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Dr. Hussein Zbib's Computational Mechanics and Materials Science Laboratory
Crystal Plasticity Framework for Polycrystalline Materials

Crystal Plasticity is a fast growing field of plasticity which attempts at providing more precise models for the predication of the mechanical response of crystalline materials by modeling basic mechanisms of deformation of crystals at the microscopic level rather than following a purely phenomenological approach as is the case of the classical theory of plasticity. Experimental observations on the deformation of crystals, pioneered by Taylor in 1938, indicate that they deform by the motion of dislocation on specific crystallographic planes in specific directions, which forms the framework of the continuum theory of plasticity. At CMMS , we are working on the development of more physical, dislocation-based models to describe the hardening properties of single and polycrystals based on models for the dislocation-dislocation interactions as well as the controversial dislocation-grain boundary interactions, which are believed to be the missing element in currently existing models. In that, we gain much insight from our well-established expertise in DDD (Discrete Dislocation Dynamics), which can provide the necessary bridging between the micro- and the macro-(continuum) scale.



Multiscale Dislocation Dynamics Plasticity (MDDP) Framework

The response of a material can be investigated at different length scales, atomic, microscopic, mesoscopic, and the continuum length scales. Continuum properties of materials are considered a homogenization of phenomena at smaller length scales, therefore, coupling models at different length scales and bridging the length-gaps that exist between different length-scale models, will bring out the details of physical response of materials. This is known as multiscale modeling. CMMS is one of the laboratories, which pioneered work in this field. At CMMS , we have successfully coupled discrete dislocation dynamics, continuum finite element, solid mechanics and heat transfer models into one 3-D model – the MDDP – Multiscale Dislocation Dynamics Plasticity.


3D Discrete Dislocation Dynamics (DDD)

A dislocation is a line defect in an otherwise perfect crystal (see picture of an edge dislocation). Dislocations are of three types: edge, screw and mixed. A dislocation is characterized by a line sense and a Burgers vector. Line sense is tangent to dislocation line and Burgers vector presents the magnitude and direction of displacement of the crystal due to presence of the dislocation. Since a dislocation is formed by displacement of crystal, a dislocation creates displacement, strain and stress fields. The displacement, strain and stress fields of some types of dislocations have been developed at CMMS . These include interfacial somigliana ring dislocation and general circular volterra dislocation. In addition, work on interaction energy and force expressions for two interfacial ring dislocation is also developed at CMMS .

Discrete dislocation dynamics is a powerful numerical tool to investigate the behavior of an ensemble of dislocations. This approach provides a direct means for modeling the behavior of dislocation groups by directly including the micromechanical and physical aspects of individual dislocations. micro3d is the name given to the discrete dislocation dynamics code developed at CMMS . micro3d, as the name suggests, is a 3-dimensional dislocation dynamics code that is build over sound theoretical basis and numerical rules developed at CMMS . micro3d has shown capability of capturing phenomena observed in real crystals such as Frank-Read source, formation (zipping) of junctions and dipoles, formation of jogs, cross-slip, irradiation induced hardening, formation of defect-free channels in irradiated single crystals, and dislocation walls.

Dislocation boundaries present one of the dislocation structures created during plastic deformation, which hold valuable information about the characteristics of the plastic deformation history. Several analytical and numerical studies have been conducted on 2D analysis of simplified configurations of dislocation boundaries. However, real experimentally observed dislocation boundaries have not received much attention. At CMMS we are carrying out a 3D multiscale analysis of geometrically necessary boundaries (GNBs). The characteristics of these GNBs are extracted from experimental results.



Fracture Mechanisms, Damage, and Voids in Materials

The purpose of fracture mechanics is to design structures to avoid failure. Fracture mechanics is build on the basis that materials have flaws (or cracks) that reduce the strength and useful service life of the components. Successful characterization of these cracks lead towards models that predict the real material response. Since a crack is formed by displacement of the material, it carries displacement, strain and stress fields. People at CMMS developed solutions for stress fields of cylindrical cracks using stress intensity factors and dislocation pile-ups theory. Interaction between cylindrical cracks have also been studied. The study of crack initiation, propagation, and driving mechanism is also one of the research interests at CMMS . Presently, modeling of microcracking mechanisms in brittle materials in under study.

Damage and voids in materials can significantly reduce the strength of materials and their forming properties. The problem becomes even more critical in case of superplastic materials. Superplastic materials show extreme ductility that is useful for forming processes in manufacturing industry. However, at large forming ratios, the voids grow and coalesce causing premature failure. CMMS has contributed towards constitutive modeling of damage, parametric studies of void growth, and size effects in superplastic deformation.



Strain Gradient Plasticity: Theory and Computational Modeling

Phenomenological constitutive equations for plastic deformation are usually developed with the basic assumption for uniformity of the deformation field, or by homogenization of the field over a macroscopic representative element. This, in turn, coupled with simple nondimensional analysis within the classical continuum theory of plasticity, leads to the development of homogeneous constitutive equations that relate the flow stress to some internal variable, such as strain hardening, strain rate, and volume fractions of second phase particles in composites. However, there are circumstances where the size of the microstructure, such as particle size and spacing, significantly influences the overall mechanical properties of the material. This becomes even more crucial when the size of the plastic deformation zone and the magnitude of the strain gradient within it becomes comparable to the size of the underlying dislocation structure. Gradient plasticity theory takes into account these size effects by incorporating strain gradients into the expression of the flow stress of materials. At CMMS , scientists have contributed towards development of gradient plasticity theory by investigating and modeling strain gradients and size effects in metals, metallic alloys, soil, and metal matrix composites. The role of strain gradients is investigated in adiabatic shear banding, elastoplasticity, and viscoplasticity. Recently, a thermodynamical theory of gradient elastoplasticity with dislocation density tensor is proposed.




Superplastic materials are a unique class of materials that has the ability to undergo extraordinary tensile ductility. An elongation in excess of 200% is usually indicative of superplasticity. Fine grain size, forming temperature and controlled strain rate are required to achieve structural superplasticity. Superplastic deformation is characterized by low flow stress and high sensitivity of the flow stress to strain rate. Since the superplastic forming processes present an efficient forming process, much research work has been done to characterize superplastic deformation. CMMS has contributed to this research field with the development of constitutive models of superplastic deformation, optimization of superplastic blow-forming, and studies of multi-axial deformation.