A One-Dimensional Nonlocal Damage-Plasticity Model for Ductile Materials

This paper presents a new 1-D non-local damage-plasticity deformation model for ductile materials. It uses the thermodynamic framework described in Houlsby and Puzrin (2000) and holds, nevertheless, some similarities with Lemaitre’s (1971) approach. A 1D finite element (FE) model of a bar fixed at one end and loaded in tension at the other end is introduced. This simple model demonstrates how the approach can be implemented within the finite element framework, and that it is capable of capturing both the pre-peak hardening and post-peak softening (generally responsible for models instability) due to damage-induced stiffness and strength reduction characteristic of ductile materials. It is also shown that the approach has further advantages of achieving some degree of mesh independence, and of being able to capture deformation size effects. Finally, it is illustrated how the model permits the calculation of essential work of rupture (EWR), i.e. the specific energy per unit cross-sectional area that is needed to cause tensile failure of a specimen.     

Sixty years of dislocations

It is well-known that with the appearance of three independent papers by Taylor, Polanyi and Orowan in the year 1934, the concept of crystal dislocations was born. Since then, dislocation theory has had many spectacular successes. It is quite appropriate therefore to be aware of the state of development of this exciting subject, sixty years after its discovery. A flavour for the vast subject of the applications of dislocation mechanisms to real materials is presented by choosing three examples, one each, drawn from metallurgy, physics and electronics. The topic of ‘Strength of metals and alloys’ is the first one, as this is also the author’s area of research. The phenomenon of solidification and crystal growth forms the next topic, especially in view of the seminal contributions made by A R Verma and his school from India. Dislocations play a useful role in the strengthening of solids, but how influential are they in affecting the performance of modern semiconductor devices? In the third example, the interesting and painstaking work done to settle this question is reviewed. Can we regard carbon fibre as thetransistor of dislocation theory? How shall we understand the long-established effects such as corrosion-fatigue, superplasticity and shape memory as well as the electrochemical and electro-mechanical properties of dislocations in semiconductor and non-metallic crystals? Answers to these questions belong to the realms of the future developments in dislocations. The talk is concluded with a discussion of these topics.     

Thermomechanical Models of Irreversible Finite Deformation of Anisotropic Solids

The proposed models for irreversible finite deformation of initially anisotropic solids are based on the hypothesis of the parameters of state, for which the authors have chosen a universal parameter (temperature) and a strain component, which is analogous to volume strains in an isotropic body and represents thermal strains of an unconstrained (stress-free) anisotropic solid. The application of this hypothesis allows the strain tensor to be resolved into a reversible and irreversible components. For irreversible processes of finite deformation of hardenable materials, the authors have proposed a deformation-type model, which makes it possible to describe a change in the type of anisotropy of initially anisotropic materials in the course of deformation. For the flow-theory-type model, the limiting state function, as given in the space of irreversible strains, allows for the experimentally observed plastic flow of anisotropic crystals under the action of hydrostatic pressure only.     

Efficient and accurate approach for powder compaction problems

 In this paper, a new approach for powder cold compaction simulations is presented. A density-dependent plastic model within the framework of finite strain multiplicative hyperelastoplasticity is used to describe the highly nonlinear material behaviour; the Coulomb dry friction model is used to capture friction effects at die-powder contact; and an Arbitrary Lagrangian–Eulerian (ALE) formulation is used to avoid the (usual) excessive distortion of Lagrangian meshes caused by large mass fluxes. Several representative examples, involving structured and unstructured meshes are simulated. The results obtained agree with the experimental data and other numerical results reported in the literature. It is shown that, contrary to other Lagrangian and adaptive h-remeshing approaches recently reported for this type of problems, the present approach verifies the mass conservation principle with very low relative errors (less than 1% in all ALE examples and exactly in the pure Lagrangian examples). Moreover, thanks to the use of an ALE formulation and in contrast with other simulations, the presented density distributions do not present spurious oscillations. Received: 20 March 2002 / Accepted: 15 October 2002 The partial financial support of the Ministerio de Ciencia y Tecnología (grant number DPI 2001-2204) is gratefully acknowledged.     

Estimation of true dihedral angles and relative grain boundary energies in polycrystals using the disector

Relative grain boundary energies can be simply related to true dihedral angles, which are the angles between grain boundary planes meeting at triple edges in polycrystals. Some limited efforts in the measurement of true dihedral angles have used the technique of serial sectioning, which is usually cumbersome and time consuming. In this study the three‐dimensional probe called the ‘disector’ has been employed to evaluate true dihedral angles. This probe, combined with automated image processing, introduces precision as well as efficiency, overcomes the disadvantages of the two‐dimensional probe and is far less tedious and less complicated than serial sectioning. It is shown that the technique is relatively simple and therefore can be applied to obtain a significantly large and accurate statistical sample of true dihedral angles. The application of this method is demonstrated by evaluating the triple junction geometry and the associated relative grain boundary energies in polycrystalline 316L austenitic stainless steel.     

Analysis of crack tip plasticity for microstructurally small cracks using crystal plasticity theory

Crack tip plastic zone sizes and crack tip opening displacements (CTOD) for stationary microstructurally small cracks are calculated using the finite element method. To simulate the plastic deformation occurring at the crack tip, a two-dimensional small strain constitutive relationship from single crystal plasticity theory is implemented in the finite element code ANSYS as a user-defined plasticity subroutine. Small cracks are modeled in both single grains and multiple grains, and different crystallographic conditions are considered. The computed plastic zone sizes and CTOD are compared with those found using conventional isotropic plasticity theory, and significant differences are observed.     

轴对称空间问题的塑性解法

本文从理想材料轴对称弹塑性问题的所有基本方程出发,研究了全塑性时轴对称空间问题的塑性应变分布规律和应力场,并推导了控制应力分布的定解方程,给出了全塑性轴对称问题的通用解法。     

Efficient return algorithms for associated plasticity with multiple yield planes

A new return method for implicit integration of linear isotropic yield criteria is presented. The basic idea is to perform all the manipulations in the principal stress space and thereby achieve very simple formulae for calculating the plastic corrector stresses, based on the constant gradient of such criteria. The return formulae are in closed form and no iteration is required. The method accounts for three types of stress return: return to a single yield plane, to a discontinuity line at the intersection of two yield planes and to a discontinuity point at the intersection between three or more yield planes. The infinitesimal and the consistent elastoplastic constitutive matrix are calculated for each type of stress return, as are the conditions to ascertain which type of return is required. The method is exemplified with the Mohr–Coulomb yield criterion. Copyright © 2005 John Wiley & Sons, Ltd.     

An efficient return algorithm for non-associated plasticity with linear yield criteria in principal stress space

An efficient return algorithm for stress update in numerical plasticity computations is presented. The yield criterion must be linear in principal stress space and can be composed of any number of yield planes. Each of these yield planes may have an associated or non-associated flow rule. The stress return and the formation of the constitutive matrix is carried out in principal stress space. Here the manipulations simplify and rely on geometrical arguments. The singularities arising at the intersection of yield planes are dealt with in a straightforward way also based on geometrical considerations. The method is exemplified on non-associated Mohr–Coulomb plasticity throughout the paper.     

Numerical Study of Scale Effects of Ultra-Thin Nickel Beams

Recent experiments have shown that metallic materials display significant size effects when the characteristic length scale of non-uniform plastic deformation is close to a micron. Couple stress plasticity has been developed to explain such phenomena by Fleck and Hutchinson. The mechanical behaviors of ultra-thin nickel beams in different boundary conditions were studied with the hybrid element developed for couple stress plasticity before. Strong scale effects are found when the beam's thickness is close to the material characteristic length scale. Such phenomena will disappear if the beam' s thickness is greatly larger than the material characteristic length scale. The scale effect is the beams inherent property and it does not change with the change of support conditions.