A phase-field model for fatigue crack growth

Abstract Within this work, we utilize the framework of phase field modeling for fracture in order to handle a very crucial issue in terms of designing technical structures, namely the phenomenon of fatigue crack growth. So far, phase field fracture models were applied to a number of problems in the field of fracture mechanics and were proven to yield reliable results even for complex crack problems. For crack growth due to cyclic fatigue, our basic approach considers an additional energy contribution entering the regularized energy density function accounting for crack driving forces associated with fatigue damage. With other words, the crack surface energy is not solely in competition with the time-dependent elastic strain energy but also with a contribution consisting of accumulated energies, which enables crack extension even for small maximum loads. The load time function applied to a certain structure has an essential effect on its fatigue life. Besides the pure magnitude of a certain load cycle, it is highly decisive at which point of the fatigue life a certain load cycle is applied. Furthermore, the level of the mean load has a significant effect. We show that the model developed within this study is able to predict realistic fatigue crack growth behavior in terms of accurate growth rates and also to account for mean stress effects and different stress ratios. These are important properties that must be treated accurately in order to yield an accurate model for arbitrary load sequences, where various amplitude loading occurs.

Download Full-text

Phase-field models for fatigue crack growth

Theoretical and Applied Fracture Mechanics ◽

10.1016/j.tafmec.2019.102282 ◽

2019 ◽

Vol 103 ◽

pp. 102282 ◽

Cited By ~ 12

Author(s):

A. Mesgarnejad ◽

A. Imanian ◽

A. Karma

Keyword(s):

Fatigue Crack ◽

Fatigue Crack Growth ◽

Crack Growth ◽

Phase Field ◽

Phase Field Models

Download Full-text

A phase field modeling approach of cyclic fatigue crack growth

International Journal of Fracture ◽

10.1007/s10704-020-00468-w ◽

2020 ◽

Vol 225 (1) ◽

pp. 89-100 ◽

Cited By ~ 6

Author(s):

Christoph Schreiber ◽

Charlotte Kuhn ◽

Ralf Müller ◽

Tarek Zohdi

Keyword(s):

Fatigue Crack ◽

Fatigue Crack Growth ◽

Numerical Simulations ◽

Crack Growth ◽

Phase Field ◽

Cyclic Fatigue ◽

Phase Field Modeling ◽

Field Modeling ◽

Economical Design ◽

Crack Problems

AbstractPhase field modeling of fracture has been in the focus of research for over a decade now. The field has gained attention properly due to its benefiting features for the numerical simulations even for complex crack problems. The framework was so far applied to quasi static and dynamic fracture for brittle as well as for ductile materials with isotropic and also with anisotropic fracture resistance. However, fracture due to cyclic mechanical fatigue, which is a very important phenomenon regarding a safe, durable and also economical design of structures, is considered only recently in terms of phase field modeling. While in first phase field models the material’s fracture toughness becomes degraded to simulate fatigue crack growth, we present an alternative method within this work, where the driving force for the fatigue mechanism increases due to cyclic loading. This new contribution is governed by the evolution of fatigue damage, which can be approximated by a linear law, namely the Miner’s rule, for damage accumulation. The proposed model is able to predict nucleation as well as growth of a fatigue crack. Furthermore, by an assessment of crack growth rates obtained from several numerical simulations by a conventional approach for the description of fatigue crack growth, it is shown that the presented model is able to predict realistic behavior.

Download Full-text

Acceleration and Parallelization of a Linear Equation Solver for Crack Growth Simulation Based on the Phase Field Model

Mathematics ◽

10.3390/math9182248 ◽

2021 ◽

Vol 9 (18) ◽

pp. 2248

Author(s):

Gaku Ishii ◽

Yusaku Yamamoto ◽

Takeshi Takaishi

Keyword(s):

Linear Equation ◽

Crack Growth ◽

Phase Field ◽

Field Model ◽

Multicore Processors ◽

Phase Field Model ◽

Growth Simulation ◽

Crack Growth Simulation ◽

Simulation Based ◽

Linear Equation Solver

We aim to accelerate the linear equation solver for crack growth simulation based on the phase field model. As a first step, we analyze the properties of the coefficient matrices and prove that they are symmetric positive definite. This justifies the use of the conjugate gradient method with the efficient incomplete Cholesky preconditioner. We then parallelize this preconditioner using so-called block multi-color ordering and evaluate its performance on multicore processors. The experimental results show that our solver scales well and achieves an acceleration of several times over the original solver based on the diagonally scaled CG method.

Download Full-text

Irreversible phase field models for crack growth in industrial applications: thermal stress, viscoelasticity, hydrogen embrittlement

SN Applied Sciences ◽

10.1007/s42452-021-04593-6 ◽

2021 ◽

Vol 3 (9) ◽

Author(s):

Masato Kimura ◽

Takeshi Takaishi ◽

Sayahdin Alfat ◽

Takumi Nakano ◽

Yoshimi Tanaka

Keyword(s):

Crack Growth ◽

Phase Field ◽

Field Model ◽

Phase Field Model ◽

Gradient Flow ◽

Industrial Applications ◽

Finite Element Software ◽

Phase Field Models ◽

Hydrogen Assisted Cracking ◽

Coupling Approach

AbstractThree new industrial applications of irreversible phase field models for crack growth are presented in this study. The phase field model for irreversible crack growth in an elastic material is derived as a unidirectional gradient flow of the Francfort–Marigo energy with the Ambrosio–Tortorelli regularization, which is known to be consistent with classic Griffith fracture theory. The obtained compact parabolic-elliptic system of PDEs including two regularization parameters for space and time enables us to simulate various kinds of crack behaviors with standard finite element software, without any geometric restriction on the crack path. We extend the irreversible phase field model to thermal cracking in solder and to cracking in a viscoelastic material, keeping the compact forms of the PDEs and the energy consistency. On the other hand, for hydrogen-assisted cracking in metal, we propose a compact phase field model focusing on a kinematic jamming effect of the hydrogen by a weak coupling approach. Several numerical experiments for these three models show not only their reasonableness and usefulness but also flexible extendability of the phase field approach in fracture mechanics.

Download Full-text