Compared with traditional materials, composites have various desirable advantages, such as high strength-to-weight and stiffness-to-weight ratios, the ability to be tailored to produce required mechanical properties in specific directions, excellent wear and corrosion resistance, etc. Due to these significant advantages, there has been, in the past few decades, a rapid expansion of the incorporation of composite materials for the design and production of high performance components in various fields. Among them, metal matrix composites (MMCs), are undergoing rapid development to keep up with the requirements of aerospace and automotive industrial sector applications where minimal weight, and increased efficiency are critical. Predicting composite behaviour under hostile and demanding environments due to the combined action of thermal and mechanical loading, allow much more effective and reliable use of these materials. However, the cyclic and monotonic response of MMCs is complicated by the complex distributions of the reinforcements in the matrix (e.g. fibres, woven, whiskers or particles) which give rise to anisotropic or transversally isotropic behaviour of the material at macro-scale, and the arrangement of working loads. Most importantly, the difficulty in obtaining such a good understanding is aggregated by an easily overlooked fact that the structural integrity of composite structures/materials at macro-scale can be reduced by material degradation (or fatigue), which is caused in a micro-scale basis by external load histories.

A better understanding of the micro material scale is necessary to ensure that certain types of failure mechanism do not occur such as low cycle fatigue (LCF) crack initiation, ratchetting, creep enhanced cyclic plasticity or creep ratchetting. This involves the determination of the shakedown limit, ratchet limit, plastic strain range for LCF assessment, and creep cyclic plasticity interaction. However, such understanding is difficult to achieve, and yet to be fully explored. To address the aforementioned problems, theoretical analyses and experimental studies have been carried out extensively in past several decades. However, the former has to be limited to very simple cases and thus is not practical for engineering applications; while the latter is commonly time consuming and financially prohibitive. A practical and robust alternative to theoretical analyses and experiments for obtaining such understanding has to be the application of numerical methods due to the rapid development of digital computers and computer science.

Several multiscale techniques have been proposed in the literature; they can be collected into two classes: uncoupled and coupled multiscale approaches. The uncoupled approach is used when the structural scale and the material heterogeneity scale are very far; in this case, the homogenization technique is applied at the microscale to derive the overall constitutive response of the composite material to be used at the macroscale. On the contrary, when the size of the heterogeneities is not very far from the characteristic dimension of the structure, the uncoupled approach can fail and the homogenization cannot be fruitfully used. In this case, the full coupled multiscale analysis has to be performed. As it can be easily argued, the coupled multiscale approach is much more complex and computationally expensive with respect to the uncoupled one, based on classical homogenization procedures; for this reason, if not strictly necessary, the uncoupled approach is preferred and, hence, widely used in literature.

Metal Matrix Composites

Finite element models representing different MMC unit cells subjected to cyclic thermal load ad constant mechanical load. On the right elastic and global shakedown limits plus overall performance evaluation for all the geometries investigated. All the results are obtained by using the Linear Matching Method Framework.

Elasto-plastic homogenization of a 5 particles MMC array using an in-house periodic boundary conditions tool.

Equivalent creep strain for a single particle array for pure cyclic thermal load and for combined thermal and mechanical load, both with a creep dwell of  10 hours obtained using the extended Direct Steady Cycle Analysis within the Linear Matching Method Framework.