Elastic–plastic analysis of off-center cracks in cylindrical structures

Abstract

This paper presents new elastic and elastic±plastic ®nite element solutions of the J-integral for a pipe containing o-center through-wall cracks under pure bending. The analysis is based on a three-dimensional nonlinear ®nite element method and small-strain theory. One hundred and ®ve analyses were performed using the ABAQUS commercial code for a wide variety of crack sizes, o-center crack angles, and material hardening exponents. The results from these analyses show that the J-integral values at the two crack fronts of an o-center crack are unequal due to the loss of symmetry with respect to the bending plane of the pipe. In addition, the J-integral is larger, and hence, critical at the crack front which is farther away from the bending axis of the pipe. This is because, at that crack front, the tensile stress is larger and the component of the applied bending moment about the crack centerline has a further crack-opening eect. Also at this crack front, the J values can be lower or slightly higher than those of a symmetrically centered crack, depending on the crack size and o-centered angle. For the crack front that is closer to the bending axis, the J values are always lower than those of a symmetrically centered crack. This implies that the load-carrying capacity of a pipe is usually larger for an o-center crack than that for a symmetrically centered crack. Finally, based on these ®nite element solutions, new analytical expressions of J-integral were developed for fracture analysis of pipes containing o-center cracks. 7

Probabilistic analysis of off-center cracks in cylindrical structures

“…Due to this fact, the surface fit equations for crack front CD give reasonable approximations up to crack closure since they show the correct trend of a discontinuity at crack closure. However, since there are no data for the two smaller cracks at the point of crack closure, a region of extrapolation is needed between the final non-zero data points and the closure line [12]. The crack closure line is simply a straight line defining one edge of the extrapolation region in the (u /p)-c plane.…”

“…(11) assuming a generic N-dimensional random vector X and the performance function g(x) defined by Eq. (12). For brevity, only the results of FORM/SORM will be presented in this paper.…”

Three-dimensional J-integral evaluation for finite strain elastic–plastic solid using the quadratic tetrahedral finite element and automatic meshing methodology

“…The computational aspects and applications of the J-integral are summarized in review articles by Liebowitz et al [5] and by Broberg [6]. The J-integral approach has been applied to practical problems as seen in Firmature et al [7] and approximate evaluation techniques based on numerical solutions have been presented as seen in Allen et al [8] and Cho et al [9]. Furthermore, the J-integral approach extends to polymer and wood materials, as presented by Elmeguenni et al [10] and Pop et al [11].…”

Experimental measurement and model validation of COD in pipe under bending with off-centered circumferential crack

“…Bonora [1] proposed the Hodograph Cone Method (HCM) in which the COD distribution (shape and amplitude) and the leak area are predicted, as a function of the crack length and off-center angle, only by means of geometrical considerations. Later, Rahman et al [8] performed further numerical investigations on off-centered crack configurations, and Firmature and Rahman [9] investigated the behavior of off-center cracks in elastic-plastic regime. At the present, the HCM method is the only available solution that does not require extensive use of finite element simulation and allows quick estimation of the COD distribution and associated COA, given the crack length and the offaxis angle, and the maximum COD for the prescribed load in the centered crack configuration.…”