An Integrated Crystal Plasticity Fe System for Microforming Simulation

Abstract

Based on Voronoi tessellation and the probability theory, a VGRAIN system is created for the generation of grains and grain boundaries for micromaterials. This system requires physical parameters obtained from microstructures of materials, such as the average, minimum and maximum grain sizes. Numerical procedures have been established to link the physical parameters of a material to the control variable in a gamma distribution equation and a method has been developed to solve the probability equation. These are the basis for the development of the VGRAIN system, which can be used to generate different grain structures and shapes that follow a certain pattern according to the probability theory. Statistical analyses have been carried out to investigate the distribution of generated virtual grains. The generated virtual microstructure is then implemented in the commercial FE code, ABAQUS, for mesh generation and micromechanics analysis using crystal plasticity (CP) equations for face-centered cubic (FCC) materials, which are implemented in the commercial FE solver, ABAQUS, through the user-defined subroutines, VUMAT/UMAT. FE analyses have been carried out to demonstrate the effectiveness of the integrated system for the investigation of localized straining and necking, encountered in microforming processes, such as extrusion of micropins, deformation of microfilms and hydroforming of microtubes.

Controlled Poisson Voronoi tessellation for virtual grain structure generation: a statistical evaluation

“…Comparison of the two descriptive models, both of which describe the relationship between the grain area distribution parameter and the regularity parameter . The dotted line is the model proposed in [35] and [36], and the solid line is the improved model: (a) Global quality, (b) local quality. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 …”

“…In the beginning, Zhu et al [34] introduced a 'regularity parameter' to quantify the degree of grain size uniformity for a VT. Then, Ho et al [35] and Cao et al [36] adopted this regularity parameter to inversely produce VTs with specified regularities.…”

“…The numerical procedure to derive the regularity value implemented a simple search method with very low efficiency. Cao et al [36] attempted to improve upon this drawback by devising a statistical estimation to derive the grain size distribution based on a group of adopted physical parameters, including the mean grain size and two sampled grain sizes.…”

Numerical Simulation in Microforming for Very Small Metal Elements

“…The results showed that the scatter effect of the flow stress curve increases with increasing grain size and the achieved scatter range had a good agreement with the experimental result. Voronoi tessellation can be adopted to describe the polycrystalline aggregate [25][26][27]. Lu et al [25] proposed a mixed material model based on modified Hall-Peth relationship, surface layer model, and grained heterogeneity (e.g., grain size, shape, and deformability).…”

An integrated scheme for crystal plasticity analysis: Virtual grain structure generation

“…The value of the regularity parameter ranges from 0 to 1, corresponding to a Poisson Voronoi tessellation (PVT) and a regular hexagonal tessellation, respectively. Ho et al [32] and Cao et al [33] adopted this regularity parameter as a control parameter and proposed a scheme to produce Voronoi tessellations with specified regularity.…”