Simulia Abaqus 612 [NEW] Crack
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A lower bound limit load can be calculated by applying small displacement theory with an elastic-perfectly-plastic material model. The limit load is obtained from the point at which yielding spreads across the uncracked ligament. In finite element software, this is done by applying the loads incrementally and proportionally until the plastic zone spreads from the crack tip through the thickness of the section containing the flaw. In Abaqus, the load increment at which local collapse occurs can be determined by monitoring the equivalent plastic strain variable (PEEQ) or the active yielding (AC YIELD) variable. For surface-flaws, this definition is straight-forward as there is only one ligament (or crack tip plastic zone) to consider. However, for embedded flaws, there are two, potentially different sized, ligaments. If one ligament is significantly smaller than the other, then taking the limit load as the load causing the plastic zone to snap through the smaller of the two ligaments may result in an under prediction of the limit load. This is because relatively little yielding of the local section containing the flaw will likely have occurred.
An alternative to the spreading plastic zone method is to determine the limit load based on reference to the crack driving force estimation schemes that the failure assessment diagrams are based upon. Three methods are detailed below.
A Cartesian coordinate system was employed with the x-axis along the axis of the pipe. Due to symmetry considerations with respect to the geometry and the applied loads, one-quarter of the pipe was modelled, with an axial symmetry plane along the crack plane, and a longitudinal symmetry plane. Figure 1 illustrates the quarter pipe geometry and crack position.
For each of the linear elastic simulations, History Output Requests were created in Abaqus/CAE to evaluate the stress intensity factors (KI, KII, and KIII) and the J-integral from 10 contours surrounding the crack tip. Each simulation was checked to ensure that the output values of stress intensity factors and J-integral had converged by the outermost contour; that is, path-independence of the J-integral was obtained. Therefore, in what follows, the values reported for a given crack are the path-independent, converged values from the outermost contour.
Three linear elastic loading conditions were considered: axial stress, global bending stress and crack flank pressure. For each set of applied loads, the stress intensity factors were evaluated at each node along the crack front. The crack front was parameterised in the usual manner by the parametric crack front angle, ranging from 0° at the point of the flaw along the longitudinal symmetry plane, closer to the outer surface of the pipe, to 180° at the point of the flaw along the longitudinal symmetry plane, closer to the inner surface of the pipe. In Figure 3 the mode-I stress intensity factors (KI) is plotted against the parametric crack front angle. It can be seen that, due to the large ratio of outer diameter to wall thickness, there is very little difference between the results due to global bending stress and axial stress (ie there is very little through wall bending). 2b1af7f3a8