Homogenization of elasto-plastic functionally graded material based on representative volume element: Application to incremental forming process

In the present paper, as a first endeavor, homogenization of elasto-plastic functionally graded material (FGM) is investigated based on representative volume element (RVE) and used for the first time in the single point incremental forming (SPIF) process. The effective properties of elasto-plastic spheres-reinforced FGM composite are determined using the numerical RVE method and Mori-Tanaka model. In order to implement the homogenization equations and numerical algorithm into Abaqus Software, user-defined material, (VUMAT) and (VUSFLD) subroutines are employed. The accuracy of the proposed homogenization methodology is highlighted through comparisons of the present results with those taken from the literature and an excellent agreement is found. During SPIF process, the effect of the power-law index on the formability, plastic deformation, forming force along Z_direction and Von Mises distribution is analyzed. Parametric studies are conducted to show the influence of cone wall angle and sheet thickness on the formability and the thinning along the SPIF process.