Rapid calibration method and system for plastic damage constitutive parameters of porous metals

Abstract

The present invention relates to a rapid calibration method for the plastic damage constitutive parameters of porous metals. The method involves subjecting a ductile metal material to multiple quasi-static loading-unloading uniaxial tensile tests, obtaining the true stress and true strain of the tested ductile metal material; obtaining the effective Young's modulus of tension of the tested ductile metal material based on the true stress and true strain; obtaining the true stress of the tested ductile metal matrix material by obtaining the effective Young's modulus of tension and the true stress of the tested ductile metal material; fitting the power hardening parameters of the tested ductile metal matrix material based on the true stress of the matrix material; and calibrating the plastic damage constitutive parameters of the porous metal based on the power hardening parameters of the tested ductile metal matrix material. The method simplifies the constitutive parameter calibration process and promotes the engineering application and promotion of ductile metal plastic damage models.

Description

Technical Field

[0001] The present invention relates to the field of structural detection, and in particular to a method and system for quickly calibrating plastic damage constitutive parameters of porous metals. Background Art

[0002] Ductile metals such as carbon steel, low-alloy steel, and austenitic stainless steel are widely used in special equipment such as cranes. Previous investigations have shown that bolt breakage, leading to machine overturning and boom and tower breakage, accounts for over 80% of crane accidents. Describing the hazardous areas and failure behaviors under extreme operating conditions, such as overload and accidents, is a theoretical foundation for safety monitoring and risk assessment of critical areas of special equipment. For metal materials with a certain degree of ductility, the nucleation, growth, and aggregation of pores induced by inclusions or secondary particles within them is the root cause of material failure. Compared to classical fracture mechanics, which is applicable only to failure analysis of cracked structures, damage mechanics, based on metal physics, material mechanics, and continuum mechanics, not only describes the properties of damaged materials but also investigates the entire process leading to the formation of macroscopic cracks. This unifies the mechanisms of material damage and crack propagation, bridging the gap between classical fracture mechanics and elastoplasticity, and providing an effective approach to unifying cracked and crack-free structures.

[0003] Early research on microscopic models focused primarily on the mechanical analysis of isolated pores in rigid matrices, without considering the coupling between micropores and the matrix material, such as the softening effect of pore growth on the material and the accelerated effect of localized matrix deformation on pore growth. To address this issue, in 1977, Gurson proposed a finite-matrix cell model containing micropores in the Journal of Engineering Materials and Technology, Issue 99. He introduced the pore volume fraction as a variable reflecting the degree of microscopic damage in the material into the von Mises yield criterion to describe the influence of microscopic micropores in the material on the macroscopic plastic behavior of the material, forming a relatively complete constitutive model.

[0004] In 1984, Tvergaard and Needleman proposed in the journal Acta Metallurgica, Issue 32, a modification of the Gurson model by introducing constitutive parameters (q1 and q2) to account for the inhomogeneous stress field around the pores and the interaction between the pores. This resulted in the now widely used Gurson-Tvergaard-Needleman (GTN) model. The damage variable in the GTN model, namely the pore volume fraction, has a clear geometric meaning and physical connotation, and its nucleation and growth processes can be mathematically described. Therefore, many researchers believe that as long as realistic material parameters can be obtained, the GTN model can effectively reproduce the damage and fracture behavior of materials during deformation.

[0005] After detailed research on the material parameters of the GTN model, a series of methods including microscopic observation, fracture analysis, composition analysis, X-ray microphotography, and finite element trial and error have been introduced to calibrate the material parameters of the GTN model. However, the cellular model is still considered to be the most effective means to study the two constitutive parameters (q1 and q2) in the GTN model.

[0006] In 2018, Bourih simulated the plastic flow behavior of materials containing diffusely distributed spherical overlapping holes in the 7th issue of the journal "Journal of Materials Research and Technology", pointing out that the number of holes in the unit volume characterization unit will affect the stress response of the cell model, thereby affecting the determination of the constitutive parameters (q1 and q2), but when the number of holes reaches 100, the further increase in the number of holes has a negligible impact on the simulation results.

[0007] In 2021, Zhang used a cellular model containing a single spherical micropore in the 44th issue of the journal "Fatigue & Fracture of Engineering Materials & Structures" to analyze the cellular mechanical response under different stress states and determined the constitutive parameters of the nuclear power plant pressure pipe material STPT410.

[0008] In 2022, Bensaada published a study in the International Journal of Mechanical Sciences, Issue 217, on the mechanical response of porous materials with porosity ranging from 0.1% to 24%. He noted that the number of pores per unit volume affects the mechanical response of the cell model, but that after the number of pores reaches 100, further increases in the number of pores have a negligible effect on the simulation results (confirming the conclusions of Bourih et al. regarding the effect of pore number on simulation results). Therefore, it is recommended to set the number of pores per unit volume to above 100 to better simulate the dispersed micropores within ductile metal materials.

[0009] In 2023, Zhang used a cellular model containing 100 diffusely distributed micropores to determine the constitutive parameters of low-alloy steel SA516 and austenitic stainless steel S30408 ​​materials in the 34th issue of the journal Materials Today Communications.

[0010] Currently, the methods for determining the constitutive parameters in the ductile metal plastic damage model (i.e., the GTN model) all use a cellular model containing single or multiple spherical micropores. In order to accurately describe the mechanical response of the material at different damage stages and different stress states, it is necessary to establish a finite element analysis model containing different porosity and different stress states. This not only requires a cumbersome finite element modeling process, but also requires a large amount of computing time and computing resources, which is not conducive to the engineering application and promotion of the ductile metal plastic damage model in the field of special equipment safety assessment. Summary of the Invention

[0011] The purpose of the present invention is to provide a method and system for quickly calibrating the plastic damage constitutive parameters of porous metals, simplify the constitutive parameter calibration process, and promote the engineering application and promotion of ductile metal plastic damage models.

[0012] In order to solve the above technical problems, the technical solution of the present invention is:

[0013] In a first aspect, a method for rapidly calibrating plastic damage constitutive parameters of porous metals is provided, comprising:

[0014] Step S100: performing multiple quasi-static loading-unloading uniaxial tensile tests on a ductile metal material as a test sample to obtain the true stress and true strain of the tested ductile metal material; and obtaining the tensile effective Young's modulus of the tested ductile metal material based on the true stress and true strain;

[0015] Step S200: Obtaining a ratio of the tensile effective Young's modulus of the tested ductile metal material to the Young's modulus of the matrix material, and obtaining a true stress of the tested ductile metal matrix material based on the ratio and the true stress of the tested ductile metal material; wherein the tested ductile metal material contains micropores, and the matrix material is the portion of the tested ductile metal material that does not contain micropores;

[0016] Step S300: fitting the power hardening parameters of the tested ductile metal matrix material based on the true stress of the matrix material;

[0017] Step S400: calibrating the plastic damage constitutive parameters of the porous metal according to the power hardening parameters of the tested ductile metal matrix material.

[0018] Furthermore, step S100 includes:

[0019] Step S110: Using a ductile metal material as a test sample, a uniaxial tensile test including N quasi-static loading-unloading cycles is performed on the sample with a gauge length L0 and a gauge section cross-sectional area S0 to obtain the true stress σ of the tested ductile metal material. T and true strain ε T ;

[0020] Step S120: Use a linear function to fit the unloading curve of the (i)th stretching cycle to obtain the tensile effective Young's modulus of the tested ductile metal material in the current (i)th stretching cycle Among them, the linear function is as follows:

[0021]

[0022] Where σ T is the true stress, ε T For true strain, is the plastic strain after complete unloading of the (i)th tensile cycle, where N ≥ i ≥ 1.

[0023] Furthermore, in step S200, the true stress σ of the tested ductile metal matrix material is M The calculation method is:

[0024]

[0025] Where σ T It is the true stress directly obtained from the uniaxial tensile test of ductile metal materials. Ductile metal materials contain micropores. is the effective Young’s modulus of the ductile metallic material under test at the (i)th tensile cycle, and E is the Young’s modulus of the matrix material.

[0026] Furthermore, in step S300, the power hardening parameters of the tested ductile metal matrix material include the strain proportional limit ε0 and the work hardening exponent n; the method for fitting the power hardening parameters is:

[0027]

[0028] Where ε0 is the strain proportionality limit, n is the work hardening exponent, and E is the Young's modulus of the matrix material.

[0029] Furthermore, in step S400, the method for calibrating the plastic damage constitutive parameters of the porous metal is:

[0030] q1=a0+a1n+a2ε0+a3ε0n

[0031] q2=b0+b1n+b2ε0+b3ε0n

[0032] Where q1 and q2 are the plastic damage constitutive parameters of porous metals; ε0 is the strain proportional limit fitted in step S300, n is the work hardening exponent fitted in step S300, and a i and b i is the fitting coefficient, where subscript i=0, 1, 2, 3.

[0033] In a second aspect, a rapid calibration system for the plastic damage constitutive parameters of porous metals is provided, comprising a memory and a processor; wherein the memory stores a computer program, and when the program is executed by the processor, the rapid calibration method for the plastic damage constitutive parameters of porous metals can be implemented.

[0034] The present invention has the following beneficial effects:

[0035] The present invention only requires uniaxial tensile testing and simple data processing to obtain the constitutive parameters of the tested ductile metal material, which simplifies the constitutive parameter calibration process, avoids the professional finite element modeling and large-scale finite element calculations required for previous parameter determination, and promotes the engineering application of ductile metal plastic damage models. BRIEF DESCRIPTION OF THE DRAWINGS

[0036] Figure 1 This is a flow chart of the calibration method of the present invention;

[0037] Figure 2 is the true stress σ of ferrite steel SA508 in this embodiment including 10 quasi-static loading-unloading cycles T -True strain ε T curve chart;

[0038] Figure 3 is the plastic strain ε of the ferrite steel SA508 in this embodiment P -Effective Young's modulus E TenRelationship diagram;

[0039] Figure 4 is the true stress σ of the ferrite steel SA508 matrix material in this embodiment M -True strain ε T curve chart.

[0040] Figure 5 is used to calibrate the fitting coefficient a in this embodiment i and b i Diagram of the finite element cell model. DETAILED DESCRIPTION

[0041] In order to make the purpose, technical solutions and advantages of the present invention more clear, the present invention is further described in detail below with reference to the accompanying drawings and specific embodiments.

[0042] Please refer to Figure 1 The present invention is a rapid calibration method for plastic damage constitutive parameters of porous metals, which includes:

[0043] Step S100: performing multiple quasi-static loading-unloading uniaxial tensile tests on a ductile metal material as a test sample to obtain the true stress and true strain of the tested ductile metal material; and obtaining the tensile effective Young's modulus of the tested ductile metal material based on the true stress and true strain;

[0044] Step S200: Obtaining a ratio of the tensile effective Young's modulus of the tested ductile metal material to the Young's modulus of the matrix material, and obtaining a true stress of the tested ductile metal matrix material based on the ratio and the true stress of the tested ductile metal material; wherein the tested ductile metal material contains micropores, and the matrix material is the portion of the tested ductile metal material that does not contain micropores;

[0045] Step S300: fitting the power hardening parameters of the tested ductile metal matrix material based on the true stress of the matrix material;

[0046] Step S400: calibrating the plastic damage constitutive parameters of the porous metal according to the power hardening parameters of the tested ductile metal matrix material.

[0047] The following is for Figure 1 Each step is described in detail.

[0048] In step S100, the effective Young's modulus of tension of the tested ductile metal material is obtained; step S100 specifically includes: step S110: using the ductile metal material as the tested sample, performing a uniaxial tensile test including N quasi-static loading-unloading on the sample with a gauge length L0 and a gauge section cross-sectional area S0 to obtain the true stress σ of the tested ductile metal material T and true strain ε T ;

[0049] Step S120: Use a linear function to fit the unloading curve of the (i)th stretching cycle to obtain the tensile effective Young's modulus of the tested ductile metal material in the current (i)th stretching cycle Among them, the linear function is as follows:

[0050]

[0051] Where σ T is the true stress, ε T For true strain, is the plastic strain after complete unloading of the (i)th tensile cycle, where N ≥ i ≥ 1.

[0052] In step S200, the true stress σ of the tested ductile metal matrix material (ie, the portion of the ductile metal material without micropores) is M The calculation method is:

[0053]

[0054] Where σ T It is the true stress directly obtained from the uniaxial tensile test of ductile metal materials. Ductile metal materials contain micropores. is the effective Young’s modulus of the ductile metallic material under test at the (i)th tensile cycle, and E is the Young’s modulus of the matrix material.

[0055] In step S300, the power hardening parameters of the tested ductile metal matrix material are fitted. The power hardening parameters of the tested ductile metal matrix material include the strain proportional limit ε0 and the work hardening exponent n. The method for fitting the power hardening parameters is:

[0056] Formula (3) is used to describe the true stress σ of the matrix material after plastic deformation M -True strain ε T Relationship, fitting power enhancement parameters ε0 and n

[0057]

[0058] Where ε0 is the strain proportionality limit, n is the work hardening exponent, and E is the Young's modulus of the matrix material.

[0059] In step S400, the metal plastic damage constitutive parameters are calibrated, which specifically includes:

[0060] Step S410: Use formula (4) and formula (5) to calibrate the metal plastic damage constitutive parameters q1 and q2:

[0061] q1=a0+a1n+a2ε0+a3ε0n (4)

[0062] q2=b0+b1n+b2ε0+b3ε0n (5)

[0063] Where q1 and q2 are the plastic damage constitutive parameters of porous metals; ε0 is the strain proportional limit fitted in step S300, n is the work hardening exponent fitted in step S300, and a i and b i (i=0,1,2,3) is the fitting coefficient.

[0064] Step S420: Use formula (6) to describe the effect of microvoids inside the ductile metal on the evolution of the yield surface:

[0065]

[0066] Where σ eq is the Von Mises equivalent stress of ductile metal materials containing micropores, σ Y is the VonMises equivalent stress of the matrix material, q1 and q2 are constitutive parameters, σ kk is the hydrostatic stress, f * is the porosity rate.

[0067] The following is a specific example of obtaining the constitutive parameters of ferritic steel SA508 using the method of the present invention.

[0068] Step S100: obtaining the tensile effective Young's modulus of the tested ferritic steel SA508;

[0069] Step S110: Perform uniaxial tensile testing on a uniaxial tensile specimen with a gauge length of 50 mm and a gauge section radius of 6 mm, including 10 quasi-static loading-unloading cycles, to obtain the following: Figure 2 The true stress σ of ferritic steel SA508 is shown T -True strain ε T ;

[0070] Step S120: Fit the unloading curve of the (i)th tensile cycle (10≥i≥1) using the linear function shown in formula (7) to obtain the effective Young's modulus of the ferritic steel SA508 in the cycle: Plastic strain ε of ferritic steel SA508 P -Effective Young's modulus E Ten Development trends such as Figure 3 As shown; the linear function is as follows:

[0071]

[0072] Where σ T is the true stress, ε T For true strain, is the plastic strain after complete unloading of the (i)th stretching cycle (10≥i≥1).

[0073] Step S200: Calculate the true stress of the tested ferrite steel SA508 matrix material and determine the true stress-true strain relationship of the tested ferrite steel SA508 matrix material; specifically, calculate the true stress σ of the ferrite steel SA508 matrix material using formula (8): M , and obtain Figure 4 The true stress σ of the ferritic steel SA508 matrix material is shown M -True strain ε T ;

[0074]

[0075] Where σ T It is the true stress (including micro-voids) directly obtained from the uniaxial tensile test of ductile metal materials. is the effective Young’s modulus of the ductile metal material under test at the (i)th tensile cycle (10≥i≥1), and E is the Young’s modulus of the ferritic steel SA508 matrix material (E=202 GPa).

[0076] Step S300: fitting the power hardening parameters of the tested ferritic steel SA508 matrix material;

[0077] Formula (9) is used to describe the true stress σ of the matrix material after plastic deformation: M -True strain ε T The power enhancement parameters ε0 = 0.00236 and n = 0.127 were obtained by fitting. The method for fitting the power enhancement parameters is:

[0078]

[0079] Where ε0 is the strain proportional limit, n is the work hardening exponent, and E is the Young's modulus of the ferritic steel SA508 matrix material (E = 202 GPa).

[0080] In step S400, the metal plastic damage constitutive parameters are calibrated, which specifically includes:

[0081] Step S410: Substitute the strain proportional limit and work hardening exponent (ε0 = 0.00236, n = 0.127) of the tested ductile metal matrix material fitted in step S300 into formula (10) and formula (11) respectively to calibrate the damage constitutive parameters of ferritic steel SA508, and obtain q1 = 1.69, q2 = 0.69.

[0082] q1=1.766-0.736n+12.767ε0-31.621ε0n (10)

[0083] q2=0.811-0.715n-13.656ε0+10.182ε0n (11)

[0084] Wherein, ε0 is the strain proportional limit, and n is the work hardening exponent. In this embodiment, ε0=0.00236, and n=0.127.

[0085] In this specific embodiment, the fitting coefficient a in formulas (10) and (11) of step S400 is i and b i The method to obtain is:

[0086] In the finite element analysis software, Figure 5 The cubic cell model shown in the figure contains 100 equally sized and diffusely distributed spherical micro-voids in a cubic cell with a side length of L = 10 mm. The total porosity of the 100 micro-voids is 5%. By setting different combinations of strain proportional limit ε0 and work hardening exponent n (ε0 = 0.1%, 0.2%, 0.4% and n = 0.05, 0.1, 0.2), the matrix material with different work hardening behaviors is simulated. The true stress σ after plastic deformation of the matrix material is M -True strain ε T The relationship is described by formula (9). Figure 5 The cell model shown is along the x-axis (denoted as p x ), y-axis (denoted as p y ), z axis (denoted as p z ) Different stress combinations are applied in three directions (p x :p y :p z =1:0:0, 1:0.5:0.5, 1:0.65:0.65, 1:0.75:0.75), and calibrate the fitting coefficient a by analyzing the stress change i and b i (i=0,1,2,3), as shown in Table 1:

[0087] Table 1 Fitting coefficient values ​​calibrated by finite element cell model

[0088] Fitting coefficients <![CDATA[a0]]> <![CDATA[a1]]> <![CDATA[a2]]> <![CDATA[a3]]> Calibration results 1.766 -0.736 12.767 -31.621 Fitting coefficients <![CDATA[b0]]> <![CDATA[b1]]> <![CDATA[b2]]> <![CDATA[b3]]> Calibration results 0.811 -0.715 -13.656 10.182

[0089] Step S420: Use formula (12) to describe the effect of microvoids inside ferritic steel SA508 on the evolution of the yield surface:

[0090]

[0091] Where σ eq is the Von Mises equivalent stress of ductile metal materials containing micropores, σ Yis the VonMises equivalent stress of the matrix material, q1 and q2 are constitutive parameters, σ kk is the hydrostatic stress, f * is the porosity rate.

[0092] The method of the present invention requires only uniaxial tensile testing and simple data processing to obtain the constitutive parameters of the tested ductile metal material. This simplifies the constitutive parameter calibration process, avoids the specialized finite element modeling and extensive finite element calculations previously required for parameter determination, and promotes the engineering application and promotion of ductile metal plastic damage models. In this embodiment, the uniaxial tensile test has a dedicated national standard, "GB / T 228.1-2010 Metallic Materials Room Temperature Tensile Test Method." The uniaxial tensile test method used in the present invention is substantially consistent with the national standard. The uniaxial tensile test of the present invention is characterized by including N quasi-static loading and unloading cycles, while the national standard uses monotonic loading.

[0093] The present invention also provides a rapid calibration system for the plastic damage constitutive parameters of porous metals, which is characterized by comprising a memory and a processor; wherein the memory stores a computer program, and when the program is executed by the processor, it can implement the above-mentioned rapid calibration method for the plastic damage constitutive parameters of porous metals.

[0094] The parts not involved in the present invention are the same as the existing technology or are implemented by using the existing technology.

[0095] The above content is a further detailed description of the present invention in conjunction with specific embodiments, and the specific implementation of the present invention should not be considered to be limited to these descriptions. For those skilled in the art of the present invention, without departing from the concept of the present invention, several simple deductions or substitutions can be made, which should be considered to fall within the scope of protection of the present invention.

Claims

1. A rapid calibration method for plastic damage constitutive parameters of porous metals, characterized by: include Step S100: performing multiple quasi-static loading-unloading uniaxial tensile tests on a ductile metal material as a test sample to obtain the true stress and true strain of the tested ductile metal material; and obtaining the tensile effective Young's modulus of the tested ductile metal material based on the true stress and true strain; Step S200: Obtaining a ratio of the tensile effective Young's modulus of the tested ductile metal material to the Young's modulus of the matrix material, and obtaining a true stress of the tested ductile metal matrix material based on the ratio and the true stress of the tested ductile metal material; wherein the tested ductile metal material contains micropores, and the matrix material is the portion of the tested ductile metal material that does not contain micropores; Step S300: fitting the power hardening parameters of the tested ductile metal matrix material based on the true stress of the matrix material; Step S400: calibrating the plastic damage constitutive parameters of the porous metal according to the power hardening parameters of the tested ductile metal matrix material; In step S200, the true stress σ of the tested ductile metal matrix material is M The calculation method is: Where σ T It is the true stress directly obtained from the uniaxial tensile test of ductile metal materials. Ductile metal materials contain micropores. is the effective Young’s modulus of the ductile metal material under test in the i-th tensile cycle, and E is the Young’s modulus of the matrix material.

2. The rapid calibration method for plastic damage constitutive parameters of porous metal according to claim 1, characterized in that: Step S100 includes: Step S110: Using a ductile metal material as a test sample, a uniaxial tensile test including N quasi-static loading-unloading cycles is performed on the sample with a gauge length L0 and a gauge section cross-sectional area S0 to obtain the true stress σ of the tested ductile metal material. T and true strain ε T ; Step S120: Use a linear function to fit the unloading curve of the i-th stretching cycle to obtain the tensile effective Young's modulus of the tested ductile metal material in the current i-th stretching cycle Among them, the linear function is as follows: Where σ T is the true stress, ε T For true strain, is the plastic strain after complete unloading of the i-th tensile cycle, where N ≥ i ≥ 1.

3. The rapid calibration method for plastic damage constitutive parameters of porous metal according to claim 1, characterized in that: In step S300, the power hardening parameters of the tested ductile metal matrix material include the strain proportional limit ε0 and the work hardening exponent n; the method for fitting the power hardening parameters is: Where ε0 is the strain proportionality limit, n is the work hardening exponent, and E is the Young's modulus of the matrix material.

4. The rapid calibration method for plastic damage constitutive parameters of porous metal according to claim 3, characterized in that: In step S400, the method for calibrating the plastic damage constitutive parameters of porous metal is: q1=a0+a1n+a2ε0+a3ε0n q2=b0+b1n+b2ε0+b3ε0n Where q1 and q2 are the plastic damage constitutive parameters of porous metals; ε0 is the strain proportional limit fitted in step S300, n is the work hardening exponent fitted in step S300, and a i and b i is the fitting coefficient, where subscript i=0, 1, 2, 3.

5. Rapid calibration system for plastic damage constitutive parameters of porous metals, characterized by: including memory and processor; Wherein, the memory stores a computer program, and when the program is executed by the processor, it can implement the rapid calibration method of the plastic damage constitutive parameters of porous metals as described in any one of claims 1 to 4.

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