Indian Journal of Engineering & Materials Sciences Vol. 19, February 2012, pp. 5-16 Stress intensity factors under combined tension and torsion loadings A E Ismail a *, A K Ariffin b , S Abdullah b & M J Ghazali b a Department Engineering Mechanics, Faculty of Mechanical & Manufacturing, Engineering, Universiti Tun Hussein Onn Malaysia, 86400 Batu Pahat, Johor, Malaysia b Department Mechanical & Materials Engineering, Faculty of Engineering & Built Environment, Universiti Kebangsaan Malaysia, 43600 UKM Bangi, Selangor, Malaysia Received 13 December 2010; accepted 22 February 2012 This paper numerically discusses the stress intensity factor (SIF) calculations for surface cracks in round bars subjected to combined loadings. Different crack aspect ratios, a/b ranged from 0.0 to 1.2 and the relative crack depth, a/D in the range of 0.1 to 0.6 are considered. Since the loading is non-symmetrical, the whole finite element model is constructed. Then, both tension and torsion loadings are remotely applied to the finite element model and the SIFs are determined along the crack front of various crack geometries. An equivalent SIF method is then explicitly used to combine the individual SIF obtained using different loadings. A comparison is made between the combined SIFs obtained using the equivalent SIF method and finite element analysis (FEA) under similar loadings. It is found that the equivalent SIF method successfully predicted the combined SIF for Mode I. However, discrepancies between the results, which have been determined from the different approaches, occurred when F III is involved. Meanwhile, it is also noted that the predicted SIF using FEA is higher than the predicted through the equivalent SIF method due to the crack face interactions. Keywords: Stress intensity factor, Surface crack, Finite element analysis, Combined loadings Cylindrical bars are generally used to transmit power from one point to another. The bars can be subjected to cyclic stresses which can cause mechanical damages and sometime experienced premature failure 1 . The initiations of fatigue cracks on the surface are normally due to mechanical defects such as notches 2 and metallurgical defects 3,4 . In services, a rotating shaft can generally be subjected to combined loading due to its self-weight, which also induces a tension stress instead of torsion loadings. In fact, any arbitrary shapes of crack initiation may grow and take a semi-elliptical shape 5 . Linear elastic fracture mechanics (LEFM) has been used to analyse stress intensity factors (SIFs) along the crack front. The solution of SIFs for a wide range of crack geometries under Mode I loading has been reported elsewhere in the literature 6-16 . However, the calculated SIFs, subjected to Mode III and the SIFs under combined loadings such as tension and torsion are rarely studied 12-16 . Therefore, the aim of this study is to obtain the SIFs for semi-elliptical surface cracks subjected to tension, torsion and the combination of loadings. According to the literature 12-15 , the SIFs subjected to combined loadings are rarely studied. Since the combined SIF can be obtained directly by combining the different mode of SIFs without considering the influence of crack interaction. This numerical work is carried out to investigate whether the SIFs from different modes can be explicitly combined and compared to the ones using the FEA. Finally, the result discrepancies between the two methods are also discussed in term of the mesh deformation, which mainly focused on the crack face interaction. Evaluation of Fracture Parameters Stress intensity factors The finite element method is an appropriate approach to calculate the stress intensity factor (SIF) for linear elastic fracture mechanics problems. In order to determine the SIFs, a displacement extrapolation method 17 is used in this study. Several other works have implemented a similar method are also available 18,19 . In order to analyse the cracks, it is frequently modelled as a semi-elliptical crack shape. This due to the fact, any arbitrary crack shapes will grow to take semi-elliptical crack geometry 5 . Figure 1 shows an arbitrary crack shape where the crack face is parallel to the x-axis and the z-axis is normal to the ___________ *Corresponding author (E-mail: [email protected])
Stress intensity factors under combined tension and torsion loadings
May 20, 2023
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