Plastic multipliers as driving variables of numerical simulation in elastoplasticity

Statics of elasto-plastic media is stated in terms of eigenstrains acting upon a background elastic problem with fixed (initial) stiffness. In order to minimize the number of unknowns and to provide computationally cheap algorithms plastic multipliers are used as main driving variables. Fixed-point type iterations are suggested for computing plastic multipliers within the load increment. Numerical experiments results are shown to be in good correlation with other software results. A range of problems is outlined where the usage of the proposed algorithms can be advantageous.     

Physics-based plasticity model incorporating microstructure changes for severe plastic deformation

During machining processes, materials undergo severe deformations that lead to different behavior than in the case of slow deformation. The microstructure changes, as a consequence, affect the materials properties and therefore influence the functionality of the component. Developing material models capable of capturing such changes is therefore critical to better understand the interaction process–materials. In this paper, we introduce a new physics model associating Mechanical Threshold Stress (MTS) with Dislocation Density (DD) models. The modeling and the experimental results of a series of large strain experiments on polycrystalline copper (OFHC) involving sequences of shear deformation and strain rate (varying from quasi-static to dynamic) are very similar to those observed in processes such as machining. The Kocks–Mecking model, using the mechanical threshold stress as an internal state variable, correlates well with experimental results and strain rate jump experiments. This model was compared to the well-known Johnson–Cook model that showed some shortcomings in capturing the stain jump. The results show a high effect of rate sensitivity of strain hardening at large strains. Coupling the mechanical threshold stress dislocation density (MTS–DD), material models were implemented in the Abaqus/Explicit FE code. The model shows potentialities in predicting an increase in dislocation density and a reduction in cell size. It could ideally be used in the modeling of machining processes.     

A continuum model for intermittent deformation of single crystal micropillars

Strain bursts are often observed during compression tests of single crystal micropillars. In this work, we formulate a new continuum model that accounts for the strain bursts within the framework of crystal plasticity. The strain bursts are separated from the loading stage (nearly elastic loading) by introducing a dimensionless constant in the continuum model, and are detected by load serrations. The boundary conditions in the context of micropillar compression are studied and they are shown to be changing and unpredictable as plastic deformation proceeds. To evaluate the validity of our model, finite element simulations of the uniaxial compression tests on nickel micropillars are performed. Our simulations produce clearly visible strain bursts during the plastic flow and the produced intermittent flows are comparable with the experimental observations. For the bulk crystal, a series of strain bursts is identified in the course of plastic flow, despite an apparently smooth stress–strain response. We also show that the intermittent flow is intensified in the micrometer-scale due to both increasing numbers of the successive strain bursts and increasing amplitude of the strain burst, when the specimen size decreases. Finally, we show that the occurrences of the strain bursts are always associated with negative values of the second-order work.     

Multi-mechanism models: Present state and future trends

The paper gives a review of the main features introduced in the multi-mechanism models, of the present possibilities and of further developments.In the two last decades, various materials and mechanical effects were studied using multi-mechanism model types. Particular attention was given to the possible link between the mechanism definitions and the physical deformation sources. The main results of these works are first recalled. Propositions of future development for the multi-mechanism models are finally given.     

From Dislocation Motion to an Additive Velocity Gradient Decomposition, and Some Simple Models of Dislocation Dynamics

A mathematical theory of time-dependent dislocation mechanics of unrestricted geometric and material nonlinearity is reviewed. Within a ``small deformation" setting, a suite of simplified and interesting models consisting of a nonlocal Ginzburg Landau equation, a nonlocal level set equation, and a nonlocal generalized Burgers equation is derived. In the finite deformation setting, it is shown that an additive decomposition of the total velocity gradient into elastic and plastic parts emerges naturally from a micromechanical starting point that involves no notion of plastic deformation but only the elastic distortion, material velocity, dislocation density and the dislocation velocity. Moreover, a plastic spin tensor emerges naturally as well.     

An Eulerian hybrid WENO centered-difference solver for elastic–plastic solids

We present a finite-difference based solver for hyper-elastic and viscoplastic systems using a hybrid of the weighted essentially non-oscillatory (WENO) schemes combined with explicit centered difference to solve the equations of motion expressed in an Eulerian formulation. By construction our approach minimizes both numerical dissipation errors and the creation of curl-constraint violating errors away from discontinuities while avoiding the calculation of hyperbolic characteristics often needed in general finite-volume schemes. As a result of the latter feature, the formulation allows for a wide range of constitutive relations and only an upper-bound on the speed of sound at each time is required to ensure a stable timestep is chosen. Several one- and two-dimensional examples are presented using a range of constitutive laws with and without additional plastic modeling. In addition we extend the reflection technique combined with ghost-cells to enforce fixed boundaries with a zero tangential stress condition (i.e. free-slip).     

Helium and point defect accumulation: (i) microstructure and mechanical behaviour

Ferritic/martensitic (F/M) steels are good candidate structural materials for the future fusion reactors and spallation sources. However, irradiation of steels is known to produce hardening, loss of ductility, shift in ductile to brittle transition temperature (DBTT) and reduction of fracture toughness and creep resistance starting at low doses. Helium (He), produced by transmutation during the irradiation, also impacts mechanical properties. Numerous experimental and theoretical studies on the evolution of the microstructure of steels under irradiation have been conducted until now. We review the effect of irradiation-induced point defects and in particular of He on the mechanical properties of F/M steels. To cite this article: R. Schäublin et al., C. R. Physique 9 (2008).     

Statistical aspects of the identification of material parameters for elasto-plastic models

Summary The presented method to identify material parameters for inelastic deformation laws is based on the numerical analysis of inhomogeneous stress and strain fields received from suitable experiments. Tensile and bending tests were carried out to obtain elastic and hardening parameters. The deformation law for small elasto-plastic strains is presented as a system of nonlinear differential and algebraic equations (DAE) consisting of the stress–strain relation, evolution equations for the internal variables and the yield condition. Different rules for the evolution equations of isotropic, kinematic and distorsional hardening are proposed. The DAE are discretized using an implicit Euler method, and the resulting system of nonlinear algebraic equations is solved using the Newton method. Deterministic optimization procedures are preferred to identify material parameters from a least-squares functional of numerical and measured comparative quantities. The gradient of the objective function was calculated using a semianalytical sensitivity analysis. Due to measurement errors, the optimal sets of material parameters are non unique. The approximate estimation of confidence regions and the calculation of correlation coefficients is presented. The results of several optimization processes for material parameters of elasto-plastic deformation laws show a good agreement between measured and calculated values, but they show also problems which may occur if systematic errors will not be recognized and deleted. Received 30 September 1999; accepted for publication 8 March 2000     

On The Maximum Friction Law for Rigid/Plastic,Hardening Materials

For a rigid/plastic, hardening material model, it is shown that the velocity fields adjacent to surfaces of maximum friction must satisfy the sticking condition. This means that the stress boundary condition, the maximum friction law, may be replaced by the velocity boundary condition. Axisymmetric flows without rotation and planar flows are considered.     

Characterization of nonlinear response in quasi-unidirectional E-glass fabric reinforced polypropylene composites under off-axis tensile loading

The present paper addressed the nonlinear stress-strain response in quasi-unidirectional E-glass fabric reinforced polypropylene composites under off-axis tensile loading. A series of monotonic and cyclic loading-unloading tensile tests were carried out. Both irreversible strains and stiffness degradation were observed in cyclic loading-unloading tests, which indicate that the nonlinear response of composites was induced by a combination of damage and plasticity. A coupled damage-plasticity model was employed to describe the nonlinear off-axis tensile stress-strain relation of materials. In this model, a plastic potential function together with associated plastic flow rule were adopted to assess the evolution of plastic strains. The damage variables in forms of stiffness degradation were expressed as a Weibull function of the effective stress. A full suite of model parameters was experimentally determined from cyclic loading-unloading tensile tests. The stress-strain curves predicted by this model agreed well with experimental results.