Submarine and onshore pipelines transport enormous quantities of oil and gas vital to the economies of virtually all nations. Any failure to ensure safe and continuous operation of these pipelines can have serious economic implications, damage the environment and cause fatalities. A prerequisite to safe pipeline operation is to ensure their structural integrity to a high level of reliability throughout their operational lives. This integrity may be threatened by volumetric and shear ductile micro- and macro-fracture processes under long time loading or continuous operation. In this paper a mathematically consistent damage model for predicting the damage in pipeline structures under tensile and shear loading is considered. A detailed study of widely used damage models (e.g., Lemaitre’s and Gurson’s models) has been published in the literature. It has been shown that Gurson’s damage model is not able to adequately predict fracture propagation path under shear loading, whereas Lemaitre’s damage model (Lemaitre, 1985) shows good results in this case (e.g., Hambli 2001, Mkaddem et al. 2004). The opposite effect can be observed for some materials by using Gurson’s damage model in the case of tensile loading (e.g., Tvergaard and Needleman 1984; Zhang et al. 2000; Chen and Lambert 2003; Mashayekhi et al. 2007) and wiping die bending process (Mkaddem et al. 2004). Therefore, the mathematically consistent damage model which takes into account the advantages of both Lemaitre’s and Gurson’s models has been developed. The model is based on the assumption that the damage state of materials can be described by a damage tensor ωij. This allows for definition of two scalars that are ω = ωkk/3 (the volume damage) (Lukyanov, 2004) and α = ωij′ωij′ (a norm of the damage tensor deviator ωij′ = ωij −ωδij) (Lukyanov, 2004). The ω parameter describes the accumulation of micro-pore type damage (which may disappear under compression) and the parameter α describes the shear damage. The proposed damage model has been implemented into the finite element code ABAQUS by specifying the user material routine (UMAT). Based on experimental research which has been published by Lemaitre (1985), the proposed isotropic elastoplastic damage model is validated. The results for X-70 pipeline steel are also presented, discussed and future studies are outlined.
Propagation of a Spherical Wave in Elastoplastic Medium with Complex Equations of State
