A Unified Numerical Approach for Multiaxial Fatigue Limit Evaluation

Abstract

A unified numerical approach to evaluate the endurance limit for general multiaxial fatigue loading, under proportional or nonproportional loading, is presented. A minimum circumscribed ellipsoid approach is proposed for computing the amplitude and mean value of the equivalent shear stress, and an efficient numerical algorithm is developed for solving the min-max problem by using a constrained optimization method. The approach is general and efficient, especially suitable for computer-aided design and optimization. With this approach, nonproportional loading effects can be taken into account, overcoming limitations of many other multiaxial fatigue criteria. Experimental results collected from the literature are compared with results predicted by the numerical approach proposed in this paper. The comparison shows that the predictions agree well with experiments for both proportional and nonproportional loading situations.

Fretting fatigue – Experimental and numerical approaches

“…Several methods have been developed in recent decades for computing the shear stress amplitude value efficiently from the stress history [15][16][17][18][19][20][21]. These methods can be classified into two main groups.…”

“…loading path more sensitively. Li et al [15] were among the first to introduce the minimum circumscribed ellipsoid (MCE) method. Zouain et al in [18] then proposed significant modifications in their MCE approach.…”

On the multiaxial fatigue assessment of complex three-dimensional stress concentrators

“…In this context, the orientation of the critical plane is recommended here to be determined through the Shear StressMaximum Variance Method (s-MVM) [17,18]. In more detail, contrary to other existing techniques such as the Longest Chord [19], Longest Projection [20], Minimum Circumscribed Circle [21], and Minimum Circumscribed Ellipse Method [22][23][24][25], the s-MVM postulates that the orientation of the critical plane can be determined by locating those material planes containing the direction experiencing the maximum variance of the resolved shear stress. This approach is seen to be very efficient from a numerical point of view, since, as soon as the variance and co-variance terms characterising the load history under investigation are known, the computational time required to reach convergence is not affected by the length of the stress signal being post-processed [17] -the Reader is referred to Ref.…”

Multiaxial high-cycle fatigue criterion considering crack initiation and non-propagation

“…Moreover, such estimation methods should use material properties that are readily available. Two conventional methods of estimating multiaxial high-cycle fatigue are the critical plane approach [1][2][3], and the stress invariant approach [4][5][6][7][8][9][10]. The critical plane approach uses the maximum shear stress and the normal stress acting on the critical plane and the stress invariant approach uses the equivalent shear stress amplitude and hydrostatic stress.…”