CN117150858B - Crack-containing continuous fiber reinforced resin matrix composite three-dimensional finite element modeling method - Google Patents
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- 239000000835 fiber Substances 0.000 title claims abstract description 55
- 239000011159 matrix material Substances 0.000 title claims abstract description 35
- 239000002131 composite material Substances 0.000 title claims abstract description 32
- 238000000034 method Methods 0.000 title claims abstract description 23
- 239000011347 resin Substances 0.000 title claims abstract description 23
- 229920005989 resin Polymers 0.000 title claims abstract description 23
- 239000000463 material Substances 0.000 claims abstract description 29
- 238000004364 calculation method Methods 0.000 claims abstract description 21
- 238000012545 processing Methods 0.000 claims abstract description 6
- 230000010354 integration Effects 0.000 claims description 18
- 238000012216 screening Methods 0.000 claims description 7
- 238000005520 cutting process Methods 0.000 claims description 4
- 239000002657 fibrous material Substances 0.000 claims description 4
- 238000006243 chemical reaction Methods 0.000 claims description 2
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- 238000000265 homogenisation Methods 0.000 abstract description 2
- 238000011160 research Methods 0.000 description 5
- 230000008859 change Effects 0.000 description 3
- 230000007547 defect Effects 0.000 description 3
- 238000010586 diagram Methods 0.000 description 3
- 230000008676 import Effects 0.000 description 3
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- 239000003822 epoxy resin Substances 0.000 description 2
- 238000012986 modification Methods 0.000 description 2
- 230000004048 modification Effects 0.000 description 2
- 229920000647 polyepoxide Polymers 0.000 description 2
- 239000011165 3D composite Substances 0.000 description 1
- 229920000049 Carbon (fiber) Polymers 0.000 description 1
- 238000013459 approach Methods 0.000 description 1
- 230000009286 beneficial effect Effects 0.000 description 1
- 239000004917 carbon fiber Substances 0.000 description 1
- 230000015556 catabolic process Effects 0.000 description 1
- 238000006731 degradation reaction Methods 0.000 description 1
- 238000011161 development Methods 0.000 description 1
- 238000002474 experimental method Methods 0.000 description 1
- 238000000605 extraction Methods 0.000 description 1
- 239000003733 fiber-reinforced composite Substances 0.000 description 1
- 230000002706 hydrostatic effect Effects 0.000 description 1
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- 230000008569 process Effects 0.000 description 1
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Abstract
The invention relates to a crack-containing continuous fiber reinforced resin matrix composite three-dimensional finite element modeling method, which comprises 1) establishing a matrix model; 2) Building a fiber model; 3) Establishing a lane integral area model; 4) Adding prefabricated cracks for the three-dimensional model according to the calculation requirement; 5) Grid division of a three-dimensional model; 6) Obtaining an independent grid model; 7) Voxel processing is carried out on the lane integral area by using a Python script; 8) And (5) keeping other conditions of the imported model unchanged, and performing calculation. The invention has scientific and reasonable design, can ensure the integrity and regularity of the grid of the integral area of the crack front gird, meets the calculation requirement of fracture mechanics related parameters, and ensures the accuracy and reliability of calculation results; the method realizes the calculation of the crack front fracture related parameters of the crossing multicomponent material, is different from the traditional homogenization theoretical analysis, and can obtain the influence of material mismatch on the model stress state and fracture performance.
Description
Technical Field
The invention belongs to the technical field of finite element modeling of continuous fiber reinforced resin matrix composite materials, and particularly relates to a three-dimensional finite element modeling method of a continuous fiber reinforced resin matrix composite material containing cracks.
Background
Continuous fiber reinforced resin based composites with high specific strength and specific stiffness are increasingly used in engineering applications. However, various defects and cracks may be generated during the production process or actual service of the components thereof. These defects tend to be the source of crack initiation and propagation, and therefore how to accurately obtain the mechanical properties of the continuous fiber reinforced resin matrix composites containing cracks is a problem to be solved.
Currently, research on the impact of cracks in continuous fiber reinforced resin matrix composites is mainly focused on the macroscopic scale. Many scholars have tried to apply part of the theory in fracture mechanics to continuous fiber reinforced resin based composites in an effort to reach the desired conclusion. However, most of the research methods are based on homogenization of materials, but based on the related theory of the homogenized materials, the failure process of the composite materials cannot be truly represented. The continuous fiber reinforced resin matrix composite is different from the traditional homogeneous material in stress state and failure mode when bearing load due to the unique microstructure, and the complex internal structure of the continuous fiber reinforced resin matrix composite also enables the continuous fiber reinforced resin matrix composite to show very large dispersibility in various performances. Therefore, a finite element calculation method considering cracks on the basis of the actual microstructure of the continuous fiber reinforced resin matrix composite material has become a very important research means in the field of composite material research.
Nevertheless, most of the related studies on microstructure are still based on two-dimensional models or axisymmetric models, which have a great limitation in themselves, while the three-dimensional model-based studies are still based on the theory of homogeneity. It remains a difficulty how to build a three-dimensional finite element model of a continuous fiber reinforced resin matrix composite containing cracks.
In order to accurately obtain the stress state and the fracture parameter at the crack front in a complex structure, development of a general crack-containing continuous fiber reinforced resin matrix composite three-dimensional finite element model building method is needed, and on the basis of ensuring the accuracy of a calculation result, building and solving of the three-dimensional finite element model can be conveniently and rapidly realized so as to meet the demands of research and application.
Disclosure of Invention
The invention aims to overcome the defects of the prior art, and provides a three-dimensional finite element modeling method for a continuous fiber reinforced resin matrix composite material containing cracks, which is used for establishing a finite element model containing fibers and complete three-dimensional structures of the cracks, and meanwhile, keeping the regularity of a gird integral grid of a crack tip area model and realizing the accurate calculation of relevant parameters of crack fronts.
The invention solves the technical problems by the following technical proposal:
a three-dimensional finite element modeling method for a crack-containing continuous fiber reinforced resin matrix composite material is characterized by comprising the following steps of: the method comprises the following steps:
1) And (3) establishing a matrix model: adopting finite element analysis software ABAQUS to establish a three-dimensional finite element model with a required corresponding size, and inputting the elastic modulus E and Poisson ratio v of a matrix material;
2) And (3) building a fiber model: establishing an independent fiber structure three-dimensional model according to a composite material structure, inputting the elastic modulus E, the shear modulus G and the Poisson ratio v of the composite material, setting the material orientation according to the fiber arrangement state of the composite material, and combining a matrix model and a fiber model by using a Merge function built in ABAQUS software to form a complete structure model of a main body region;
3) Establishing a lane integral area model: establishing a girth integration area model corresponding to the girth integration area according to the shape and the size of the crack front, cutting off the corresponding position of the crack front in the combined complete structure model by using a Cut function, and combining the independent girth integration area model with the complete structure model after cutting off treatment by adopting a Tie binding mode to form a three-dimensional model;
4) Adding prefabricated cracks for the combined three-dimensional model according to calculation requirements by using a built-in Crack function of ABAQUS software;
5) Grid division is carried out on a main body area of the three-dimensional model by adopting a 10-node tetrahedral unit with reduced integral, grid division is carried out on a lane integral area of the three-dimensional model by adopting a 20-node hexahedral unit with reduced integral, and grids at crack tips are encrypted and singular units are introduced, so that a focusing ring type grid is adopted;
6) Load and boundary conditions are set according to the calculated requirements, an inp file is generated by using a data checking function, and the inp file is reintroduced into ABAQUS to obtain an independent grid model;
7) Voxel processing is carried out on the lane integral region by using a Python script, the fine annular grid is divided according to the space coordinates, so that the corresponding region of the matrix material and the corresponding region of the fiber material are distinguished, and the independent grids of the corresponding regions are assigned with material properties and material directions;
8) And (5) keeping other conditions of the imported independent grid model unchanged, and calculating the related parameters of the finite element according to the requirement.
And, the three-dimensional model of the original fiber structure is reserved in the step 2) for the subsequent voxelized Python script to call, and the elastic modulus E in three directions is independently input for the anisotropic fiber material 11 、E 22 、E 33 Shear modulus G in three directions 12 、G 13 、G 23 Poisson ratio v in three directions 12 ，v 13 ，v 23 。
In step 3), the mesh size of the lane integration area is usually much smaller than that of the main area due to the need of both calculation accuracy and calculation cost, the main area with thicker mesh is selected as the main surface, and the lane integration area with finer mesh is the secondary surface, so as to perform Tie binding processing.
In the step 5), the main body area is meshed in a free mesh mode; the gird integrating area is subjected to grid division in a mode of sweeping grids; singular units are introduced at the crack tip, one face at the contact crack front collapses, and intermediate nodes on four sides adjacent to the collapsed face move to 1/4 of the point towards the collapsed face.
In the step 7), a Python script is used to screen the independent grid model, a three-dimensional model is independently established as a screening boundary, for the division of the girth integration area, a three-dimensional model of an original fiber structure is used, the Python script adjusts screening conditions according to the units used by the grid model, for the 20-node hexahedral units used by the girth integration area, the space coordinates of all 20 nodes are extracted, the acquired node coordinates are averaged, and the obtained result is used as the core coordinates of the grid unit; and then dividing the captured core coordinates of the grid cells by using the target area continuous boundary parts established in advance, and compiling grids with the core coordinates in the target area boundary to realize the giving of the attribute of the part of cells and realize the conversion from continuous boundaries to discrete boundaries.
The invention has the advantages and beneficial effects that:
1. according to the method for modeling the crack-containing continuous fiber reinforced resin matrix composite three-dimensional finite element, disclosed by the invention, under the condition that complex structures such as fibers and cracks exist, the integrity and regularity of grids of a crack front gird integral region can be ensured, the calculation requirements of fracture mechanics related parameters are met, and the accuracy and reliability of a calculation result are ensured.
2. The method for modeling the three-dimensional finite element of the crack-containing continuous fiber reinforced resin matrix composite material can be suitable for calculating the finite element model of the crack-containing three-dimensional composite material with different structures, materials and fiber arrangement forms.
3. The three-dimensional finite element modeling method for the continuous fiber reinforced resin matrix composite containing the cracks realizes the calculation of the relevant parameters of crack front fracture of the cross-over multicomponent material, is different from the traditional uniform theoretical analysis, and can obtain the influence of material mismatch on the stress state and fracture performance of the model.
Drawings
FIG. 1 is a schematic diagram of a modeling flow of the present invention;
FIG. 2 is a schematic diagram of a finite element model of a single-side notched tensile specimen comprising a square arrangement of fiber solid structures in accordance with the present invention;
FIG. 3 is a schematic illustration of interference between the integration zone of the present invention and a fiber;
FIG. 4 is a schematic diagram of the integration area of the lane after the modification of the cell attributes of the present invention;
FIG. 5 is a plot of Mises stress results of the bulk finite element model of the present invention along the crack front;
FIG. 6 is a graph of stress triaxial results of a finite element model according to the present invention along a crack front;
FIG. 7 is a graph of the Lode angle results of the finite element model of the present invention along the crack front;
FIG. 8 is a graph of J-integration results of a finite element model of the present invention along the crack front.
Detailed Description
The invention is further illustrated by the following examples, which are intended to be illustrative only and not limiting in any way.
As shown in fig. 1, according to the three-dimensional finite element modeling method of the continuous fiber reinforced resin matrix composite material with cracks, a square unidirectional fiber reinforced composite material RVE unit cell model with pre-cracks is calculated:
(1) Model creation and editing
Finite element models containing fiber structures were modeled using three-dimensional finite elements, and a representative model was created in the form of a single-sided notched tensile specimen, as shown in fig. 2. The ratio of span H to width W of the model was H/w=5, the ratio of thickness B to width W of the model was set to B/w=1, the ratio of crack length a to width W of the model was a/w=0.4, where w=20 mm, while applying a tensile load of 1MPa at the distal end of the model, and the analysis step was selected as a static general analysis step. To achieve the calculation of the subsequent aim, four anisotropic fibers are artificially added in a square arrangement mode, and the volume fraction of the fibers is V f＝ 40%, 50%, 60% by volume fraction V f The control mode of (2) is as follows:
wherein: r is the fiber bundle radius.
The model was divided into a two-phase system of fibers and a matrix, wherein the fibers were T300 carbon fibers, the matrix was epoxy resin, and the specific material parameters are shown in Table 1.
TABLE 1 Material related parameters for three-dimensional finite element models
Wherein: epoxy resin is regarded as isotropic material, E 11 And v 12 T300 is a transverse isotropic material, E, for its modulus of elasticity and Poisson's ratio 11 、E 22 、E 33 Modulus of elasticity in three directions, G 12 、G 13 、G 23 Shear modulus in three directions, v 12 ，v 13 ，v 23 Poisson's ratio in three directions, where 1 is the main direction, i.e. along the length of the fiber.
And independently establishing a main body area model and a lane integral area model according to the flow, and performing Tie binding. The subject region model uses a free mesh approach to mesh and uses tetrahedral cells C3D10R. The lane integration area is meshed using a swept mesh manner, and hexahedral cells C3D20R are used. The Crack tip degradation unit is controlled to be a single node by adding a pre-Crack through the Crack function, wherein the parameter t=0.25 of the intermediate node of the second-order grid option. Since the girth integration region overlaps with the region where the fiber is located, voxel processing is performed on the girth integration region in accordance with the spatial coordinates where the fiber is located, as shown in fig. 3.
Before the voxelization, a matrix material property is given to the lane integral region, and the material property and the material direction are given to the main body region according to the actual structure. And converting the complete model into an independent grid model, taking the independent fiber model as a script calling object, screening the gird integral area unit by using a Python script, and automatically compiling the unit with the core coordinates in the fiber space coordinates by the script. The cell material properties and material directions within the collection are then manually modified to meet the actual structure, and the modified integration area model of the girth is shown in FIG. 4.
The Python script used herein is written by the programming software Visual Studio, and the specific execution code is shown below.
from abaqus import*
from abaqusConstants import*
import numpy as np
model＝mdb.models["Model Name"]
partRef＝model.parts["Reference Part"]
partOri＝model.parts["Original Part"]
elements＝partOri.elements
nodes＝partOri.nodes
labels＝[]
cells＝partRef.cells
for element in elements:
nodeIndex＝element.connectivity
center＝np.array([0.0,0.0,0.0])
for index in nodeIndex:
center+＝nodes[index].coordinates
center/＝20
findCell＝cells.findAt((center,),printWarning＝False)
iflen(findCell):
labels.append(element.label)
partOri.Set(elements＝elements.sequenceFromLabels(labels＝labels),name＝"Set-Change")
Wherein "Model Name" is a Model Name in ABAQUS, "Reference Part" is a Part Name in ABAQUS that is the boundary of the ideal Model for the voxelization, and "Original Part" is an independent grid Part Name in ABAQUS that requires the voxelization. The screening conditions can be adjusted according to the different using units, and a statement of 'center/=20' is used for the C3D20R unit. Units inside the ideal material boundary after script execution, i.e., units that require attribute reassignment, are written into the Set-Change.
(2) Test data processing
According to the finite element calculation model established in the mode, the structural integrity is guaranteed, and the regularity of grids of the integral area of the crack front edge girth is guaranteed. Thus, more accurate crack tip related parameters can be obtained, here exemplified by stress triaxial at the crack front, the Lode angle and the J-integral.
The stress triaxial concrete expression is as follows:
wherein: sigma (sigma) m For hydrostatic stress, sigma e Is Mises equivalent stress as follows:
wherein: sigma (sigma) 1 、σ 2 、σ 3 The first principal stress, the second principal stress and the third principal stress.
The specific expression of the Lode angle is as follows:
wherein ζ is a Lode angle-related parameter, and the expression is:
and the principal stress in each direction of the crack tip can be extracted by taking the crack front edge node as a path, and the calculation of the stress triaxial degree and the Lode angle can be realized through the formula.
The calculation and extraction of J integral are realized by an ABAQUS built-in program, and can be directly output from the dat file of ABAQUS through the calculation of the lane integral.
(3) Stress redistribution due to material mismatch
In a three-dimensional isotropic material open crack model, the values of the stress parameters along the crack front are substantially unchanged except for a very small area near the surface of the model, as can be confirmed in many related studies. The addition of the complex structure causes the system to have elastic mismatch effect, so that the stress distribution is redistributed, and the stress distribution along the front edge of the crack is not uniform any more and changes along with the change of the structure.
Under the conditions of H/w=5, b/w=1, a/w=0.4, the calculation was performed at V f Mises stress along crack front, stress triaxial, lode angle and J integral taken at =40%, 50%, 60%, and the results are shown in FIGS. 5-8, and it is clearly observed that the calculated results are identical to those of the homogeneous isotropic material (V f =0%) difference. In a study based on the conventional homogeneity theory, the results obtained are similar to V f The results in =0% showed strong consistency except in limited areas of the model surface, and the effect of the fiber on crack front stress state and fracture parameter generation could not be accurately described. In the model built by the invention, the relevance of Mises stress, stress triaxial degree, lode angle and J integral curve change and model structure change can be clearly observed, the stress redistribution caused by material mismatch is more in line with the actual stress state in the composite material, and the curve and structure relevance can be explained through the existing theory and experiment.
Although the embodiments of the present invention and the accompanying drawings have been disclosed for illustrative purposes, those skilled in the art will appreciate that: various substitutions, changes and modifications are possible without departing from the spirit and scope of the invention and the appended claims, and therefore the scope of the invention is not limited to the embodiments and the disclosure of the drawings.
Claims (4)
1. A three-dimensional finite element modeling method for a crack-containing continuous fiber reinforced resin matrix composite material is characterized by comprising the following steps of: the method comprises the following steps:
1) And (3) establishing a matrix model: adopting finite element analysis software ABAQUS to build a three-dimensional finite element model with required corresponding size, and inputting the elastic modulus of the matrix materialEAnd poisson's ration；
2) And (3) building a fiber model: building a three-dimensional model of an individual fiber structure according to the composite structure, and inputting the elastic modulus of the composite materialEModulus of shearGAnd poisson's rationSetting material orientation according to the fiber arrangement state of the composite material, and combining a matrix model and a fiber model by using a Merge function built in ABAQUS software to form a complete structure model of a main body area;
3) Establishing a lane integral area model: establishing a girth integration area model corresponding to the girth integration area according to the shape and the size of the crack front, cutting off the corresponding position of the crack front in the combined complete structure model by using a Cut function, and combining the independent girth integration area model with the complete structure model after cutting off treatment by adopting a Tie binding mode to form a three-dimensional model;
4) Adding prefabricated cracks for the combined three-dimensional model according to calculation requirements by using a built-in Crack function of ABAQUS software;
5) Grid division is carried out on a main body area of the three-dimensional model by adopting a 10-node tetrahedral unit with reduced integral, grid division is carried out on a lane integral area of the three-dimensional model by adopting a 20-node hexahedral unit with reduced integral, and grids at crack tips are encrypted and singular units are introduced, so that a focusing ring type grid is adopted;
in the step 5), the main body area is meshed in a free mesh mode; the gird integrating area is subjected to grid division in a mode of sweeping grids; a singular unit is introduced at the tip of the crack, one surface at the front edge of the contact crack collapses, and the middle nodes on four sides adjacent to the collapsed surface move to 1/4 of the split point towards the collapsed surface;
6) Load and boundary conditions are set according to the calculated requirements, an inp file is generated by using a data checking function, and the inp file is reintroduced into ABAQUS to obtain an independent grid model;
7) Voxel processing is carried out on the lane integral region by using a Python script, the fine annular grid is divided according to the space coordinates, so that the corresponding region of the matrix material and the corresponding region of the fiber material are distinguished, and the independent grids of the corresponding regions are assigned with material properties and material directions;
8) And (5) keeping other conditions of the imported independent grid model unchanged, and calculating the related parameters of the finite element according to the requirement.
2. The method for three-dimensional finite element modeling of a crack-containing continuous fiber reinforced resin matrix composite material according to claim 1, wherein the method comprises the following steps of: the three-dimensional model of the original fiber structure is reserved in the step 2) for the subsequent voxelized Python script to call, and the elastic modulus of three directions are independently input for the anisotropic fiber materialE 11 、E 22 、E 33 Shear modulus in three directionsG 12 、G 13 、G 23 Poisson's ratio in three directionsv 12 ，v 13 ，v 23 。
3. The method for three-dimensional finite element modeling of a crack-containing continuous fiber reinforced resin matrix composite material according to claim 1, wherein the method comprises the following steps of: the main body area is selected as a main surface in the step 3), and the lane integral area is a secondary surface.
4. The method for three-dimensional finite element modeling of a crack-containing continuous fiber reinforced resin matrix composite material according to claim 1, wherein the method comprises the following steps of: in the step 7), a Python script is used for screening an independent grid model, a three-dimensional model is independently established as a screening boundary, for the division of a girth integration area, a three-dimensional model of an original fiber structure is used, the Python script adjusts screening conditions according to units used by the grid model, for 20 node hexahedral units used by the girth integration area, the space coordinates of all 20 nodes are extracted, the acquired node coordinates are averaged, and the obtained result is used as the core coordinates of the grid unit; and then dividing the captured core coordinates of the grid cells by using the target area continuous boundary parts established in advance, and compiling grids with the core coordinates in the target area boundary to realize the giving of the attribute of the part of cells and realize the conversion from continuous boundaries to discrete boundaries.
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