Keywords: elastoplastic fracture analysis, J-integral evaluation, cylindrical shells, symmetrically centred cracks, through-wall cracks, off-centre crack, combined bending and tension.

Elastoplastic fracture analysis of cracked cylindrical components which can be found in different power plants, gas pipelines and in other industrial equipments has received considerable attention during recent years. An accurate computation of the fracture response characteristics, such as crack opening displacement and -integral, represent a key for prediction of integrity and reliability of degraded structural components. A through-wall circumferential crack in cylindrical shells is a representative model for the leak-before-break and pipe flaw evaluations. Loading conditions, such as pure bending, pure tension and combined bending and tension, are mainly considered in references [1,2,3,4,5]. A postulated through-wall crack size is often calculated on the basis of its symmetric placement with respect to the bending plane [1,4,5]. However, in reality, the off-centre cracks can occur due to random imperfections around the cylinder circumference. To evaluate the -integral, special influence functions have been introduced [2,3]. A realistic evaluation of pipes fracture response demands consideration of more complex loading condition including combined bending and internal pressure. When fracture mechanics analysis is performed for through-wall cracked pipes subjected to internal pressure, it is a typical practice to transform the effect of pressure by the pressure-induced axial tension [4,5]. The hoop stress effect on the fracture response characteristics has been considered only in a limited number of studies [4].

The objective of this work is to obtain a new elastoplastic solution of the -integral for cylinders containing off-centre through-wall cracks subjected to combined bending and internal pressure loads. As is usual in literature, only the tension force due to the pressure is included, while the hoop stress effect is neglected. Three-dimensional nonlinear finite element computations are performed within the finite element program ABAQUS [6]. Under the assumption of small elastoplastic strain, the constitutive law characterizing the stress-strain response of mild steel is represented by the well-known Ramberg-Osgood model. In all tests, non-proportional loading approach is applied at constant internal pressure of. The small and the medium crack length under variation of the off-centre crack angles are considered. The high accuracy of the numerical results is exhibited, which is demonstrated in comparison with other solutions available in literature.

The computational results for thin-walled pipes with intermediate cracks subjected to the combined bending and axial tension show that the values for off- center cracks are smaller than those for symmetric cracks. This statement is excepted for the offset crack angle of 15 where the values at the crack front which is farther away from the bending axis are slightly higher than those for the symmetric centered crack. This demonstrates that for any crack size there is a limit-offset angle for which the -integral values at the one crack front exceed those of the centered crack. These effects are also presented and described in Reference [3] for the case of pure bending loading and for intermediate and large cracks. For the combined bending and axial tension considered in this study, this effect is slightly higher than that for pure bending. It should be noted that the elastoplastic behavior of an off-center cracked cylinder is very similar to its elastic response.

1

Brust, F.W., Rahman S., Ghadiali N.D., "Elastic-plastic analysis of small cracks in tubes", Journal of Offshore Mechanics and Arctic Engineering,117, 57-62, 1995. doi:10.1115/1.2826991

2

Rahman S., Brust, F.W., Ghadiali N.D., Wilkowski G.M., "Crack-opening- area for circumferential through-wall cracks in pipes-Part I: analytical models", International Journal of Pressure Vessels and Piping 75, 357-373, 1998. doi:10.1016/S0308-0161(97)00081-1

3

Firmature R., Rahman S., "Elastic-plastic analysis of off-center cracks in cylindrical structures", Engineering Fracture Mechanics, 66, 15-39, 2000. doi:10.1016/S0013-7944(99)00135-6

4

Firmature R., Rahman S., "Elastic-plastic analysis of off-center cracks in cylindrical structures", Engineering Fracture Mechanics, 66, 15-39, 2000. doi:10.1016/S0013-7944(99)00135-6

5

Kim Y.J., Huh N.S., Kim Y.J., "Reference stress based elastic-plastic fracture analysis for circumferential through-wall-cracked pipes under combined tension and bending", Engineering Fracture Mechanics, 69, 367-388, 2002. doi:10.1016/S0013-7944(01)00074-1

6

ABAQUS, "User's guide and theoretical manual", Version 6.2, Hibbitt, Karlsson & Serensen, Inc. 2001.

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