Expected principal stress directions under multiaxial random loading. Part I: theoretical aspects of the weight function method

Multiaxial effects on LCF behaviour and fatigue failure of AZ31B magnesium extrusion

“…Detailed information about the loading amplitudes, phase angle and most importantly initial crack orientation were not reported for each specimen. Carpinteri and coworkers [85][86][87][88][89] proposed a multiaxial high-cycle fatigue criterion based on critical plane approach. According to this criterion, the critical plane is determined using average principal stress directions because they vary with time.…”

“…The averaging process was employed by weigh function method. The significance of the proposed idea in [85,86] is the fact that it does not assume that final fracture plane is normal to one of the principal stress directions even though it is known that principal stresses are fundamental in life prediction. Carpinteri et al [85][86][87][88][89] were able to obtain satisfactory prediction of the cracking plane.…”

A Review of Critical Plane Orientations in Multiaxial Fatigue Failure Criteria of Metallic Materials

“…Directions n and s may be computed by three methods: the weight function method, the damage accumulation method, the variance method. The weight function method (Macha, 1988, 1989, Carpinteri et al, 1999a consists in the weighted averaging process of the parameters which describe the instantaneous locations of the principal stress axes. Averaged directions of the principal stress axes determine averaged directions of maximum shear stresses as well.…”

A stress-based fatigue criterion to assess high-cycle fatigue under in-phase multiaxial loading conditions

“…The calculation of the critical plane is performed in two steps. First, the weighted mean direction of the maximum principal stress under multiaxial random loading is estimated [20][21][22][23][24][25]. According to this concept, the fatigue failure assessment is presented by considering a quadratic combination of the maximum normal stress (r max ) and the shear stress amplitude (s a ) in the following form:…”