Abstract
The simulation model represents the microstructure that can accurately analyze and predict composites’ micro-stresses and mechanical properties. The conventional representative volume element (RVE) model can only contain one single-particle form. It makes that all the particles in the simulation model have the same shape, which is significantly different from actual particles. In the present study, four typical particle-modeling methods were adopted to establish geometric models to analyze the particle morphology and RVE size selection rules. Particles with the same granularity and similar volume were selected to generate RVE models with randomly distributed particles to predict the mechanical properties and analyze the micro-stress. The micro-stress distribution of the matrix and particles conformed to the rule of normal distribution, while the stress of the interphase does not conform to this law. The particle morphology has a negligible effect on the stress distribution of the matrix; however, it has a significant influence on the stress distribution of particles and interphases, especially during plastic deformation. Furthermore, the micro-stress of composites containing nanoparticles also conforms to the above law, but the stress of the interphase is more minor, and the stress of particles is more dispersed than composites with micron particles.
1 Introduction
Particulate-reinforced metal matrix composites (PRMMCs) disperse particulate-reinforced particles in a continuous metal matrix to obtain superior mechanical properties over matrix materials [1]. PRMMCs have been extensively used in the aerospace, automotive, and aviation industries because of their high strength, wear resistance, high-temperature resistance, and low density [2,3]. Most of the mechanical properties of PRMMCs are significantly determined by the properties and proportion of reinforced particles, metal matrix, and the interface between the particles and matrix. In addition, the morphology, size, and distribution of particles significantly affect the micro-stress [4,5]. The properties of composites are mainly explored using experimental, analytical, and simulation methods.
In general, experimental methods are the most direct and effective methods to verify the properties of composites, and thus, many studies have adopted practical methods. Some researchers use experimental methods to study the effect of particle size and volume fractions on composites’ mechanical properties and fracture behavior [6,7,8]. In addition, the microstructures, interface, and mechanical properties of composites are related to the preparation processes [9,10,11,12].
The time and workforce cost of obtaining the influence law of even a single factor through experiments is exceptionally high, whereas establishing a reliable and validated simulation model is not only an effective and economical approach to investigate the mechanical properties but also can obtain some specific data that are difficult to measure experimentally. Many micromechanics theories, such as the Eshelby equivalent particle, Mori–Tanaka (M–T), and strain gradient plasticity methods, have been proposed to predict the properties of PRMMCs and study the microscopic stress mechanism.
Eshelby [13,14] proposed an equivalent particle model, which could solve the problems associated with the elastic mechanics of a single ellipsoid particle located in an infinite matrix without considering the interaction among particles. Weiland et al. [15] accurately predicted the thermal stresses for fiber and whisker-reinforced aluminum alloys under thermal-cycling conditions using an improved Eshelby equivalent particle model. Mori and Tanaka [16] proposed an average stress field method based on the Eshelby equivalent particle model, which considers the interactions among particles. The main problem of the M–T and Eshelby methods is that they can only solve the elastic problem without considering the particle shape and aspect ratio. Hence, the strain gradient plasticity theory was developed to predict particle size dependence. Fleck et al. [17,18,19] developed a phenomenological plasticity law where stresses depended on the strain and strain gradient. Huang et al. [20] improved the strain gradient plasticity theory based on a microscopic mechanism combined with the strain gradient theory. Zhang et al. [21] strengthened the conventional stress–strain expression of the strain gradient theory based on the Taylor dislocation model, which considered the influence of particle size on the strength and rigidity of composites. Cao et al. [22] proposed a modified Taylor-based nonlocal theory of plasticity to quantify the individual contributions of size-dependent geometrically necessary dislocation strengthening of particle-reinforced metal matrix composites.
Although the proposed micromechanics theories could be used to predict the mechanical properties of composites, they had some limitations in analyzing the influence of particle shape, particle distribution, and other factors on the properties and micro-stress of composites. Hence, the finite element method (FEM) combined with the micromechanics theory has been widely used to analyze the properties of PRMMCs, from two-dimensional (2D) models to three-dimensional (3D) models.
Indeed, 2D FEM models have been broadly used to analyze mechanical properties and manufacturing processes because of their high calculation efficiency and modeling convenience. Qin et al. [23] established a representative volume element (RVE) model of composites with different particle shapes, including circles, regular hexagons, squares, and triangles, to study the influence of particle shape on the residual thermal stress and strain field. Xue et al. [24] investigated the impact of particle size on the plastic strengthening effect of PRMMCs using a unit cell model and the strain gradient theory. The simulation and experimental results satisfactorily agreed. Ayyar and Chawla [25] developed a particle random dispersion 2D model to analyze the influence of the particle size, orientation, shape, and distribution on the growth of cracks. Image analysis techniques were used to obtain the cluster size distribution and coefficient of variance in the mean near-neighbor particle spacing. Zhang et al. [26] used a 2D embedded element model and FEM of PRMMCs containing circular particles to explore the influence of interface on the strengthening considering the stiffness and thickness of the interface. Yan et al. [3] adopted a 2D RVE model with a random distribution of circular particles to determine the influence of particle size on the deformation of SiC/Al composites. Yuan et al. [5] used rectangular and elliptical particle 2D RVE models with different particle sizes to simulate the uniaxial tensile test. They found that the shape of particles and interface had a significant influence on the properties of composites. Duan et al. [27] developed a three-phase friction model that considered the effect of matrix adhesion, two-body abrasion, and three-body rolling to improve the simulation accuracy in SiC/Al composite machining using an FEM model of randomly distributed round particles. Wu et al. [28] established a 2D RVE model of SiC/Al composites to investigate the effect of the cutting depth and speed on the surface roughness.
In addition, 2D FEM models can reflect on the 2D particle shape, 2D particle distribution, and volume fraction with high efficiency. In contrast, the 3D FEM can calculate 3D realistic particles, micro-stress, and other complex properties. Spherical and ellipsoidal reinforcement particles were first introduced into the 3D FEM. Meng and Wang [29] adopted a micromechanical FEM with spherical particles arranged on a body-centered cubic distribution to predict the interface strength. Su et al. [30] developed a polyhedral particle generation method to study the relationship between the particle size, particle distribution, volume fraction, and properties of composites. Wu et al. [31,32] used the ANSYS parametric design language to establish FEMs of SiC/PVDF with spherical and polyhedron particles randomly distributed to analyze the influence of SiC particle size and volume fraction on the elastic modulus of composites. Jin and Pelegri [33] modified a random sequential adsorption algorithm to increase the volume fraction of the RVE model. Gao et al. [34,35] used a 3D model with network particle architecture. They found that composites with a particle network architecture exhibited a higher stiffness and strength than a homogeneous distribution. Shao et al. [36] investigated the particle size-dependent flow and interface damage using an axisymmetric unit cell model incorporating the dislocation punched zone model, Taylor-based nonlocal theory of plasticity, and cohesive zone model (CZM). Sheng et al. [37] proposed an advanced numerical method to generate more realistic 3D models for concrete-like particle-reinforced composites with a high-volume fraction, significantly reducing the modeling time compared to the random sequence adsorption method. Recently, they also considered the convexity and concavity of the particles [38].
To establish a realistic microstructure of composites, computerized tomography and 3D reconstruction techniques are commonly used in medicine to create microscopic composites models. Ayyar and Chawla [39] proposed a 3D natural structure microstructure model using a serial section approach and an embedded cell approach to analyze crack debonding and growth. Williams et al. [40] investigated the debonding behavior of an interface using three types of FEMs with different particle shapes, which included reconstructed particles using a continuous slicing method together with ellipsoidal and spherical particles.
The combination of FEM and micromechanics theory can consider the influence of particle shape, proportion, distribution, and size on the behavior of composites and the mutual force between particles and matrix to simulate the actual performance of composites. The 3D FEM has incomparable advantages in analyzing the anisotropic properties and the real stress and damage state of composites considering the real microscopic structure or similar microstructure.
Although many FEMs have been introduced for PRMMCs to investigate the micro-stress and mechanical properties, the shape of particles in RVE models is relatively single and straightforward, entirely different from the actual condition. Therefore, four typical particle modeling methods were adopted in this study, and an analytical geometry theory was derived. The influence of different modeling parameters on the particle volume was analyzed, and a group of parameters with the same particle size and similar volume were selected to establish RVE models with random particle distributions. The RVE model can contain one or four types of particles. The size of RVE models was analyzed by comprehensively considering the RVE volume fraction accuracy, anisotropic mechanical properties, and computational efficiency. The tensile properties of SiC/Al were predicted by applying a uniaxial tensile load to the RVE models, and the micro-stress distributions were analyzed using sub-model boundary conditions at a strain of 0.1 and 1%.
2 Numerical modeling
2.1 Cohesive zone models
Perfectly bonded [41,42], completely de-bonded, damaged interphase [43], adhesion interface, and cohesive interface [29] have been utilized in earlier studies. This study considered the interphase between matrix and particles by introducing CZM. The constitutive equation of the proposed CZM was established according to the traction–separation law, as shown in Figure 1. The traction stress vector
where T is the constitutive thickness of the interface element. Subsequently, the elastic constitutive relations of the CZM can be expressed as
where
Traction–separation law of a cohesive element.
The failure mechanism for the interface involves three stages, including damage initiation, damage evolution, and complete damage. The quadratic stress failure criterion is considered for damage initiation [44]. Damage is assumed to initiate when a quadratic interaction function involving the nominal stress ratio reaches 1, which is represented as
where
where
The damage evolution law describes the rate at which the material stiffness is degraded once the corresponding initiation criterion is reached. The scalar damage variable D monotonically evolves from 0 to 1 upon further loading after damage initiation. The evolution of the damage variable D can be expressed as
where
The fracture energy t
2.2 Material properties
In this study, 20 vol% SiC/Al composites were selected as the test objects. SiC particles behaved as elastic–plastic isotropic solids characterized by their elastic modulus
![Figure 2
Tensile stress–strain curves of Al and SiC/Al [29].](/document/doi/10.1515/ntrev-2022-0112/asset/graphic/j_ntrev-2022-0112_fig_002.jpg)
Tensile stress–strain curves of Al and SiC/Al [29].
2.3 Random particle generation
The morphology of the SiC particles was irregular, and four methods were used to generate different particle geometries, including the Delaunay triangulation method (DTM), polygon extrusion method (PEM), cuboid cutting method (CCM), and ellipsoid method (EM). The particles generated by the first three methods are polyhedral and can be described using the same parameters. The arbitrary particle geometry calculation was performed in MATLAB, and geometry information was saved in files with the same XML format. The particle-generating processes using the first three methods are shown in Figure 3. This particle generation method above can be used for SiC particles and other polyhedral reinforced particles, such as waste glass powder [45].
Schematic diagram of particle modeling: (a) DTM, (b) PEM, and (c) CCM.
DTM is based on the Delaunay triangulation algorithm to generate convex polyhedron particles by vertices that are randomly selected on the surface of a triaxial ellipsoid, where n vertices were selected using the parametric equation of the ellipsoid as follows:
where xi, y
i
, and z
i
are the coordinate values of the ith random point of the polyhedron. R
x
, R
y
, and R
z
are the half-axis lengths of the triaxial ellipsoid.
PEM extrudes the polygon in the X–Y plane along the Z-direction
where
CCM cut off a part of the cuboid by a randomly tangent plane of an ellipsoid inside the cuboid. The lengths of the sides of the cuboid were
where
2.4 RVE models and boundary conditions
The RVE geometry can be created in ABAQUS using a Python script. In addition to the shape and position of the particles, their orientation was random. Each particle added to the RVE model follows a subordinate process. The randomly generated particles are rotated at any angle around the X-, Y-, and Z-axis, respectively. Subsequently, the particle is moved to any position within the matrix boundary, using the geometric center of the particle as the reference point. Moreover, no intersection among particles was allowed during the random placement of particles. The Boolean operation of ABAQUS was employed to judge the intersection between the particles. There is no intersection if the number of cells is increased by one after adding one particle. Otherwise, the particles should be relocated. The advantage of this method is that arbitrary shapes of particles can be considered without considering the complex intersection detection algorithm. Parts of the particles outside the matrix can also be removed using Boolean subtraction. The amount of the matrix occupied by the particles was excised to obtain the geometric model of the matrix utilizing the Boolean operation.
The 3D structural models of 20 vol% SiC/Al composites with reinforced SiC particles were created in the Cartesian coordinate system as shown in Figure 4(d), and the single-particle RVE model was completed as shown in Figure 4(c). Moreover, 4-node linear tetrahedron elements (C3D4) were used to mesh the 3D structural models of the matrix and particles with a mesh size of 0.1 times the particle size. Cohesive elements with zero thickness were inserted between the particles and the matrix interface. The RVE mesh of SiC/Al is shown in Figure 4(e). A schematic representation of the uniaxial tensile load on the global model is shown in Figure 4(a). The regions at X = 0, Y = 0, and Z = 0 are fixed in the X-, Y-, and Z-DOF, respectively, and a displacement load of U along the loading X (Y or Z) direction. The sub-model boundary condition was applied to the sub-RVE models, as shown in Figure 4(b). A uniaxial tensile load was applied to the global model. The sub-model was set with boundary conditions and constraint degrees of freedom perpendicular to each surface of the RVE model.
(a) Uniaxial tensile load of RVE, (b) uniaxial tensile load of global model and sub-model boundary conditions, (c) single-particle RVE geometry, (d) multi-particles RVE geometry, and (e) RVE mesh.
3 Results and discussion
3.1 Particle morphology analysis with different modeling methods
Four particle generation methods were employed in this study, among which three ways were random polyhedral particles, and one method was ellipsoid. The shape of polyhedral particles changes with N, where N DTM (N DTM = 3, 4, 5, …) and N PEM (N PEM = 6, 8, 10, …) represent the number of polyhedron vertices, and N CCM (N CCM = 0, 1, 2, 3, …) indicates the number of initial cuts by random planes. In addition, the particle volume changes with N; thus, k is defined to represent the particle volume as follows:
where
According to the modeling process, the particle volume generated by DTM or PEM increases, and the volume of the CCM particle decreases with an increase in N.
Thus, 200 particles were randomly created for each N (N = 5, 10, 15, 20, 25, 30) to obtain a similar volume of particles produced by different methods, considering the efficiency of particle generation. The tenth maximum value k was selected for DTM and PEM; however, the tenth minimum value k was chosen for CCM. The relationship between N and k is shown in Figure 5(a), and it can also be fitted by a cubic polynomial, as expressed in equations (15)–(17).
(a) N–k curve, (b) particle morphology, (c) histogram of the quantity of face, face edge, and vertex, and (d) histogram of face area and volume.
The particle modeling parameters were determined as k = 0.32, N DTM = 22, N CCM = 20, and N PEM = 6. The created particles are shown in Figure 5(b). The particle shape, created using DTM and CCM, is randomly polyhedral. The particles with a triangular prism shape are created using PEM. The shape of particles generated by EM is spherical, completely different from the other particles. Two hundred particles were generated using the selected parameters. The statistical regularities of the face number of the particle, side number of each face, number of particle vertex, area of each face, and particle volume are analyzed, as shown in Figure 5(c) and (d). The magnitude relationship between the number of faces of particles is DTM > CCM > PEM > EM, and the face number in CCM is random. The magnitude relationship between the average number of sides on each face is CCM > PEM > DTM > EM, in which the faces of particles created by DTM are triangular surfaces. Particles created by PEM are composed of several quadrilaterals and two identical polygonal surfaces. The number of sides of each face in particles created by CCM is uncertain, and significant differences exist in the number of sides between different faces because of cuts. Each face’s average area size relationship is EM > PEM > CCM > DTM, where the particles created by CCM or DTM have smaller areas. The volume of particles produced by different methods is identical, and the average size is EM > CCM > PEM > DTM. Consequently, the particles created in other ways exhibit significant differences in morphology.
3.2 RVE size selection and uniaxial tensile simulation
The size of RVE is related to the accuracy of the geometric and simulation models and calculation efficiency. Therefore, a reasonable RVE size should be considered before simulation analysis. This study considered an RVE containing multiple particles with a length of 10, 15, 20, and 25 µm and the unit cell RVE model. The size of the single-particle RVE was calculated according to the volume of the particle; therefore, the volume fraction is error free. The relationship between the RVE volume fraction and RVE size is shown in Figure 6(a). The volume fraction of RVE is closer to 20% with an increase in the RVE size, whereas the quantity of mesh increases significantly. The mesh quantity was roughly related to the RVE size to the third power, as shown in Figure 6(b). The higher the mesh size of the RVE model, the lower the computational efficiency. The average stress and strain can be calculated using equations (18) and (19). The mean stress corresponding to a strain of 2% was used as the strength standard to analyze the performance of RVE.
where RF
i
is the support reaction force on the fixed surface,
(a) Histograms of different RVE sizes and volume fractions, (b) mesh quantity, (c) stress at a strain of 2%, and (d) tensile stress–strain curve.
Figure 6(c) presents the average stress and error of the RVE model when the strain is 2% in the X, Y, and Z directions. The average stress error in the three directions decreased with an increase in the RVE size. The more significant average stress error of the RVE model by PEM compared with the other three single-particle RVE models is mainly related to the particle shape and orientation. The average stress predicted by the single-particle RVE model at a strain of 2% is smaller than that of the multi-particle RVE model, except for the single-particle RVE model by PEM. Therefore, the final size of RVE is 20 µm, which is four times the size of particles and thus can obtain a higher calculation accuracy and efficiency.
The stress–strain curves of the RVE simulations with different particle morphologies are illustrated in Figure 6(d). The order of the stress corresponding to a strain of 2% is PEM > C4M > CCM > DTM > EM, where C4M is the RVE model with four-particle morphologies and the proportion of each type of particle in C4M is equal. The tensile curves predicted by CCM, DTM, and C4M are comparable to the experimental results. In contrast, the tensile stress obtained by PEM and EM at a strain of 2% is more extensive and smaller than that of the experiment, respectively. The simulation results prove that the shape of particles affects the tensile properties, and the properties of composites can be adjusted by mixing particles of various forms. The stress–strain result predicted by C4M is more suitable for the experimental results.
3.3 Stress distribution with different microparticles
Uniaxial tensile strain loads of 0.1 and 1% were applied to the global model, and the sub-model boundary conditions based on nodes were applied to the sub-RVE models with a particle size of 5 µm, as shown in Figure 4(b). The global model contains a homogeneous material, and thus, its micro-stress is uniform. However, the stress distribution in the RVE model was uneven because of the reinforced particles in the composites.
3.3.1 Stress distribution with elastic deformation
When the strain of the global model is 0.1%, the material deforms elastically. The distribution of the micro-stresses can be described by the ratio of the element volume to the total RVE volume for each stress interval of 1 MPa. The matrix and particle micro-stress distributions of RVEs are demonstrated in Figures 7 and 8, respectively. The stress distribution is completely fitted with a normal distribution, and the coefficient of determination R 2 value is more significant than 0.95.
Matrix micro-stress distribution at 0.1% strain: (a) DTM, (b) CCM, (c) PEM, (d) EM, (e) C4M, and (f) fitting curves.
Particle micro-stress distribution at a 0.1% strain: (a) DTM, (b) CCM, (c) PEM, (d) EM, (e) C4M, and (f) fitting curves.
The expectation μ and standard deviation σ of the normal distribution can represent the mean value of stresses and dispersion of the mean stresses, respectively. The expectations and variance of the matrix stresses do not differ significantly. According to the stress contours of the matrix, the enormous stress is mainly concentrated in the sharper corner of the matrix. The matrix with EM particles has less stress concentration. Besides the parts around the particles, there is immense stress between the two particles.
The order of the expectation of the particle’s stress is
The stress distribution of the interphase does not conform to the normal distribution. The histograms of the interphase are drawn at intervals of 50 MPa, and its longitudinal axis is the proportion of the interphase area within the stress range to the total interphase area, as shown in Figure 9(a)–(e). The mean stress of the interphase is shown in Figure 9(f), and its order is
Interphase micro-stress distribution at a tensile strain of 0.1%: (a) DTM, (b) CCM, (c) PEM, (d) EM, (e) C4M, and (f) mean stress of interphase.
It can be obtained from the micro-stress distribution law of RVE models with different particle shapes under 0.1% strain that particle morphology affects the micro-stress distribution. At 0.1% strain where the composites are elastic deformation, the particle shape has little effect on the micro-stress distribution of the matrix, but it will affect the stress state of the particles and interphase. The PEM-shaped particles make the particle micro-stress larger and more dispersed. In contrast, the EM-shaped particles have a smaller average micro-stress of particles and relatively uniform distribution. The influence of the particle shape of CCM and DTM on the micro-stress is between that of PEM and EM.
The micro-stress distribution laws of particles are contrary to the interphase’s stress distribution. Thus, when the micro-stress of particles is more minor, the stress of interphase will be more immense, such as RVE with EM particles compared with PEM particles.
The micro-stress distribution of composites can be improved by mixing four types of particles into one RVE model, as shown in Figures 7(e) and 8(e). The enhancement of the tensile properties of composites is mainly realized by the influence of the particle shape on the bearing capacity of particles.
3.3.2 Stress distribution with plastic deformation
Plastic deformation occurs when the tensile strain of the global model reaches 1%. The micro-stress distributions of the matrix and particles for different RVEs are illustrated in Figures 10 and 11. The R 2 values of the particle’s stress distributions were more than 0.95; however, that of the matrix stress distribution was less than 0.8.
Matrix micro-stress distribution at a tensile strain of 1%: (a) DTM, (b) CCM, (c) PEM, (d) EM, (e) C4M, and (f) fit curves.
Particle micro-stress distribution at 1% strain: (a) DTM, (b) CCM, (c) PEM, (d) EM, (e) C4M, and (f) fit curves.
The μ and σ values of the fitting matrix stress normal distribution are entirely similar, indicating that the micro-stress distribution law of the matrix is slightly related to the particle morphology. According to the stress contours of the matrix, large stress exists in most areas of the matrix, but the matrix stress around the particles becomes more complex because of particle morphology and distribution. According to the stress contours of the matrix, it can be seen that the stress of the matrix around the particles is smaller, while the stress of the rest part is the same, and plastic deformation has occurred.
Although the shape of the particles will make the matrix stress around the particles more complex, it has no apparent influence on the stress distribution of the matrix on the whole. It greatly influences the mean stress and stress dispersion of the particles themselves as shown in Figure 11. The order of the expectation of particle stress is
As can be seen from Figure 6(d), the stress value predicted by the PEM model at 1% strain is the largest, while that predicted by the EM model is the smallest. This is because when under the same strain conditions, the matrix stress is basically the same, and the PEM-shaped particles can bear more stress load. The results predicted by the C4M model are most consistent with the experimental results, because the more particle shapes are considered, the closer the RVE model is to the real microstructure of the composites.
The histograms of the interphase are drawn at intervals of 100 MPa, and its longitudinal axis is the proportion of the interphase area within the stress range to the total interphase area, as shown in Figure 12(a)–(e). The distribution law of interphase stress at a strain of 1% is the same as that at a strain of 0.1%.
Interphase micro-stress distribution at 1% strain: (a) DTM, (b) CCM, (c) PEM, (d) EM, (e) C4M, and (f) mean stress of interphase.
It can be obtained from the micro-stress distribution law of RVE models with different particle shapes under 1% strain that the form of the particles has a negligible effect on the stress in the matrix. In contrast, it significantly influences the stress distribution of the particles and interphases. The shape of particles can change the stress-bearing capacity of particles to achieve different strengthening effects. However, the particles created by PEM cause excessive and dispersed stress on particles. The micro-stress distribution under a tensile load with EM particles was relatively uniform, but the interphase stress was larger. Particles created using DTM and CCM with similar shapes to EM have a rather dispersed stress distribution and better interphase stress distribution.
3.4 Stress distribution with nanoparticles
Uniaxial tensile strain loads of 0.1 and 1% are also applied to the sub-RVE models with the DTM particles, whose size is 500 nm. The stress–strain curves of different particle sizes and interphase thicknesses are shown in Figure 13. When the interphase thickness of the nanoparticle is the same as that of the micron particle, the predicted stress–strain curve is below the experimental curve. While the interphase thickness is reduced to 0.1 times of microparticle’s interphase thickness, the predicted results are close to the test results and RVE result with DTM microparticles. Thus, the thickness of the interphase of nanoparticles is assumed to be 0.01 μm to analyze the micro-stress distribution.
The stress–strain curves predicted by the RVE with different DTM particle sizes and interphase thickness.
As shown in Figures 14 and 15, the results show that the stress distribution law matrix, particle, and interphase are the same as above. The mean stress of particles, matrix, and interphase is almost the same at 0.1 and 1% strain compared with the RVE with microparticles. The results show that the micro-stress distribution law of composites is related to the shape of particles, but not to the size of particles. The thickness and stiffness of the interphase have a great influence on the properties of the composite. The mechanical properties of the composites can be adjusted by changing the properties of the interphase.
Micro-stress distribution with DTM nanoparticles at 0.1% strain: (a) matrix, (b) particle, and (c) interphase.
Micro-stress distribution with DTM nanoparticles at 1% strain: (a) matrix, (b) particle, and (c) interphase.
4 Conclusion
In this study, four-particle shapes with the same size and similar volume were analyzed to create RVE models. Also, an RVE method including multiple morphological particles was proposed based on the Boolean operation. The tensile properties of SiC/Al composites were predicted, and their micro-stress distributions were analyzed using the RVE models with different particle morphologies. The following conclusions were drawn:
Normal distribution is used to analyze the state of the stress distribution in composites. The micro-stress distribution of the matrix and particles of PRMMCs conforms to the law of normal distribution during elastic and plastic deformations, but the interphase stress distribution does not conform to the normal distribution.
The particle morphology has a negligible effect on the stress distribution of the matrix. However, it significantly influences the stress distribution of particles and interphase, especially during plastic deformation. There is a positive correlation between the average stress and the dispersion of micro-stress of each phase of PRMMCs. The mean stress of particles with different methods is PEM > CCM > DTM > EM. But the average stress of the interphase is the opposite.
The RVE models with simplified particles created by EM or PEM have a significant difference in predicting tensile properties. In contrast, the RVE models containing CCM and DTM particles have high prediction accuracy of tensile properties and excellent internal stress distribution.
The mechanical properties and micro-stress distribution of PRMMCs can be adjusted by mixing particles of various shapes. Novel RVE models containing multi-shaped particles can be used to design the microstructure of PRMMCs with high accuracy.
The particles with similar sizes and volumes established by different methods have apparent differences in morphology. Randomly distributed particles are not representative in the smaller RVE models. By comprehensively considering the volume fraction accuracy, anisotropic mechanical properties, and computational efficiency of different RVE models, the size of RVE models was selected as four times the particle size.
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Funding information: This study was co-supported by the National Natural Science Foundation of China (grant number 51875024), the State Key Laboratory of Virtual Reality Technology Independent Subject (grant number BUAA-VR-16ZZ-07), and CMC Science and Technology Commission National Defense Science and Technology Project Fund (grant number 2019-JCJQ-JJ-266).
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Author contributions: All authors have accepted responsibility for the entire content of this manuscript and approved its submission.
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Conflict of interest: The authors state no conflict of interest.
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