Microindentation tests as a tool for the estimate of mechanical properties and the modeling of the interfacial behavior of ceramic matrix composites

This article has the scope of presenting the usefulness of microindentation tests for the estimate of in situ mechanical properties of the matrix and fibers as well as the assessment of interfacial behavior in ceramic matrix composites. For this concern, we have choosen the example of Hi-Nicalon–BN–silicon nitride ceramic matrix composite. Using the multiple unloading procedure, which has been described in detail elsewhere [Drissi-Habti M, Nakano K. Comput Sci Technol 1997;57 (in press)], the longitudinal Young's modulus of the fiber and the matrix have been estimated. The values are in good agreement with previous results [Drissi-Habti M, Nakano K. Comput Sci Technol 1997;57 (in press)]. Using the same technique, the interfacial properties have been checked. When varying the maximum applied load and considering a constant interfacial shear stress, the presence of Poisson's effect has been identified and a model, based on a Coulomb law of friction, has been proposed to derive frictional stress values adjusted for the contribution of the expansion of the fibers. From the results presented herein, the main point which should be noted is the wide range of applications permitted by the microindentation technique for the micromechanical characterization of ceramics and ceramic matrix composites.     

Matrix cracking and interface debonding in fiber-reinforced cement-matrix composites

The processes of matrix cracking and interface debonding were studied using the high sensitivity Moire interferometry technique. The experiments were conducted with continuous steel fiber reinforced cementitious composites subjected to uniaxial tension. The initiation and propagation of cracking and debonding were observed during the tests with the specimens of different fiber-volume ratios. Based on the experiments, the fiber stress, the interface slip, the interface shear stress, and the matrix strain distribution were calculated. It was shown that interfacial frictional shear stresses were not constant either along the whole interface or at different loading levels. The strain localization was observed in the matrix where it was bonded to the fiber. The average contribution of the matrix was greater for the composites with the higher fiber-volume ratio.     

Frictional Hertzian contact between a laterally graded elastic medium and a rigid circular stamp

This study investigates the problem of sliding frictional contact between a laterally graded elastic medium and a rigid circular stamp. Analytical and computational methods are developed to evaluate the contact stresses. In the analytical formulation, spatial variation in the shear modulus of the graded medium is represented by an exponential function, and Poisson’s ratio is taken as a constant. Coulomb’s dry friction law is assumed to hold within the contact area. The two-dimensional plane elasticity problem is formulated utilizing Fourier transforms, and the resulting Cauchy-type singular integral equation of the second type is solved by applying an expansion–collocation technique. The finite element method is used in the computational analysis of the contact problem. In the finite element model, continuous variation of the shear modulus is taken into account by specifying this property at the centroid of each finite element. The finite element-based solution procedure is verified by making comparisons to the results obtained through the analytical method. Numerical results generated for the laterally graded medium with an exponential variation in the shear modulus illustrate the influences of lateral gradation and coefficient of friction upon the contact stress distributions. The capability of the proposed finite element method is further demonstrated by providing numerical results for a laterally graded medium whose shear modulus is represented by a power function.     

Influence of spatial correlations on crack bridging by frictional fibres

The effect of fibre interaction on matrix cracking in a unidirectional fibre-reinforced composite is analyzed. It is assumed that the matrix material contains a crack in a plane perpendicular to the fibres. Fibres, remaining intact, debond from the matrix and then act as bridging ligaments in the crack wake. The debonding process is accompanied by frictional sliding governed by a Coulomb friction law. Fibres are considered to be randomly located in the transverse plane. The fibre axial stress and longitudinal displacement are expressed in terms of the solution to a model problem for a single fibre in an ambient stress field due to all other fibres and applied load. The stress field produced by the other fibres is described using an ensemble averaging procedure. The radial distribution function g(r) that provides a quantitative measure of the correlations between the positions of different fibres is evaluated numerically from the Percus-Yevick equation for hard disks. The dependence of the fibre axial stress on the relative fibre-matrix displacement is examined for different values of the volume fraction of fibres. The resulting stress-displacement law is compared with results for other choices of the function g(r) and with a law given by a concentric cylinder model.     

Comparison of two contact models in the simulation of friction stir welding process

Two contact models are used to simulate the thermo-mechanical interaction process in friction stir welding. Comparison shows that the classical Coulomb friction model can be accurate enough for the simulation of friction stir welding in lower angular velocity. But in higher angular velocity, the classical Coulomb friction model fails to work due to the increase of the dynamic effect of the welding tool. Because the shear failure of material is considered in modified Coulomb friction model, the increase of the frictional stress on the tool–plate interface is limited by the shear failure. So, this model can keep valid even when the angular velocity of the welding tool is increased to a high level.     

An Approach to Estimate Interface Shear Stress of Ceramic Matrix Composites from Hysteresis Loops

An approach to estimate interface shear stress of ceramic matrix composites during fatigue loading has been developed in this paper. By adopting a shear-lag model which includes the matrix shear deformation in the bonded region and friction in the debonded region, the matrix crack space and interface debonding length are obtained by matrix statistical cracking model and fracture mechanics interface debonding criterion. Based on the damage mechanisms of fiber sliding relative to matrix in the interface debonded region upon unloading and subsequent reloading, the unloading counter slip length and reloading new slip length are determined by the fracture mechanics method. The hysteresis loops of four different cases have been derived. The hysteresis loss energy for the strain energy lost per volume during corresponding cycle is formulated in terms of interface shear stress. By comparing the experimental hysteresis loss energy with computational values, the interface shear stress corresponding to different cycles can then be derived. The theoretical results have been compared with experimental data of three different ceramic composites.     

Computational modeling of damage evolution in unidirectional fiber reinforced ceramic matrix composites

A finite element model for investigating damage evolution in brittle matrix composites was developed. This modeling is based on an axisymmetric unit cell composed of a fiber and its surrounding matrix. The unit cell was discretized into linearly elastic elements for the fiber and the matrix and cohesive elements which allow cracking in the matrix, fiber-matrix interface, and fiber. The cohesive elements failed according to critical stress and critical energy release rate criteria (in shear and/or in tension). The tension and shear aspects of failure were uncoupled. In order to obtain converged solutions for the axisymmetric composite unit cell problem, inertia and viscous damping were added to the formulation, and the resulting dynamic problem was solved implicitly using the Newmark Method. Parametric studies of the interface toughness and strength and the matrix toughness were performed. Details of the propagation of matrix cracks and the initiation of debonds were also observed.     

ELASTIC BRIDGING FOR MODELING FATIGUE CRACK PROPAGATION IN A FIBER-REINFORCED TITANIUM MATRIX COMPOSITE

Abstract— A model based upon linear elastic bridging and fiber crack tip shielding is proposed for predicting fatigue crack growth in a SCS-6/Ti-6–4 composite. The model is characterized by the fiber/matrix debond length rather than the fiber/matrix interfacial frictional shear strength used in most current fatigue models. Finite elements combined with fracture mechanics are applied for computing the local stress intensity. The local stress intensity in the matrix is then utilized to predict crack growth in the composite via comparison to monolithic fatigue crack propagation data for a similar Ti-6–4 matrix material.     

A cohesive element model for mixed mode loading with frictional contact capability

We present a model that combines interface debonding and frictional contact. The onset of fracture is explicitly modeled using the well‐known cohesive approach. Whereas the debonding process is controlled by a new extrinsic traction separation law, which accounts for mode mixity, and yields two separate values for energy dissipation in mode I and mode II loading, the impenetrability condition is enforced with a contact algorithm. We resort to the classical law of unilateral contact and Coulomb friction. The contact algorithm is coupled together to the cohesive approach in order to have a continuous transition from crack nucleation to the pure frictional state after complete decohesion. We validate our model by simulating a shear test on a masonry wallette and by reproducing an experimental test on a masonry wall loaded in compression and shear. Copyright © 2012 John Wiley & Sons, Ltd.     

Modeling Loading/Unloading Hysteresis Behavior of Unidirectional C/SiC Ceramic Matrix Composites

The loading/unloading tensile behavior of unidirectional C/SiC ceramic matrix composites at room temperature has been investigated. The loading/unloading stress–strain curve exhibits obvious hysteresis behavior. An approach to model the hysteresis loops of ceramic matrix composites including the effect of fiber failure during tensile loading has been developed. By adopting a shear-lag model which includes the matrix shear deformation in the bonded region and friction in the debonded region, the matrix cracking space and interface debonded length are obtained by matrix statistical cracking model and fracture mechanics interface debonded criterion. The two-parameter Weibull model is used to describe the fiber strength distribution. The stress carried by the intact and fracture fibers on the matrix crack plane during unloading and subsequent reloading is determined by the Global Load Sharing criterion. Based on the damage mechanisms of fiber sliding relative to matrix during unloading and subsequent reloading, the unloading interface reverse slip length and reloading interface new slip length are obtained by the fracture mechanics approach. The hysteresis loops of unidirectional C/SiC ceramic matrix composites corresponding to different stress have been predicted.     

单纤维界面强度光弹性实验和理论研究

利用光弹性实验和有限元计算两种方法对单丝拔出复合材料模型的界面剪应力进行了研究。从计算和实验两个方面证明,当在纤维自由端施加一轴向拉力后,在单丝与基体界面的埋入端附近将出现剪应力的最大值。然后,沿着单丝的埋入方向,剪应力迅速降低,在界面区的中间趋于最小值,并且基本稳定不变。由此证明,单丝增强复合材料中界面的应力传递主要集中在单丝的埋入端附近,并且在这一区域最先达到危险应力,发生界面的脱胶破坏,引起整个试件的失效。     

Fatigue Hysteresis of Carbon Fiber-Reinforced Ceramic-Matrix Composites at Room and Elevated Temperatures

When the fiber-reinforced ceramic-matrix composites (CMCs) are first loading to fatigue peak stress, matrix multicracking and fiber/matrix interface debonding occur. Under fatigue loading, the stress–strain hysteresis loops appear as fiber slipping relative to matrix in the interface debonded region upon unloading/reloading. Due to interface wear at room temperature or interface oxidation at elevated temperature, the interface shear stress degredes with increase of the number of applied cycles, leading to the evolution of the shape, location and area of stress–strain hysteresis loops. The evolution characteristics of fatigue hysteresis loss energy in different types of fiber-reinforced CMCs, i.e., unidirectional, cross-ply, 2D and 2.5D woven, have been investigated. The relationships between the fatigue hysteresis loss energy, stress–strain hysteresis loops, interface frictional slip, interface shear stress and interface radial thermal residual stress, matrix stochastic cracking and fatigue peak stress of fiber-reinforced CMCs have been established.     

Experimental studies on shear failure of freeze-bonds in saline ice:: Part II: Ice-ice friction after failure and failure energy

This paper is the second of two papers that present and discusses the results from experiments where artificially created freeze-bonds made from saline ice were tested on direct shear with the freeze-bond oriented horizontally. It discusses the friction forces after freeze-bond failure and the failure energy.The friction force showed increasing linear trends with a non-zero intercept when plotted against the normal force. It shows that for low confinements Amonton's law is insufficient. For larger confinements the values of friction coefficient were in the range of previously reported measurements in ice-ice friction. A slightly decreasing trend of the frictional forces was found when the initial ice temperature increased.A Mohr-Coulomb type of model was proposed to model the ice-ice frictional stresses as function of the normal stresses. An empirical model was obtained to describe freeze-bond failure and subsequent deformation by introducing softening of the cohesion and angle of internal friction.The failure energy had similar trends to those observed for the freeze-bond shear strength when plotted against normal confinement, initial ice temperature and submersion time. Quadratic fitting to the data of failure energy as a function of freeze-bond shear strength allowed the estimation of the elastic shear modulus of the freeze-bond by applying a simple rheological model. The values found were between 2 kPa and 6 kPa which are very low compared with the shear elastic modulus for the ice blocks.     

Compressive strength of unidirectional fiber composites with matrix non-linearity

A study has been made of the effect of fiber misalignment and non-linear behavior of the matrix on fiber microbuckling and the compressive strength of a unidirectional fiber composite. The initial fiber misalignment constituted the combined axial and shear stress state in the matrix, and the state of stress just prior to the buckling was considered to be the initial state of stress in bifurcation analysis. The expression for the critical microbuckling stress was found to be the same as that for the elastic shear-mode microbuckling stress except that the matrix elastic shear modulus was replaced by the matrix elastic-plastic shear modulus. Incremental theory of plasticity and deformation theory of plasticity were used to model the matrix non-linearity. The analysis results showed reasonable correlation with available experimental data for AS4/3501-6 and AS4/PEEK graphite composites with 2° to 4° range of initial fiber misalignment.     

The influence of Poisson contraction on matrix cracking stress in fiber reinforced ceramics

The influence of Poisson contraction on the stresses for propagating a semi-infinite fiber-bridged crack in unidirectional fiber reinforced ceramics is studied in this paper. The situation of bonded fibers that is subjected to compressive pressure due to thermal expansion mismatch between the fiber and the matrix is considered in the present analysis. The results show that the Poisson contraction has profound effects on the matrix cracking stress predictions in the ceramic matrix composites, especially for the composites with high coefficient of friction. The Poisson contraction effects can be evidenced by the comparison of the present analysis with the Aveston, Cooper and Kelly (ACK) model. The roles played by the interfacial properties of the interfacial bonding energy and the coefficient of friction on the stresses for matrix cracking are discussed.     

Aspects of residual thermal stresses in continuous-fibre-reinforced ceramic matrix composites

An analytical model is presented that predicts the thermal stresses which arise from mismatch in coefficients of thermal expansion between a fibre and the surrounding matrix in a continuous fibre composite. The model consists of two coaxial isotropic cylinders. Stress transfer between the fibre and the matrix near an unstressed free surface has been modelled by means of a shear-lag analysis. Away from the free surface the theoretical approach satisfies exactly the conditions for equilibrium and continuity of stress at the fibre-matrix interface. Application of the model to a composite consisting of a glass-ceramic calcium alumino-silicate (CAS) matrix containing unidirectional Nicalon fibres points to a strong dependence of stress on fibre volume fraction. Surface effects are significant for depths of the order of one fibre diameter. Near-surface shear stresses resulting from cooling from the stress-free temperature are sufficiently high to suggest that a portion of fibre close to the surface is debonded at room temperature. Experimental results acquired with a scanning electron microscope (SEM) equipped with a heating stage are consistent with this prediction. Consequently, the model has been modified in a simple way to incorporate frictional slip at the interface, according to the Coulomb friction law. Although detailed measurements are limited by the resolution of the technique, experimental evidence suggests that the transfer length is within an order of magnitude of the model prediction.     

Influence of friction and adhesion on the onset of plasticity during normal loading of spherical contacts

Increasing contact loading causes early transformation from elastic to elastic–plastic deformations in many conventional systems as well as micro/nano-electro-mechanical systems. The load required for yielding and the location of the onset of plasticity is critical in the robustness of systems with contacts. For frictionless (such as fully-lubricated) contacts, inception of plastic yielding occurs beneath the contact surface. However, frictional slip (contact shear) and adhesion push the inception of plastic yielding toward the contact surface. The influence of elastic mismatch, shear tractions and adhesive normal tractions on the subsurface stress field is studied analytically by superposition of the Hertzian stress field and the stress field created by the shear and additional (due to adhesion) normal tractions. Specifically, three contact conditions have been studied in this work: (i) frictionless, (ii) finite friction, and (iii) infinite friction (full stick). Also, a finite-element model is developed to verify certain assumptions in the analytical solution for the contact with finite friction. The results obtained are applied to two sets of in situ nanoindentation experiments to explain the change in the yielding behavior of submicrometer polycrystalline aluminum grains.     

单向纤维增强陶瓷基复合材料单轴拉伸行为

采用细观力学方法对单向纤维增强陶瓷基复合材料的单轴拉伸应力-应变行为进行了研究。采用Budiansky-Hutchinson-Evans（BHE）剪滞模型分析了复合材料出现损伤时的细观应力场,结合临界基体应变能准则、应变能释放率准则以及Curtin统计模型三种单一失效模型分别描述陶瓷基复合材料基体开裂、界面脱粘以及纤维失效三种损伤机制,确定了基体裂纹间隔、界面脱粘长度和纤维失效体积分数。将剪滞模型与3种单一失效模型相结合,对各个损伤阶段的应力-应变曲线进行模拟,建立了准确的复合材料强韧性预测模型,并讨论了界面参数和纤维韦布尔模量对复合材料损伤以及应力-应变曲线的影响。与室温下陶瓷基复合材料单轴拉伸试验数据进行了对比,各个损伤阶段的应力-应变、失效强度及应变与试验数据吻合较好。     

BEM analysis of crack onset and propagation along fiber–matrix interface under transverse tension using a linear elastic–brittle interface model

The behavior of the fiber–matrix interface under transverse tension is studied by means of a new linear elastic–brittle interface model. Similar models, also called weak or imperfect interface models, are frequently applied to describe the behavior of adhesively bonded joints. The interface is modeled by a continuous distribution of linear-elastic springs which simulates the presence of a thin adhesive layer (interphase). In the present work a new linear elastic–brittle constitutive law for the continuous distribution of springs is introduced. In this law the normal and tangential stresses across the undamaged interface are, respectively, proportional to the relative normal and tangential displacements. This model not only allows for the study of crack growth but also for the study of crack onset. An important feature of this law is that it takes into account the variation of the fracture toughness with the fracture mode mixity of a crack growing along the interface between bonded solids, in agreement with previous experimental results. The present linear elastic–brittle interface model is implemented in a 2D boundary element method (BEM) code to carry out micromechanical analysis of the fiber–matrix interface failure in fiber-reinforced composite materials. It is considered that the behavior of the fiber–matrix interphase can be modeled by the present model although, strictly speaking, there is usually no intermediate material between fiber and matrix. A linear-elastic isotropic behavior of both fiber and matrix is assumed, the fiber being stiffer than the matrix. The failure mechanism of an isolated fiber under transverse tension, i.e., the onset and growth of the fiber–matrix interface crack, is studied. The present model shows that failure along the interface initiates with an abrupt onset of a partial debonding between the fiber and the matrix, caused by presence of the maximum radial stress at the interface, and this debonding further develops as a crack growing along the interface.