A full shear coupling method for predicting ductile fracture of metals

Abstract

The application discloses a complete shear coupling method for realizing prediction of metal ductile fracture, and comprises the following steps: establishing a complete theoretical model based on mesoscopic damage mechanics, determining that stress triaxiality and Lode angle are main factors influencing porous damage, determining physical meaning of shear coupling damage coefficient, determining out-of-plane restraint parameter C z which is an essential factor for controlling fracture mode switching, using FORTRAN open source general scientific calculation language to write a complete shear coupling damage program, using wide stress triaxiality tensile test to verify fracture strain distribution criterion, using scanning electron microscope fracture graph and numerical simulation crack propagation result comparison verification, etc., the application firstly defines the physical meaning of shear coupling, effectively improves the calculation precision of the cell damage model in mesoscopic mechanics in prediction of metal ductile fracture, and greatly reduces the current calculation difficulty of describing metal ductile fracture.

Description

Technical Field

[0001] This invention relates to the field of metal ductile fracture prediction technology, specifically to a fully shear-coupled damage theory and fracture prediction algorithm for realizing metal ductile fracture. Background Technology

[0002] The demand for lightweight metal components in modern industrial manufacturing and production is increasing. However, lightweight structures may experience ductile fracture under ultimate loads. Currently, there is no efficient, accurate, and physically consistent model to describe the ductile fracture phenomenon in lightweight metal structures and to reveal the mechanism of ductile fracture. Current fracture research mainly focuses on classical elastoplastic fracture mechanics, using path-independent J-integrals as parameters to describe crack driving forces. However, actual ductile fracture in metals is the result of the interaction between porous damage and the plastic behavior of the material. Therefore, fracture theory can be divided into coupled and uncoupled models. Uncoupled models ignore the influence of the damage process on the plastic constitutive model of the material, and the hardening process still follows classical plastic behavior. They describe the ductile fracture process by defining a damage factor with non-physical meaning. The advantage of uncoupled models is their simplicity; the process of ductile fracture can be predicted by calibration coefficients. However, their disadvantages include low prediction accuracy, poor applicability, and lack of theoretical support.

[0003] Currently, the most widely used uncoupled models include the Modified Mohr-Coulomb (MMC) theory and the Johnson-Cook (JC) model. Coupled models positate that damage evolution accompanies plastic development, and as irreversible damage accumulates, material properties deteriorate, eventually leading to ductile fracture. The most widely used coupled model is the Gurson model based on mesoscopic damage mechanics. However, the Gurson model is based on the theory of pore growth, specifically the process where micropores increase in volume under high stress triaxiality conditions, leading to a decrease in the yield surface. Therefore, current coupled models neglect the ductile fracture mechanism caused by low porosity due to shear forces. Summary of the Invention

[0004] The purpose of this section is to outline some aspects of the embodiments of the present invention and to briefly describe some preferred embodiments. Simplifications or omissions may be made in this section, as well as in the abstract and title of this application, to avoid obscuring the purpose of these documents; however, such simplifications or omissions should not be construed as limiting the scope of the invention.

[0005] In view of the problems existing in the above and / or existing metal ductile fracture prediction models, the present invention is proposed.

[0006] Therefore, the purpose of this invention is to provide a fully coupled model for predicting ductile fracture of metals. By combining theoretical derivation with numerical simulation and verifying and comparing with actual fracture morphology, the ability to predict ductile fracture of metals is greatly improved.

[0007] To address the aforementioned technical problems, according to one aspect of the present invention, the present invention provides the following technical solution:

[0008] S1: Based on the cylindrical characteristic unit, using displacement equilibrium boundary conditions and force equilibrium boundary conditions, and according to the macroscopic and microscopic power reciprocity theorem, the approximate yield equation of the cylindrical hole under tensile load is:

[0009] ;

[0010] in For equivalent stress, Given the current yield stress, For average stress, Given the current porosity, , , These are the material fitting constants;

[0011] S2: It is clear that under tensile and shear loads, porosity mainly originates from pore nucleation in the microscopic damage mechanism. ), Pore growth ( ) and shear connection of pores ( It consists of three parts, which can be specifically written as:

[0012] ;

[0013] The porosity nucleation term can be expressed as:

[0014] ;

[0015] In the formula The porosity coefficient is the number of pores. and These are the standard deviation and average value of the nucleation of normally distributed pores in the material. Equivalent plastic strain;

[0016] The porosity component caused by pore growth is expressed as: In the formula The sum of the diagonals of the plastic strain rate tensor. It is a Kronecker tensor;

[0017] S3: This invention patent proposes a novel shear damage coefficient with coupled physical meaning, which characterizes a new parameter based on out-of-plane restraint. Its expression is:

[0018] ;

[0019] In the formula, 1, 2, and 3 represent the three principal directions in any three-dimensional Cartesian coordinate system. For stress triaxiality. The triaxiality is divided into high-stress triaxiality state and low-stress triaxiality state based on the critical value.

[0020] S4: The porosity change caused by shearing is:

[0021] ;

[0022] In the formula The Rhodes angle parameter of the material;

[0023] S5: The fully shear-coupled model contains two ductile fracture mechanisms, when the crack tip is under high stress triaxiality ( The material undergoes high-porosity damage driven by hydrostatic stress; conversely, when the crack tip is in a shear-dominated, low-stress triaxial state ( Under the action of shear deviatoric strain, nucleated pores in the material undergo low-porosity fracture due to elongation and shear deformation. The complete shear-coupled damage failure criterion is as follows:

[0024] ;

[0025] For the first time, it was clearly pointed out that the failure of ductile fracture in metals is the result of a competitive mechanism under the influence of out-of-plane restraint.

[0026] S6: Use the Fortran scientific computing language to write the fully shear-coupled model in steps S1 to S5 into a finite element calculation program. First, calculate the equivalent test stress, then determine the current yield stress, calculate the test yield equation, update the current porosity, and finally determine whether the crack has propagated.

[0027] S7: In the fully shear-coupled model, only the initial porosity is present. and fracture strain The initial porosity was calibrated using single-sided notched tensile specimens of different geometric dimensions, and the fracture strain was calibrated using wide-stress triaxial tensile tests.

[0028] S8: By comparing the fracture surface of a single-sided notched tensile specimen with the finite element calculation results of fully shear coupled damage, it was verified that porous damage occurs when the crack tip is under high stress triaxiality, while low-porosity shear fracture occurs when the crack tip is under low stress triaxiality.

[0029] Compared with existing technologies, the beneficial effects of this invention are as follows: It proposes for the first time a fully shear-coupled damage model, clearly indicating that out-of-plane constraint is a key factor affecting ductile fracture in metals. When the crack tip is under high stress, the material undergoes porous damage dominated by hydrostatic pressure; when the crack tip is under low stress triaxiality, the material undergoes low-porosity fracture caused by shearing. A fully shear-coupled damage calculation model is written using the Fortran scientific computing language to achieve dynamic expansion of ductile fracture in metals. The accuracy of the fully shear damage model is verified through finite element fracture simulation and fracture morphology comparison. Compared with traditional uncoupled or semi-coupled fracture models, this invention significantly improves the accuracy of predicting metal fracture while scientifically revealing the competitive mechanism of ductile fracture in metals. Attached Figure Description

[0030] To more clearly illustrate the technical solutions of the embodiments of the present invention, the present invention will be described in detail below with reference to the accompanying drawings and detailed embodiments. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort. Wherein:

[0031] Figure 1 This is a schematic diagram of a cylindrical pore feature unit in a fully shear coupling method for predicting ductile fracture of metals in this invention.

[0032] Figure 2 This is a schematic diagram showing the distribution of the fully shear coupling damage coefficient in the principal stress space in a fully shear coupling method for predicting ductile fracture of metals according to the present invention.

[0033] Figure 3 This is a load-displacement diagram illustrating the load-displacement method for calibrating initial porosity using a single-sided notch tensile fracture test, which is part of the fully shear-coupled method for predicting ductile fracture in metals according to the present invention.

[0034] Figure 4 This is a schematic diagram of the calculation results of the optimal initial porosity calculated by the error algorithm in a fully shear coupling method for predicting ductile fracture of metals in this invention.

[0035] Figure 5 This is a schematic diagram of a specimen used in a wide-stress triaxial tensile fracture test to calibrate fracture strain under different stress triaxial conditions in a fully shear coupling method for predicting ductile fracture of metals according to the present invention.

[0036] Figure 6 This is a schematic diagram illustrating the calculation results of fracture strain over a wide stress triaxiality range using a fully shear-coupled method for predicting ductile fracture of metals according to the present invention.

[0037] Figure 7 This is a schematic diagram showing the comparison between the finite element calculation results written in FORTRAN language and the fracture surface of a single-sided notched tensile specimen in a fully shear coupling method for predicting ductile fracture of metals according to the present invention. Detailed Implementation

[0038] This invention provides a fully coupled model for predicting ductile fracture of metals. By combining theoretical derivation with numerical simulation and verifying and comparing with actual fracture morphology, it greatly improves the ability to predict ductile fracture of metals.

[0039] The specific steps of this fully shear-coupled algorithm for predicting ductile fracture in metals are as follows:

[0040] S1: Based on a cylindrical feature unit, as shown in the diagram. Figure 1 As shown, by using displacement equilibrium boundary conditions as shown in Equation 1 and force equilibrium boundary conditions as shown in Equation 2, the following equilibrium equations can be obtained:

[0041] ;(Formula 1)

[0042] ;(Formula 2)

[0043] in and These represent the macroscopic stress and strain components, respectively. According to the theorem of reciprocity between macroscopic and microscopic power, we can obtain Formula 3:

[0044] ;(Formula 3)

[0045] As shown Figure 1 As shown, it is assumed that the velocity field of the fully shear-coupled model satisfies Equation 4:

[0046] (Formula 4);

[0047] The cylindrical pore feature element satisfies the axisymmetric volume incompressibility condition, i.e., Equation 5:

[0048] (Formula 5);

[0049] The macroscopic strain components in the three directions also satisfy the incompressibility condition as shown in equations (6), (7), and (8):

[0050] (Formula 6);

[0051] (Formula 7);

[0052] (Formula 8);

[0053] Assuming the matrix material is an ideal steel-plastic material, the microscopic plastic strain power can be expressed as Equation 9:

[0054] (Formula 9);

[0055] In the formula This can be expressed as Formula 10:

[0056] (Formula 10);

[0057] in , , and ;

[0058] Substituting Equation 10 into the macroscopic mechanical equilibrium equation Formula 11 is obtained:

[0059] (Formula 11);

[0060] Now, square both sides of Equation 11 to eliminate the intermediate variable. Formula 12 is obtained:

[0061] (Formula 12);

[0062] Finally, the approximate yield equation for the cylindrical pore characteristic element is obtained by simplification as Equation 13:

[0063] (Formula 13);

[0064] in For equivalent stress, Given the current yield stress, For average stress, Given the current porosity, , , These are the material fitting constants;

[0065] S2: It is clear that under tensile and shear loads, porosity mainly originates from pore nucleation. ), Pore growth ( ) and shear connection of pores ( The three parts can be specifically written as Formula 14;

[0066] (Formula 14);

[0067] The porosity nucleation term can be expressed as Equation 15:

[0068] (Formula 15);

[0069] In the formula The porosity coefficient is the number of pores. and These are the standard deviation and average value of the nucleation of normally distributed pores in the material. Equivalent plastic strain;

[0070] The porosity component caused by pore growth is expressed by Formula 16:

[0071] (Formula 16);

[0072] In the formula It is the sum of the diagonals of the plastic strain rates. It is a Kronecker tensor;

[0073] S3: This invention patent proposes a novel parameter to characterize out-of-plane restraint effects. Its expression is shown in Formula 17:

[0074] (Formula 17);

[0075] In the formula, 1, 2, and 3 represent the three principal directions in any three-dimensional Cartesian coordinate system. For stress triaxiality, with The critical values ​​are divided into high-stress triaxiality state and low-stress triaxiality state. In the subsequent examples of this invention, direction 1 represents the crack propagation direction, direction 2 represents the external load application direction, and direction 3 represents the out-of-plane free necking direction.

[0076] S4: Determining that the porosity change caused by shear is the result of competition between high and low stress states, first identify the variables related to the stress state, such as stress triaxiality. ) and Rhodes angle parameters ( (as shown in Formulas 18 and 19);

[0077] (Formula 18);

[0078] (Formula 19);

[0079] In the formula It is the first invariant of the stress tensor. and These are the second and third invariants of the deviatoric stress tensor, respectively. The porosity increment caused by shearing, as expressed in classical empirical formulas, can be represented by Formula 20:

[0080] (Formula 20);

[0081] Here is the empirical correction factor, where Substituting Equations 18 and 19 into the empirical formula for shear porosity increment, we obtain Equation 21, which is a shear correction term dependent on the Rhodes angle and stress triaxiality.

[0082] (Formula 21);

[0083] Formula 17, i.e., the shear correction coefficient related to out-of-plane constraint, is used. Substituting into Equation 21, we obtain Equation 22, which has a fully coupled shear correction term:

[0084] (Formula 22);

[0085] In the formula The Rhodes angle parameter of the material;

[0086] definition The damage coefficient for complete shear coupling is shown in the diagram. Figure 2 The Monte Carlo algorithm was used to verify the distribution of the fully shear-coupled damage coefficient in the principal stress space. It was clearly shown that the fully shear-coupled damage coefficient decreases with the decrease of stress triaxiality, which is completely consistent with the porosity distribution characteristics of the experimental fracture surface.

[0087] S5: The fully shear-coupled model contains two ductile fracture mechanisms, when the crack tip is under high stress triaxiality ( The material undergoes high-porosity damage driven by hydrostatic stress; conversely, when the crack tip is in a shear-dominated, low-stress triaxial state ( Under the action of shear deviatoric strain, the nucleated pores in the material undergo low-porosity fracture, which is caused by the elongation and shear deformation of the pores. This is expressed by Equation 23:

[0088] (Formula 23);

[0089] Formula 8 explicitly states for the first time that ductile fracture failure of metals is the result of a competitive mechanism under the influence of out-of-plane restraint.

[0090] S6: Use the Fortran scientific computing language to write the fully shear-coupled model in steps S1 to S5 into a finite element calculation program. First, calculate the equivalent test stress (Equation 24), determine the current yield stress (Equation 25), calculate the test yield equation (Equation 26), calculate the current porosity (Equation 27), and determine whether crack propagation occurs (Equation 28).

[0091] (Formula 24);

[0092] The equivalent test stress in the formula can be expressed as: , It is the deviatoric stress tensor;

[0093] (Formula 25);

[0094] In the formula The tangential stiffness of the material. The yield stress;

[0095] (Formula 26);

[0096] (Formula 27);

[0097] (Formula 28);

[0098] S7: In the fully shear-coupled model, only the initial porosity is present. and fracture strain For the coefficients to be calibrated, X80 pipeline steel was used as the verification material. The initial porosity was first calibrated using six sets of single-sided notched tensile specimens with different geometric dimensions. Seven initial porosities of 0.002, 0.003, 0.004, 0.005, 0.006, 0.008, and 0.010 were set for numerical simulation. The load-crack nozzle opening displacement curve (P-CMOD) was used for calibration. The calculation results are shown in the figure. Figure 3 As shown, the initial porosity value that minimizes the overall error is calculated using Formula 29. The optimal initial porosity for X80 pipeline steel is determined to be 0.006. The calculation results are illustrated in the diagram. Figure 4 As shown;

[0099] (Formula 29);

[0100] In formula 29 The initial porosity is Time and Experiment Load values ​​under the same crack opening displacement;

[0101] As shown Figure 5 As shown, the fracture strain was determined using seven sets of tensile specimens with different geometries. As shown Figure 6 As shown, by fitting the exponential function of Formula 30, the results are obtained within the wide stress triaxial range ( The fracture criterion;

[0102] (Formula 30);

[0103] S8: As shown in the diagram Figure 7As shown, the fracture surface of the single-sided notched tensile specimen is compared with the finite element calculation results of the fully shear coupled damage, which verifies that porous damage occurs when the crack tip is under high stress triaxiality, while low-porosity shear fracture occurs when the crack tip is under low stress triaxiality.

Claims

1. A fully shear-coupled method for predicting ductile fracture in metals, characterized in that, include: S1: Based on the theorem of reciprocal power between macroscopic and microscopic levels, the approximate yield equation for the cylindrical hole characteristic element is determined as follows: ; S2: According to the micro-damage mechanism, the porosity originates from three parts, namely, pore nucleation ( ), Pore growth ( ), pore shear connection ( ); S3: Determine the shear damage coefficient with coupled physical meaning Its characterization is based on the effect of out-of-plane restraint on pore shear connectivity, and its expression is explicitly stated as: ; S4: Determine the porosity changes caused by shearing. ,in satisfy: ; S5: Determine the two ductile fracture mechanisms in the fully shear-coupled model. The damage failure criterion for fully shear-coupled model is: ; S6: Use the Fortran scientific computing language to write the damage equations from steps S1 to S5 into a finite element calculation program; S7: Determine the fracture strain under different triaxial stress states. The initial porosity in the complete shear damage model was calibrated. S8: Compare the fracture surface obtained from the single-sided notch tensile test with the finite element calculation results of the fully shear coupled damage.

2. The fully shear-coupled method for predicting ductile fracture of metals according to claim 1, characterized in that, In step S1, the specific steps for determining the approximate yield equation of the cylindrical hole feature element are as follows: the equilibrium equation is established using displacement equilibrium boundary conditions and force equilibrium boundary conditions. Then, assuming a fully shear-coupled feature element that satisfies the volume incompressibility condition under axisymmetric conditions, the approximate yield equation is determined based on the theorem of reciprocal micro and macro power.

3. The fully shear-coupled method for predicting ductile fracture of metals according to claim 1, characterized in that, In step S3, a new shear damage coefficient with fully coupled physical meaning is defined. Its physical meaning lies in the macroscopic stress ( ) / Strain state( By combining the microscopic pore shear coupling damage mechanism, it is clarified that the porosity change caused by pore shear connection is affected by out-of-plane restraint.

4. The fully shear-coupled method for predicting ductile fracture of metals according to claim 1, characterized in that, In step S5, it was determined that the fully shear-coupled model contains two ductile fracture mechanisms, when the crack tip is under high stress triaxiality ( The material undergoes high-porosity damage driven by hydrostatic stress; conversely, when the crack tip is in a shear-dominated, low-stress triaxial state ( The nucleated pores in the material undergo low-porosity fracture due to shear strain, which causes the pores to be elongated and sheared.

5. The fully shear-coupled method for predicting ductile fracture of metals according to claim 1, characterized in that, In step S6, the Fortran scientific computing language is used to compile the complete shear coupling theory into a finite element calculation program. The main steps are: first, calculate the equivalent test stress; then, determine the current yield stress; calculate the test yield equation; update the current porosity; and finally, determine whether the crack has propagated.

6. The fully shear-coupled method for predicting ductile fracture of metals according to claim 1, characterized in that, In step S7, a wide-stress triaxial tensile specimen is used to measure the fracture strain ( Calibration was performed by determining the initial porosity using a load-displacement curve. ).

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