Phase-field study of crack nucleation and propagation in elastic–perfectly plastic bodies

Brach, Stella; Tanné, Erwan; Bourdin, Blaise; Bhattacharya, Kaushik

doi:10.1016/j.cma.2019.04.027

Cited by 29 publications

(13 citation statements)

References 37 publications

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“…This intermittent stick-slip nature is also observed in other applications at different scales. For example, plane strain elastic-perfectly plastic medium is found to host intermittent crack propagation where crack is pinned by plastic zone and finite jump in nucleation is observed (Brach et al, 2019). Intermittent stick-slip behavior is also observed in crystal plasticity through avalanches in stress-strain response of a micropillar assisted by dislocation pinning (Sethna et al, 2017).…”

Section: Discussionmentioning

confidence: 99%

Spatio-temporal clustering of seismicity enabled by off-fault plasticity

Mia¹,

Abdelmeguid²,

Elbanna³

2022

Preprint

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Earthquakes are among nature’s deadliest and costliest hazards. Understanding mechanisms for earthquake nucleation, propagation, and arrest is key for developing reliable operational forecasts and next generation seismic hazard models. While significant progress has been made in understanding source processes in linear elastic domains, the response of the rocks near the fault is complex and likely to be inelastic due to the extreme stresses and deformations associated with fault slip. The effect of this more realistic fault zone response on seismic and aseismic fault slip is poorly understood. Here, we simulate sequence of earthquake and aseismic slip of a fault embedded in an elastic-viscoplastic bulk subject to slow tectonic loading. We show that off-fault plasticity significantly influences the source characteristics. Specifically, off-fault plasticity may lead to partial ruptures and emergence of spatial segmentation as well as hierarchical temporal seismic clustering. Furthermore, co-evolution of fault slip and off-fault bulk plasticity may lead to heterogeneous rupture propagation and results in pockets of slip deficit. While the energy dissipated through plastic deformation remains a small fraction of the total energy budget, its impact on the source characteristics is disproportionally large through the redistribution of stresses and viscous relaxation. Our results suggest a new mechanism of dynamic heterogeneity in earthquake physics that can be active for both small and large earthquakes and may have important implications on earthquake size distribution and energy budget. Furthermore, this plasticity-induced self-limiting crack dynamics may be relevant for other dynamic fracture applications and design of dynamically tough materials.

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Section: Discussionmentioning

confidence: 99%

Spatio-temporal clustering of seismicity enabled by off-fault plasticity

Mia¹,

Abdelmeguid²,

Elbanna³

2022

Preprint

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“…This issue has been partially addressed in [18] by solving the fracture problem (1) via different alternating minimization algorithms, which delivered the same results. Here, the functional E is first minimized with respect to (u, p ) while holding the fracture variable α fixed, and then minimized with respect to α while holding (u, p ) fixed.…”

Section: Variational Phase-field Modelmentioning

confidence: 95%

“…The fracture problem is solved by minimizing E with respect to the displacement field u, the plastic strain p and the damage variable α [1,18] u * , * p , α * = arg min…”

Section: Variational Phase-field Modelmentioning

confidence: 99%

“…The current study extends such analysis to elastic-plastic layered materials, as plasticity is expected to greatly impact the evolution of the fracture process and thus the effective fracture toughness. To this end, we use an elastic-plastic phase-field formulation which couples elasticity, perfect plasticity and fracture in a rate-independent setting [1,18]. A surfing boundary condition [39] is applied to macroscopically propagate a crack at different layer angles.…”

Section: Introductionmentioning

confidence: 99%

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Effects of plasticity on the anisotropy of the effective fracture toughness

Brach

2020

Preprint

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This paper investigates the effects of plasticity on the effective fracture toughness. A layered material is considered as a modelling system. An elastic-plastic phase-field model and a surfing boundary condition are used to study how the crack propagates throughout the material and the evolution of the effective toughness as a function of the layer angle. We first study three idealized situations, where only one property among fracture toughness, Young's modulus and yield strength is heterogeneous whereas the others are uniform. We observe that in the case of toughness and strength heterogeneity, the material exhibits anomalous isotropy: the effective toughness is equal to the largest of the point-wise values for any layer angle except when the layers are parallel to the macroscopic direction of propagation. As the layer angle decreases, the crack propagates along the brittle-to-tough interfaces, whereas it goes straight when the layers have different yield strength but uniform toughness. We find that smooth deflections in the crack path do not induce any overall toughening and that the effective toughness is not proportional to either the cumulated fracture energy or the cumulated plastic work. In the case of elastic heterogeneity, the material is anisotropic in the sense of the effective toughness, as the latter varies as a function of the layer angle. Four toughening mechanisms are active: stress fluctuations, crack renucleation, plastic dissipation and plastic blunting. Finally, we consider a layered medium comprised of compliant-tough-weak and stiff-brittle-strong phases, as it is the case for many structural composites. We observe a transition from an interface-dominated to a plasticity-dominated failure regime, as the phase constituents become more ductile. The material is anisotropic in the sense of the effective toughness.

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“…T. Gerasimov et al 23 proved that the irreversibility constraint of the crack phase-field is a constrained minimization problem. Bhattacharya et al 24 presented variational gradient damage formulation of ductile failure that naturally couples elasticity, perfect plasticity, and fracture in the rate-independent setting. In this work, small plastic deformation is considered to take place in the location of the notch root or crack tip.…”

Section: A Related Approach Is Introduced By Mcauliffe and Waismanmentioning

confidence: 99%

Fracture Investigation of the Ductile Materials Using Phase-Field Model

Esmailzadeh

Pour

Behnagh³

et al. 2020

Preprint

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Phase-field models have been the subject of a great deal of research in recent years. Investigations have revealed that the phase-field model is capable of generating complex crack patterns. This is gained by replacing the sharp discontinuities with a scalar phase damage field comprising the diffuse crack topology. In the previous models, cracks are blurred into the surrounding areas due to introducing dependency of degradation function to a single parameter, strain threshold. The stable crack initiation and propagation require estimation of complex higher-order degradation function, which should be solved either by a new iteration scheme or using extremely small loading increment. However, this demands considerably high computational cost. In this study, the nonlinear coupled system comprising the linear momentum equation and the diffusion-type equation governing the phase-field evolution is solved concurrently through a Newton-Raphson approach. Moreover, an improved degradation function and staggered iteration scheme are solved by a one-step paradigm is proposed. Such that the computational costs can be reduced, and the stability of crack propagation can be improved. A phase-field model for ductile fracture is carried out in the commercial finite element software Abaqus by means of UEL and UMAT subroutines. Post-processing of simulation results is implemented through an added subroutine implemented in the visualization module. Several benchmark problems show the proposed model's ability to reproduce some essential phenomenological characteristics of ductile fracture as documented in the experimental literature.

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Phase-field study of crack nucleation and propagation in elastic–perfectly plastic bodies

Cited by 29 publications

References 37 publications

Spatio-temporal clustering of seismicity enabled by off-fault plasticity

Spatio-temporal clustering of seismicity enabled by off-fault plasticity

Effects of plasticity on the anisotropy of the effective fracture toughness

Fracture Investigation of the Ductile Materials Using Phase-Field Model

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