A Simulation Method for Thermal Constitutive Damage and Failure of 3D Printed Fiber Reinforced Composites

Abstract

The present invention discloses a simulation method for the thermal constitutive damage failure of 3D printed fiber-reinforced composites, comprising the following steps: constructing a three-dimensional simulation model using the results of XCT slice scanning and performing mesh division on the three-dimensional simulation model; describing the finite deformation constitutive relationship of the meshed three-dimensional simulation model based on the work conjugate pair of the second Piola Kirchhoff stress and the Green Lagrange strain, and constructing a constitutive model for 3D printed fiber-reinforced composites; developing a damage failure model for 3D printed fiber-reinforced composites based on the maximum stress criterion; using the Kriging surrogate model to describe the influence of temperature on mechanical properties, and respectively establishing correlation equations between the elastic constants, yield stress, maximum strength of the damage failure model of 3D printed fiber-reinforced composites and temperature; under transverse tension, changing the temperature conditions for simulation. Its remarkable effect is that the simulation results are basically consistent with the experimental results, and the simulation effect is good.

Description

Technical Field

[0001] The present invention relates to the technical field of simulation calculation of 3D printed fiber-reinforced composites, and particularly to a simulation method for thermo-constitutive damage failure of 3D printed fiber-reinforced composites. Background Art

[0002] Additive manufacturing technology, or 3D printing technology, has become a powerful tool in the field of rapid prototyping and a research hotspot in this field in the past decade. Its manufacturing principle is based on data formed by computer-aided design models or tomography scans. Using metal powders or filaments as raw materials, through a computer system to control an energy source (heat sources such as electron beams, laser beams), the discrete materials spread layer by layer are scanned and solidified, so as to directly form a three-dimensional part, precisely controlling its microstructure in the material forming process, and quickly manufacturing 3D complex objects of any shape.

[0003] Continuous fiber-reinforced composites are high-strength, high-rigidity, and high-toughness composites made of continuous fibers as reinforcing materials and thermoplastic resins as the matrix through the process of melt impregnation of thermoplastic resins.

[0004] In terms of the current research status, due to the lack of experimental data and theoretical models, the prediction of the performance of 3D printed fiber-reinforced composite structures under thermo-mechanical coupling restricts the accuracy and reliability of the prediction model.

[0005] Therefore, it is necessary to propose a simulation calculation method applicable to 3D printed fiber-reinforced composites, that is, a simulation method for the constitutive damage failure model of 3D printed fiber-reinforced composites under thermo-mechanical coupling, aiming to enrich the theoretical model and improve the accuracy and reliability. Summary of the Invention

[0006] Aiming at the deficiencies of the prior art, the purpose of the present invention is to provide a simulation method for thermo-constitutive damage failure of 3D printed fiber-reinforced composites, which can overcome the limitations brought by the lack of current experimental data and theoretical models and improve the simulation accuracy and reliability.

[0007] To achieve the above object, the technical solution adopted by the present invention is as follows:

[0008] A simulation method for thermo-constitutive damage failure of 3D printed fiber-reinforced composites, characterized in that it includes the following steps:

[0009] Step 1: Construct a three-dimensional simulation model using the XCT slice scan results and perform mesh division on the three-dimensional simulation model;

[0010] Step 2: Describe the finite deformation constitutive relationship of the meshed three-dimensional simulation model based on the work conjugate pair of the second Piola Kirchhoff stress and the Green Lagrange strain, and construct the constitutive model of 3D printed fiber-reinforced composites;

[0011] Step 3: Develop a damage failure model for 3D printed fiber-reinforced composites based on the maximum stress criterion, based on the constitutive model of 3D printed fiber-reinforced composites;

[0012] Step 4: Use the Kriging surrogate model to describe the influence of temperature on mechanical properties, and establish the correlation equations between the elastic constants, yield stress, and maximum strength of the damage failure model of 3D printed fiber-reinforced composites and temperature respectively;

[0013] Step 5: Under transverse tension, change the temperature conditions for simulation.

[0014] Further, the specific steps for constructing the three-dimensional simulation model using the XCT slice scan results in Step 1 are as follows:

[0015] Extract the contour features of the specimen without pores according to the RGB values of the XCT slice images;

[0016] According to the form of the contour features and the pore content of the specimen obtained by XCT analysis, convert the contour features into an actual three-dimensional model.

[0017] Further, when meshing the three-dimensional simulation model in Step 1, a mixed division method of quadrilaterals and triangles is used for the surface meshing in the radial direction of the specimen, and the volume mesh of the specimen is created by stretching the surface mesh.

[0018] Further, when constructing the constitutive model of 3D printed fiber-reinforced composites by describing the finite deformation constitutive relationship of the meshed three-dimensional simulation model based on the work conjugate pair of the second Piola Kirchhoff stress and the Green Lagrange strain in Step 2, the Liu-Huang-Stout yield criterion is used to describe the anisotropic yield surface of 3D printed fiber-reinforced composites, and the associated flow criterion is used to describe the nonlinear evolution of 3D printed fiber-reinforced composites.

[0019] Further, the expression for describing the anisotropic yield surface of 3D printed fiber-reinforced composites using the Liu-Huang-Stout yield criterion is:

[0020]

[0021] Among them, F, G, H, L, M, N, I, J, K are the anisotropic parameters of the 3D printed fiber-reinforced composite filaments under different temperature conditions, σ 11 、σ22 , σ 33 are the normal stress components in all directions, and

[0022]

[0023]

[0024] where is the strain tensor rate of change; is the rate of change of the plastic hardening coefficient of the 3D printed fiber-reinforced composite material.

[0025] Furthermore, when developing the damage failure model of the 3D printed fiber-reinforced composite material based on the maximum stress criterion in step 3, the axial failure model acts on the overall area, and the transverse failure model and the shear failure model are only applied to the bonding area between the filaments.

[0026] Furthermore, the mathematical expression of the damage failure model of the 3D printed fiber-reinforced composite material is:

[0027]

[0028] where σ f1t,T , σ f1c,T are respectively the maximum strengths of the 3D printed fiber-reinforced composite material filaments under axial tension and compression at temperature T; σ f2t,T , σ f2c,T are respectively the maximum strengths of the 3D printed fiber-reinforced composite material filaments under transverse tension and compression at temperature T; is the maximum in-plane shear strength of the 3D printed fiber-reinforced composite material filaments at temperature T.

[0029] Furthermore, the correlation equation between the elastic constants and temperature of the damage failure model of the 3D printed fiber-reinforced composite material in step 4 is:

[0030]

[0031] where E 11 is the elastic modulus in the 1 direction, E 22 is the elastic modulus in the 2 direction, G 12 is the shear modulus in the 12 plane, and T is the temperature;

[0032] The correlation equation between the yield stress and temperature of the damage failure model of the 3D printed fiber-reinforced composite material is:

[0033]

[0034] where σ 1t,T , σ1c，T are the yield stresses of the 3D printed fiber-reinforced composite wire under axial tension and compression at temperature T; σ 2t,T 、σ 2c，T are the yield stresses of the 3D printed fiber-reinforced composite wire in the transverse direction under tension and compression at temperature T; is the in-plane shear yield stress of the 3D printed fiber-reinforced composite wire at temperature T; The correlation equation between the maximum strength of the 3D printed fiber-reinforced composite damage failure model and temperature is:

[0035]

[0036] where, σ f1t,T 、σ f1c，t are the maximum strengths of the 3D printed fiber-reinforced composite wire under axial tension and compression at temperature T; σ f2t,T 、σ f2c，T are the maximum strengths of the 3D printed fiber-reinforced composite wire in the transverse direction under tension and compression at temperature T; is the in-plane shear maximum strength of the 3D printed fiber-reinforced composite wire at temperature T.

[0037] Furthermore, the temperature change range of the temperature condition described in step 5 is 23°C to 230°C.

[0038] The remarkable effect of the present invention is:

[0039] The present invention combines the finite element model of 3D printed fiber-reinforced composites, the constitutive and damage models of 3D printed fiber-reinforced composite wires, and considers the temperature effect and anisotropy influence, conducts simulation calculations on the 3D printed fiber-reinforced composite structure, and obtains effective simulation prediction results and experimental data that conform to the actual situation. BRIEF DESCRIPTION OF THE DRAWINGS

[0040] Figure 1 is the flowchart of the method of the present invention;

[0041] Figure 2 is the process of specimen feature extraction and three-dimensional model conversion of the present invention;

[0042] Figure 3 is the mesh division method of the present invention;

[0043] Figure 4 is the schematic diagram of the model of the present invention;

[0044] Figure 5 is the schematic diagram of the result of the change of material parameters with temperature in the present invention;

[0045] Figure 6 is the simulation result diagram of the present invention under transverse (90 degrees) tension at different temperatures. Specific Embodiments

[0046] The specific embodiments and working principles of the present invention will be further described in detail below with reference to the accompanying drawings.

[0047] As Figure 1 shown, an embodiment of the present invention provides a simulation method for the thermal constitutive damage failure of 3D printed fiber-reinforced composites, and the specific steps are as follows:

[0048] Step 1: Construct a three-dimensional simulation model using the XCT slice scan results and perform mesh division on the three-dimensional simulation model;

[0049] In this example, the specific steps for constructing a three-dimensional simulation model using the XCT slice scan results are as follows:

[0050] Process the XCT slice images through the computer vision library in Python software, and extract the contour features in the specimen that do not contain pores according to the RGB values of the XCT slice images;

[0051] According to the form of the contour features and the pore content of the specimen obtained by XCT analysis, convert the contour features into an actual three-dimensional model through SOLIDWORKS software. To ensure the accuracy and feasibility of the simulation calculation, replace the contour features with regular filament features, characterize both sides of the filament with elliptical features, and characterize the middle part with quadrilaterals. The schematic diagram of the specimen feature extraction and three-dimensional model conversion process is as Figure 2 .

[0052] In this example, the specific steps for performing mesh division on the three-dimensional simulation model are as follows:

[0053] In this embodiment, considering that the features in some areas are small, a mixed division method of quadrilaterals and triangles is used for the surface mesh division in the radial direction of the specimen, and the volume mesh is created by stretching the surface mesh, as Figure 3 shown. The loading methods for the simulation calculations of all different loading types adopt displacement loading, and the calculation method is explicit calculation. The six end faces of the specimen are as Figure 4As shown in the figure, the right end face of the three-dimensional simulation model is set1, and the left end face is set2; the upper end face of the model is set3, and the lower end face is set4; the front end face of the model is set5, and the rear end face is set6. The boundary conditions for axial tension and compression are as follows. The x-direction of the set1 face is used as the direction of tension or compression, and the displacement distance is set to 0.1mm / -0.1mm. The set2 face is subjected to a constraint condition in the x-direction. The boundary conditions for transverse tension or compression are as follows. The y-direction of the set3 face is used as the direction of tension or compression, and the displacement distance is set to 0.1mm for tension and -0.5mm for compression. The set4 face is subjected to a constraint condition in the y-direction. The boundary conditions for shear are as follows. The action surface for shear loading is set1, and the direction is the y-direction. The displacement distance is set to 0.1mm. The set2 face, the set3 face, and the set4 face are all subjected to a constraint condition in the y-direction. The set6 end face is subjected to a constraint condition in the z-direction and remains stationary.

[0054] Step 2: Describe the finite deformation constitutive relationship of the meshed three-dimensional simulation model based on the work conjugate pair of the second Piola Kirchhoff stress and the Green Lagrange strain, and construct a 3D printed fiber-reinforced composite constitutive model.

[0055] Among them, the Green-Lagrange strain tensor E is calculated from the deformation gradient F, and the calculation formula is as follows:

[0056]

[0057] Among them, I is the unit tensor. The deformation gradient F considers thermal expansion deformation, elastic deformation, and plastic deformation. The thermal expansion deformation considers the anisotropy of 3D printed fibers, and the calculation method of the thermal eigenstrain α is as follows:

[0058]

[0059] When there is no influence of temperature change in the numerical simulation analysis process, the influence of thermal expansion deformation can be ignored. Therefore, the calculation formula for the second Piola-Kirchhoff stress S is as follows:

[0060] S = C T (E - α - E p )

[0061] Among them, C T is the elastic matrix at temperature T, and E p is the thermoplastic deformation.

[0062] Due to the significant anisotropy of 3D printed fiber-reinforced composites under different temperature conditions during axial tensile compression and transverse tensile compression loading, the Liu-Huang-Stout yield criterion is adopted to describe the anisotropic yield surface of 3D printed fiber-reinforced composites, and the calculation formula is as follows:

[0063]

[0064] where F, G, H, L, M, N, I, J, and K are the anisotropic parameters of the 3D printed fiber-reinforced composite filaments under different temperature conditions, and σ 11 , σ 22 , σ 33 are the normal stress components in each direction, and is the shear stress component in each direction.

[0065] Considering that the 3D printed fiber-reinforced composite filaments are transversely isotropic, the calculation formulas for the anisotropic parameters are as follows respectively:

[0066]

[0067]

[0068] where σ 1t,T , σ 1c,T are the yield stresses of the 3D printed fiber-reinforced composite filaments under axial tension and compression at temperature T respectively; σ 2t,T , σ 2c，T are the yield stresses of the 3D printed fiber-reinforced composite filaments under transverse tension and compression at temperature T respectively; is the in-plane shear yield stress of the 3D printed fiber-reinforced composite filaments at temperature T; is the out-of-plane shear yield stress of the 3D printed fiber-reinforced composite filaments at temperature T.

[0069] The expression for describing the non-linear evolution of 3D printed fiber-reinforced composites using the associated flow criterion is:

[0070]

[0071] where is the strain tensor rate of change; is the rate of change of the plastic hardening coefficient of the 3D printed fiber-reinforced composite. The hardening coefficient is calculated by Newton-Raphson iteration.

[0072] Step 3: Based on the constitutive model of 3D printed fiber-reinforced composites, develop a damage failure model of 3D printed fiber-reinforced composites on the basis of the maximum stress criterion, where the axial failure model acts on the overall area, and the transverse failure model and shear failure model are only applied to the bonding area between filaments;

[0073] The mathematical expression of the 3D printing fiber-reinforced composite damage failure model is as follows:

[0074]

[0075] where σ f1t,T and σ f1c,T are respectively the maximum strengths of the 3D printing fiber-reinforced composite filaments under axial tension and compression at temperature T; σ f2t,T and σ f2c，T are respectively the maximum strengths of the 3D printing fiber-reinforced composite filaments under transverse tension and compression at temperature T; is the maximum in-plane shear strength of the 3D printing fiber-reinforced composite filaments at temperature T.

[0076] Step 4: Use the Kriging surrogate model to describe the influence of temperature on mechanical properties, and establish the correlation equations between the elastic constants, yield stress, and maximum strength of the 3D printing fiber-reinforced composite damage failure model and temperature;

[0077] In this example, the correlation equation between the elastic constants of the 3D printing fiber-reinforced composite damage failure model and temperature is:

[0078]

[0079] where E 11 is the elastic modulus in the 1 direction, E 22 is the elastic modulus in the 2 direction, G 12 is the shear modulus in the 12 plane, and T is the temperature;

[0080] In this example, the correlation equation between the yield stress of the 3D printing fiber-reinforced composite damage failure model and temperature is:

[0081]

[0082] where σ 1t,T and σ 1c，T are respectively the yield stresses of the 3D printing fiber-reinforced composite filaments under axial tension and compression at temperature T; σ 2t,T and σ 2c，T are respectively the yield stresses of the 3D printing fiber-reinforced composite filaments under transverse tension and compression at temperature T; is the in-plane shear yield stress of the 3D printing fiber-reinforced composite filaments at temperature T;

[0083] In this example, the correlation equation between the maximum strength of the 3D printing fiber-reinforced composite damage failure model and temperature is:

[0084]

[0085] Among them, σ f1t,T and σ f1c，T are respectively the maximum strengths of the 3D printed fiber-reinforced composite wire under axial tension and compression at temperature T; σ f2t,T and σ f2c，T are respectively the maximum strengths of the 3D printed fiber-reinforced composite wire in the transverse direction under tension and compression at temperature T; is the maximum in-plane shear strength of the 3D printed fiber-reinforced composite wire at temperature T.

[0086] After experiments, the results of the material parameters varying with temperature are as shown in Figure 5 .

[0087] Step 5: Under transverse (90-degree) tension, perform simulations at temperature conditions of 23°C, 80°C, 130°C, 180°C, and 230°C respectively. The simulation results are as shown in Figure 6 .

[0088] In summary, the embodiments of the present invention combine the finite element model of the 3D printed fiber-reinforced composite, the wire constitutive and damage models, and consider the temperature effect and anisotropy influence, perform simulation calculations on the 3D printed fiber-reinforced composite structure, and obtain effective simulation prediction results and experimental data that conform to the actual situation.

[0089] The above only describes the preferred embodiments of the present invention in detail and is not intended to limit the present invention. Any modifications, equivalent replacements, and improvements made within the spirit and principle of the present invention shall be included within the protection scope of the present invention.

[0090] It should be understood that although the steps in the flowchart of the embodiments of the present invention are shown in sequence according to the arrows, these steps do not necessarily need to be executed in the order indicated by the arrows. Unless there is a clear indication in this article, the execution of these steps has no strict order limit, and these steps can be executed in other orders. Moreover, at least a part of the steps in each embodiment may include multiple sub-steps or multiple stages. These sub-steps or stages do not necessarily need to be executed at the same time, but can be executed at different times. The execution order of these sub-steps or stages does not necessarily need to be sequential, but can be executed alternately or in turn with at least a part of other steps or sub-steps or stages of other steps.

[0091] Other embodiments of the present disclosure will be readily apparent to those skilled in the art after considering the disclosure in the specification and the embodiments. This application is intended to cover any variations, uses, or adaptations of the present disclosure that follow the general principles of the present disclosure and include known common general knowledge or conventional technical means in the technical field not disclosed in the present disclosure. The specification and the embodiments are only regarded as exemplary, and the true scope and spirit of the present disclosure are pointed out by the claims.

Claims

1. A simulation method for thermo-constitutive damage failure of 3D printed fiber-reinforced composites, characterized in that, It includes the following steps: Step 1: Construct a three-dimensional simulation model using the XCT slice scan results and perform mesh division on the three-dimensional simulation model; Step 2: Based on the work conjugate pair of the second Piola Kirchhoff stress and the Green Lagrange strain, describe the finite deformation constitutive relationship of the meshed three-dimensional simulation model, and construct a constitutive model for 3D printed fiber-reinforced composites; Step 3: Based on the constitutive model of 3D printed fiber-reinforced composites, develop a damage failure model for 3D printed fiber-reinforced composites based on the maximum stress criterion; Step 4: Use the Kriging surrogate model to describe the influence of temperature on mechanical properties, and establish the correlation equations between the elastic constants, yield stress, and maximum strength of the damage failure model of 3D printed fiber-reinforced composites and temperature respectively; Step 5: Under transverse tension, change the temperature conditions for simulation; When constructing the constitutive model of 3D printed fiber-reinforced composites based on the work conjugate pair of the second Piola Kirchhoff stress and the Green Lagrange strain to describe the finite deformation constitutive relationship of the meshed three-dimensional simulation model in Step 2, the Liu-Huang-Stout yield criterion is used to describe the anisotropic yield surface of 3D printed fiber-reinforced composites, and the associated flow criterion is used to describe the non-linear evolution of 3D printed fiber-reinforced composites; The expression for describing the anisotropic yield surface of 3D printed fiber-reinforced composites using the Liu-Huang-Stout yield criterion is: Among them, F, G, H, L, M, N, I, J, K are anisotropic parameters of 3D printed fiber-reinforced composite filaments under different temperature conditions, and σ 11 , σ 22 , σ 33 are normal stress components in all directions, and is the shear stress component in all directions; The expression for describing the non-linear evolution of 3D printed fiber-reinforced composites using the associated flow criterion is: Among them, is the strain tensor rate of change; is the rate of change of the plastic hardening coefficient of the 3D printed fiber-reinforced composite material.

2. The simulation method for thermo-constitutive damage failure of 3D printed fiber-reinforced composites according to claim 1, wherein: The specific steps for constructing a three-dimensional simulation model using the XCT slice scan results in Step 1 are as follows: According to the RGB values of the XCT slice images, extract the contour features of the specimen that do not contain pores; According to the form of the contour features and combined with the pore content of the specimen obtained by XCT analysis, convert the contour features into an actual three-dimensional model.

3. The simulation method for thermo-constitutive damage failure of 3D printed fiber-reinforced composites according to claim 2, wherein: When performing mesh division on the three-dimensional simulation model in Step 1, a mixed division method of quadrilaterals and triangles is used for the surface mesh division in the radial direction of the specimen, and the creation of the volume mesh of the specimen is carried out by stretching the surface mesh.

4. The simulation method for thermo-constitutive damage failure of 3D printed fiber-reinforced composite materials according to claim 1, characterized in that: When developing a damage failure model for 3D printed fiber-reinforced composites based on the maximum stress criterion in Step 3, the axial failure model acts on the overall area, and the transverse failure model and shear failure model are only applied to the bonding area between the filaments.

5. The simulation method for thermo-constitutive damage failure of 3D printed fiber-reinforced composites according to claim 4, wherein: The mathematical expression of the damage failure model of 3D printed fiber-reinforced composites is: Among them, σ f1t,T and σ f1c,T are the maximum strengths of the 3D printed fiber-reinforced composite wire under axial tension and compression at temperature T, respectively; σ f2t,T and σ f2c,T are the maximum strengths of the 3D printed fiber-reinforced composite wire in the transverse direction under tension and compression at temperature T, respectively; is the maximum in-plane shear strength of the 3D printed fiber-reinforced composite wire at temperature T.

6. The simulation method for thermo-constitutive damage failure of 3D printed fiber-reinforced composites according to claim 1, wherein: The correlation equation between the elastic constant of the damage failure model of 3D printed fiber-reinforced composites and temperature in Step 4 is: Among them, E 11 is the elastic modulus in the 1 direction, E 22 is the elastic modulus in the 2 direction, G 12 is the shear modulus in the 1-2 plane, and T is the temperature; The correlation equation between the yield stress of the damage failure model of 3D printed fiber-reinforced composites and temperature is: Among them, σ 1t,T and σ 1c,T are the yield stresses of the 3D printed fiber-reinforced composite wire under axial tension and compression at temperature T, respectively; σ 2t,T and σ 2c,T are the yield stresses of the 3D printed fiber-reinforced composite wire in the transverse direction under tension and compression at temperature T, respectively; is the in-plane shear yield stress of the 3D printed fiber-reinforced composite wire at temperature T; The correlation equation between the maximum strength of the damage failure model of 3D printed fiber-reinforced composites and temperature is: Among them, σ f1t,T and σ f1c,T are the maximum strengths of the 3D printed fiber-reinforced composite wire under axial tension and compression at temperature T, respectively; σ f2t,T and σ f2c,T are the maximum strengths of the 3D printed fiber-reinforced composite wire in the transverse direction under tension and compression at temperature T, respectively; is the maximum in-plane shear strength of the 3D printed fiber-reinforced composite wire at temperature T.

7. The simulation method for thermo-constitutive damage failure of 3D printed fiber-reinforced composites according to claim 1, characterized in that: In Step 5, the temperature change range of the temperature condition is 23°C to 230°C.

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