Bhasker Paliwal

Atomistic–continuum interphase model for effective properties of composite materials containing nano-inhomogeneities

Classical micromechanics were revised to study the elastic properties of heterogeneous materials containing nano-inhomogeneities. Contrary to previous studies, this work introduces the concept of an interphase, in contrast to a sharp interface, to account for the interface excess stress effect at the nano-scale. The interphases constitutive properties are derived from atomistic simulations within the continuum framework. These properties are then incorporated in a micromechanics-based interphase model to compute the effective properties of nano-composites. This scale transition approach bridges the gap between discrete systems (atomic level interactions) and continuum mechanics. An advantage of this approach is that it combines atomistic with continuum models that consider inhomogeneity and interphase morphology. It thereby enables us to account simultaneously for both the shape and the anisotropy of a nano-inhomogeneity and interphase at the continuum level when we compute a materials overall properties. In so doing, it frees us from making any assumptions about the interface characteristics between matrix and the nano-inhomogeneity.

Analytical close-form solutions to the elastic fields of solids with dislocations and surface stress

The concept of eigenstrain is adopted to derive a general analytical framework to solve the elastic field for 3D anisotropic solids with general defects by considering the surface stress. The formulation shows the elastic constants and geometrical features of the surface play an important role in determining the elastic fields of the solid. As an application, the analytical close-form solutions to the stress fields of an infinite isotropic circular nanowire are obtained. The stress fields are compared with the classical solutions and those of complex variable method. The stress fields from this work demonstrate the impact from the surface stress when the size of the nanowire shrinks but becomes negligible in macroscopic scale. Compared with the power series solutions of complex variable method, the analytical solutions in this work provide a better platform and they are more flexible in various applications. More importantly, the proposed analytical framework profoundly improves the studies of general 3D anisotropic materials with surface effects.

Practical aspects of using Hertzian ring crack initiation to measure surface flaw densities in glasses: influence of humidity, friction and searched areas

Ring crack initiation loads on glass, using spherical Tungsten carbide (WC) and glass (G) indenters, are measured and analysed. Our measurements demonstrate that environmental humidity plays a key role in determining the load to fracture; experiments conducted without controlling this variable cannot be used to obtain material properties. The role of friction is explicitly considered for dissimilar (WC–G) elastic contacts. For this material pair, the stresses at fracture are well described by a boundary lubrication value of friction coefficient. The fracture loads are used in a fracture-mechanics formulation to calculate crack sizes on glass surfaces. The ‘searched-area’ concept for dissimilar contacts is described, and used to provide crack density values for these surfaces.

Nanomechanical modeling of interfaces of polyvinyl alcohol (PVA)/clay nanocomposite

Abstract We study interfacial debonding of several representative structures of polyvinyl alcohol (PVA)/pyrophillite-clay systems – both gallery-interface (polymer/clay interface in the interlayer region containing polymer between clay layers stacked parallel to each other) and matrix-interphase (polymer/clay interphase-region when individual clay layers are well separated and dispersed in the polymer matrix) – using molecular dynamics simulations, while explicitly accounting for shearing/sliding (i.e. Mode-II) deformation mode. Ten nanocomposite geometries (five 2-D periodic structures for tension and five 1-D periodic structures for shearing) were constructed to quantify the structure-property relations by varying the number density of polymer chains, length of polymer chains and model dimensions related to the interface deformation. The results were subsequently mapped into a cohesive traction–separation law, including evaluation of peak traction and work of separation that are used to characterise the interface load transfer for larger length scale micromechanical models. Results suggest that under a crack nucleation opening mode (i.e. Mode-I), the matrix-interphase exhibits noticeably greater strength and a greater work of separation compared to the gallery-interface; however, they were similar under the shearing/sliding mode of deformation. When compared to shearing/sliding, the tensile peak opening mode stresses were considerably greater but the displacement at the peak stress, the displacement at the final failure and the work of separation were considerably lower. Results also suggest that PVA/clay nanocomposites with higher degree of exfoliation compared with nanocomposites with higher clay-intercalation can potentially display higher strength under tension-dominated loading for a given clay volume fraction.

Smooth Yield Surface Constitutive Modeling for Granular Materials

In this paper, the authors present an internal state variable (ISV) cap plasticity model to provide a physical representation of inelastic mechanical behaviors of granular materials under pressure and shear conditions. The formulation is dependent on several factors: nonlinear elasticity, yield limit, stress invariants, plastic flow, and ISV hardening laws to represent various mechanical states. Constitutive equations are established based on a modified Drucker–Prager cap plasticity model to describe the mechanical densification process. To avoid potential numerical difficulties, a transition yield surface function is introduced to smooth the intersection between the failure and cap surfaces for different shapes and octahedral profiles of the shear failure yield surface. The ISV model for the test case of a linear-shaped shear failure surface with Mises octahedral profile is implemented into a finite element code. Numerical simulations using a steel metal powder are presented to demonstrate the capabilities of the ISV cap plasticity model to represent densification of a steel powder during compaction. The formulation is general enough to also apply to other powder metals and geomaterials. [DOI: 10.1115/1.4034987]

Continuum Modelling of Shear-Coupled Grain Boundary Migration

The deformation accommodation mechanisms associated to grain boundaries (GBs) significantly affect the mechanical behavior of nano-polycrystals. Among these mechanisms, stress-induced GB migration is now seen to compete or interplay with other intra-granular and GB mechanisms in a wide range of temperatures. A complete micromechanics-based model is here proposed using the concepts of continuum thermodynamics and kinematics to derive a new constitutive model able to describe stress-induced GB migration. Like non diffusive phase-transformations, stress-induced GB migration can be considered on the thermodynamics point of view of conservative nature (diffusionless but thermally activated) until high temperature with respect to melting point. Here, in the framework of continuum micro-mechanics which should be easily implemented in a polycrystalline model, we will first describe the micromechanical framework: the kinematics and the thermodynamics associated with additive mechanisms including plastic deformation in the bulk crystals, GB migration and GB sliding. For the sake of illustration of the present general theory, we will focus on planar bi-crystals and only perfect shear-coupling GB migration situations of [001] symmetric tilt GBs in Cu. Numerical examples and responses of the micromechanical model are given for these bi-crystals considering both isotropic and anisotropic elasticity. These ones are fed by computer-aided MD simulations for which deformation mechanisms are identified.