Yu.G. Matvienko et alii, Frattura ed Integrità Strutturale, 34 (2015) 255-260; DOI: 10.3221/IGF-ESIS.34.27 255 Focussed on Crack Paths The concept of the average stress in the fracture process zone for the search of the crack path Yu.G. Matvienko, M.M. Semenova Mechanical Engineering Research Institute of the Russian Academy of Sciences, Russia. ygmatvienko@gmail.com A BSTRACT . The concept of the average stress has been employed to propose the maximum average tangential stress (MATS) criterion for predicting the direction of fracture angle. This criterion states that a crack grows when the maximum average tangential stress in the fracture process zone ahead of the crack tip reaches its critical value and the crack growth direction coincides with the direction of the maximum average tangential stress along a constant radius around the crack tip. The tangential stress is described by the singular and nonsingular ( T -stress) terms in the Williams series solution. To demonstrate the validity of the proposed MATS criterion, this criterion is directly applied to experiments reported in the literature for the mixed mode I/II crack growth behavior of Guiting limestone. The predicted directions of fracture angle are consistent with the experimental data. The concept of the average stress has been also employed to predict the surface crack path under rolling-sliding contact loading. The proposed model considers the size and orientation of the initial crack, normal and tangential loading due to rolling–sliding contact as well as the influence of fluid trapped inside the crack by a hydraulic pressure mechanism. The MATS criterion is directly applied to equivalent contact model for surface crack growth on a gear tooth flank. K EYWORDS . Crack path; Maximum average tangential stress; T -stress; Mixed mode; Rolling-sliding. I NTRODUCTION eneral aspects of the concept based on calculation of the average stress over the length of the process zone are described in Refs. [1-6] for a solid with cracks or notches. These references demonstrate an advantage of the critical average stress criterion over the classical elastic and elastic-plastic fracture mechanics criteria because this criterion avoids the confusion of applying the unrealistic continuum mechanics stress singularity to the fracture process zone in the vicinity of the crack (or notch) tip. For example, the failure criterion of the average stress within an effective distance has been successfully employed to relate the apparent fracture toughness in specimens with notches to the fracture toughness obtained from deeply cracked specimens (e.g., [4]). In this case, the effective distance corresponds to the point with a minimum of the stress gradient which requires finite element analysis to obtain the effective distance [5]. It should be noted that the effect of the high stress gradient ahead of the crack/notch tip can be taken into account by means of the theory of critical distance using the stress at some critical distance [6]. The theory of critical distances was very successful in predicting the fracture strength of ceramic materials. Thus, the concept based on averaging the stress over the fracture process zone length can be successfully applied to cracks or notches. The concept of the average stress has been employed to propose the maximum average tangential stress (MATS) criterion under mixed mode I/II loading for predicting the direction of fracture angle. The effect of the G

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