Issue 33

A. Bolchoun et alii, Frattura ed Integrità Strutturale, 33 (2015) 238-252; DOI: 10.3221/IGF-ESIS.33.30 239 react with a shorter fatigue life to non-proportional loadings [1]. This behavior is also exhibited by welded joints of steel, aluminum and magnesium [2-6]. If fatigue life evaluation is performed using stress-based hypotheses, taking non- proportionality into account in a correct manner is a rather difficult task. Most of the stress-based hypotheses compute a longer fatigue life under non-proportional loadings unless there is some explicit non-proportionality measure ‘built in’ into the hypothesis. Examples of such hypotheses are ESSH [7], SSCH [3, 5], MWCM [8]. For other stress-based hypotheses an external non-proportionality factor can be introduced and so improve fatigue assessment under non-proportional loadings. Such non-proportionality factors similarly to the stress-based hypotheses can be subdivided into two large families: the integral and the critical plane based factors. To the first family belong the non-proportionality factors introduced by Bishop [9], Gaier [10], Sonsino [7] and the new non-proportionality factor based on the statistical correlation of stress components [11], which is presented in the current paper. These factors make use of integral stress values. The non- proportionality factors by Susmel (MWCM) [8] and Kanazawa [12] are critical plane based values. For factors of this type a critical plane (in both cases plane with the highest shear stress amplitude) is determined and then certain stress relations, which belong to the critical plane are computed and used as a non-proportionality measure. The non-proportionality factors introduced by Gaier and Bishop are an improvement over the factor introduced by Chu et al. [13], which does depend on the choice of coordinate system. Most of the non-proportionality factors under discussion attend values between 0 and 1 also evaluation of variable amplitude loadings can be performed using all the factors. Other important features are independence on material properties (only the time-dependent stress tensor path is used for evaluation of the non-proportionality) as well as independence on the choice of the coordinate system. As an illustration for the application of the non-proportionality factors the Findley criterion is used to evaluate fatigue life of aluminum and magnesium welded joints. N ON - PROPORTIONALITY FACTORS OF INTEGRAL TYPE his class of non-proportionality factors involves some form of integral evaluation of stresses in different planes. Depending on the situation those can be planes orthogonal to the specimen surface (plane stress state) or arbitrary oriented planes (general stress state). Computation of these factors to variable amplitude loadings can require a sufficiently fine sampling of the time-dependent loading path and/or a sophisticated integration procedure. With the only exception all factors discussed in this section yield values between 0 and 1, with 0 being the value for the proportional loading and 1 being ascribed to the ‘most non-proportional case’. Exact definition of the ‘most non-proportional case’ is different for each factor. Non-proportionality factors due to Bishop and Gaier Bishop proposed two measures of the non-proportionality or, more precisely, out-of-phase measures [9]. Non- proportionality obtained due to the presence of mean stresses in the case of in-phase time-dependent parts is neglected. The measures are based on the notion of the principal axes of a tensor path. A stress tensor x xy xz xy y yz xz yz z                     σ (1) is mapped to the vector   ,  2 ,  ,  2 ,  2 ,   x xy y xz yz z         σ x (2) The scaling factor 2 for the shear stresses results in the identity: 1 2 1 2 :   x x σ σ (3) for any two vectors 1 x and 2 x , on which the tensors 1 σ and 2 σ respectively are mapped. The identity (3) in turn results in the independence of the choice of the coordinate system for the values introduced below. A tensor path is defined if T