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J. Eng. Mater. Technol. 2002;124(1):1. doi:10.1115/1.1418363.
Commentary by Dr. Valentin Fuster

TECHNICAL PAPERS

J. Eng. Mater. Technol. 2001;124(1):2-6. doi:10.1115/1.1418364.

The dislocation densities and arrangement parameters and the crystallite size and size-distributions are determined in tensile or cyclically deformed polycrystalline copper specimens by X-ray diffraction peak profile analysis. The Fourier coefficients of profiles measured by a special high resolution X-ray diffractometer with negligible instrumental broadening have been fitted by the Fourier transforms of ab-initio size and strain profiles. It is found that in the fatigued samples the dislocations are mainly of edge type with strong dipole character. In the fatigued specimens the dislocation densities are found to be larger than in the tensile deformed samples when the saturation and flow stress levels are the same.

Commentary by Dr. Valentin Fuster
J. Eng. Mater. Technol. 2001;124(1):7-12. doi:10.1115/1.1421612.

The combined effect of the lattice friction and localized obstacles on the individual dislocation velocity is considered. First the two effects are considered separately. The velocity of an individual dislocation is described by the Hirth-Lothe equation for the case of lattice friction and by a power law for the case of localized obstacles. The power law is modified to introduce a static waiting time: the time a dislocation has to wait in its equilibrium configuration at an obstacle until it breaks away by virtue of thermal activation. As a next step, a combination of the two mechanisms is described. A dynamic waiting time is introduced: it corresponds to a situation when a dislocation overcomes the obstacle before it reaches the equilibrium configuration. The model provides a good description of the effects when they are independent, and also gives an interpolation of the two regimes. A simulation for a model material is proposed to illustrate the transition between the two regimes. This unified model is tested against experimental data for in-situ deformation of monocrystalline germanium in a transmission electron microscope. The purpose is to determine an equivalent power law exponent in a regime of plastic flow that does not follow a proper power law. The resolution is not complete because the strength of the localized obstacles is not known. However, the results are promising and allow a discussion relating to the strength of localized obstacles.

Commentary by Dr. Valentin Fuster
J. Eng. Mater. Technol. 2001;124(1):13-22. doi:10.1115/1.1419017.

A study has been made of the deformation and recrystallization textures of 99.99% pure copper sheets which were cross rolled by 82 and 96% reduction in thickness and recrystallized in a salt bath at 450°C for 1h. The deformation texture was approximated by the {011}〈755〉 orientation as the major component and {001}〈100〉 as a minor component. These deformation texture components were well simulated using the rate sensitive relaxed constraints model. The {001}〈100〉 orientation was calculated to be metastable while the {011}〈755〉 orientation was located in the middle of the rotation path between the stable orientations in two cross rolling directions. The recrystallization texture in the center layer of the 96% cross-rolled copper sheet was approximated by {86 50 9}〈10 34 94〉 for each rolling direction. The evolution of the recrystallization texture was discussed based on the strain energy release maximization model.

Commentary by Dr. Valentin Fuster
J. Eng. Mater. Technol. 2001;124(1):23-26. doi:10.1115/1.1420195.

The effect of single grain boundaries on the Portevin Le Cha⁁telier (PLC) effect was investigated by depth sensing Vickers indentation. The experiments were carried out in load control. Independently appearing PLC bands were observed in the plastic volume and they were attributed to the hindered dislocation motion through the grain boundary. The hardening effect of the grain boundary and the release of the piled-up dislocations were also observed. This transient effect is manifested in a dynamic over-shooting in the hardness decrease, which is the consequence of the PLC effect as it is reproduced also by a phenomenological numerical model.

Commentary by Dr. Valentin Fuster
J. Eng. Mater. Technol. 2001;124(1):27-40. doi:10.1115/1.1420196.

In this paper, intermediate modeling of polycrystalline plasticity is proposed for rigid viscoplatic large deformations. This approach is based on the use of a bicrystal as the elementary local element representing the polycrystal. The local homogenization is obtained by considering the bicrystal volume-averaging and the jump conditions at the assumed planar interface between the two crystals. Two interaction laws based on Taylor and Sachs type assumptions are proposed. These bicrystal-based averaging schemes are different from the classical Taylor and Sachs models since they allow for stresses and strains to vary from one single crystal to the other. We simulate uniaxial tension and compression as well as plane strain compression tests. Results in terms of stress-strain curves are shown in comparison to those of the pure Taylor and Sachs models. We also show results for texture evolution and discuss their comparison with the experimental measurements.

Commentary by Dr. Valentin Fuster
J. Eng. Mater. Technol. 2001;124(1):41-47. doi:10.1115/1.1421049.

Dislocation densities, arrangements and long range internal stresses in cold rolled polycrystalline Cu, Ni, and Al, as well as in cold torsioned Fe, were determined by X-ray diffraction profile analysis using synchrotron radiation. At different deformation degrees, scanning measurements across single grains with a focal spot of less than 50 μm were carried out, in order to inform on the features of the deformation induced substructure. At small deformations including stage III, the dislocation densities and internal stresses are uniform within single grains while at higher deformations in stages IV and V, the dislocation densities and long range internal stresses exhibit opposite fluctuations. In stage IV these fluctuations correspond to the formation of polarized tilt walls (PTW’s) from polarized dipole walls (PDW’s). In contrast to the PDW’s, the PTW’s cause a much higher misorientation in between adjacent lattice areas. This transformation, which is the main element of the progressing fragmentation process during large strain deformation, occurs in all metals studied regardless of dislocation mobility and/or lattice type. Approaching higher strains in stage V, however, these parameters gain some importance especially when the deformation occurs in an iterative way. If the mobility is high, marked static recovery takes place between the single deformation passes, which results in decreases of both dislocation density and local internal stress, and no formation of PTW’s is observed.

Commentary by Dr. Valentin Fuster
J. Eng. Mater. Technol. 2001;124(1):48-54. doi:10.1115/1.1421050.

This paper assesses, via X-ray microbeam diffraction, the effects of development of dislocation substructure on the distribution of sub-grain misorientations in annealed OFHC copper deformed to large strains for compression, for shear, and for sequences of compression followed by shear. Polychromatic synchrotron x-radiation was used to study samples from four strain histories: virgin specimens, 50% effective strain in compression, 100% effective strain in torsion, and 50% compressive strain followed by 50% torsion. A very narrow beam illuminated an approximately 15 μm diameter column through the sample, and the microstructure of the specimens was mapped by translating the sample along two orthogonal axes perpendicular to the beam by increments of 10 μm. The beam diameter was considerably smaller than the average grain size in the virgin material. Both the degree of substructure formation and the nature of the distributed microstructure were quantified from the resulting Laue diffraction patterns. The polychromatic diffraction patterns of the polycrystalline samples consisted of well-defined streaks, and the azimuthal angular width of the streaks increased with plastic strain in a manner consistent with the scaling of the misorientation distribution of high angle boundaries for sub-grains reported recently using electron microscopy techniques limited to thin foils or thin surface layers. A lattice spin correction is introduced based on this scaling law in a simple extended Taylor scheme of polycrystal plasticity to achieve a retardation of texture development that is consistent with experimental results.

Commentary by Dr. Valentin Fuster
J. Eng. Mater. Technol. 2001;124(1):55-61. doi:10.1115/1.1421051.

TRansformation Induced Plasticity (TRIP) phenomenon results from the competition between two basic mechanisms, namely the orientation and accommodation. An accurate description of such a behavior is closely related to a good evaluation of the contribution of each mechanism in the overall response of the material. The main objective of this work is to provide an analysis of the different mechanisms at the microscale governing the TRIP phenomenon. The interaction between these mechanisms is experimentally displayed through nonproportional loading paths corresponding to the “creep” test. A micromechanical model is presented and tested under such conditions.

Commentary by Dr. Valentin Fuster
J. Eng. Mater. Technol. 2001;124(1):62-70. doi:10.1115/1.1421052.

Averaging models are proposed for viscoplastic and elastic-viscoplastic heterogeneous materials. The case of rigid viscoplastic materials is first discussed. Large deformations are considered. A first class of models is based on different linearizations of the nonlinear local response. A second class of models is obtained from approximate solutions of the nonlinear Eshelby problem. In this problem, an ellipsoid with uniform nonlinear properties is embedded in an infinite homogeneous matrix. An approximate solution is obtained by approaching the matrix behavior with an affine response. Using this solution of the nonlinear Eshelby problem, the average strain rate is calculated in each phase of the composite material, each phase being represented by an ellipsoid embedded in an infinite reference medium. By adequate choices of the reference medium, different averaging models are obtained (self-consistent scheme, nonlinear Mori Tanaka model[[ellipsis]]). Finally, elasticity is included in the modelling, but with a restriction to small deformations.

Commentary by Dr. Valentin Fuster
J. Eng. Mater. Technol. 2001;124(1):71-77. doi:10.1115/1.1421350.

A recent strain hardening model for late deformation stages (Estrin, Y., Tóth, L.S., Molinari, A., and Bréchet, Y., Acta Materialia, 1998, “A dislocation-based model for all hardening stages in large strain deformation,” Vol. 46, pp. 5509-5522) was generalized for the 3D case and for arbitrary strain paths. The model is based on a cellular dislocation arrangement in which a single- phase material is considered as a composite of a hard skeleton of cell walls and soft cell interiors. An important point in the approach is the evolution of the volume fraction of the cell walls which decreases with the deformation and gives rise to a plateau-like behavior (Stage IV) followed by a drop-off (Stage V) of the strain hardening rate observed at large strains. The hardening model was implemented into the viscoplastic self-consistent polycrystal model to predict hardening curves corresponding to different proportional loading paths. The calculated curves were evaluated to elucidate the path dependence of hardening.

Commentary by Dr. Valentin Fuster
J. Eng. Mater. Technol. 2001;124(1):78-87. doi:10.1115/1.1421351.

We present a framework coupling continuum elasto-viscoplasticity with three-dimensional discrete dislocation dynamics. In this approach, the elastic response is governed by the classical Hooke’s law and the viscoplastic behavior is determined by the motion of curved dislocations in a three-dimensional space. The resulting hybrid continuum-discrete framework is formulated into a standard finite element model where the dislocation-induced stress is homogenized over each element with a similar treatment for the dislocation-induced plastic strain. The model can be used to investigate a wide range of small scale plasticity phenomena, including microshear bands, adiabatic shear bands, stability and formation of dislocation cells, thin films and multiplayer structures. Here we present results pertaining to the formation of deformation bands and surface distortions under dynamic loading conditions and show the capability of the model in analyzing complicated deformation-induced patterns.

Commentary by Dr. Valentin Fuster
J. Eng. Mater. Technol. 2001;124(1):88-96. doi:10.1115/1.1421611.

A multiple slip dislocation-density based crystalline formulation has been coupled to a kinematically based scheme that accounts for grain-boundary (GB) interfacial interactions with dislocation densities. Specialized finite-element formulations have been used to gain detailed understanding of the initiation and evolution of large inelastic deformation modes due to mechanisms that can result from dislocation-density pile-ups at GB interfaces, partial and total dislocation-density transmission from one grain to neighboring grains, and dislocation density absorption within GBs. These formulations provide a methodology that can be used to understand how interactions at the GB interface scale affect overall macroscopic behavior at different inelastic stages of deformation for polycrystalline aggregates due to the interrelated effects of GB orientations, the evolution of mobile and immobile dislocation-densities, slip system orientation, strain hardening, geometrical softening, geometric slip compatibility, and localized plastic strains. Criteria have been developed to identify and monitor the initiation and evolution of multiple regions where dislocation pile-ups at GBs, or partial and total dislocation density transmission through the GB, or absorption within the GB can occur. It is shown that the accurate prediction of these mechanisms is essential to understanding how interactions at GB interfaces affect and control overall material behavior.

Commentary by Dr. Valentin Fuster

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