PSI - Issue 39

2

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

291

Peer-review under responsibility of CP 2021 – Guest Editors Keywords: Creep crack transition, plastic to creep transition, material inhomogeneity, configurational forces

1. Introduction As our demand with the material is increasing in various applications such as nuclear power plants, jet engines etc. a single homogeneous material is being replaced by two different materials joined together. Such dissimilar metals welded together are being studied in the field of nuclear power plant and aerospace components where high temperature causes the metallic materials to creep (Budden & Curbishley 2000, Li et al. 2020, Wang et al. 2013). The behavior of crack under such components are complex and has been studied using C * integral (Anisworth 1997, Budden & Curbishley 2000) as well as stress distribution at crack tip for small, medium and large scale yielding under elastic plastic deformation by Shih & Asaro (1988, 1989) and Shih et al. (1991). The relation of C * with the rate of crack extension under creep deformation was found to be well describable under extensive creep condition. Budden and Churbishley analyzed using Finite element analysis, the effect of change in creep properties on C t -integral using Abaqus Commercial software (Abaqus 6.18) of two materials with same creep exponent ( n ) but different creep coefficient ( A ) in a power law parameters described as, ̇ = (1) In the analyses by Li et al. (2020) on elastic plastic material using extended finite element method (XFEM), it was found that the amount of mismatch affects the stress corrosion cracking (SCC) in a way that a lower mismatch results in a faster SCC crack growth and vice versa. Wang et al. (2013), found that the J - Δ a behaviour differs for different location around weld zone for stainless steel (SS) and A508 buttered weld. The differences in the crack driving force, which is reflected in the crack growth or growth rate under creep condition around an interface between two differently deforming material is because of the material forces which influence the crack tip. This phenomenon has been in detail discussed by Kolednik et al. (2014) and has been used to improve the fracture resistance of polypropylene by Tiwari et al. (2020). In this work, the interface between two differently deforming material is treated as a material inhomogeneity. In a homogeneous elastic plastic material under small strain assumption, the total strain is composed of elastic and plastic parts. The strain energy density is symbolized with ϕ , where only the elastic part of the strain energy density, ϕ e , is recoverable. In this analysis, the concept of configurational forces (CF) are applied (Maugin 1999). The CF in the bulk of a material which deforms under elastic plastic condition, f ep , can be evaluated by Eq. (2) (Simha et al. 2008), ep = ∙ . (2) However, the conventional way of configurational force comes from the configurational stress tensor and can be evaluated by Eq. (3), = − ▽∙ ( − T ) ( 3) In Eq. (3), ▽∙ denotes the divergence of the configurational stress tensor (in the reference configuration), I the identity tensor, F T the transposed of the deformation gradient, and S the 1st Piola-Kirchhoff stress tensor. It follows that CFs appear in plastically deformed regions of the body and that the J -integral becomes path dependent (Kolednik et al. 2014).

Nomenclature A

creep coefficient in a power law creep Thickness of compact tension specimen

B C

Configurational stress