Issue 37

Y. Wang et alii, Frattura ed Integrità Strutturale, 37 (2016) 241-248; DOI: 10.3221/IGF-ESIS.37.32 242 Fatigue criteria based on the concept of the critical plane are generally considered to be more accurate for multiaxial fatigue life estimation [1]. As far the low/medium cycle fatigue regime is concerned, the most successful criteria are seen to be those proposed by Smith, Watson and Topper [3], Brown & Miller [4, 5], Fatemi & Socie [6], and Susmel [7, 8]. As to the determination of the orientation of the critical plane, the MVM and the MDM are widely discussed in Refs [9- 11]. The MVM assumes that the damage in any material plane can be related to the variance of the stress/strain signal in that plane. The plane on which the variance of the resolved shear stain/stress reaches its maximum value is defined as the critical plane. The MDM postulates that the critical plane is that material plane which experiences the maximum extent of fatigue damage. The rainflow cycle counting method [12] has been most widely and successfully used under uniaxial loading. Among the methods dealing with VA multiaxial loading histories, Bannantine and Socie’s (BS) method [13] and Wang and Brown’s method [14, 15] deserve to be mentioned explicitly. Formalising an appropriate damage accumulation model is another tricky problem to be addressed properly in order to estimate fatigue damage under VA multiaxial loading [16,17]. Miner’s linear damage rule [18] is still the most used rule. In this paper, the accuracy of the MVM and the MDM in predicting the orientation of the critical plane is assessed. The accuracy of three procedures suitable for estimating multiaxial fatigue lifetime of metallic materials is checked against experimental data taken from the literature. The considered design procedures are as follows: (a) Procedure A: FS criterion applied with MDM, BS cycle counting method and Miner’s linear rule; (b) Procedure B: FS criterion applied with MVM, BS cycle counting method and Miner’s linear rule; (c) Procedure C: MMCCM applied with MVM, rainflow counting method and Miner’s linear rule. F ATIGUE CRITERIA FS criterion atemi and Socie [6] proposed a shear-strain based multiaxial fatigue criterion that can be expressed as follows:     0 0 c f f b f f y max n, N2 N2 G k1 2               (1) where   / 2 is the shear stain amplitude relative to the critical plane,  n,max is the maximum normal stress, k is a material constant, and   y is the material yield strength. MMCCM criterion The MMCCM [7, 8] postulates that the degree of multiaxiality and non-proportionality of the stress state at the critical location can be quantified through the following stress ratio: a max n, a n,a n,m        (2) where   a denotes the shear stress amplitude relative to the critical plane,  n,m and  n,a are the mean value and the amplitude of the stress normal to the critical plane, respectively, and  n, max is the maximal normal stress relative the critical plane. For a given value of    the profile of the corresponding modified Manson–Coffin curve can be described by using the following general relationship:                c f f b f f a N2 ) ( ' N2 G ) ( ' (3) where  ’ f (  ), b(  ),  ’ f (  ), and c(  ) are fatigue constants that can be determined from the fully-reversed uniaxial and torsional fatigue curves [7, 8]. F