A self - Consistent higher-order strain gradient plasticity analysis of micropolar dual-phase crystalline FGM made of Titanium-boride/ Titanium

A self-consistent higher order couple stress model is based on Fleck - Hutchinson Strain Gradient Plasticity to consider flexural behavior of brittle - ductile microscale structures. The dual phasic functionally graded material made of Titanium-boride/Titanium structure is modeled by defining a material flow stress which reflects a parameter of combined effective length scale, dependent on Geometrically Necessary Dislocations. The dual phasic crystalline micro-beam is built with the properties having continuously and non-linearly variation along the thickness. The perfectly plastic behavior of micropolar functionally graded material is described by incorporating a ductile –like mixture law, so-called TTO model, possessing a simple possibility of transition through defining a graded phase acting as an equilibrium mixed phase. Further, the effects of the elastic foundation and temperature rise on the plastic deformations are investigated. While an energy method is used to derive governing equations, the obtained results are verified individually in three steps.