PSI - Issue 2_A

Haiyang Yu et al. / Procedia Structural Integrity 2 (2016) 565–572

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H. Yu, JS. Olsen, J.He, Z. Zhang / Structural Integrity Procedia 00 (2016) 000–000 3 Jothi et al., 2014) and the grain boundary is simulated with the cohesive zone model Alvaro et al. (2015). The cohesive parameters for the grain boundary are obtained from first-principles calculations (Yamaguchi et al., 2006). In this manner, the actual failure of the model can be observed. The transient hydrogen diffusion is performed, and hydrogen concentration at each time step is used to update the cohesive strength of the grain boundary according to the hydrogen degradation law proposed by the current authors (Yu et al., 2016) thereby leading to hydrogen induced fracture. Within this framework, the effects of grain misorientation and grain size as well as their interaction with the pre-crack size are investigated. 2. Methodology This section presents the problem definition as well as a detailed description of the hydrogen embrittlement simulation in the four-grain nickel aggregate on the continuum level. 2.1. Model description This paper aims to investigate a four grain nickel system with the uniaxial loading applied in the y direction, as shown in Figure 1. The grain interior is modelled with anisotropic (orthotropic) elasticity and the elastic parameters are chosen according to the crystal orientations (Li et al., 2009; Jothi et al., 2014). The local 1 − direction of the orthotropic elasticity tensor corresponds to the [100] direction of the single grain, the 2 − direction to the [010] direction and the 3 − direction to the [001] direction. Rotations of grains are performed around the [001] axis resulting in various misorientation angles ranging between 0 ◦ < θ < 90 ◦ . For easiness to parameterize, the bottom grains are assumed to be fixed with their [100] directions coinciding with the global x axis while the upper grains are tilted in symmetry as shown in the figure. It is then expected from the description above that failure would initiate as Mode I crack in the transverse grain boundary, and this part is modelled as a cohesive interface. In cohesive zone modelling, damage is processed inside a layer of cohesive elements that are inserted along the fracture path between solid elements. The constitutive behavior of cohesive elements is described by the so-called traction separation law (TSL) (Needleman, 1990). The TSL is usually characterized by the critical cohesive stress σ C which characterizes the strength of the cohesive element and the critical separation δ C which defines the failure point. The area below the traction separation curve is called the separation energy Γ C . For detailed information regarding the cohesive zone model and TSL, the readers are referred to (Needleman, 2014). The TSL used in the present study is the bilinear one (Alvaro et al., 2015). The parameters of the TSL is determined based on the first-principles calculation of grain boundary decohesion in nickel symmetrical tilt grain boundaries (Yamaguchi et al., 2006), which gives δ C = 6 . 67 × 10 − 6 mm and Γ C = 0 . 004 N/mm . These values apply for all the cases considered in this work. The length of each cubic grain is L and an initially sharp crack of 2 a is introduced in the center of the aggregate. In the present study, the case without initial crack, i.e. a/L = 0 and the case with an initial crack of a/L = 0 . 25 are considered. The grain size effect is also investigated by selecting different length values L = 5 µm, 10 µm, 50 µm . Continuous hydrogen supply C B ( t ) = 1 . 5 wppm is provided on the outer boundary of the aggregate and the inside is initially hydrogen free C I ( t = 0) = 0 , as shown in Figure 1. Hydrogen is assumed to redistribute through the stress driven transient mass diffusion process. The diffusivity of hydrogen in Nickel is selected as D L = 1 . 9 × 10 − 14 m 2 /s at 288 K and the partial volume of hydrogen in nickel as Ω = 3 . 39Å 3 (Song and Curtin, 2011). No difference in hydrogen diffusion parameters between the grain interior phase and the grain boundary phase is considered at the present stage. The presence of hydrogen will cause degradation of the cohesive strength according to the hydrogen enhanced decohesion mechanism (Oriani, 1972), which is described by the so-called hydrogen degradation law (Yu et al., 2016) σ c σ c,H =0 = 0 . 421 e − 2 . 227 C I + 0 . 579 (1)