PSI - Issue 66

Aditya Khanna et al. / Procedia Structural Integrity 66 (2024) 370–380 Author name / Structural Integrity Procedia 00 (2025) 000–000

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conducted in Section 5 to separate the effects of residual stress and crack tip plasticity on crack closure. Main outcomes of this work are briefly outlined in Section 6. Nomenclature crack length of a standard CT specimen, measured from the load line out-of-plane thickness of a standard CT specimen width of a standard CT specimen, measured from the load line to the back face normalised crack length, ⁄ Young’s modulus of the specimen Yield stress defined at 0.2% strain offset load applied to the CT specimen using a clevis and pin arrangement max maximum value of the applied cyclic load min minimum value of the applied cyclic load op crack tip opening load ̅ 0 nondimensionalised open-crack compliance Back-face strain max Back-face strain at maximum cyclic load res Back-face strain under unloaded condition Mode I Stress Intensity Factor (SIF) at the crack tip max , ap SIF due to maximum cyclic load min , ap SIF due to minimum cyclic load res SIF in the unloaded specimen due to the residual stress field max Superposition of SIF due to maximum cyclic load and SIF due to residual stress min Superposition of SIF due to minimum cyclic load and SIF due to residual stress op crack tip opening SIF Stress Ratio, i.e., ratio of the minimum cyclic stress (or SIF) to the maximum cyclic stress (or SIF) ap The applied stress ratio, i.e., the ratio of min , ap and max , ap act The actual stress ratio, i.e., the ratio of min and max Crack tip opening load ratio 2. Compliance methods for evaluating residual Stress Intensity Factor Based on finite element modelling, Newman Jr. et al. (2011) provide the following compliance expression for compact tension specimens in terms of the back face strain: ̅ 0 = − ( ) ⁄ = (1.41 − 1.462 +20.25 2 − 26.83 3 +11.45 4 ) (1 − ) 2 ⁄ (1) where 0.2 ≤ 0.95 and = ⁄ . The subscript 0 implies “open crack” compliance. Here is the applied load, is the specimen width, is the specimen thickness, and is the crack length. The dimensions and measured from the load line for compact tension specimens as per ASTM E647. During fatigue testing, the nondimensional open crack compliance ̅ 0 can be evaluated by fitting as straight line through the linear portion of the load-strain curve, as shown in Figure 1. If the strain reading is “zeroed” for an unloaded specimen at an intermediate crack length , then the strain magnitude at maximum applied load is simply max ( )= ̅ 0 ( ) max ⁄ . Following crack extension = − after additional cycles of fatigue loading, the change in the maximum strain magnitude in the absence of residual strain should be max = � ̅ 0 ( ) − ̅ 0 ( ) � max ⁄ . However, the observed change in maximum strain magnitude with crack extension can be less or more than expected. The discrepancy res can be referred to as the residual strain increment and its magnitude and sign depends upon the residual stress field distribution, as illustrated in Figure 1.