Modelling And Simulation Of Cyclic Response And Fatigue Failure Of Fiber Reinforced Ductile Composites

Continuous fiber-reinforced metal matrix composites, shortened by MMC_f, are made up of matrix and reinforcement. The former usually consists of metal or alloy and the latter is composed of many kinds of fibers. More distinctly, it is characterized by a continuous metal or alloy matrix which is equably crammed with other constituent phases. As a heterogeneous and anisotropic material, this composite has an inspiring prospect of wide practical applications, especially in aeronautic and aerospace structures, such as advanced turbine engines and ultrasonic aerocraft, which displays unique superior performance as compared to other conventional materials. In many typical applications, MMC_f are subjected to a cyclic mechanical loading along with a superimposed variation in temperature. This type of complicated loading condition is referred to as cyclic thermomechanical loading. To submit an efficient employment and to take advantage of the entire application potential, it is an urgent task to require a through understanding of the micro-mechanism for the progressive failure under thermo-mechanical static and cyclic loading and to develop methodology to predict their strength and fatigue life.As a matter of fact, the failure process of the composites includes the ceaseless accumulation of damage, gradual degradation of property and stress redistribution. Based upon the shear lag model, we have presented a micromechanically analytical model using an influence function superimposition technique to derive stress profiles for any configuration of breaks in MMC_f under thermo-mechanical loading, by considering the effect of variations in fiber strength, local matrix tensile yield and interface yield (or sliding). Compared with the other models, both the matrix tensile stress and the fiber tensile one have been taken into account. The shear stress is transferred through the interface between fiber and matrix. The local plasticity is modeled by the elastic, perfectly-plastic shear stress-strain relation. In this study, we have restricted our attention to establish a model characterizing progressive failure of MMC_f from the view of micromechanism, which are concerned with the both matrix tensile yield and interface yield and debonding around broken fibers. A broken fiber, accompanying with its yielding matrix and its yielding interface and its debonding interface is called as a damage entity. The case of the interactions among these multi entities is divided into two sub-cases: a single fiber break and a single matrix break, so the solution for the shear yield of interphase or matrix tensile yielding or matrix tensile yield and interface shear yield triggered by multiple fiber breaks can be availably obtained. According to the fact of dramatic localization of stress disturbance, a simplified model is adopted, through taking the governing differential equations controlled inside some limited regions which are affected by broken fibers. The characteristics of stress distribution for multiple damages under thermomechanical loading illustrate that the stress distribution is strongly sensitive to the outside surroundings, such as mechanical load and temperature, especially for in-phase and out-of-phase conditions. It is due to the sharp decline of the yield stress for the matrix with the rising temperature. The experimental observations can further emphasize that this superimposition is not merely simple but completely feasible. For such a non-elastic case, it is reasonable for the solved case to satisfy the origin condition through superimposition, more importantly, including the interactions among those disfigurements.Under static loading, the peculiarity of the tensile damage process appears to be progressive: Since the fiber strength exhibits large variability due to statistic distribution of defect, the first fiber break, usually, takes place at very early loading stage, leading to local thermo plasticity for matrix and interface around the broken fiber. Consequently, the microstress is redistributed due to local stress concentration. More fiber breaks and serious local plastic deformation occur as the applied load increases further, leading to the final failure of the composite at some loading level. In other word, the ultimate failure of the fiber-reinforced composites is largely dominated by accumulation of the large amounts of fiber breakage. Therefore, based upon the micromechanically analytical model under multiple damages, considering that the tensile strength of fibers follows a two-parameter Weibull distribution, a 2-D Monte-Carlo model is developed to simulate failure process for MMC_f under tensile thermo-mechanical loading, which is a combination of fiber fracture, local matrix tensile yield and interface yield throughout the application of applied loading. The macro stress-strain response for the composites shows that the microdamage mechanism is derived from a dominant "critical cluster" of breaks. The results from the several hundred Monte-Carlo simulations indicate that the ultimate tensile strength of the composites not only depends upon the composite length and width, but also is dominated by fiber strength statistics and stress redistribution due to progressive microdamage. Secondly, The mean tensile strength of the composite strongly depends on the magnitude ofβ. As the scatter of the fiber tensile strength increases the tensile strength for composites will dramatically decrease. On the other hand, it is shown that weak link scaling works very well within some limited range, which leads us to a significative conclusion that larger sizes are required to produce weak link scaling with smaller shape parameterβ. Modeling of the thermo-mechanical failure process of the fiber composite materials with ductile matrix helps us a comprehensive understanding of damage behavior and failure mechanism, which can be extended to approaches to fatigue life modeling of ductile matrix composites.In regime 1 for the fatigue life diagram of the maximum applied strain versus the cycles to failure, its corresponding failure micro-mechanism is rested with fiber breakage under high applied strain and low cycles. Just for the statistical particularity of fiber tensile strength, very small fiber break, usually, take places at peak values during the first loading cycle, stimulating local cyclic plasticity deformation for constituent material and interfacial debonding around the fiber break, then the microstress is redistributed in order to release the internal enriched force. Accompanying serious local plastic deformation and debonding, more and more fiber will continually be fractured as the number of load cycles increases further, leading to the fatigue failure of MMC_f. The distinctive property for this regime is the progressive failure and the sensitivity of fatigue life to the amplitude of applied loads. Based on the above characteristics of progressive damage mechanisms, a micromechanical model was then introduced to predict the evolution of fatigue damage, which described the development of a constituent micro-mechanical damage model and reflected the nonlinear cyclic response for the metal matrix, taking into account the behavior of each constituent (i.e. the fibers, the matrix and the interface) of the composite. The alternating plastic shear strain range of matrix is taken as an important index for debonding. Constitutive equations incorporating the effect of damage development and evolution are developed at the constituent level and then used to predict the overall behavior of the material system. The fatigue failure process is modeled by Monte-Carlo method. It is illustrated that the fatigue life of such a composite depends on the evolution of damage, which is a combination of fiber fracture, interfacial debonding, slipping and inelastic matrix deformation during the regular service life. Note that two curves for fatigue life cross over one another, i.e. the fatigue life for in-phase TMF conditions at higher stresses was considerably less than those obtained under the comparable out-of-phase TMF conditions. On the other hand, in the case of low-stress, the fatigue life for in-phase conditions is seen to increase considerably from that obtained under comparable out-of-phase conditions. This is due to the difference of the dominated failure mode for this two TMF conditions. Micro structural parameters are also studied to investigate the dependence of thermo-mechanical fatigue life on these factors. To our delight, the curve of fatigue life of MMC_f under thermo-mechanical loading is quantitatively related to the local thermo-plasticity of matrix properties, the volume fraction, the statistical strength of fiber and the interface characters between fiber and matrix.It is a very challenging task for fiber-reinforced metal matrix composites to be predicted the complex deformation behavior and to be controlled the damage tolerance characteristics under thermo-mechanical loading. To our surprise, it has engendered considerable scientific and technological interest for a long time. Its peculiarity and difficulty is how to gather up those meso and micro damage mechanisms, which can strongly affect the macro-mechanical behaviors, and its evolution, thereby the analysis of mechanical performance for heterogeneous materials can be established upon the scientific understanding. The project aims to develop a theoretic model that can predict thermomechanical strength and fatigue life of fiber reinforced metal-matrix composites and to preferably disclose the inherent relation between such thermo-mechanical propeties and the micromechanical mechanism of damage. The brightest point is that through multi-scale continuum mechanics the macro mechanical behavior can be qualitatively and quantitatively related to micro-factor of deformation and failure. It is shown that this adoptive method serves a new route for analyzing multi-scale mechanical behavior for materials/structures. Therefore, this research is expected to take an important effect on promoting our understanding ability of damage and failure behavior and enhancing our capability for comprehending and predicting the tensile strength and thermomechanical fatigue life for MMC_f. In a word, it is self-evident for the engineering application value and scientific significance.