Computational modelling of impact damage in brittle materials

Introduction Metal forming process Analysis and technology in metal forming Plasticity and viscoplasticity Methods of analysis The finite element method (1) The finite element method (2) Plane-strain problems Axisymmetric isothermal forging Steady state processes of extrusion and drawing Sheet metal forming Thermo-viscoplastic analysis Compaction and forging of porous metals Three dimensional problems Preform design in metal forming Solid formulation, comparison of two formulations, and concluding remarks Index.

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Metal Forming and the Finite-Element Method

A new method of modeling material behavior which accounts for the dynamic metallurgical processes occurring during hot deformation is presented. The approach in this method is to consider the workpiece as a dissipator of power in the total processing system and to evaluate the dissipated power co-contentJ = ∫o σ e ⋅dσ from the constitutive equation relating the strain rate (e) to the flow stress (σ). The optimum processing conditions of temperature and strain rate are those corresponding to the maximum or peak inJ. It is shown thatJ is related to the strain-rate sensitivity (m) of the material and reaches a maximum value(J max) whenm = 1. The efficiency of the power dissipation(J/J max) through metallurgical processes is shown to be an index of the dynamic behavior of the material and is useful in obtaining a unique combination of temperature and strain rate for processing and also in delineating the regions of internal fracture. In this method of modeling, noa priori knowledge or evaluation of the atomistic mechanisms is required, and the method is effective even when more than one dissipation process occurs, which is particularly advantageous in the hot processing of commercial alloys having complex microstructures. This method has been applied to modeling of the behavior of Ti-6242 during hot forging. The behavior of α+ β andβ preform microstructures has been exam-ined, and the results show that the optimum condition for hot forging of these preforms is obtained at 927 °C (1200 K) and a strain rate of 1CT•3 s•1. Variations in the efficiency of dissipation with temperature and strain rate are correlated with the dynamic microstructural changes occurring in the material.

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Modeling of dynamic material behavior in hot deformation: Forging of Ti-6242

Shiro Kobayashi

Papers

Methods of Analysis

Metal Forming and the Finite-Element Method

New Solutions to Rigid-Plastic Deformation Problems Using a Matrix Method

Ductile Fracture in Axisymmetric Extrusion and Drawing—Part 2: Workability in Extrusion and Drawing

Rigid-Plastic Finite-Element Analysis of Plane Strain Rolling