Issue34

Z. Marciniak et alii, Frattura ed Integrità Strutturale, 34 (2015) 1-10; DOI: 10.3221/IGF-ESIS.34.01 2 determine critical plane position. Many scientists became interested in these studies, which resulted in numerous contacts and team work, e.g. with Carpinteri [5, 6], Sakane [7], Sonsino [8], Dragon [9], Petit [9], and others. The purpose of this study is to present academic achievements of Professor Macha. M ATHEMATICAL MODELS AND THEIR EXPERIMENTAL VERIFICATION ne of the first criteria proposed by E. Macha for multiaxial random loads [1, 2] has the following form:   max ( ) ( ) ns n t B t K t F     (1) where ( ) ns t  and ( ) n t  are: shear stress and normal stress in fracture plane, respectively; and B, K, F – constants for the selection of a given criterion version. Initially, in this criterion fracture plane was regarded as the critical plane. However subsequent analyses make it possible to observe that this plane changes especially for elastic-plastic materials. Detailed criterion guidelines are: (i) fatigue crack is generated (caused) by the activity of normal stresses σ n (t) and shear stresses τ ns (t) in the direction s  in plane with normal n  , (ii) direction s  is concurrent with average direction of shear stresses. In the criteria related to critical plane it is very important to determine critical plane position. In order to determine its position, it was proposed to apply the weight function method. The weight function method involves finding averaged positions of main axes directions through properly selected weight functions W k . 1 1 1 1 ˆ cos L k k k l W W     , 2 2 1 1 ˆ cos L k k k m W W     , 3 3 1 1 ˆ cos L k k k n W W     , (2) where: 1 L k k W W    - sum of weights, L – number of averages,  1 , β 2 ,  3 – angles between main stresses and axes in the Cartesian coordinates, (  1 , x), (  2 , y), (  3 , z), respectively Then, critical plane position is being determined relative to these averaged directions. 6 weight functions are demonstrated in the study [1]: - Weight I – W k = 1 – it is assumed that each position of the main axes has the same effect on the critical plane position, - Weight II – 1 1min 1max 1min k k W        for k = 1, 2,…,N – this weight reduces the impact of maximum main stress  1 (t) value on the critical plane position, - Weight III – 1 1 0 0 1 1 k af k k af for a W a for a                for k = 1, 2,…,N – according to this weight , only those positions of main axes are averaged, for which maximum stress value is  1 (t)  a·  f , where  f is fatigue limit, - Weight IV – 1 1 0 1 k e k k e for R W for R              for k = 1, 2,…,N – only those positions of main axes are averaged, for which maximum stress value  1 (t) is higher than product of Poisson’s ratio and yield point, O