Phase Field Crack Growth Model with Hydrogen Embrittlement
As an application of the phase field model for crack propagation in elastic body, chemical-diffuse crack growth model with the effect of the hydrogen embrittlement is considered. Numerical results show the difference of crack path between data with the ef
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Abstract As an application of the phase field model for crack propagation in elastic body, chemical-diffuse crack growth model with the effect of the hydrogen embrittlement is considered. Numerical results show the difference of crack path between data with the effects and data without the effect. Temporal evolution of the normalized difference of phase field depict the time when start the difference of crack path.
1 Phase Field Approach for Crack Propagation To know about fracture is very important to make our life safe. Most of the studies about fracture are focused on its threshold of breaking materials. Many numerical simulations are done with extended finite element method (XFEM) using suitable threshold value of breaking [1]. Since there are various crack propagation models in fracture mechanics, the phase field approximation of the crack has some advantages of mathematical and numerical treatment of this phenomena. In [2, 3], the author and Kimura introduced the phase field crack growth model which is based on the elastic-fracture energy by Francfort-Marigo [4] with the Ambrosio–Tortorelli’s approximation [5]. This model describes the temporal evolution of crack using the phase field that shows the crack surface as the continuous function. This uses the similar derivation of the time-dependent Ginzburg–Landau equation which assumes the dissipative property of its free energy at nearly equilibrium state. There are many difficulties in computation of the crack growth, remeshing for new crack surface, blow-up of the stress on the crack tip, however, this model equation makes possible to compute the crack growth with branching, etc., by the well-known numerical methods. It is also remarked that adaptive mesh method, especially adaptive mesh FEM, is effective to calculate this phase field model of crack growth. This model has also an advantage for extension to the complex crack growth. In this paper, crack growth model with chemical reaction which takes effect to the elastic T. Takaishi (B) Hiroshima Kokusai Gakuin University, Aki-ku Nakano 6-20-1, Hiroshima, Japan e-mail: [email protected] © Springer Nature Singapore Pte Ltd. 2017 H. Itou et al. (eds.), Mathematical Analysis of Continuum Mechanics and Industrial Applications, Mathematics for Industry 26, DOI 10.1007/978-981-10-2633-1_3
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properties and toughness is introduced. When chemical reaction proceeds, elasticity and toughness change. Basically, two method can be considered as followings: (A) adding new descriptions in energy, (B) adding new equation in this system. In the next section, a phase field model with hydrogen embrittlement is considered with the type (B). In Sects. 3 and 4, some numerical results of it are shown and a simple method which can estimate the effect is proposed.
2 Phase Field Crack Growth Model with Hydrogen Embrittlement Various factor changes the brittleness of the material, such as UV irradiation, rust, etc. Here, we focus on the hydrogen embrittlement of the steel material. hydrogen in the steel pla
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