PSI - Issue 39

Abhishek Tiwari / Procedia Structural Integrity 39 (2022) 290–300 Abhishek Tiwari/ Structural Integrity Procedia 00 (2019) 000–000

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C *

Line integral in creep deformation Line integral in creep deformation

C t

Elastic Modulus

E

F T

Transpose of deformation gradient

I J

Identity tensor

Line integral to calculate the crack driving force

Line integral to calculate the crack driving force with only elastic strain energy density Line integral to calculate the crack driving force with total strain energy density

J ep

J nlel

P L S

Force applied on a CT specimen model

distance between crack tip and the interface intersection with the crack plane

First Piola Kirchoff Stress

W

Width of compact tension specimen

initial crack length initial ligament length

a o b o f Σ f ec

configurational forces appearing at the interface Σ configurational forces appearing in elastic creep deformation configurational forces appearing in elastic+plastic+creep deformation

f epc

n n

creep exponent in a power law creep normal vector to the contour

Δ a amount of crack extension Φ strain energy density Σ sharp interface between two differently deforming materials in reference configuration σ Couchy stress σ o Yield strength σ u Ultimate tensile strength

Poisson’s ratio ̇ creep strain rate uniform plastic strain ▽∙ divergence of a tensor CDF crack driving force CT compact tension SCC stress corrosion cracking SS stainless steel XFEM extended finite element method

1.1 Configurational forces under creep condition: Similar to Eq. (2), for other types of deformations such as creep and thermal strains, the configurational forces can be calculated by replacing plastic strain with eigen-strains such as thermal or creep strain as shown in Eq. (4). ec = ∙ . (4) Similarly, epc , can be calculated for elastic plastic creep material. CFs appear in regions where eigen-strains are present in a body, since ∇ ⋅ C becomes non-zero. Eigen-strains can be treated in the same way as the plastic strains (Simha et al., 2005), and the magnitude of the bulk CFs follows a