Engineering Plasticity and Its Applications

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Authors: Young Won Chang
Abstract: An internal variable theory has been proposed to account for the essential microstructures during inelastic deformation. The framework of the theory is built on the basis of well known dislocation dynamics to provide the concept of an internal strain tensor as the most fundamental deformation state variable. The plastic and inelastic strain rate tensors are then naturally defined and also a kinematics relation among them can further be derived from the time rate of change of this internal strain tensor, which in fact accounts for the evolution of microstructures during inelastic deformation. To complete the theory, the constitutive relations between the various stress variables and their conjugate deformation rate variables are then derived based on the dislocation kinetics. The theory is then further extended to describe the structural superplasticity, taking this slip zone model with dislocation pile-ups as the major accommodation mechanism for grain boundary sliding. The experimental results obtained from the various crystalline materials are then presented and compared with each other in relation to the internal variable theory for inelastic deformation.
Authors: Han Qing Jiang, Keh Chih Hwang, Young Huang
Abstract: It is commonly believed that continuum mechanics theories may not be applied at the nanoscale due to the discrete nature of atoms. We developed a nanoscale continuum theory based on interatomic potentials for nanostructured materials. The interatomic potential is directly incorporated into the continuum theory through the constitutive models. The nanoscale continuum theory is then applied to study the mechanical deformation and thermal properties of carbon nanotubes, including (1) pre-deformation energy; (2) linear elastic modulus; (3) fracture nucleation; (4) defect nucleation; (5) electrical property change due to mechanical deformation; (6) specific heat; and (7) coefficient of thermal expansion. The nanoscale continuum theory agrees very well with the experiments and atomistic simulations without any parameter fitting, and therefore has the potential to be utilized to complex nanoscale material systems (e.g., nanocomposites) and devices (e.g., nanoelectronics).
Authors: David L. McDowell, Hae Jin Choi, Jitesh Panchal, Ryan Austin, Janet Allen, Farrokh Mistree
Abstract: Design has traditionally involved selecting a suitable material for a given application. A materials design revolution is underway in which the classical materials selection approach is replaced by design of material microstructure or mesostructure to achieve certain performance requirements such as density, strength, ductility, conductivity, and so on. Often these multiple performance requirements are in conflict in terms of their demands on microstructure. Computational plasticity models play a key role in evaluating structure-property relations necessary to support simulation-based design of heterogeneous, multifunctional metals and alloys. We consider issues related to systems design of several classes of heterogeneous material systems that is robust against various sources of uncertainty. Randomness of microstructure is one such source, as is model idealization error and uncertainty of model parameters. An example is given for design of a four-phase reactive powder metal-metal oxide mixture for initiation of exothermic reactions under shock wave loading. Material attributes (e.g. volume fraction of phases) are designed to be robust against uncertainty due to random variation of microstructure. We close with some challenges to modeling of plasticity in support of design of deformation and damage-resistant microstructures.
Authors: Alan Needleman, E. Van der Giessen, Vikram Deshpande
Authors: Yoji Shibutani, Tomohito Tsuru
Abstract: The present paper summarizes the crystallographic dependence of the displacement burst behavior observed in nanoindentation using two single crystalline aluminum (Al) materials and copper (Cu) with three kinds of surface indices, namely (001), (110) and (111). From the critical indent load at the first burst, the critical resolved shear stresses (CRSSs) of the collective dislocation nucleation were estimated in reference to molecular dynamics (MD) simulations. These are almost one-tenth of the shear modulus, which are close to the ideal values. We explain the nanoplastic mechanics by a comprehensive energy balance model to describe the linear relation between the indent load and the burst width of the first displacement burst and by the nucleation model consisting of three-dimensional discrete dislocations to evaluate the number of dislocations nucleating. The distance between the emitted dislocation loops of Al is found to be fairly large. Thus, Al is expected to exhibit a less tangled network of dislocations just below the indentation than Cu, which has a lower stacking fault energy.
Authors: Viggo Tvergaard
Abstract: Cavitation instabilities have been predicted for a single void in a ductile metal stressed under high triaxiality conditions. In experiments for a ceramic reinforced by metal particles a single dominant void has been observed on the fracture surface of some of the metal particles bridging a crack, and also tests for a thin ductile metal layer bonding two ceramic blocks have indicated rapid void growth. Analyses for these material configurations are discussed here. When the void radius is very small, a nonlocal plasticity model is needed to account for observed size-effects, and recent analyses for the influence of such size-effects on cavitation instabilities are presented. When a metal contains a distribution of micro voids, and the void spacing compared to void size is not extremely large, the surrounding voids may affect the occurrence of a cavitation instability at one of the voids. This has been analyzed for a material containing a periodic distribution of spherical voids with two different void sizes, where the stress fields around larger voids may accelerate the growth of smaller voids. Another approach has been an analysis of a unit cell model in which a central cavity is discretely represented, while the surrounding voids are represented by a porous ductile material model in terms of a field quantity that specifies the variation of the void volume fraction in the surrounding metal.
Authors: Kwang Seok Lee, Won Kyu Bang, Tae Kwon Ha, Sang Ho Ahn, Young Won Chang
Abstract: The formability of a Zr41.2Ti13.8Cu12.5Ni10Be22.5 bulk metallic glass has been investigated in the present study in relation to the heating rate. A series of extrusion tests after rapid heating has been performed in a laboratory scale together with sheet forming tests after slow heating for comparison purpose. The basic processing map based on dynamic materials model (DMM) and compression test data has been utilized to evaluate feasible forming conditions. The macroscopic formability, classified by fully formed, partially formed or a catastrophic fracture, is found to have a good correspondence with the iso-efficiency contour in the processing map. The region of high power dissipation efficiencies with η>0.8 is found to be broaden by avoiding crystallization events due to reduced exposure time in extrusion process with a faster heating rate.
Authors: Feng Huan Sha, Long Mao Zhao, Gui Tong Yang
Abstract: The dynamic buckling caused by propagation of a stress wave in single-wall carbon nanotube subjected to impact torque is investigated. The single-wall carbon nanotube is modeled by a cylindrical shell with semi-infinite length, and the dynamic buckling under impact torque is reduced to a bifurcation problem caused by the propagation of torsion stress wave. The bifurcation problem can be converted to solving a group of nonlinear algebraic equations. The numerical computation is carried out, and the effects of the different parameters on dynamic buckling are discussed. It is found that if critical buckling time of the carbon nanotube is different, the corresponding buckling model is different, too. Relation between the critical buckling stress and the critical buckling time is given. Molecular-dynamic simulations of torsional deformation of a single-wall carbon nanotube have been used to obtain the critical buckling strain, which is 0.064. In this work, the critical buckling strain obtained by the continuum model is 0.061, which is very close to the value 0.064. Single-wall carbon nanotubes have very much powerful anti-impact torque, and the critical buckling shearing stress can reach up to 132GPa.

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