Now showing 1 - 10 of 10
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    Mesoscopic unit cell analysis of ductile failure under plane stress conditions
    (01-06-2023)
    Chouksey, Mayank
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    Ductile failure under plane stress conditions is analyzed at the meso-scale using periodic unit cell model simulations of void growth in a plastically deforming matrix. Equivalent strains to failure by the onset of plastic instability at the macro-scale are estimated using the loss of ellipticity criterion for the equilibrium equations. Failure loci obtained from the cell model simulations are compared with the predictions of an instability-based ductile failure model and the Hosford–Coulomb damage indicator model, under both proportional and non-proportional loading conditions. The instability-based model is shown to quantitatively predict the shape of the failure locus under proportional loading, including the presence of a cusp at uniaxial tension and a ductility minimum under plane strain tension, in the absence of heuristic adjustable parameters in the failure criterion. It is shown that the characteristic shape of the plane stress failure locus is primarily due to the Lode dependence of the failure criterion, and not the damage growth law as assumed in the damage indicator models. Under non-proportional loading involving a step change in loading direction at an intermediate strain, the instability-based model correctly predicts the non-linear variation of the failure strain as a function of the intermediate strain; unlike a linear variation predicted by the damage indicator models, which is not in agreement with the cell model simulations. Forming limit curves showing the strains to the onset of localized necking in thin sheets are also obtained from the cell model simulations using an appropriate modification of the macroscopic instability criterion.
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    Effective yield criterion for a porous single crystal accounting for void size effects
    (01-09-2021)
    Khavasad, Prakash H.
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    The growth of sub-grain voids in crystalline materials is affected by plastic anisotropy as well as void size effects. In this paper, an effective yield criterion is derived for a porous single crystal using homogenization theory and limit analysis. A two dimensional planar model of a single crystal containing a random distribution of cylindrical voids is assumed. The effective yield criterion is derived using plastic limit load analysis of a hollow cylindrical representative volume element, containing a concentric cylindrical void in a single crystalline matrix. A conventional strain gradient plasticity model with an embedded material length scale is assumed for the matrix, in order to account for the void size dependence of yielding. The yield loci and void growth rates predicted by the model under plane strain conditions are validated by comparison with numerical results obtained using finite elements, as well as prior analytical results for the special case of size independent matrix behavior. The model predictions for the size dependence of the yield stress as well as void growth under proportional loading conditions are discussed with reference of known results from experiments and lower scale dislocation dynamics simulations.
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    Relating porosity with ductility in a commercial AA7075 alloy: A combined experimental and numerical study
    (01-10-2020)
    Tak, Tawqeer Nasir
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    Prakash, Aditya
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    Lodh, Arijit
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    Narayana Murty, S. V.S.
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    Samajdar, Indradev
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    Guruprasad, P. J.
    In this paper, the effect of porosity on the ductility of as-cast AA7075 (a commercial highstrength aluminum alloy) was investigated. The as-cast material was processed through hot upsetting, and specimens with different porosity content were achieved. These were then subjected to tensile and compression tests. It was shown that the tensile ductility exhibited a near sigmoidal dependence on the porosity content. Compressive ductility, on the other hand, was not affected by the initial porosity content. In addition, direct observations, on an X-ray microscope (XRM), enabled 3-dimensional imaging of the porosity evolution during plastic deformation. Numerical simulations using a homogenized damage model, the Gurson-Tvergaard-Needleman (GTN) approach, was used for predicting the mechanical responses. The continuum model, which accounted for the growth and coalescence of spherical voids, captured the overall experimental patterns reasonably well.
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    The stress field of an infinite set of discrete dislocations
    The two-dimensional stress fields induced by a set of infinitely many parallel edge dislocations are difficult to estimate as those of individual dislocations decay slowly. A simple numerical method to compute them is proposed. The method is based on series summation using a convergence factor, (Formula presented.) that decays rapidly with radial distance r from the field point, and letting the positive parameter (Formula presented.) numerically through Richardson extrapolation. The present method is more general than a lattice summation method with explicit spurious stress cancellation that is widely used in the literature. Furthermore, the spurious long-range stresses are cancelled in the present method without explicit evaluation.
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    An analysis of Lode effects in ductile failure
    (01-08-2021)
    Torki, M. E.
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    Benzerga, A. A.
    An isotropic multi-surface model of porous material plasticity is derived and employed to investigate the effects of the third stress invariant in ductile failure. The constitutive relation accounts for both homogeneous and inhomogeneous yielding of a material containing a random distribution of voids. Individual voids are modeled as spheroidal but the aggregate has no net texture. Ensemble averaging is invoked to operate a scale transition from the inherently anisotropic meso-scale process of single-void growth and coalescence to some macroscopic volume that contains many voids. Correspondingly, expressions for effective yield and associated evolution equations are derived from first principles, under the constraint of persistent isotropy. It is found that the well-known vertex on the hydrostatic axis either disappears for sufficiently flat voids or develops into a lower-order singularity for elongated ones. When failure is viewed as the onset of an instability, it invariably occurs after the transition to inhomogeneous yielding with the delay between the two depending strongly upon the Lode parameter. The strain to failure is found to be weakly dependent on the Lode parameter for shear-dominated loadings, but strongly dependent on it near states of so-called generalized tension or compression. Experimentally determined fracture loci for near plane stress states are discussed in light of the new findings.
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    Crack initiation and growth in 316LN stainless steel: Experiments and XFEM simulations
    (15-10-2022)
    Sidharth, R.
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    Nikhil, R.
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    Krishnan, S. A.
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    Moitra, A.
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    Vasudevan, M.
    A methodology for computer simulation of ductile fracture in engineering structures using the eXtended Finite Element Method (XFEM) is presented. Crack initiation is modeled using an instability-based failure criterion derived from the micromechanics of void coalescence. The criterion depends on the state of stress at failure, strain hardening and the void volume fraction, whose evolution as a function of plastic strain is obtained using a physics-based void growth law. Material separation is modeled using the cohesive zone method, where cohesive surface elements are dynamically inserted into continuum elements that satisfy the failure criterion. The methodology is illustrated by comparing the model predictions with experimental data on uncracked and pre-cracked 316LN stainless steel specimens. It is shown that, using a set of parameters calibrated from standard tests, the model is able to quantitatively predict fracture in a variety of specimens. In contrast, widely used continuum damage models are unable to predict fracture in the different specimen types using a single set of material parameters.
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    Ductile failure under non-proportional loading
    (01-07-2022)
    Chouksey, Mayank
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    Ductile failure by void growth in an elasto-plastic material subjected to non-proportional loading, involving step changes in the stress triaxiality or the Lode parameter, is investigated using periodic unit cell model simulations. The equivalent strains to failure by the onset of void coalescence, defined as the localization of plasticity along a band of voids at the micro-scale, are determined as a function of the loading path parameters. The observed trends for the ductility under non-proportional loading are found to be inconsistent with the predictions of a continuum damage mechanics model based on the attainment of a constant critical damage variable, even if the model has been calibrated to predict accurate results for the ductility under proportional loading. It is shown that a recently developed failure criterion based on the onset of plastic instability in a porous material, coupled with a micromechanics-based void growth law, predicts the loading path dependence of failure under non-proportional loading, in better agreement with the cell model simulation results than the continuum damage model. In particular, the triaxiality dependence of the ductility is found to be primarily due to the hydrostatic stress dependence of void growth, while the Lode dependence is primarily due to the instability-based failure criterion with a relatively minor effect of the Lode parameter on void growth. Implications of these findings on the current modeling approaches to ductile failure under shear dominated loading are discussed.
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    Analysis of localized necking in anisotropic sheet metals
    (01-10-2023) ;
    Sidharth, R.
    The ductility of sheet metals during forming operations is limited by a plastic instability leading to necking in the thickness direction along a narrow band. The critical condition for the onset of localized necking depends on constitutive effects such as plastic anisotropy, strain hardening and softening due to damage growth. Using the classical bifurcation analysis of Rice and co-workers, we derive a general analytical solution for localized necking in elastic–plastic thin sheets obeying arbitrary yield criteria and the normality flow rule. The criterion is illustrated for the case of plastically orthotropic sheets obeying Hill-type yield criteria, for which the model predictions for the localization strains are compared with explicit finite element simulations of sheet necking. Existing results in the literature are recovered for the special case of materials that exhibit in-plane isotropy and power law strain hardening.
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    Exploring subtle features of yield surfaces of porous, ductile solids through unit cell simulations
    (01-12-2020)
    Chouksey, Mayank
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    Basu, Sumit
    A general computational technique for deriving macro yield surfaces from unit cells with a given microstructure has been proposed in a companion paper (Chouksey, M., Keralavarma, S. M., Basu, S., 2019, “Computational investigation into the role of localization on yield of a porous ductile solid,” Journal of the Mechanics and Physics of Solids, 130,pp. 141–164). Using this technique, macro yield surfaces for porous ductile solids, represented by cuboidal unit cells containing ellipsoidal voids, have been generated and compared with suitable analytical yield criteria. These yield surfaces exhibit vertex-like features when the principal directions of the macro stress coincides with the axes of the ellipsoidal void. In this work, we study the effects of void spacing and orientation with respect to the principal directions nα (α∈[1,3]) of the macro stress. Subtle changes in the yield surface are revealed when its traces are plotted on octahedral or meridional section planes in stress space. Further, the possibility of utilizing the computational framework to automatically generate complete macro yield surfaces by sampling the entire macro stress space, for a given microstructure, is demonstrated with examples where the space of applied macro stress states are limited by suitable assumptions.
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    A discrete dislocation dynamics model of creep in polycrystals
    (01-10-2023)
    Tak, Tawqeer Nasir
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    Prakash, Aditya
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    Samajdar, Indradev
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    Guruprasad, P. J.
    The dislocation creep represents high temperature plastic deformation of metallic materials. However, the subject is usually approached with constitutive and phenomenological formulations. The notable exceptions are the recent use of numerical modeling. For example, single-crystal discrete dislocation dynamics (DDD) has been adopted to involve dislocation glide and climb together with diffusion of vacancies. This naturally provides a physics-based framework for dislocation creep. However, the existing model(s) are limited to single crystals and hence are limited in scope. This study extended a single crystal dislocation creep model into polycrystalline ensemble. This was then used to simulate steady state creep rate (ε˙) with respect to creep stress (σ), temperature (T) and grain size (d) in polycrystalline aluminum. Our virtual experiments showed an Arrhenius relationship between ε˙ and T, and a power law scaling with σ. Further, our simulations also revealed a power law increase in ε˙ with d. This is striking, as available experimental data indicate both grain size dependence as well as independence. The answer to this apparent contradiction also emerged from our numerical simulations. It was shown that ε˙ is controlled by interactions of dislocations with static obstacles and grain boundaries. Dominance of static obstacles, in particular, significantly diminished the grain size effect. The role of dislocation mean free path on the pinning and dislocation creep behavior of polycrystalline metallic material was thus mechanistically established.