PSI - Issue 42

Zeng Chen et al. / Procedia Structural Integrity 42 (2022) 180–188 Author name / Structural Integrity Procedia 00 (2019) 000 – 000

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1. Introduction Components with flaws, that generally exist in a variety of equipment and facilities, can be subject to complex operational loadings. Once fracture of those critical components occurs, then catastrophic failures can be caused eventually. Thus, a structural integrity assessment with high accuracy must be conducted before and during their service. Current flaw assessment procedures, like BS 7910 in the UK and ASTM in the USA, mainly recommend standard fracture toughness test specimens that are designed with long cracks and large thicknesses (E1820-20b, 2020; Standard, 2013). However, a large amount of experimental data showed that only the lower bound fracture toughness can be obtained with these standard specimens while the toughness tested from the thin and shallow cracked specimens is much higher (Gao & Dodds Jr, 2001; Link & Joyce, 1995; Sorem et al., 1991). That is because the crack-tip field of those standard specimens has large triaxial stress and is highly constrained, which limits the extent of plastic deformation. This resistance of the structure to plastic deformation around the crack tip is defined as the crack-tip constraint (Brocks & Schmitt, 1995). Generally, a loss of crack-tip constraint can cause an increase in fracture toughness. Therefore, to make the best use of the low constraint effect and reduce over-conservatism in structural integrity assessment, it is important to quantify the constraint level and to correlate it with fracture toughness variation. The crack-tip constraint is often divided into in-plane and out-of-plane. In the past decades, many different constraint parameters were proposed to characterize in-plane and out-of-plane constraints separately such as T stress, A 2 , Q , h and T z . The elastic-plastic in-plane constraint parameter Q , developed by O’Dowd and Shih, is a stress triaxiality parameter to reflect the hydrostatic stress level at the crack tip (O'Dowd & Shih, 1991, 1992): = − ( ) 0 , = 2 0 = 0 (1) Where σ θθ is the crack opening stress and (σ θθ ) SSY is the crack opening stress under SSY (Small Scale Yielding), r is the distance from the crack tip, θ is the angle in polar coordinates, σ 0 is the material yield stress and J is the J integral. A negative Q value represents low triaxial stress and a low constraint, whereas a positive one represents the opposite conditions. However, it was difficult to quantify the combined effect of constraints in different directions in real cases for the above parameters. Thus, some unified measurement parameters were introduced to characterize the combined effect. Anderson and Dodds used a normalised area surrounded by σ 1 /σ 0 =C as a unified constraint parameter for cleavage fracture. The σ 1 is the maximum principal stress, σ 0 is the yield stress and C is an arbitrary constant (Dodds et al., 1991; Dodds et al., 1993). Mostafavi et al. further studied the Anderson – Dodds method and modified that model, then introduced a unified constraint parameter φ that was defined as the area of the plastic region at fracture, A c normalised by the reference plastic region at fracture for a standard specimen, A ref (Mostafavi et al., 2010, 2011a, 2011b). They believed that in-plane and out-of-plane constraint have a similar effect on the plastic region area at fracture, and the parameter φ is equally sensitive to both. = (2) For these two widely accepted constraint parameters mentioned above, their effectiveness was validated generally using specimens with uniaxial loading such as C(T) and SEN(B). However, a large number of industrial equipment experiences different loading modes other than uniaxial. The multi-axiality effect on the constraint and further fracture toughness is also not negligible. Therefore, it is necessary to investigate the effectiveness of those parameters on this effect. In this study, a large amount of bending experiments were conducted to capture the effect of biaxiality. A series of numerical modelling were performed. An investigation of parameter Q and unified parameters φ based on the experimental data and simulation results was discussed.