PSI - Issue 13

Yuebao Lei / Procedia Structural Integrity 13 (2018) 571–577 Y Lei/ Structural Integrity Procedia 00 (2018) 000–000

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sometimes, irrelevant to the J behaviour when the section containing the crack is not the weakest location in the component and, for this case, a local limit load could be more appropriate. A local limit load corresponds to a loading level at which gross plasticity occurs in the crack ligament and may be relevant to ligament fracture. Unlike the global limit load which can be physically demonstrated by the load-load point displacement behaviour of the structure, the local ligament yielding ahead of the deepest point of the crack may have little effect on the global deformation behaviour [Lei (2007)]. In a FE limit load analysis considering an elastic-perfectly plastic material, local yielding may be judged by monitoring the plastic zone in the ligament of interest and the local limit load is taken as the applied load when the plastic zone penetrates the ligament in a limited area or spreads throughout the whole ligament. There is no strict definition for the local limit. The general lower bound limit load theorem cannot be directly used for local ligament yielding because the plastic zone for this case is surrounded by an elastic material zone and there is no easy way to set up links between the local stress distribution and the applied loads. In engineering, the local limit loads are normally estimated by defining an effective load-carrying area [Lei (2016)] including the defect and applying the limit load theorem to this local section. The local limit load solutions which are currently used in structural integrity assessment are derived under the assumption that the ligament in a defective structure collapses when the material in a limited area around the defect yields. The size and shape of this area are defined usually to consider the ligament size or the thickness of the defective wall and the shape of the defect. Therefore, local limit load solutions obtained in this way normally depend on the definition of this area. For complex components or components under complex load combinations, it is not easy to judge whether the defect location is the weakest point of the component under known load types. Also, the contribution of each load to ligament yielding may not be explicitly determined. In these cases, the effective load carrying area method cannot be used to define a local limit load and Connors (2005) proposed a method using a local model to define the local limit load. Connors simply “cut” a slice through the thickness of the component from the crack tip to be assessed. This slice is a single edge cracked plate (SECP) with a width of the component thickness containing a crack of length equal to the real crack depth. The fixed-end plane stress limit load of this SECP under remote membrane stress, which is the crack plane membrane stress from uncracked-body elastic stress analysis for the real loading conditions, is used as a local limit load of the real defective component. This method ignores the effects of the deformation of surrounding materials and finite crack length and is proved [Lei (2016)] to be much too conservative for deep cracks. In this paper, a new local limit load model is developed for shell/plate type components with surface cracks. The new model predicts the yielding of the ligament along the thickness of the components based on the crack location uncracked-body elastic stress conditions but also includes the effects of the ligaments along the crack length (see Fig. 1) and the deformation of the surrounding material to reduce the conservatism of the Connors model. The global limit load of this model is used as the local limit load of the defective component in the J-prediction using the reference stress scheme aimed to obtain more accurate but conservative J predictions. This model will then be validated using some 3-D finite element (FE) J results for semi-elliptical cracks in plates, cylinders and elbows. 2. Development of the local limit load model For elastic materials, the SIF mainly depends on the local uncracked-body stress distributions at the crack location due to the loads applied remotely to a component. This is why in an elastic FE cracked-body analysis the SIF can be alternatively calculated by applying the local uncracked-body stress distribution to the crack faces. For elastic-plastic materials, the elastic-plastic fracture parameter, J , also strongly depends on the local uncracked-body stress distribution at the crack location if the stress re-distribution due to plastic deformation is not significant. However, unlike the SIF calculation, the elastic-plastic J cannot be directly linked to the local stress. In this case, the local stress distribution may be used to define the limit loads corresponding to crack ligament yielding and such a load could be used to estimate J via the reference stress method. For a small surface crack in a component, the load corresponding to crack ligament yielding is normally lower than the global limit load of the defective component. This means that, after crack ligament yielding, plastic deformation in the ligament and the near area is controlled by the elastic zone surrounding the local area containing the crack, until global yielding takes place [Lei (2007)]. In order to correctly describe the plastic deformation behaviour of the crack ligament, an ideal local model should also include the effect of the surrounding elastic zone. Therefore, the new local limit load model considers the material containing the whole crack with ligaments along the crack length (see Fig. 1).