Product: Abaqus/Standard
This example verifies and illustrates the use of the extended finite element method (XFEM) in Abaqus/Standard to predict dynamic crack propagation of a beam with an offset edge crack. The specimen is subjected to a mixed-mode impact loading. Both two- and three-dimensional models are studied. The crack paths and crack initiation angles presented are compared to the experimental results of John and Shah (1990).
A beam with an offset edge crack is studied. The specimen, shown in Figure 1.19.3–1, has a length of 0.2286 m, a thickness of 0.0254 m, and a width of 0.0762 m. The distance between supports is 0.2032 m. To induce a mixed-mode fracture, an initial crack with a length of 0.019 m is made at an offset distance of 0.06604 m measured from the midspan in the specimen. A velocity boundary condition is imposed at the midspan of the specimen to simulate a dynamic impact:
= 0.06 m/s and 
= 1.96 × 10–4 s.The material data for the bulk material properties in the enriched elements are 
= 31.37 GPa, 
= 2400 kg/m3, and 
= 0.2.
The response of cohesive behavior in the enriched elements in the model is specified. The maximum principal stress failure criterion is selected for damage initiation, and an energy-based damage evolution law based on a power law fracture criterion is selected for damage propagation. The relevant material data are as follows: 
= 10.45 MPa, 
= 19.58 N/m, 
= 19.58 N/m, 
= 19.58 N/m, 
= 1.0, 
= 1.0, and 
= 1.0.
Figure 1.19.3–2 shows the crack profile when 
= 1.3 × 10–3 s. The crack propagates at an angle of 58°, which is in reasonable agreement with the experimental result of 60°.
Two-dimensional plane strain model under mixed-mode impact loading.
Three-dimensional tetrahedron model under mixed-mode impact loading.
Three-dimensional brick model with reduced integration under mixed-mode impact loading.
Script to generate the three-dimensional brick model with reduced integration under mixed-mode impact loading in Abaqus/CAE simulated using the XFEM-based cohesive segments approach.
