Computational and theoretical aspects of a grain-boundary model that accounts for grain misorientation and grain-boundary orientation

Gottschalk, Daniel; McBride, Andrew; Reddy, B. D.; Javili, Ali; Wriggers, Peter; Hirschberger, C.B.

doi:10.1016/j.commatsci.2015.09.048

Cited by 44 publications

(20 citation statements)

References 35 publications

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“…Single-crystal plasticity can be used to predict the mechanical behavior of single-crystal specimens under complex loading conditions, but also single-crystal components like turbine blades in jet engines (Cailletaud et al, 2003). The same theory can be used also to derive the behaviour of metal polycrystals from the behaviour of individual grains, by combining the description of sets of interacting grains with a model of the transgranular behaviour (Mika and Dawson, 1998;Staroselsky and Anand, 1998;Barbe et al, 2001;Cailletaud et al, 2003;Gottschalk et al, 2016).…”

Section: Introductionmentioning

confidence: 99%

Phase‐field modelling of fracture in single crystal plasticity

2016

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We propose a phase-field model for ductile fracture in a single crystal within the kinematically linear regime, by combining the theory of single crystal plasticity as formulated in Gurtin et al. (2010) and the phase-field formulation for ductile fracture proposed by Ambati et al. (2015) . The model introduces coupling between plasticity and fracture through the dependency of the so-called degradation function from a scalar global measure of the accumulated plastic strain on all slip systems. A viscous regularization is introduced both in the treatment of plasticity and in the phase-field evolution equation. Testing of the model on two examples for face centred cubic single crystals indicates that fracture is predicted to initiate and develop in the regions of the maximum accumulated plastic strain, which is in agreement with phenomenological observations. A rotation of the crystallographic unit cell is shown to affect the test results in terms of failure pattern and corresponding global and local response.

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Section: Introductionmentioning

confidence: 99%

Phase‐field modelling of fracture in single crystal plasticity

2016

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“…For simplicity, we have ignored surface energies on the exterior boundary and along crystal boundaries. Energies in crystal boundaries will play a role when establishing physically realistic interface conditions, eg, Ekh et al, 38 Gottschalk et al, 39 and Gurtin and Needleman. 40 Since this paper focuses on homogenization, and since inter-crystal conditions only come in as a modeling choice, we have chosen to disregard such surface energies.…”

Section: Dissipation Inequality and Basic Constitutive Relationsmentioning

confidence: 99%

Bounds on the effective response for gradient crystal inelasticity based on homogenization and virtual testing

Carlsson

Larsson

Runesson

2019

Numerical Meth Engineering

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This paper presents the application of variationally consistent selective homogenization applied to a polycrystal with a subscale model of gradient-enhanced crystal inelasticity. Although the full gradient problem is solved on Statistical Volume Elements (SVEs), the resulting macroscale problem has the formal character of a standard local continuum. A semi-dual format of gradient inelasticity is exploited, whereby the unknown global variables are the displacements and the energetic micro-stresses on each slip-system. The corresponding time-discrete variational formulation of the SVE-problem defines a saddle point of an associated incremental potential. Focus is placed on the computation of statistical bounds on the effective energy, based on virtual testing on SVEs and an argument of ergodicity. As it turns out, suitable combinations of Dirichlet and Neumann conditions pertinent to the standard equilibrium and the micro-force balance, respectively, will have to be imposed. Whereas arguments leading to the upper bound are quite straightforward, those leading to the lower bound are significantly more involved; hence, a viable approximation of the lower bound is computed in this paper. Numerical evaluations of the effective strain energy confirm the theoretical predictions. Furthermore, heuristic arguments for the resulting macroscale stress-strain relations are numerically confirmed. KEYWORDSboundary conditions, computational homogenization, gradient crystal plasticity Int J Numer Methods Eng. 2019;119:281-304. wileyonlinelibrary.com/journal/nme

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“…Thus, the flow rule connects the minimization of the RBV upon transmission with the maximization of RSSes. The GB model [67] has been implemented within a two-dimensional setting in [86] and, recently, also within three dimensions [90]. In this model, so-called inter-action coefficients describe the interaction of slip systems in adjacent grains,…”

Section: Crystal Plasticity Models Taking Into Account Geometrical Slmentioning

confidence: 99%

“…At first, an overview is given on the geometric slip transmission criteria used in experiments and computational models including perspectives on additional criteria and considerations. Then, the sophisticated GB theory of [67] (recently implemented in three dimensions in [90]) is analyzed for the single slip case and the connections to the transmission criteria are discussed. Finally, the geometrical criteria are compared for the single slip case and conclusions are drawn on limitations of these geometric factors.…”

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confidence: 99%

Review on slip transmission criteria in experiments and crystal plasticity models

et al. 2015

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A comprehensive overview is given of the literature on slip transmission criteria for grain boundaries in metals, with a focus on slip system and grain boundary orientation. Much of this extensive literature has been informed by experimental investigations. The use of geometric criteria in continuum crystal plasticity models is discussed. The theoretical framework of Gurtin (2008, J. Mech. Phys. Solids 56, p. 640) is reviewed for the single slip case. This highlights the connections to slip transmission criteria from the literature that are not discussed in the work itself. Different geometric criteria are compared for the single slip case with regard to their prediction of slip transmission. Perspectives on additional criteria, investigated in experiments and used in computational simulations, are given.

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Computational and theoretical aspects of a grain-boundary model that accounts for grain misorientation and grain-boundary orientation

Cited by 44 publications

References 35 publications

Phase‐field modelling of fracture in single crystal plasticity

Phase‐field modelling of fracture in single crystal plasticity

Bounds on the effective response for gradient crystal inelasticity based on homogenization and virtual testing

Review on slip transmission criteria in experiments and crystal plasticity models

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