Crystal plasticity modeling

M.F. Horstemeyer et al A multiscale analysis of fixed-end simple shear using molecular dynamics, crystal plasticity, and a macroscopic internal state variable theory. Modell. Sim. Mat. Sci. Eng. 11, 265-286 (2003)... 

V.S. Deshpande et al Discrete dislocation plasticity modeling of short cracks in single crystals. Acta Mater. 51, 1-15 (2003)... 

This equation says that the critical stress on the slip system can change as a result of the accumulation of plastic strain on the slip system. The accumulation of plastic strain on the slip system is measured in terms of the shear strain yp. The matrix hap is the so-called hardening matrix and is the backbone of a hardening law for single crystal plasticity. One of the dominant tasks facing those who aim to build viable models of plasticity on the basis of insights at the dislocation level is to probe the veracity of expressions like that given above. 

From the perspective of the present discussion, our key objective is to uncover the detailed crystallographic underpinnings of single crystal plasticity. From the standpoint of a finite element model of such plasticity, what distinguishes the kinematic treatment of fee A1 from that of hep Zn In a word, the primary distinction is the presence of different slip systems in these different materials. The notion of a slip system refers to a partnership between two directions, the slip plane normal and the slip direction. 

As a result of these arguments, within the confines of continuum models of single crystal plastic deformation, the total plastic strain rate can be written as... 

Computational Mechanics at the Mesoscale by A. Needleman, Acta Mater. 48, 105 (2000) offers a deeper perspective on the multiscale aspects of modeling plasticity than that offered in the current chapter. Needleman s discussion descends from the perspective of crystal plasticity to the level of dislocation dynamics. 

Rheology experiments also give information in the determination of wax appearance temperatures of crude oils. In this research, WATs of crude oils were determined by viscometry from the point where the experimental curve deviates from the extrapolated Arrhenius curve (Figure 4). It was observed that all crude oils, except highly asphaltenic samples, are Newtonian fluids above their wax appearance temperatures. The flow behaviour of crude oils is considerably modified by the crystallization of paraffins corresponding to the variation of the apparent viscosity with temperature. Below the WAT, flow becomes non-Newtonian and approaches that of the Bingham and Casson plastic model [17,18]. 

We have now discussed in turn, the stresses required to produce yield, the relationship between stress and plastic strain increment, the structural reorientation occurring as a result of yield, and the relationship between constant strain-rate yield and features of non-linear recoverable creep deformation. Theoretical models to describe the behaviour have ranged from single crystal plasticity through to the oriented continuum ideas of plasticity and viscoelasticity. On many points both the experimental data and the interpretations appear almost contradictory and it is therefore helpful to see if any common ground can be established. 

The idealization of the two coupled crystalline and amorphous components of HDPE as joined sandwich elements and their interactive plastic deformation by crystal plasticity and amorphous flow comes close to the assumptions of the Sachs model of interaction. Thus, the composite model employing a Sachs-type interaction law does indeed result in quite satisfactory predictions both for the stress-strain curve and for the texture development in plane-strain compression flow and even in other modes of deformation (Lee et al. 1993b). In the following sections we discuss the application of the composite model to plane-strain compression flow and compare the findings of the model with results from corresponding experiments. 

The crystalline phase follows a few independent slip systems in which classical crystal plasticity theories cannot be utilized to model them [93-95]. Similar to the metallic crystalline phases, inelastic deformation in crystalline polymeric systems follows three different mechanisms (a) crystallographic slip, (b) twining, and (c) Martensite transformations [96]. All these mechanisms leave the crystallographic axis inextensible and provide less than five independent... 

Pawlak A, Galeski A (2005) Plastic deformation of crystalline polymers the role of cavitation and crystal plasticity. Macromolecules 38 9688-9697 Peterlin A (1971) Molecular model of drawing polyethylene and polypropylene. J Mater Sci 6 490 Popli R, Mandelkem L (1987) Influence of structural and morphological factors on the mechanical properties of the polyethylenes. J Polym Sci B Polym Phys 25 441 Read D, Duckett R, Sweeny J, Mcleish T (1999) The chevron folding instability in thermoplastic elastomers and other layered material. J Phys D Appl Phys 32 2087-2099 Resconi L, Cavallo L, Fait A, Piemontesi F (2000) Selectivity in propene polymerization with metallocene catalysts. Chem Rev 100 1253... 

Vidoli S, Sciaiia G (2002) A model for crystal plasticity based on micro-slip descriptors. Continuum Mech Thermodyn 14 425-435... 

A Prakash, SM Weygand, H Riedel, Modelling the evolution of texture and grain shape in Mg alloy AZ31 using the crystal plasticity finite element method. Computational Materials Science, 2009, 45, 744—750. 

At the microscale, dislocation dynamics simulations implement the equations of continuum elasticity theory to track the motion and interaction of individual dislocations under an applied stress, leading to the development of a dislocation microstructure and single-crystal plastic deformation. In our multiscale modeling... 

Figure 14.12 Notched Izod impact strength data (on crystallized PET) for samples of toughened polymer as a function of the ratio of interparticle distance O, amorphous x, crystalline [28]. Reprinted with permission from Pecorini, T. J. and Calvert, D., in Toughening of Plastics - Advances in Modelling and Experiments, Pearson, R. A., Sue, H.-J. and Yee, A. F. (Eds), ACS Symposium Series, 759, American Chemical Society, Washington, DC, 2000, Ch. 9, pp. 141-158. Copyright (2000) American Chemical Society...

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