On the homogenization of metal matrix composites using strain gradient plasticity

The homogenized response of metal matrix composites（MMC） is studied using strain gradient plasticity.The material model employed is a rate independent formulation of energetic strain gradient plasticity at the micro scale and conventional rate independent plasticity at the macro scale. Free energy inside the micro structure is included due to the elastic strains and plastic strain gradients. A unit cell containing a circular elastic fiber is analyzed under macroscopic simple shear in addition to transverse and longitudinal loading. The analyses are carried out under generalized plane strain condition. Micro-macro homogenization is performed observing the Hill-Mandel energy condition,and overall loading is considered such that the homogenized higher order terms vanish. The results highlight the intrinsic size-effects as well as the effect of fiber volume fraction on the overall response curves, plastic strain distributions and homogenized yield surfaces under different loading conditions. It is concluded that composites with smaller reinforcement size have larger initial yield surfaces and furthermore,they exhibit more kinematic hardening.

Deformation efficiency, homogeneity, and electrical resistivity of pure copper processed by constrained groove pressing

Constrained groove pressing（CGP） is a new severe plastic deformation method suitable for producing ultra-fine grained sheet metals. In this work, the processing efficiency for a muti-pass CGP of pure copper was investigated. With a relatively small groove width of 2 mm and tight constraint, a sharp variation of mechanical properties with pass number is observed. Subgrains with the size of＊0.5 lm have distinct boundaries, which is the predominant feature in the microstructure after three passes. The evolution of deformation homogeneity characterized by micro-hardness distribution was examined in detail.Observations of optical micrographs and fracture surface morphology confirm the evolution rule. The relation between electrical resistivity and accumulative plastic strain was discussed. Crystalline defects, micro-cracks, and microstructure uniformity together determine the change of electrical resistivity of CGP copper.

An eigenelement method and two homogenization conditions

Under inspiration from the structure-preserving property of symplectic difference schemes for Hamiltonian systems, two homogenization conditions for a representative unit cell of the periodical composites are proposed, one condition is the equivalence of strain energy, and the other is the deformation similarity. Based on these two homogenization conditions, an eigenelement method is presented, which is characteristic of structure-preserving property. It follows from the frequency comparisons that the eigenelement method is more accurate than the stiffness average method and the compliance average method.

Evaluation of sample scale effect on geomechanical tests

The size of the rock specimen affects the stress concentrates in the vicinity of the top/bottom of the rock specimen during the evaluation of the geomechanical parameters in the laboratory,which causes un-reliable results.However,the appropriate size for geomechanical evaluation is not well understood yet because of limitations in the sampling and analysis.In this study,a series of numerical simulations using a finite element package was conducted to investigate the effect of sample aspect ratio,fluid saturation,and porosity,on the mechanical behavior of the rock under elastic and poroelastic conditions.In addition,two concepts,stress/strain homogeneity index(SHI)and representative elementary volume(REV),were developed to find out the appropriate sample size.The results show that the presence of stiff platens,which are dissimilar to the specimen material,causes significant stress concentration in the two ends of the specimen.The concentration of stress in the specimen reduces when the aspect ratio increases.An optimum aspect ratio(length-to-diameter equal to 3)was observed by SHI analysis which after that the changes in stress concentration are insignificant.The REV size analysis confirms the obtained optimum aspect ratio by SHI analysis.The saturated specimens show a lower magnitude of stress than applied stress because of the presence of pore pressure,which can carry a portion of the stress.The higher void ratio results in lower strength of the specimen.This study could be beneficial for the better design of geomechanical tests to have reliable results.