Studies On Micromorphic Elasto-Plasticity Theory And Its Applications

Since the classical elasto-plasticity theory does not possess any material intrinsiclength scale parameter, it is incapable of capturing the scale-dependent phenomena ofcellular solid at the millimeter scale and of metal at the micron and submicron scales,and the Bauschinger effect of the thin film plasticity. In this paper, based on themicromorphic elasto-plasticity theory under the framework of continuum mechanics,the elastic size effect at macro-scale and the size and Bauschinger effects at micro-scaleare investigated.The simple shear and uniaxial tension of a constrained layer and simple shear of abimaterial strip are carried out analytically, by using the micromorphic elastic theoryand the second gradient theory. The close links between these two theories is alsoillustrated. The micromorphic elastic theory reduces to the second gradient theory whenthe coupling factor, which plays the role of penalty parameter, approaches infinity.However, the former cannot degrade to the latter in the whole region for the uniaxialtension problem. The computational results show that with certain internal constraints,the finite element formulations, which are originally developed for the micromorphicelastic theory, can be used to approximately simulate the complex boundary valueproblem of second gradient theory. Moreover, the higher order boundary conditionimposed on the boundaries and the material in-homogeneity can lead to the elastic sizeeffect.The plane strain wedge indentation of a thin film on a substrate is investigatednumerically by employing the small deformation version of micromorphic isotropichardening plasticity model. A two-dimensional finite element framework based on themodel is formulated and implemented into the finite element code by developing aneight-node mixed interpolation isoparametric element. It is the straight generalization ofthe radial return method in the context of classicalJ2flow plasticity model to themicromorphic theory to determine the plastic deformation. The internal length scale andhardening modulus of thin film have significant influence on the actual hardness. For agiven indentation depth, the indentation force and hardness increase with the increasingintrinsic length scale. For the soft film/hard substrate system, the force and hardness increase with decreasing film thickness, and the hardening effect of hard substrateincreases. For the hard film/soft substrate system, the force and hardness diminish as thethickness of film decreases, and the softening effect of soft substrate rises.The micromorphic isotropic/kinematic hardening plasticity model accounting forthe backstress is presented. The equation of generalized flow stress, the constitutive lawof micro-couple-stress and the evolution equation of micro-couple-backstress are relatedto the material characteristic length scale. The numerical formulations for the model areoutlined. The generalized consistent tangent modulus is derived to achieve the parabolicconvergence of the global nodal force equilibrium equation. Furthermore, plasticbehaviors in material with microstructure under cyclic loading, such as size effect,ratcheting effect and plastic shakedown phenomenon, are investigated. It is shown thatthe thinner the film thickness, or the smaller the sample size, the harder the mechanicalbehavior. Also, the mixed hardening model is employed to investigate the size andBauschinger effects of freestanding Cu thin films undergoing plane strain uniaxialtension. The calculation results are compared quantitatively with the experimental data.The boundary layer, in which significant micro-deformation gradient and plasticdeformation arise, generate near the passivation-film interface and internal grainboundary. The scalar measurement of backstress increases linearly with the pre-strain.