Simulation of Plastic Deformation

Baskes (1999) has discussed the status role of this kind of modelling and simulation, citing many very recent studies. He concludes that modelling and simulation of materials at the atomistic, microstructural and continuum levels continue to show progress, but prediction of mechanical properties of engineering materials is still a vision of the future . Simulation cannot (yet) do everything, in spite of the optimistic claims of some of its proponents. 

This kind of simulation requires massive computer power, and much of it is done on so-called supercomputers . This is a reason why much recent research of this kind has been done at Los Alamos. In a survey of research in the American national laboratories, the then director of the Los Alamos laboratory, Siegfried Hecker (1990) explains that the laboratory has worked closely with all supercomputer vendors over the years, typically receiving the serial No. I machine for each successive model . He goes on to exemplify the kinds of problems in materials science that these extremely powerful machines can handle. 

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A. S. Argon, P. H. Mott, and U. W. Suter, Phys. Status Solidi B, 172, 193 (1992). Simulation of Plastic Deformation in a Flexible Chain Glassy Polymer. 

Deng, D., Argon, A. S., and Yip, S. (1989d) Simulation of plastic deformation in a two-dimensional atomic glass by molecular dynamics IV, Phil. Trans. Roy. Soc., 329, 613-640. 

Li L (1994) Atomistic simulation of plastic deformation mechanisms in crystalline polyethylene, MSc thesis, Massachusets Institute of Technology, Cambridge, MA, pp. 1-58. 

An effort to investigate the kinematics of plastic deformation in glassy atactic polypropylene was presented by Mott, Argon, and Suter.Using an atomistic simulation for strains up to 20%, the authors observed that the plastic rearrangement of the structure was revealed in the microstructural stress—strain behavior (i.e., smooth reversible portions bounded by irreversible sharp drops in the stress values). 

The method of molecular dynamics (MD) provides a remarkable opportunity for the observation of various mechanisms of processes taking place on a micro-(nano-) level, and for the evaluation of the probability of such processes by repeating experiments dozens of times. Figure IX-37 shows the MD simulation of the deformation and fracture of a two-dimensional crystal. Plastic deformation and formation of a dislocation (AB) at elevated temperature (upper part) and the formation of a brittle crack at low temperature (lower part) are shown in Fig. IX-37, a, while simultaneous processes of crack nucleation influenced by the presence of foreign atoms, and their propagation to the tip of the crack, taking place at elevated temperature, are illustrated in both lower and upper portions of Fig. IX-37, b [40,41]. 

Here, the atomistic-continuum model is applied to the study of plastic deformation of BPA-PC. First, the elastic constants of BPA-PC are calculated by atomistic simulation. These values are used as the elastic constants for the matrix throughout the simulated deformation. Then, the system, i.e., the continuum matrix with its atomistic inclusion, is deformed stepwise up to a strain of about 0.2. The overall system is constrained to exactly follow a predescribed deformation sequence, but the atomistic inclusion is free to follow any strain path consistent with the misfit stresses acting between it and the matrix. The result is a new look at the behavior of a glassy polymeric inclusion deformed plastically in a surrounding elastic medium. 

To date, results have been obtained for minimum-energy type simulations of elastic deformations of a nearest-neighbor face-centered cubic (fee) crystal of argon [20] with different inclusion shapes (cubic, orthorhombic, spherical, and biaxially ellipsoidal). On bisphenol-A-polycarbonate, elastic constant calculations were also performed [20] as finite deformation simulations to plastic unit events (see [21]). The first molecular dynamics results on a nearest-neighbor fee crystal of argon have also become available [42]. The consistency of the method with thermodynamics and statistical mechanics has been tested to a satisfactory extent [20] e.g., the calculations with different inclusion shapes all yield identical results the results are independent of the method employed to calculate the elastic properties of the system and its constituents (constant-strain and constant-stress simulations give practically identical values). 

Multiscale models are making possible both the integration of insight between scales to improve overall understanding and the integration of simulations with experimental data. For example, in the case of plastic deformation of metals, one can incorporate constitutive theory for plastic displacements into macroscopic evolution equations, where parameterization of the constitutive equations is derived from analysis of MD simulations. 

Average wear rates for the C/PE, M/M and C/C bearings are listed in Table 2 for standard and microseparation (separation) testing in imits of iranVmillion cycles [3,5,6]. These are conq>ared to in-vivo results in mmVyear reported in a recent review paper by Tipper [4] for C/PE [7,8,9], M/M [10,11,12] and C/C [13,14]. The wear of C/PE in the Prosim simulator (superior/inferior separation 0.7 mm) was foimd to reduce with microseparation by a factor of 4, to a lower level than observed clinically [5]. Plastic deformation was observed on the rim of the polyethylene inserts in the order of 0.5 mm, while no damage was observed on the alumina ceramic heads. Clinical observations of plastic deformation on polyethylene insert rims have not been reported. However, past wear studies have generally only consider the main bearing area. 

The procedure to calculate fiber orientation is the same as explained above, but their implementation into explicit solvers and non-linear material models is more complex than it is for quasi-static load-cases and purely elastic material models. The fiber orientation is characterized by a so called orientation distribution function (ODE) that describes the chance of a fiber being oriented into a certain direction. For isotropic, elastic matrix materials an integral of the individual stiffness in every possible direction weighted with the ODE provides the complete information about the anisotropic stiffness of the compound. However, this integral can not be solved in case of plastic deformation as needed for crash-simulation. Therefore it is necessary to approximate and reconstruct the full information of the ODE by a sum of finite, discrete directions with their stiffness, so called grains [10]. Currently these grains are implemented into a material description and different methods of formulation are tested. 

In addition, on the basis of analogous specimens, the accumulation of damage and plastic deformation of metal structure were simulated. These results provide the possibility to obtain the prediction charts of the metal work s residual resource. 

Based on the discussion in earlier sections of this chapter, one may expect atomically flat incommensurate surfaces to be superlubric. Indeed the first suggestion that ultra-low friction may be possible was based on simulations of copper surfaces.6,7 Furthermore, the simulations of Ni(100)/(100) interfaces discussed in the previous section showed very low friction when the surfaces were atomically flat and misoriented (see the data for the atomically flat system between 30° and 60° in Figure 21). In general, however, it is reasonable to assume that bare metals are not good candidates for superlubric materials because they are vulnerable to a variety of energy dissipation mechanisms such as dislocation formation, plastic deformation, and wear. 

Figure 5 represents a typical evolution of the dislocation pattern during the deformation. The simulation was performed in a 20 mm diameter crystal, with 2 initial basal planes activated (one system in each plane) at the beginning of the deformation. It clearly appears that the double cross-slip mechanism propagates the plasticity in many other basal planes. One can also notice the asymmetry in the plane expansion due to the dislocation interactions. 

Nanoscratch tests have been used to simulate the effect of third-body particulate wear debris on component surface scratching during use. The load at which the co-efficient of friction or friction force suddenly increases is identified as the critical load, and is used to evaluate scratch resistance and adhesion strength. The depth-sensing nanoindenter, usually equipped with a conical indenter, can elucidate the mode of failure, whether elastic/plastic deformation, cracking, or delamination. 

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