Multiaxial loading

Much more has been published over the last 50 years concerning the crack growth approach" than the crack nucleation approach for rubber. Consequently, the crack growth approach enjoys a relatively more mature position than the crack nucleation approach. In recent years, the development of equivalence parameters that work in cases involving multiaxial loading has renewed interest in the crack nucleation approach. 

Mars, W.V., Heuristic approach for approximating energy release rates of small cracks under finite strain, multiaxial loading, in Elastomers and Components—Service Life Prediction Progress and Challenges, Coveney, V., Ed., OCT Science, Philadelphia, 2006, 89. 

Mars, W.V. and Fatemi, A., The correlation of fatigue crack growth rates in rubber subjected to multiaxial loading using continuum mechanical parameters. Rubber Chem. TechnoL, 80, 169, 2007. 

Fundamentals and Applications Edited by J.G. Blauel and K.-H. Schwalbe ESIS 10 Fatigue under Biaxial and Multiaxial Loading... 

Criteria 2, 5, and 6 are generally used for yielding, or the onset of plastic deformation, whereas criteria 1,3, and 4 are used for fracture. The maximum shearing stress (or Tresca [3]) criterion is generally not true for multiaxial loading, but is widely used because of its simplicity. The distortion energy and octahedral shearing stress criteria (or von Mises criterion [4]) have been found to be more accurate. None of the failure criteria works very well. Their inadequacy is attributed, in part, to the presence of cracks, and of their dominance, in the failure process. 

Further work will be focusing on lifetime prediction methods for gas turbine materials (superalloys) and experiments on fracture mechanics in superalloys as well as finite element calculations of multiaxial loaded tubes and validation of multiaxial tests (tension, torsion, internal pressure). 

Under the action of multiaxial loads, crack precursors wifi develop in a manner that reflects their particular loading experiences. It may be assumed that a crack precursor is present at every point, and that the crack precursor may occur in any orientation. By computing the rate at which each possible precursor will develop, it can be determined (Mars, 2002) which particular precursor(s) will develop the fastest. The orientation of this precursor identifies the critical plane on which cracks will develop, which is needed in order to accurately estimate fatigue life. 

Several critical plane analysis methods have been independently proposed and studied in the last decade (Mars, 2002 Mars and Fatemi, 2006a,b Saintier et al., 2006a,b Harbour et al., 2008b Andriyana and Saintier, 2010 Zine, 2011 Ayoub et al., 2012). They are noteworthy for their ability to provide a detailed and accurate account of the effects of multiaxial loading on fatigue life, and for their ability to predict the plane in which cracks will develop. 

The fact that the energy release rate of a small crack surrounded by homogenously strained material scales linearly with the size of the crack, for all multiaxial loading states, has been established from experience (Gough and Muhr, 2005), and can be established mathematically by considering the balance of configurational stresses (Ait-Bachir et al., 2012). 

Fatigue of fiber reinforced composites under multiaxial loading... 

This chapter is a revised version of Chapter 10, Fatigue of fiber reinforced composites under multiaxial loading by M. Quaresimin and R. Talreja, originally published in Fatigue Life Prediction of Composites and Composite Structures ed. A. P. Vassilopoulos, Woodhead Publishing Limited, 2010 (ISBN 978-1-84569-525-5). 

Another model explicidy developed for life prediction under multiaxial loading is that by Fawaz and EUyin [76—78] the actual multiaxial loading conditions and load ratio are considered through modification of a reference fatigue curve. 

The amount of data generated under global (external) multiaxial loading can be used as reference to discuss the influence of the main design parameters on the fatigue strength... 

The way to resolve the problem is quite clear, although not very straightforward. In fact, a predictive criterion of general validity and wide applicability can be developed only on the basis of an accurate description and understanding of the damage mechanisms under multiaxial loading, incorporating these quantitatively into the model formulation. 

A recent review by the authors [1] presents several works on fatigue damage under multiaxial loading. Unfortunately, most of these describe damage evolution... 

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