Void configuration under constrained deformation in ductile matrix materials

SiC particle reinforced Al 2025 aluminum alloy composite is used for tensile tests. The ductile fracture by nucleation, growth and coalescence of micro voids, particle cracking and the interfacial debonding under the different constraint conditions, which are obtained by changing the notch radius, is analyzed. The effect of the local constraint on the respective damage phenomenon is analyzed using the axi-symmetric unit cell FE model by changing the local stress triaxiality and side constraint. The results show that the fracture process of the notched tensile bar is simulated well and the damage phenomena agree qualitatively with the experimental ones. Finally the effect of constraint on the void configuration and coalescence is investigated experimentally using three-dimensional fracture surface observations using the SEM (scanning electron microscope) and three-dimensional imaging analysis method. The constraint effect is analyzed by changing the specimen’s shape. The experimental results show that the void aspect ratio is decreased with increases of SiC particle volume fraction in aluminum alloy. The final void volume fraction at fracture also changes by the specimen shape and the material’s structure.     

Failures analysis of particle reinforced metal matrix composites by microstructure based models

This paper discusses the methodology of microstructure based elastic–plastic finite element analysis of particle reinforced metal matrix composites. This model is used to predict the failure of two dimensional microstructure models under tensile loading conditions. A literature survey indicates that the major failure mechanism of particle reinforced metal matrix composites such as particle fracture, interfaces decohesion and matrix yielding is mainly dominated by the distribution of particles in the matrix. Hence, analyses were carried out on the microstructure of random and clustered particles to determine its effect on strength and failure mechanisms. The finite element analysis models were generated in ANSYS, using scanning electron microscope images. The percentage of major failures and stress–strain responses were predicted numerically for each microstructure. It is evident from the analysis that the clustering nature of particles in the matrix dominates the failure modes of particle reinforced metal matrix composites.     

Automatic generation of 2D micromechanical finite element model of silicon–carbide/aluminum metal matrix composites: Effects of the boundary conditions

Two-dimensional finite element (FE) simulations of the deformation and damage evolution of Silicon–Carbide (SiC) particle reinforced aluminum alloy composite including interphase are carried out for different microstructures and particle volume fractions of the composites. A program is developed for the automatic generation of 2D micromechanical FE-models with randomly distributed SiC particles. In order to simulate the damage process in aluminum alloy matrix and SiC particles, a damage parameter based on the stress triaxial indicator and the maximum principal stress criterion based elastic brittle damage model are developed within Abaqus/Standard Subroutine USDFLD, respectively. An Abaqus/Standard Subroutine MPC, which allows defining multi-point constraints, is developed to realize the symmetric boundary condition (SBC) and periodic boundary condition (PBC). A series of computational experiments are performed to study the influence of boundary condition, particle number and volume fraction of the representative volume element (RVE) on composite stiffness and strength properties.     

FRACTURE CHARACTERISTICS OF BOROSILICATE GLASSES REINFORCED BY METALLIC PARTICLES

Abstract— The fracture behaviour of borosilicate glass reinforced by molybdenum and/or vanadium particles has been investigated. For the addition of 5 vol% molybdenum particles, two processing procedures have been tested and the influence of volume fraction of vanadium particles (in the range 2 to 30 vol%) on fracture resistance has been assessed. The use of chevron-notched specimens in three-point bending has been shown to be a reliable method for the evaluation of fracture toughness even at toughness levels of order 0.7 to 1.3 MPa √m. The existence of subtle differences in fracture behaviour of glass-composites having comparable volume fractions of molybdenum particles but obtained by two different processing procedures has been established by statistical treatment of the fracture toughness data. An increase in the volume fraction of metallic particles results in an increase of the fracture resistance and the measured fracture toughness level. Toughening mechanisms which have been identified include both the plastic deformation of particles and the bridging of cracks by ductile particles. Some particle cleavage and debonding has been observed, which indicates that a decrease in particle plasticity, probably induced by processing or due to constraints imposed by the rigid matrix, is responsible for a smaller than expected enhancement of the fracture toughness.     

Failure processes in particulate filled polypropylene

In this paper the common degradation effect of silicon oxide filler on fracture strain and fracture toughness of isotactic polypropylene is investigated by analysing the failure processes in the composite material by microscopic methods. Experiments demonstrate that, although fracture of the polymer regions absorbs considerable energy by plastic deformation, void formation and cracking of the interface between the polymer and the filler usually requires very little energy. These weak interfaces do not resist cracking and are the cause of brittleness in particulate filled systems. The crucial parameters influencing the fracture data of the composite were found to be the volume fraction of the filler and the interfacial adhesion between polymer matrix and particles. As the interfacial fracture energy is usually much smaller than the polymer fracture energy, the composite toughness drops when filler is added. Using a model which describes the individual steps of crack formation and final fracture, an attempt is made to explain the decrease of crack resistance of the polymer matrix with increasing filler fraction and to calculate the fracture energy of the composite by introducing partial values of crack resistance of the matrix and the interface, respectively. In addition, it is discussed how a coarse spherulitic morphology of the matrix, as produced by isothermal crystallization from the melt, can modify this behaviour.     

Stress triaxiality effect on void nucleation in ductile metals

The stress triaxiality effect on the strain required for void nucleation by particle‐matrix debonding has been investigated by means of micromechanical modelling. A unit‐cell model considering an elastic spherical particle embedded in an elastic‐plastic matrix was developed to the purpose. Particle‐matrix decohesion was simulated through the progressive failure of a cohesive interface. It has been shown that the parameters of matrix‐particle cohesive interface are correlated with macroscopic material properties. Here, a simple relationship for the maximum cohesive opening at interface failure as a function of material fracture toughness and yield stress has been derived. Results seem to confirm that, increasing stress triaxiality, the strain at which void nucleation is predicted to occur decreases exponentially in a similar way as for fracture strain. This result has substantial implications in modelling of ductile damage because it indicates that if the stress triaxiality is high enough, ductile fracture can occur at plastic strain lower than that necessary to nucleate damage for moderate or low stress triaxiality regime.     

Numerical analysis on the effects of particle configuration on the damage and mechanical properties of particle reinforced MMCs under dynamic compression

Three finite element (FE) models were constructed based on a typical SEM micrograph of particle reinforced metal matrix composites (PRMMCs) in this paper. These models had similar particle distribution but different particle configuration, and were used to investigate the effects of particle configuration on the damage evolution and mechanical properties of PRMMCs under dynamic compression. The calculating results showed that the damage was pronounced in particle corners and matrix ligaments between closely aligned particles, and it was more severe in the regions of particle clusters. The irregular particles share high loads, and they are prone to be damaged during dynamic deformation of PRMMCs. By smoothing the particle surfaces, the yield strength and initial strain hardening of PRMMCs were reduced, whereas the strain hardening at large strain deformation was enhanced. These effects of particle configuration on the damage and effective properties of PRMMCs were promoted by increasing the strain rates.     

Failure of cemented granular materials under simple compression: experiments and numerical simulations

We investigate the strength and failure properties of a model cemented granular material under simple compressive deformation. The particles are lightweight expanded clay aggregate beads coated by a controlled volume fraction of silicone. The beads are mixed with a joint seal paste (the matrix) and molded to obtain dense cemented granular samples of cylindrical shape. Several samples are prepared for different volume fractions of the matrix, controlling the porosity, and silicone coating upon which depends the effective particle–matrix adhesion. Interestingly, the compressive strength is found to be an affine function of the product of the matrix volume fraction and effective particle–matrix adhesion. On the other hand, it is shown that particle damage occurs beyond a critical value of the contact debonding energy. The experiments suggest three regimes of crack propagation corresponding to no particle damage, particle abrasion and particle fragmentation, respectively, depending on the matrix volume fraction and effective particle–matrix adhesion. We also use a sub-particle lattice discretization method to simulate cemented granular materials in two dimensions. The numerical results for crack regimes and the compressive strength are in excellent agreement with the experiments.     

Anisotropic ductile fracture of Al 2024 alloys

The anisotropic fracture of the 2024-T351 aluminium alloy is investigated using a micromechanics-based damage model accounting for the effect of the void aspect ratio and void distribution. The 2024-T351 Al alloy contains precipitation free bands in which most void nucleating particles are located. The presence of these bands, which are parallel to the rolling direction, primarily controls the distribution of damage and overall fracture anisotropy. The primary void nucleating particles also present a preferential elongation in the rolling direction. These key microstructural features have been determined using quantitative characterisation methods. The effects of void shape and void spacing on the fracture behaviour are elucidated by means of FE cell calculations. FE simulations of cylindrical notched round bars loaded in different orientations are made and compared with experimental data, allowing a better understanding of the damage process as well as the limitations of the modelling approach.     

Polymers toughened with rubber microspheres: an analytical solution for stresses and strains in the rubber particles at equilibrium and rupture

Large strains in rubber toughened polymers cause void formation and growth in the rubber particles and yielding in the matrix. Void formation usually precedes plasticity in the matrix around the particle and previous papers have proposed models for the relationship between rubber surface energy, volume strain energy and void growth. In this paper, it is shown that another volume criterion must also be satisfied arising from the fact that in all these models, no decohesion is allowed at the particle-matrix interface. A fracture mechanics approach, where linear and nonlinear elasticity are assumed for the matrix and the rubber particle, respectively, is used to define a void formation criterion depending on the rubber fracture surface energy. After formation, the stability of the void is examined, taking into account the volume conservation between matrix and particle and the stress due to surface tension when the void size is very small. A size effect is observed, indicating that voids cannot grow in small particles. The required value of fracture energy in a particle on a microscopic scale is discussed.     

高体积含量颗粒增强复合材料的一个细观力学模型Ⅱ: 弹塑性与损伤分析

在高体积含量颗粒增强复合材料细观弹性分析的基础上, 引入了细观塑性和细观损伤模型: 基体用服从Von Mises 屈服准则的理想弹塑性材料模拟, 用沿圆柱形基体轴线方向的平均应力(即对称面上的应力) 来判断基体的屈服, 并将基体的塑性部分简化为圆柱状轴对称区域。建立了基体和颗粒/ 基体界面统一的损伤准则, 该准则同时考虑了最大应变和三轴应力的影响, 通过对细观塑性和细观损伤在空间取向上的平均, 建立了材料宏观模量的折减法则。用该细观力学模型, 数值模拟了一种实际金属基复合材料的强度实验, 理论模型与实验结果吻合。      

Effects of particle clustering on the tensile properties and failure mechanisms of hollow spheres filled syntactic foams: A numerical investigation by microstructure based modeling

Particle clustering originated from manufacturing process is thought to be one of the critical factors to the mechanical performance of hollow spheres filled syntactic foams. Although experimental evidence provides a qualitative understanding of the effects of particle clustering on the mechanical properties of syntactic foams, a quantitative assessment cannot be made in the absence of an appropriate micromechanical modeling strategy. In this study, three-dimensional microstructures of syntactic foams with different degrees of particle clustering were reconstructed based on random sequential adsorption (RSA) method. Three-phase finite element models considering the progressive damage behavior of the microsphere–matrix interface were accordingly developed by means of representative volume element (RVE) to quantitatively investigate the effects of particle clustering on the tensile properties and failure mechanisms of syntactic foams. The simulation results indicate that the elastic behavior of syntactic foams is insensitive to the degree of particle clustering, but the strength properties as well as the failure mechanisms are significantly influenced by the degree of particle clustering. From the micromechanical viewpoint, the clustered regions containing higher concentration of microspheres than the average volume fraction would serve as crack initiation sites due to stress concentration, and consequently lead to a negative effect on tensile strength, fracture strain, and interfacial damage of syntactic foams.     

Dilatational bands in rubber-toughened polymers

A theory is advanced to explain the effects of rubber particle cavitation upon the deformation and fracture of rubber-modified plastics. The criteria for cavitation in triaxially-stressed particles are first analysed using an energy-balance approach. It is shown that the volume strain in a rubber particle, its diameter and the shear modulus of the rubber are all important in determining whether void formation occurs. The effects of rubber particle cavitation on shear yielding are then discussed in the light of earlier theories of dilatational band formation in metals. A model proposed by Berg, and later developed by Gurson, is adapted to include the effects of mean stress on yielding and applied to toughened plastics. The model predicts the formation of cavitated shear bands (dilatational bands) at angles to the tensile axis that are determined by the current effective void content of the material. Band angles are calculated on the assumption that all of the rubber particles in a band undergo cavitation and the effective void content is equal to the particle volume fraction. The results are in satisfactory agreement with observations recorded in the literature on toughened plastics. The theory accounts for observed changes in the kinetics of tensile deformation in toughened nylon following cavitation and explains the effects of particle size and rubber modulus on the brittle-tough transition temperature.     

Modelling macroscopic imperfections for the prediction of flow localization and fracture

Ductile materials subjected to plastic deformation experience the different stages of void nucleation, growth and coalescence that eventually lead to ductile fracture. Several models have been proposed to assess the influence of this damage on flow localization and fracture. In general, the plastic behaviour is represented by a constitutive model for porous or damaged materials. It is typical to introduce a material imperfection, with porosity higher than average, which evolves up to localization and fracture. However, the void volume fraction in the imperfection is chosen more or less arbitrarily. In the present work, a model that evaluates this void volume fraction more rigorously is developed. The forming limit diagram (FLD) for a dual phase‐steel is calculated using the damage‐based imperfection calculation and validated with experimental results. The effect of void shape on the imperfection porosity level and limit strains in sheet forming is also assessed with the present method.     

Progressive failure monitoring and analysis in aluminium by in situ nondestructive evaluation

Damage initiation and progression in precipitate hardened alloys are typically linked to the failure of second phase particles that result from the precipitation process. These particles have been shown to be stress concentrators and crack starters as a result of both particle debonding and fracture. In this investigation, a precipitate hardened aluminium alloy (Al 2024‐T3) is loaded monotonically to investigate the role the particles have in the progressive failure process. The damage process was monitored continuously by combining the acoustic emission method either with in situ scanning electron microscopy or X‐ray microcomputed tomography to obtain both surface and volume microstructural information. Particles were observed to fracture only in the elastic regime of the material response, while void growth at locations predominantly near particles were found to be associated with progressive failure in the plastic region of the macroscopic response. Experimental findings were validated by fracture simulations at the scale of particle‐matrix interface.     

Internal stresses and voids in SiC particle reinforced aluminum composites for heat sink applications

Metal-matrix composites (MMC) are being developed for power electronic IGBT modules, where the heat generated by the high power densities has to be dissipated from the chips into a heat sink. As a means of increasing long term stability a base plate material is needed with a good thermal conductivity (TC) combined with a low coefficient of thermal expansion (CTE) matching the ceramic insulator. SiC particle reinforced aluminum (AlSiC) offers the high TC of a metal with the low CTE of a ceramic. Internal stresses are generated at the matrix-particle interfaces due to the CTE mismatch between the constituents of the MMC during changing temperatures. Neutron and synchrotron diffraction was performed to evaluate the micro stresses during thermal cycling. The changes in void volume fraction, caused by plastic matrix deformation, are visualized by synchrotron tomography. The silicon content in the matrix connecting the particles to a network of hybrid reinforcement contributes essentially to the long term stability by an interpenetrating composite architecture.     

MMCs with controlled non-uniform distribution of submicrometre Al2O3 particles in 6061 aluminium alloy matrix

Abstract

By employing spherical agglomerate of submicrometre Al₂O₃ particles, a novel composite with controlled non-uniform reinforcement distribution was produced by the squeeze casting technique. The resulting composite has a microstructure in which composite spheres, consisting of Al reinforced by small Al₂O₃ particles, are uniformly distributed in a particle free Al matrix. The response of mechanical properties to the controlled non-uniform distribution of the reinforcement was investigated and the fracture mechanism was discussed in order to understand experimentally the influence of particle clustering on the deformation characteristics. It is demonstrated that a composite with such a controlled microstructure exhibits significant increase in ultimate tensile strength (UTS), elastic modulus, and also a slight increase in ductility compared to composite with a homogeneous microstructure at a given volume fraction. It is proposed that the composite spheres act as units of reinforcement when subjected to deformation and contribute positively to the modulus, UTS, and hardness. The higher ductility is attributed to the extensive ductile deformation of the Al matrix. In addition, the highly restrained deformation observed in the interagglomerate region can also be beneficial to the high strength.     

Effects of particle plasticity characteristics on local interface stress in particle reinforced composite during uniaxial tension

For elastoplastic particle reinforced metal matrix composites, failure may originate from interface debonding between the particles and the matrix, both elastoplastic and matrix fracture near the interface. To calculate the stress and strain distribution in these regions, a single reinforcing particle axisymmetric unit cell model is used in this article. The nodes at the interface of the particle and the matrix are tied. The development of interfacial decohesion is not modelled. Finite element modelling is used, to reveal the effects of particle strain hardening rate, yield stress and elastic modulus on the interfacial traction vector (or stress vector), interface deformation and the stress distribution within the unit cell, when the composite is under uniaxial tension. The results show that the stress distribution and the interface deformation are sensitive to the strain hardening rate and the yield stress of the particle. With increasing particle strain hardening rate and yield stress, the interfacial traction vector and internal stress distribution vary in larger ranges, the maximum interfacial traction vector and the maximum internal stress both increase, while the interface deformation decreases. In contrast, the particle elastic modulus has little effect on the interfacial traction vector, internal stress and interface deformation.     

Numerical modelling of particle distribution effects on fatigue in Al–SiCp composites

Various reports in the literature have highlighted the effects of particle distribution on the fatigue behaviour of particulate reinforced metal matrix composites (PMMCs), although few attempts have been made at modelling such effects. A micromechanical understanding of the effects of clustering on short crack growth behaviour in Al–SiC_p composites has been achieved via finite element modelling. Comparison of preliminary models with the literature has shown that shielding/anti-shielding effects were significantly affected by the relative sizes of the particle and the overall model such that, when edge effects were removed, a crack was predicted to be accelerated rather than decelerated as it propagated through closely spaced pairs of particles. Consistent differences were identified between models with homogeneous versus clustered particle arrangements in terms of crack path morphologies and local crack–tip stress intensity fluctuations. Furthermore, predicted influences of clustering on growth rates in the numerical models were found to be consistent with previous experimental results (i.e. growth rates rose with increased clustering), demonstrating that load transfer effects associated with changes in particle distribution may play a direct role in controlling the growth of short cracks in these materials.     

Fracture Behavior of Particle Reinforced Metal Matrix Composites

The contributions of the reinforcement volume fraction and annealing temperatures to crack opening force and propagation energy are systematically studied by three point bending tests and by SEM investigations. The bending test data show that for the same reinforcement volume fraction, 2618 and 7075 Al composites require much higher force to open the cracks than 6061 matrix. This relates to the much higher levels of solute elements which causes matrix hardening. Studies reveal that the energy absorption level of the materials during crack propagation depends on both matrix strength and ductility which relates to the reinforcement volume fraction, composition and heat treatment conditions. Large deformation zones are found in front of the crack tip before crack propagation which indicate a ductile failure mode for the composites. Studies also reveal that cracks initiate generally at the particle/matrix interfaces for the low volume fraction reinforced composites. However, for the high volume fraction reinforced composites, crack initiation has been found from both reinforcement/matrix interfaces and broken particles. This indicates that increasing reinforcement volume fraction and matrix strengthening tend to change the fracture mode from interface debonding to particle cleavage cracking.