IIT Madras is a public technical and research university located in Chennai, Tamil Nadu. Founded in 1959, it is recognised as an Institute of National Importance.

IIT Madras has been ranked as the top engineering institute in India for four years in a row by the National Institutional Ranking Framework of the MHRD

It currently offers undergraduate, postgraduate and research degrees across 16 disciplines in Engineering, Sciences, Humanities and Management. About 596 faculty belonging to science and engineering departments and centres of the Institute are engaged in teaching, research and industrial consultancy.

IIT Madras

We present a new computational approach for modeling dislocation creep in metals using kinetic Monte Carlo simulation of thermally activated dislocation glide, extending the discrete dislocation dynamics method of plasticity. The method is used to study the problem of power-law creep in precipitation strengthened Aluminum single crystals. The new model predicts creep rates and stress exponents consistent with their known ranges from experiments.

Department of Aerospace Engineering

TMS Annual Meeting

A discrete dislocation model of creep in single crystals

The two-dimensional discrete dislocation dynamics (2D DD) method, consisting of parallel straight edge dislocations gliding on independent slip systems in a plane strain model of a crystal, is often used to study complicated boundary value problems in crystal plasticity. However, the absence of truly three dimensional mechanisms such as junction formation means that forest hardening cannot be modeled, unless additional so-called '2.5D' constitutive rules are prescribed for short-range dislocation interactions. Here, results from three dimensional dislocation dynamics (3D DD) simulations in an FCC material are used to define new constitutive rules for short-range interactions and junction formation between dislocations on intersecting slip systems in 2D. The mutual strengthening effect of junctions on preexisting obstacles, such as precipitates or grain boundaries, is also accounted for in the model. The new '2.5D' DD model, with no arbitrary adjustable parameters beyond those obtained from lower scale simulation methods, is shown to predict athermal hardening rates, differences in flow behavior for single and multiple slip, and latent hardening ratios. All these phenomena are well-established in the plasticity of crystals and quantitative results predicted by the model are in good agreement with experimental observations. © 2016 Elsevier Ltd.

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Journal of the Mechanics and Physics of Solids

Strain hardening in 2D discrete dislocation dynamics simulations: A new '2.5D' algorithm

Plastic anisotropy in the form of texture development and void shape evolution can significantly affect damage growth rates and overall strain to failure in ductile materials. A criterion for the onset of coalescence, which is the transition from void growth by diffuse plastic deformation to localized plasticity in the ligament connecting neighboring voids, is a critical component of any predictive model for ductile fracture. In this paper, a new micromechanics-based criterion for void coalescence, combining both forms of anisotropy above, is developed using homogenization and limit analysis of a hollow cylindrical representative volume element made of an orthotropic material of the Hill type. Two possible modes of coalescence, corresponding to necking instability and shear strain localization in the transverse inter-void ligament, are accounted for in the analysis. The final form of the coalescence criterion has an interesting symmetry with Gurson-type yield criteria for porous materials and is shown to be an improvement over existing models for the special case of isotropic matrix behavior. For validation of the analytical model, quasi-exact numerical coalescence loci are computed using a finite elements based limit analysis method for the special case of transversely isotropic materials. The analytical model is shown to be in good agreement with the numerical data, except for highly oblate void shapes approaching penny shape cracks. A heuristic modification for the model is proposed, which significantly improves the model predictions in that limit. © 2016 Elsevier Ltd. All rights reserved.

International Journal of Plasticity

A criterion for void coalescence in anisotropic ductile materials

We present a new computational approach for modeling dislocation creep in metals using kinetic Monte Carlo simulation of thermally activated dislocation glide, extending the discrete dislocation dynamics method of plasticity. The method is used to study the problem of power-law creep in precipitation strengthened Aluminum single crystals. The new model predicts creep rates and stress exponents consistent with their known ranges from experiments.

World University root node

A Discrete Dislocation Model of Creep in Single Crystals

The objective of this paper is to perform numerical assessment of a micromechanical model of porous metal plasticity developed previously by the authors. First, upper bound estimates for the yield loci are computed using homogenization and limit analysis of a spheroidal representative volume element containing a confocal spheroidal void, neglecting elasticity. Unlike in the development of the analytical model, the computational limit analysis is performed without recourse to approximations so that the obtained yield loci are rigorous upper bounds for the true criterion. Next, the model's macroscopic dilatancy at incipient plastic flow is compared against that of the numerical limit analysis approach. Finally, finite-element calculations, with elasticity included, are presented for transversely isotropic porous unit-cells loaded axisymmetrically. The effective stress-strain response as well as evolution of the unit-cell porosity and void aspect ratio are compared with theoretical predictions. © 2015 Elsevier Ltd. All rights reserved.

Mechanics of Materials

Numerical assessment of an anisotropic porous metal plasticity model

A framework for solving problems of dislocation-mediated plasticity coupled with point-defect diffusion is presented. The dislocations are modeled as line singularities embedded in a linear elastic medium while the point defects are represented by a concentration field as in continuum diffusion theory. Plastic flow arises due to the collective motion of a large number of dislocations. Both conservative (glide) and nonconservative (diffusion-mediated climb) motions are accounted for. Time scale separation is contingent upon the existence of quasi-equilibrium dislocation configurations. A variational principle is used to derive the coupled governing equations for point-defect diffusion and dislocation climb. Superposition is used to obtain the mechanical fields in terms of the infinite-medium discrete dislocation fields and an image field that enforces the boundary conditions while the point-defect concentration is obtained by solving the stress-dependent diffusion equations on the same finite-element grid. Core-level boundary conditions for the concentration field are avoided by invoking an approximate, yet robust kinetic law. Aspects of the formulation are general but its implementation in a simple plane strain model enables the modeling of high-temperature phenomena such as creep, recovery and relaxation in crystalline materials. With emphasis laid on lattice vacancies, the creep response of planar single crystals in simple tension emerges as a natural outcome in the simulations. A large number of boundary-value problem solutions are obtained which depict transitions from diffusional to power-law creep, in keeping with long-standing phenomenological theories of creep. In addition, some unique experimental aspects of creep in small scale specimens are also reproduced in the simulations. © 2015 Elsevier Ltd. All rights reserved.

High-temperature discrete dislocation plasticity

Negative strain-rate sensitivity due to dynamic strain aging in Aluminium-5XXX alloys leads to reduced ductility and plastic instabilities at room temperature, inhibiting application of these alloys in many forming processes. Here a hierarchical multiscale model is presented that uses (i) quantum and atomic information on solute energies and motion around a dislocation core, (ii) dislocation models to predict the effects of solutes on dislocation motion through a dislocation forest, (iii) a thermo-kinetic constitutive model that faithfully includes the atomistic and dislocation scale mechanisms and (iv) a finite-element implementation, to predict the ductility as a function of temperature and strain rate in AA5182. The model, which contains no significant adjustable parameters, predicts the observed steep drop in ductility at room temperature, which can be directly attributed to the atomistic aging mechanism. On the basis of quantum inputs, this multiscale theory can be used in the future to design new alloys with higher ductility.© 2014 Macmillan Publishers Limited. All rights reserved.

Nature Communications

Quantum-to-continuum prediction of ductility loss in aluminium-magnesium alloys due to dynamic strain aging

The effect of loading path on the fracture locus was examined theoretically by means of cell model calculations. Two-dimensional axisymmetric finite element analyses were conducted to simulate plastic deformation of a material containing a periodic distribution of initially spherical voids. In the cell model, failure is defined to correspond to an abrupt loss of overall load bearing capacity. The cylindrical unit cells were subjected to loading along several radial paths, characterized by constant values of stress triaxiality. The strain-to-failure was recorded for each path and the locus relating it to triaxiality was thus uniquely determined. The process was repeated for a set of non-radial loading paths in which uniaxial loading was applied up to some strain level, followed by loading at constant triaxiality. For these cases, the time-weighted average value of stress triaxiality was used to plot the fracture locus. It was found that the failure locus for nonradial loadings differs substantially from that for radial paths. In fact, the nonradial locus does not represent a one-to-one relationship between average triaxiality and strain-to-failure. In addition, by varying the strain level&nbsp;<math xmlns="http://www.w3.org/1998/Math/MathML"><mrow is="true"><msubsup is="true"><mrow is="true"><mi is="true">E</mi></mrow><mrow is="true"><mi is="true">e</mi></mrow><mrow is="true"><mo is="true">∗</mo></mrow></msubsup></mrow></math>&nbsp;at which the load path is changed, a family of failure loci is generated, indexed by&nbsp;<math xmlns="http://www.w3.org/1998/Math/MathML"><mrow is="true"><msubsup is="true"><mrow is="true"><mi is="true">E</mi></mrow><mrow is="true"><mi is="true">e</mi></mrow><mrow is="true"><mo is="true">∗</mo></mrow></msubsup></mrow></math>.

On the path-dependence of the fracture locus in ductile materials – Analysis

We report two-dimensional discrete dislocation dynamics simulations of combined dislocation glide and climb leading to "power-law" creep in a model aluminum crystal. The approach fully accounts for matter transport due to vacancy diffusion and its coupling with dislocation motion. The existence of quasiequilibrium or jammed states under the applied creep stresses enables observations of diffusion and climb over time scales relevant to power-law creep. The predictions for the creep rates and stress exponents fall within experimental ranges, indicating that the underlying physics is well captured. © 2012 American Physical Society.

Physical Review Letters

Power-law creep from discrete dislocation dynamics

Large strain finite element calculations of unit cells subjected to triaxial axisymmetric loadings are presented for plastically orthotropic materials containing a periodic distribution of aligned spheroidal voids. The spatial distribution of voids and the plastic flow properties of the matrix are assumed to respect transverse isotropy about the axis of symmetry of the imposed loading so that a two-dimensional axisymmetric analysis is adequate. The parameters varied pertain to load triaxiality, matrix anisotropy, initial porosity and initial void shape so as to include the limiting case of penny-shaped cracks. Attention is focussed on comparing the individual and coupled effects of void shape and material anisotropy on the effective stress-strain response and on the evolution of microstructural variables. In addition, the effect of matrix anisotropy on the mode of plastic flow localization is discussed. From the results, two distinct regimes of behavior are identified: (i) at high triaxialities, the effect of material anisotropy is found to be persistent, unlike that of initial void shape and (ii) at moderate triaxialities the influence of void shape is found to depend strongly on matrix anisotropy. The findings are interpreted in light of recent, microscopically informed models of porous metal plasticity. Conversely, observations are made in relation to the relevance of these results in the development and calibration of a broader set of continuum damage mechanics models. © 2011 Elsevier Ltd. All rights reserved.

International Journal of Solids and Structures

Void growth and coalescence in anisotropic plastic solids

Experimental measurements and simulation results for the evolution of plastic deformation and hardening in micropillars are compared. The stress–strain response of high-symmetry Cu single crystals is experimentally determined using in situ micropillar compression. Discrete dislocation simulations are conducted within a two-dimensional plane-strain framework with the dislocations modeled as line singularities in an isotropic elastic medium. Physics-based constitutive rules are employed for an adequate representation of hardening. The numerical parameters entering the simulations are directly identified from a subset of experimental data. The experimental measurements and simulation results for the flow stress at various strain levels and the hardening rates are in good quantitative agreement. Both flow strength and hardening rate are size-dependent and increase with decreasing pillar size. The size effect in hardening is mainly caused by the build-up of geometrically necessary dislocations. Their evolution is observed to be size-dependent and more localized for smaller sample volumes, which is also reflected in local crystal misorientations.

Acta Materialia

Work hardening in micropillar compression: In situ experiments and modeling

Plastic constitutive relations are derived for a class of anisotropic porous materials consisting of coaxial spheroidal voids, arbitrarily oriented relative to the embedding orthotropic matrix. The derivations are based on nonlinear homogenization, limit analysis and micromechanics. A variational principle is formulated for the yield criterion of the effective medium and specialized to a spheroidal representative volume element containing a confocal spheroidal void and subjected to uniform boundary deformation. To obtain closed form equations for the effective yield locus, approximations are introduced in the limit-analysis based on a restricted set of admissible microscopic velocity fields. Evolution laws are also derived for the microstructure, defined in terms of void volume fraction, aspect ratio and orientation, using material incompressibility and Eshelby-like concentration tensors. The new yield criterion is an extension of the well known isotropic Gurson model. It also extends previous analyses of uncoupled effects of void shape and material anisotropy on the effective plastic behavior of solids containing voids. Preliminary comparisons with finite element calculations of voided cells show that the model captures non-trivial effects of anisotropy heretofore not picked up by void growth models. © 2010 Elsevier Ltd. All rights reserved.

A constitutive model for plastically anisotropic solids with non-spherical voids

The development of improved ductile damage models for plastically anisotropic materials has received limited attention in the literature. We derive a new yield criterion for materials containing spheroidal voids embedded in a Hilltype orthotropic matrix. The coupling of void shape evolution with the plastic anisotropy of the matrix leads to improved predictions for the yield surface as well as the evolution of microstructural variables. An alternative numerical approach is also developed to derive rigorous upper-bounds to the yield loci for anisotropic porous materials of a given microstructure. Under conditions of transverse isotropy, i.e. spheroidal voids in a transversely isotropic matrix, and axisymmetric loading, the numerical approach delivers quasi-exact results. Comparison of the analytical and numerical yield loci for selected material properties indicates significant improvements with respect to previous models from the literature.

12th International Conference on Fracture 2009, ICF-12

A micromechanics-based ductile damage model incorporating plastic anisotropy and void shape effects

Prediction of ductile fracture in structural metallic materials requires some representation of microstructural effects, including the plastic anisotropy that is associated with initial or induced polycrystalline textures and the microscopic processes of void growth and coalescence. With the objective of characterizing existing continuum models, we present a finite-element study of cylindrical unit cells, consisting of spheroidal voids embedded in an orthotropic Hill matrix, subjected to proportional loading paths. Two-dimensional axisymmetric calculations are employed for the case of transverse isotropy and axisymmetric loading about the void axis. The effective cell model responses are compared with predictions from an extended model of anisotropic void growth, which is the subject of an accompanying paper.

Finite-element analyses of combined void shape and plastic anisotropy effects in ductile fracture

We derive a new yield function for materials containing spheroidal voids embedded in a perfectly-plastic anisotropic Hill-type matrix. Using approximate limit-analysis and a restricted set of trial velocity fields, analytical yield loci are derived for a hollow, spheroidal volume element containing a confocal spheroidal void. Alternatively, the yield loci are determined through numerical limit-analysis, i.e., employing a larger set of velocity fields. The numerical results are quasi-exact for transversely isotropic materials under axisymmetric loading. We show that an enhanced description of admissible microscopic deformation fields results in a close agreement between analytical and numerical macroscopic yield loci. To cite this article: S.M. Keralavarma, A.A. Benzerga, C. R. Mecanique 336 (2008).

Comptes Rendus - Mecanique

An approximate yield criterion for anisotropic porous media

A new inicromechanics-based yield criterion is developed for anisotropic porous metals incorporating the effects of void shape and plastic anisotropy of the material on the constitutive response. Example yield loci are presented for material properties representative of C.P. grade Ti, and shown to be in good agreement with more accurate yield data determined numerically. Potential benefits of using the new criterion in finite element simulations of hot-working operations on Ti-based components are discussed.

A constitutive model of cavitation-induced damage in Ti alloys

A two-dimensional (2D) discrete dislocation plasticity framework, which incorporates some three-dimensional mechanisms through constitutive additions, is used to analyse the response to uniaxial tension of nanoscale bilayer thin films. Frank-Read sources, modelled as junction dipoles in 2D, act as sources of dislocations. Infinite, homogeneous medium fields of the discrete dislocations are superposed with a non-singular complementary field that enforces the boundary conditions and accounts for image stresses arising from the difference in elastic properties between the layers. The resulting boundary value problem is solved using the finite element method. Analysis has been carried out for fully coherent bilayer Al/Cu and Cu/Ni films oriented for double slip. The analysis accounts for the effects of three key mechanisms: resistance to dislocation nucleation and motion due to elastic modulus mismatch (e.g. Koehler barrier); single-dislocation bow-out within layers (Orowan process) and slip blocking at interfaces (Hall-Petch mechanism). The relative importance of each mechanism is studied as a function of the bilayer thickness. The results indicate a significant strengthening with decreasing bilayer thickness. Conclusions are drawn regarding the possible causes of the observed strengthening. © 2007 IOP Publishing Ltd.