K_I–T estimation for embedded flaws in pipes – Part II: Circumferentially oriented cracks

Abstract

This paper, in parallel to the investigation on axially embedded cracks reported in the companion paper, presents a numerical study on the linear-elastic K_I and T-stress values over the front of elliptical cracks circumferentially embedded in the wall of a pipe/cylindrical structure, under a uniform pressure applied on the inner surface of the pipe. The numerical procedure employs the interaction-integral approach to compute the linear-elastic stress-intensity factor (SIF) K_I and T-stress values for embedded cracks with practical sizes at different locations in the wall of the pipe. The parametric study covers a wide range of geometric parameters for embedded cracks in the pipe, including: the wall thickness to the inner radius ratio (t/R_i), the crack depth over the wall thickness ratio (a/t), the crack aspect ratio (a/c) and the ratio of the distance from the centerline of the crack to the outer surface of the pipe over the pipe wall thickness (e_M/t). The parametric investigation identifies a significant effect of the remaining ligament length on both the T-stress and K_I values at the crack-front location (denoted by point O) nearest to the outer surface of the pipe and at the crack-front location (denoted by point I) nearest to the inner surface of the pipe. The numerical investigation establishes the database to derive approximate functions from a nonlinear curve-fitting procedure to predict the T-stress and K_I values at three critical front locations of the circumferentially embedded crack in a pipe: points O, I and M. The proposed T-stress and K_I functions utilize a combined second-order polynomial and a power-law expression, which presents a close agreement with the T-stress and K_I values computed from the very detailed finite element models. The comparison between the circumferentially embedded crack and the axially embedded crack indicates that both the T-stress and K_I values at crack-front points O and I in a circumferential crack equal approximately 50% the T-stress and K_I values at the corresponding front locations in an axial crack with the same crack depth ratio, the same crack aspect ratio and the same pipe wall thickness to the inner radius ratio.

Introduction

Cylindrical structures, e.g., oil and gas pipelines and pressure vessels, contain potentially crack-like defects caused by, e.g., lack of fusion during the welding procedure. These cracks may grow to critical sizes sufficient to cause catastrophic structural failure during the operation of the pipelines and pressure vessels. Recent research work reported by SINTEF shows that embedded circumferential flaws in the wall of a pipe can, in certain circumstances, impose a more critical threat to the safety of pipelines under internal pressures, than does a surface crack with the same size [1]. The contrast difference in the plasticity constraints drives both different crack driving forces and different fracture resistance along the front of a surface crack from those along the front of an embedded crack. Recent research findings [2], [3], [4] prove that crack-front constraints, characterized often by the linear-elastic T-stress field, vary severely the fracture resistance measured by the fracture resistance J–R curve. However, engineering practices of the integrity assessment of the cracked pipe structures, as outlined in API 579 [5] or BS7910 [6], predicate primarily on the material fracture toughness derived from high-constraint fracture specimens. Acknowledging the effect of crack-front constraints, Zhu and Leis [7] apply the constraint-corrected J–R curve to the fracture assessment of surface cracks in pipelines made of API X80 steels. Similarly, Ruggieri and Cravero [8] implement the constraint-modified failure assessment diagram in the structural integrity assessment of axial surface cracks in pipelines made of X65 steels. Accurate estimations of both the similitude parameter, K_I, and the linear-elastic T-stress, therefore, become essential in the failure assessment of cylindrical structures, which embed a welding defect in the wall thickness.

The T-stress represents the second, constant term in the classical Williams’ solution [9] for the elastic crack-tip stress field. It defines a uniform stress parallel to the crack plane. Extensive numerical investigations [10], [11] prove that a zero or positive T-stress field characterizes a crack-front condition that constrains the plastic deformation within a very localized small region ahead of the crack tip, while a negative T-stress causes significant stress redistributions near the crack tip and the plastic deformation thus extends to a relatively larger region ahead of the crack tip than a positive T-stress configuration. Previous researchers [1], [12], [13] recognize the effect of crack-front constraints on the fracture resistance and the growth for a circumferential surface crack and for an embedded circumferential crack in the wall of pipes. The low plasticity constraints in the circumferential surface cracks in the wall of a pipe enhance the fracture resistance and delay the crack growth compared to a highly-constraint crack front under the same crack driving force. Kim [14] proves, from combined experimental and numerical studies, that the high-constraint compact tension, C(T) specimen, provides conservative estimations on the fracture resistance for surface cracks in pipes. Jayadevan et al. [15] and Ostby et al. [16] find, through a series of extensive numerical investigations, that the presence of biaxial loading increases significantly the crack driving force in circumferential surface cracks in the wall of a pipe subjected to tension [15] and bending [16].

The last two decades observe substantial developments in catalogue solutions for the linear-elastic K_I and T-stress values via numerical and analytical methods for circumferential cracks in pipes, mainly addressing surface cracks. Wallbrink et al. [17] propose a semi-analytical approach which utilizes the stress field in the undamaged structure to compute the stress-intensity factors for circumferentially cracked pipes. Bergman and Brickstad [18] adopt the line spring elements to compute the SIF values for internal circumferential cracks in pipes. Varfolomeyev and Busch [19] derive the SIF solutions for circumferential through-wall cracks in the cylinder, using the weight function approach. Poette and Albaldejo [20] present the SIF and the influence functions for semi-elliptical, internal surface cracks in pipes under tension and bending loads. Kim and Budden [21] report the approximate solutions to the J-integral and COD values for circumferential through-wall cracks in pipes under tension and bending loads, including the correction for plasticity. For the T-stress investigation, where relatively fewer solutions remain available, a few researchers [22], [23] report the polynomial T-stress approximation for an internal circumferential crack subjected to internal pressure or remote bending.

The current study aims to provide simple approximate solutions to the linear-elastic K_I and T-stresses at critical locations along the embedded crack front in the wall of a steel pipe subjected to an internal pressure. The numerical procedure utilizes the interaction-integral approach to compute the elastic K_I and T-stress along the front of the circumferentially embedded, elliptical cracks in the wall of a steel cylinder, similar to the study reported in the companion paper [24]. Subsequent data analysis develops a parametric expression for the K_I and T-stress values at three locations along the embedded crack front, through a nonlinear curve-fitting procedure.

This paper starts with an introduction on the computational procedures including a very brief summary of the interaction-integral approach and a brief description on the nonlinear curve-fitting procedure, both of which have been described in more details in the companion paper [24]. The following section discusses the numerical T-stress results and the proposed T-stress function for three critical crack-front points for different crack locations, sizes, aspect ratios and pipe wall thicknesses. The subsequent section presents the finite element results for SIF values with respect to different geometric parameters, together with the proposed K_I function. The next section compares the SIF and T-stress values computed from the circumferentially embedded cracks and those obtained from the axially embedded cracks reported in the companion paper [24]. The last section summarizes the main conclusions drawn from the current study.