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

Asymmetric single point incremental forming of sheet metal

Meta-analysis of risk factors for cutaneous melanoma: III. Family history, actinic damage and phenotypic factors

: Procedures for using a computer for the complete solution to plane strain as well as axisymmetric deformation problems have been developed. The velocity, strain rate, total effective strain, and stress distributions were obtained for two commercially pure lead specimens extruded in a forward extrusion process using white lead in oil as a lubricant. The axisymmetric extrusion was carried out at a speed of 1/8 in./min through a conical die having a 45 degrees half cone angle with a 2:1 extrusion ratio, and the plane-strain extrusion through a tapered die having a 45 degrees half taper angle with a 1.66:1 extrusion ratio. (Author)

Computer application to the visioplasticity method.

A Theory of Shear Spinning of Cones

Perform design by the three-dimensional finite element method has been carried out for plain ring rolling and T-section profiled ring rolling. The application of the backward tracing scheme for perform design in ring rolling processes demonstrates, for the first time, the extension of the scheme into three dimensions. The preform design in plain ring rolling aims at obtaining a preform which simulates a final plain ring product with uniform axial height. Loading simulations were carried out for two progressively modified preforms derived from the result of loading simulations with a rectangular-shaped ring. Then, backward tracing was applied to obtain a final preform for the specified product configuration of uniform axial height. The preform in the T-section profiled ring rolling process was to be designed to simulate a final profiled ring product with complete filling in the groove and uniform axial height. The final preform shape for plain ring rolling was selected as a trial preform in T-section profiled ring rolling. A more satisfactory preform was obtained from the backward tracing results. It was shown by forward simulation that the final preform was good enough to satisfy the design criteria.

Preform design in ring rolling processes by the three-dimensional finite element method

A plasticity theory is developed for a powdered metal compact. The yield criterion used for sintered powdered metals is modified for describing asymmetric behavior of powdered metal compacts in tension and in compression. Three parameters α, δ, and p are involved in the yield function. The two parameters, α and δ, are determined from the behavior of sintered powdered compacts as functions of relative density R. Green strength vs relative density R relationship for powdered metal compacts is used for defining completely the yield function with the effect of relative density. Predictions are made for compaction pressures as functions of relative density for unidirectional, bidirectional and isostatical compaction, and compared with experimental data for copper and iron powders. Also yield surfaces for various density levels are compared with the experimental data with copper powders.

Shiro Kobayashi

Papers

Computer application to the visioplasticity method.

A Theory of Shear Spinning of Cones

Preform design in ring rolling processes by the three-dimensional finite element method

Deformation characterization of powdered metals in compaction

Application of FEM Modeling to Simulate Metal Flow in Forging a Titanium Alloy Engine Disk