PSI - Issue 13

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

897

2

Krom [5], in which a generalized hydrogen transport equation has been exhibited, accounting for the trapping by dislocation, led to FE simulations in the framework of small scale plasticity. In these works, trapped and diffusive hydrogen concentrations are assumed to be at equilibrium, following Oriani [6], while kinetic trapping might also be considered [7,8]. Recently, these kind of computations have been adapted to the polycrystal scale [9], from which statistical analysis of failure initiation risk can be extracted. This paper focused on the U-Bend test modeling, at both macroscopic and polycrystalline scale. First, modeling assumptions are presented. The U-bend test setup is then introduced, and few results shown.

Nomenclature C L

Diffusive hydrogen concentration Trapped hydrogen concentration

C T N T N L  T  L

Trap density

Interstitial site density 

Trap sites occupancy, C T =N T  T Interstitial sites occupancy, C L =N L  L

2. Modeling of the material hydrogen interactions In this work,  -iron is considered, for which all of the relevant parameters can be found in the literature. Transport and trapping equations are first presented, and then, the mechanical behaviour, at both macroscopic and crystal scale. In this case, only the 12 slip systems {110}  111  for bcc structures are considered. All of the models are implemented in Abaqus FE software, as explained in previous works [8-10]. 2.1. Transport and trapping model The hydrogen concentration C is partitioned in two populations, namely the diffusive one ( C L ) and the trapped one ( C T ) [5]. Considering that hydrogen diffusion is assisted by mechanical stress field though the hydrostatic pressure [4,11,12], the temporal evolution of C might be written as [4,5]

L T     C C  



D V

C

  

  

L H

(1)

 



C P 

D C

L L

L H

  

t

t

t

RT

with





T  



C

N

T

T

(2)





N

T

T







t

t

t

N T is assumed to depend only on the equivalent plastic strain (for pure iron material, see [4,13]). Two trapping modelling are used: one based on the McNabb and Foster kinetic equation (so called “transient trapping”) [7,8] and the other based on the Oriani’s equilibrium assumption (so called “equilibrium trapping”) [6-8]. Diffusion and kinetic trapping parameters for  -iron are extracted from literature [4,5,14-16]. 2.2. Mechanical behavior Both isotropic mechanical behavior and anisotropic crystal plasticity are considered to describe mechanical behavior. At the macroscopic scale, isotropic elasticity is described with Young modulus E and the Poisson ratio  , while isotropic hardening is described by a Voce-type law   0 1 C p Y sat R e        (3) where 0 , R sat and C are material parameters identified from tensile test.