Method for constructing finite discrete element model of composite material based on micrometer indentation experiment
By combining micrometer indentation experiments and K-means clustering analysis with inversion calculations and Cohesive element insertion, a finite discrete element model of composite materials was constructed. This solved the problem of simulating mechanical heterogeneity in traditional modeling methods and achieved higher-precision damage simulation of composite materials.
Patent Information
- Application Number
- CN202511609082.4
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2025-11-05
- Publication Date
- 2026-02-06
AI Technical Summary
Existing technologies struggle to accurately simulate the mechanical heterogeneity of composite materials caused by component interface effects. Traditional modeling methods are costly and cannot reflect the impact of local performance differences on fracture behavior. Continuous medium models are also difficult to simulate crack propagation in brittle composite materials.
A method based on micrometer indentation experiments was adopted. The phase materials of the composite material were divided by K-means clustering analysis. The elastic, plastic and brittle parameters of each phase were calculated by inversion to construct a finite discrete element model. The finite element model was then transformed into a finite discrete element model by inserting Cohesive elements.
It improves the precision and accuracy of simulating the damage evolution mechanism of composite materials, enabling realistic simulation of the damage and failure process of materials, and enhancing the reliability and accuracy of simulation results.
Smart Images
Figure CN121483449A_ABST
Abstract
Description
Technical Field
[0001] This invention belongs to the field of finite discrete element model construction technology for composite materials, specifically relating to a method for constructing a finite discrete element model for composite materials based on micrometer indentation experiments. Background Technology
[0002] The development of modern high technology is inseparable from composite materials. The depth of research and the breadth of application of composite materials, as well as the speed and scale of their production development, have become important indicators for measuring a country's scientific and technological advancement. The establishment of composite material models is a core foundation for revealing multi-scale performance coupling mechanisms, supporting cost reduction and efficiency improvement in engineering design, and driving innovation in new materials. However, the mechanical heterogeneity of composite materials due to component interface effects makes it difficult to simulate damage in composite materials.
[0003] Currently, traditional modeling methods require the separation and extraction of each phase component for individual testing, which is costly and damages the original material structure; macroscopic homogenization models cannot reflect the impact of local performance differences on fracture behavior. While existing microindentation techniques can obtain local mechanical responses in situ, they are only used for material performance calibration and have not yet been deeply coupled with multiphase identification and fracture prediction. Furthermore, continuous medium models struggle to simulate crack propagation in brittle composite materials. Summary of the Invention
[0004] This invention aims to provide a method for constructing a finite discrete element model of composite materials based on micron-indentation experiments. The test operation is simple and convenient, and the model is accurately established. It solves the problem that the mechanical heterogeneity of composite materials caused by component interface effects makes the damage evolution mechanism extremely complex, and traditional models are unable to accurately reflect the mechanical properties and failure mechanism of composite materials.
[0005] Therefore, the technical solution adopted in this invention is: a method for constructing a finite discrete element model of composite materials based on micron-indentation experiments, comprising the following steps:
[0006] Step S1: Grind and polish the composite material sample until the surface roughness meets the requirements for micron-level indentation testing; select any test area on the surface of the composite material sample, perform micron-level indentation testing, and calculate the reduced modulus E of each indentation point representing that area based on the load-displacement curve obtained from the micron-level indentation test. r Hardness H; microscopic observation of each indentation point and calculation of the average area A of the indentation point.
[0007] Step S2, due to the material's reduced modulus E r There is a direct proportional relationship between the hardness H and the mechanical parameter (E). i H iUsing the feature vector as an example, a data matrix is constructed. K-means clustering analysis is used to classify the composite material into weak phase, intermediate phase, and strong phase materials according to the micromechanical properties. Then, based on the classification results of the K-means algorithm, the indentation curves of each phase material are extracted, and the elastic parameters, plastic parameters, and brittleness of the phase are calculated based on the indentation curves.
[0008] Step S3: Based on the contact stiffness S and residual depth h obtained from the mechanical properties and indentation curve characteristics of each phase material above... f Maximum indentation depth h max For each phase material, the elastic modulus E and the yield strength Y are elastic parameters. n Strength coefficient R, elastic stiffness K of the cohesive element in the brittle parameter c , traction force T, failure displacement d f Inversion calculations were performed to obtain the elastic, plastic and brittle parameters at the microscale of each phase material, and a single-phase material micron-indentation model was constructed based on the above parameters.
[0009] Step S4: The proportion of the number of indentation curves corresponding to each phase material after classification to the total number of indentation curves is taken as the content proportion of each phase material in the composite material; a large-size multiphase material micro-indentation model is constructed, which is composed of n phase materials. The phase materials in the large-size model are randomly distributed according to the proportion, and the size area of each phase material is the average area A of the indentation points, thus obtaining the composite material model.
[0010] Step S5: Perform appropriate mesh generation on the composite material model components and insert Cohesive elements into each element body to transform the finite element model constructed in step S4 into a finite discrete element model; substitute the elastic parameters, plastic parameters, and brittle parameters of each phase material obtained in step S3 into the finite discrete element model to complete the model construction.
[0011] A further preferred embodiment is that, in step S1, the surface of the composite material is sanded step by step to ensure that the surface roughness meets the requirements of the indentation test, which is a reasonable operation.
[0012] The micrometer indentation test used a 7×7 matrix of points with a 200mN load, and the reduced modulus E of each indentation point representing the region was calculated based on the Oliver-Pharr method. r Hardness H n The indentation points were observed under a magnification of 1000 to 1300 times using SEM, and the average area A of the indentation points was calculated. The parameters were set reasonably.
[0013] More preferably, in step S2, three data points are selected using the K-means clustering algorithm, each data point (E... i H i The three phases (weak, intermediate, and strong) are used as the centroids for clustering mechanical properties, respectively. The K-means algorithm is used for iterative analysis, and the silhouette coefficient M is used as a reference index to select the most reasonable centroid as the corresponding phase's mechanical property cluster centroid. That is, the closer the silhouette coefficient M is to 1, the better the clustering effect, and the closer it is to -1, the worse the clustering effect. In this way, the most reasonable centroid is selected as the corresponding phase's mechanical property cluster centroid, ensuring data accuracy.
[0014] Based on the classification results of the K-means algorithm, the indentation curves belonging to each phase are extracted. Then, the reduced modulus is calculated based on the indentation curves of each phase, and the average value is taken as the elastic modulus E of each phase. The contact stiffness of each phase is calculated based on the indentation curves of each phase, and the average value is taken as the contact stiffness S of each phase. The residual depth is extracted based on the indentation curves of each phase, and the average value is taken as the residual depth h of each phase. f The maximum load is extracted from the indentation curves of each phase, and their average value is taken as the maximum load F of each phase. max The calculated data is reasonable, and the deduction steps are reasonable.
[0015] More preferably, in step S3, a single-phase material micron-indentation model is constructed in ABAQUS. The step for determining the inversion of elastic parameters involves using the reduced modulus E obtained from the indentation experiment as a basis, selecting the Poisson's ratio v (common for this material) as the basic elastic parameter E1 for elastic modulus inversion, inputting the basic elastic parameter E1 into the pre-constructed two-dimensional micron-indentation model, and constructing a fully elastic single-phase material micron-indentation experimental model. Displacement control is then used to press the indenter down to the maximum indentation depth h in the indentation experiment. max The indenter is unloaded until it completely leaves the sample surface. The Y-direction reaction force RF2 and Y-direction displacement U2 of the indenter reference point are exported from the ABAQUS post-processing history output. The U2-RF2 curve is plotted, and the initial 10% of the unloading segment's relevant data is extracted to calculate its tangent slope and obtain the contact stiffness S. i (i=1, 2, 3…n), and compare with the contact stiffness S of the experimental curve. If S i If the value is greater than S, then the input material elastic modulus is reduced to E. i If S i If it is less than S, then increase the input material elastic modulus to E. i Until the nth time, 95% × S ≤ S n If the value is ≤105%×S, then the input material elastic modulus E is considered to be... nThe results meet the experimental characteristics and the requirements of ABAQUS simulation, the calculated data are reasonable, and the deduction steps are reasonable.
[0016] More preferably, in step S3, the step of inverting and determining the plastic parameters involves, based on the determination of the elastic parameters, utilizing the indentation residual depth h f Plasticity parameters are obtained through inversion. The material is assumed to be isotropic, and a common linear elastic power-hardening constitutive relation is selected as the stress-strain relationship. The yield strength Y is set. j (j=1, 2, 3…m) in the range (0.0001×E) n 0.1×E n Within the range of ), and based on the material characteristics, the hardening index k = 0.1, 0.2 … 0.5 is selected. Based on the linear elastic power-law hardening constitutive relation, the strength coefficient R in the plastic stage is calculated. j Based on existing parameters, construct the stress-strain curve C of the material. j The relevant parameters of the plastic region of the curve are substituted into the plastic parameters of the single-phase material with a known elastic modulus. Displacement control is used to press the indenter down to the maximum indentation depth h in the indentation experiment. max The indenter is unloaded until it completely leaves the sample surface. The Y-direction reaction force RF2 and Y-direction displacement U2 of the indenter reference point are exported from the ABAQUS post-processing history output. The U2-RF2 curve is plotted, and the residual depth h of the simulation curve is extracted. fj Residual depth h of indentation experiment f Compare them, if h fj Greater than h f Then reduce the input material yield strength Y i Calculate the strength coefficient R i And the linear elastic power-hardening constitutive relation was reconstructed to obtain the plastic stress-plastic strain curve C. j If h fj Less than h f Then, increasing the input material yield strength Y i Calculate the strength coefficient R i And reconstruct the linear elastic power-hardening constitutive relation; until the nth time, 95%×h f ≤h fn ≤105%×h f Then it is assumed that the input material yield strength Y is at this time. n The results meet the experimental characteristics and the requirements of ABAQUS simulation, the calculated data are reasonable, and the deduction steps are reasonable.
[0017] More preferably, in step S3, the inversion step for the brittle parameters involves globally inserting Cohesive elements into the single-phase material whose elastic and plastic parameters are already determined, based on the finite element model after the elastic and plastic parameters are determined, and using the maximum load F. max Invert the brittle parameters and adjust the traction force T in the Cohesive element. i and the destructive displacement d fi (i=1, 2, 3…n), using displacement control, the indenter is pressed down to the maximum indentation depth h in the indentation experiment. max The indenter is unloaded until it completely leaves the sample surface; the Y-direction reaction force RF2 and Y-direction displacement U2 of the indenter reference point are exported from the ABAQUS post-processing history output, the U2-RF2 curve is plotted, and the maximum load F of the simulated curve is extracted. maxi With the maximum load F of the indentation test max Compare; if F maxi Greater than F max This reduces the cohesive traction force T. i With the failure displacement d fi If F maxi Less than F max This increases the cohesive traction force Ti and the failure displacement d. fi Substitute the brittleness parameter into the inversion and repeat; until the nth time at the brittleness parameter T p E coh n (The elastic modulus of the cohesive unit at the nth time), d fn Below, the F of the simulated curve maxn Satisfy 95%×F max ≤F maxn ≤105%×F max It is believed that the brittleness parameter at this point conforms to the experimental characteristics and the finite-discrete element model has been completed.
[0018] The calculated data is reasonable, and the deduction steps are reasonable.
[0019] More preferably, in step S4, the number of indentation curves for the weak phase, intermediate phase, and strong phase are x, respectively. 弱 x 中 x 强 The total number of indentations X = x 弱 +x 中 +x 强 Then the proportion of each phase k i =x i / X, (i = weak, medium, strong), i.e., k 弱 =Number of weak-phase indentation curves / Total number of indentation curves, k 中 =Number of mid-phase indentation curves / Total number of indentation curves, k强 =Number of strong phase indentation curves / Total number of indentation curves; Based on the size of a single indentation area in SEM, the model is divided into multiple unit cells, each representing a phase. All unit cells are single-phase materials, and the unit cell area should be consistent with the indentation area size A; The area A of the large-size multiphase material micron-indentation model is constructed using ABAQUS. 大 ≥50×A, this multiphase material micro-indentation model consists of n phase materials, where n=A. 大 / A;n 弱 =k 弱 ×n;n 中 =k 中 ×n;n 强 =k 强 ×n; and according to this ratio, the phase materials in the large-size model are randomly distributed to obtain the composite material model, which can be built quickly.
[0020] More preferably, in step S5, the model is divided into multiple unit cells based on the size of a single indentation area under SEM. Each unit cell represents a phase and can be considered as a single-phase material. The size of the unit cell area should be consistent with or similar to the size of the indentation area A. The elastic parameters, plastic parameters, and brittle parameters of each phase material obtained in step S3 are substituted into each phase unit cell of the model component to realize the heterogeneity of the composite material component ratio and phase position, and finally form a finite discrete element model of the composite material with accurate model data.
[0021] The beneficial effects of this invention are:
[0022] (1) Compared with the mechanical heterogeneity of existing composite materials caused by component interface effects, this application constructs a finite discrete element model. Compared with the traditional modeling method, which requires the separation and extraction of each phase component for individual testing, the macroscopic homogenization model cannot reflect the influence of local performance differences on fracture behavior. Based on the indentation curve response characteristics in the micrometer indentation experiment, this application selects different characteristic parameters and calculates elastic parameters, plastic parameters and brittle parameters through the inversion method, so that the simulation results are more in line with reality and further improve the accuracy of the simulation.
[0023] (2) The model in this invention is constructed entirely around the actual micron indentation experiment. The mechanical parameters and component ratios obtained are more suitable for constructing a material finite discrete element model at the micron scale. Compared with other inventions or studies that require multiple experiments to obtain different mechanical parameters or component ratios, and the parameters obtained are more applicable to macroscopic experiments, the model results of this invention are more reliable at the micron scale.
[0024] (3) Compared with the existing finite element simulation of micron indentation experiments, the finite element model is cleverly transformed into a finite discrete element model by inserting Cohesive elements. Cohesive elements can simulate the interaction of multiple materials, thereby avoiding component interface effects. Therefore, it can realistically simulate the process of material damage and failure without being disturbed by the heterogeneity of composite materials. Based on the finite element only considering the elastic-plastic parameters of the material, the brittle parameters of the material are added, which is more in line with reality.
[0025] In summary, the present invention has the advantages of more realistic simulation results, high simulation accuracy, and strong data reliability. Attached Figure Description
[0026] Figure 1 This is an observation diagram of a 200mN 7×7 indentation matrix based on micrometer indentation testing.
[0027] Figure 2 This is a demonstration diagram of the load-displacement curve of the micrometer indentation test.
[0028] Figure 3 This is a flowchart of cluster analysis based on the K-means algorithm.
[0029] Figure 4 This is a schematic diagram of the clustering analysis results based on the K-means algorithm.
[0030] Figure 5 This is a schematic diagram of the indentation curve characteristics.
[0031] Figure 6 This is a flowchart for obtaining the elastic modulus of a single phase suitable for simulation based on the inversion method.
[0032] Figure 7 This is a flowchart of obtaining the yield strength and constitutive relation of a single phase suitable for simulation based on the inversion method.
[0033] Figure 8 This is a flowchart of the process for obtaining cohesive parameters suitable for simulation of a single phase based on the inversion method.
[0034] Figure 9 This is a conceptual diagram of the finite discrete element method for composite materials. Detailed Implementation
[0035] The present invention will be further described below with reference to the embodiments and accompanying drawings:
[0036] Combination Figure 1 — Figure 9 As shown, a method for constructing a finite discrete element model of composite materials based on micrometer indentation experiments is described, with the following specific steps:
[0037] Step S1: Grind and polish the composite material sample until the surface roughness meets the requirements for micron-level indentation testing; select any test area on the surface of the composite material sample, perform micron-level indentation testing, and calculate the reduced modulus E of each indentation point representing that area based on the load-displacement curve obtained from the micron-level indentation test. r Hardness H n Microscopic observation was performed on each indentation point, and the average area A of the indentation points was calculated.
[0038] Step S1.1: Polish the surface of the composite material, such as shale, with sandpaper in stages to ensure that the surface roughness of the shale meets the requirements of the indentation test.
[0039] Step S1.2: Select any test area on the surface of the composite material sample and perform a micron-level indentation test with a 200mN load at 7×7 matrix points. Based on the load-displacement curve obtained from the micron-level indentation test, calculate the reduced modulus E of each indentation point representing the region using the Oliver-Pharr method. r Hardness H n .
[0040] Step S1.3: Use SEM to observe each indentation point under a magnification of 1000 to 1300 times and calculate the average area A of the indentation points.
[0041] Step S2.1, due to the material's reduced modulus E r There is a direct proportional relationship between the hardness H and the mechanical parameter (E). i H i ( ) are used as feature vectors to construct a data matrix.
[0042] Step S2.2, as follows Figure 3 As shown, K-means clustering analysis was used to classify the composite material into weak phase, intermediate phase, and strong phase materials based on its micromechanical properties. Using the K-means clustering algorithm, three particles were selected, namely (E... i H i (i = weak, medium, strong) serves as the centroid for the mechanical properties clustering of the weak, medium, and strong phases.
[0043] Step S2.3: Use the K-means algorithm for iterative analysis, calculate the Euclidean distance from each data point to the centroid, assign it to the cluster to which the nearest centroid belongs, update the centroid, and recalculate the centroid of each cluster as the mean of the data points within the cluster.
[0044] Step S2.4: Using the profile coefficient M as a reference index, the most reasonable centroid is selected as the cluster centroid of the mechanical properties of the corresponding phase. The sample profile coefficient M is calculated by the quantized cohesion and quantized dispersion of each sample. iThe silhouette coefficient M of a cluster is equal to the silhouette coefficient M of each sample in the cluster. i The average value.
[0045] That is, the closer the silhouette coefficient M is to 1, the better the clustering effect; the closer it is to -1, the worse the clustering effect. Repeat step S2.3, calculating the centroid of each cluster as the mean of the data points within that cluster, until M equals or approaches 1. The final result is as follows: Figure 4 As shown.
[0046] Step S2.5: Then, based on the classification results of the K-means algorithm, extract the indentation curves of each phase material, and calculate the elastic parameters, plastic parameters and brittleness of the phase according to the indentation curves.
[0047] Based on the classification results of the K-means algorithm, the indentation curves belonging to each phase are extracted. Then, the reduced modulus is calculated according to the indentation curves of each phase, and the average value is used as the elastic modulus E of each phase to calculate the elastic parameters of that phase.
[0048] The contact stiffness of each phase is calculated based on the indentation curves of each phase, and the average value is used as the contact stiffness S of each phase to calculate the elastic parameters of that phase.
[0049] The residual depth is extracted based on the indentation curves of each phase, and their average values are calculated as the residual depth h of each phase. f This is used to calculate the plasticity parameters of the phase.
[0050] The maximum load is extracted from the indentation curves of each phase, and their average value is taken as the maximum load F of each phase. max This is used to calculate the brittleness of the phase.
[0051] Following the steps above, the data was obtained, and the weakness E was identified. r The Pa is 35 GPa, and H is 1.25 GPa; the middle term E r The Pa is 42 GPa, and H is 1.8 GPa; the strength is E. r The value is 54 GPa, and H is 2.1 GPa.
[0052] Step S3: Based on the contact stiffness S and residual depth h obtained from the mechanical properties and indentation curve characteristics of each phase material above... f Maximum indentation depth h max For each phase material, the elastic modulus E and the yield strength Y are elastic parameters. n Strength coefficient R, elastic stiffness K of the cohesive element in the brittle parameter c , traction force T, failure displacement d f Inversion calculations were performed to obtain the elastic, plastic and brittle parameters at the microscale of each phase material, and a single-phase material micron-indentation model was constructed based on these parameters.
[0053] The following steps take a single mesophase as an example; the method for inverting weak and strong terms is the same.
[0054] Step S3.1: Construct a two-dimensional micro-indentation model using ABAQUS. In this process, according to the ABAQUS modeling workflow, a series of steps are performed, including component construction, material assignment, component assembly, analysis step setting, interaction, boundary condition setting, job setting, and visualization processing.
[0055] Step S3.2: Based on the reduced modulus E obtained from the indentation experiment, the Poisson's ratio v, which is common for this material, is selected as the basic elastic parameter E1 for the elastic modulus inversion.
[0056] Input the basic elastic parameter E1 into the established two-dimensional microindentation model to construct a fully elastic single-phase material microindentation experimental model.
[0057] Displacement control is used to press the indenter down to the maximum indentation depth h in the indentation experiment. max h max The diameter is 2.5 μm, and the pressure head is unloaded until it is completely removed from the sample surface.
[0058] Export the Y-direction reaction force RF2 and Y-direction displacement U2 of the indenter reference point from the ABAQUS post-processing history output, plot the U2-RF2 curve, and extract the relevant data of the initial 10% of the unloading section to calculate its tangent slope and obtain the contact stiffness S. i (i=1, 2, 3…n), and compared with the contact stiffness S of the experimental curve.
[0059] Middle item S 中 It is 231.2 mN / mm, which is the slope of the tangent line at the initial unloading segment. If S i If the value is greater than S, then the input material elastic modulus is reduced to E. i If S i If it is less than S, then increase the input material elastic modulus to E. i .
[0060] elastic modulus E i Input the model and repeat the above steps until, in the nth iteration, 95% × S ≤ S n If the value is ≤105%×S, then the input material elastic modulus E is considered to be... n This meets the requirements of experimental characteristics and ABAQUS simulation.
[0061] The above process is as follows Figure 6 As shown, the final inversion result is: when S n When = 230.87 mN / mm, E n =0.7GPa.
[0062] Step S3.3: Based on the determined elastic parameters, utilize the residual indentation depth h f Plasticity parameters are obtained through inversion. The material is assumed to be isotropic, and a common linear elastic power-hardening constitutive relation is selected as the stress-strain relationship of the material.
[0063] Set yield strength Y j (j=1, 2, 3…m) in the range (0.0001×E) n 0.1×E n Within the range of ), and based on the material characteristics, the hardening index k = 0.1, 0.2 … 0.5 is selected. Based on the linear elastic power-law hardening constitutive relation, the strength coefficient R in the plastic stage is calculated. j Based on the characteristics of the rock material in this experiment, the hardening index was selected as k=0.2.
[0064] Construct the stress-strain curve C of the material based on existing parameters. j The relevant parameters of the plastic region of the curve are substituted into the plastic parameters of the single-phase material with a known elastic modulus. Displacement control is used to press the indenter down to the maximum indentation depth h in the indentation experiment. max h max The diameter is 2.5 μm, and the pressure head is unloaded until it is completely removed from the sample surface.
[0065] Export the Y-direction reaction force RF2 and Y-direction displacement U2 of the pressure head reference point from the ABAQUS post-processing history output, plot the U2-RF2 curve, and extract the residual depth h of the simulation curve. fj Residual depth h of indentation experiment f Compare them.
[0066] If h fj Greater than h f Then reduce the input material yield strength Y i Calculate the strength coefficient R i And the linear elastic power-hardening constitutive relation was reconstructed to obtain the plastic stress-plastic strain curve C. j If h fj Less than h f Then, increasing the input material yield strength is h. fj Calculate the strength coefficient R i And the linear elastic power-hardening constitutive relation was reconstructed to obtain the plastic stress-plastic strain curve C. j ;
[0067] The obtained plastic stress-strain curve C j Substitute this into the ABAQUS model and repeat the above steps until the nth time, 95%×h f ≤h fn ≤105%×h fThen it is assumed that the input material yield strength Y is at this time. n This meets the requirements of experimental characteristics and ABAQUS simulation.
[0068] The final result is the median yield strength Y. n中 The strength is 12 MPa, and the strength coefficient R n中 It is 30.14 MPa.
[0069] Step S3.3, as follows Figure 8 As shown, based on the finite element model with the elastic and plastic parameters determined above, Cohesive elements are globally inserted into the single-phase material with the elastic and plastic parameters already determined. The Cohesive elements simulate the weak surfaces of the material prone to fracture, using the maximum load F from the indentation curve. max Invert the brittleness parameters.
[0070] Adjusting the traction force T in the Cohesive unit i and the destructive displacement d fi (i=1, 2, 3…n), using displacement control, the indenter is pressed down to the maximum indentation depth h in the indentation experiment. max And unload until the pressure head is completely removed from the sample surface.
[0071] Export the Y-direction reaction force RF2 and Y-direction displacement U2 of the pressure head reference point from the ABAQUS post-processor's history output, plot the U2-RF2 curve, and extract the maximum load F from the simulated curve. maxi With the maximum load F of the indentation test max Compare them.
[0072] If F maxi Greater than F max This reduces the cohesive traction force Ti and the failure displacement d. f i; if F maxi Less than F max This increases the cohesive traction force Ti and the failure displacement d. fi Substitute the brittleness parameters into the inversion and perform a new inversion.
[0073] Until the nth time at the brittle parameter T n E coh n (The elastic modulus of the cohesive unit at the nth time), d fn Below, the F of the simulated curve maxn Satisfy 95%×F max ≤F maxn ≤105%×F max It is believed that the brittleness parameter at this point conforms to the experimental characteristics and the finite-discrete element model has been completed.
[0074] The final result is the mid-term traction force T. n中 The failure displacement is d, which is 0.8 MPa. n中 It is 0.01μm.
[0075] Repeat the above steps to perform parameter inversion on the weaknesses and strengths, and finally obtain the following result: Weakness: Elastic modulus E n弱 =0.33GPa, yield strength Y n弱 =7MPa, strength coefficient R n弱 =15.32MPa, traction force T n弱 The failure displacement is d, which is 0.3 MPa. n弱 0.006 μm; Middle term: Elastic modulus E n中 =0.7GPa, yield strength Y n中 =12MPa, strength coefficient R n中 =30.14MPa, traction force T n中 The failure displacement is d, which is 0.8 MPa. n中 0.01 μm; Strengths: Elastic modulus E n强 =1.1GPa, yield strength Y n强 =25MPa, strength coefficient R n强 =48.64MPa, traction force T n强 The failure displacement is d, which is 1.3 MPa. n强 It is 0.015μm;
[0076] Step S4: The proportion of the number of indentation curves corresponding to each phase material after classification to the total number of indentation curves is taken as the content proportion of each phase material in the composite material; a large-size multiphase material micron indentation model is constructed. The multiphase material micron indentation model is composed of n phase materials. The phase materials in the large-size model are randomly distributed according to the proportion, and the size area of each phase material is the average area A of the indentation points, thus obtaining the composite material model.
[0077] The number of indentation curves for the weak phase, intermediate phase, and strong phase are x, respectively. 弱 x 中 x 强 The total number of indentations X = x 弱 +x 中 +x 强 Then the proportion of each phase k i =x i / X, (i = weak, medium, strong), i.e., k 弱 =Number of weak-phase indentation curves / Total number of indentation curves, k 中 =Number of mid-phase indentation curves / Total number of indentation curves, k 强 =Number of strong phase indentation curves / Total number of indentation curves.
[0078] Based on the results, k 弱 = 46%, k 中 =44%, k 强 =10%.
[0079] The size and area A of a large-size multiphase material microindentation model constructed using ABAQUS 大 ≥50×A, this multiphase material micro-indentation model consists of n phase materials, where n=A. 大 / A;n 弱 =k 弱 ×n;n 中 =k 中 ×n;n 强 =k 强 ×n; and according to this ratio, the phase materials in the large-size model are randomly distributed to obtain the composite material model.
[0080] Step S5, as follows Figure 9 As shown, the indentation area A of a single indentation in the experiment was observed and calculated using SEM, and used as the area of each phase unit cell. A finite element model of a specimen of appropriate size was constructed. Based on the unit cell area and the size of the single indentation area under SEM, the model was divided into multiple unit cells. Each unit cell represents a phase. All unit cells are single-phase materials, and the size of the unit cell area should be consistent with the size of the indentation area A.
[0081] Appropriate meshing is performed on the composite material model components, and Cohesive elements are inserted into each element body to transform the finite element model into a finite discrete element model.
[0082] Then, the elastic, plastic and brittle parameters of each phase material obtained in step S3 are substituted into the large-scale model constructed in step S4 to complete the model construction.
[0083] The elastic, plastic and brittle parameters of each phase material obtained in step S3 are substituted into each phase unit of the model component to realize the heterogeneity of the composite material component ratio and phase position, and finally form a finite discrete element model of the composite material.
Claims
1. A method for constructing a finite discrete element model of composite materials based on micron-indentation experiments, characterized in that, Includes the following steps: Step S1: Grind and polish the composite material sample until the surface roughness meets the requirements for micron-level indentation testing; select any test area on the surface of the composite material sample, perform micron-level indentation testing, and calculate the reduced modulus E of each indentation point representing that area based on the load-displacement curve obtained from the micron-level indentation test. r Hardness H; microscopic observation of each indentation point and calculation of the average area A of the indentation point. Step S2, due to the material's reduced modulus E r There is a direct proportional relationship between the hardness H and the mechanical parameter (E). i H i Using the feature vector as an example, a data matrix is constructed. K-means clustering analysis is used to classify the composite material into weak phase, intermediate phase, and strong phase materials according to the micromechanical properties. Then, based on the classification results of the K-means algorithm, the indentation curves of each phase material are extracted, and the elastic parameters, plastic parameters, and brittleness of the phase are calculated based on the indentation curves. Step S3: Based on the contact stiffness S and residual depth h obtained from the mechanical properties and indentation curve characteristics of each phase material above... f Maximum indentation depth h max For each phase material, the elastic modulus E and the yield strength Y are elastic parameters. n Strength coefficient R, elastic stiffness K of the cohesive element in the brittle parameter c , traction force T, failure displacement d f Inversion calculations were performed to obtain the elastic, plastic and brittle parameters at the microscale of each phase material, and a single-phase material micron-indentation model was constructed based on the above parameters. Step S4: The proportion of the number of indentation curves corresponding to each phase material after classification to the total number of indentation curves is taken as the content proportion of each phase material in the composite material; a large-size multiphase material micro-indentation model is constructed, which is composed of n phase materials. The phase materials in the large-size model are randomly distributed according to the proportion, and the size area of each phase material is the average area A of the indentation points, thus obtaining the composite material model. Step S5: Perform appropriate mesh generation on the composite material model components and insert Cohesive elements into each element body to transform the finite element model constructed in step S4 into a finite discrete element model; substitute the elastic parameters, plastic parameters, and brittle parameters of each phase material obtained in step S3 into the finite discrete element model to complete the model construction.
2. The method for constructing a finite discrete element model of composite materials based on micron-indentation experiments according to claim 1, characterized in that: In step S1, the surface of the composite material is sanded stepwise with sandpaper to ensure that the surface roughness meets the requirements of the indentation test. The micron-level indentation test uses a 7×7 matrix of points with a 200mN load. The reduced modulus E of each indentation point representing the region is calculated based on the Oliver-Pharr method. r Hardness H n We used SEM at 1000-1300x magnification to observe each indentation point under microscopic conditions and calculated the average area A of the indentation points.
3. The method for constructing a finite discrete element model of composite materials based on micron-indentation experiments according to claim 1, characterized in that: In step S2, the K-means clustering algorithm is used to select 3 data points, each data point (E i H i The mechanical properties of the weak, intermediate, and strong phases were clustered and analyzed using the K-means algorithm. The silhouette coefficient M was used as a reference index to select the most reasonable centroid as the corresponding phase's mechanical property cluster centroid. A silhouette coefficient M closer to 1 indicates better clustering, while a closer to -1 indicates poor clustering. Based on the K-means algorithm classification results, the indentation curves of each phase were extracted. The reduced modulus was calculated based on the indentation curves, and its average value was used as the elastic modulus E of each phase. The contact stiffness was calculated based on the indentation curves, and its average value was used as the contact stiffness S of each phase. The residual depth was extracted based on the indentation curves, and its average value was used as the residual depth h of each phase. f The maximum load is extracted from the indentation curves of each phase, and their average value is taken as the maximum load F of each phase. max .
4. The method for constructing a finite discrete element model of composite materials based on micrometer indentation experiments according to claim 1, characterized in that, In step S3, a single-phase material micron-indentation model is constructed in ABAQUS. The inversion determination step for the elastic parameters is as follows: using the reduced modulus E obtained from the indentation experiment... r As a foundation, the Poisson's ratio v, which is common for this material, is selected as the basic elastic parameter E1 for elastic modulus inversion. The basic elastic parameter E1 is input into the established two-dimensional micro-indentation model to construct a fully elastic single-phase material micro-indentation experimental model. Displacement control is used to press the indenter down to the maximum indentation depth h in the indentation experiment. max The indenter is unloaded until it completely leaves the sample surface. The Y-direction reaction force RF2 and Y-direction displacement U2 of the indenter reference point are exported from the ABAQUS post-processing history output. The U2-RF2 curve is plotted, and the initial 10% of the unloading segment's relevant data is extracted to calculate its tangent slope and obtain the contact stiffness S. i (i=1, 2, 3…n), compare with the contact stiffness S of the experimental curve, if S i If the value is greater than S, then the input material elastic modulus is reduced to E. i If S i If it is less than S, then increase the input material elastic modulus to E. i (i=1, 2, 3…n); until the nth time, 95%×S≤S n If the value is ≤105%×S, then the input material elastic modulus E is considered to be... n This meets the requirements of experimental characteristics and ABAQUS simulation.
5. The method for constructing a finite discrete element model of composite materials based on micron-indentation experiments according to claim 4, characterized in that: In step S3, the inversion determination step for the plastic parameters involves, based on the determination of the elastic parameters, utilizing the indentation residual depth h. f Plasticity parameters are obtained through inversion. The material is assumed to be isotropic, and a common linear elastic power-hardening constitutive relation is selected as the stress-strain relationship. The yield strength Y is set. j (j=1, 2, 3…m) in the range (0.0001×E) n 0.1×E n Within the range of ), and based on the material characteristics, the hardening index k = 0.1, 0.2 … 0.5 is selected. Based on the linear elastic power-law hardening constitutive relation, the strength coefficient R in the plastic stage is calculated. j Based on existing parameters, construct the stress-strain curve C of the material. j The relevant parameters of the plastic region of the curve are substituted into the plastic parameters of the single-phase material with a known elastic modulus. Displacement control is used to press the indenter down to the maximum indentation depth h in the indentation experiment. max The indenter is unloaded until it completely leaves the sample surface. The Y-direction reaction force RF2 and Y-direction displacement U2 of the indenter reference point are exported from the ABAQUS post-processing history output. The U2-RF2 curve is plotted, and the residual depth h of the simulated curve is extracted. fj Residual depth h of indentation experiment f Compare them, if h fj Greater than h f Then reduce the input material yield strength Y i Calculate the strength coefficient R i And the linear elastic power-hardening constitutive relation was reconstructed to obtain the plastic stress-plastic strain curve C. j If h fj Less than h f Then, increasing the input material yield strength Y i Calculate the strength coefficient R i And reconstruct the linear elastic power-hardening constitutive relation; until the nth time, 95%×h f ≤h fn ≤105%×h f Then it is assumed that the input material yield strength Y is at this time. n This meets the requirements of experimental characteristics and ABAQUS simulation.
6. The method for constructing a finite discrete element model of composite materials based on micron-indentation experiments according to claim 5, characterized in that: In step S3, the inversion step for the brittle parameters involves globally inserting Cohesive elements into the single-phase material with determined elastic and plastic parameters based on the finite element model obtained from the above-mentioned elastic and plastic parameters, using the maximum load F. max Invert the brittle parameters and adjust the traction force T in the Cohesive element. i and the destructive displacement d fi (i=1, 2, 3…n), using displacement control, the indenter is pressed down to the maximum indentation depth h in the indentation experiment. max The indenter is unloaded until it completely leaves the sample surface; the Y-direction reaction force RF2 and Y-direction displacement U2 of the indenter reference point are exported from the ABAQUS post-processing history output, the U2-RF2 curve is plotted, and the maximum load F of the simulated curve is extracted. maxi With the maximum load F of the indentation test max Compare; if F maxi Greater than F max This reduces the cohesive traction force T. i With the failure displacement d fi If F maxi Less than F max This increases the cohesive traction force Ti and the failure displacement d. fi Substitute the brittleness parameter into the inversion and repeat; until the nth time at the brittleness parameter T p E coh n (The elastic modulus of the cohesive unit at the nth time), d fn Below, the F of the simulated curve maxn Satisfy 95%×F max ≤F maxn ≤105%×F max It is believed that the brittleness parameter at this point conforms to the experimental characteristics and the finite-discrete element model has been completed.
7. The method for constructing a finite discrete element model of composite materials based on micrometer indentation experiments according to claim 1, characterized in that: In step S4, the number of indentation curves for the weak phase, intermediate phase, and strong phase are x, respectively. 弱 x 中 x 强 The total number of indentations X = x 弱 +x 中 +x 强 Then the proportion of each phase k i =x i / X, (i = weak, medium, strong), i.e., k 弱 =Number of weak-phase indentation curves / Total number of indentation curves, k 中 =Number of mid-phase indentation curves / Total number of indentation curves, k 强 =Number of strong phase indentation curves / Total number of indentation curves; Based on the size of a single indentation area in SEM, the model is divided into multiple unit cells, each representing a phase. All unit cells are single-phase materials, and the unit cell area should be consistent with the indentation area size A; The area A of the large-size multiphase material micron-indentation model is constructed using ABAQUS. 大 ≥50×A, this multiphase material micro-indentation model consists of n phase materials, where n=A. 大 / A;n 弱 =k 弱 ×n;n 中 =k 中 ×n;n 强 =k 强 ×n; and according to this ratio, the phase materials in the large-size model are randomly distributed to obtain the composite material model.
8. The method for constructing a finite discrete element model of composite materials based on micron-indentation experiments according to claim 7, characterized in that: In step S5, the model is divided into multiple unit cells based on the size of a single indentation area under SEM. Each unit cell represents a phase and can be considered as a single-phase material. The size of the unit cell area should be consistent with the size of the indentation area A. The elastic parameters, plastic parameters, and brittle parameters of each phase material obtained in step S3 are substituted into each phase unit cell of the model component to realize the heterogeneity of the composite material component ratio and phase position, and finally form a finite discrete element model of the composite material.