On the Connection between Continuum Crystal Plasticity and the Mechanics of Discrete Dislocations

This work aims at linking the levels of the continuum crystal plasticity with that of discrete dislocations. First, some former results about the kinematics of discrete dislocations are recalled. Then the fields at the continuum level are constructed by averaging the corresponding fields at the dislocation level. Under the assumptions of small elastic strains, small lattice curvature at the dislocation level and statistical homogeneity at the scale of the representative volume element the classical forms of the balance equations for the continuous fields can be retrieved. In addition, a multiplicative decomposition the deformation gradient in an elastic part and an irreversible part is achieved. While the elastic strains are assumed to be small, the plastic strains can be arbitrarily large

Simulation of Non-Isothermal Mechanical Tests on a Single Crystal Nickel-Basis Superalloy

An extension of the constitutive viscoplastic model of Meric and Cailletaud is presented. The new model accounts for coupling of plasticity and viscoplasticity to describe the rate dependence at low and moderate temperatures. The model contains two boundaries: an elastic one and a viscoplastic one. Between the boundaries, the only contribution to yielding is the rate dependent viscoplastic mechanism. Once the viscoplastic boundary is reached, an additional rate independent flow mechanism becomes active. However, the extended model is not able to predict properly both creep and long-term relaxation tests simultaneously. Therefore, a deformation-induced softening is assumed, which is supposed to mainly affect static recovery. The model has been calibrated with the mechanical tests on a single crystal nickel-basis superalloy. The uniaxial tests have been carried out in the temperature interval 600°C – 1100°C in [001], [011] and [111] specimens. The predicted creep, relaxation and non-isothermal cyclic tests exhibit reasonable agreement with the experimental observations

Tensile Properties of the Individual Phases in Unreacted Multifilament Nb3_{3}Sn Wires

The room temperature elastic and plastic properties under uniaxial tensile loading of the different phases of an un-reacted, internal-tin process, Nb$_{3}$Sn wire have been determined by tensile tests of whole wires and of extracted Ta, Nb and Nb alloy filaments, as well as by indentation hardness measurements in metallographic wire cross sections

Modelling avalanches in martensites

Solids subject to continuous changes of temperature or mechanical load often exhibit discontinuous avalanche-like responses. For instance, avalanche dynamics have been observed during plastic deformation, fracture, domain switching in ferroic materials or martensitic transformations. The statistical analysis of avalanches reveals a very complex scenario with a distinctive lack of characteristic scales. Much effort has been devoted in the last decades to understand the origin and ubiquity of scale-free behaviour in solids and many other systems. This chapter reviews some efforts to understand the characteristics of avalanches in martensites through mathematical modelling.Comment: Chapter in the book "Avalanches in Functional Materials and Geophysics", edited by E. K. H. Salje, A. Saxena, and A. Planes. The final publication is available at Springer via http://dx.doi.org/10.1007/978-3-319-45612-6_

Modelling at the dislocation level the reinforcement of alloys by hard precipitates: The example of Ni-base superalloys

Experimentshow that the strength of Ni-base superalloystrongly depends on the actual morphology of the $\gamma/\gamma'$ microstructure. This makes a multiphase micro-mechanical modelling indispensable for a reliable safety analysis. Unfortunately, the classical crystal plasticity theory leads to erroneous predictions, when applied to the scale of the $\gamma/\gamma'$ microstructure. This paper suggests that this failure is related to a breakdown of the meaning of plastic strain at the scale of the size of dislocation loops. We propose a global modelling of the $\gamma/\gamma'$ compound that overcomes the deficiencies of local crystal plasticity at this description level

Hysteresis In Discrete-systems of Possibly Interacting Elements With A Double-well Energy

We study in this paper the hysteretic behavior of a discrete system constituted by a finite number of elements ("snap-springs") whose energy has two parabolic wells. The guideline idea is that, in many circumstan?es, hysteresis can be due to the presence of relative minimizers of a potential ("metastable states") in which the system might get locked during its quasistatic evolution. A careful investigation is thus carried out of the relative minimizers of the total energy of our system of snap-springs under imposed total displacement, and of the barriers separating them. This is done both in the case of noninteracting elements and in the case in which some interaction is present that gives rise in the energy to an extra "coherence" term of special form. The results allow discussion of various hysteretic phenomenal also in the presence of vibrational motion of the elements. This study of a simple but suggestive discrete system will hopefully prove itself of help in understanding the implications regarding hysteresis of certain continuum theories recently proposed to model phase transitions in the solid state, in which the energy density is assumed, as here, to be biparabolic, and in which the coherence energy term we adopt arises in a natural way when equilibria involving mixtures of kinematically noncoherent phases are considered. In these cases the optimal microstructures are known to be layered, and physically this gives a good basis to our discrete calculation

One-dimensional Quasi-static Nonisothermal Evolution of Shape-memory Material Inside the Hysteresis Loop

We study in this paper the quaistatic nonisothermal process of a one-dimensional bar consisting of a two-phase shape-memory material. The system of p.d.e.'s governing the evolution of the bar is obtained by means of a temperature-dependent hysteretic stress-strain law that we formulate as a "plasticity" criterion and a hysteresis operator. The constitutive theory is developed here on the basis of the mixture approach proposed by Muller [1] and of a natural extrapolation of the isothermal experimental data regarding the behavior of the material inside the hysteresis loop recently described Muller and Xu [2]. Numerical simulations are presented for three initial and boundary-value problems of interest with regard to uniaxial stretching experimental tests