This training package includes workshops that teach you the XFEM method to simulate crack growth. This tutorial package enables you to model crack propagation in any 2D and 3D dimensional model. In addition, you will learn about the Paris law, direct cyclic approach, traction-separation law, and other theories that help you to simulate a crack growth problem in this package
In this chapter, we go through the simulation of fatigue in Abaqus by a 2D planar deformable model. You will use constant amplitude loading to predict debonding growth at the interfaces in low-cycle fatigue analysis. Moreover, damage modeling is achieved through the use of a traction-separation law across the fracture surface.
abaqus fatigue crack growth tutorial
This tutorial is about predicting fatigue crack growth life under constant amplitude loading through the Extended Finite Element Method (XEFM) for a 3D steel model. You will design a 3D model and a crack in the middle of one edge and predict how the crack grows through the part. You will get a full explanation of fatigue in the Abaqus Documentation.
Z-cracks has been designed to deal with complex 3D cracked industrial structures, as shown in the movies: it has capacities to model complex cracked surfaces even with contact, to perform enegetic integrals on curved fronts and under mixed mode loading to extract stress intensity factors (or energy release rate in the most suitable direction), to apply simple, complex or user developped propagation laws in fatigue, all within a integrated user interface (shown on the second movie with real-time computations).
The range of application of the software is from initiated cracks to long cracks under fatigue loading (stationnary studies are always possible). Concerning crack initiation and damage to fracture transition, techniques are under developement at Onera and Ecole des Mines - ParisTech but not avaible for commercial usage.
in Abaqus/Standard models quasi-static crack growth in two dimensions (planar and axisymmetric) for all types of fracture criteria and in three dimensions (solid, shells, and continuum shells) for VCCT and the low-cycle fatigue criteria; and
The Paris regime is bounded by the energy release rate threshold, , below which there is no consideration of fatigue crack initiation or growth, and the energy release rate upper limit, , above which the fatigue crack will grow at an accelerated rate. is the critical equivalent strain energy release rate calculated based on the user-specified mode-mix criterion and the bond strength of the interface. The formulae for calculating have been provided above for different mixed mode fracture criteria. You can specify the ratio of over and the ratio of over . The default values are and . Figure 11.4.3–6 Fatigue crack growth govern by Paris law.
The onset of delamination growth refers to the beginning of fatigue crack growth at the crack tip along the interface. In a low-cycle fatigue analysis the onset of the fatigue crack growth criterion is characterized by , which is the relative fracture energy release rate when the structure is loaded between its maximum and minimum values. The fatigue crack growth initiation criterion is defined as
At the end of cycle , Abaqus/Standard extends the crack length, , from the current cycle forward over an incremental number of cycles, to by releasing at least one element at the interface. Given the material constants and , combined with the known node spacing at the interface elements at the crack tips, the number of cycles necessary to fail each interface element at the crack tip can be calculated as , where j represents the node at the jthe crack tip. The analysis is set up to release at least one interface element after the loading cycle is stabilized. The element with the fewest cycles is identified to be released, and its is represented as the number of cycles to grow the crack equal to its element length, . The most critical element is completely released with a zero constraint and a zero stiffness at the end of the stabilized cycle. As the interface element is released, the load is redistributed and a new relative fracture energy release rate must be calculated for the interface elements at the crack tips for the next cycle. This capability allows at least one interface element at the crack tips to be released after each stabilized cycle and precisely accounts for the number of cycles needed to cause fatigue crack growth over that length.
For most crack propagation simulations using VCCT, the deformation can be nearly linear up to the point of the onset of crack growth; past this point the analysis becomes very nonlinear. In this case a linear scaling method can be used to effectively reduce the solution time to reach the onset of crack growth.
Crack propagation problems using the VCCT criterion are numerically challenging. The following tips will help you create a successful Abaqus/Standard model:An analysis with the VCCT criterion requires small time increments. Abaqus/Standard tracks the location of the active crack front node by node when the VCCT criterion is used. Therefore, the crack front is allowed to advance only a single node forward in any single increment (although such an advance may take place across the entire crack front in three-dimensional problems). Because an analysis using the VCCT criterion provides detailed results of the growth of the crack, you will need small time increments, especially if the mesh is highly refined.
The VCCT and low-cycle fatigue criteria not only support two-dimensional models (planar and axisymmetric) but also three-dimensional models with contact pairs involving first-order underlying elements (solids, shells, and continuum shells). In Abaqus/Standard use of the VCCT criterion in two-dimensional models with contact pairs involving higher-order underlying elements is limited to crack fronts that are aligned with the corner nodes of the higher-order element faces. Use of the low-cycle fatigue criterion with contact pairs involving higher-order underlying elements is not supported.
The magnitude of the separation is governed by the cohesive law until the cohesive strength of the cracked element is zero, after which the phantom and the real nodes move independently. To have a set of full interpolation bases, the part of the cracked element that belongs in the real domain, , is extended to the phantom domain, . Then the displacement in the real domain, , can be interpolated by using the degrees of freedom for the nodes in the phantom domain, . The jump in the displacement field is realized by simply integrating only over the area from the side of the real nodes up to the crack; i.e., and . This method provides an effective and attractive engineering approach and has been used for simulation of the initiation and growth of multiple cracks in solids by Song (2006) and Remmers (2008). It has been proven to exhibit almost no mesh dependence if the mesh is sufficiently refined.
The Paris regime is bounded by the energy release rate threshold, , below which there is no consideration of fatigue crack initiation or growth, and the energy release rate upper limit, , above which the fatigue crack will grow at an accelerated rate. is the critical equivalent strain energy release rate calculated based on the user-specified mode-mix criterion and the fracture strength of the bulk material. The formulae for calculating have been provided above for different mixed mode fracture criteria. You can specify the ratio of over and the ratio of over . The default values are and .
The onset of fatigue crack growth refers to the beginning of fatigue crack growth at the crack tip in the enriched elements. In a low-cycle fatigue analysis the onset of the fatigue crack growth criterion is characterized by , which is the relative fracture energy release rate when the structure is loaded between its maximum and minimum values. The fatigue crack growth initiation criterion is defined as
Once the onset of the fatigue crack growth criterion is satisfied at the enriched element, the crack growth rate, , can be calculated based on the relative fracture energy release rate, . The rate of the crack growth per cycle is given by the Paris law if
At the end of cycle , Abaqus/Standard extends the crack length, , from the current cycle forward over an incremental number of cycles, to by fracturing at least one enriched element ahead of the crack tips. Given the material constants and , combined with the known element length and the likely crack propagation direction at the enriched elements ahead of the crack tips, the number of cycles necessary to fail each enriched element ahead of the crack tip can be calculated as , where j represents the enriched element ahead of the th crack tip. The analysis is set up to advance the crack by at least one enriched element after the loading cycle is stabilized. The element with the fewest cycles is identified to be fractured, and its is represented as the number of cycles to grow the crack equal to its element length, . The most critical element is completely fractured with a zero constraint and a zero stiffness at the end of the stabilized cycle. As the enriched element is fractured, the load is redistributed and a new relative fracture energy release rate must be calculated for the enriched elements ahead of the crack tips for the next cycle. This capability allows at least one enriched element ahead of the crack tips to be fractured completely after each stabilized cycle and precisely accounts for the number of cycles needed to cause fatigue crack growth over that length.
Interaction module: Create Interaction: select initial step: XFEM Crack Growth: select crack: Interaction manager: select interaction in step: Edit: toggle on/off Allow crack growth in this step
Y.F. Gao, A.F. Bower, "A simple technique for avoiding convergence problems in finite element simulations of crack nucleation and growth on cohesive interfaces." Modelling and Simulation in Materials Science and Engineering 12, 453-463, 2004 2ff7e9595c
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