PSI - Issue 37

Cheng Qian et al. / Procedia Structural Integrity 37 (2022) 926–933 Cheng Qian et al./ Structural Integrity Procedia 00 (2019) 000 – 000

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2.2. Fracture toughness tests The SE(B) and SE(T) specimens were notched directly to the final nominal a 0 / W ratios of 0.25 and 0.50, using electrical discharge machining (EDM) with a 0.10 mm ( 0.004’’ ) diameter wire. All the specimens had dimension of B = W = 12 mm. The SE(B) specimens had a span-to-width ratio of S / W = 4 and the SE(T) specimens had a daylight to-width ratio of H / W = 10. Specimens were side grooved by a total reduction of 15% B , with the side-groove angle being 45  and the root radius being 0.5 mm. All tests were carried out at room temperature. For the J - R curve testing, a single specimen technique with the unloading compliance method was applied following ASTM E1820-18a, ASTM (2018) and CanmetMATERIALS procedures in Shen et al. (2008 and 2009) for SE(B) and SE(T) specimens, respectively. A three-clip-gauge arrangement with one integral knife-edge to measure CTODs based on J -conversion methods in ASTM (2018) and Shen et al. (2009) and a separate double-clip gauge fixture according to Park et al. (2015) with knife-edges at two different heights were used to simultaneously measure the CTODs based on the ExxonMobil method in Tang et al. (2010). The commercial software ABAQUS was used for FEA. Only one quarter of each specimen was modeled due to symmetric condition. For SE(B) models, two contact rollers were modeled as analytical surfaces to simulate the loading and supporting in a real test. A distance of load-line displacement ( LLD ) from test was applied on the upper roller. For SE(T) models, the upper and lower surfaces outside of the daylight length region were clamped and loaded with LLD from test. A blunt crack tip with a diameter of 0.10 mm was modelled to simulate the actual EDM notch configuration as well as to facilitate the finite-strain analysis. For the finite element models, 8-node C3D8R brick elements were adopted. The smallest in-plane element size was about 0.002 W . In the out-of-plane (i.e. z -) direction, the model was divided into 15 layers between mid-plane and the root of the side groove, with higher mesh density near the root, and four uniform layers in the side-groove region. Mesh sensitivity analyses showed that such mesh density was adequate to evaluate the local stress field, global response behavior as well as fracture toughness. A typical model had a total number of nodes and elements of 50802 and 45640, respectively. The J -integral was computed by the virtual crack extension method at each layer along the crack front and averaged based on the trapezoidal rule. At the last step of loading, the difference between J mid corresponding to the 45 th and 40 th contour was about 3%, taken as the path- independent ‘far - field’ converged J -value. 3.2. Constraint parameters The Q parameter in O’Dowd et al. (1991 and 1992) was used to quantify the difference between the reference and actual stress fields ahead of the crack tip. As an alternative definition of Q HHR , Q SSY was calculated based on modified boundary layer analysis in O’Dowd et al. (1994). In this study, a semi-circle 2D plane-strain model divided into 60 fans and 100 rings surrounding the crack tip was developed in FEA to calculate the small-scale-yielding ( SSY ) stress field according to Dodds et al. (1991). Zhu et al. (2001) proposed Q LM , which was found to be independent of the applied load under large-scale-yielding ( LSY ). Zhu et al. (2007) subsequently proposed Q BM to account for the fact that Q LM is unable to quantify the crack-tip constraint for bending specimens under large loading conditions. Both Yang et al. (1993) and Chao et al. (1997) proposed the J - A 2 solution of the crack-stress field based on the rigorous asymptotic analysis of a plane-strain crack. Although there are two roots of the quadratic equation of A 2 only the smaller one was used in this study. Chao et al. (2004) also proposed A 2 BM to characterize the crack-tip constraint for bending dominated specimens. The final two stress-based constraint parameters to be evaluated included the stress triaxiality parameter h in Hancock et al. (1993) which is defined as the ratio of  m to  e and the out-of-plane constraint parameter T z proposed by Guo (1993 and 1995). In terms of the plastic zone-based constraint parameters, He et al. (2019) proposed that the equivalent plastic zone radius C p (based on the plastic work of external load dissipated in the plastic zone at the crack tip) could work as a 3. Finite element analysis 3.1. Finite element model