Analysis of the Micro/Meso Scale Sheet Forming by Strain Gradient Plasticity and its Characterization of Tool Feature Size Effects

Abstract

For conventional metal forming, finite element (FE) method becomes a powerful tool in process design. However, conventional material models cannot describe material behaviors precisely in micro/meso scale due to the size/scale effects. As a result, know-how obtained in traditional macro-forming is not suitable for the micro-forming process. In micro/meso scale forming process, the reaction force, localized stress concentration and formability are not only dependent on the strain distribution and strain path but also the strain gradient and strain gradient path caused by decreased scale. This study presented a model based on conventional mechanism based strain gradient (CMSG) plasticity. A user-defined material (UMAT) subroutine incorporating the CMSG plasticity in the ABAQUS finite element (FE) program was established. Based on the subroutine, FE simulations were performed to analyze the effects of the channel width in sheet forming process of micro-channel features. Die sets were fabricated according to the scale law and Micro/meso scale sheet forming experiments were conducted to study the effect of channel width in the die. Experimental results indicated that the CMSG plastic theory achieved better agreements compared to the conventional plastic theory. It found that the influence of the strain gradient to the forming process increased with the decrease of the geometrical parameters of the tools. Furthermore, various tool geometrical parameters were designed by Taguchi Method to explore the feature size effects caused by the decrease of tool geometrical dimensions. According the scale law, similarity difference and the similarity accuracy were calculated to evaluate the size effects. Greater equivalent strain gradient was found with the decrease of the tool geometric dimension, which lead larger maximum reaction force error due to increasing size effects. The main effect plots for equivalent strain gradient and reaction force indicated that the influence of the tools clearance was larger than punch radius, die radius and die width.