Notch-root elastic-plastic strain-stress estimations in particulate metal matrix composites (PMMCs) under general loading conditions

Determining the stress and strain histories at the point of highest stress concentration in particulate metal matrix composites (PMMCs) is complicated particularly when they have a finite concentration of particles, the matrix material in the vicinity of the notch is elastic-plastic, and when multiaxial cyclic loads are applied to the component. In this research, two alternative analytical models are developed and implemented to estimate the composite elastic-plastic strain and stress histories in PMMC components subjected to multiaxial cyclic loads. The models are formulated using proposed energy-based approximate relations and the developed PMMCs elastic-plastic constitutive model. Each model consists of a set of nonlinear relations that can be solved to estimate the notch root parameters, from an elastic analysis. The models presented thus provide an easy to implement approximation to the otherwise rather complex non-linear problem.; The analytical results are compared to the local strains, obtained using 3D image correlation technology, at the depth of circumferential notched PMMC specimens subjected to multiaxial cyclic non-proportional loading. The results of the comparison show that the proposed models work well for the geometries and load paths considered. Both models are in good agreement with the experimental results in terms of the trends of the local shear and axial strains, and also agree quantitatively well with the experimental results.; As stated, the formulated notch root approximate relations require the development or adoption of a suitable elastic-plastic constitutive model. In this thesis, two cyclic plasticity models developed originally for homogeneous materials, the Mroz multi-surface model and the endochronic theory of plasticity, were incorporated into two constitutive models that were developed to respect the heterogeneous nature of PMMCs. The models results were compared to experimental results obtained on tubular PMMCs specimens made of 6061 aluminum alloy reinforced with 10 and 20% by volume of alumina (Al2O 3) subjected to multiaxial cyclic loads. It was observed that the developed models correlate well with the trends observed in the experimental results. However, for the load paths investigated, the endochronic theory-based PMMCs constitutive model gave better qualitative predictions of the experimental results than did the Mroz-based PMMCs constitutive model predictions, and was used in the notch root elastic-plastic strain-stress formulations.