fitting curve.

Figure 11. Pretreatment of high-magnification tensile fracture morphology and fitting curve of sheet processed by torsional flattening at room temperature: (a) original picture; (b) grayscale adjustment; (c) histogram equalization; (d) binarization; and (e) fitting curve.

Figure 12. Stress-strain curve of sheet processed by ARPT-TF-R.

Figure 13. Fitting curve of the relationship between tensile elongation and fractal dimension of sheet processed by torsional flattening at room temperature: (a) yield strength; (b) tensile strength; and (c) elongation.

Figure 14. Comparison of hardnesses between original sheet and sheet subjected to ARPT-TF-R.

Figure 15. Fitting curve of relationship between hardness and fractal dimension of sheet subjected to torsional flattening at room temperature.

Table 1. Chemical composition and content of 5083 aluminum alloy.

Element	Mg	Mn	Si	Cr	Ti	Fe	Cu	Zn
Content [wt%]	4.0~4.9	0.4~1.0	0.40	0.05~0.25	0.15	0.4	0.1	0.25

Table 2. Process abbreviation definition table.

Abbreviation	Definition
ARPT	Alternate ring-groove pressing torsion
TF	Torsional flattening
R	Room temperature
ARPT-TF-R	Alternate ring-groove pressing torsion and torsional flattening at room temperature

Table 3. Fractal dimension of SEM morphology of tensile fracture of the sheet prepared by ARPT-TF-R.

Sheet Shape	Fractal Dimension
Sheet Shape	D₁	D₂	Average Value
Original plate	1.7894	1.7904	1.7899
1 ARPT-TF-R-Low multiple	1.7803	1.8101	1.7952
1 ARPT-TF-R-High multiple	1.7771	1.8148	1.7960
2 ARPT-TF-R-Low multiple	1.7826	1.7879	1.7853
2 ARPT-TF-R-High multiple	1.8012	1.8330	1.8171

Table 4. Tensile properties of sheet prepared by ARPT-TF-R.

Sheet Shape	Yield Strength [MPa]	Tensile Strength [MPa]	Elongation [%]	Fractal Dimension
Original plate	110	311	16.9	1.7899
1ARPT-TF-R	245	340	15.6	1.7956
2ARPT-TF-R	275	345	12.2	1.8012

Table 5. Fitting results of relationship between tensile properties and fractal dimension of 5083 sheet metal.

Tensile Parameters	f(x,y) = ax + bxy
Tensile Parameters	a	b
Yield strength	0.4988	8.746
Tensile strength	0.9282	2.367
Elongation	0.776	−53.91

Table 6. Tables of hardness and fractal dimensions of sheet subjected to ARPT-TF-R.

Sheet Shape	Hardness [HV]	Fractal Dimension
Original plate	92.027	1.7899
1ARPT-TF-R	100.913	1.7956
2ARPT-TF-R	103.917	1.8012

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Zhang, C.; Wang, Y.; Wang, M.; Li, W.; Zhang, C.; Luo, J. Relationship Between Fracture Fractal and Mechanical Properties of 5083 Aluminum Alloy Sheet Prepared by Alternate Ring-Groove Pressing and Torsion. Metals 2024, 14, 1382. https://doi.org/10.3390/met14121382

AMA Style

Zhang C, Wang Y, Wang M, Li W, Zhang C, Luo J. Relationship Between Fracture Fractal and Mechanical Properties of 5083 Aluminum Alloy Sheet Prepared by Alternate Ring-Groove Pressing and Torsion. Metals. 2024; 14(12):1382. https://doi.org/10.3390/met14121382

Chicago/Turabian Style

Zhang, Chunhui, Yu Wang, Mingxin Wang, Wenhao Li, Chunxiang Zhang, and Junting Luo. 2024. "Relationship Between Fracture Fractal and Mechanical Properties of 5083 Aluminum Alloy Sheet Prepared by Alternate Ring-Groove Pressing and Torsion" Metals 14, no. 12: 1382. https://doi.org/10.3390/met14121382

APA Style

Zhang, C., Wang, Y., Wang, M., Li, W., Zhang, C., & Luo, J. (2024). Relationship Between Fracture Fractal and Mechanical Properties of 5083 Aluminum Alloy Sheet Prepared by Alternate Ring-Groove Pressing and Torsion. Metals, 14(12), 1382. https://doi.org/10.3390/met14121382

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Relationship Between Fracture Fractal and Mechanical Properties of 5083 Aluminum Alloy Sheet Prepared by Alternate Ring-Groove Pressing and Torsion

Abstract

1. Introduction

2. Process and Test Methods

2.1. Materials

2.2. Process Method

2.3. Test Method

3. Microstructure Analysis

3.1. Metallographic Structure Analysis of Plate After Processing

3.2. Tensile Fracture Morphology Analysis

4. Calculation of Fractal Dimension of Tensile Fracture Morphology

5. Relationship Between Tensile Mechanical Properties and Fractal Dimension

6. Relationship Between Hardness and Fractal Dimension

7. Conclusions

Supplementary Materials

Author Contributions

Funding

Data Availability Statement

Conflicts of Interest

References

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