Phase field fracture in elasto-plastic solids: Variational formulation for multi-surface plasticity and effects of plastic yield surfaces and hardening

Fang, Jianguang; Wu, Chengqing; Li, Jun; Liu, Qiang; Wu, Chi; Sun, Guangyong; Li, Qing

doi:10.1016/j.ijmecsci.2019.03.012

Cited by 73 publications

(31 citation statements)

References 42 publications

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“…In the literature two major groups of ductile phase-field implementations exist. The first group [107,62,108,59] uses the energy of the plastic deformation to sustain damage evolution, while the other [109,54,110] defines a critical strain and a penalty function to achieve fracture. The advantage of the first method is that the strain energy function satisfies the laws of thermodynamics, however in plasticity if the material heals it can maintain part of its resistance independently of the plastic strain [98].…”

Section: Variablementioning

confidence: 99%

“…Since the method was originally introduced, it became surprisingly popular in the fracture science community. Several implementations were proposed to follow dynamic [46,47,48,49,50,51,52] and ductile [53,54,55,56,57,58,59,60] fracture. Surprisingly, formulations concentrating on the effect of plasticity on the dynamic crack propagation is still scarce.…”

Section: Introductionmentioning

confidence: 99%

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An open-source Abaqus implementation of the phase-field method to study the effect of plasticity on the instantaneous fracture toughness in dynamic crack propagation

Molnár

Gravouil

Seghir

et al. 2020

Computer Methods in Applied Mechanics and Engineering

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Brittle and ductile dynamic fracture in solids is a complex mechanical phenomenon which attracted much attention from both engineers and scientists due to its technological interests. Modeling cracks in dynamic cases based on a discontinuous description is difficult because it needs additional criteria for branching and widening. Due to the very short time scales and the spatial complexity of the dynamic problem, its experimental analysis is still very difficult. Therefore, researchers still have to rely on numerical simulations to find a deeper explanation for many observed phenomena. This study is set out to investigate the effect of plasticity on dynamic fracture propagation. On the other hand, the diffuse phase-field formulation makes it possible to initiate, propagate, arrest or even branch cracks while satisfying the basic principles of thermodynamics. An implicit, staggered elastoplastic version of the phase-field approach was implemented in the commercial finite element code Abaqus through the UEL option. By means of simple examples we show that localized ductile deformations first increase both resistance and toughness. Then, after a maximum value, the resistance starts to decrease with a significant increment in energy dissipation. By favoring shear deformation over tensile failure the fracture pattern changes. First the branching disappears, then the crack propagation angle changes and becomes a shear band. Finally, we observed the increment of the instantaneous dynamic stress intensity factor during the acceleration stage of the crack without introducing a rate dependent critical fracture energy. We explained this phenomenon with the increasing roughness of the fracture surface.

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Section: Variablementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

An open-source Abaqus implementation of the phase-field method to study the effect of plasticity on the instantaneous fracture toughness in dynamic crack propagation

Molnár

Gravouil

Seghir

et al. 2020

Computer Methods in Applied Mechanics and Engineering

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“…In this subsection, the governing equations for coupled damage phase-field and plasticity are derived according to the literature [15][16][17]20,28,[32][33][34][35] to clarify the proposed modifications. According to Griffith's theory, a fracture is defined by a criterion based on the equilibrium of the surface energy and the elastic energy stored in the material.…”

Section: Overview Of Governing Equations Evolutionmentioning

confidence: 99%

“…where σ yv is the initial yield stress, σ y0,∞ is the saturation hardening stress, n is the hardening exponent, and H is the hardening modulus [36]. The plastic dissipated energy density is [35]…”

Section: Overview Of Governing Equations Evolutionmentioning

confidence: 99%

A Modified Phase-Field Damage Model for Metal Plasticity at Finite Strains: Numerical Development and Experimental Validation

Živković

Dunić

Milovanović

et al. 2020

Metals

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Steel structures are designed to operate in an elastic domain, but sometimes plastic strains induce damage and fracture. Besides experimental investigation, a phase-field damage model (PFDM) emerged as a cutting-edge simulation technique for predicting damage evolution. In this paper, a von Mises metal plasticity model is modified and a coupling with PFDM is improved to simulate ductile behavior of metallic materials with or without constant stress plateau after yielding occurs. The proposed improvements are: (1) new coupling variable activated after the critical equivalent plastic strain is reached; (2) two-stage yield function consisting of perfect plasticity and extended Simo-type hardening functions. The uniaxial tension tests are conducted for verification purposes and identifying the material parameters. The staggered iterative scheme, multiplicative decomposition of the deformation gradient, and logarithmic natural strain measure are employed for the implementation into finite element method (FEM) software. The coupling is verified by the ‘one element’ example. The excellent qualitative and quantitative overlapping of the force-displacement response of experimental and simulation results is recorded. The practical significances of the proposed PFDM are a better insight into the simulation of damage evolution in steel structures, and an easy extension of existing the von Mises plasticity model coupled to damage phase-field.

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“…Nevertheless, it was not a trivial task to track the evolution of complex multiple fracture surfaces. Therefore, considerable research efforts have been recently devoted to the phase‐field fracture model, in which material damage is regarded to be a progressively diffusive, rather than a sharp and discrete process. In this context, a phase‐field function is typically employed to depict discontinuous cracks internally.…”

Section: Introductionmentioning

confidence: 99%

Level‐set topology optimization for maximizing fracture resistance of brittle materials using phase‐field fracture model

Fang

Zhou

et al. 2020

Numerical Meth Engineering

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Summary Fracture is one of the most common failure modes in brittle materials. It can drastically decrease material integrity and structural strength. To address this issue, we propose a level‐set (LS) based topology optimization procedure to optimize the distribution of reinforced inclusions within matrix materials subject to the volume constraint for maximizing structural resistance to fracture. A phase‐field fracture model is formulated herein to simulate crack initiation and propagation, in which a staggered algorithm is developed to solve such time‐dependent crack propagation problems. In line with diffusive damage of the phase‐field approach for fracture; topological derivatives, which provide gradient information for the topology optimization in a LS framework, are derived for fracture mechanics problems. A reaction‐diffusion equation is adopted to update the LS function within a finite element framework. This avoids the reinitialization by overcoming the limitation to time step with the Courant‐Friedrichs‐Lewy condition. In this article, three numerical examples, namely, a L‐shaped section, a rectangular slab with predefined cracks, and an all‐ceramic onlay dental bridge (namely, fixed partial denture), are presented to demonstrate the effectiveness of the proposed LS based topology optimization for enhancing fracture resistance of multimaterial composite structures in a phase‐field fracture context.

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Phase field fracture in elasto-plastic solids: Variational formulation for multi-surface plasticity and effects of plastic yield surfaces and hardening

Cited by 73 publications

References 42 publications

An open-source Abaqus implementation of the phase-field method to study the effect of plasticity on the instantaneous fracture toughness in dynamic crack propagation

An open-source Abaqus implementation of the phase-field method to study the effect of plasticity on the instantaneous fracture toughness in dynamic crack propagation

A Modified Phase-Field Damage Model for Metal Plasticity at Finite Strains: Numerical Development and Experimental Validation

Level‐set topology optimization for maximizing fracture resistance of brittle materials using phase‐field fracture model

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