PSI - Issue 41

234 Karolina Głowacka et al. / Procedia Structural Integrity 41 (2022) 232 – 240 Głowacka K., Łagoda T./ Structural Integrity Procedia 00 ( 2019) 000 – 000 notation, i.e. 1 = , 2 = , 6 = . The most popular stress criteria include the maximum strain criterion and the Azzi-Tsai-Hill criterion proposed by Sun at all. (1996). In the case of the maximum strain criterion, in fact, the stresses in each direction are analyzed separately, so this criterion will not be taken into account in this study aimed at analyzing the complex stress state. For comparison with the Azzi-Tsai-Hill (ATH) criterion in the form Hill (1942) and Azzi and Tsai (1965) ( 1 ) 2 + ( 2 ) 2 − 1 2 2 + ( 6 ) 2 = 1 (1) the criterion proposed by Norris (1962) will be considered, which has a form of ( 1 ) 2 + ( 2 ) 2 − 1 2 + ( 6 ) 2 = 1 (2) As can be seen from formulas (1) and (2), these criteria have a very similar form and genesis, because they are a generalization of the Huber-Mises-Hencky criterion for orthotropic materials, they differ only in the value in the denominator of the component concerning the relation between normal stresses occurring in both directions. The Norris criterion was taken into account primarily because although the ATH criterion is among the most popular criteria, in fact the Norris criterion better reflects the generalization of the HMH hypothesis. Assuming the parallelism of the basic fatigue characteristics of the specimens cut at 0° and 90° and defining the values of X, Y and S, which are maximum values of stress in different directions, we modified criteria proposed by Azzi-Tsai-Hill based on (1) = √ 1 2 + ( 2 ) 2 − 1 2 + ( 6 ) 2 (3) and by Norris – eq. (2) = √ 1 2 + ( 2 ) 2 − 1 2 + ( 6 ) 2 (4) Here it should be noted that in the case of an incomplete plane stress state ( 2 = 0 ) we obtain the Gough-Pollard criterion (1935) known and popularly used in fatigue. This criterion has already been used in the case of static tests of the composites Łagoda at all. (2019) . Additionally, it can be noticed that a special case of the presented criterion is the situation when = √3 . Then the equation takes the form of the Huber-Mises-Hencky criterion commonly used to describe isotropic material tests in static and in the case of proportional fatigue tests It is also worth adding that although the determination of the value of equivalent stresses is not a popular solution in the case of composite materials analysis, in the literature one can find experimental studies which show that certain unified parameters of a very similar form can be successfully applied. An example is the work published by Plumtree and Cheng (1999), in which a parameter was proposed that considers the occurring normal and shear stresses occurring in the laminate in fatigue tension in terms of the direction of the fibers ’ arrangement. As it has been proved, they have obtained the correct characteristics, both when the stresses determining the failure were normal and shear stresses. Kawai (2004) proposed the use of criterion (3) as a function of the specimens cut angle in relation to the composite directivity in the form ∗ = ( ) , (5) where ( ) is a function dependent on the angle θ and strength in directions X, Y, S. 3