O. Richmond

A deformation theory of plasticity based on minimum work paths

Abstract A deformation theory of plasticity is proposed wherein the deformation paths for material elements are assumed and the plastic work becomes dependent on displacements. Among the infinite possible ways to assume deformation paths, one has been chosen that has several advantages when materials harden isotropically. Earlier, this path was shown to require the minimum work path to achieve a desired strain. Here, a mathematical description of a constitutive law of deformation plasticity is developed based upon this path for rigid-plastic and for elastoplastic materials. The proposed deformation theory provides a convenient theoretical basis for FEM applications involving analysis, and especially design, of forming processes.

Three dimensional characterization and modeling of particle reinforced metal matrix composites: part I Quantitative description of microstructural morphology

In this first of a two part sequence of papers, 3-D microstructures of Si particle reinforced aluminum matrix composites are computationally constructed by assembling digitally acquired micrographs obtained by serial sectioning. The material samples considered vary in volume fraction and in particle size. Furthermore, equivalent microstructures with actual particles replaced by ellipses (in 2-D) or ellipsoids (in 3-D) are computationally simulated for efficiency. The equivalent microstructures are tessellated by a particle surface based algorithm into a mesh of Voronoi cells. Various 3-D characterization functions are developed to identify particle size, shape, orientation and spatial distribution in the actual materials and to compare with 2-D micrographs. Through this analysis, differences between 2- and 3-D characterization are established. Results indicate that it may not be sufficient to use 2-D section information for characterizing detailed microstructural features like particle shapes, orientations and near-neighbor distances. The second part of this sequence of papers will describe the important relationship of these features to damage evolution in these same materials. This sequence of papers is perhaps one of the first on 3-D physical characterization of the phase and damage structure for this class of materials.

Ideal forming—I. Homogeneous deformation with minimum plastic work

Abstract Ideal homogeneous deformation is defined as the path which produces a desired homogeneous deformation with minimum plastic work. Under rather broad assumptions, it is shown that this path corresponds to a path of minimum effective strain. The minimum work path is achieved when (1) the principal material lines are fixed with respect to the material during deformation, and (2) the ratio of principal true strain rates is constant. This path is unique for materials having smooth yield surfaces, such as Mises materials. For materials having pointed yield surfaces, the two conditions are only partially required and the path is not unique. For Tresca materials, an ideal path is achieved when only the major principal material line is fixed. For isotropic materials, the fixed material lines may be chosen arbitrarily; but, for anisotropic materials they are more restrictive.

Ideal forming—II. Sheet forming with optimum deformation

Abstract A method is proposed for the design of ideal forming processes. The objective is to directly determine ideal configurations for both the initial and the intermediate stages that are required to form a specified final shape. At the start, it is assumed that formability of local material elements is optimum when they deform in minimum work paths. The ideal global process is then defined as the one having such local deformations optimally distributed in a final shape. Mathematical procedures for implementing these conditions are derived. Primary emphasis is placed upon forming of sheet (membrane) materials under plane-stress conditions, although many of the ideas are applicable to more general forming processes. Sample results illustrate optimum process parameters which the ideal forming theory can provide.

Strain rate potential for metals and its application to minimum plastic work path calculations

Abstract In this work, a definition of the strain rate potential for plastically deforming metals is proposed. This potential is defined in six-dimensional deviatoric strain rate space, and its gradient provides deviatoric stresses in the flowing material. For isotropic FCC metals, it is shown that the plastic behavior predicted with this proposed phenomenological description is identical to the behavior predicted with the Taylor/Bishop and Hill polycrystal plasticity model. For orthotropic FCC metals, six material coefficients characterize the anisotropy. This potential provides a definition of the effective strain rate. Together with a work-hardening curve, this equation completely describes the plastic behavior of isotropically hardening metals. This definition is useful for the calculation of work along minimum plastic work paths, as is illustrated for an isotropic FCC metal and a strongly textured aluminum alloy, subjected both to pure shear and simple shear deformation modes.

An experimental-computational approach to the investigation of damage evolution in discontinuously reinforced aluminum matrix composite

Abstract A combined experimental–computational approach to study the evolution of microscopic damage to cause failure in commercial SiC particle reinforced DRAs is dealt with. Determination of aspects of microstructural geometry that are most critical for damage nucleation and evolution forms a motivation for this work. An interrupted testing technique is invoked where the load is halted in the material instability zone, following necking but prior to fracture. Sample microstructures in the severely necked region are microscopically examined in three dimensions using a serial sectioning method. The micrographs are then stacked sequentially on a computer to reconstruct three-dimensional microstructures. Computer simulated equivalent microstructures with elliptical or ellipsoidal particles and cracks are constructed for enhanced efficiency, which are followed by tessellation into meshes of two- and three-dimensional Voronoi cells. Various characterization functions of geometric parameters are generated and sensitivity analysis is conducted to explore the influence of morphological parameters on damage. Micromechanical modeling of two-dimensional micrographs are conducted with the Voronoi cell finite element method (VCFEM). Inferrences on the initiation and propagation of damage are made from the two-dimensional simulations. Finally, the effect of size and characteristic lengths of representative material element (RME) on the extent of damage in the model systems is investigated.

The influence of hydrostatic pressure on the ductility of AlSiC composites

Abstract Tensile tests with superimposed hydrostatic pressures were performed on two types of metal matrix composite: 2014 Al with 20% SiC particles and 2124 Al with 14% SiC whiskers. In the materials with SiC particulate, the ductility increases rapidly with pressure and the mode of damage initiation is by particle fracture. Materials containing SiC whiskers exhibit a different fracture mode involving whisker matrix decohesion, and strain localization which results in shear fracture.

Blank shape design for a planar anisotropic sheet based on ideal forming design theory and FEM analysis

Abstract A sequential design procedure to optimize sheet forming processes was developed utilizing ideal forming design theory, FEM analysis and experimental trials. For demonstration purposes, this procedure was used to design a blank shape for a highly anisotropic aluminum alloy sheet (2090-T3) that results in a deep-drawn, circular cup with minimal earing. All blank shape design methods require a certain number of iterations. However, the sequential procedure can be more effective than the other iterative methods based on FEM analysis in conjunction with experimental trials or on experimental trials alone. For this design demonstration, the anisotropic constitutive behavior of the 2090-T3 sheet was expressed using plastic potentials previously proposed by Barlat et al . The implementation of the anisotropic strain-rate potential in the ideal forming design code is also briefly summarized.

AN ATOMISTIC DISLOCATION MECHANISM OF PRESSURE-DEPENDENT PLASTIC FLOW IN ALUMINUM

Abstract An embedded atom (EAM) potential was employed to examine the lattice resistance to dislocation motion in pure aluminum under pressure. The sign and the magnitude of the pressure effect on glide (Peierls) stress in Al are obtained by direct atomistic calculation (molecular statics technique) in agreement with experimental data (Richmond and Spitzig, Pressure Dependence and Dilatancy of Plastic Flow . Int. Union of Theoretical and Applied Mechanics, 1980). Additionally, a significant transient dilatancy is observed associated with the activated state of dislocation motion. The latter result supports the conclusion reached in Richmond and Spitzig ( Pressure Dependence and Dilatancy of Plastic Flow . Int. Union of Theoretical and Applied Mechanics, 1980) and Spitzig and Richmond ( Acta metall. , 1984, 32 , 457) that pressure-dependent slip in metals is due to the interaction of a transient activation dilatancy of the moving dislocations with external pressure. Although in pure aluminum the tension–compression yield strength differential (SD) is only about 0.3%, the effect is significant for quantitative modeling of the performance of high strength aluminum alloys in tension and compression.

The effect of void shape on the development of damage and fracture in plane-strain tension

Abstract T he plane-strain tensile failure of a low carbon steel containing stringered manganese sulfide inclusions is analysed. Models of the material microstructure are developed using results from scanning electron microscopy to obtain the particle coordinates, sizes and shapes, and using Dirichlet tessellations to obtain local area fractions. Finite element analyses of these models are then carried out to examine the effects of inclusion shape and interactions on void growth. In these analyses, the relatively soft, noncoherent inclusions are modeled as voids. Finally, ductility predictions are made using continuum bifurcation analysis on a modified Gurson-type constitutive relation for porous media, and these predictions are compared with experimental values.