Method for calculating strain rate effect on mechanical properties of gradient nanostructured metal

Abstract

The present application relates to the technical field of metal material impact behavior simulation, and particularly relates to a method for calculating strain rate effect of mechanical properties of gradient nanostructured metal. The method comprises the following steps: setting initial conditions of coarse-grained metal and gradient nanostructured metal; obtaining material parameters, structure information and experimental results of the coarse-grained metal and the gradient nanostructured metal; adjusting the grain of the two kinds of metal, obtaining determined parameters after adjustment, and then obtaining simulated stress-strain curves; optimizing and adjusting the determined parameters; predicting uniaxial tensile / compressive performance of the gradient nanostructured metal under different grain size gradient structures; and predicting the influence of different strain rates on the tensile / compressive elastic-plastic constitutive behavior of the material. The present application takes the elastic-plastic theory as the core and combines the material microstructure characteristics, effectively improves the accuracy of the strain rate effect simulation prediction, and successfully solves the technical pain point of large prediction deviation of the existing method.

Description

Technical Field

[0001] This invention relates to the field of impact behavior simulation technology for metallic materials, and in particular to a method for calculating the strain rate effect of the mechanical properties of gradient nanostructured metals. Background Technology

[0002] With the continuous improvement of social productivity, various industries have placed higher demands on the mechanical properties of materials, enabling humans to improve their overall performance by altering their microstructure. In 1981, Professor H. Gleiter first proposed the concept of "nanostructured materials," explaining their structural characteristics. Engineering applications not only require metallic materials to possess high strength, high toughness, and fatigue resistance, but also excellent impact resistance. Therefore, greater attention needs to be paid to the mechanical behavior of nanostructured metals under dynamic conditions.

[0003] Introducing gradient structures into the microstructure of materials allows for the improvement of one or more properties without sacrificing original characteristics, providing a promising approach to enhancing the overall performance of materials. The gradient structure of gradient nanostructured metallic materials endows them with excellent mechanical properties. In fact, the plastic deformation behavior of materials is influenced by strain rate and temperature. To better calculate and predict the dynamic deformation behavior of gradient nanostructured metals, it is crucial to establish a corresponding theoretical system to describe the comprehensive properties of these materials, thereby guiding and predicting practical applications. Summary of the Invention

[0004] The purpose of this invention is to overcome the shortcomings of the prior art and provide a method for calculating the strain rate effect of the mechanical properties of gradient nanostructured metals.

[0005] The objective of this invention is achieved through the following technical solution: a method for calculating the strain rate effect of the mechanical properties of gradient nanostructured metals, comprising the following steps: (1) Set the initial conditions for coarse-grained metals and gradient nanostructured metals; the initial conditions include: both elastic-plastic stress and strain are 0, and strain rate loading is performed at different strain rates by normalizing the dislocation density to 1; (2) Material parameters, structural information and experimental results of coarse-grained metal and gradient nanostructured metal were obtained by tensile / compression experiments and characterization, respectively; the material parameters include the size of the Burgers vector and the Taylor parameter; the structural information includes the grain size gradient distribution law of the gradient nanostructured metal and the grain size distribution law of the coarse-grained metal; the experimental results include the true stress-strain curves of uniaxial tensile / compression of the coarse-grained metal and the gradient nanostructured metal at different strain rates; (3) Based on the material parameters and structural information, the strain gradient parameters of the grains of the two metals, the non-thermal related dislocation evolution KM model, the back stress related parameters and the thermal related Klepaczko model are adjusted, and the determined parameters are obtained through the adjustment; based on the material parameters, structural information and the determined parameters, the three stages of elasticity, yielding and strengthening in the real stress-strain curves of the two metals are simulated respectively, and the simulated stress-strain curves are obtained. (4) The determined parameters are optimized and adjusted according to the degree of agreement between the simulated stress-strain curve and the real stress-strain curve, so that the simulated stress-strain curve and the real stress-strain curve are further aligned, thereby obtaining improved parameters. (5) Keep the material parameters, structural information and refined parameters unchanged; change the grain size gradient distribution law of the gradient nanostructure metal, and predict the uniaxial tensile / compressive properties of the gradient nanostructure metal under different grain size gradient structures; change the strain rate, and predict the effect of different strain rates on the uniaxial tensile / compressive properties of the gradient nanostructure metal.

[0006] Further, step (2) includes the following sub-steps: (2.1) Engineering stress-strain curves of the coarse-grained metal and the gradient nanostructured metal at different strain rates were obtained by tensile / compression experiments and characterization. (2.2) The engineering stress-strain curve is converted into a real stress-strain curve using a conversion formula.

[0007] Furthermore, step (2) further includes: fitting the grain size gradient distribution law into a function according to the grain size change with the distance from the surface, and obtaining the grain size gradient distribution function.

[0008] Furthermore, the grain size gradient distribution function is: ;in, Represents the grain size gradient distribution function, Represents the size of surface grains, Represents the surface grain size and the grain size growth rate. Represents the growth rate of grain size, This represents the depth from the surface.

[0009] Furthermore, the adjustment of the strain gradient parameter in step (3) makes the stress-strain curves of the elastic and yield stages in the simulated stress-strain curve match the stress-strain curves of the elastic and yield stages in the real stress-strain curve; the adjustment of the non-thermally related dislocation evolution KM model makes the stress-strain curve of the strengthening stage in the simulated stress-strain curve match the stress-strain curve of the strengthening stage in the real stress-strain curve; the adjustment of the back stress related parameter makes the slope of the stress-strain curve of the strengthening stage in the simulated stress-strain curve match the slope of the stress-strain curve of the strengthening stage in the real stress-strain curve even more closely; the adjustment of the thermally related Klepaczko model makes the simulated stress-strain curve match the real stress-strain curve at different strain rates.

[0010] Furthermore, the strain gradient parameter is adjusted by regulating the grain strain gradient parameter in the dislocation density of the grain boundary dislocation stacking region. The dislocation density in the grain boundary dislocation accumulation region is ;in, The thickness of the region representing the grain boundary dislocation accumulation is 3.6 nm. The geometric parameter is 1. Represents grain strain gradient parameters, represents the grain size gradient distribution function, and b represents the magnitude of the Burgers vector; Adjustment of the non-thermally dependent dislocation evolution KM model: The non-thermally dependent dislocation evolution KM model is ,in, Represents the scaling factor, Represents temperature-related parameters, and All are adjustable constants. Represents the dislocation density inside the grain. Represents plastic strain; the rate of dislocation multiplication is controlled by adjusting the scaling factor. and To adjust the annihilation rate of dislocations; The adjustment of the back stress-related parameters: The back stress-related parameters include the number of dislocations and the slip band spacing. When the slope of the strengthening stage in the simulated stress-strain curve is lower than the slope of the strengthening stage in the real stress-strain curve, the number of dislocations or the slip band spacing can be increased. The adjustment of the thermally related Klepaczko model: By adjusting the strain rate-related parameters p and q in the thermally related Klepaczko model, the simulated stress-strain curves at different strain rates are made to match the experimental data.

[0011] Furthermore, in the adjustment of the thermally related Klepaczko model, the parameter q affects the strain rate sensitivity. Increasing the value of q makes the stress response to strain rate steeper, thus improving the rate sensitivity. The parameter p determines the stress saturation characteristics. Increasing p makes the thermally activated related stress reach saturation faster, improving the rate sensitivity in the low strain rate range, but weakening the rate sensitivity in the high strain rate range. Decreasing p delays the saturation of the thermally activated related stress, allowing the rate sensitivity to maintain a strong response over a wider strain rate range.

[0012] Further, step (5) specifically includes: changing the grain size gradient distribution law of the gradient nanostructure metal specifically means changing the growth rate of the grain size, and the prediction result is that as the growth rate of the grain size increases; changing the strain rate, and the prediction result is that as the strain rate increases, the corresponding real stress under the same real strain increases significantly.

[0013] The beneficial effects of this invention are as follows: This method, based on elastoplastic theory and combined with the microstructural characteristics of materials, effectively improves the accuracy of strain rate effect simulation and prediction, successfully solving the technical pain point of large prediction deviations in existing methods, and possessing the outstanding advantages of solid theory and accurate prediction. Simultaneously, this method performs numerical calculations based on the MATLAB platform, which is simple to operate and produces stable and reliable results, significantly reducing the cost of related experiments and demonstrating its high computational efficiency and strong practicality. Furthermore, this method can also provide a solid theoretical basis for material preparation, guiding process optimization to improve the high strain rate mechanical properties of materials, thereby providing strong theoretical support and practical guidance for the engineering application of related technologies. Attached Figure Description

[0014] Figure 1 A flowchart of a method for calculating the strain rate effect of the mechanical properties of gradient nanostructured metals; Figure 2 This is a gradient distribution diagram of grain size in gradient nanostructured iron. Figure 3 To simulate the stress-strain curves of coarse-structured iron under three different compression rates; Figure 4 Simulation of stress-strain curves for gradient nanostructured iron at three different compression rates; Figure 5 This is a graph showing the change of true stress with strain rate under different gradient distribution parameters when the true strain reaches 10%. Figure 6 The image shows the stress variation of gradient nanostructured iron at real strains of 5%, 10%, and 15%, from a low strain rate of 10^-4 / s to a high strain rate of 10^4 / s. Detailed Implementation

[0015] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and not all embodiments. All other embodiments obtained by those skilled in the art based on the embodiments of this invention without inventive effort are within the scope of protection of this invention.

[0016] like Figure 1 As shown, this invention provides a method for calculating the strain rate effect of the mechanical properties of gradient nanostructured metals, comprising the following steps: (1) Set the initial conditions for coarse-grained metals and gradient nanostructured metals; the initial conditions include: both elastic-plastic stress and strain are 0, and strain rate loading is performed at different strain rates by normalizing the dislocation density to 1.

[0017] (2) Material parameters, structural information and experimental results of coarse-grained metal and gradient nanostructured metal were obtained by tensile / compression experiments and characterization, respectively. The material parameters include the size of the Burgers vector b and the Taylor parameter M. The structural information includes the grain size gradient distribution law of gradient nanostructured metal and the grain size distribution law of coarse-grained metal. The experimental results include the real stress-strain curves of uniaxial tensile / compression of coarse-grained metal and gradient nanostructured metal at different strain rates.

[0018] Further, step (2) includes the following sub-steps: (2.1) Engineering stress-strain curves of the coarse-grained metal and the gradient nanostructured metal at different strain rates were obtained by tensile / compression experiments and characterization. (2.2) The engineering stress-strain curve is converted into a real stress-strain curve using a conversion formula.

[0019] Specifically, the conversion formula is: True stress-strain curve = Engineering stress-strain curve * (1 + Engineering strain curve), True strain curve = ln(1 + Engineering strain curve).

[0020] Furthermore, step (2) further includes: fitting the grain size gradient distribution law into a function according to the grain size change with the distance from the surface, and obtaining the grain size gradient distribution function.

[0021] Furthermore, the grain size gradient distribution function is: ;in, Represents the grain size gradient distribution function, Represents the size of surface grains, Represents the surface grain size and the grain size growth rate. Represents the growth rate of grain size, This represents the depth from the surface.

[0022] like Figure 2 As shown, the grain size gradient distribution of gradient nano-Fe is used as an example; Figure 2 The data includes discrete grain size distributions measured experimentally and fitting results; the horizontal axis indicates the depth or distance extending from the material surface inward, and the vertical axis indicates the grain size, in nanometers.

[0023] (3) Based on the material parameters and structural information, the strain gradient parameters of the grains of the two metals, the non-thermal related dislocation evolution KM model, the back stress related parameters and the thermal related Klepaczko model are adjusted, and the determined parameters are obtained through the adjustment; based on the material parameters, structural information and the determined parameters, the elastic, yield and strengthening stages in the real stress-strain curves of the two metals are simulated respectively, and the simulated stress-strain curves are obtained.

[0024] Furthermore, the adjustment of the strain gradient parameter in step (3) makes the stress-strain curves of the elastic and yield stages in the simulated stress-strain curve match the stress-strain curves of the elastic and yield stages in the real stress-strain curve; the adjustment of the non-thermally related dislocation evolution KM model makes the stress-strain curve of the strengthening stage in the simulated stress-strain curve match the stress-strain curve of the strengthening stage in the real stress-strain curve; the adjustment of the back stress related parameter makes the slope of the stress-strain curve of the strengthening stage in the simulated stress-strain curve match the slope of the stress-strain curve of the strengthening stage in the real stress-strain curve even more closely; the adjustment of the thermally related Klepaczko model makes the simulated stress-strain curve match the real stress-strain curve at different strain rates.

[0025] Furthermore, the strain gradient parameter is adjusted by regulating the grain strain gradient parameter in the dislocation density of the grain boundary dislocation stacking region. The dislocation density in the grain boundary dislocation accumulation region is ;in, The thickness of the region representing the grain boundary dislocation accumulation is 3.6 nm. The geometric parameter is 1. Represents grain strain gradient parameters, represents the grain size gradient distribution function, and b represents the magnitude of the Burgers vector; Adjustment of the non-thermally dependent dislocation evolution KM model: The non-thermally dependent dislocation evolution KM model is ,in, Represents the scaling factor, Represents temperature-related parameters, and All are adjustable constants. Represents the dislocation density inside the grain. Represents plastic strain; the rate of dislocation multiplication is controlled by adjusting the scaling factor. and To adjust the annihilation rate of dislocations.

[0026] The adjustment of the back stress-related parameters: The back stress-related parameters include the number of dislocations N and the slip band spacing Lamdan. When the slope of the strengthening stage (work hardening rate) in the simulated stress-strain curve is lower than the slope of the strengthening stage in the real stress-strain curve, the number of dislocations N or the slip band spacing Lamdan can be increased.

[0027] The adjustment of the thermally related Klepaczko model: By adjusting the strain rate-related parameters p and q in the thermally related Klepaczko model, the simulated stress-strain curves at different strain rates are made to match the experimental data.

[0028] Specifically, the The range is approximately between 10 and 100. The range is approximately between 10^-5 and 10^-1, the stated The range is approximately 0.1-10, the number of dislocations N is approximately 10^2-10^4, and the slip band spacing Lamdan is approximately 10^-8-10^-7.

[0029] Furthermore, in the adjustment of the thermally related Klepaczko model, the parameter q affects the strain rate sensitivity. Increasing the value of q makes the stress response to strain rate steeper, thus improving the rate sensitivity. The parameter p determines the stress saturation characteristics. Increasing p makes the thermally activated related stress reach saturation faster, improving the rate sensitivity in the low strain rate range, but weakening the rate sensitivity in the high strain rate range. Decreasing p delays the saturation of the thermally activated related stress, allowing the rate sensitivity to maintain a strong response over a wider strain rate range.

[0030] Specifically, the parameters p and q range approximately from 10^-6 to 10^-4.

[0031] (4) The determined parameters are optimized and adjusted according to the degree of agreement between the simulated stress-strain curve and the real stress-strain curve, so that the simulated stress-strain curve and the real stress-strain curve are further aligned, thereby obtaining improved parameters.

[0032] like Figure 3As shown, the stress-strain curves of coarse-structured iron at three different compression rates are simulated as an example; the simulation results and experimental results of the stress-strain curves are included.

[0033] like Figure 4 As shown, the stress-strain curves of gradient nanostructured iron at three different compression rates are simulated as an example; the simulation results and experimental results of the stress-strain curves are included.

[0034] (5) Keep the material parameters, structural information and refined parameters unchanged; change the grain size gradient distribution law of the gradient nanostructure metal, and predict the uniaxial tensile / compression properties of the gradient nanostructure metal under different grain size gradient structures; change the strain rate, and predict the effect of different strain rates on the uniaxial tensile / compression properties (tensile / compression elastoplastic constitutive behavior) of the material.

[0035] Furthermore, step (5) specifically includes: Specifically, changing the grain size gradient distribution law of the gradient nanostructured metal involves changing the grain size growth rate, with the prediction result showing that as the grain size growth rate increases, the actual stress corresponding to the same actual strain also increases significantly with the increase of the strain rate.

[0036] As an example, the change in the grain size gradient distribution of the gradient nano-iron shows that as the grain size growth rate increases, the strain rate sensitivity remains enhanced, and its overall stress amplitude ( Figure 5 The vertical axis then decreases.

[0037] like Figure 5 The image shown represents the predicted results of the grain size gradient distribution law of the altered gradient nanostructure metal, showing the change of the actual stress with strain rate under different gradient distribution parameters when the actual strain reaches 10%.

[0038] like Figure 6 The figure shows the predicted results of changing the strain rate, representing the stress change of gradient nanostructured iron from a low strain rate of 10^-4 / s to a high strain rate of 10^4 / s under actual strains of 5%, 10%, and 15%. It includes experimentally measured data points and simulated prediction curves for this strain rate range.

[0039] Specifically, step (5) has the following effects: a. By relying on a small number of experiments to determine model parameters, the accuracy of predictions can be ensured, and experimental costs can be significantly reduced and the material performance testing cycle can be shortened. b. Quantify the performance influence of grain size gradient and strain rate to provide a calculation basis for grain size gradient structure design; c. To provide a computational path for exploring the complex situation of the coupling effect between grain size structure and strain rate loading conditions.

[0040] This invention provides a numerical calculation method for the uniaxial tensile / compressive mechanical properties of metals with grain size gradient distribution with depth under different strain rates, using Matlab software.

[0041] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A method for calculating the strain rate effect on the mechanical properties of gradient nanostructured metals, characterized in that, Includes the following steps: (1) Set the initial conditions for coarse-grained metals and gradient nanostructured metals; The initial conditions include: both elastic-plastic stress and strain are 0, and strain rate loading at different strain rates is handled by normalizing the dislocation density to 1. (2) Material parameters, structural information and experimental results of coarse-grained metal and gradient nanostructured metal were obtained by tensile / compression experiments and characterization, respectively; the material parameters include the size of the Burgers vector and the Taylor parameter; the structural information includes the grain size gradient distribution law of the gradient nanostructured metal and the grain size distribution law of the coarse-grained metal; the experimental results include the true stress-strain curves of uniaxial tensile / compression of the coarse-grained metal and the gradient nanostructured metal at different strain rates; (3) Based on the material parameters and structural information, the strain gradient parameters of the grains of the two metals, the non-thermal related dislocation evolution KM model, the back stress related parameters and the thermal related Klepaczko model are adjusted, and the determined parameters are obtained through the adjustment; based on the material parameters, structural information and the determined parameters, the three stages of elasticity, yielding and strengthening in the real stress-strain curves of the two metals are simulated respectively, and the simulated stress-strain curves are obtained. (4) The determined parameters are optimized and adjusted according to the degree of agreement between the simulated stress-strain curve and the real stress-strain curve, so that the simulated stress-strain curve and the real stress-strain curve are further aligned, thereby obtaining improved parameters. (5) Keep the material parameters, structural information and refined parameters unchanged; change the grain size gradient distribution law of the gradient nanostructure metal, and predict the uniaxial tensile / compressive properties of the gradient nanostructure metal under different grain size gradient structures; change the strain rate, and predict the effect of different strain rates on the uniaxial tensile / compressive properties of the gradient nanostructure metal.

2. The method for calculating the strain rate effect of the mechanical properties of gradient nanostructured metals according to claim 1, characterized in that, Step (2) includes the following sub-steps: (2.1) Engineering stress-strain curves of the coarse-grained metal and the gradient nanostructured metal at different strain rates were obtained by tensile / compression experiments and characterization. (2.2) The engineering stress-strain curve is converted into a real stress-strain curve using a conversion formula.

3. The method for calculating the strain rate effect of the mechanical properties of gradient nanostructured metals according to claim 1, characterized in that, Step (2) further includes: fitting the grain size gradient distribution law into a function according to the grain size change with the distance from the surface, and obtaining the grain size gradient distribution function.

4. The method for calculating the strain rate effect of the mechanical properties of gradient nanostructured metals according to claim 3, characterized in that, The grain size gradient distribution function is: ;in, Represents the grain size gradient distribution function, Represents the size of surface grains, Represents the surface grain size and the grain size growth rate. Represents the growth rate of grain size, This represents the depth from the surface.

5. The method for calculating the strain rate effect of the mechanical properties of gradient nanostructured metals according to claim 1, characterized in that, The adjustment of the strain gradient parameter in step (3) makes the stress-strain curves of the elastic and yield stages in the simulated stress-strain curve match the stress-strain curves of the elastic and yield stages in the real stress-strain curve; the adjustment of the non-thermally related dislocation evolution KM model makes the stress-strain curve of the strengthening stage in the simulated stress-strain curve match the stress-strain curve of the strengthening stage in the real stress-strain curve; the adjustment of the back stress related parameter makes the slope of the stress-strain curve of the strengthening stage in the simulated stress-strain curve match the slope of the stress-strain curve of the strengthening stage in the real stress-strain curve even more closely; the adjustment of the thermally related Klepaczko model makes the simulated stress-strain curve match the real stress-strain curve at different strain rates.

6. The method for calculating the strain rate effect of the mechanical properties of gradient nanostructured metals according to claim 5, characterized in that, The strain gradient parameter is adjusted by regulating the grain strain gradient parameter in the dislocation density of the grain boundary dislocation stacking region. The dislocation density in the grain boundary dislocation accumulation region is ;in, The thickness of the region representing the grain boundary dislocation accumulation is 3.6 nm. The geometric parameter is 1. Represents grain strain gradient parameters, represents the grain size gradient distribution function, and b represents the magnitude of the Burgers vector; Adjustment of the non-thermally dependent dislocation evolution KM model: The non-thermally dependent dislocation evolution KM model is ,in, Represents the scaling factor, Represents temperature-related parameters, and All are adjustable constants. Represents the dislocation density inside the grain. Represents plastic strain; the rate of dislocation multiplication is controlled by adjusting the scaling factor. and To adjust the annihilation rate of dislocations; The adjustment of the back stress-related parameters: The back stress-related parameters include the number of dislocations and the slip band spacing. When the slope of the strengthening stage in the simulated stress-strain curve is lower than the slope of the strengthening stage in the real stress-strain curve, the number of dislocations or the slip band spacing can be increased. The adjustment of the thermally related Klepaczko model: By adjusting the strain rate-related parameters p and q in the thermally related Klepaczko model, the simulated stress-strain curves at different strain rates are made to match the experimental data.

7. The method for calculating the strain rate effect of the mechanical properties of gradient nanostructured metals according to claim 6, characterized in that, In the adjustment of the thermally related Klepaczko model, the parameter q affects the strain rate sensitivity. Increasing the value of q makes the stress response to strain rate steeper, thus improving the rate sensitivity. The parameter p determines the stress saturation characteristics. Increasing p makes the thermally activated stress reach saturation faster, improving the rate sensitivity in the low strain rate range, but weakening the rate sensitivity in the high strain rate range. Decreasing p delays the saturation of the thermally activated stress, allowing the rate sensitivity to maintain a strong response over a wider strain rate range.

8. The method for calculating the strain rate effect of the mechanical properties of gradient nanostructured metals according to claim 1, step (5) specifically includes: Specifically, changing the grain size gradient distribution law of the gradient nanostructured metal involves changing the grain size growth rate, with the prediction result showing that as the grain size growth rate increases, the actual stress corresponding to the same actual strain also increases significantly with the increase of the strain rate.

Images