Estimating the orientation of Stage I crack paths through the direction of maximum variance of the resolved shear stress |
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Affiliation: | 1. Department of Civil and Structural Engineering, The University of Sheffield, Mappin Street, Sheffield S1 3JD, UK;2. Department of Engineering, University of Ferrara, via Saragat 1, 44100 Ferrara, Italy;3. Mechanical Science and Engineering Department, University of Illinois at Urbana-Champaign, 1206 West Green Street, Urbana, IL 61801, USA;1. Division 9.4, Bundesanstalt für Materialforschung und-prüfung (BAM), 12205 Berlin, Germany;2. Institute of Physics of Materials, Czech Academy of Science, Zizkova 22, Brno 616 00, Czech Republic;3. Faculty of Civil Engineering, Brno University of Technology, Veveri 331/95, Brno 602 00, Czech Republic;4. Department of Industrial Engineering, University of Trento, via Sommarive 9, 38123 Povo, Italy |
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Abstract: | Our formalisation of the Shear Stress-Maximum Variance Method takes as a starting point the hypothesis that, in ductile materials subjected to fatigue loading, the crack initiation planes, i.e. the so-called Stage I planes, are those containing the direction experiencing the maximum variance of the resolved shear stress. From a computational point of view, the most remarkable implication of the above assumption is that, as soon as the variance and covariance terms characterising the considered load history are known, the effective time needed to estimate the orientation of the critical plane does not depend on the length of the load history itself. Further, such a computational efficiency is seen to be associated with an high-level of accuracy in estimating fatigue lifetime of both plain and notched engineering components, this holding true under constant as well as under variable amplitude uniaxial/multiaxial fatigue loading. In this scenario, by assuming that the orientation of Stage I planes can directly be determined through the orientation of Stage II crack paths, the present paper investigates whether, independently from the degree of multiaxiality and non-proportionality of the applied loading history, the direction of maximum variance of the resolved shear stress is also capable of accurately estimating the orientation of Stage I crack paths. |
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Keywords: | Critical plane Crack initiation Multiaxial fatigue Stage I plane |
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