PSI - Issue 5

Sameera Naib et al. / Procedia Structural Integrity 5 (2017) 1417–1424 Naib et al./ Structural Integrity Procedia 00 (2017) 000 – 000

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1. Introduction

The goal of structural integrity assessment is the evaluation of acceptability of detected defects. For welded connections, the assessment procedure is not straightforward due to the presence of heterogeneity in welds in terms of both constitutive (strength and strain hardening) properties and toughness. In the context of this paper, weld heterogeneity implies the presence of local constitutive variations. Nomenclature p02 R Yield strength in terms of 0.2% proof stress (N/mm 2 ) m R Ultimate tensile strength (N/mm 2 ) n Strain hardening exponent (-) eq,pl  Equivalent plastic strain (-) eq,pl-max  Maximum equivalent plastic strain (-)  Shear stress (N/mm 2 ) max  Maximum shear stress (N/mm 2 ) CMOD Crack mouth opening displacement (mm) CTOD Crack tip opening displacement (mm) DIC Digital image correlation HV5 Vickers hardness at 5kgf indentation force OM Strength overmatching weld region UM Strength undermatching weld region SE(T) Single Edge notched Tension (test specimen) These variations influence the distributions of strains and stresses around the notch present in a welded structure when subjected to loads. An important approach to estimate the integrity of a structure in operation is by determining the maximum load it can withstand before collapse. This load is generally termed as ‘limit load’ or ‘plastic load’ based on the method of determination (Gerdeen, 1979). Miller. (1988), in his review paper, pointed out that two-dimensional plane strain cases of single edge notched plates were analysed extensively using slip line field theory. Using this theory, the upper bound limit load solutions were obtained by several researchers. This concept was extended to the welds during early 1990s. 1.1. Slip line theory in heterogeneous welds Slip line field theory is a plasticity based analytical approach used to model plastic deformations in metallic bodies at plain strain conditions. This theory derives trajectories of maximum shear stresses in a rigid, ideally plastic body which is deforming plastically. It is based on severe assumptions involving isotropic and homogeneous material, and rigid plasticity (absence of strain hardening). Integration of stresses allows to calculate the limit load of highly simplified configurations such as the Single Edge notched Tension (SE(T)) test, for which slip line field theory predicts straight slip lines, originating from the defect tip at an angle of 45° with respect to the loading direction. Despite its severe assumptions, slip line theory has been utilized by researchers to obtain analytical equations for different weld configurations. Joch et al. (1993) put forward limit load solutions considering the mismatch between welds for plane strain problems. They obtained the solutions assuming perfectly plastic mismatch problem and a straight-line deformation mechanism. They showed t hat the simplification of deformation bands (to straight lines) gives over-estimation of limit loads as it follows from upper bound theorem of limit load theory. Similar development of limit load solutions followed, by considering different crack geometries using plain strain conditions. For example, Hao et al. (1997) constructed slip line fields for Center Cracked Tensile (CC(T)) panel with a mismatched joint, including an analytical methodology to estimate slip line deviations at bi-material interfaces. An analysis of plastic deformations in complex heterogeneous welds (including strain hardening) was performed by Hertelé et al. (2016). They considered a welded SE(T) specimen under uniaxial tension loading. Strain concentration bands originating from the defect tip were simplified into “slip lines”, defined as trajectories of maximum equivalent strain. Based on Digital Image Correlation (DIC), non-linear slip line trajectories deviating from 45° were observed, and this was attributed to