Inelastic deformation of metal matrix composites

A theoretical model capable of predicting the thermomechanical response of continuously reinforced metal matrix composite laminates subjected to multiaxial loading was developed. A micromechanical model is used in conjunction with nonlinear lamination theory to determine inelastic laminae response. Matrix viscoplasticity, residual stresses, and damage to the fiber/matrix interfacial zone are explicitly included in the model. The representative cell of the micromechanical model is considered to be in a state of generalized plane strain, enabling a quasi two-dimensional analysis to be performed. Constant strain finite elements are formulated with elastic-viscoplastic constitutive equations. Interfacial debonding is incorporated into the model through interface elements based on the interfacial debonding theory originally presented by Needleman, and modified by Tvergaard. Nonlinear interfacial constitutive equations relate interfacial tractions to displacement discontinuities at the interface. Theoretical predictions are compared with the results of an experimental program conducted on silicon carbide/titanium (SiC/Ti) unidirectional, (O4), and angle-ply, (+34)(sub s), tubular specimens. Multiaxial loading included increments of axial tension, compression, torque, and internal pressure. Loadings were chosen in an effort to distinguish inelastic deformation due to damage from matrix plasticity and separate time-dependent effects from time-independent effects. Results show that fiber/matrix debonding is nonuniform throughout the composite and is a major factor in the effective response. Also, significant creep behavior occurs at relatively low applied stress levels at room temperature

A kinematically enhanced constitutive model for progressive damage analysis of unidirectional fiber reinforced composites

The application of fiber reinforced laminated composite structures has been increasing steadily in many engineering disciplines due to their high specific strength and stiffness, corrosion resistance, exceptional durability and many other attractive features over the last few decades. A comprehensive strength and failure assessment of these structures made of composite materials is extremely important for a reliable design of these structures and it has been a major focus of many researchers in this field for a long time. To the best of our knowledge, the majority of the existing studies based on macro based continuum approach are particularly focussed on capturing the effective elastic properties and final failure envelop of the composite material, while the subsequent post-yield inelastic behaviour or the entire nonlinear response is often overlooked. Composite structures with such diverse applications can be subjected to complex loading conditions such as impacts, severe dynamic loads or extreme thermal loads which can lead to a significant damage or complete failure of these structures. It is therefore essential to predict the entire nonlinear response and failure of these structures in many situations for a better design with higher confidence. This problem is quite challenging, specifically with a macro based continuum approach, as the actual failure initiates at the micro scale in the form of matrix cracking, fiber rupture or fiber-matrix interface failure which propagate gradually, accumulate together and finally manifested as macroscale structural failure. Thus tracking the details on the entire failure evolution process from microscale to macroscale is necessary for accurately modelling the structural failure. A detailed micromechanical modelling approach, where all constituents are explicitly modelled, can capture all these microscale failure processes and their evolutions in details but such modelling strategy is not computationally feasible for failure analysis for large structures due to a huge gap between micro/fiber and macro/structural scales. Thus the analysis of these structures requires an innovative modelling approach that can represent and capture the essential features of these microscale failure details, while at the same time, should be computationally efficient like a macro based continuum model for undertaking large scale structural analysis. In this study, a new three-dimensional kinematically enhanced macro-based constitutive model is developed which is applicable at the lamina/ply scale of these laminated composite structures. A novel analytical technique is developed for upscaling the nonlinear response from the fiber/micro scale to the ply scale which is the key for achieving such precise modelling of composites with feasible computational resources. The proposed approach utilized a strategy of strain field enhancements kinematically to account for different rate of deformations in the local fields within a fiber reinforced composite (FRC) ply. Based on these considerations, closed-form analytical expressions are derived which can be used conveniently to express the average macro strain increments of the entire volume element in terms of strain increments in the local fields and vice versa. This modelling strategy provides an opportunity to incorporate both fiber and matrix constitutive responses as well as their interactions into the overall ply response. To this end, a thermodynamics-based continuum model is developed using damage mechanics and plasticity theory to capture the constitutive response of the matrix. This has incorporated two predominant failure mechanisms in the matrix, which are permanent plastic deformation and loss of stiffness. For the fiber-matrix interface that includes interfacial debonding, an anisotropic damage model is developed to account for the directional dependence of the softening response in FRC ply due to fiber debonding failure. The proposed approach and models are developed in incremental forms, allowing the applications in both linear and nonlinear ranges of behaviour. Their verification with available analytical and numerical approaches together with the validation against a wide range of experimental data show both features and good potentials of the proposed approach.Thesis (Ph.D.) (Research by Publication) -- University of Adelaide, School of Civil, Environmental and Mining Engineering, 201

The Hill and Eshelby tensors for ellipsoidal inhomogeneities in the Newtonian potential problem and linear elastostatics

In 1957 Eshelby showed that a homogeneous isotropic ellipsoidal inhomogeneity embedded in a homogeneous isotropic host would feel uniform strains and stresses when uniform strains or stresses are applied in the far-field. Of specific importance is the uniformity of Eshelby's tensor S. Following this paper a vast literature has been generated using and developing Eshelby's result and ideas, leading to some beautiful mathematics and extremely useful results in a wide range of application areas. In 1961 Eshelby conjectured that for anisotropic materials only ellipsoidal inhomogeneities would lead to such uniform interior fields. Although much progress has been made since then, the quest to prove this conjecture is still not complete; numerous important problems remain open. Following a different approach to that considered by Eshelby, a closely related tensor P=S D^0 arises, where D^0 is the host medium compliance tensor. The tensor P is associated with Hill and is of course also uniform when ellipsoidal inhomogeneities are embedded in a homogeneous host phase. Two of the most fundamental and useful areas of applications of these tensors are in Newtonian potential problems such as heat conduction, electrostatics, etc. and in the vector problems of elastostatics. Micromechanical methods established mainly over the last half-century have enabled bounds on and predictions of the effective properties of composite media. In many cases such predictions can be explicitly written down in terms of the Hill, or equivalently the Eshelby tensor and can be shown to provide excellent predictions in many cases. Here this classical problem is revisited and a large number of results for problems that are felt to be of great utility in a wide range of disciplines are derived or recalled