Robert Peyroux

Thermomechanical couplings and pseudoelasticity of shape memory alloys

Abstract Energy balances of a polycrystalline CuZnAl Shape Memory Alloy are performed using infrared and calorimetric techniques. The experiments underline the main role of temperature variations induced by deformation process on the stress–strain curves. A thermodynamic analysis shows variations essentially due to the latent heat of phase change and indicates a very small intrinsic dissipated energy compared with deformation work or latent heat. On the basis of these results, a behaviour model that takes account of thermomechanical couplings is proposed. Implemented in a finite elements code, this model is used to verify the consistency and the potentialities of such an approach by means of numerical experiments.

Vibrational dynamics of confined granular materials.

By means of two-dimensional contact dynamics simulations, we analyze the vibrational dynamics of a confined granular layer in response to harmonic forcing. We use irregular polygonal grains allowing for strong variability of solid fraction. The system involves a jammed state separating passive (loading) and active (unloading) states. We show that an approximate expression of the packing resistance force as a function of the displacement of the free retaining wall from the jamming position provides a good description of the dynamics. We study in detail the scaling of displacements and velocities with loading parameters. In particular, we find that, for a wide range of frequencies, the data collapse by scaling the displacements with the inverse square of frequency, the inverse of the force amplitude, and the square of gravity. Interestingly, compaction occurs during the extension of the packing, followed by decompaction in the contraction phase. We show that the mean compaction rate increases linearly with frequency up to a characteristic frequency and then it declines in inverse proportion to frequency. The characteristic frequency is interpreted in terms of the time required for the relaxation of the packing through collective grain rearrangements between two equilibrium states.

Short-time dynamics of a packing of polyhedral grains under horizontal vibrations

Abstract.We analyze the dynamics of a 3D granular packing composed of particles of irregular polyhedral shape confined inside a rectangular box with a retaining wall subjected to horizontal harmonic forcing. The simulations are performed by means of the contact dynamics method for a broad set of loading parameters. We explore the vibrational dynamics of the packing, the evolution of solid fraction and the scaling of dynamics with the loading parameters. We show that the motion of the retaining wall is strongly anharmonic as a result of jamming and grain rearrangements. It is found that the mean particle displacement scales with inverse square of frequency, the inverse of the force amplitude and the square of gravity. The short-time compaction rate grows in proportion to frequency up to a characteristic frequency, corresponding to collective particle rearrangements between equilibrium states, and then it declines in inverse proportion to frequency.

Analyse expérimentale et modélisation numérique des couplages thermomécaniques dans les matériaux solides

In the first part, the theoretical and experimental framework used to present the thermomechanical behaviour of solid materials is briefly recalled. The main feature of the experimental approach relies on the use of thermographical techniques allowing us to deduce, from the thermal data, the distribution of heat sources arising during the mechanical transformation. In the particular case of homogeneous thermomechanical tests, an energy balance can be performed and used to derive the behavioural constitutive equations. When heterogeneities occur, the infrared images facilitate the analysis of localization mechanisms. In the second part, basic aspects of homogenization techniques are reiterated. Related to thermomechanical couplings, homogenization improves the description of the behaviour of materials and structures in which microstructural phenomena have a significant influence at the macroscopic scale. Several finite element simulations are shown concerning the thermoviscoelasticity of polymers, the thermoelasticity coupled with damage in composites, and the pseudoelastic behaviour related to the solid-solid phase change of shape memory alloys.

Modélisation numérique des couplages en thermomécanique des solides

ABSTRACT In a first part the thermodynamic framework used to introduced the behavioral constitutive equations of solid materials is reminded. Using illustrative examples, the different terms of the energy balance are introduced, specially those due to thermomechanical coupling mechanisms. In a second part the main concepts on multiscale approach are introduced, focussing on coupling aspects, and the way of embedding coupled constitutive equations in a finite element code is discussed. We finally present four applications to illustrate the above- mentioned approaches.

Phenomenological Constitutive Equations for Numerical Simulations of SMA's Structures. Effects of Thermomechanical Couplings

Tension-compression tests at different room temperatures and at different strain rates have been performed on Shape Memory Alloys (CuZnAl, NiTi) using a thermomechanical device. The experiments underline the main role of the temperature variations induced by the deformation process on the stress-strain curves. These variations are essentially due to the latent heat of phase change and the analysis of the associated energy balances shows that the intrinsic dissipated energy remains very small compared to deformation work or latent heat of phase change. On the basis of these results, a behavioral model is proposed that assumes an intrinsic dissipation identically equal to zero and that considers anisothermal deformation processes. This model, written under the formalism of Generalized Standard Materials takes into account the thermoelastic couplings and considers two self-accommodating martensite variants. It is implemented in a finite element code realized to predict the effects of thermomechanical couplings. An implicit integration scheme is used to derive at each step in time the fields stress, strain, temperature, and volume proportions of phases. At each step and due to the thermomechanical coupling, we have to solve non-symmetric linear systems. Numerical simulations are shown first to verify the coherence with the experimental results obtained under uniaxial loading, and secondly to underline the practical interest of such an approach to design SMAs structures.

Influence of Particle Shape on Shear Stress in Granular Media

We analyze the contact and force networks in a dense confined packing of pentagonal particles simulated by means of the contact dynamics method. The particle shape effect is evidenced by comparing the data from pentagon packing and from a packing with identical characteristics except for the circular shape of the particles. A surprising observation is that the pentagon packing develops a lower structural anisotropy than the disk packing. We show in this work that this weakness is compensated by a higher force anisotropy that leads to enhanced shear strength of the pentagon packing. With the polygonal shape of the particles, the strong force chains are mostly composed of edge-to-edge contacts with a marked zig-zag aspect.

Multiscale thermomechanical approaches to SMA behaviour

This paper presents, in a synthetic way, several works performed on shape memory alloys (SMAs). Three scales of description are used according to whether one seeks to numerically predict the possible microstructural configurations of phases in equilibrium or the behavior of a mono- and polycrystal of SMA during a phase transition.

Propagation of Phase Change Front in Monocrystalline SMA

Calorimetric effects related to the propagation of phase change front in a monocrystalline sample of CuZnAl shape memory alloy were derived from thermographic data analysis. During a load-controlled test, the displacement of the front induces a creep of the sample strongly depending on thermal exchanges with the surroundings. The main role played by the thermomechanical couplings can be pointed out by reversing the heat flux at the boundary of the sample: this leads to an inversion of the front propagation way associated with a recovery of the creep strain. We propose a behavioral modelling that takes into account the thermomechanical couplings accompanying the phase transition in single-crystal CuZnAl samples. The goal of this model is to put forward the significant role played by the heat diffusion in the propagation mode of the phase change fronts. Numerical simulations show the existence of phase change fronts such as the observed ones, and give good predictions of the calorimetric and kinematic effects accompanying the propagation.

Thermomechanical Couplings and Scale Transitions in Mechanics of Materials

Mechanics of Materials has experienced this last decade a considerable expansion. The widening, to non strictly mechanic sciences, of available knowledge and data about the material behaviour has permitted to get a global view of the phenomena accompanying the deformation processes. The use of innovative experimental techniques, the writing of consistent theoretical framework and the recourse to high-performance numerical methods allow to analyse, to understand and to simulate the materials behaviour. Two research areas are particularly active these last years. On the one hand, the analysis of the microstructure of materials reveals the phenomena associated with the deformation process, and the use of scale transition techniques permits to integrate this description and to derive a more valuable macroscopic modelling. On the other hand, these phenomena often require variables that complete the classical displacements, strain or efforts of the mechanics. The taking into account of a temperature or a volumic fraction of phase in the constitutive equations implies the modelling of couplings between variables and the derivation of an adapted framework. The interest of this approach is again to get a more valuable description of the material behaviour, and also to use these additional variables as real tracers of the deformation process of the material.