International Journal of Fatigue 22 (2000) 1–9 www.elsevier.com/locate/ijfatigue Fatigue growth simulation of part-through flaws in thick-walled pipes under rotary bending Andrea Carpinteri * , Roberto Brighenti, Andrea Spagnoli Department of Civil Engineering, University of Parma, Parco Area delle Scienze 181/A, 43100 Parma, Italy Received 19 May 1999; received in revised form 20 September 1999; accepted 20 September 1999 Abstract The fatigue growth of a circumferential external surface flaw in a thick-walled round pipe subjected to rotary bending is simulated numerically. A three-dimensional finite element analysis is carried out to obtain the stress–strain field of the cracked structural component for any position of the flaw. The crack front is assumed to have an elliptical-arc shape during the whole propagation, as has been deduced from several experimental investigations. The results for rotary bending are compared to those for cyclic bending.  1999 Elsevier Science Ltd. All rights reserved. Keywords: Round pipe; Circumferential external surface flaw; Rotary bending; SIF (Stress–Intensity Factors); Fatigue crack growth; Fatigue frac- ture mechanics 1. Introduction The fatigue behaviour of surface flaws in round bars has been examined by several authors (for example, see [1–7]), and a few studies have been carried out on cir- cumferential edge flaws in pipes [1,2,8–14]. Structural hollow cylinders are subjected to cyclic loading in many practical applications. For example, tubular components are frequently used as columns supporting offshore structures, and fatigue loads resulting from wave action are significant on them [15]. In order to analyse the fatigue strength of hollow cyl- inders, rotary bending tests are usually performed, that is to say, the bending moment M is applied to a pipe while it rotates around its axis. Consequently, the pos- ition of a surface flaw continuously changes due to the rotational movement of the cylinder. The same problem but for round bars has recently been examined in [16,17]. In the present paper, a circumferential external surface flaw in a metallic round pipe under rotary bending is considered (Fig. 1). The crack front is assumed to be an elliptical arc during the whole propagation, as several * Corresponding author. Tel.: + 39-0521-905922; fax: + 39-0521- 905924. E-mail address: carpint@parma1.eng.unipr.it (A. Carpinteri) 0142-1123/00/$ - see front matter  1999 Elsevier Science Ltd. All rights reserved. PII:S0142-1123(99)00115-2 experimental investigations have shown [18,19], and therefore the flaw configuration can be described by the relative crack depth x=a/t in correspondence to the deep- est point A on the crack front, and the flaw aspect ratio a=a/b (Fig. 2). The position of the flaw is identified by the parameter J which measures the angle between the loading axis l–l (perpendicular to the vector M) and the symmetry axis c–c; such angle is assumed to be positive if it is clockwise from l to c. The ratio R*=R/t between the internal radius of the pipe and its wall thickness is assumed to be equal to 1 (thick-walled pipe), but the results presented in the following change only slightly for 0.5R*2. The finite element method and the superposition prin- ciple are applied to compute the stress–intensity factor (SIF) distribution along the front of the defect for any value of the angle J. The fatigue crack growth is numeri- cally simulated by employing a two-parameter theoreti- cal model [3] based on the Paris–Erdogan law. It is shown that these flaws tend to follow preferred propa- gation paths in the diagram of a against x, with negli- gible differences when comparing the results obtained for rotary bending to those for cyclic bending.