Issue 48

M. K. Hussain et alii, Frattura ed Integrità Strutturale, 48 (2019) 599-610; DOI: 10.3221/IGF-ESIS.48.58 599 Focused on “Showcasing Structural Integrity Research in India” Evaluation of mixed mode (I/II) notch stress intensity factors of sharp V-notches using point substitution displacement technique Mirzaul Karim Hussain, K.S.R.K. Murthy Department of Mechanical Engineering, Indian Institute of Technology Guwahati, Guwahati-781039, India mirzaul@iitg.ac.in , https://orcid.org/0000-0003-4300-360X ksrkm@iitg.ac.in, https://orcid.org/0000-0002-9112-8557 A BSTRACT . In this paper, determination of the accurate notch stress intensity factors (NSIFs) have been demonstrated using a recently proposed technique: The point substitution displacement technique (PSDT) for the sharp V- notched configurations. In this technique, certain optimal point(s) on the notch flanks are obtained where the displacements are found to be highly accurate. Using the PSDT, the NSIFs are determined from the finite element (FE) displacements at these optimal point(s). The NSIFs of two pure mode I and two mixed mode (I/II) examples have been determined and excellent agreement of the present results with the published results is observed. The PSDT is efficient, robust and easy to be implemented in the available FE code. K EYWORDS . V-notch; NSIF; Stress intensity; Finite element; Mixed mode Citation: Hussain, M. K., Murthy, K. S. R. K., Evaluation of mixed mode (I/II) notch stress intensity factors of sharp V-notches using point substitution displacement technique, Frattura ed Integrità Strutturale, 48 (2019) 599-610. Received: 30.11.2018 Accepted: 25.02.2019 Published: 01.04.2019 Copyright: © 2019 This is an open access article under the terms of the CC-BY 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. I NTRODUCTION harp V-notches are frequently encountered in many engineering applications and structures. Due to the presence of these notches, a very high local stresses and stress gradient is observed close to the notch tip. The presence of notch drastically decreases the load-bearing capacity of the component and may cause damage to structures subjected to both static and variable loads. Therefore, a very accurate assessment of the strength of the singularity is desired near the notch tip. Williams [1] investigated plane V-notched configurations. In linear elastic fracture mechanics (LEFM), notch stress intensity factors (NSIFs) are widely used to characterize the singular stress field in the vicinity of the notch tip. The singularity stress field in the vicinity of the notch tip can be stated in the form of      1 ij Kr f here K is the notch stress intensity factor, r is the radial distance from the notch tip,   1 is the order of stress singularity and    ij f are the angular stress components [1]. Due to the widespread use of the NSIFs in brittle [2-7] and fatigue [8, 9] fracture criteria, many efforts have been put forward to develop various post-processing techniques [10-29] to calculate NSIFs. Gross and Mendelson [10] and Carpenter [11] determined NSIFs of sharp V-notches using the boundary collocation method. Chen [12] proposed a body force method to evaluate the NSIFs for problems under tensile and in-plane bending loadings. Noda et al. [13] also used body force method to calculate the NSIFs. Ju and Chung [14] and Liu et al. [15] used S