PSI - Issue 13

Y. Charles et al. / Procedia Structural Integrity 13 (2018) 896–901 Yann Charles / Structural Integrity Procedia 00 (2018) 000–000

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At the polycrystal scale, the anisotropic elasticity is defined through C ij elastic constants, while the crystal plasticity is described by the following classical viscous formulation [17,18] 1 0 , with n c c c a h                         with 2 0 , 0 and sech s c h h qh h h             (4) q is a latent hardening coefficient and  is the cumulated shear strain. h 0 ,  0 ,  s are material- parameters, identified so that the overall response of a representative elementary volume matches with the macroscopic mechanical behavior. Last, no interactions between hydrogen and the mechanical behaviors are here accounted for. The used mechanical parameters are taken from [9]. The hydrogen related parameters at the crystal scale are the same than at the macroscopic scale, except for N T . To insure an equivalence of the hydrogen transport process at both scales (see Fig. 8 and 12b in [9]), 0.57 N T is used instead of N T .

36 mm

30 mm

R=2.5 mm R=5 mm

U=-11.33 mm

Fig. 1. U-Bend test principle: (a) three point bending test; (b) tools removal and bold tightening; (c) hydrogen charging.

P H (MPa)

(a) (c) Fig. 2. (a) Equivalent plastic strain and (b) hydrostatic pressure repartition. ¼ of the sample is removed for visualization purpose only. (c) Evolution with time of the average diffusion and trapped concentration in the sample, considering both transient and instantaneous trapping process. The arrow indicates the polycrystal location for the submodelling computations (see below, section 3.2) 3. Application on the U-bend test The U-bend test, which is not a standardized approach [3], is commonly used to characterize metallic sheets sensitivity to corrosion or hydrogen (see e.g. [19,20] for application on automotive steel characterisation). The test setup used for simulation is illustrated on Fig. 1. The considered metal sheet (1  10  80 mm 3 ) is modelled in 3D, using 62318 quadratic tetrahedron elements, with full integration. Tools are assumed to be rigid cylinders. Boundary conditions definition at step (b-c) are described in [10]. 3.1. Macroscopic results In Fig. 2 are plotted the relevant mechanical field for the transport and trapping equation (equations 1 and 2), as well as the evolution with time of the amount of hydrogen in the sample, for both transient and instantaneous trapping. All results presented correspond to the step (c) in Fig. 1, t =0s corresponding to its beginning. Accounting for a kinetic trapping leads to a faster apparent hydrogen diffusion process, due to a more progressive filling of traps, as illustrated by the fields of trap sites occupancy on Fig. 3. It can especially be observed the influence of the plastic strain on the (b)