Modelling Quasicrystal Plastic Deformation By Means of Constitutive Equations
- PDF / 44,070 Bytes
- 6 Pages / 596 x 842 pts (A4) Page_size
- 40 Downloads / 221 Views
Modelling Quasicrystal Plastic Deformation By Means of Constitutive Equations M. Feuerbacher1, P. Schall1, Y. Estrin2, Y. Bréchet3, and K. Urban1 1 Forschungszentrum Jülich GmbH, D-52425 Jülich, Germany 2 IWW, TU Clausthal, 38678 Clausthal-Zellerfeld, Germany 3 LTPCM, 38402 St. Martin d’ Heres, France ABSTRACT The interpretation of plastic deformation experiments on quasicrystals is a challenging task due to the occurrence of changes of the structure during deformation. In this paper, we present a quantitative model for quasicrystal plasticity on the basis of a constitutive-equations Ansatz, which takes these effects into account. A single-internal-variable model of the kind commonly used for describing crystal plasticity, is adapted for the description of the dislocation density evolution in a quasicrystal. In addition, we introduce a structural parameter that accounts for the evolution of order in the course of plastic deformation. The numerical solution of the resulting set of evolution equations yields the flow stress and the dislocation density as a function of strain, which can be directly compared to corresponding experimental curves obtained on icosahedral Al-Pd-Mn. An excellent agreement between experiment and the calculated curves obtained using our model is found. INTRODUCTION The mechanisms of plastic deformation of crystals and quasicrystals are fundamentally different due to the lack of translational symmetry of the latter. Dislocations moving through a quasicrystalline material necessarily alter the structure and leave behind a defected plane. It was shown experimentally [1, 2] as well as by molecular dynamics simulations [3] that a plane of phason defects („phason wall“) is created in the wake of a moving dislocation. Since the introduction of phasons into a quasicrystal structure leads to a departure from the ideal quasiperiodic order, one can conclude that the degree of order in a quasicrystal decreases as a result of plastic deformation. The influence of a change of the degree of order on the plastic properties of a material have been discussed by Fisher [4], who evaluated the stress contribution due to disordering in short-range ordered materials. Quasicrystals possess extraordinarily high brittle-to-ductile transition temperatures, on the order of 70 to 80 % of their liquidus temperature [5]. Plastic deformation to considerable strains can only be carried out at elevated temperatures, where recovery inevitably takes place at a considerable rate. Thus, we are facing another source of structural changes during plastic deformation. As shown by Messerschmidt et al. [6], dynamic recovery processes have a substantial influence on the plastic deformation of quasicrystals. In quasicrystal plasticity one has therefore to cope with two sources of structural changes, which makes it difficult to interpret the results of plastic deformation experiments. This refers particularly to incremental tests, such as strain-rate jumps and temperature changes, as well as to stress relaxations, which are widely used to
Data Loading...
