"ZOOM" SEMINAR

School of Mechanical Engineering Seminar
Wednesday, December 23, 2020 at 14:00

Extension of the Virtual Crack Closure Technique and Clifford Algebra for Three-Dimensional Problems

by

Elad Farksh

Ph.D. student under to supervision of Prof. Banks-Sills

The Virtual Crack Closure Technique (VCCT) was first presented in 1977 for calculating stress intensity factors of cracks in linear elastic, homogeneous and isotropic material. It makes use of the Irwin crack closure integral to obtain values of the modes I, II and III energy release rates from finite element data. It was seen in the literature that it was difficult to obtain accurate results for interface cracks. In Banks-Sills and Farkash, (2016), a way was found to overcome this difficulty for this method allowing accurate calculation of stress intensity factors for two-dimensional problems of an interface crack between two dissimilar linear elastic, homogeneous and isotropic materials with fine meshes. To this end, the virtual crack extension consists of a number of elements rather than one element as was used in previous studies.

In this investigation, the VCCT is extended to two-dimensional interface cracks between two anisotropic materials (Farkash and Banks-Sills, 2017). In addition, it is extended to three-dimensional problems containing a straight through finite length interface crack and a penny-shaped interface crack. Materials chosen for study were homogeneous and isotropic, as well as bimaterial isotropic and anisotropic. Excellent results are obtained when compared to analytical solutions. A criterion for determining the number of elements used for the numerical calculations is presented and shown to provide accurate results. For this criterion, new energy release rates were presented, namely, the dual energy release rates. In addition, it was found that although quarter-point elements are recommended for calculations of the stress intensity factors using the J and M-integral methods, it is not recommended for the VCCT (Farkash and Banks-Sills, 2020). New results were obtained for several problems.

The next part of the thesis consisted of extending a Clifford algebra (Clifford, 1873) for anisotropic bodies. The initial hope was to use it for solving crack problems. This does not appear to be possible. A discussion of this, as well as progress made for solving three-dimensional problems of anisotropic materials is presented.

https://zoom.us/j/96584758181?pwd=WC9PMXdsYzJ3NFdEN2Q5ZUtOZEVjdz09 The meeting will be recorded and made available on the School’s site.