C. Fressengeas

Instability and localization of plastic flow in shear at high strain rates

Abstract S hear band formation in a thermal viscoplastic heat conducting material is described in a simple shear test at high strain rate with inertia effects. The classical perturbation method is discussed, and a new relative perturbation method accounting for non-steadiness of plastic flow is presented. They respectively provide instability and localization criteria which are compared. Furthermore both are compared to available nonlinear exact results and to experimental data. The influence of material parameters, initial imperfections, and boundary conditions is described.

Inertia and thermal effects on the localization of plastic flow

Abstract The influence of inertia and thermal effects (heat conduction, thermal softening) on the ductility is studied within the theoretical framework of a one-dimensional model for uniaxial tension. A linearized study of stability is discussed; nonlinear quasi-static and dynamic analyses are presented; they allow for a proper description of at least a part of the dynamic growth, and the adiabatic decrease of ductility. The theoretical results are compared with the available experimental data. The limitations of the analyses are discussed.

Spatial coupling in jerky flow using polycrystal plasticity

A multiscale approach including a finite element framework for polycrystal plasticity is used to model jerky flow, also known as the Portevin-Le Chatelier effect. The local constitutive behavior comprises the standard description of the negative strain rate sensitivity of the flow stress in the domain of instability. Due to stress gradients inherent to the polycrystal formulation, the spatial coupling involved in the spatio-temporal dynamics of jerky flow is naturally accounted for in the model, without using any ad hoc gradient constitutive formulation. For the first time, the static, hopping and propagating band types are recovered in constant strain-rate tests, as well as the temporal properties of the stress serrations. The associated dynamic regimes are characterized and found consistent with recent experimental evidence of both chaos and self-organized criticality in Al-Mg polycrystals.

Effect of rate sensitivity on slip system activity and lattice rotation

Abstract Viscoplastic constitutive models are used for crystals subjected to large strains and high strain-rates; they are based on the assumption that plastic strain occurs by viscous crystallographic slip. Rate-sensitivity and strain-rate effects on crystallographic shears and lattice rotations are investigated; it is shown that large strain-rate sensitivities such as those observed at very high strain rates and at high temperatures may increase the total number of significantly active slip systems and decrease the amount of plastic spin. This leads to contrasted texture evolutions in tension and simple shear which are described.

Multifractal Burst in the Spatiotemporal Dynamics of Jerky Flow

The collective behavior of dislocations in jerky flow is studied in Al-Mg polycrystalline samples subjected to constant strain rate tests. Complementary dynamical, statistical, and multifractal analyses are carried out on the stress-time series recorded during jerky flow to characterize the distinct spatiotemporal dynamical regimes. It is shown that the hopping type B and the propagating type A bands correspond to chaotic and self-organized critical states, respectively. The crossover between these types of bands is identified by a large spread in the multifractal spectrum. These results are interpreted on the basis of competing scales and mechanisms.

The hidden order behind jerky flow

Jerky flow, or the Portevin-Le Chatelier effect, is investigated at room temperature by applying statistical, multifractal and dynamical analyses to the unstable plastic flow of polycrystalline Al-Mg alloys with different initial microstructures. It is shown that a chaotic regime is found at medium strain rates, whereas a self-organized critical dynamics is observed at high strain rates. The cross-over between these two regimes is signified by a large spread in the multifractal spectrum. Possible physical mechanisms leading to this wealth of patterning behavior and their dependence on the strain rate and the initial microstructure are discussed.

Chapter 57 Collective behaviour of dislocations in plasticity

Publisher Summary This chapter discusses the collective dislocation behavior in cyclic deformation. During plastic flow, the spatial arrangement of the dislocation structure essentially derives from a competition between two factors. When it exists, the interaction of dislocations with strong and dense localized obstacles other than dislocations (small clusters and precipitates, lattice friction and Peierls forces) tends to induce rather uniform dislocation distributions. In such conditions, the plastic flow properties of the bulk material may simply reflect the behavior of isolated mobile dislocations. In contrast, the mutual interactions of dislocations, both local and long ranged, become all the more important as dislocations multiply. Thus, the contribution of dislocation interactions to the flow stress increases during plastic flow. At a certain stage that is characterized by a critical stress, strain, or dislocation density, the collective dislocation behavior sets in which is characterized by the emergence of dislocation-rich and dislocation-poor regions. This is usually referred to as dislocation patterning.

Dislocation transport using an explicit Galerkin/least-squares formulation

An explicit Galerkin/least-squares formulation is introduced for a quasilinear transport equation in field dislocation mechanics (FDM) and applied to the study of the kinematics of dislocation density evolution in the following physical contexts: annihilation of dislocations, expansion of a polygonal dislocation loop and simulation of a Frank–Read source. Stability analysis is carried out for the corresponding linear one-dimensional (1D) case. The formulation reduces to the Lax–Wendroff finite difference scheme for the 1D equation when equal weighting is used for the Galerkin and least-squares terms and the shape functions are linear. This conditionally stable method leads to a symmetric well-conditioned system of equations with constant coefficients, making it attractive for large-scale problems.It is shown that the transport equation, in the contexts mentioned above simplifies to the Hamilton–Jacobi equations governing geometrical optics and level-set methods. The weak solutions to these equations are not unique, and the numerical method is able to capture solutions corresponding to shock as well as rarefraction waves by appropriate algorithmic modifications.

Time distribution of stress drops, critical strain and crossover in the dynamics of jerky flow

Abstract The distribution in time of stress drops in the jerky flow of several Al–Mg alloys is investigated in velocity controlled tensile tests, in relation with the crossover from hopping to propagating bands. The distribution evolves from randomness for static bands to increasing regularity for hopping bands. This evolution culminates in a power law distribution, which breaks down into a highly disordered behaviour at the crossover with propagating bands. The critical incubation strain for the Portevin–Le Chatelier (PLC) effect is shown to follow a parallel evolution when the applied strain rate is increased. An ‘inverse’ evolution is observed until the crossover is met, followed by a ‘normal’ increase of the critical strain in the propagating regime. Both aspects are discussed in relation with characteristic time scales and microstructure evolution with strain.

Coupled phase transformations and plasticity as a field theory of deformation incompatibility

The duality between terminating discontinuities of fields and the incompatibilities of their gradients is used to define a coupled dynamics of the discontinuities of the elastic displacement field and its gradient. The theory goes beyond standard translational and rotational Volterra defects (dislocations and disclinations) by introducing and physically grounding the concept of generalized disclinations in solids without a fundamental rotational kinematic degree of freedom (e.g. directors). All considered incompatibilities have the geometric meaning of a density of lines carrying appropriate topological charge, and a conservation argument provides for natural physical laws for their dynamics. Thermodynamic guidance provides the driving forces conjugate to the kinematic objects characterizing the defect motions, as well as admissible constitutive relations for stress and couple stress. We show that even though higher-order kinematic objects are involved in the specific free energy, couple stresses may not be required in the mechanical description in particular cases. The resulting models are capable of addressing the evolution of defect microstructures under stress with the intent of understanding dislocation plasticity in the presence of phase transformation and grain boundary dynamics.