Brown University School of Engineering

Joint Materials/Solid Mechanics Seminar Series “Crystal Plasticity and Evolutionary Yield Functions for Modeling of Forming and Failure of Sheet Metals”

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Monday, December 10, 2012 4:00pm - 5:00pm

Joint Materials/Solid Mechanics Seminar Series “Crystal Plasticity and Evolutionary Yield Functions for Modeling of Forming and Failure of Sheet Metals” Farhang Pourboghrat Professor, Department of Mechanical Engineering, Michigan State University, East Lansing, MI 48824-1226 Abstract - Crystal plasticity relates the plastic behavior of crystalline materials to their microstructures. It can be used as a computational tool for the analysis of metal forming processes, microcrack initiation, crack propagation, fatigue, creep, texture design, and calculation of damage parameters and evolutionary coefficients of yield functions, fracture criteria and FLD diagrams. In order to describe the plastic deformation by the crystallographic glide, three objectives must be met; 1) determination of active slip systems, 2) determination of shear rate on active slip systems, and 3) overcoming the problem arising from non-uniqueness of active slip systems in an arbitrary strain path. Using an optimization technique, single crystal yield functions were developed to meet the above objectives, and to serve as a constitutive model for the forming analysis of polycrystalline metals. In the first part of the presentation, the author will present the rate-independent, dual mixed (DM) and combined constraints crystal plasticity (CCCP) models which were implemented into ABAQUS as a UMAT. These models require as input the initial texture of the metal (from OIM), the appropriate active slip systems, and the hardening parameters for each slip system. As output, these models calculate the total plastic deformation, shear rate for each slip system, and the texture evolution. Currently, the hardening for each slip system is calculated using a phenomenological hardening model accounting for self and latent hardenings. The author is also working on a dislocation density based model to calculate slip resistances for each slip system. In order to perform macroscale FE simulation of metal forming problems, Taylor’s assumption is invoked where each grain is assumed to undergo the same deformation rate. To accurately represent the plastic behavior of a polycrystalline metal, currently as many as 50-100 grain orientations are considered at each FE integration point. The accuracy and efficiency of DM and CCCP constitutive models were verified by simulating the bulging and hydroforming of a 6061-T4 aluminum tube [2010], bulging of a niobium sheet, and the shear deformation of a tin solder joint [2012]. In the second part of the presentation, the author will discuss a new approach in which the anisotropy coefficients of phenomenological yield functions are evolved as a function of parameters such as temperature and the effective plastic strain to account for the deformation induced anisotropy of the metal. Such yield functions have been developed for warm forming of aluminum [2007], and niobium sheet [2007]. Crystal plasticity is also being used to calculate the forming limit diagram (FLD). A plan is currently underway to develop evolutionary yield functions for multi-phase, advanced high strength steels (AHSS). Zamiri, A., Pourboghrat, F., “A Novel Yield Function for Single Crystals Based on Combined Constraints Optimization,” Int. J. Plasticity, Vol. 26, Issue 5, (2010) 731-746. Darbandi, P., Bieler, T., Pourboghrat, F., Lee, T.K., “Crystal Plasticity Finite Element Analysis of Deformation Behavior in Multiple-Grained Lead-Free Solder Joints,” Journal of Electronic Materials, 2012 (in print). Zamiri, A., and Pourboghrat, F., “Characterization and Development of an Evolutionary Yield Function for Superconducting Niobium Sheets,” Int. J. Solids and Structures, 44 (2007) 8627-8647. Abedrabbo, N., Pourboghrat, F. and Carsley, J., “Forming of AA5182-O and AA5754-O at Elevated Temperatures using Coupled Thermo-Mechanical Finite Element Models,” Int. J. Plasticity, 23 (2007) 841-875. Monday, December 10, 2012 4:00-5:00 pm B&H Room 190