ORNL researchers have significantly improved the accuracy of computed crack stress intensity factors by incorporating the ORNL-developed "modified quarter-point" element (MQP) into boundary integral fracture codes. This improvement in accuracy makes it feasible to reliably model real problems, particularly those where cracks follow curved paths. This new method is currently being applied to failure in thermal barrier coatings.
The ability to do crack propagation simulations relies on computing accurate stress intensity factors at crack tips. The major advance was in 1975, when Henshell and Shaw, and independently Barsoum, devised the "quarter-point" (QP) crack tip element. The crack opening displacement is a function of the square root of the distance to the tip, and this element successfully captures this behavior. For 25 years the quarter-point has been the standard element used in finite and boundary element analyses. However, experience has shown that while the quarter-point produces reasonably accurate opening (K_I) stress intensity factors, it is far less successful in predicting K_II (sliding) and K_III (twisting). As a result, it is more difficult to accurately predict curved crack growth.
In 1998, Gray and Paulino (SIAM J. Appl. Math., 58, pp.428-455) proved that, irregardless of the geometry of the problem, the crack tip displacement satisfies a constraint, namely that the term linear in the distance to the tip must vanish. We have now devised a "modified quarter-point" element (MQP) which incorporates this constraint, and have implemented it in a two-dimensional boundary integral fracture code. In test cases (see table below) where the stress intensity factors are known exactly, this modified element has produced spectacularly more accurate results. Most significantly, the order of magnitude improvement for the K_II mode is essential for treating real problems where cracks follow curved paths. A primary application of this work will be in the analysis of the failure of thermal barrier coatings.
exact QP %error MQP %error center crack K_I 79.267 81.117 2.33 79.262 6.3E-5 2 coplanar cracks K_I 57.073 58.385 2.30 57.032 7.2E-4 2 curved cracks K_I 32.112 34.396 7.11 32.264 0.47 2 curved cracks K_II 11.969 8.991 24.88 11.520 3.75