Heterogeneous and homogenized models for predicting the indentation response of particle reinforced metal matrix composites

In this study, three-dimensional heterogeneous and homogenized finite element models are used to predict the indentation response of particle reinforced metal matrix composites (PRMMCs). The matrix is assumed to have elasto-plastic behavior whereas the particles (uniform in size and spherical in shape) are assumed to be harder than the matrix, and possess linear elastic behavior. The particles (25 % by volume) are randomly distributed in the metal matrix. Two modeling approaches are used. In the first approach, the PRMMC is fully replaced by an equivalent homogenous material, and its material properties are obtained through homogenization using representative volume element approach under periodic boundary conditions. In second approach, a small cubical volume under the indenter is modeled as heterogeneous material with randomly distributed particles, whereas the remaining domain is assigned equivalent material properties obtained through homogenization. The elastic material properties obtained through simulations are found within Hashin–Shtrikman bounds. A suitable size cubical volume consisting of heterogeneities under the indenter is established by considering different cubical volumes so as to capture the actual indentation response. The simulations are also carried out for different particle sizes to establish a suitable particle size. These simulations show that the second modeling approach yields harder indentation response as compared to first modeling approach due to the local particle concentration under the indenter.     

Effect of interface diffusion on the strain and stress stability of particulate reinforced electrostrictive materials

This paper presents an analytical method to solve the creep rate and stress relaxation behaviors of particle reinforced electrostrictive composites induced by the interface diffusion between particle and electrostrictive matrix, subjected to external electric fields. Based on the microstructures evolution theory and electroelastic theory of electrostrictive materials, the thermodynamic equations of creep rate and stress relaxation induced by the interface diffusion are, respectively, deduced and solved. The investigation results show that the strain and stress stabilities of particle reinforced electrostrictive materials can be enhanced by optimizing the shape, stiffness and volume fraction of reinforced particles.     

Creep rupture behaviors of a laser melting deposited TiC/TA15 in situ titanium matrix composite

The creep rupture behaviors of a laser melting deposited in situ TA15 titanium matrix composite reinforced by 10.8 vol.% TiC particulates were investigated at 873 and 923 K. The as-deposited TiC reinforcements were mainly in near-equiaxed and coarse dendritic with a stoichiometry of TiC_0.71. The composite exhibited a superior creep resistance to the monolithic titanium alloy. The creep rupture mechanism was dominated by a mixture of particle cracking, interface debonding and interparticle voiding. Voids nucleated at broken particles, debonded interfaces and interparticle matrix at the initial stage of rupture. The growth, coalescence and transverse linkage of these voids through the matrix contributed to the final failure of the composite. The strengthening in creep resistance of the composite was mainly attributed to the load transfer from the matrix to the particle reinforcements and the refinement of the Widmanstätten matrix.     

Determination of creep parameters from indentation creep experiments: a parametric finite element study for single phase materials

Abstract

This paper explores the possibilities of determining creep parameters for a simple Norton law material from indentation creep testing. Using creep finite element analysis the creep indentation test technique is analysed in terms of indentation rates at constant loads. Emphasis is placed on the evolving stress distribution in front of the indenter during indentation creep. Moreover the role of indenter geometry, size effects and of macroscopic constraints is explicitly considered. A simple procedure is proposed to translate indentation creep results into constitutive creep equations for cases where the dimensions of the tested material are significantly larger than the indenter. The influence of macroscopic constraints becomes important when the size of the indenter is of the same order of magnitude as the size of the testing material. As a striking example for size effects and for macroscopic constraints the indentation creep process in a thin film is analyzed. The results contribute to a better mechanical understanding of indentation creep testing.     

Numerical Study of Creep Damage Behavior of Thin Film/Substrate Systems under Indentation

A numerical study has been performed on the creep damage development of the thin film/substrate systems by the Kachanov‐Rabothov damage law. The emphasis was to study the influence of the modulus ratio of the substrate to the thin film, the size of the indenter and the indentation stress. Results show that two obvious damage zones are found ahead of the indenter. One is at the edge of the indenter, the other is at the interface ahead of the indenter edge. The influence of the modulus ratio of the substrate to the thin film on the indentation damage is not obvious before a certain creep time, and later, the greater modulus ratio of the substrate to the thin film has the smaller damage rate. And the indentation depth rate and the damage rate are also affected by the size of the indenter and indentation stress.     

Effects of random particle dispersion and size on the indentation behavior of SiC particle reinforced metal matrix composites

This study investigates the effects of particle size, volume fraction, random dispersion and local concentration underneath a spherical indenter on the indentation response of particle reinforced metal matrix Al 1080/SiC composites. The ceramic particles in certain sizes and volume fractions were randomly distributed through the composite structure in order to achieve a similar structure to an actual microstructure as possible. The particle size and volume fraction affected considerably indentation depths and deformed indentation surface profiles. The indentation depth increases with increasing particle size, but decreases with increasing particle volume fraction. The experimental indentation depths were in agreement with numerical indentation depths in case the local particle concentration effect is considered. The local particle concentration plays an important role on the peak indentation depth. For small particle sizes and large volume fractions the random particle distribution affects the deformed surface profiles as well as the indentation depths. However, its effect is minor on residual stress and strain distributions rather than levels in the indentation region.     

Statistics for the strength and lifetime in creep-rupture of model carbon/epoxy composites

A theoretical model and experimental data are presented for the strength and lifetime in creep-rupture of unidirectional, carbon fiber/epoxy matrix microcomposites at ambient conditions. The model ‘microcomposites’ consisted of seven parallel carbon fibers (Hercules IM-6) embedded in an epoxy matrix (Dow DER 331 epoxy/No. 26 hardener) and forming an approximately hexagonal array. The results are interpreted by means of the model which involves Weibull distributions for fiber strength, micromechanical stress-redistribution, and power-law, matrix creep around noncatastrophic fiber breaks from which the creep-rupture originates. For the microcomposites, the model yields approximate Weibull strength and lifetime distributions with parameters depending on the various model parameters. Also obtained is a power-law relationship between stress level and lifetime whose exponent depends on the Weibull shape parameter for fiber strength, the creep exponent for the matrix, and the critical cluster size for failed fibers in the microcomposite. The experimental results agree quite well with theoretical predictions though time-dependent debonding appeared to be part of the failure process; this debonding was observed in independent experiments.     

Determination of the creep exponent of a power-law creep solid using indentation tests

Based on dimensional analysis, we analysed the indentation of a rigid indenter into a power-law creep solid for which the relationship between the stress and the strain rate is given by . It is shown that under a described condition the creep exponent n can be determined without invoking the detail knowledge of the indenter profile and the shape of the indented solid. The result reported herein should be useful for interpreting the data of nanoindentation into a power-law creep solid in the case that the indented solid is not a flat half-space and/or the indenter has tip defects. The performance of the simple method to evaluate the creep exponent is examined by using numerical experiments and its limitations also discussed. An erratum to this article can be found at     

Constitutive behaviors of composites with interface debonding: the extended Mori–Tanaka method for uniaxial tension

Debonding of particle/matrix interfaces can significantly affect the macroscopic behavior of composite materials. We have used a nonlinear cohesive law for particle/matrix interfaces to study the effect of interface debonding on the macroscopic behavior of particle-reinforced composite materials subject to uniaxial tension. The Mori–Tanaka method, which is suitable for composites with high particle volume fraction, is extended to account for interface debonding. At a fixed particle volume fraction, small particles lead to the hardening behavior of the composite while large particles yield softening. The interface sliding may contribute significantly to the macroscopic behavior of the composite.     

Finite element analysis of quasi‐static indentation of woven fabric textile composites using different nose shape indenters

The finite element FE analysis of quasi‐static indentation event of various nose shape rigid indenters into woven fabric composite with carbon fiber as reinforcement has been performed and discussed in detail. It was found that indenter nose shape has large influence in terms of absorbed energy, indentation at failure and damage area. The FE software, ABAQUS^® was employed to simulate quasi‐static response of woven composite unit cell. Exhaustive parametric studies have been conducted with an aim to analyze the effect of change in indenter geometry on the indentation response of the woven composite unit cell. The developed FE model for the purpose of validation was compared with available experimental results and was found to be in reasonably good agreement. The failure morphologies, damage shape and damage size were evaluated, compared and deeply discussed for different nose shape indenters. Largest damaged areas were observed for flat and truncated indenters while the smallest for the conical one.     

Micromechanics analysis of particulate-reinforced composites and their failure mechanisms

Stress fields and failure mechanisms have been investigated in composites with particles either surface treated or untreated under uniaxial tension. Previous experimental observation of failure mechanisms in a composite with untreated particles showed that tensile cracks occurred mostly at the polar region of the particle and grew into interfacial debonding. In a composite with surface-treated particles, however, shear yielding and shear cracking proceeded along the interphase-matrix interface at the polar area of the matrix and thus may improve the mechanical behaviour of the material. The finite element calculations showed that octahedral shear stress at the polar and longitudinal areas of the particle treated by coupling agents is much larger than that of materials with untreated particles, and the shear stress distribution around the interface is sensitive to the interphase property. The results suggest that a three-phase model can describe the composites with surface-treated fillers.     

A constitutive model of particulate-reinforced composites taking account of particle size effects and damage evolution

This paper deals with a constitutive model of particulate-reinforced composites which can describe the evolution of debonding damage, matrix plasticity and particle size effects on deformation and damage. An incremental damage model of particulate-reinforced composites based on the Mori–Tanaka’s mean field concept has been extended to consider the particle size effects by using the Nan–Clarke’s simple method. The particle size effect on deformation is realized by introducing dislocation plasticity for stress–strain relation of in situ matrix in composites, and the particle size effect on damage is described by a critical energy criterion for particle–matrix interfacial debonding. For composites containing particles of various sizes, the effects of particle size distribution is incorporated into the model. Influence of debonding damage, particle size and particle volume fraction on overall stress–strain response of composites is discussed based on numerical results.     

Fibre-matrix bond strength studies of glass,ceramic, and metal matrix composites

An indentation test technique for compressively loading the ends of individual fibres to produce debonding has been applied to metal, glass, and glass-ceramic matrix composites; bond strength values at debond initiation are calculated using a finite-element model. Results are correlated with composite longitudinal and interlaminar shear behaviour for carbon and Nicalon fibre-reinforced glasses and glass-ceramics including the effects of matrix modifications, processing conditions, and high-temperature oxidation embrittlement. The data indicate that significant bonding to improve off-axis and shear properties can be tolerated before the longitudinal behaviour becomes brittle. Residual stress and other mechanical bonding effects are important, but improved analyses and multiaxial interfacial failure criteria are needed to adequately interpret bond strength data in terms of composite performance.     

Influence of particle size and debonding damage on an elastic–plastic singular field around a crack-tip in particulate-reinforced composites

This paper deals with the influence of particle size and debonding damage on an elastic–plastic singular field around a crack-tip in particulate-reinforced composites (PRCs). Finite element analysis has been carried out on a crack-tip field in PRCs with debonding damage and containing various sized particles. The finite element method is developed based on a micromechanics model of PRCs by Tohgo et al. (Compos Part A 41:313–321, 2010) which can describe the debonding damage of particles from matrix and the particle size effect on deformation and damage. The influence of particle size and debonding damage on an elastic–plastic singular field around a crack-tip is discussed based on the numerical results. The stress distribution ahead of a crack-tip in the composites shifts upward with decreasing particle size unless the debonding damage develops. In the composites with damage, the debonding damage occurs from a crack-tip and progresses ahead of a crack-tip. The stress distribution shifts downward in the damage zone. It is concluded that the crack-tip field is strongly affected by the particle size and debonding damage.     

Effect of loading rate on the creep behaviour of epoxy resin insulators by nanoindentation

In the present work, the effect of loading rate on indentation creep was studied. Indentation creep tests were conducted on epoxy resin to provide creep deformation under constant load, contact creep compliance and cut-off time using a Berkovich indenter. Several loading rates, ranging from 0.25 to 6 mN/s, were used to perform the tests. The results showed that there is a strong loading rate dependence on creep response of the epoxy resin under indentation. Contact creep compliance and cut-off time decreased with increasing loading rate. In contrast, an increase in reduced modulus, hardness, displacement variation and contact creep compliance variation during the holding time was noticed. The loading rate sensitivity on creep response under indentation can be attributed to viscoelastic response prior to holding segment and strain rate effect on yield stress of the epoxy resin. This study provided an insight to understand the loading rate dependence on creep behaviour of epoxy resin under indentation.     

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.     

Study on stress evolution in SiC particles during crack propagation in cast hybrid metal matrix composites using Raman spectroscopy

The evolution of stress in the SiC particles during crack propagation under monotonic loading in a cast hybrid MMC was investigated by micro Raman spectroscopy. The experiment was carried out in situ in the Raman spectroscopy. Experimental results showed that cracks due to monotonic loading propagated by the debonding of the particle/matrix interface and particle fracture. Secondary cracks those formed in front of the main crack tip coalesced with the main crack in subsequent loading and final failure occurred. A high decrease in stress (several hundreds in MPa) was observed with the interfacial debonding at the interface and with the particle fracture on the particle. Moreover, the critical tensile stresses for particle–matrix interface debonding and particle fracture developed in hybrid MMC were also estimated during the crack propagation.     

Design and construction of a micro‐indenter for tribological investigations

Characterisation of erosion contact conditions remains a challenge due to the chaotic morphology of eroded surfaces. The present work presents details on the design and construction of a low load micro‐indenter to investigate the initial stages of particle impact. Spherical ZrO₂ particles and angular SiC particles have been fitted onto stainless steel indenter tips to simulate contact between eroding particles on an aluminium surface. Contact loads between 50 and 1800 mN were utilised to elucidate the effects of load and indentation depth. Indented craters were subsequently imaged by the scanning electron microscope (SEM), revealing its particle dependent morphology. Crater area and depths from both types of particles were also quantified and subsequently correlated to the indentation load. It was demonstrated that contact pressure generated by angular particles are 1.5 times higher than those from spherical particles, resulting in greater plastic deformation and larger crater area at high loads. The work carried out during indentations were also calculated, it was shown that indentation experiments can be utilised for simulating dynamic erosion experiments under a large velocity range.     

界面性质对颗粒增强复合材料破坏模式影响的数值模拟分析

运用材料破坏过程分析M FPA2D 系统, 对颗粒增强复合材料的变形、损伤及破坏过程进行了数值模拟分析。主要分析了界面性质对破坏模式的影响。模拟结果表明, 增强颗粒与基体的界面对复合材料的宏观性能有很大影响。在理想界面条件下, 破坏模式以界面附近基体的破裂为主, 在非理想界面(且为弱界面) 条件下, 破坏模式以颗粒与基体的脱粘较为明显。      

有界面脱粘时颗粒增强金属基复合材料的弹塑性性能分析

基于Mori-Tanaka理论和Eshelby等效夹杂理论,假定基体和增强相界面结合完好,推导出在力的边界条件下两相复合材料各组成相的应力、应变以及复合材料的体平均应变和应力,并考虑了基体和增强颗粒热膨胀系数引起的热应变以及各相塑性应变的影响.在此基础上,假定基体和复合材料均为各向同性材料,颗粒仅产生弹性变形,基体产生弹塑性变形且满足Mises屈服准则和等向强化准则,由颗粒所受的拉应力控制界面的脱粘,脱粘概率由Weibull分布函数来描述,脱粘后的颗粒等效为孔洞,采用割线模量法讨论了球形颗粒增强金属基复合材料有界面脱粘时的弹塑性性能,理论预测与实验结果吻合较好.