Phase field damage fracture model method for multiphase material
The phase field damage fracture model is constructed through the phase field method theory, and the problem of prediction of mesoscopic damage fracture of carbon fiber reinforced composite materials in the prior art is solved, and accurate simulation of cracks and expansion of multiphase materials is achieved.
Patent Information
- Application Number
- CN202510267804.6
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2025-03-07
- Publication Date
- 2025-07-11
AI Technical Summary
The prior art is difficult to accurately predict the form and path of damage and fracture of carbon fiber reinforced composites at mesoscopic scales, and there are limitations in numerical simulation methods.
The phase field method theory is adopted, and the concept of phase field parameter is introduced through crack diffusion representation, and the phase field damage fracture model is constructed, including the crack surface density function and fracture energy functional, the phase field evolution law and control equation are established, and the crack cracking and expansion simulation of multiphase materials is carried out.
It realizes efficient and accurate simulation of cracking and expansion behavior of multiphase materials, and provides an efficient numerical calculation method that can predict crack propagation paths.
Smart Images
Figure CN120297027A_ABST
Abstract
Description
Technical Field
[0001] The present invention belongs to the technical field of fracture mechanics, and relates to a fracture phase-field method for composite materials, and specifically to a phase-field damage fracture model method for multiphase materials that can predict the crack propagation path of multiphase materials. Background Art
[0002] As a multiphase material with excellent mechanical properties, carbon fiber reinforced composite materials are widely used in fields such as automobile manufacturing, aerospace, and civil construction. During the processes of processing, transportation, and use, defects will inevitably occur inside carbon fiber reinforced composite materials, and the accumulation of these defects is an important factor affecting the damage and fracture of the material at the macroscopic scale. By establishing the correspondence between the mesoscopic structure and macroscopic mechanical behavior of carbon fiber reinforced composite materials, thereby predicting the damage and fracture process of carbon fiber reinforced composite materials, this is of great significance for exploring the damage and fracture mechanism of complex carbon fiber reinforced composite materials.
[0003] In recent years, the research on the damage and fracture problems of carbon fiber reinforced composite materials has mainly been divided into two categories: experimental analysis and numerical simulation. However, it is usually difficult to accurately obtain the form and path of damage and fracture at the mesoscopic scale of the material through experimental analysis, and it has high requirements for experimental equipment, which means that there are many limitations in using experimental analysis methods to study the damage and fracture problems of carbon fiber reinforced composite materials at the mesoscopic scale. Benefiting from its characteristics of being unaffected by experimental equipment and external factors, the numerical simulation method can more conveniently study the relationship between damage and fracture at the mesoscopic scale of the material and macroscopic mechanical behavior. Among many numerical simulation methods, the phase-field method can more accurately simulate complex processes such as crack initiation and propagation, and has great advantages in simulating the damage and fracture process of materials. Therefore, establishing a phase-field damage fracture model method that can be used for multiphase materials has important engineering practical value. Summary of the Invention
[0004] The present invention provides a phase-field damage fracture model method for multiphase materials. This method is based on the phase-field method theory, introduces the concept of phase-field parameters through crack smearing representation, determines the fracture energy according to the fracture surface functional, and further constructs the phase-field evolution law and control equations, and finally establishes a phase-field damage fracture model to realize the phase-field damage fracture simulation of multiphase materials.
[0005] The technical solution of the present invention is: a phase-field damage fracture model method for multiphase materials, including the following steps:
[0006] S1: Smear the cracks of the multiphase material, and construct the functional relationship between the crack surface density function and the fracture surface;
[0007] S2: Determine the fracture energy according to the fracture surface functional, and combine with the elastic body strain energy density function to determine the total potential energy functional of the cracked multiphase material;
[0008] S3: Derive the control equation and the phase-field damage evolution equation based on the relationship between the external work and the total potential energy of the multi-phase material with cracks.
[0009] S4: Establish a phase-field damage fracture model for the multi-phase material, and simulate and predict the crack initiation and propagation behavior of the multi-phase material based on the phase-field damage fracture model of the multi-phase material.
[0010] Furthermore, in step S1, the method for the dispersion treatment of cracks is as follows:
[0011] S11: Introduce an auxiliary field variable φ to represent the topological structure of the sharp crack. When φ = 0, it represents the undamaged state of the material, and when φ = 1, it represents the completely damaged state of the material. Considering that in the numerical solution process, the step function φ will lead to non-convergent results, an exponential function is selected to approximate the non-smooth crack topology.
[0012] S12: Construct a differential equation according to the exponential function. Since the real crack field will make the crack density functional take an extreme value, use the variational method to construct the crack density functional, and further obtain the regular expression of the crack density functional.
[0013] Furthermore, when determining the total potential energy functional of the multi-phase material with cracks in step S2, it is necessary to first determine the potential energy functional of the single-phase material, and then obtain the total potential energy functional of the multi-phase material with cracks by superimposing the potential energies of different single-phase materials. The specific steps for determining the total potential energy functional of the multi-phase material with cracks are as follows:
[0014] S21: The total potential energy of the elastic body with cracks can be obtained from the elastic strain energy and the crack surface dissipation energy. First, determine the fracture energy by integrating the critical energy release rate on the crack surface according to the fracture surface functional.
[0015] S22: Assume that only the tensile load is considered for the failure of the isotropic material, and introduce a monotonically decreasing function to describe the strain energy degradation of the elastic material, so as to obtain the elastic strain energy density containing the crack field.
[0016] S23: Determine the total potential energy of the single-phase material with cracks according to the elastic strain energy obtained in S22 and the crack surface dissipation energy obtained in S21. The specific expression of the total potential energy functional of the single-phase material is as follows:
[0017]
[0018] Among them, to prevent the elastic energy dominated by the tensile load from being 0 and avoid numerical singularities when the phase-field parameter approaches 1, the parameter k ∈ (0, 1].
[0019] S24: Compared with single-phase materials, due to the differences in material phases of multi-phase materials, the differences in material properties lead to differences in the fracture energy required to form cracks. The total potential energy of multi-phase materials can be obtained by superimposing the potential energies of different single-phase materials. For the multi-phase material model with cracks, the specific expression of the total potential energy functional is as follows:
[0020]
[0021] where ψ(ε) is the elastic strain energy density function, G c is the critical energy release rate, Ω represents the entire elastic body region, Γ represents the crack surface, and the subscript numbers represent different single-phase materials.
[0022] Furthermore, in step S3, the method for determining the control equation of damage fracture and the phase field evolution equation of the multi-phase material with cracks is specifically as follows:
[0023] S31: According to the first law of thermodynamics, the work done by external forces is converted into the total potential energy Π in the elastic body. First, the variational form of the external work is given;
[0024] S32: Calculate the first-order variational equation of the total potential energy of the multi-phase material with cracks with respect to the phase field and the first-order variational equation with respect to the strain field;
[0025] S33: Substitute the total potential energy functional of the multi-phase material with cracks obtained in S24 into the variational form of the total potential energy of the multi-phase material to further obtain the variational form of the total potential energy of the multi-phase material;
[0026] S34: Determine the control equation of damage fracture and the phase field evolution equation of the multi-phase material with cracks according to the relationship between the external work and the total potential energy of the elastic body.
[0027] Furthermore, in step S4, the method for establishing the phase field damage fracture model of the multi-phase material and simulating and predicting the crack initiation and propagation behavior of the multi-phase material is specifically as follows:
[0028] S41: Discretize the multi-phase material by finite elements and establish a finite element model on the finite element simulation platform;
[0029] S42: Due to the problem of unstable crack propagation, the present invention uses the staggered algorithm to decouple and calculate the displacement field and phase field of the multi-phase material. Call the UMAT subroutine to calculate the displacement field according to the material constitutive and external loads, and then call the user element subroutine UEL to calculate the phase field according to the displacement field;
[0030] S43: Perform damage evolution on the phase field model, perform post-processing analysis, and realize the simulation and prediction of the damage fracture of the multi-phase material.
[0031] Beneficial effects: The present invention provides a phase-field damage fracture model method for multiphase materials. Based on the phase-field method theory, the concept of phase-field parameters is introduced through the representation of crack dispersion. The fracture energy is determined according to the fracture surface functional, and the phase-field evolution law and control equations are further constructed. Finally, a phase-field damage fracture model is established to simulate the phase-field damage fracture of multiphase materials. Description of the Drawings
[0032] Figure 1 Schematic diagram of the geometric model of the tensile test of two-phase materials (unit: mm).
[0033] Figure 2 Schematic diagram of the geometric model of the tensile test of three-phase materials containing 7 fibers (unit: mm).
[0034] Figure 3 Schematic diagram of the simulation results of the tensile test of two-phase materials.
[0035] Figure 4 Schematic diagram of the simulation results of the tensile test of three-phase materials containing 7 fibers. Specific Embodiments
[0036] The present invention provides a phase-field damage fracture model method for multiphase materials. The technical solutions of the present invention will be further described below with reference to the drawings, but are not limited thereto. Any modification or equivalent replacement of the technical solutions of the present invention without departing from the spirit and scope of the technical solutions of the present invention shall be covered by the protection scope of the present invention.
[0037] The present invention provides two specific examples of the above-mentioned phase-field damage fracture model method for multiphase materials. The following will specifically describe the implementation manners of the present invention according to the drawings and examples.
[0038] The implementation steps of the present invention mainly include:
[0039] S1: Disperse the cracks of the multiphase material, and construct the functional relationship between the crack surface density function and the fracture surface.
[0040] S2: Determine the fracture energy according to the fracture surface functional, and combine the elastic body strain energy density function to determine the total potential energy functional of the multiphase material with cracks.
[0041] S3: Obtain the control equation and the phase-field damage evolution equation according to the relationship between the external force work and the total potential energy of the multiphase material with cracks.
[0042] S4: Establish a phase-field damage fracture model of the multiphase material, and simulate and predict the crack initiation and propagation behavior of the multiphase material according to the phase-field damage fracture model of the multiphase material.
[0043] Specifically, in step S1, based on the phase-field method theory, the concept of the phase-field parameter is introduced through crack dispersion representation. The regularization auxiliary field variable φ is defined as the phase-field parameter of the crack, and the functional relationship between the crack surface and the phase-field parameter is constructed:
[0044]
[0045] where Γ represents the crack surface, φ represents the phase-field function, l c represents the crack length dimension parameter, and Ω represents the elastic body region.
[0046] Specifically, in step S2, considering the asymmetry of the mechanical behavior of multiphase materials under tension and compression, the elastic strain energy density is divided into two parts dominated by tensile and compressive loads. Here, it is assumed that only the tensile load on the isotropic material is considered for failure, and the monotonically decreasing function g(φ)=(1 - φ) 2 + k is used to describe the strain energy degradation of the elastic material.
[0047] Figure 1 of the two-phase material and Figure 2 The total potential energy functionals of two examples of three-phase materials can both be expressed by the strain energy and the phase-field parameter. The total potential energy functionals ∏1 and ∏2 of the two-phase material and the three-phase material can be expressed as:
[0048]
[0049] Specifically, in step S3, the total potential energy functionals of the two-phase material and the three-phase material determined in step S2 are respectively substituted into the variational form of the total potential energy of the elastic body, and the variational forms of the total potential energy of the two-phase material and the three-phase material are further obtained. According to the relationship between the external work and the total potential energy of the elastic body, the control equations for damage and fracture of the multiphase material with cracks and the phase-field evolution equation are determined, thereby establishing a damage and fracture model for the multiphase material.
[0050] Specifically, in step S4, according to Figure 1 and Figure 2 the two examples shown, a numerical model is established and the damage and fracture of the two example models are simulated and predicted. The specific implementation process is as follows:
[0051] S41: According to Figure 1 and Figure 2 the two examples shown, a finite element model is established in ABAQUS.
[0052] Figure 1 Shown is the geometric model of the two-phase material tensile test. A notch with a length of a is prefabricated on the left side, regarded as the initial crack. A uniform displacement load is applied in the vertical direction at the upper end of the model, a vertical direction constraint is applied at the lower end, and the leftmost end is fixed. Figure 1 For the two-phase material model shown, two materials with different mechanical properties are considered. The elastic moduli of the two-phase materials are respectively set to Es = 21 GPa and E h = 210 GPa; The critical energy release rates are G cs = 2.7×10 -4 kN / mm and G ch = 2.7×10 -3 kN / mm; The Poisson's ratio is 0.3. The initial crack length a = 0.1 mm, and the length dimension parameter l c = 0.005 mm. Quadrilateral elements are mainly used, and the four-node bilinear plane strain quadrilateral element (CPE4 element) and the three-node linear plane strain triangular element (CPE3 element) are used to mesh the model. Mesh refinement is carried out on the predicted crack path of the model, and the refined mesh size h = 0.0025 mm. The displacement increment Δu of the load step is 10 -5 mm.
[0053] Figure 2 The geometric model of the tensile test of the three-phase material is shown. An initial crack with a length of 7 μm is prefabricated in the middle fiber. A vertical upward tensile displacement load is applied to the upper end of the model, a vertical direction constraint is applied to the lower end, and the leftmost end is fixed. Figure 2 The three-phase material model shown considers a three-phase material composed of carbon fiber T300, epoxy resin, and the interface phase. The material parameters of carbon fiber T300 are E f = 230 GPa, the Poisson's ratio is 0.2, G cf = 1×10 -4 kN / mm; The material parameters of epoxy resin are E m = 3.2 GPa, the Poisson's ratio is 0.3, G cm = 8×10 -5 kN / mm; The material parameters of the interface phase are E g = 10 GPa, the Poisson's ratio is 0.3, G cp = 1×10 -4 kN / mm. The length dimension parameter l c = 0.7 μm. Mesh refinement is carried out on the predicted crack path of the model, and the refined mesh size h = 0.35 μm. The displacement increment Δu of the load step during the calculation is 10 -3 mm.
[0054] S42: Call the UEL subroutine in each element. By reading the displacement field of the element at the beginning of each increment step, calculate the element phase field value. Assemble the residual and the element stiffness matrix according to the calculation results. Then call the UMAT subroutine at each integration point, read the element phase field value, update the element stress and the Jacobian matrix according to the results, then update the elastic strain energy and the plastic work, and finally output the damage nephogram according to the calculation results.
[0055] S43: Calculate and output the damage nephograms of two instance models. As Figure 3 and Figure 4 shown, the model established according to the present invention can effectively simulate the damage of multi-phase materials containing cracks and effectively predict the initiation and propagation paths of cracks.
[0056] The crack propagation morphology simulated by the present invention is consistent with general test results and other simulation results. The method of the present invention applies simple boundaries and can effectively predict the crack propagation path of multi-phase materials, providing an efficient and accurate numerical calculation method for the simulation of crack propagation in multi-phase materials. The scope of the present invention is defined by the appended claims and their equivalents.
Claims
1. A phase-field damage fracture model method for multiphase materials, characterized in that: Specifically, it includes the following steps: S1: Disperse the cracks of the multiphase material, and construct the functional relationship between the crack surface density function and the fracture surface; S2: Determine the fracture energy according to the fracture surface functional, and combine with the elastic strain energy density function to determine the total potential energy functional of the cracked multiphase material; S3: Obtain the control equation and the phase field damage evolution equation according to the relationship between the external work and the total potential energy of the cracked multiphase material; S4: Establish the phase field damage fracture model of the multiphase material, and simulate and predict the crack initiation and propagation behavior of the multiphase material according to the phase field damage fracture model of the multiphase material.
2. The method for a multiphase material damage and fracture model according to claim 1, characterized in that: Step S1 is based on the phase field method theory. By introducing the concept of phase field parameters through crack dispersion representation, the damage evolution process of cracks is described using the regularized auxiliary field variable φ, and the functional relationship between the crack surface and the phase field parameters is further constructed.
3. A method for a multiphase material damage and fracture model according to claim 1, characterized in that: Step S2 is specifically as follows: S21: Considering the asymmetry of the mechanical behavior of the multiphase material under tensile and compressive loads, the elastic strain energy density is divided into two parts dominated by tensile and compressive loads for processing; S22: Assume that only the tensile load is considered for the failure of the multiphase material, and a monotonically decreasing function g(φ) = (1 - φ) 2 + k is used to describe the strain energy degradation of the multiphase material, and the value of the independent parameter k of the monotonic function is restricted to prevent the elastic properties dominated by the tensile load from being zero, and to avoid numerical singularities when the phase field parameter φ approaches 1; S23: By calculating the potential energy of the single-phase material respectively, and then further superimposing the potential energy of the single-phase material according to the combination method of the multiphase material to determine the total potential energy of the multiphase material. According to the combination of the multiphase material, different material potential energies are superimposed to determine that the total potential energy functional of the cracked multiphase material is expressed as: where ψ(ε) is the elastic strain energy density function, ε represents the strain, G c is the critical energy release rate, Ω represents the entire elastic body region, Γ represents the crack surface, the subscript numbers represent different single-phase materials, γ is the surface density function, φ represents the phase field parameter, and u represents the displacement.
4. A method for a multiphase material damage and fracture model according to claim 1, characterized in that: Step 3 is specifically as follows: S31: According to the first law of thermodynamics, the external work is converted into the internal potential energy of the elastic body, and the functional relationship between the external work of the cracked multiphase material converted into the potential energy of the elastic body is determined; S32: Calculate the first-order variational equation of the total potential energy of the cracked multiphase material with respect to the phase field and the first-order variational equation with respect to the strain field; S33: According to the variational form of the functional relationship of the cracked multiphase material and the first-order variational equation of the total potential energy with respect to the phase field and the first-order variational equation with respect to the strain field calculated in S32, substitute the total potential energy functional of the cracked multiphase material into the functional relationship determined in step S31 to construct the phase field evolution law and the control equation of the multiphase material.
5. A method for a multiphase material damage and fracture model according to claim 1, characterized in that: Step S4 is specifically as follows: S41: Use the finite element simulation platform to discretize the multiphase material model, define the multiphase material properties and apply boundary conditions; S42: Decouple and solve the phase field and displacement field of the multiphase material model through the staggered algorithm. Call the UMAT subroutine to calculate the displacement field according to the constitutive and external loads of the material, and then call the UEL subroutine to calculate the element phase field value using the element displacement field value; S43: Perform damage evolution on the phase field model, perform post-processing, and output the phase field damage nephogram.