Fracture analysis device, fracture analysis method and fracture analysis program

Abstract

To provide a fracture analysis device capable of performing limit evaluation for a wide range of fracture phenomena, including shear fracture.SOLUTION: A fracture analysis device 1 for calculating a generation amount and a growth amount of voids based on a GTN model, which is a damage mechanics model, comprises a damage mechanics model calculation unit 13 having a convergence calculation unit 15 that sets a volumetric plastic strain increment Δεp to 0 under a condition where no tensile stress acts (σh≥0) and performs plastic correction calculation for nonlinear behavior using an iterative method only for a deviation component Δεq of a plastic strain increment.SELECTED DRAWING: Figure 3

Description

[Technical field]

[0001] The present invention relates to a fracture analysis device, a fracture analysis method, and a fracture analysis program. [Background technology]

[0002] In power plants where aging continues to progress, improving the accuracy of soundness assessment techniques for aging equipment is important for improving safety and extending the plant's lifespan. For example, assessments are carried out on pressure vessels in nuclear power plants that take into account aging degradation such as embrittlement due to irradiation. However, traditional assessment methods can have issues with the assessment accuracy. For this reason, fracture assessments using coupling analysis with damage mechanics models such as the Gurson-Tvergaard-Needleman (GTN) model are being considered.

[0003] The GTN model is a type of damage mechanics model that takes into account the processes of void generation, growth, and coalescence in metallic materials, and is used in fracture analysis. Examples of analysis using the GTN model include a transformation analysis method using the GTN model for deformation analysis of compressible materials (see Patent Document 1), and an inspection method in which a damage mechanics model including the GTN model can be applied to remaining life evaluation (see Patent Document 2). [Prior art documents] [Patent documents]

[0004] [Patent Document 1] JP 2020-094980 A [Patent Document 2] Patent Publication No. 2021-006801 Summary of the Invention [Problem to be solved by the invention]

[0005] It is known that in reliability assessment of actual structures, evaluation of shear-type fracture may be necessary depending on the structure and assumed loading conditions. By performing fracture analysis using damage mechanics models such as the GTN model mentioned above to evaluate the limits of actual structures, optimization of safety factors in equipment design may be considered.

[0006] On the other hand, the GTN model only considers the isotropic growth of voids, and therefore has the problem that it cannot consider the generation and growth of flattened voids. In response to this, the shear GTN model has been proposed, which takes into account the growth of flattened voids under shear conditions. h ≧0), the generation and growth of voids cannot be taken into account, making it impossible to model destruction due to shear load.

[0007] An object of the present invention is to solve the above problems and provide a fracture analysis device capable of performing limit evaluations for a wide range of fracture phenomena including shear fracture. [Means for solving the problem]

[0008] In order to solve the above problems, the fracture analysis device calculates the amount of void generation and growth based on the GTN model, which is a damage mechanics model of the present invention, and performs fracture analysis under the condition where no tensile stress acts (σ h ≧0), and the volumetric plastic strain increment Δε p is set to 0, and the deviation component of the plastic strain increment Δε q The damage mechanics model calculation unit has a convergence calculation unit that performs plastic correction calculation for nonlinear behavior using an iterative method only for the damage mechanics model. Effect of the Invention

[0009] According to the present invention, limit assessment can be performed for a wide range of fracture events including shear fracture, and therefore the present invention can contribute to the advancement of limit assessment technology for structures. [Brief description of the drawings]

[0010] [Figure 1] FIG. 2 is a diagram showing an example of mesh division of a two-dimensional model of a flat plate with a slit in a GTN model that is a damage mechanics model of the fracture analysis device of the embodiment. [Diagram 2] FIG. 13 is a diagram showing the results of FE analysis using a conventional method and the results of a flat plate tensile test using an actual device. [Diagram 3] FIG. 2 is a configuration diagram of a fracture analysis device. [Figure 4] FIG. 1 is a flow chart showing an overview of the processing steps of a destruction analysis device. [Diagram 5] This figure shows the FE analysis results of the fracture analysis device and the results of a plate tensile test using an actual device. DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0011] Hereinafter, an embodiment of the present invention will be described in detail with reference to the drawings. Fig. 1 is a diagram showing an example of mesh division of a two-dimensional model of a flat plate with a slit in the GTN model, which is a damage mechanics model of the fracture analysis device of the embodiment. In Fig. 1, Constraint indicates the constraint condition in the analysis, and Disp. indicates the displacement direction. In addition, in order to show the fracture analysis results in detail, the mesh corresponding to the fracture position is displayed in an enlarged manner.

[0012] The following describes the FE analysis (finite element analysis) performed on the tensile test of the flat plate with slits. Although details will be described later, the fracture analysis device of the embodiment performs a fracture analysis under the condition where no tensile stress acts (hydrostatic stress σ h The method is characterized by using a program or a computing device incorporating an evaluation formula that takes into account the generation and growth of flattened voids in the case where the voids are flattened (≥0).

[0013] Here, the results of the fracture analysis using the conventional method will be explained with reference to FIG. FIG. 2 shows the results of a conventional FE analysis 21 regarding the void volume function (void volume fraction) and the results of a flat plate tensile test 22 using an actual device.

[0014] In the FE analysis results 21, as the void volume function (void volume fraction) increases, the shading is expressed in lighter colors, which can be considered to be a fracture state. However, in the conventional FE analysis, the shear condition (hydrostatic stress σ h = 0), no voids are generated, so the void volume fraction at the position corresponding to the fracture position of the test piece in the flat plate tensile test results 22 does not increase, and the analysis results cannot be correlated with the fracture state of the flat plate test piece. Hereinafter, a detailed description will be given of the fracture analysis device according to the embodiment, which can evaluate a wide range of fracture phenomena including shear fracture.

[0015] FIG. 3 is a configuration diagram of the destruction analysis device 1 according to the embodiment. The fracture analysis device 1 comprises a data input unit 11, an FE analysis calculation unit 12 made up of a damage mechanics model calculation unit 13 that implements the fracture analysis method of the present invention, a data storage unit 16, and a data output unit 17.

[0016] Specifically, the destruction analysis device 1 is an information processing device equipped with a CPU (Central Processing Unit), a RAM (Random Access Memory) for temporarily storing data, a HDD / SSD / ROM (Read Only Memory) for recording programs and data, and an input section for user operations and analysis data, and a display section such as a display for displaying analysis results.

[0017] The CPU executes the programs stored in the HDD / SSD and ROM to realize the functions of the FE analysis calculation unit 12. Details will be described later.

[0018] The data input unit 11 is an input unit that reads in condition data to be calculated by the FE analysis calculation unit 12. For example, not only node and element information of the FE analysis model required for FE analysis, but also information such as parameters and commands required for calculation of constraint conditions, load conditions, material properties, etc. are input.

[0019] The data storage unit 16 is a RAM or an HDD / SSD, and stores temporary data required for executing the FE analysis, as well as the FE analysis results. The data output unit 17 is a display unit that displays the strain and stress of the FE analysis results in the form of a distribution map or the like, and outputs numerical data as text data.

[0020] The FE analysis calculation unit 12 is a model that numerically analyzes ductile fracture due to the generation and growth of voids, and has a damage mechanics model calculation unit 13 that performs calculations using the GTN model, and is configured to separately process the plastic correction calculation of plastic strain increment and the calculation of void volume fraction depending on the stress conditions.

[0021] The FE analysis calculation unit 12 and the damage mechanics model calculation unit 13 perform the following processing in a general-purpose finite element analysis software to obtain the amount of voids generated and the amount of growth. That is, in the plastic correction calculation, the condition where no tensile stress acts (hydrostatic stress σ h ≧0), the volumetric plastic strain increment Δε p is set to 0, and the deviation component of the plastic strain increment Δε q Only for the specimen, an iterative method such as the Newton-Raphson method is used to calculate plastic corrections for nonlinear behavior.

[0022] In detail, the FE analysis calculation unit 12 and the damage mechanics model calculation unit 13 calculate the absolute values ​​of the two nonlinear constitutive equations Ψ1 and Ψ2 defined by the equations (1) and (2) at an arbitrary reference value (for example, 10 -7 ) is satisfied.

[0023]

number

[0024]

number

[0025] In addition, the pore volume fraction f *is defined as the cumulative increase in the pore volume fraction defined by equation (3).

[0026]

number

[0027] The increment f due to the generation of vacancies in the above equation (3) nucl is defined by equation (4). In the conventional analysis method, the condition where no tensile stress acts (σ h ≧0), the increment f due to the generation of vacancies nucl was set to 0. In the fracture analysis device of the embodiment, the condition where no tensile stress acts (σ h ≧0), and the correction factor W defined in equation (5) (σ) is used to define the occurrence of flattened voids.

[0028] In other words, the condition where no tensile stress acts (σ h ≧0), the condition where tensile stress acts (σ h <0) due to the generation of vacancies nucl Add the correction coefficient W defined in equation (5) to the equation. (σ) The increase due to the occurrence of voids is corrected by multiplying by f nucl I asked them to do so.

[0029]

number

[0030]

number

[0031] As described above, the FE analysis calculation unit 12 and the damage mechanics model calculation unit 13 calculate the condition where no tensile stress acts (σ h ≧0) and the condition where tensile stress acts (σ h <0), iterative calculation is performed using different evaluation formulas. For this reason, the damage mechanics model calculation unit 13 of the embodiment includes a convergence calculation unit (σ h<0)14 and the convergence calculation part (σ h ≧0)15 is set.

[0032] FIG. 4 is a flow diagram showing an overview of the processing steps of the calculation program of the GTN model related to the fracture analysis device of the embodiment.

[0033] In step S1, the data input unit 11 reads initial conditions for inputting information such as nodes and element information of the FE analysis model required for the FE analysis, as well as parameters and commands required for calculations of constraint conditions, load conditions, and material properties.

[0034] In step S2, the FE analysis calculation unit 12 calculates an elastic trial stress by an elastic-plastic analysis from the strain increment calculated by the analysis solver, and calculates a hydrostatic stress σ h and the von Mises stress σ eq The initial condition calculation process is performed to calculate: In step S3, the FE analysis calculation unit 12 obtains a yield surface of the parameters of the GTN model (GTN parameters) and calculates the yield function Φ.

[0035] In step S4, the FE analysis calculation unit 12 judges whether the yield function Φ is less than 0, that is, whether the specimen is in an elastic state (not in a yielded state). If the yield function Φ is less than 0 (Yes in S4), the process proceeds to step S8, and if the yield function Φ is not less than 0 (No in S4), the process proceeds to step S5.

[0036] In step S5, the FE analysis calculation unit 12 calculates a hydrostatic stress σ h But σ h Determine whether σ is ≥ 0 or not, and h If .gtoreq.0 (Yes in S5), proceed to step S6. h If it is not ≧0 (No in S5), proceed to step S9. h is σ h ≧0 is the condition where no tensile stress acts or where hydrostatic stress is compressive, σ h The case where Eq. (1) is <0 is sometimes called the condition under which tensile stress acts or the condition under which hydrostatic stress becomes tensile.

[0037] In step S6, the damage mechanics model calculation unit 13 of the FE analysis calculation unit 12 executes the convergence calculation unit (σ h ≧0)15, so that equations (1) and (2) are satisfied, the volumetric plastic strain increment Δε p is set to 0, and the deviation component of the plastic strain increment Δε q The plastic correction for nonlinear behavior is calculated using an iterative method such as the Newton-Raphson method for only the pl The isotropic component Δε p , the volumetric plastic strain increment Δε p It is sometimes called.

[0038] In step S7, the damage mechanics model calculation unit 13 calculates (σ h ≧0), the correction coefficient W defined in formula (5) (σ) The pore volume fraction is calculated based on the formula defined using:

[0039] In step S8, the data output unit 17 outputs the FE analysis result of the pore volume fraction. An example of the FE analysis result in steps S7 and S8 will be described later with reference to FIG.

[0040] In step S9, the damage mechanics model calculation unit 13 of the FE analysis calculation unit 12 executes the convergence calculation unit (σ h <0)14, the plastic strain increment Δε pl The isotropic component Δε p and deviation component Δε q A convergence calculation is performed using an iterative method for the two variables.

[0041] In step S10, the damage mechanics model calculation unit 13 calculates (σ h <0) The pore volume fraction is calculated based on the formula, and the process proceeds to step S8.

[0042] Specifically, the FE analysis program for the GTN model consisting of steps S1 to S4, S9 to S10, and S8 is added to the process of steps S5 to S7 under the condition where no tensile stress acts (hydrostatic stress σ h ≧0) and the volumetric plastic strain increment Δε in the equivalent plastic strain increment p is set to 0, and the deviation component of the plastic strain increment Δε q The process of calculating the amount of voids generated and grown by calculating the plastic correction for nonlinear behavior using an iterative method such as the one-dimensional Newton-Raphson method for only the voids, and the process of calculating the amount of voids generated and grown by the (σ h ≧0), the correction coefficient W defined in formula (5) (σ) This is achieved by incorporating a process for calculating the pore volume fraction based on an equation defined using

[0043] This makes it possible to perform FE analysis using the improved GTN model, thereby improving the accuracy of evaluation of ductile fracture.

[0044] FIG. 5 shows FE analysis results 51 under shear conditions, which are conditions under which no tensile stress acts, using the fracture analysis device of the embodiment, and plate tensile test results 52 using an actual device.

[0045] 2, in the FE analysis result 51, as the void volume function (void volume fraction) increases, the shading is expressed in lighter colors, which can be regarded as a fracture state. The positions of lighter colors where the void volume fraction is large in the FE analysis result 51 correspond to the fracture positions of the flat test piece in the flat plate tensile test result 52 of the actual machine, so that the fracture phenomenon can be reproduced by the fracture analysis device of the embodiment.

[0046] Therefore, according to the fracture analysis device of the embodiment, it becomes possible to apply the device to pure shear, and it becomes possible to expand the range of application of fracture analysis. [Explanation of symbols]

[0047] 1. Destruction analysis equipment 11 Data Entry Section 12 FE analysis calculation section 13 Damage mechanics model calculation section 14 Convergence calculation section (σ h <0) 15 Convergence calculation section (σ h ≧0) 16 Data storage section 17 Data output section

Claims

1. A fracture analysis device that calculates the generation and growth rate of voids based on a GTN model, which is a damage mechanics model, Conditions under which no tensile stress acts (σ h ≥ 0), and the volumetric plastic strain increment Δε p is set to 0, and the deviation component of the plastic strain increment Δε q A damage mechanics model calculation unit having a convergence calculation unit that performs plastic correction calculation for nonlinear behavior using an iterative method only for the damage mechanics model calculation unit. Destruction analysis equipment.

2. 2. The destruction analysis apparatus according to claim 1, The damage mechanics model calculation unit calculates the damage mechanics model under the condition where no tensile stress acts (σ h ≧0), the condition where tensile stress acts (σ h <0) the increment f due to the generation of vacancies nucl The correction coefficient W defined in equation (1) is added to the equation. (σ) The increase due to the generation of voids is corrected by multiplying by f nucl I tried to ask for Destruction analysis equipment. [0010]

3. A fracture analysis method for calculating an amount of void generation and growth based on a GTN model, which is a damage mechanics model, comprising: The elastic trial stress is calculated by elastic-plastic analysis from the strain increment calculated by the analysis solver, and the hydrostatic stress σ h and the von Mises stress σ eq and calculating calculating a yield function Φ and determining whether the yield function Φ is less than 0; The condition where the yield function Φ is less than 0 and no tensile stress acts (σ h ≧0), two nonlinear constitutive equations Ψ １ , Ψ ２ The volumetric plastic strain increment Δε p is set to 0, and the deviation component of the plastic strain increment Δε q For only the specimen, a plastic correction calculation for nonlinear behavior is performed using an iterative method, and the condition under which tensile stress acts (σ h <0), two nonlinear constitutive equations Ψ １ , Ψ ２ The plastic strain increment Δε pl The isotropic component Δε p and deviation component Δε q and performing convergence calculation for the two variables by an iterative method. Fracture analysis methods.

4. The fracture analysis method according to claim 3, further comprising: Conditions under which no tensile stress acts (σ h ≧0), and the condition where tensile stress acts (σ h <0) the increment f due to the generation of vacancies nucl Add the correction coefficient W defined in equation (2) to the equation. (σ) The increase due to the generation of voids is corrected by multiplying by f nucl determining a Fracture analysis methods. [0025]

5. Computer Conditions under which no tensile stress acts (σ h ≥ 0), and the volumetric plastic strain increment Δε p is set to 0, and the deviation component of the plastic strain increment Δε q a damage mechanics model calculation unit having a convergence calculation unit that performs a plastic correction calculation for nonlinear behavior using an iterative method only for the damage mechanics model; This is a fracture analysis program that functions as a damage mechanics model and calculates the amount of voids that are generated and grow based on the GTN model.

6. 6. The fracture analysis program according to claim 5, The computer, Conditions under which no tensile stress acts (σ h ≧0), the condition where tensile stress acts (σ h <0) the increment f due to the generation of vacancies nucl Add the correction coefficient W defined in equation (3) to the equation. (σ) The increase due to the generation of voids is corrected by multiplying by f nucl This serves as a damage mechanics model calculation unit for calculating Fracture analysis program. [0030]

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