A multi-phase field model of planar dislocation networks

In this paper we extend the phase-field model of crystallographic slip of Ortiz (1999 J. Appl. Mech. ASME 66 289–98) and Koslowski et al (2001 J. Mech. Phys. Solids 50 2957–635) to slip processes that require the activation of multiple slip systems, and we apply the resulting model to the investigation of finite twist boundary arrays. The distribution of slip over a slip plane is described by means of multiple integer-valued phase fields. We show how all the terms in the total energy of the crystal, including the long-range elastic energy and the Peierls interplanar energy, can be written explicitly in terms of the multi-phase field. The model is used to ascertain stable dislocation structures arising in an array of finite twist boundaries. These structures are found to consist of regular square or hexagonal dislocation networks separated by complex dislocation pile-ups over the intervening transition layers

Concurrent algorithms for transient nonlinear FE analysis

A two-parameter class of time-stepping algorithms for nonlinear structural dynamics is investigated. What sets the present method apart from other concurrent algorithms is the fact that it can be used to some advantage in sequential machines as well. Thus, substantial speed-ups are obtained on a single processor as the number of subdomains is increased. An additional O(p) speed-up is obtained when p processors are utilized. The test case discussed is being repeated for a mesh comprising four times as many elements, in an effort to understand how the large scale asymptotic speed-ups are attained. A three dimensional example involving finite deformations and free body motions is also being pursued. A code optimized for concurrency in the Alliant FX8 computer is being finalized. This will provide the means for testing the performance of the algorithm in a multiprocessor environment

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

Constitutive model for plasticity in an amorphous polycarbonate

A constitutive model for describing the mechanical response of an amorphous glassy polycarbonate is proposed. The model is based on an isotropic elastic phase surrounded by an SO(3) continuum of plastic phases onto which the elastic phase can collapse under strain. An approximate relaxed energy is developed for this model on the basis of physical considerations and extensive numerical testing, and it is shown that it corresponds to an ideal elastic-plastic behavior. Kinetic effects are introduced as rate-independent viscoplasticity, and a comparison with experimental data is presented, showing that the proposed model is able to capture the main features of the plastic behavior of amophous glassy polycarbonate

A Variational r-Adaption and Shape-Optimization Method for Finite-Deformation Elasticity

This paper is concerned with the formulation of a variational r-adaption method for finite-deformation elastostatic problems. The distinguishing characteristic of the method is that the variational principle simultaneously supplies the solution, the optimal mesh and, in problems of shape optimization, the equilibrium shapes of the system. This is accomplished by minimizing the energy functional with respect to the nodal field values as well as with respect to the triangulation of the domain of analysis. Energy minimization with respect to the referential nodal positions has the effect of equilibrating the energetic or configurational forces acting on the nodes. We derive general expressions for the configuration forces for isoparametric elements and nonlinear, possibly anisotropic, materials under general loading. We illustrate the versatility and convergence characteristics of the method by way of selected numerical tests and applications, including the problem of a semi-infinite crack in linear and nonlinear elastic bodies; and the optimization of the shape of elastic inclusions

Evolution of anodic stress corrosion cracking in a coated material

In the present paper, we investigate the influence of corrosion driving forces and interfacial toughness for a coated material subjected to mechanical loading. If the protective coating is cracked, the substrate material may become exposed to a corrosive media. For a stress corrosion sensitive substrate material, this may lead to detrimental crack growth. A crack is assumed to grow by anodic dissolution, inherently leading to a blunt crack tip. The evolution of the crack surface is modelled as a moving boundary problem using an adaptive finite element method. The rate of dissolution along the crack surface in the substrate is assumed to be proportional to the chemical potential, which is function of the local surface energy density and elastic strain energy density. The surface energy tends to flatten the surface, whereas the strain energy due to stress concentration promotes material dissolution. The influence of the interface energy density parameter for the solid–fluid combination, interface corrosion resistance and stiffness ratios between coating and substrate is investigated. Three characteristic crack shapes are obtained; deepening and narrowing single cracks, branched cracks and sharp interface cracks. The crack shapes obtained by our simulations are similar to real sub-coating cracks reported in the literature

An Exactly Solvable Phase-Field Theory of Dislocation Dynamics, Strain Hardening and Hysteresis in Ductile Single Crystals

An exactly solvable 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

An Innovative University Course for Cooperating Teachers

The transformation of a course for certifying cooperating teachers in Puerto Rico is described. The course was transformed to strengthen the teaching of science and mathematics and to make the course more congruent with the educational principles of constructivism promoted by the CETP projects at the national level, including Puerto Rico. The 45-hour requirement was distributed over nine days. The Open Space strategy was modified to include multiple active teaching-learning and assessment techniques, which promoted a learning environment based on trust, dedication, and the commitment of all participants to learn and help each other learn. Even more relevant was the fact that more content was covered and in more depth. The modified version of the course was offered to secondary level science and mathematics teachers, especially to teachers who work at the practicum centers that are part of the PR-CETP