A phase field model for elastic-gradient-plastic solids undergoing hydrogen embrittlement

Kristensen, Philip K.; Niordson, Christian Frithiof; Martínez‐Pañeda, Emilio

doi:10.1016/j.jmps.2020.104093

Cited by 124 publications

(57 citation statements)

References 95 publications

(123 reference statements)

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“…Thus, the length scale has been considered exclusively a regularizing parameter. However, there is an increasing interest in investigating the implications of considering a finite phase field length scale and the resulting analogies with gradient damage models [10,53,54]. As discussed in §1, the consideration of a finite ℓ > 0 + introduces a critical stress proportional to 1/ℓ, which is absent in Griffith’s formulation and linear elastic fracture mechanics.…”

Section: Resultsmentioning

confidence: 99%

An assessment of phase field fracture: crack initiation and growth

Kristensen

Niordson

Martínez‐Pañeda

2021

Phil. Trans. R. Soc. A.

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The phase field paradigm, in combination with a suitable variational structure, has opened a path for using Griffith’s energy balance to predict the fracture of solids. These so-called phase field fracture methods have gained significant popularity over the past decade, and are now part of commercial finite element packages and engineering fitness- for-service assessments. Crack paths can be predicted, in arbitrary geometries and dimensions, based on a global energy minimization—without the need for ad hoc criteria. In this work, we review the fundamentals of phase field fracture methods and examine their capabilities in delivering predictions in agreement with the classical fracture mechanics theory pioneered by Griffith. The two most widely used phase field fracture models are implemented in the context of the finite element method, and several paradigmatic boundary value problems are addressed to gain insight into their predictive abilities across all cracking stages; both the initiation of growth and stable crack propagation are investigated. In addition, we examine the effectiveness of phase field models with an internal material length scale in capturing size effects and the transition flaw size concept. Our results show that phase field fracture methods satisfactorily approximate classical fracture mechanics predictions and can also reconcile stress and toughness criteria for fracture. The accuracy of the approximation is however dependent on modelling and constitutive choices; we provide a rationale for these differences and identify suitable approaches for delivering phase field fracture predictions that are in good agreement with well-established fracture mechanics paradigms. This article is part of a discussion meeting issue ‘A cracking approach to inventing new tough materials: fracture stranger than friction’.

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Section: Resultsmentioning

confidence: 99%

An assessment of phase field fracture: crack initiation and growth

Kristensen

Niordson

Martínez‐Pañeda

2021

Phil. Trans. R. Soc. A.

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“…In agreement with fracture mechanics, phase field predicts a strength dominated behaviour (i.e., sensitive to the choice of ) when the initial defect is smaller than the transition flaw size, and a fracture dominated response (i.e., governed by G c ) for larger cracks [26]. In elastic-plastic materials, cracking always takes place at G = G c if the initial flaw is sufficiently large but the dissipation (R-curve) is influenced by [31]. As expected, both the peak load and the CMOD at the maximum load increase with the increasing G m , see Fig.…”

Section: Sensitivity Studymentioning

confidence: 99%

Phase field predictions of microscopic fracture and R-curve behaviour of fibre-reinforced composites

Tan

Martínez‐Pañeda

2021

Composites Science and Technology

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We present a computational framework to explore the effect of microstructure and constituent properties upon the fracture toughness of fibre-reinforced polymer composites. To capture microscopic matrix cracking and fibre-matrix debonding, the framework couples the phase field fracture method and a cohesive zone model in the context of the finite element method. Virtual single-notched three point bending tests are conducted. The actual microstructure of the composite is simulated by an embedded cell in the fracture process zone, while the remaining area is homogenised to be an anisotropic elastic solid. A detailed comparison of the predicted results with experimental observations reveals that it is possible to accurately capture the crack path, interface debonding and load versus displacement response. The sensitivity of the crack growth resistance curve (R-curve) to the matrix fracture toughness and the fibre-matrix interface properties is determined. The influence of porosity upon the R-curve of fibre-reinforced composites is also explored, revealing a stabler response with increasing void volume fraction. These results shed light into microscopic fracture mechanisms and set the basis for efficient design of high fracture toughness composites.

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“…Variational phase field methods for fracture are enjoying a notable success [ 1 , 2 ]. Among many others, applications include shape memory alloys [ 3 ], glass laminates [ 4 , 5 ], hydrogen-embrittled alloys [ 6 , 7 ], dynamic fracture [ 8 , 9 ], fiber-reinforced composites [ 10 , 11 , 12 , 13 ], functionally graded materials [ 14 , 15 , 16 ], fatigue crack growth [ 17 , 18 ], and masonry structures [ 19 ]. The key to the success of the phase field paradigm in fracture mechanics is arguably three-fold.…”

Section: Introductionmentioning

confidence: 99%

A Unified Abaqus Implementation of the Phase Field Fracture Method Using Only a User Material Subroutine

2021

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We present a simple and robust implementation of the phase field fracture method in Abaqus. Unlike previous works, only a user material (UMAT) subroutine is used. This is achieved by exploiting the analogy between the phase field balance equation and heat transfer, which avoids the need for a user element mesh and enables taking advantage of Abaqus’ in-built features. A unified theoretical framework and its implementation are presented, suitable for any arbitrary choice of crack density function and fracture driving force. Specifically, the framework is exemplified with the so-called AT1, AT2 and phase field-cohesive zone models (PF-CZM). Both staggered and monolithic solution schemes are handled. We demonstrate the potential and robustness of this new implementation by addressing several paradigmatic 2D and 3D boundary value problems. The numerical examples show how the current implementation can be used to reproduce numerical and experimental results from the literature, and efficiently capture advanced features such as complex crack trajectories, crack nucleation from arbitrary sites and contact problems. The code developed is made freely available.

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A phase field model for elastic-gradient-plastic solids undergoing hydrogen embrittlement

Cited by 124 publications

References 95 publications

An assessment of phase field fracture: crack initiation and growth

An assessment of phase field fracture: crack initiation and growth

Phase field predictions of microscopic fracture and R-curve behaviour of fibre-reinforced composites

A Unified Abaqus Implementation of the Phase Field Fracture Method Using Only a User Material Subroutine

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