A phase field model for the growth and characteristic thickness of deformation-induced twins

Grilli, Nicolò; Cocks, A.C.F.; Tarleton, Edmund

doi:10.1016/j.jmps.2020.104061

Cited by 28 publications

(15 citation statements)

References 95 publications

(144 reference statements)

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“…In this paper we use crystal plasticity finite element (CPFE) simulations (Grilli 2016;Irastorza-Landa et al 2017b), a continuum model for discrete twins (Grilli et al 2020b) and a cohesive zone model for intragranular fracture (Grilli et al 2021b) to answer these questions. The material of interest is α-uranium, which is the stable phase of uranium at room temperature (Cahn 1951).…”

Section: Introductionmentioning

confidence: 99%

“…The CPFE method includes the plastic deformation due to all slip and twin systems (Roters et al 2018;Irastorza-Landa et al 2017a). Recently, continuum models have been developed to describe the nucleation and growth of discrete twins with a specific thickness (Grilli et al 2020b). A twin variable ϕ β varies from 0 (untwinned region) to 1 (twinned region) when a twin of type β forms (Liu et al 2018(Liu et al , 2019.…”

Section: Introductionmentioning

confidence: 99%

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Modelling the nucleation and propagation of cracks at twin boundaries

Grilli

Cocks

2021

Int J Fract

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Fracture arising from cracks nucleating and propagating along twin boundaries is commonly observed in metals that exhibit twinning as a plastic deformation mechanism. This phenomenon affects the failure of macroscopic mechanical components, but it is not fully understood. We present simulations in which a continuum model for discrete twins and a cohesive zone model are coupled to aid the understanding of fracture at twin boundaries. The interaction between different twin systems is modelled using a local term that depends on the continuum twin variables. Simulations reveal that the resolved shear stress necessary for an incident twin to propagate through a barrier twin can be up to eight times the resolved shear stress for twin nucleation. Interface elements are used at the interfaces between all bulk elements to simulate arbitrary intragranular cracks. An algorithm to detect twin interfaces is developed and their strength has been calibrated to give good agreement with the experimentally observed fracture path. The elasto-plastic deformation induced by discrete twins is modelled using the crystal plasticity finite element method and the stress induced by twin tips is captured. The tensile stress caused by the tip of an incident twin on a barrier twin is sufficient to nucleate a crack. A typical staircase fracture path, with cracks propagating along the twin interfaces, is reproduced only if the strength of the twin interfaces is decreased to about one-third of the strength of the bulk material. This model can be used to help understand fracture caused by the activation of multiple twin systems in different materials.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Modelling the nucleation and propagation of cracks at twin boundaries

Grilli

Cocks

2021

Int J Fract

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“…The behaviour of the grains is described using a crystal plasticity model coupled with a continuum model for discrete twins (Grilli et al 2020b). A variable ϕ is used to represent discrete twins.…”

Section: Crystal Plasticity Modelmentioning

confidence: 99%

Coupling a discrete twin model with cohesive elements to understand twin-induced fracture

2021

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The interplay between twinning and fracture in metals under deformation is an open question. The plastic strain concentration created by twin bands can induce large stresses on the grain boundaries. We present simulations in which a continuum model describing discrete twins is coupled with a crystal plasticity finite element model and a cohesive zone model for intergranular fracture. The discrete twin model can predict twin nucleation, propagation, growth and the correct twin thickness. Therefore, the plastic strain concentration in the twin band can be modelled. The cohesive zone model is based on a bilinear traction-separation law in which the damage is caused by the normal stress on the grain boundary. An algorithm is developed to generate interface elements at the grain boundaries that satisfy the traction-separation law. The model is calibrated by comparing polycrystal simulations with the experimentally observed strain to failure and maximum stress. The dynamics of twin and crack nucleation have been investigated. First, twins nucleate and propagate in a grain, then, microcracks form near the intersection between twin tips and grain boundaries. Microcracks appear at multiple locations before merging. A propagating crack can nucleate additional twins starting from the grain boundary, a few micrometres away from the original crack nucleation site. This model can be used to understand which type of texture is more resistant against crack nucleation and propagation in cast metals in which twinning is a deformation mechanism. The code is available online at https://github.com/TarletonGroup/CrystalPlasticity. Graphic Abstract

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“…In recent years, crystal plasticity models have been coupled with phase-field (PF) methods to study the twinning mechanisms [141][142][143][144][145], where twinning is modeled as a phase transformation, and plastic deformation is computed using crystal plasticity methods. Phase-field models, first started by Khachaturian [146], have been successful to predict austenite-martensite transformation in steels [147] and tetragonal-monoclinic transformation in zirconia [148].…”

Section: Coupled Crystal Plasticity and Phase-field Model (Cp-pfm)mentioning

confidence: 99%

“…In hcp Mg, Pi et al [149] used the phase-field model to study the tensile twins using twin interfacial energy as a driving force. Later, the coupled CP-PF models are successfully used to study deformation behavior associated with slip induced plasticity, and twinning and detwinning [141], twin nucleation and thickening [142,143], twin morphologies [144], and twin interactions with other slip systems, twins, and grain boundaries [142,145].…”

Section: Coupled Crystal Plasticity and Phase-field Model (Cp-pfm)mentioning

confidence: 99%

A Review on Capturing Twin Nucleation in Crystal Plasticity for Hexagonal Metals

Paudel

Giri

Priddy

et al. 2021

Metals

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Owing to its ability to incorporate Schmid’s law at each integration point, crystal plasticity has proven a powerful tool to simulate and predict the slip behavior at the grain level and the ensuing heterogeneous stress/strain localization and texture evolution at the macroscopic level. Unfortunately, notwithstanding substantial efforts during the last three decades, this remarkable capability has not been replicated for materials where twinning becomes a noticeable deformation mechanism, namely in the case of low-stacking fault energy cubic, orthorhombic, and hexagonal close-packed structures. The culprit lies in the widely adopted unphysical pseudo-slip approach for capturing twin formation. While the slip is diffuse, twinning is a localized event that occurs as a drastic burst of a confined number of partial twinning dislocations establishing an interface that pursues growth through a thread of perfect twinning dislocations in the sense of bicrystallography. Moreover, at earlier stages, twin nucleation may require atomic diffusion (Shuffling) and faceting, generally demanding higher stress levels not necessarily on the twin shear plane, while triaxiality at adequate sites might be needed or preferred such as lower grain boundary misorientations or other twin boundaries. Identifying a mathematical framework in the constitutive equations for capturing these twin formation sensitivities has been a daunting challenge for crystal plasticity modelers, which has stalled ameliorating the design of key hexagonal materials for futuristic climate change-related industries. This paper reviews existing approaches to incorporating twinning in crystal plasticity models, discusses their capabilities, addresses their limitations, and suggests prospective views to fill gaps. The incorporation of a new physics-based twin nucleation criterion in crystal plasticity models holds groundbreaking potential for substantial progress in the field of computational material science.

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A phase field model for the growth and characteristic thickness of deformation-induced twins

Cited by 28 publications

References 95 publications

Modelling the nucleation and propagation of cracks at twin boundaries

Modelling the nucleation and propagation of cracks at twin boundaries

Coupling a discrete twin model with cohesive elements to understand twin-induced fracture

A Review on Capturing Twin Nucleation in Crystal Plasticity for Hexagonal Metals

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