MULTI-SCALE DUAL-PHASE CYCLIC PLASTICITY WITH QUANTITATIVE TRANSITIONS AND SIZE EFFECTS OF LAYERED STRUCTURES
Fan Jinghong~(1,2) Gao Zhihui~1 Zeng Xiangguo~11 Department of Engineering Mechanics,Chongqing University (Campus A),Chongqing 400044,China2 Division of Mechanical Engineering,Alfred University,New York 14802,USA
A method is developed for cyclic elastoplastic analysis across micro/meso/macro scales which is effective for the quantitative transition of physical variables and for evaluating the size effects of microstruc- tures.By using the improved self-consistent seheme proposed by Fan and carrying out a delicate mesoscop- ic analysis based on a shear-lag model,the size effects including the thickness of hard and soft layers relative to the inclusion dimension are obtained on the overall elastoplastic responses of materials up to 50 cycles. The dominant characteristics of the analysis rare that the characteristic dimensions of a microstructure such as the thickness of the layers and the inclusion dimension can be explicitly incorporated into the formulation. Results of numerical analysis using only 4 plastic constants show that the thicker the layer relative to the in- clusion size,the softer the material in producing more plastic strain values for a given applied stress ampli- tude.This is in agreement with the well-known experimental rule that the yield strength of layered structures is inversely proportionul to the square root of the spacing between layers.It is found that ratcheting depends very much on the size of the layered-structure and that the thinner the relative thickness of the layer the less the ratchetiug displacement.This finding may be used to explain why phenomenological models on ratcheting are not quite successful so far,indicating the significance of aeross scale analysis in understanding issues which have existed for a long time.