PSI - Issue 25

R. Baptista / Procedia Structural Integrity 25 (2020) 186–194

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Author name / Structural Integrity Procedia 00 (2019) 000–000

Nomenclature α

initial crack angle β hole angular position ∆ crack increment ∆ elapsed number of cycles ∆ �� crack diving force θ crack propagation direction λ biaxial load ratio φ load phase σ nominal applied stress σ θθ tangential stress τ r θ radial stress a crack length B Biaxliality ratio K I mode I stress intensity factor K II mode II stress intensity factor r radial distance to crack front R stress ratio T stress parallel to the crack faces

1. Introduction Originally defined by Westergaard in 1939, the biaxial stress field around a crack tip has been experimentally and numerically studied by many authors. Some have found discrepancies between Westergaard equations and experimental results. Therefore, Williams (1961) proposed the introduction of T-Stress, a non-singular term added to Westergaard eq. (1-3), representing the stress parallel to the crack face. �� � √� � �� � � � � �� � �� � � � � � �� � � � �� � �� � � � �� � � (1) �� � √� � �� � � � � � � � � �� � � �� � � �� � (2) �� � √� � �� � � � � �� � �� �� � ��� � �� (3) where � and �� are the mode I and mode II Stress Intensity Factor (SIF) and , are the stress field point polar co-ordinates, considering the crack front as the origin. T-Stress , is the stress parallel to the crack faces. Since then there has been an active discussion whether T-Stress role on brittle fracture, fatigue crack growth (FCG) under linear elastic fracture mechanics or size and shape of the plastic zone around the crack tip is important. Earlier work by Williams and Ewing (1984) identified clear discrepancies between experimental brittle fracture crack propagation direction and maximum tangential stress (MTS) criterion under mixed mode conditions. According to these authors, the difference may be explained considering the non-singular T-Stress term. Yukio et al. (1983) also studied T-Stress influence using cruciform specimens under biaxial loading conditions, concluding that although T Stress values did not influence the initial crack propagation direction, MTS criterion was not suitable for crack propagation prediction. Recent work by Zakeri et al. (2011) or Breitbarth et al. (2018) show a clear influence of T Stress signal and value over fracture toughness and fatigue crack propagation, with negative values of T leading to a higher fracture toughness and more stable crack propagation. Therefore, authors like Smith et al. (2001) or Miao et al. (2017) have modified existing crack propagation criteria to include T-Stress effects. While Ayatollahi et al. (2012) developed new specimens, introducing holes around the crack front, in order to obtain specific T-Stress values. Yet, other authors like Melin (2002) have concluded that T-Stress signal and value has no role over crack propagation stability or control. Gupta et al. (2015) have extensively reviewed the role of T-Stress in fracture mechanics, mentioning that one must reassess T-Stress role over crack path stability regarding it’s physical and mathematical origin.