On degradation functions in phase field fracture models

Kuhn, Charlotte; Schlüter, Alexander; Müller, Ralf

doi:10.1016/j.commatsci.2015.05.034

Cited by 282 publications

(134 citation statements)

References 36 publications

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“…The currently available phase-field formulations of brittle fracture encompass static and dynamic models. We mention the papers by Amor et al [7], Miehe et al [8,9], Kuhn and Müller [10], Pham et al [11], Borden et al [12], Mesgarnejad et al [13], Kuhn et al [14], Ambati et al [15], Wu et al [16], where various formulations are developed and validated. Recently, the framework has been also extended to ductile (elasto-plastic) fracture [17][18][19][20][21][22], pressurized fracture in elastic and porous media [23,24], fracture in films [25] and shells [26][27][28], and multi-field fracture [29][30][31][32][33][34][35][36].…”

Section: Introductionmentioning

confidence: 99%

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A non-intrusive global/local approach applied to phase-field modeling of brittle fracture

Gerasimov

Noii

Allix

et al. 2018

Adv. Model. and Simul. in Eng. Sci.

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This paper aims at investigating the adoption of non-intrusive global/local approaches while modeling fracture by means of the phase-field framework. A successful extension of the non-intrusive global/local approach to this setting would pave the way for a wide adoption of phase-field modeling of fracture, already well established in the research community, within legacy codes for industrial applications. Due to the extreme difference in stiffness between the global counterpart of the zone to be analized locally and its actual response when undergoing extensive cracking, the main foreseen issues are robustness, accuracy and efficiency of the fixed point iterative algorithm which is at the core of the method. These issues are tackled in this paper. We investigate the convergence performance when using the native global/local algorithm and show that the obtained results are identical to the reference phase-field solution. We also equip the global/local solution update procedure with relaxation/acceleration techniques such as Aitken's 2 -method, the Symmetric Rank One and Broyden's methods and show that the iterative convergence can be improved significantly. Results indicate that Aitken's 2 -method is probably the most convenient choice for the implementation of the approach within legacy codes, as this method needs only tools already available for the so-called sub-modeling approach, a strategy routinely used in industrial contexts.

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Section: Introductionmentioning

confidence: 99%

“…is given by (13) and (14). Option 2 One preserves the representations (19) and (20), and, in contrast to (21), imposes only a weak continuity between λ C and λ L on .…”

Section: We Now Introduce Two Functions Onmentioning

confidence: 99%

A non-intrusive global/local approach applied to phase-field modeling of brittle fracture

Gerasimov

Noii

Allix

et al. 2018

Adv. Model. and Simul. in Eng. Sci.

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“…This interpretation presents several advantages from a physical point of view. First of all, this additional length parameter could be related to the maximal stress that the material can sustain and hence introduces additional experimentally validated size effects which are not present in the Griffith model of fracture mechanics, see the work of [6][7][8][9] among others. Secondly, the tension-compression asymmetry phenomenon as observed for brittle materials can be easily formulated directly in the gradient damage model.…”

Section: Introductionmentioning

confidence: 99%

Numerical investigation of dynamic brittle fracture via gradient damage models

Marigo

Guilbaud

et al. 2016

Adv. Model. and Simul. in Eng. Sci.

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Background: Gradient damage models can be acknowledged as a unified framework of dynamic brittle fracture. As a phase-field approach to fracture, they are gaining popularity over the last few years in the computational mechanics community. This paper concentrates on a better understanding of these models. We will highlight their properties during the initiation and propagation phases of defect evolution. Methods: The variational ingredients of the dynamic gradient damage model are recalled. Temporal discretization based on the Newmark-β scheme is performed. Several energy release rates in gradient damage models are introduced to bridge the link from damage to fracture. Results and discussion: An antiplane tearing numerical experiment is considered. It is found that the phase-field crack tip is governed by the asymptotic Griffith's law. In the absence of unstable crack propagation, the dynamic gradient damage model converges to the quasi-static one. The defect evolution is in quantitative accordance with the linear elastic fracture mechanics predictions. Conclusion: These numerical experiments provide a justification of the dynamic gradient damage model along with its current implementation, when it is used as a phase-field model for complex real-world dynamic fracture problems.

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“…[129][130][131][132] However, there is no direct application of PF methods to predict the effect of radiation-induced microstructures on mechanical properties. In irradiated materials the most important contribution of the PF method consisted of improving the understanding and prediction of void and gas bubble swelling, which impacts the thermos-mechanical properties of materials.…”

Section: Irradiation Effects On Mechanical Thermal and Magnetic Promentioning

confidence: 99%

A review: applications of the phase field method in predicting microstructure and property evolution of irradiated nuclear materials

Sun

et al. 2017

npj Comput Mater

127

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Complex microstructure changes occur in nuclear fuel and structural materials due to the extreme environments of intense irradiation and high temperature. This paper evaluates the role of the phase field method in predicting the microstructure evolution of irradiated nuclear materials and the impact on their mechanical, thermal, and magnetic properties. The paper starts with an overview of the important physical mechanisms of defect evolution and the significant gaps in simulating microstructure evolution in irradiated nuclear materials. Then, the phase field method is introduced as a powerful and predictive tool and its applications to microstructure and property evolution in irradiated nuclear materials are reviewed. The review shows that (1) Phase field models can correctly describe important phenomena such as spatial-dependent generation, migration, and recombination of defects, radiation-induced dissolution, the Soret effect, strong interfacial energy anisotropy, and elastic interaction; (2) The phase field method can qualitatively and quantitatively simulate two-dimensional and three-dimensional microstructure evolution, including radiation-induced segregation, second phase nucleation, void migration, void and gas bubble superlattice formation, interstitial loop evolution, hydrate formation, and grain growth, and (3) The Phase field method correctly predicts the relationships between microstructures and properties. The final section is dedicated to a discussion of the strengths and limitations of the phase field method, as applied to irradiation effects in nuclear materials. npj Computational Materials (2017) 3:16 ; doi:10.1038/s41524-017-0018-y INTRODUCTIONHigh energy particle (such as neutron, ion, and electron) radiation can create major changes in the shape and thermo-mechanical properties of nuclear fuels and structural components of nuclear reactors. These changes are caused by radiation-induced evolution of compositions and microstructures. The main effects of radiation on reactor materials are: (1) dimensional change associated with gas bubble swelling, void swelling, grain growth, and creep; 1-5 (2) loss of ductility and increase in ductile-brittle transition temperature (DBTT) due to the formation of secondphase precipitates, self-interstitial atomic (SIA) loops, and dislocation networks; 6, 7 (3) oxidation and corrosion accelerated by high temperature, fission products, and radiation damage; 8-10 and (4) local and bulk changes in chemical composition, including irradiation-enhanced segregation of alloy components and phase separation.11-17 Figure 1 shows typical microstructures observed in irradiated materials.9, 18-21 The radiation-induced heterogeneity of the microstructures depends on the initial phase and defect structure of the fresh (non-irradiated) materials and on the type and severity of the radiation environment. Fundamental understanding of heterogeneous three-dimensional microstructure evolution is crucial to the development of advanced radiation tolerant materials that can significa...

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On degradation functions in phase field fracture models

Cited by 282 publications

References 36 publications

A non-intrusive global/local approach applied to phase-field modeling of brittle fracture

A non-intrusive global/local approach applied to phase-field modeling of brittle fracture

Numerical investigation of dynamic brittle fracture via gradient damage models

A review: applications of the phase field method in predicting microstructure and property evolution of irradiated nuclear materials

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