PSI - Issue 42

Yuebao Lei et al. / Procedia Structural Integrity 42 (2022) 80–87

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

complex structures in assessments, a local limit load model has been developed by Lei (2018) for plate/shell type components containing surface defects. The newly-developed local limit load model is a plate of finite width containing a rectangular surface crack. The dimensions of the cracked plate are determined based on the crack dimensions and thickness of the real component at the crack location. The model is loaded by the primary stresses of the component at the crack location obtained from elastic uncracked-body stress analysis, including the membrane and through-thickness bending stresses normal to the crack plane and the membrane and shear stresses parallel to the crack plane. This model has been validated by Lei (2019a) using the finite element (FE) elastic-plastic J- integral results for defective plates and cylinders under various load types and load combinations (without bending stress parallel to the crack plane). The results showed that when the limit load evaluated using the newly-developed local limit load model is used in the reference stress J scheme developed by Ainsworth (1984), the FE J results can be conservatively predicted with improved accuracy compared with other local limit load solutions. However, recent examinations by Lei (2019b) on defective elbows and by Madew (2019) on pipe branches show that there could also be strong bending stress parallel to the crack plane at the crack location and ignoring this parallel bending stress might overestimate limit load values and lead to non-conservative J predictions when this limit load is used in the reference stress J scheme. In this paper, the effects of stress parallel to the crack plane on elastic-plastic J and the limit load will be investigated and the local limit load model developed by Lei (2018) will be modified to include such effects. A plate containing a semi-elliptical surface crack is selected as a typical surface crack case to investigate the effects of the bending stress parallel to the crack plane on the elastic-plastic J and limit load. Elastic and elastic-plastic FE analyses will be used to obtain J values for the surface-cracked plate under stress normal to the crack plane or under biaxial stress plus through-thickness bending with/without bending stress parallel to the crack plane. Then a limit load/reference stress estimation method considering the bending stress parallel to the crack plane will be developed and validated using the FE J results via the use of the reference stress J scheme (Ainsworth (1984)). Finally, the obtained limit load estimation method will be used to modify the local limit load model. 2. Cases considered in FE fracture analyses A semi-elliptical surface crack of depth a and length 2 c in a plate of width 2 W and thickness t is considered in this investigation. The dimensions of the plate are shown in Fig. 1, where L is the half-length of the plate which is assumed to be large compared with the plate width and the thickness so that the St Venant principle may be applied at the crack plane. The stresses applied to the cracked plate are membrane stress, σ m , and through-thickness bending stress, σ b , normal to the crack plane and the membrane stress, σ 2m , and bending stress, σ 2b , parallel to the crack plane (see Fig. 1). The membrane stresses, σ m and σ 2m , are positive when they are tensile. For bending stresses, σ b and σ 2b , the positive value is defined as tensile stress at the cracked surface of the plate. For cases with σ 2b =0, the global limit load solutions have been developed by Lei and Budden (2015) and may be expressed, with σ y the yield stress, as � = �� � = � ( ⁄ , ⁄ , , � ) � | � ⁄ | for � ≠ 0 0 for � = 0 (1) � = 2 3 �� � = � 4λ � for � ≠ 0 Ω( ⁄ , ⁄ , � ) � | � ⁄ | for � = 0 (2) �� = σ ��� � ⁄ (3) where �� , �� and ��� are the limit values of � , � and �� , respectively, and � , � and �� are their normalised forms, respectively. The functions Φ and Ω in Eqns. (1) and (2) are given in Lei and Budden (2015) and, for proportional loading, the load ratios in Eqns. (1)-(3), , � and � , are defined as follows. = � (6 � ) ⁄ for � ≠ 0, � = �� � ⁄ for � ≠ 0, � = �� � ⁄ for � ≠ 0 (4)