CN106525612B - The construction method of polycarbonate sand stone concrete based on stretching and compression experiment - Google Patents

Abstract

The invention discloses a kind of construction methods of polycarbonate sand stone concrete based on stretching and compression experiment, and the construction method for solving existing polycarbonate constitutive model constructs the technical problem of constitutive model order of accuarcy difference.Technical solution is by the linear elasticity stage of polycarbonate, yielding stage, the description in strain softening stage and strain hardening stage, carry out a large amount of different strain rate, at a temperature of tensile and compression test and add unloading test, relevant parameter of its material model under ture stress-strain has been determined, particularly by add unloading test by the internal injury of material to mechanical property influence write-in constitutive model in；Reasonable optimization has been carried out to the parameter in model, ensure that the order of accuarcy of constitutive model while reducing number of parameters, meanwhile, also achieve the effective unified combination for stretching constitutive model and compressing constitutive model.

Description

A method for constructing a unified constitutive model of polycarbonate based on tensile and compressive experiments

technical field

The invention relates to a method for constructing a polycarbonate constitutive model, in particular to a method for constructing a polycarbonate unified constitutive model based on tensile and compression experiments.

Background technique

Polycarbonate (PC), as a typical thermoplastic amorphous polymer, is widely used in aerospace, automobile, high-speed rail and construction due to its good impact resistance, high specific stiffness and specific strength, and light transmission properties. field. Since the service environment of polycarbonate products such as aerospace and high-speed rail includes harsh service conditions such as high temperature difference, high-speed impact, and large pressure difference, there are high requirements for the mechanical properties of polycarbonate. It can not only play its role in various fields, but also replace some tests through numerical simulation, which will greatly reduce the manufacturing cost of the industry and bring more benefits.

Polycarbonate has a strong dependence on strain rate and temperature. At the same time, it is easy to find through experiments and literature that polycarbonate exhibits different mechanical properties in the process of tension and compression, its yield strength, strain softening and hardening. are somewhat different. In order to comprehensively characterize the mechanical properties of polycarbonate, it is necessary to construct a unified constitutive model based on tensile and compressive tests. At present, the research on the unified constitutive model of polycarbonate at home and abroad mainly includes the following two:

Literature 1 "Kan Cao, Yang Wang, Yu Wang. Experimental investigation and modeling of the tension behavior of polycarbonate with temperature effects from low to high strain rates, International Journal of Solids and Structures, 2014, Vol.51(13), p2539-2548" In , a constitutive model based on its engineering stress-strain curve was established through tensile tests at different temperatures and strain rates. However, because the engineering stress-strain curve cannot reflect the real properties of the material during deformation, it is insufficient in characterizing the strain hardening phenomenon of polycarbonate. On the other hand, the asymmetry exhibited by polycarbonate during tension and compression makes it particularly important to construct constitutive models including different stress forms. This method does not involve the mechanical properties of compression, so in the Insufficient accuracy in characterizing the stress process of polycarbonate.

Document 2 "Sai S.Sarva,Mary C.Boyce.Mechanics of Polycarbonate during High-rate Tension.Journal of mechanics of materials and structures, 2007, Vol.2(10), p1853-1880" carried out a series of tension-compression The constitutive model of polycarbonate including linear elasticity, yielding, strain softening and strain hardening stages is constructed. However, it involves a large number of statistical averages in the modeling process, which is more complicated in the process of determining parameters through experiments, and does not consider the internal damage of the material while using continuum mechanics to explain the essence; at the same time, the model uses affine Network theory is used to simulate the stretching of molecular networks, and it is difficult to simulate the entanglement and disentanglement between polymer material segments during the real deformation process.

The above existing constitutive models are difficult to accurately describe the exact mechanism of polycarbonate deformation, so its mechanical properties cannot be characterized efficiently and accurately.

SUMMARY OF THE INVENTION

In order to overcome the shortcomings of poor accuracy of the existing polycarbonate constitutive model building methods, the present invention provides a polycarbonate unified constitutive model building method based on tensile and compression experiments. Through the description of the linear elastic stage, yield stage, strain softening stage and strain hardening stage of polycarbonate, a large number of tensile and compressive tests at different strain rates and temperatures, as well as loading and unloading tests are carried out, and the material model is determined in this method. The relevant parameters under the true stress and strain, especially the influence of the internal damage of the material on the mechanical properties are written into the constitutive model through the loading and unloading test; the parameters in the model are reasonably optimized, and the number of parameters is reduced while ensuring the constitutive model. The accuracy of the model, and at the same time, it also realizes the effective and unified combination of the tensile constitutive model and the compression constitutive model.

The technical scheme adopted by the present invention to solve its technical problems: a method for constructing a polycarbonate unified constitutive model based on tensile and compression experiments, which is characterized by comprising the following steps:

(a) Obtain its true stress-strain curve by performing tensile or compressive tests on polycarbonate, and calculate the elastic modulus E according to its elastic stage:

where E is the elastic modulus of polycarbonate, σ is the true stress obtained from the test, and ε is the true strain.

(b) Based on the tensile and compressive test data of polycarbonate, the nonlinear relationship between yield stress and temperature and strain rate is obtained, which is expressed by the following formula:

where σ _y is the yield stress of polycarbonate, is the equivalent strain rate during the test, _Th is the homologous temperature, and K, C _r , C _t , and m are the relevant test parameters.

(c) Determine the internal damage status of the material according to the corresponding loading and unloading tests. And the relationship between damage and plastic strain is obtained from the data:

where ω is the damage variable of polycarbonate, is the equivalent plastic strain, and C _ω and x are test-related parameters.

(d) The experimental strain softening and strain hardening data are analyzed, and the relationships between the available true stress and damage variables, yield stress and equivalent plastic strain are as follows:

where σ is the true stress of polycarbonate, ω is the damage variable, σ _y is the yield stress, is the equivalent plastic strain, and C _h and γ are the relevant parameters.

(e) Fit and solve the parameters of the tensile and compressive tests in the unified constitutive model respectively, and write the obtained constitutive model into the finite element software for simulation calculation, and compare the stress-strain curve obtained from the simulation with the actual stress-strain of the test. The curves are compared to verify the correctness of the unified constitutive model.

The beneficial effects of the present invention are: the method can carry out a large number of tensile and compression tests and loading and unloading tests at different strain rates and temperatures through the description of the linear elastic stage, yield stage, strain softening stage and strain hardening stage of polycarbonate. , the relevant parameters of the material model under the true stress and strain are determined, especially the influence of the internal damage of the material on the mechanical properties is written into the constitutive model through the loading and unloading test; the parameters in the model are reasonably optimized, and the parameters are reduced. At the same time, the accuracy of the constitutive model is ensured, and the effective and unified combination of the tensile constitutive model and the compression constitutive model is also realized.

The present invention will be described in detail below with reference to the accompanying drawings and specific embodiments.

Description of drawings

Figure 1 is a graph showing the linear relationship between yield stress and tensile ambient temperature in the method of the present invention.

Figure 2 is a graph of the bilinear relationship between yield stress in the method of the present invention and logarithmic strain rate in a tensile test.

Figure 3 is a graph of the damage variable versus plastic strain in a tensile test in the method of the present invention.

4 is a comparison diagram of the curve obtained by the unified constitutive model and the true stress-strain curve in the tensile state at 25° C. and the strain rate of 0.1s ⁻¹ in the embodiment of the method of the present invention.

5 is a comparison diagram of the curve obtained by the unified constitutive model and the true stress-strain curve under the tensile state at 25° C. and the strain rate of 4500 s ⁻¹ in the embodiment of the method of the present invention.

Detailed ways

Refer to Figures 1-5. The specific steps of the construction method of the polycarbonate unified constitutive model based on the tensile and compression experiments of the present invention are as follows:

The tensile and compressive parameters in the unified constitutive model are not the same, but due to the same test method and parameter determination method, the following is only for polycarbonate at different temperatures (-60-120°C) and different strain rates (0.0005s ^{- 1} , 0.001s ^-1 , 0.01s ^-1 , 0.1s ^-1 , 1400s ^-1 , 2000s ^-1 , 3500s ^-1 , 4500s ^-1 ) under the tensile test data obtained, the relevant parameters were fitted, and The calculated results are compared with the real test results.

Step 1: Obtain the true stress-strain curve of polycarbonate under the current conditions (25°C, 0.01s ^-1 ) through a quasi-static uniaxial tensile test, and calculate its elastic modulus according to the data in its linear elastic stage:

where E is the elastic modulus of polycarbonate, σ is the true stress obtained from the test, and ε is the true strain.

Step 2: According to the tensile test data at different temperatures and strain rates, the nonlinear relationship between yield stress, temperature and strain rate is obtained, which is expressed by the following formula:

where σ _y is the yield stress of polycarbonate, is the equivalent strain rate during the test, _Th is the homologous temperature, K, C _r , C _t , m are the relevant test parameters, and the equivalent strain rate And the homologous temperature T _h is represented by the following formula:

in, is the deviator of the strain increment, T is the ambient temperature in the test, _Tr is the room temperature of 25°C, and _Tg represents the glass transition temperature of polycarbonate, which is 150°C. Figures 1 and 2 show the relationship between temperature, strain rate and yield stress in tensile state, respectively. In tensile state, yield stress shows a linear decreasing trend with the increase of temperature; at the same time, yield stress increases with temperature. The increase in strain rate exhibits a bilinear increase.

Step 3: Determine the internal damage of the material through multiple tensile loading and unloading tests. For discrete test data, the damage variable can be derived from:

where ω is the damage variable of polycarbonate, E ₀ is the initial elastic modulus, is the value of the elastic modulus during loading and unloading. The calculated discrete damage variable data are integrated to obtain the relationship between damage and plastic strain:

where ω is the damage variable of polycarbonate, is the equivalent plastic strain, and C _ω and x are test-related parameters. Figure 3 shows the relationship between the damage variable and the plastic strain. The damage variable and the plastic strain of the material become an exponential function. The initial stage increases rapidly with the plastic strain, and then the trend gradually becomes gentle.

Step 4: Analyze the strain softening and strain hardening data in the stress-strain curve of the tensile test, and sort out the relationship between the true stress and damage variables, yield stress and equivalent plastic strain as follows:

where σ is the true stress of polycarbonate, ω is the damage variable, σ _y is the yield stress, is the equivalent plastic strain, and C _h and γ are the relevant parameters.

Step 5: Write the unified constitutive model into the subroutine module in the nonlinear finite element software Ls-dyna, and establish the model, constraints and loads under the same conditions as the test. The model is numerically simulated, and the obtained stress-strain curve is compared with the actual stress-strain curve of the test to verify the correctness of the unified constitutive model. Figures 4 and 5 show the experimental data and simulation data of the true stress-strain curves of polycarbonate tensile specimens at strain rates of 0.1s ^-1 , 4500s ^-1 , and temperature of 25°C, respectively, and stress-strain curves It shows obvious elastic, yielding, strain softening and strain hardening stages. The calculated results are in good agreement with the experimental results, which further confirms the accuracy of the unified constitutive model.

Table 1 gives the relevant parameter values in the polycarbonate constitutive model in the tensile state.

Claims (1)

1. A method for constructing a polycarbonate unified constitutive model based on a tensile or compression experiment is characterized by comprising the following steps:

(a) the actual stress-strain curve of the polycarbonate is obtained by carrying out a tensile or compression test on the polycarbonate, and the elastic modulus E is calculated according to the elastic stage:

wherein E is the elastic modulus of the polycarbonate, sigma is the real stress obtained by the test, and epsilon is the real strain;

(b) according to the tensile or compressive test data of the polycarbonate at different temperatures and strain rates, the nonlinear relation between the yield stress and the temperature and strain rate is obtained and is represented by the following formula:

in the formula, σ_yIs the yield stress of the polycarbonate,is the equivalent strain rate, T, in the course of the test_hIs the temperature of the same system,

homologous temperature T_hIs represented by the following formula

K,C_r,C_tM is the relevant test parameter, where T is the test temperature, T_rIs a reference temperature, T_gIs the glass transition temperature of the polycarbonate;

(c) determining the internal damage condition of the material through a plurality of times of stretching or compressing loading and unloading tests; for discrete test data, the damage variable was found according to the following formula:

in the formula, ω is the damage variable of the polycarbonate, E₀Is the initial modulus of elasticity of the polymer,is the value of the modulus of elasticity during loading and unloading; integrating the calculated discrete damage variable data to obtain the relation between the damage and the plastic strain:

wherein ω is a damage variable of the polycarbonate,for equivalent plastic strain, C_ωAnd x is a test-related parameter;

(d) the strain softening and strain hardening data in the tensile or compressive test stress-strain curve are analyzed and the relationship between the real stress and the damage variable, the yield stress and the equivalent plastic strain are obtained by sorting as follows:

wherein σ is the true stress of the polycarbonate, ω is the damage variable, σ_yIs the yield stress of the steel, and,for equivalent plastic strain, C_hAnd gamma is the relevant parameter;

(e) and respectively carrying out fitting solution on each parameter related to a tensile test or a compression test in the unified constitutive model, writing the obtained constitutive model into finite element software for simulation calculation, comparing a stress-strain curve obtained by simulation with a real stress-strain curve of the test, and verifying the correctness of the unified constitutive model.