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

A plasticity theory is summarized for a powdered metal compact. The constitutive equation is applied to the variational principle and its discretization is developed. The discretized formulation has been implemented into the finite element code and the program has been tested and applied to simulations of axisymmetric die pressings with copper powders. The simulation includes single-action and double-action pressings of solid cylinders as well as cylindrical rings. Predictions are made for density distributions, mean stress distributions, load-stroke relationships, average density as function of height, average density as function of radius, pressure distributions along die-walls and punches, and force fraction transmitted to the stationary punch. Some of the predicted solutions are compared with experimental observations from the literature. It was found that the results from the finite element analysis, in general, agree very well with the experimental observations.

Application of the finite element method to powdered metal compaction processes

Three problems, namely, autofrettage process, plastic upsetting of a solid cylinder, and plane-strain and axisymmetric extrusion, are treated for residual stress calculation. A thick-walled cylinder consisting of two loosely fitted concentric cylinders of different materials is subjected to various levels of internal pressure. The residual stresses were calculated with an emphasis on the case where the inner surface of the cylinder yields again upon removal of the internal pressure. Comparison between the calculations and the measurements is given. The residual stresses in plastic upsetting of a solid cylinder were calculated by the finite-element method. An attempt was also made to simulate the real situation in extrusion by the finite-element method. An estimation of the residual stress distribution is then discussed for axisymmetric extrusion problems.

Calculation of Residual Stresses in Plastic Deformation Processes

A New Analysis of the Forces in Orthogonal Metal Cutting

Plastic Instability in Simple Stretching of Sheet Metals

The metal-forming processes of shell nosing at elevated temperatures were analyzed by the finite-element method. The strain-rate effects on materials properties and the flow stress dependence on temperatures were included in the finite-element analysis. A thermodynamic theory of visco-plasticity based on rational mechanics was adapted to a rigid-plastic material idealization. An implicit scheme is used for the time integration of heat transfer equations, which is coupled to the plasticity equations. The nine-node quadrilateral elements with quadratic velocity distribution were used for the workpiece, and four-node quadrilateral elements were used for the die in the heat transfer analysis and temperature calculations. The coupled analysis of heat transfer and deformation was applied to the forming of AISI 1045 steel shells. Correlation between simulation and experimental results are good.

Shiro Kobayashi

Papers

Application of the finite element method to powdered metal compaction processes

Calculation of Residual Stresses in Plastic Deformation Processes

A New Analysis of the Forces in Orthogonal Metal Cutting

Plastic Instability in Simple Stretching of Sheet Metals

An Investigation of the Shell Nosing Process by the Finite-Element Method. Part 2: Nosing at Elevated Temperatures (Hot Nosing)