PSI - Issue 5

Kulbir Singh et al. / Procedia Structural Integrity 5 (2017) 294–301 Kulbir Singh/ StructuralIntegrity Procedia 00 (2017) 000 – 000

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total obstacle density in calculation of λ value and average strength of obstacles α A . The value of ξ (~ 4) is found to be independent of temperature and only dependent upon the strain rate as per the dislocation dynamics (DD) simulation (Robertson et al. 2013).

3.2. Mobile Dislocation Density

In case of irradiation, ρ tot increases and also through DD simulation it is observed that there is significant increase in ρ m (Gururaj et al. 2015). This increase in ρ m may be attributed to interaction of irradiation defects with screw dislocation lines. When screw dislocation line interacts with interstitial loop it forms jogs of size comparable to the size of the loop (can be smaller in few cases). This create pinning of screw dislocations as the jogs (steps) are in different plane and step line have nature of edge dislocation and subsequently acts as source of mobile dislocation for their further generation. Each time the screw dislocation interacts with the interstitial loop there is strong probability of the creation of the mobile dislocation source. In BCC-Fe materials helical jogs are mostly unstable and hence tend to collapse by emitting a new prismatic loop after unpinning completes at displaced position. As per the DD simulation (Gururaj et al. 2015) (Robertson et al. 2013) on interaction of irradiation defects with dislocations, it is estimated that 5-10 screw-loop interactions must take place before the interstitial loop moves out of the lath due to shift in its position after each interaction. This phenomenon of formation of new sources and subsequently generation of mobile dislocation is incorporated in current constitutive model. The rate of increase of mobile dislocations due to interaction with irradiation defects is expressed in terms of irradiation defects density change as: ̇ = 0 ( ) ̇ where κ is the number of screw- loop interaction produce source before irradiation loop’s removal from lath and r 0 is the initial ratio of ρ irr and ρ m . 4. Finite element modeling and validation Finite deformation framework is adapted for finite element analysis to solve dislocation based material model to predict the behavior under applied load. Material orientation is taken such that the crystallographic direction [1̅ 49] of BCC crystal is aligned with loading axis. Validation of the material model is carried out by comparing critical resolved shear stress with experimental results (Spitzig 1973) (Quesnel et al. 1975) (Kuramoto et al. 1979) on pure iron crystal (see Fig. 1). The results are in good agreement and material model is predicting the temperature sensitivity satisfactorily. This agreement can be considered as significant in view of independence of critical resolved shear stress from geometry. A tensile load in form of displacement equivalent to 10 % global strain in initial longitudinal direction is simulated using beam case of a mono-crystalline at strain rate of 10 -4 s -1 . Numerical simulations on beam case are carried out at different temperature values within a range of 100 K to 325 K for non-irradiated case and irradiated case. Irradiation conditions effect is considered in terms of loop size of defect (diameter 5 nm) with irradiation defect cluster density of 1×10 22 loops/m 3 . Irradiation temperature is accounted in total irradiation defect density value by size term. Values of various material parameters used in the material model are listed in Table 1.

Table 1.Material parameters. Parameter Value

Parameter Value

Parameter Value

b E

0.2481 mm

p q

0.593 1.223 10 nm 2 nm

f c

6

236.4-0.0459T GPa

k B

8.6173×10

-5 eV/K

ν

0.35

D

K self

100

ΔH 0

0.76 eV 360 MPa 1.0×10

y prop

κ α

4

̇

ρ 50×10 12 m -2 α α irr 0.3 B initial 4×10 12 m -2

τ 0

0.7 0.1

coll

-6 s -1

0

non-coll

n

50

10.5×10

-11 MPa.s -1