CN114912309A - Multi-scale simulation method for vibration fatigue damage of 2.5D woven composite material - Google Patents

Abstract

The invention relates to a multi-scale simulation method for vibration fatigue damage of a 2.5D woven composite material, embedding a unit cell finite element model into the minimum section of a macro finite element model working section of a 2.5D woven composite material vibration fatigue test piece, setting the material of a unit cell model embedding area on the macro finite element model as an isotropic material with extremely small elastic modulus, constraining nodes of the unit cell finite element model in a unit mesh of the macro finite element model by utilizing 'embedded' constraint, and combining to obtain a multi-scale model, setting an analysis step of numerical simulation based on a fatigue loading simulation method of fixed cycle jumping, developing numerical calculation of a finite element model by combining a failure criterion and a material performance degradation rule which are specially provided for 2.5D woven composite material vibration fatigue damage simulation, and realizing multi-scale simulation of 2.5D woven composite material vibration fatigue damage. The method has the advantages of low calculation cost, high calculation efficiency and high prediction precision.

Description

A Multiscale Simulation Method for Vibration Fatigue Damage of 2.5D Woven Composites

technical field

The invention belongs to the technical field of virtual simulation of composite materials, and relates to a multi-scale simulation method for vibration fatigue damage of 2.5D woven composite materials.

Background technique

Replacing metal materials with resin-based composites with low density, high specific strength, high specific stiffness and good durability is an important technical way to achieve engine weight reduction and efficiency, and has become the mainstream trend of the new generation of aero-engines. Due to the unique inter-layer interlocking structure, 2.5D woven composite material overcomes the shortcomings of weak interlayer performance and poor impact resistance of laminate composite materials. In addition, 2.5D woven composite materials also have the advantages of low preparation cost and strong designability, and have better manufacturability than ordinary 3D woven composite materials. Significant advantages make 2.5D woven composites ideal for making engine blades. Aero-engine blades are used in severe vibration and fatigue environments. A typical case is that the journals of engine blades are under bending vibration fatigue loading conditions. It is well known that vibration fatigue is a worse working condition than ordinary fatigue. Therefore, the safety of materials under vibration fatigue conditions must be fully considered when structural design and analysis of 2.5D woven composite blades. D woven composite materials vibration fatigue damage prediction model puts forward an urgent need.

2.5D woven composite material is an emerging material for engine blades, and the research on its vibration fatigue behavior is still very limited. Most of the existing numerical simulation methods for vibration fatigue of 2.5D woven composite material use a macro-scale finite element model. , that is, without considering the microstructural characteristics of the inner yarn of the 2.5D woven composite material, the material in the whole structure is regarded as a uniform anisotropic material, and the 9 engineering constants of the material measured by the mechanical test are used to define Macromodulus and Poisson's ratio of the material. 2.5D woven composite is a heterogeneous material with obvious three-dimensional yarn structure, and the characterization and description of its damage behavior must be focused on the unit cell scale. Therefore, the prediction of vibration fatigue damage of 2.5D woven composite must be Based on the unit cell model, but if the model of the entire structure is refined to the unit cell scale, the amount of calculation will be very large. In order to take into account the requirements of high prediction accuracy and engineering applications for low computational cost and high computational efficiency, a 2.5D woven composite The multi-scale model of material vibration fatigue damage simulation is the only feasible technical approach at present. At present, most of the multi-scale models of 2.5D woven composites focus on the simulation of the internal damage evolution law of the material under static loading, and there is still a lack of multi-scale models specially used to predict the internal micro-damage state of 2.5D woven composites during vibration fatigue loading. mock method. In addition, most of the existing multi-scale simulation methods for 2.5D woven composites are based on the idea of global model-sub-model. The specific implementation method is to define the interface at the corresponding position on the macro model and the sub-model. The data at the interface is saved according to the specified step size, and the external load is removed or part of the external load is retained as needed, or after the load is enlarged, the data is transferred to the sub-model of the meso-scale for calculation again. It can be seen that the global model-sub-model is used. The model method requires two calculations and analysis, and the operation is cumbersome. In addition, in order to ensure the matching of the global model and the sub-model, it is necessary to artificially enlarge the interface data calculated by the macro finite element model. The selection of the amplification factor is often highly dependent on the experience of the engineer. Therefore, this method is inconvenient and cumbersome to operate in practice. Engineering applications are very limited.

The safety and reliability design of 2.5D woven composite blade journals under vibration fatigue conditions is an engineering issue that the industry is very concerned about. The above working conditions can be simplified as a 2.5D woven composite material cantilever beam bending loading condition Therefore, in engineering practice, there is an urgent need for a multi-scale simulation method for vibration fatigue damage of 2.5D woven composites with high prediction accuracy and high computational efficiency. .

SUMMARY OF THE INVENTION

The purpose of the present invention is to propose a multi-scale simulation method for vibration fatigue damage of 2.5D woven composite materials, and to analyze the damage state inside the material during the first-order bending vibration fatigue loading process of 2.5D woven composite materials under any load level. Make fast, accurate forecasts.

In order to solve this technical problem, the technical scheme of the present invention is:

A multi-scale simulation method for vibration fatigue damage of 2.5D woven composite materials is provided,

By embedding the unit cell finite element model at the minimum section of the working section of the macro finite element model of the 2.5D woven composite vibration fatigue test piece, the material in the embedded area of the unit cell model on the macro finite element model is set as a material with an extremely small elastic modulus. Amount of isotropic material, using "embedded" constraints to constrain the nodes of the unit cell finite element model to the element mesh of the macro finite element model, and combine to obtain a multi-scale model, and set the numerical value based on the fatigue loading simulation method of fixed period jumps The simulation analysis step, combined with the failure criteria and material performance degradation rules specially proposed for the vibration fatigue damage simulation of 2.5D woven composite materials, carry out numerical calculation of the finite element model in the CAE software to realize the vibration fatigue damage of 2.5D woven composite materials. The multi-scale simulation of ; the specific steps are as follows:

Step 1. Establish a single-cell finite element model:

According to the weaving structure of the 2.5D woven prefab, the unit cell finite element model of the 2.5D woven composite material was established, and the material parameters were set for the matrix and yarn in the unit cell finite element model respectively; The width direction and its dimensions, where the length and width directions of the unit cell model depend on the real yarn distribution in the vibration fatigue test piece;

The specific method is as follows: if the length direction of the vibration fatigue test piece is the warp extension direction, the warp extension direction in the unit cell model is the length direction of the unit cell model, and the weft extension direction is the width direction of the unit cell model; if the vibration fatigue test piece length The direction is the extension direction of the weft yarn, then the extension direction of the weft yarn in the unit cell model is the length direction of the unit cell model, and the extension direction of the warp yarn is the width direction of the unit cell model;

Step 2: Establish a macroscopic finite element model of the vibration fatigue test piece that divides the embedded area of the unit cell model and other areas:

First, the macroscopic finite element model of the vibration fatigue test piece is established in the software. Then, according to the width w of the unit cell model and the minimum width W of the working section area of the vibration fatigue test piece, calculate the number n of the finite element model to be embedded in the unit cell,

Secondly, take the center of the working section of the vibration fatigue test piece as the center of the embedded area of the unit cell model, the length of the unit cell model as the length of the embedded area of the unit cell model, and the total width of n unit cell models (n*w) as the unit cell model. The width of the embedded area of the cell model is determined, thereby determining the embedded area of the unit cell model on the macroscopic finite element model of the vibration fatigue test piece, and cutting this part into independent parts from the macroscopic model.

The unit cell model embedding region is defined as an isotropic material, the material elastic modulus is set to a minimum value (0.001MPa), and the Poisson's ratio is set to 0.3. Other areas on the macroscopic finite element model are defined as orthotropic materials, and the local coordinate system of the material is set, according to the 9 material engineering constants (ie E ₁ , E ₂ , E 1 , E 2 , E ) of the 2.5D woven composite material measured by the test. ₃ , v ₁₂ , v ₁₃ , v ₂₃ , G ₁₂ , G ₁₃ , G ₂₃ ) to define elastic moduli and Poisson's ratios in different directions for materials in other regions.

Step 3. Combination of multi-scale models:

Embed n unit cell finite element models into the unit cell model embedding region on the macroscopic finite element model of the 2.5D woven composite vibration fatigue test piece, and then use the embedded region to constrain the nodes of the unit cell finite element model into the element mesh of the macroscopic finite element model of the vibration fatigue test piece;

Step 4. Set the constraints and load conditions of the combined multi-scale finite element model

The following constraints and load conditions are set for the multi-scale finite element model of the combined vibration fatigue test piece: the upper and lower surfaces of the area between the end face on the side without the central hole and the middle working section of the multi-scale model are set with clamping constraints (constraint nodes). translation and rotation degrees of freedom); the multi-scale model has a displacement-type load applied to the upper edge of the end face on one side of the central hole, and the displacement direction is perpendicular to the upper surface of the macroscopic finite element model of the test piece and upwards. The specific value of the displacement depends on the actual The amplitude of the free end of the test piece under vibration fatigue loading;

Step 5. Define the failure criteria of the matrix and yarn in the unit cell finite element model and the degradation rules of mechanical properties after damage

For the fatigue loading simulation method of fixed cycle jumps, in order to simulate the damage of N ₀ =10 ⁶ every fixed cycle, the following failure criteria for the matrix and yarn are specially proposed.

The failure criterion of the matrix is defined as: the Von Mises stress (or Von Mises stress) of the matrix is greater than 0.8 times the tensile strength of the matrix; the failure criterion of the yarn is defined as: the transverse stress in the yarn or the stress in the thickness direction of the yarn is greater than 0.8 times. Yarn transverse tensile strength;

After the failure criterion is met, the mechanical properties of the matrix and the yarn are degraded. The degradation rule is: if the stress level of the yarn meets the failure criterion, the transverse modulus of the yarn is reduced to a minimum value (0.001MPa); The stress level of the matrix meets the failure criterion, and the elastic modulus of the matrix is reduced to a minimum value (0.001MPa);

Step 6. Set the analysis steps and numerical calculation parameters for simulating fatigue loading for the finite element model

According to the idea of the fatigue loading simulation method with fixed period jumps, the analysis steps for simulating fatigue loading are set in the software for the finite element model;

Step 7. Vibration fatigue damage simulation based on multi-scale model numerical calculation

According to the failure criteria and mechanical property degradation rules of the yarn and matrix in the unit cell defined in step 5, a subprogram is written, and the damage state variable (statev) is defined in the subprogram as the characterization quantity of the failure criterion, and the finite element method is carried out in the software. The associated settings of the model and the subprograms are used to numerically calculate the multi-scale finite element model established above by using the software. The simulation results of the embedded unit cell finite element model are individually retrieved from the numerical calculation results of the multi-scale model, and the damage state variable (statev) cloud diagrams of the yarn and the matrix in the unit cell finite element model are viewed incrementally. The evolution law of the internal microscopic damage state of the material in the working section of the 2.5D woven composite test piece during the vibration fatigue loading process of each fixed cycle N ₀ =10 ⁶ was obtained.

The specific calculation method of n described in step 2 is: dividing the minimum width W of the working section of the test piece by the width w of the unit cell model, and taking the integer part of the result as n.

The specific method of step 6 is as follows: define a "Tabular" type load spectrum in the software, and define a "load-unload" cycle module, where the number of cycle modules n is equal to the number of fatigue loading cycles N divided by the fixed cycle number. N ₀ ; then, define a general static analysis step with a time length of 1 in the software, set the calculation increment step of the current analysis step to a fixed value of 1/n, and set the loading spectrum type of the current analysis step to the above definition Loading spectrum of type "Tabular".

The method is suitable for the prediction of the internal micro-damage state of the 2.5D woven composite material during the first-order resonance fatigue loading process based on the cantilever beam bending, which simulates the vibration condition of the journal of the engine blade.

This method is suitable for vibration fatigue damage simulation of 2.5D woven composite dumbbell specimens with a central hole on one side (the purpose of the hole is to add counterweight).

The vibration fatigue load is a periodic sinusoidal fatigue load spectrum with a stress ratio of R=-1.

The 2.5D woven composite material is a resin-based composite material prepared by resin transfer molding (RTM).

The simulation method is suitable for the prediction of vibration fatigue damage behavior of 2.5D woven composites under dry conditions at room temperature.

This method is based on the fatigue loading simulation method of fixed-cycle jumps, and is suitable for the case of fixed-cycle jumps N ₀ =10 ⁶ . It can also be used in other cases, but the adopted failure criterion needs to be adjusted.

The beneficial effects of the present invention are:

In the method of the invention, the unit cell finite element model of the 2.5D woven composite material is embedded at the minimum section of the working section of the macroscopic finite element model of the vibration fatigue test piece, and the material in the embedded area of the unit cell model on the macroscopic finite element model is set as a kind of Isotropic materials with extremely small elastic modulus, the materials in other areas of the macroscopic finite element model are set according to the 9 material engineering constants on the macroscopic scale of the 2.5D woven composite obtained by the material mechanics test, and then use the "embedded" Constraints Constrain the nodes of the unit cell finite element model to the element grid of the macro finite element model, and further based on the fatigue loading simulation method of fixed cycle jumping, combined with the intra-unit cell proposed for the vibration fatigue damage simulation of 2.5D woven composite materials. The failure criteria of yarn and matrix and the degradation rules of mechanical properties can realize the micro-damage state of yarn and matrix inside the material during the first-order bending vibration fatigue loading process of the 2.5D woven composite cantilever beam under the vibration condition of the journal of the engine blade. Multiscale simulation of its evolution.

(1) Vibration fatigue under bending loading is a typical working condition of engine blade journals. The method proposed in the present invention can predict the damage initiation and damage of 2.5D woven composite materials during the first-order bending vibration fatigue loading process under any stress level. Evolution and final damage state to help designers determine design allowables for 2.5D woven composite blade structures for engines;

(2) According to the structural characteristics, the high stress area of the working section of the test piece is simulated by the unit cell finite element model considering the internal yarn structure, and other areas are simulated by the macroscopic finite element model based on the assumption of material homogenization. The prediction method that uses the macro finite element model to simulate the entire test piece has higher prediction accuracy, and can predict the micro-damage state of the yarn and matrix inside the material;

(3) Compared with the multi-scale simulation method based on the global model-sub-model that needs to carry out two numerical calculations, the method of the present invention only needs to carry out one numerical calculation for the multi-scale model, and does not need to set the data between the global model and the sub-model. It has the advantages of simple, fast and easy engineering application;

(4) In terms of modeling strategy, this method innovatively divides the unit cell embedded region on the macroscopic finite element model, and sets the material in this region as an isotropic material with a very small elastic modulus, and then Embed the unit cell finite element model in this region, and use the embedded region to constrain the nodes of the unit cell finite element model to the element mesh of the macro finite element model, compared to embedding the macro finite element model into the unit cell The method of embedding the unit cell finite element model after the area is removed, and then directly binding the contact surface between the macro model and the unit cell model, this method can effectively avoid reducing the stress concentration caused by the geometric discontinuity of the model, and can ensure that the load and deformation are within the Effective transfer between two scales of finite element models, so as to obtain high-precision simulation results of the internal stress field of the unit cell model.

(5) The method is versatile and extensible, and can be extended to other more complex working conditions, as well as the simulation of vibration fatigue behavior of 2.5D woven composite structures with more complex structural forms.

Description of drawings

Figure 1 is the configuration and size structure diagram of the vibration fatigue test piece;

Figure 2 is a schematic diagram of a modeling scheme of a multi-scale model;

Figures 3(a)-(c) are the cloud diagrams of the internal damage state of the unit cell model when the vibration fatigue loading times are 1×10 ⁶ , 5×10 ⁶ and 1×10 ⁷ , respectively;

Fig. 4(a)～(c) are the CT inspection results of the internal damage state of the working section of the real test piece when the vibration fatigue loading times are 1×10 ⁶ , 5×10 ⁶ and 1×10 ⁷ respectively;

FIG. 5 is a flow chart of the multi-scale simulation method for vibration fatigue damage of 2.5D woven composite materials of the present invention.

Among them, 1 is the unit cell weaving configuration of the 2.5D woven composite; 2 is the unit cell finite element model of the first 2.5D woven composite to be embedded; 3 is the second 2.5D woven composite to be embedded The unit cell finite element model of the composite material; 4 is the geometric model of the vibration fatigue test piece; 5 is the embedded area of the unit cell finite element model on the macro finite element model; 6 is other areas on the macro finite element model; 7 is the combined 2.5 D Multiscale model of vibration fatigue test pieces of woven composites.

Detailed ways

In order to make the purpose, technical solutions and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be described clearly and completely below with reference to the accompanying drawings in the embodiments of the present invention. The features of various aspects of the embodiments of the present invention will be described in detail below. In the various drawings and the following description, well-known structures and techniques have not been shown in order to avoid unnecessarily obscuring the present invention.

Fig. 5 is a flowchart of the method of the present invention. In this method, the unit cell finite element model of the 2.5D woven composite material is embedded in the minimum section of the working section of the macro finite element model of the vibration fatigue test piece, and the unit cell model on the macro finite element model is embedded The material of the region is set to an isotropic material with a very small elastic modulus, and the nodes of the unit cell finite element model are then constrained to the element mesh of the macroscopic finite element model using "embedded" constraints; further based on the fixed period The jump fatigue loading simulation method, combined with the failure criteria and material performance degradation rules specially proposed for the vibration fatigue damage simulation of 2.5D woven composite materials, carry out numerical calculation in CAE software to realize the vibration fatigue loading process of 2.5D woven composite materials. Multi-scale simulation of microscopic damage state of yarn and matrix inside medium material.

To this end, the unit cell finite element model of the 2.5D woven composite material was first established according to the yarn structure of the preform, and then the number of the unit cell finite element models to be embedded was determined according to the size of the test piece and the size of the unit cell model, and thus Determine the embedded area of the unit cell model on the macroscopic finite element model, and divide the embedded area of the unit cell model into an independent part; set the material of the embedded area of the unit cell model to a macroisotropic with a very small elastic modulus Materials, the materials in other areas of the macroscopic finite element model are set according to the 9 material engineering constants on the macroscopic scale of the 2.5D woven composite material obtained by the material mechanics test, and then the unit cell finite element model is moved to the macroscopic finite element model. The unit cell model is embedded in the region, and the nodes of the unit cell model are constrained to the element mesh of the macro finite element model by using the embedded region function of the software;

Further, according to the fatigue loading simulation method of fixed cycle jump, the analysis step and calculation increment step are set in the software, and the constraints and load conditions for simulating the real test loading conditions are set for the multi-scale finite element model obtained by the combination. Based on the analysis of the test results, a subprogram is written for the failure criteria and mechanical property degradation rules of the yarn and matrix within a single cell, which are specially proposed for the vibration fatigue damage simulation of 2.5D woven composites.

The damage state variables are defined in the subroutine, and the finite element model and the subroutine are set in the CAE software. The calculation is submitted for the multiscale model in the CAE software. After the numerical calculation is completed, the numerical calculation results of the entire multiscale model are separately obtained. The results of the unit cell finite element model are retrieved, and the cloud diagram of the damage state variables in the unit cell finite element model is viewed incrementally, and the prediction results of the internal damage state of the material in the working section of the test piece under different cycles during the vibration fatigue test are obtained.

This method has the advantages of low computational cost and high prediction accuracy, and can effectively predict the microscopic damage state and damage evolution law of the 2.5D woven composite material during the vibration fatigue loading process.

The technical scheme of the present invention will be further described in detail below in conjunction with the accompanying drawings and the examples of damage behavior simulation of the cantilever beam of the 2.5D woven composite material test piece during the first-order bending vibration fatigue loading process:

1. Description of test piece and vibration fatigue test loading

(a) Configuration and dimensions of vibration fatigue test pieces

The configuration and specific dimensions of the 2.5D woven composite vibration fatigue test piece are shown in Figure 1, where the length direction of the test piece is the warp direction of the 2.5D woven composite material. The dimensional parameters in Figure 1 are as follows: length L=110mm, width B=20mm, width W=20mm at the narrowest section of the working section, arc radius R=20mm of the working section, and diameter D=6mm of the circular hole for counterweight assembly.

(b) 2.5D Woven Preform Description

2.5D woven preform is composed of warp yarn, weft yarn and interlining warp yarn, and the yarn specification is T800-6k*2. The density of the weft yarn is 6 pieces/cm, and the number of layers is 6. The density of warp yarns is 4 pieces/cm, and the number of layers is 5. The density of the interlining warp yarns is 4 pieces/cm, and the number of layers is 5. T800 carbon fiber is a transversely isotropic material, and all 6 engineering constants required to define the mechanical properties of the material are: (modulus of elasticity in the longitudinal direction of the fiber) E _f = 295GPa, (modulus in the transverse direction of the fiber) E _t = 10GPa , (fiber longitudinal and transverse shear modulus) G _ft = 5GPa, (fiber transverse shear modulus) G _tt = 5 GPa, (fiber longitudinal and transverse Poisson's ratio) v _ft = 0.3, (fiber transverse Poisson's ratio) v _tt = 0.4 .

(c) 2.5D woven composite description

The 2.5D woven composite board used for cutting into vibration fatigue test pieces is formed by RTM process, and the resin used is a double horse resin (EC230R). The nominal thickness of the board is 4mm, and the fiber volume content is 56%. Nine material engineering constants to characterize the macroscopic basic mechanical properties of 2.5D woven composites are obtained by mechanical testing, which are: (modulus in warp direction) E ₁ =66.1GPa, (modulus in weft direction) E ₂ =59.2GPa, ( Thickness direction modulus) E ₃ =8.11GPa, (in-plane longitudinal and transverse shear modulus) G ₁₂ =4.84 GPa, (interlaminar shear modulus) G ₁₃ =2.88 GPa, (in-plane transverse and transverse shear modulus) G ₂₃ =3.23GPa, (Poisson's ratio of length and width) v ₁₂ =0.085, (Poisson's ratio of length and thickness) v ₁₃ =0.51, (Poisson's ratio of width and thickness) v ₂₃ =0.42. According to the test results of static tensile properties, the warp tensile strength X _t of the 2.5D woven composite is 691 MPa. The elastic modulus of the matrix EC230R is Em = _4.5GPa , the Poisson's ratio is _vm = 0.3, and the matrix tensile strength σ _m =119 MPa. The longitudinal tensile strength of the yarn X _f =1900MPa, the yarn is bound together by the matrix in the transverse direction, so the transverse tensile strength Y _f of the yarn is numerically equal to the matrix tensile strength σ _m , that is, Y _f = 119MPa. (Supplementary description of the meaning of each modulus)

(d) Description of 2.5D woven composites vibration fatigue test

Based on the loading scheme of cantilever beam bending, the first-order bending vibration fatigue test was carried out on the 2.5D woven composite specimen. The load spectrum was a periodic sine wave, and the stress ratio used was R=-1. By controlling the strain on the upper surface of the vibration fatigue test piece, combined with the stress calibration results, the stress level of the vibration fatigue test is controlled. In this embodiment, the stress level in the vibration fatigue test is selected as the warp tensile strength X of the 2.5D woven composite material _At this time, the amplitude of the free end of the test piece is 4 mm, and the number of cycles of fatigue loading is 10 ⁷ times in total.

2. Multi-scale model establishment and numerical calculation

According to the description of the vibration fatigue test piece and the vibration fatigue test loading method in this embodiment described in the previous section, the multi-scale model for the prediction of vibration fatigue damage of 2.5D woven composite materials is established according to the following steps, and numerical calculation is carried out to obtain the Prediction results of internal damage states of materials during vibration fatigue loading.

软件建立2.5D机织树脂基复合材料的全厚度单胞几何模型，根据前面所述的纱线和基体组分各自的材料基本力学性能参数，在软件中为单胞模型中的纱线设置6个材料工程常数，分别为：E_f＝295GPa，E_t＝10GPa，G_ft＝5GPa，G_tt＝5GPa，v_ft＝0.3，v_tt＝0.4；同时为单胞模型中的基体设置材料的弹性模量和泊松比，分别为E_m＝4.5GPa和v_m＝0.3。设置单胞3个方向的网格尺寸和单元类型。在本实施例中3个方向的网格个数均为50个，单元类型设置为完全积分的8节点六面体单元(C3D8)，完成单胞有限元模型的建模后，导出模型的input文件，该input文件中存储着2.5D机织树脂基复合材料单胞有限元模型的全部信息，包括局部坐标系、纱线和基体力学参数、纱线的几何与空间分布等。(1) Step 1, according to the unit cell weaving configuration 1 of the 2.5D woven composite material, the component material parameters and the nominal thickness of the vibration fatigue test piece, use

The software establishes a full-thickness unit cell geometric model of 2.5D woven resin matrix composites. According to the basic mechanical properties of the respective materials of the yarn and matrix components described above, the software sets 6 for the yarn in the unit cell model. A material engineering constant is: E _f = 295GPa, E _t = 10GPa, G _ft = 5GPa, G _tt = 5GPa, v _ft = 0.3, v _tt = 0.4; at the same time, set the elasticity of the material for the matrix in the unit cell model Modulus and Poisson's ratio, _Em = 4.5 GPa and _vm = 0.3, respectively. Sets the grid size and element type for the 3 directions of the unit cell. In this example, the number of meshes in the three directions is 50, and the element type is set to a fully integrated 8-node hexahedron element (C3D8). After the modeling of the unit cell finite element model is completed, the input file of the model is exported, The input file stores all the information of the 2.5D woven resin matrix composite unit cell finite element model, including local coordinate system, mechanical parameters of yarn and matrix, geometry and spatial distribution of yarn, etc.

(2) Step 2, establish a macroscopic finite element model of the vibration fatigue test piece that divides the embedded area of the unit cell model and other areas

First, according to the geometric configuration and size of the vibration fatigue test piece, a geometric model of the vibration fatigue test piece is established in the software4. Then, according to the width w of the unit cell model and the minimum section width W of the working section area of the vibration fatigue test piece, calculate the number n of the finite element model to be embedded in the unit cell. The specific calculation method is as follows: let the minimum section width W of the working section of the test piece Divide by the width w of the unit cell model and take the integer part of the result as n. Next, take the center of the working section of the vibration fatigue test piece as the center of the embedded area of the unit cell model, the length of the unit cell model as the length of the embedded area of the unit cell model, and the total width of n unit cell models (n*w) as the The width of the embedded area of the unit cell model, thereby determining the embedded area of the unit cell model on the macroscopic finite element model of the vibration fatigue test piece, and cutting this part into independent parts from the macroscopic model. In this example, the number of unit cell models to be embedded is 2, and the unit cell model embedding area 5 on the macroscopic finite element model is determined according to the method described above, so that the macroscopic finite element model is divided into different areas, so that The unit cell model embedded area 5 forms a separate part.

软件中为宏观模型上单胞模型嵌入区域5和其它区域6设置不同的材料力学性能参数，其中将单胞模型嵌入区域5的材料定义为各向同性材料，材料弹性模量E设置为极小值(0.001MPa)，泊松比v设置为0.3。宏观模型其它区域6的材料定义为正交各向异性材料，设置材料局部坐标系，并按照试验测得的2.5D机织复合材料宏观尺度上的9个材料工程常数(即E₁,E₂,E₃,v₁₂,v₁₃,v₂₃,G₁₂,G₁₃,G₂₃)为其它区域6的材料设置不同方向的材料弹性模量和泊松比。对宏观模型进行网格划分，并定义单元类型为C3D8。exist

In the software, different material mechanical properties parameters are set for the unit cell model embedded area 5 and other areas 6 on the macro model. The material in the unit cell model embedded area 5 is defined as an isotropic material, and the material elastic modulus E is set to be extremely small value (0.001 MPa), Poisson's ratio v was set to 0.3. The materials in other areas 6 of the macro model are defined as orthotropic materials, the material local coordinate system is set, and the 9 material engineering constants (ie E ₁ , E ₂ ) on the macro scale of the 2.5D woven composite material measured by the test are used. , E ₃ , v ₁₂ , v ₁₃ , v ₂₃ , G ₁₂ , G ₁₃ , G ₂₃ ) set the material elastic modulus and Poisson’s ratio in different directions for the materials in other regions 6 . Mesh the macro model and define the element type as C3D8.

(3) Step 3, the combination of multi-scale models

软件，得到Import the input file of the single-cell finite element model obtained in step 1 into

software, get

软件界面下显示的2.5D机织复合材料的单胞有限元模型，在

软件的装配模块下导入2个单胞有限元模型2，3，以及步骤二得到的划分了单胞模型嵌入区域和其它区域的振动疲劳试验件的宏观有限元模型。将两个单胞模型的长度方向旋转到与试验件宏观模型的长度方向一致，并将2个单胞模型并排到一起，然后将其平移到宏观有限元模型上的单胞嵌入区域5，使2个单胞模型与单胞嵌入区域5完全重合。随后，切换到

软件的接触模块下，利用软件的嵌入式约束(embedded region)功能，将2个单胞有限元模型2，3的所有节点约束到振动疲劳试验件的宏观有限元模型的单元网格中，得到组合后的多尺度有限元模型7。exist

The unit cell finite element model of the 2.5D woven composite material displayed under the software interface, in

Under the assembly module of the software, import two unit cell finite element models 2 and 3, and the macroscopic finite element model of the vibration fatigue test piece obtained in step 2, which divides the embedded area of the unit cell model and other areas. Rotate the length direction of the two unit cell models to be consistent with the length direction of the macroscopic model of the test piece, and place the two unit cell models side by side, and then translate them to the unit cell embedding area 5 on the macroscopic finite element model, so that The 2 unit cell models completely coincide with the unit cell embedded region 5. Then, switch to

Under the contact module of the software, the embedded region function of the software is used to constrain all nodes of the two unit cell finite element models 2 and 3 to the element mesh of the macroscopic finite element model of the vibration fatigue test piece, and obtain Combined multiscale finite element model7.

(4) Step 4: Set the constraints and load conditions of the combined multi-scale finite element model

软件的加载模块，对组合后的多尺度有限元模型7设置如下约束条件和载荷条件：多尺度模型无中心孔一侧的端面到中间工作段之间区域的上、下表面设置固支约束(约束节点的平动和转动自由度)；多尺度模型有中心孔一侧端面的上方边线施加位移型载荷，位移的方向为垂直于试验件多尺度有限元模型的上表面并朝上，对本实施例，由于振动疲劳试验中控制的试验件自由端的振幅为4mm，因此模拟中位移载荷的数值设置为4mm；switch to

The loading module of the software sets the following constraints and load conditions for the combined multi-scale finite element model 7: Clamping constraints are set on the upper and lower surfaces of the area between the end face on the side of the multi-scale model without the central hole and the middle working section ( The translational and rotational degrees of freedom of the constraint nodes); the multi-scale model has a displacement-type load applied to the upper edge of the end face on one side of the central hole, and the direction of the displacement is perpendicular to the upper surface of the multi-scale finite element model of the test piece and upwards. For example, since the amplitude of the free end of the test piece controlled in the vibration fatigue test is 4mm, the value of the displacement load in the simulation is set to 4mm;

(5) Step 5, define the failure criteria of the matrix and yarn in the unit cell finite element model and the degradation rules of mechanical properties after damage.

For the fatigue loading simulation method of fixed cycle jumps, in order to simulate the damage state of N ₀ =10 ⁶ for each fixed cycle, the following failure criteria for the matrix and yarn in the unit cell model are specially proposed. The failure criterion of the matrix is defined as: the Von Mises stress (or Von Mises stress) of the matrix is greater than 0.8 times the tensile strength σ _m of the matrix; the failure criterion of the yarn is defined as: the transverse stress in the yarn (displayed as S22 in the software interface) ) or the yarn thickness direction stress (displayed as S33 in the software interface) is greater than 0.8 times the yarn transverse tensile strength Y _f ; after meeting the failure criterion, the material mechanical properties are degraded for the matrix and yarn, and the degradation rules are: If the stress level of the yarn meets the failure criterion, the transverse modulus E _tt of the yarn is reduced to a minimum value (0.001MPa); if the stress level of the matrix meets the failure criterion, the elastic modulus E _m of the matrix is reduced to The minimum value (0.001MPa); the reason for using 0.8 times the tensile strength of the matrix and the tensile strength in the transverse direction of the yarn as the strength threshold in the failure criterion is to consider the cumulative damage caused by the jump in the number of fatigue cycles of 10 ⁶ .

(6) Step 6: Set the analysis steps and numerical calculation parameters for simulating fatigue loading for the finite element model

软件中为有限元模型设置模拟疲劳加载的分析步，针对本实施例，具体方法如下：在软件中定义一个“Tabular”类型的载荷谱，设置“加载-卸载”循环模块(加载设置为参数1，卸载设置为参数0)，其中循环模块的个数n等于拟模拟的疲劳加载循环次数N(10⁷)除以固定跳跃循环周次N₀(10⁶)，因此循环模块的个数n＝10；然后，在软件中定义一个时间长度为1的通用静态分析步，将当前分析步的计算增量步设置为固定值1/n(即0.1)，并将当前分析步的加载谱类型设置为上述定义的“Tabular”类型的载荷谱。According to the idea of the fatigue loading simulation method of fixed cycle jump, in

The software sets the analysis step for simulating fatigue loading for the finite element model. For this embodiment, the specific method is as follows: define a "Tabular" type load spectrum in the software, and set the "load-unload" cycle module (the loading is set to parameter 1 , unloading is set to parameter 0), where the number n of cycle modules is equal to the number of fatigue loading cycles N(10 ⁷ ) to be simulated divided by the number of fixed jump cycles N ₀ (10 ⁶ ), so the number of cycle modules n = 10; Then, define a general static analysis step with a time length of 1 in the software, set the calculation increment step of the current analysis step to a fixed value of 1/n (ie 0.1), and set the loading spectrum type of the current analysis step. Loading spectrum of type "Tabular" as defined above.

(7) Step 7, the vibration fatigue damage simulation based on the multi-scale model numerical calculation.

软件中进行多尺度有限元模型和umat子程序的关联设置，利用

软件对上述建立的多尺度有限元模型进行数值计算。从整个多尺度模型的计算结果中单独调取内嵌的单胞有限元模型的结果，逐增量步地查看单胞模型中损伤状态变量(statev)的云图，在软件界面下损伤状态变量(statev)显示为符号SDV设置当SDV大于1时云图显示为灰色，单胞模型上显示出的灰色区域的大小、位置和分布即为2.5D机织复合材料振动疲劳试验件工作段区域单胞内基体和纱线的损伤状态，根据步骤六的分析步设置，增量步每增加一步，代表模拟的振动疲劳循环加载次数向前跳跃了固定循环周次N₀＝10⁶，通过逐增量步地查看单胞内SDV的云图，可以对每累计10⁶次疲劳循环加载的2.5D机织复合材料振动疲劳试验件工作段处材料内部的损伤状态进行模拟仿真；利用配备了12核CPU，内存为8GB的计算机进行多尺度模型的数值计算，计算时间约79min，图3(a)～3(c)分别展示了2.5D机织复合材料振动疲劳试验件分别累计经历了1×10⁶、5×10⁶、1×10⁷次循环后工作段处材料内部损伤状态的模拟结果，其中灰色区域代表已经失效的材料。可见随着循环次数的增加，单胞内部的损伤区域逐渐变大。此外根据SDV指示的损伤因子的数值，可知随着振动疲劳循环次数的增加，单胞内部的损伤程度也越来越严重。图4(a)～4(c)分别展示了2.5D机织复合材料振动疲劳试验件分别累计经历1×10⁶、5×10⁶、1×10⁷次循环后真实试验件工作段处损伤状态的CT检测结果。可见，数值模拟得到的损伤状态和对应的累计循环次数下真实试验件内部损伤的CT检测结果基本吻合，说明了本发明提出的模拟方法具有较高的预测精度。此外，真实的物理试验大约耗时19小时，而基于本发明提出的多尺度模拟方法的数值计算仅耗时约79分钟，数值模拟可以给出与真实试验基本吻合的损伤状态，并且可量化损伤程度，可见本发明提出的一种2.5D机织复合材料振动疲劳损伤的多尺度模拟方法具有高效、快捷的优点，在实际工程设计中具有可观的应用前景。According to the failure criterion and material property degradation rules defined in step 5, write the umat subprogram, in which the constitutive, failure criterion, and damage indicating whether the failure criterion is satisfied or not are defined for the yarn and matrix in the 2.5D woven composite material respectively. State variables (statev), degradation rules after yarn and matrix failure, etc. Among them, the damage state variable (statev) is a key parameter to ensure that the damage state is transmitted between different analysis steps, and it is also a quantitative indicator to characterize the damage degree of the internal yarn and matrix. exist

In the software, the multi-scale finite element model and the umat subroutine are associated with the settings, using

The software performs numerical calculation on the multi-scale finite element model established above. From the calculation results of the entire multi-scale model, the results of the embedded unit cell finite element model are individually retrieved, and the cloud map of the damage state variable (statev) in the unit cell model is viewed incrementally. In the software interface, the damage state variable ( statev) is displayed as the symbol SDV setting. When the SDV is greater than 1, the cloud image is displayed in gray, and the size, location and distribution of the gray area displayed on the unit cell model is the unit cell in the working section of the 2.5D woven composite material vibration fatigue test piece. The damage state of the matrix and yarn, according to the analysis step setting in step 6, each increment of incremental step means that the number of simulated vibration fatigue cyclic loading jumps forward by the fixed cycle number N ₀ =10 ⁶ . By viewing the cloud map of SDV in a unit cell, the damage state inside the material at the working section of the 2.5D woven composite material vibration fatigue test piece loaded every 10 ⁶ fatigue cycles can be simulated; using a 12-core CPU, memory The numerical calculation of the multi ^- scale model is carried out for an 8GB computer, and the calculation time is about 79 minutes. The simulation results of the internal damage state of the material at the working section after ×10 ⁶ and 1×10 ⁷ cycles, where the gray area represents the failed material. It can be seen that with the increase of the number of cycles, the damaged area inside the unit cell gradually becomes larger. In addition, according to the value of the damage factor indicated by SDV, it can be seen that with the increase of the number of vibration fatigue cycles, the damage degree inside the unit cell becomes more and more serious. Figures 4(a) to 4(c) show the damage of the real test piece at the working section of the 2.5D woven composite material vibration fatigue test piece after accumulative cycles of 1×10 ⁶ , 5×10 ⁶ , and 1×10 ⁷ , respectively. Status of CT test results. It can be seen that the damage state obtained by the numerical simulation is basically consistent with the CT detection result of the internal damage of the real test piece under the corresponding cumulative cycle times, which shows that the simulation method proposed in the present invention has high prediction accuracy. In addition, the real physical test takes about 19 hours, while the numerical calculation based on the multi-scale simulation method proposed in the present invention only takes about 79 minutes. The numerical simulation can give the damage state basically consistent with the real test, and the damage can be quantified It can be seen that a multi-scale simulation method for vibration fatigue damage of 2.5D woven composite materials proposed by the present invention has the advantages of high efficiency and speed, and has considerable application prospects in practical engineering design.

Claims (9)

1.2.5D Multi-scale simulation method for vibration fatigue damage of woven composite materials, characterized in that: In the multi-scale simulation method, the unit cell finite element model is embedded in the minimum section of the working section of the macroscopic finite element model of the 2.5D woven composite material vibration fatigue test piece, and the material in the embedded area of the unit cell model on the macroscopic finite element model is set as: An isotropic material with a very small elastic modulus, using "embedded" constraints to constrain the nodes of the unit cell finite element model to the element mesh of the macro finite element model, and combining to obtain a multi-scale model, based on fixed periodic jumps The fatigue loading simulation method set up the analysis step of numerical simulation, combined with the failure criteria and material performance degradation rules specially proposed for the 2.5D woven composite material vibration fatigue damage simulation, carry out the numerical calculation of the finite element model, and realize the 2.5D woven composite material. Multiscale simulation of vibration fatigue damage; includes the following steps: Step 1. Establish a single-cell finite element model According to the weaving structure of the 2.5D woven prefab, the unit cell finite element model of the 2.5D woven composite material was established, and the material parameters were set for the matrix and yarn in the unit cell finite element model respectively; The width direction and its size, where the length and width directions of the unit cell model depend on the real yarn distribution in the vibration fatigue test piece, the specific methods are as follows: If the length direction of the vibration fatigue test piece is the warp extension direction, the warp extension direction in the unit cell model is the length direction of the unit cell model, and the weft extension direction is the width direction of the unit cell model; if the length direction of the vibration fatigue test piece is the weft extension direction direction, the extension direction of the weft yarn in the unit cell model is the length direction of the unit cell model, and the extension direction of the warp yarn is the width direction of the unit cell model; Step 2: Establish a macroscopic finite element model of the vibration fatigue test piece that divides the embedded area of the unit cell model and other areas First, the macroscopic finite element model of the vibration fatigue test piece is established. Then, according to the width w of the unit cell model and the minimum width W of the working section area of the vibration fatigue test piece, calculate the number n of the finite element model to be embedded in the unit cell; Secondly, take the center of the working section of the vibration fatigue test piece as the center of the embedded area of the unit cell model, the length of the unit cell model as the length of the embedded area of the unit cell model, and the total width of the n unit cell models as the length of the embedded area of the unit cell model. width, thereby determining the embedded area of the unit cell model on the macroscopic finite element model of the vibration fatigue test piece, and cutting this part into independent parts from the macroscopic model. The embedded area of the unit cell model is defined as an isotropic material, the elastic modulus of the material is set to 0.001MPa, and the Poisson's ratio is set to 0.3; other areas on the macroscopic finite element model are defined as orthotropic materials, and the material local coordinate system is set , and define the elastic modulus and Poisson's ratio in different directions for materials in other regions according to the 9 material engineering constants of the macro-scale 2.5D woven composites measured by the test; Step 3. Combination of multi-scale models Embed n unit cell finite element models into the unit cell model embedding area on the macroscopic finite element model of the 2.5D woven composite material vibration fatigue test piece, and then use the embedded constraints to constrain the nodes of the unit cell finite element model to the vibration fatigue test in the element mesh of the macroscopic finite element model; Step 4. Set the constraints and load conditions of the combined multi-scale finite element model The following constraints and load conditions are set for the multi-scale finite element model of the combined vibration fatigue test piece: the upper and lower surfaces of the area between the end face on the side without the central hole and the middle working section of the multi-scale model are set with clamping constraints; The model has a displacement-type load applied to the upper edge of the end face on one side of the center hole, and the displacement direction is perpendicular to the upper surface of the macroscopic finite element model of the test piece and faces upwards. The specific value of the displacement depends on the amplitude of the free end of the test piece under real vibration fatigue loading; Step 5. Define the failure criteria of the matrix and yarn in the unit cell finite element model and the degradation rules of mechanical properties after damage For the fatigue loading simulation method of fixed cycle jumps, in order to simulate the damage of N ₀ =10 ⁶ every fixed cycle, the following failure criteria for the matrix and yarn are specially proposed; The failure criterion of the matrix is defined as: the Von Mises stress of the matrix is greater than 0.8 times the tensile strength of the matrix; the failure criterion of the yarn is defined as: the transverse stress in the yarn or the stress in the yarn thickness direction is greater than 0.8 times the transverse tensile strength of the yarn ; After the failure criterion is met, the mechanical properties of the matrix and the yarn are degraded. The degradation rule is: if the stress level of the yarn meets the failure criterion, the transverse modulus of the yarn is reduced to a minimum value; if the stress level of the matrix To meet the failure criterion, reduce the elastic modulus of the matrix to a minimum value, the minimum value is 0.001MPa; Step 6. Set the analysis steps and numerical calculation parameters for simulating fatigue loading for the finite element model According to the idea of the fatigue loading simulation method with fixed period jumps, the analysis steps for simulating fatigue loading are set in the software for the finite element model; Step 7. Vibration fatigue damage simulation based on multi-scale model numerical calculation According to the failure criterion and mechanical property degradation rule of the yarn and matrix in the unit cell defined in step 5, the damage state variable is defined as the characterization quantity of the failure criterion, and the association setting of the finite element model and subprogram is carried out in the software, and the above establishment is established by the software. The multi-scale finite element model was numerically calculated. The simulation results of the embedded unit cell finite element model are individually retrieved from the numerical calculation results of the multi-scale model, and the damage state variable cloud diagrams of the yarn and the matrix in the unit cell finite element model are viewed incrementally, and each experience The evolution law of the internal microscopic damage state of the material in the working section of the 2.5D woven composite test piece during the vibration fatigue loading process of the fixed cycle N ₀ =10 ⁶ . 2. The multi-scale simulation method according to claim 1, characterized in that: the specific calculation method of n described in step 2 is: dividing the minimum width W of the working section of the test piece by the width w of the unit cell model, and taking the integer of the result part as n. 3. multi-scale simulation method according to claim 1, is characterized in that: the concrete method of step 6 is as follows: define a load spectrum of "Tabular" type in software, define " load-unload " cycle module, wherein the cycle module's The number n is equal to the number of fatigue loading cycles N to be simulated divided by the fixed cycle number N ₀ ; then, define a general static analysis step with a time length of 1 in the software, and set the calculation increment of the current analysis step to be fixed value 1/n, and set the loading spectrum type of the current analysis step to the "Tabular" type of loading spectrum defined above. 4. The multi-scale simulation method according to claim 1, characterized in that: the method is suitable for simulating the vibration condition of the journal of the engine blade, in the first-order resonance fatigue loading process of the 2.5D woven composite material based on cantilever beam bending Prediction of microscopic damage states within materials. 5 . The multi-scale simulation method according to claim 1 , wherein the method is suitable for the vibration fatigue damage simulation of a 2.5D woven composite material dumbbell specimen with a central hole on one side. 6 . 6 . The multi-scale simulation method according to claim 1 , wherein the vibration fatigue load is a periodic sinusoidal fatigue load spectrum with a stress ratio of R=-1. 7 . 7 . The multi-scale simulation method according to claim 1 , wherein the 2.5D woven composite material is a resin-based composite material prepared by a resin transfer molding process. 8 . 8 . The multi-scale simulation method according to claim 1 , wherein the simulation method is suitable for predicting the vibration fatigue damage behavior of 2.5D woven composite materials in a dry state at room temperature. 9 . 9 . The multi-scale simulation method according to claim 1 , wherein the method is based on a fatigue loading simulation method of fixed-period skipping, and is suitable for the case where the number of fixed skipping periods is N ₀ =10 ⁶ . In other cases, adjustment failures are made. 10 . The same rules apply.

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