A method for a shear instability criterion of heterogeneous materials

Abstract

The present invention provides a method for shear instability criterion of heterogeneous materials, which specifically includes the following steps: (1) Conduct mechanical property tests on jet materials under various dynamic conditions to obtain the JC dynamic constitutive relationship of heterogeneous materials; (2) Conduct perturbation analysis on the materials based on the JC dynamic constitutive relationship to obtain the shear instability criterion of the materials; (3) Substitute the JC dynamic constitutive parameters into the shear instability criterion to obtain the critical strain of material shear instability. The present invention has a reasonable concept, fully considers the influence of multi-phase inclusions and strain gradient effects of materials on shear instability, can be widely applied to various new heterogeneous materials, and can obtain the shear instability criterion at low cost, efficiently and accurately.

Description

Technical Field

[0001] The present invention relates to the technical field of experimental techniques for the dynamic mechanical behavior of materials, and particularly to a method for shear instability criterion of heterogeneous materials. Background Art

[0002] Shear band is a common failure mode of materials under dynamic loading. During this process, the material undergoes extremely severe deformation, and a large amount of heat generated by plastic deformation is concentrated in a narrow area with a width of only about dozens of micrometers, showing highly localized characteristics. The failure criterion of materials has always been a practical issue that has received key attention in various fields. However, the shear band phenomenon is extremely complex, covering multiple rate processes and involving force-heat coupling, which undoubtedly poses a huge challenge to the accurate judgment of material failure. For those new materials with high performance, due to the lack of corresponding shear instability criteria, their practical applications have been greatly restricted. Therefore, in-depth research and obtaining the shear instability criterion of materials are of great significance for promoting the development of new materials.

[0003] The traditional shear instability criterion was proposed by Academician Bai Yilong in 1982. At that time, the development degree of the field of material science was limited, and relevant research and practice mainly focused on relatively single material systems. Under this background, this criterion was mainly applicable to homogeneous crystalline metal materials. The internal structure of such materials is uniform, and the atomic arrangement is regular and orderly, enabling the criterion established based on its characteristics to relatively accurately describe and predict the occurrence of shear instability of materials under specific conditions. However, as time goes by, continuous breakthroughs have been made in the field of materials science. To meet the increasingly stringent requirements of modern engineering for material properties, researchers have explored an effective method to improve material properties by adding reinforcing particles to the metal matrix. In this composite material system, there are obvious differences in the physical properties and mechanical behaviors between the reinforcing particles and the metal matrix. When the material is deformed under force, due to the poor deformation coordination between the particles and the matrix, extremely serious non-uniform effects will occur. The strain states in the region around the particles and the matrix far from the particles are completely different, and the strain gap between the two is extremely large, which in turn leads to significant strain gradient characteristics in the macroscopic deformation process of the material. This complex deformation behavior makes the shear instability criterion originally constructed based on the characteristics of homogeneous materials difficult to accurately depict the shear instability phenomenon of such composite materials and has seriously failed to meet the requirements of practical engineering applications.

[0004] In current engineering practices, considering the mechanical responses of materials under complex dynamic loads, most existing materials adopt the JC dynamic constitutive form to describe their mechanical behaviors. The JC dynamic constitutive model comprehensively considers various factors such as the strain rate effect, temperature effect, and stress state of materials, and can accurately reflect the changes in the mechanical properties of materials under actual working conditions. Therefore, if in-depth research can be carried out and a shear instability criterion applicable to various materials can be successfully obtained under JC dynamic constitutive conditions, it will not only fill the key gaps in the current material property evaluation system, provide a more accurate and reliable theoretical basis for engineering design and material selection, and help improve the safety and reliability of engineering structures, but also have immeasurable great value in promoting the development of materials science towards higher performance and more complex systems.

[0005] In summary, it is necessary to further innovate the existing technologies. Summary of the Invention

[0006] In view of the technical problems existing in the above-mentioned background technology, the present invention proposes a method for obtaining a shear instability criterion for heterogeneous materials. Its concept is reasonable, fully considering the influence of non-uniform deformation (strain gradient), and can be widely applied to various materials, and can obtain the shear instability criterion at low cost, efficiently, and accurately.

[0007] To solve the above technical problems, a method for a shear instability criterion for heterogeneous materials provided by the present invention specifically includes the following steps:

[0008] (1) Conduct mechanical property tests on the material under various dynamic conditions to obtain the JC dynamic constitutive relationship of the heterogeneous material as:

[0009] ;

[0010] wherein, in the above formula is the flow stress, is the yield stress under reference conditions, B is the strain hardening coefficient, n is the strain hardening index, is the strain, C is the strain rate hardening coefficient, is the ratio of the actual strain rate to the reference strain rate, m is the thermal softening index; the dimensionless temperature , T is the actual temperature, T 0 is the reference temperature, T m is the melting temperature;

[0011] (2) Conduct perturbation analysis on the material based on the JC dynamic constitutive relationship to obtain the shear instability criterion of the material; the specific process is as follows:

[0012] (2.1)Construct the basic momentum equation and energy equation describing the deformation of the material:

[0013] ;

[0014] where, ρ is the density, is the differential operator, t is the time coordinate, β is the work - heat conversion coefficient, c is the specific heat, λ is the thermal conductivity, y is the space coordinate;

[0015] (2.2)Superpose perturbations on the uniform solution:

[0016] ;

[0017] where, are the uniform solutions of strain, flow stress and temperature respectively in sequence; are the perturbations of strain, flow stress and temperature respectively in sequence;

[0018] ;

[0019] where, are the small perturbation amounts of strain, flow stress and temperature respectively in sequence; is the natural exponential, is the perturbation growth rate, i is the imaginary unit, k is the perturbation wave number;

[0020] (2.3)Substitute into the momentum equation and energy equation in the above step (2.1) to obtain a linear equation system:

[0021] ;

[0022] (2.4)Differentiate the JC constitutive relation in the step (1):

[0023] ;

[0024] where,

[0025] ;

[0026] where, d is the differential operator, are the work - hardening, strain - rate hardening and thermal - softening exponents respectively in sequence, is the characteristic stress, is the current strain rate;

[0027] (2.5) Substitute the differential relation into step (2.3) to obtain a homogeneous system of equations:

[0028] ;

[0029] (2.6) Using the condition for non - zero solutions, i.e., the coefficient determinant equals 0, obtain the spectral equation:

[0030] ;

[0031] If there exists a solution greater than 0, it indicates that instability may exist, and obtain the shear instability criterion for the material:

[0032] ;

[0033] (3) Substitute the JC dynamic constitutive parameters in the JC dynamic constitutive relation of the heterogeneous material into the shear instability criterion to obtain the critical strain of the material's shear instability.

[0034] The method for the shear instability criterion of heterogeneous materials, wherein the specific process of step (3) is: write a calculation program according to the result of the initial criterion obtained in step (2.6), substitute the JC constitutive parameters of the material, and start from strain 0, with a step size of 0.01, and iteratively calculate the critical instability strain that satisfies the criterion.

[0035] The method for the shear instability criterion of heterogeneous materials, wherein the iterative calculation of the critical instability strain that satisfies the criterion specifically simulates the mechanical behavior of the material under specific conditions according to the JC constitutive model, and calculates the criterion value for each cycle. When the criterion meets the instability condition, stop the calculation and output the critical strain; the loop calculation process is as follows:

[0036] (3.01) Strain calculation

[0037] Divide the current loop number by 100 as the strain value for this cycle;

[0038] (3.02) Stress calculation

[0039] Calculate the current stress value according to the JC constitutive model;

[0040] (3.03) Plastic work calculation

[0041] Calculate the plastic work within the current step size;

[0042] (3.04) Temperature rise calculation

[0043] Calculate the temperature rise generated due to the conversion of plastic work according to the plastic work;

[0044] (3.05) Temperature update

[0045] Calculate the next temperature, that is, add the temperature rise to the current temperature;

[0046] (3.06) Thermal softening index calculation

[0047] Calculate the thermal softening index according to the JC constitutive model;

[0048] (3.07) Strain hardening index calculation

[0049] Calculate the strain hardening index according to the JC constitutive model;

[0050] (3.08) Criterion calculation

[0051] Calculate the criterion value based on the above calculation results;

[0052] (3.09) Instability judgment

[0053] Judge whether the current criterion value is greater than 1. If it is greater than 1, it is considered that the instability condition is satisfied and the loop is exited;

[0054] (3.10) Result output

[0055] After the loop ends, divide the current loop count by 100 and output it as the critical strain.

[0056] Adopting the above technical solution, the present invention has the following beneficial effects:

[0057] The present invention has a reasonable concept. Based on the dynamic JC constitutive model of materials, it takes into account the influence of strain gradient effects on mechanical properties, and fully considers the influence of strain hardening, strain rate hardening, and thermal softening effects on the material shear instability criterion, and can obtain the material shear instability criterion at low cost, efficiently, and accurately.

[0058] The present invention can directly convert the abstract shear instability criterion into an imageable critical instability strain in the commonly used JC constitutive form in engineering, which is convenient for direct reference in engineering. Compared with the prior art, it is more direct and convenient, and is not only applicable to inhomogeneous materials, but also can be widely used for various metal materials; at the same time, it also fully considers the internal characteristics and external loading characteristics of the materials, fills the blank of the current lack of corresponding criteria, can better predict the material failure behavior, avoid disasters to a certain extent, and save economic and labor costs; furthermore, it provides reference codes, which are more convenient to directly use for different materials under different working conditions. Description of the drawings

[0059] In order to more clearly illustrate the specific embodiments of the present invention or the technical solutions in the prior art, the following will briefly introduce the drawings required for the description of the specific embodiments or the prior art. Obviously, the drawings in the following description are some embodiments of the present invention. For those of ordinary skill in the art, without creative efforts, other drawings can also be obtained based on these drawings.

[0060] Figure 1 It is a flowchart of the method for the shear instability criterion of the present invention for heterogeneous materials. Specific embodiments

[0061] The following will clearly and completely describe the technical solutions of the present invention with reference to the drawings. Obviously, the described embodiments are some embodiments of the present invention, rather than all of them. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative efforts belong to the scope of protection of the present invention.

[0062] The following further explains the present invention in conjunction with specific embodiments.

[0063] As Figure 1 shown, a method for the shear instability criterion of heterogeneous materials provided in this embodiment specifically includes the following steps:

[0064] S100. First, obtain the basic parameters of the material: density ρ , specific heat c , work-heat conversion coefficient β ; then conduct a dynamic mechanical property test on the material to obtain the JC dynamic constitutive relationship of the heterogeneous material as:

[0065] ;

[0066] Wherein, in the above formula is the flow stress, is the yield stress under reference conditions, B is the strain hardening coefficient, n is the strain hardening index, is the strain, C is the strain rate hardening coefficient, is the actual strain rate compared to the reference strain rate, m is the thermal softening index; the dimensionless temperature , T is the actual temperature, T 0 is the reference temperature, T m is the melting temperature;

[0067] S200. Next, based on the JC dynamic constitutive relation, perform a stability analysis on the material to obtain a general instability criterion;

[0068] S210. Construct the basic momentum equation and energy equation describing the deformation of the material:

[0069] ;

[0070] where ρ is the density, is the differential operator, t is the time coordinate, β is the work - heat conversion coefficient, c is the specific heat, λ is the thermal conductivity, y is the space coordinate;

[0071] S220. Superimpose perturbations on the uniform solution:

[0072] ;

[0073] where are the uniform solutions of strain, flow stress, and temperature respectively; are the perturbations of strain, flow stress, and temperature respectively.

[0074] ;

[0075] where are the small perturbation quantities of strain, flow stress, and temperature respectively; is the natural exponential, is the perturbation growth rate, i is the imaginary unit, k is the perturbation wave number;

[0076] ;

[0077] where

[0078] ;

[0079] S230. Substitute the momentum equation and energy equation in step S210 above to obtain a linear system of equations:

[0080] ;

[0081] S240. Differentiate the JC constitutive relation in step S100 above:

[0082] ;

[0083] where

[0084] ;

[0085] where d is the differential operator, are the work hardening, strain rate hardening, and thermal softening exponents, respectively, is the characteristic stress, is the current strain rate.

[0086] S250. Obtain the homogeneous equations:

[0087] ;

[0088] S260. Use the condition of non - zero solutions, that is, the coefficient determinant equals 0, to obtain the spectral equation:

[0089] ;

[0090] If there exists a solution greater than 0, it means that instability may exist, and the initial criterion is obtained:

[0091] .

[0092] S300. Substitute the JC dynamic constitutive parameters into the instability criterion to obtain the critical strain of material shear instability. Specifically: Write a calculation program according to the result of the initial criterion obtained in the above step S260, substitute the JC constitutive parameters of the material, and start from strain 0, with a step size of 0.01, and iteratively calculate the critical instability strain that satisfies the criterion.

[0093] Among them, writing a calculation program according to the result of the initial criterion is to write a calculation program for the general instability criterion. Set the material parameters in the calculation program, and given the loading strain rate of the material, the critical instability strain can be obtained.

[0094] The above iterative calculation of the critical instability strain that satisfies the criterion is specifically to simulate the mechanical behavior of the material under specific conditions according to the JC constitutive model, and at the same time calculate the criterion value of each cycle. When the criterion meets the instability condition, stop the calculation and output the critical strain; the loop calculation process is as follows:

[0095] (3.01) Strain calculation

[0096] Take the current loop number divided by 100 as the strain value of this cycle;

[0097] (3.02)Stress calculation

[0098] Calculate the current stress value according to the JC constitutive model;

[0099] (3.03)Plastic work calculation

[0100] Calculate the plastic work within the current step size;

[0101] (3.04) Temperature rise calculation

[0102] Calculate the temperature rise due to plastic work conversion based on plastic work;

[0103] (3.05) Temperature update

[0104] Calculate the next temperature by adding the temperature rise to the current temperature;

[0105] (3.06) Calculation of thermal softening index

[0106] The thermal softening index was calculated according to the JC constitutive model;

[0107] (3.07) Calculation of strain hardening exponent

[0108] The strain hardening exponent was calculated according to the JC constitutive model;

[0109] (3.08) Criteria calculation

[0110] Calculate the criterion value according to the above calculation results;

[0111] (3.09) Instability judgment

[0112] Determine whether the current criterion value is greater than 1. If it is greater than 1, it is considered that the instability condition is met and the loop is exited;

[0113] (3.10) Result output

[0114] After the cycle is completed, the current number of cycles is divided by 100 as the critical strain output.

[0115] The reference Matlab code is as follows:

[0116] clc;

[0117] clear;

[0118] num = 200; %preset maximum number of loops

[0119] stress = zeros(1,num); % Initialize stress

[0120] T = 300*ones(1,num); % Initialize temperature

[0121] strain = zeros(1,num); % Initialize strain

[0122] pho = 11.23e3; %Material density

[0123] c = 400; % material specific heat

[0124] T0 = 300; Tm = 2473; % Reference temperature and melting point temperature

[0125] srref = 5e-4; % Reference strain rate

[0126] sr = 5e3; % Test strain rate

[0127] beta = 0.7; % Material work-heat conversion coefficient

[0128] A = 821; B = 2905; n = 0.5764; C = 0.0036; m = 0.8881; % Material JC constitutive parameters, stress unit MPa

[0129] crit = zeros(1,num); % Criterion value for each loop

[0130] for i = 1:1:num

[0131] strain(i) = i / 100; % Calculate strain

[0132] stress(i) = (A+B*strain(i)^(n))*(1+C*log(sr / srref))*(1-(T(i)-T0) / (Tm-T0))^(m)*1e6; % Calculate stress according to JC constitutive

[0133] dw = stress(i)*0.01; % Calculate plastic work within the step size

[0134] dT = beta*dw / pho / c; % Calculate the temperature rise converted by plastic work

[0135] T(i+1)=T(i) + dT; % Calculate the temperature at the next step

[0136] P = (A+B*strain(i)^(n))*(1+C*log(sr / srref))*(1-(T(i)-T0) / (Tm-T0))^(m-1) / (Tm-T0)*1e6; %

[0137] Calculate the thermal softening index

[0138] Q = (B*(n)*strain(i)^(n-1))*(1+C*log(sr / srref))*(1-(T(i)-T0) / (Tm-T0))^(m)*1e6; % Calculate the strain hardening index

[0139] crit(i) = beta*stress(i)*P / (pho*c*Q); % Calculate the criterion

[0140] if crit(i)>1; % Determine whether the criterion meets the instability condition

[0141] break % If instability is met, break out of the loop

[0142] end

[0143] end

[0144] i / 100 % Output the critical strain.

[0145] The following further explains with the new W high-entropy alloy as the material.

[0146] The density of this material is 11.23 g / cm 3 , the specific heat is 400 J / kg K, the melting point is 2373 K, and the work-heat conversion coefficient is 0.7.

[0147] JC constitutive parameters: A = 821; B = 2905; n = 0.5764; C = 0.0036; m = 0.8881.

[0148] Set the loading strain rate to 5×10 3 s -1 , and running the calculation program can obtain a critical strain of 1.38.

[0149] The concept of the present invention is reasonable. Based on the dynamic JC constitutive of the material, it takes into account the influence of the strain gradient effect on the mechanical properties, and fully considers the influence of strain hardening, strain rate hardening, and thermal softening effects on the material shear instability criterion, and can obtain the material shear instability criterion at low cost, efficiently, and accurately.

[0150] Finally, it should be noted that: the above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit it; although the present invention has been described in detail with reference to the foregoing embodiments, those of ordinary skill in the art should understand that: they can still modify the technical solutions recorded in the foregoing embodiments, or perform equivalent replacements on some or all of the technical features; and these modifications or replacements do not make the essence of the corresponding technical solutions deviate from the scope of the technical solutions of the embodiments of the present invention.

Claims

1. A method for shear instability criterion of heterogeneous materials, characterized in that, Specifically, it includes the following steps: Step 1: Conduct mechanical property tests on the material under various dynamic conditions to obtain the JC dynamic constitutive relationship of the inhomogeneous material as: ； Among them, in the above formula is the flow stress, is the yield stress under reference conditions, B is the strain hardening coefficient, n is the strain hardening exponent, is the strain, C is the strain rate hardening coefficient, is the actual strain rate over the reference strain rate, m is the thermal softening exponent; dimensionless temperature , T is the actual temperature, T 0 is the reference temperature, T m is the melting temperature; Step 2: Conduct perturbation analysis on the material based on the JC dynamic constitutive relationship to obtain the shear instability criterion of the material. The specific process is as follows: Step 2.1: Construct the basic momentum equation and energy equation describing the deformation of the material: ； Among them, ρ is the density, is the differential operator, t is the time coordinate, β is the work-heat conversion coefficient, c is the specific heat, λ is the thermal conductivity, y is the space coordinate; Step 2.2: Superimpose perturbations on the uniform solution: ； wherein, are respectively the uniform solutions of strain, flow stress, and temperature in sequence; are respectively the perturbations of strain, flow stress, and temperature in sequence; ； wherein, are respectively small disturbance quantities of strain, flow stress, and temperature in sequence; is the natural exponential, is the disturbance growth rate, i is the imaginary unit, k is the disturbance wave number; Step 2.3: Substitute the momentum equation and energy equation in Step 2.1 above to obtain a linear equation system: ； Step 2.4: Differentiate the JC constitutive relationship in Step 1: ； Where, ； where d is the differential operator, are the work hardening, strain rate hardening, and thermal softening exponents, respectively, is the characteristic stress, is the current strain rate; Step 2.5: Substitute the differential relationship into the homogeneous equation system obtained in Step 2.3: ； Step 2.6: Use the condition of non-zero solution, that is, the coefficient determinant is equal to 0, to obtain the spectral equation: ； If there exists a solution greater than 0, it indicates that instability may exist, and the shear instability criterion of the material is obtained: ； Step 3: Substitute the JC dynamic constitutive parameters in the JC dynamic constitutive relationship of the inhomogeneous material into the shear instability criterion to obtain the critical strain of material shear instability.

2. The method for shear instability criterion of heterogeneous materials according to claim 1, characterized in that, The specific process of Step 3 is as follows: Write a calculation program according to the result of the initial criterion obtained in Step 2.6, substitute the JC constitutive parameters of the material, start from 0 for the strain, and iterate with a step size of 0.01 to calculate the critical instability strain that satisfies the criterion.

3. The method for the shear instability criterion of heterogeneous materials according to claim 2, wherein The iterative calculation of the critical instability strain that satisfies the criterion is specifically to simulate the mechanical behavior of the material under specific conditions according to the JC constitutive model, and calculate the criterion value of each cycle at the same time. When the criterion meets the instability condition, stop the calculation and output the critical strain. The loop calculation process is as follows: Step 3.01: Strain calculation Take the current loop count divided by 100 as the strain value of this cycle; Step 3.02: Stress calculation Calculate the current stress value according to the JC constitutive model; Step 3.03: Plastic work calculation Calculate the plastic work within the current step size; Step 3.04: Temperature rise calculation Calculate the temperature rise generated due to the conversion of plastic work according to the plastic work; Step 3.05: Temperature update Calculate the temperature of the next step, that is, add the temperature rise to the current temperature; Step 3.06: Thermal softening index calculation Calculate the thermal softening index according to the JC constitutive model; Step 3.07: Strain hardening index calculation Calculate the strain hardening index according to the JC constitutive model; Step 3.08: Criterion calculation Calculate the criterion value according to the strain hardening index and thermal softening index obtained from the above calculations, that is ; Step 3.09: Instability judgment Judge whether the current criterion value is greater than 1. If it is greater than 1, it is considered that the instability condition is met and jump out of the loop; Step 3.10: Result output After the loop ends, take the current loop count divided by 100 as the critical strain output.

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