Finite separation method: an efficient boundary element crack modeling technique

Abstract

In computational fracture mechanics, great benefits are obtained from the reduced modeling dimension order and the accurate integral formulation of the boundary element method (BEM). However, the direct representation of co-planar surfaces (i.e., cracks) causes a degeneration of the standard displacement BEM formulation which can only be circumvented with special modeling techniques. Aiming to simplify the generalized application of the BEM to fracture mechanics problems, this paper presents a two-dimensional crack modeling approach. The method uses the direct BEM displacement formulation within a single-domain model to efficiently and precisely calculate any mixed mode crack tip stress intensity factor. Details of the application of the method are presented, while its accuracy and reliability are demonstrated through numerous comparisons with benchmark results.

Modeling and monitoring of tooth fillet crack growth in dynamic simulation of spur gear set

“…On the other hand, it decreases with an augmentation of the tooth number. The observed trends agree with published descriptions [24][25][26]. Moreover, as reported by Lewicki et al [18] or by Refs.…”

“…They were evaluated using the displacement extrapolation method integrated into the Finite Separation Method developed by the authors in [24]. Ref.…”

Prediction of thin-rimmed gear crack propagation from a factorial design approach

“…Accuracy of SIF values is critical for crack propagation simulations to be able to correctly define propagation rates ( da/dN ) and crack orientations (θ). The FSM ability to provide accurate SIF, when used along with QPE and displacement extrapolation, has been demonstrated for numerous mixed mode cases 23 . The FSM maximum deviation on K I and K II was shown to be less than 1% when compared to analytical solutions.…”

“…Usually, this is circumvented with mixed‐formulation or multi‐domain approaches 20 . However, a new simple BE crack modelling technique called the Finite Separation Method (FSM) has been recently proposed, 23 and prevents BEM degeneration by imposing a negligible gap (δ) between crack faces. This approach limits the model to a single domain, consequently to the standard displacement BEM formulation, thus leading to simpler BE representation and reduced computation times 23 …”

“…The crack face separation δ is fixed at 1 × 10 −2 μm. Accurate solutions are obtained with a gradually refined mesh imposed at each new crack segment ( da ), with h s = da/10 and h t = da/20 , while previous segments are uniformly discretized 23 (Fig. 2).…”