PSI - Issue 82

M.S. KannanKulavan et al. / Procedia Structural Integrity 82 (2026) 44–50 KannanKulavan et al. / Structural Integrity Procedia 00 (2026) 000–000

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2

a

a a

R o

R o

R i

R i

P i

P i

a

P o

P o

(a)

(b)

Fig. 1: Schematic representation of (a) inner and (b) outer double edge-cracked circular annulus subjected to internal pressure P i and external pressure P o .

derive the weight function, FEM is used to obtain T-stress values for two reference crack-face loading configurations: uniform pressure and linearly varying pressure. These two load cases form a complete basis for symmetric crack-face tractions and are su ffi cient to construct the weight function. Since the derivation involves numerical input from FEM combined with analytical integration over the uncracked stress field, the resulting weight function is semi-analytical in nature Ayatollahi et al. (1998); Fett (1997). Once derived, the weight function enables direct evaluation of T-stress for arbitrary loading by integrating it with the stress field of the uncracked annulus, which is obtained from the parametric Lame´ solution Srinath (2016). This approach avoids the need for repeated FEM simulations across varying crack lengths, pressure ratios, or radius ratios. Compared to full-field FEM—which is computationally intensive and sensitive to mesh refinement near the crack tip—the weight function method provides a more e ffi cient and scalable framework for constraint analysis. Numer ous studies on the evaluation and influence of T-stress have been reported in the literature for various geometries and loading conditions Fett (2001); Wang (2002); Omar et al. (2016); Zhou et al. (2019). For annular geometries, where curvature and pressure gradients significantly influence fracture behavior, this method o ff ers accurate T-stress evaluation with minimal computational overhead. The objective of this work is to apply the existing weight functions to evaluate T-stress in both inner and outer double edge cracked annuli under varying pressure ratios as shown in Fig. 1. The results reveal how geometry and loading interact to influence constraint, o ff ering insights for fracture-safe design of annular components.

2. Theoretical Framework

2.1. T-stress in Fracture Mechanics

In linear elastic fracture mechanics (LEFM), the crack-tip stress field is described using the Williams expansion, which includes both singular and non-singular terms. While the stress intensity factor (SIF) governs the magnitude of the singular term, the non-singular term—known as the T-stress—modifies the crack-tip constraint and influences the stability of crack propagation Betego´n and Hancock (1991); Du et al. (1991). Its sign and magnitude a ff ect the shape of the plastic zone and the likelihood of crack kinking or stable extension.