Alberto M. Cuitiño

Computational modelling of single crystals

The physical basis of computationally tractable models of crystalline plasticity is reviewed. A statistical mechanical model of dislocation motion through forest dislocations is formulated. Following Franciosi and co-workers (1980-88) the strength of the short-range obstacles introduced by the forest dislocations is allowed to depend on the mode of interaction. The kinetic equations governing dislocation motion are solved in closed form for monotonic loading, with transients in the density of forest dislocations accounted for. This solution, coupled with suitable equations of evolution for the dislocation densities, provides a complete description of the hardening of crystals under monotonic loading. Detailed comparisons with experiment demonstrate the predictive capabilities of the theory. An adaptive finite element formulation for the analysis of ductile single crystals is also developed. Calculations of the near-tip fields in Cu single crystals illustrate the versatility of the method.

Nanoscale phase field microelasticity theory of dislocations: model and 3D simulations

The first Phase Field model of evolution of a multi-dislocation system in elastically anisotropic crystal under applied stress is formulated. The model is a modification and extension of our Phase Field Microelasticity approach to the theory of coherent phase transformations. The long-range strain-induced interaction of individual dislocations is calculated exactly and is explicitly incorporated in the Phase Field formalism. It also automatically takes into account the effects of “short-range interactions”, such as multiplication and annihilation of dislocations and a formation of various metastable microstructures involving dislocations and defects. The proposed 3-dimensional Phase Field model of dislocations does not impose a priori constraints on possible dislocation structures or their evolution paths. Examples of simulation of the FCC 3D system under applied stress are considered.

A phase-field theory of dislocation dynamics, strain hardening and hysteresis in ductile single crystals

A phase-field theory of dislocation dynamics, strain hardening and hysteresis in ductile single crystals is developed. The theory accounts for: an arbitrary number and arrangement of dislocation lines over a slip plane; the long-range elastic interactions between dislocation lines; the core structure of the dislocations resulting from a piecewise quadratic Peierls potential; the interaction between the dislocations and an applied resolved shear stress field; and the irreversible interactions with short-range obstacles and lattice friction, resulting in hardening, path dependency and hysteresis. A chief advantage of the present theory is that it is analytically tractable, in the sense that the complexity of the calculations may be reduced, with the aid of closed form analytical solutions, to the determination of the value of the phase field at point-obstacle sites. In particular, no numerical grid is required in calculations. The phase-field representation enables complex geometrical and topological transitions in the dislocation ensemble, including dislocation loop nucleation, bow-out, pinching, and the formation of Orowan loops. The theory also permits the consideration of obstacles of varying strengths and dislocation line-energy anisotropy. The theory predicts a range of behaviors which are in qualitative agreement with observation, including: hardening and dislocation multiplication in single slip under monotonic loading; the Bauschinger effect under reverse loading; the fading memory effect, whereby reverse yielding gradually eliminates the influence of previous loading; the evolution of the dislocation density under cycling loading, leading to characteristic ‘butterfly’ curves; and others.

Full-field measurements of heterogeneous deformation patterns on polymeric foams using digital image correlation

The ability of a digital image correlation technique to capture the heterogeneous deformation fields appearing during compression of ultra-light open-cell foams is presented in this article. Quantitative characterization of these fields is of importance to understand the mechanical properties of the collapse process and the energy dissipation patterns in this type of materials. The present algorithm is formulated in the context of multi-variable non-linear optimization where a merit function based on a local average of the deformation mapping is minimized implicitly. A parallel implementation utilizing message passing interface for distributed-memory architectures is also discussed. Estimates for optimal size of the correlation window based on measurement accuracy and spatial resolution are provided. This technique is employed to reveal the evolution of the deformation texture on the surface of open-cell polyurethane foam samples of different relative densities. Histograms of the evolution of surface deformation are extracted, showing the transition from unimodal to bimodal and back to unimodal. These results support the interpretation that the collapse of light open-cell foams occurs as a phase transition phenomenon.

Phase field microelasticity theory and modeling of multiple dislocation dynamics

The phase field theory and model of a multidislocation dynamics in an elastically anisotropic crystal under applied stress is developed. The proposed three-dimensional (3D) model is a particular case of our phase field microelasticity model of the stress-induced martensitic transformations. A spontaneous self-organization of dislocations in the evolving ensemble, which involves multiplication/annihilation and movement of dislocations controlled by their elastic interaction, is described by the Ginzburg–Landau kinetic equation. Examples of 3D computer simulation of dislocation dynamics are considered.

Ductile fracture by vacancy condensation in f.c.c. single crystals

We explore the feasibility of vacancy condensation as the void-nucleating mechanism underlying ductile fracture by void growth and coalescence in single crystals at room temperature. Vacancies are presumed to be primarily generated by the dragging of intersection jogs. The equations governing the rate of growth of voids by vacancy condensation are derived. These equations are used to follow the evolution of vacancy concentrations and void sizes in the Wang and Anderson [Acta metall. 39, 779 (1991)] [1] Σ9 test. We find that, when pipe diffusions are taken into account, the time required for the nucleation of a macroscopic void in the near-tip region is of the order of one minute, which is well within the time-scale of quasistatic fracture tests.

A micromechanical model of hardening, rate sensitivity and thermal softening in BCC single crystals

The present paper is concerned with the development of a micromechanical model of the hardening, rate-sensitivity and thermal softening of bcc crystals. In formulating the model, we specifically consider the following unit processes: double-kink formation and thermally activated motion of kinks; the close-range interactions between primary and forest dislocations, leading to the formation of jogs; the percolation motion of dislocations through a random array of forest dislocations introducing short-range obstacles of different strengths; dislocation multiplication due to breeding by double cross-slip; and dislocation pair annihilation. The model is found to capture salient features of the behavior of Ta crystals such as: the dependence of the initial yield point on temperature and strain rate; the presence of a marked stage I of easy glide, specially at low temperatures and high strain rates; the sharp onset of stage II hardening and its tendency to shift towards lower strains, and eventually disappear, as the temperature increases or the strain rate decreases; the parabolic stage II hardening at low strain rates or high temperatures; the stage II softening at high strain rates or low temperatures; the trend towards saturation at high strains; the temperature and strain-rate dependence of the saturation stress; and the orientation dependence of the hardening rate.

Three-dimensional nonlinear open-cell foams with large deformations

Abstract In this article, a hyperelastic formulation for light and compliant foams which accounts for nonlinear effects at material and kinematic levels is introduced. This theory is applicable to a large number of 2- and 3-D irregular open-cell structures. An expression for the strain-energy function is proposed which includes bending and stretching contributions. Although this description allows for irregularity in the structure at local or cell level, it also assumes that the macro structure is homogeneous, i.e. built by repetition of the same irregular unit cell. This micromechanical formulation has explicit correlation with the foam structure, and therefore it preserves in the constitutive relation the symmetries or directional properties of the corresponding structures, including the cases of re-entrant foams which exhibit negative Poisson’s ratio effects. Due to the introduction of nonlinear kinematics, the evolution of the structure during the loading process and its effects on the constitutive behavior can be traced, including the cases where configurational transformations are present leading to non-convex strain-energy functions. Several examples of the stress–strain behavior for arbitrary large homogeneous deformations in a diamond-like structure are presented. The effect of the structure reorientation on the transition of local deformation mechanisms is clearly shown. The development of texture and anisotropy induced by the deformation process is also demonstrated. Finally, the role of the deformation mechanisms on the relation between foam stiffness and foam density is analyzed.

Three-dimensional crack-tip fields in four-point-bending copper single-crystal specimens

The three-dimensional near-tip fields in copper single crystals loaded in four-point bending are characterized numerically. For comparison purposes, the corresponding plane-strain fields are also computed numerically and their asymptotic behavior determined semi-analytically. On the basis of these analyses, we investigate: (i) the dependence of the fields on the hardening law; (ii) the degree of correlation between surface and interior fields in finite specimens; and (iii) the degree of correlation between plane-strain and three-dimensional fields. In particular, we endeavor to ascertain the extent to which surface observations of near-tip fields in single crystals, such as those obtained by Moire interferometry, are representative of interior fields, and the extent to which these are representative of plane-strain fields. Our calculations reveal marked differences in the pattern of slip activity in the interior and on the surface of the specimen. These discrepancies, in turn, result in significant variations in the state of stress and strain. These observations suggest that, for the test geometries under consideration, surface observations provide only an indirect measure of conditions in the interior, and point to a need for the development of experimental techniques enabling the direct observation of interior fields.

Mixing order of glidant and lubricant – Influence on powder and tablet properties

The main objective of the present work was to study the effect of mixing order of Cab-O-Sil (CS) and magnesium stearate (MgSt) and microlayers during mixing on blend and tablet properties. A first set of pharmaceutical blend containing Avicel PH200, Pharmatose and micronized acetaminophen was prepared with three mixing orders (mixing order-1: CS added first; mixing order-2: MgSt added first; mixing order-3: CS and MgSt added together). All the blends were subjected to a shear rate of 80 rpm and strain of 40, 160 and 640 revolutions in a controlled shear environment resulting in nine different blends. A second set of nine blends was prepared by replacing Avicel PH200 with Avicel PH102. A total of eighteen blends thus prepared were tested for powder hydrophobicity, powder flow, tablet weight, tablet hardness and tablet dissolution. Results indicated that powder hydrophobicity increased significantly for mixing order-1. Intermediate hydrophobic behavior was found for mixing order-3. Additionally, mixing order 1 resulted in improved powder flow properties, low weight variability, higher average tablet weight and slow drug release rates. Dissolution profiles obtained were found to be strongly dependent not only on the mixing order of flowing agents, but also on the strain and the resulting hydrophobicity.