Large Strain Response of Kinematic Hardening Elastoplasticity with the Logarithmic Rate: Swift Effect in Torsion

Recently, a new Eulerian rate type kinematic hardening elastoplasticity model has been established by utilizing the newly discovered logarithmic rate. It has been proved that this model is unique among all the objective kinematic hardening elastoplastic models with all possible objective corotational stress rates and other known objective stress rates by virtue of the self-consistency criterion: the hypoelastic formulation intended for elastic behaviour must be exactly integrable to deliver a hyperelastic relation. The finite simple shear response of this model has been studied and shown to be reasonable for both shear and normal stress components. The objective of this work is to further study the large deformation response of this model, in particular the well-known Swift effect, in torsion of thin-walled cylindrical tubes with free ends. Analytical perturbation solution and numerical solution are presented for the case of linear kinematic hardening at large compressible deformation. It is shown that the prediction from the foregoing model is in good accord with experimental data reported in literature.     

Weak Forms of Shakedown for Elastic–Plastic Structures Exhibiting Ductile Damage

A special weak-form shakedown is studied for elastic–plastic internal-variable material models with nonlinear hardening, damageable elastic moduli and damageable yield surface, in the hypothesis of ductile damage, (i.e. damage induced by plastic strains), but the precise evolutive law of damage being left unspecified. Sufficient weak-form shakedown theorems are presented, one static and another kinematic, each assessing whether eventually plastic deformations cease together with their consequences, including ductile damage. A two-sided delimitation is provided, within which the weak-form shakedown safety factor can be located. An upper bound to the post-transient damage for a particular isotropic damage model is also proposed. A simple numerical application is presented. Sommario. Si studia una forma speciale debole di adattamento strutturale per materiali elasto-plastici con variabili interne e con incrudimento non lineare, nonché moduli elastici e superficie di plasticità soggetti a danno duttile (cioè indotto dalle deformazioni plastiche) con una non precisata legge evolutiva. Si presentano due teoremi sufficienti per l'adattamento in forma debole, ciascuno essendo capace di predire se la deformazione plastica infine cessa unitamente alle sue conseguenze, compreso il danno duttile. Si definisce una delimitazione bilaterale entro la quale ricade il fattore di sicurezza associato a questa forma debole di adattamento. Si propone altresì una delimitazione superiore per il danno accumulato nella fase transitoria nel caso di un tipo particolare di danno isotropo. Si presenta una semplice applicazione numerica.     

An application of Curie’s principle to elastoplastic dynamics

This paper deals with the stability and the dynamics of a harmonically excited elastic–perfectly plastic unsymmetrical oscillator. Stability of the periodic orbits is analytically investigated with a perturbation approach. The occurrence of ratcheting effect is discussed for this system, and is related to the loss of symmetry of the periodic orbit in the phase space. Curie’s principle of symmetry is numerically verified for the symmetrical system with positive damping. Therefore, the observation of ratcheting phenomenon is necessarily associated to a breaking of symmetry in the constitutive behaviour, or in the forcing term. However, the generalized version of Curie’s principle has to be considered when a negative damping is introduced.     

Effects of the stress state on plasticity and ductile failure of an aluminum 5083 alloy

The experimental and numerical work presented in this paper reveals that stress state has strong effects on both the plastic response and the ductile fracture behavior of an aluminum 5083 alloy. As a result, the hydrostatic stress and the third invariant of the stress deviator (which is related to the Lode angle) need to be incorporated in the material modeling. These findings challenge the classical J₂ plasticity theory and provide a blueprint for the establishment of the stress state dependent plasticity and ductile fracture models for aluminum structural reliability assessments. Further investigations are planned to advance, calibrate and validate the new plasticity and ductile fracture models.     

Macro modelling and homogenization for transformation induced plasticity of a low-alloy steel

Metal forming processes are important technologies for the production of engineering structures. In order to optimize the resulting material properties, it becomes necessary to simulate the entire forming process by taking into account physical effects such as phase transformations. In this work, we concentrate on the phase change from austenite to martensite and present a macroscopic material model, which combines the effect of classical plasticity with the effect of transformation induced plasticity (TRIP). An extensive experimental database for a low-alloy steel is used for parameter identification, thus taking into account the effects of uniaxial compressive and tensile stress on the kinetics of phase transformation at different temperatures. For temperatures below the martensite start temperature with simultaneous stresses above the yield limit, it is difficult to obtain experimental data. Consequently, a numerical homogenization technique is employed for this case. In a further part of this paper, an effective integration scheme is provided, which is implemented into a commercial finite element program. In a finite element simulation, the austenite to martensite phase transformation in a shaft subjected to thermal loading is investigated.     

New discrete element models for elastoplastic problems

The discrete element method （DEM） has attractive features for problems with severe damages, but lack of theoretical basis for continua behavior especially for nonlinear behavior has seriously restricted its application. The present study proposes a new approach to developing the DEM as a general and robust technique for modeling the elastoplastic behavior of solid materials. New types of connective links between elements are proposed, the interelement parameters are theoretically determined based on the principle of energy equivalence and a yield criterion and a flow rule for DEM are given for describing nonlinear behavior of materials. Moreover, a numerical scheme, which can be applied to modeling the behavior of a continuum as well as the transformation from a continuum to a discontinuum, is obtained by introducing a fracture criterion and a contact model into the DEM. The elastoplastic stress wave propagations and the tensile failure process of a steel plate are simulated, and the numerical results agree well with those obtained from the finite element method （FEM） and corresponding experiment, and thus the accuracy and efficiency of the DEM scheme are demonstrated.     

The role of the weakest-link mechanism in controlling the plasticity of micropillars

We present a computational study on the effects of sample size on the strength and plastic flow characteristics of micropillars under compression loading. We conduct three-dimensional simulations using the parametric dislocation dynamics coupled with the boundary element method. Two different loading techniques are performed. The plastic flow characteristics as well as the stress-strain behavior of simulated micropillars are shown to be in general agreement with experimental observations. The flow strength versus the diameter of the micropillar follows a power law with an exponent equal to -0.69. A stronger correlation is observed between the flow strength and the average length of activated dislocation sources. This relationship is again a power law, with an exponent -0.85. Simulation results with and without the activation of cross-slip are compared. Discontinuous hardening is observed when cross-slip is included. Experimentally observed size effects on plastic flow and work-hardening are consistent with a “weakest-link activation mechanism”.     

Dynamics of texture evolution in face-centered cubic polycrystals

Texturing of polycrystals under slip-dominated plastic deformation is driven by reorientation velocity fields that arise from the lattice spin that accompanies restricted slip. Here, the dynamics of reorientation velocity fields are analyzed to isolate mechanisms by which textures develop and dissipate. Two tools are introduced to enable this analysis: linear stability analysis to assess behavior of equilibrium orientations, and a parametrization of lattice spins to enable analysis of fields without equilibria. This toolkit is applied to face-centered cubic (FCC) polycrystals and sheds new insight into texture development under three representative deformation modes: plane strain compression, pure shear and simple shear.     

A simple plasticity model for prediction of non-coaxial flow of sand

A bounding surface plasticity model for non-coaxiality, another aspect of anisotropic behavior of sands under rotation of principal stress axes; is developed in the critical state framework. Numerous experimental evidences exist that corroborate dependence of plastic shear strain rate direction on inherent fabric anisotropy. At first, general expressions for plastic strain rate with respect to possible emerge of non-coaxial flow are obtained. Consequently, using an anisotropy state parameter that is specially developed for this model and accounts for the interaction between imposed loading and soil fabric; effect of anisotropy on plastic flow direction is taken into account. Besides, novel circumstances are proposed for plastic modulus and dilatancy under rotation of principal stress axes. Finally, it is shown that the model is able to simulate successfully the non-coaxial behavior of sands subjected to principal stress axes rotation.     

On the Macroscopic Description of Stored Energy and Self Heating During Plastic Deformation

In order to describe the complex cyclic hardening and softening properties of austenitic steels, we developed a simple phenomenological plasticity model during previous work. Now, we embed the model in a thermomechanical framework such that the second law in terms of the Clausius–Duhem inequality is fulfilled. Since the thermomechanical generalisation of the model is a rather formal and in some sense an arbitrary procedure, we check the implications of the generalised phenomenological model in context of two thermomechanical investigations. First, we study the fraction of the plastic work, which is not dissipated as heat and consequently stored in the material. Second, based on some simplifying assumptions, we present a semi-analytical solution of the thermomechanical problem of a cylindrical rod heated by plastic dissipation under uniaxial tension–compression loading. In both cases, the model response is in accordance with experimental observations.