Issue 38

A. Niesłony, Frattura ed Integrità Strutturale, 38 (2016) 177-183; DOI: 10.3221/IGF-ESIS.38.24 178  abnormal behaviour of the criterion under biaxial tension-compression loading condition in comparison to the experimental results presented in the literature,  influence of phase shift between particular stress state components on the value of equivalent stress. The aim of this paper is the clear presentation of the theoretical limitation and the area of practical application of the EMS criterion. Examples based on technical experiments are recalled which confirms the correctness of discussed limitations. Provided information are highly important for engineers which are using equivalent von Mises stress in frequency domain as well as for researchers who are working on new multiaxial fatigue failure criteria where von Mises stress is using as a part of the definition. E QUIVALENT VON M ISES STRESS CRITERION IN FREQUENCY DOMAIN he main reason for creating of this document are increasingly frequent, uncritical application of the Equivalent von Mises Stress (EMS) criterion in engineering calculations in the field of fatigue assessment. Since M.T. Huber in 1904 [7] and R. von Mises in 1913 [8] publish the theoretical background of the possibility of measurement of material effort by specific work of strain EMS criterion has become the most widely used in industry and science, among others in determining equivalent uniaxial stress, yield strength limit or other parameters used for example in constitutive equations [9]. Without going into details about derivation, which are well presented in many publications, the final equation for equivalent stress EMS criterion can be written as follow:         EMS xx yy yy zz zz xx xy yz zx 2 2 2 2 2 2 1 6 2                          (1) or         EMS xx xx xx xx xx yy zz zz xx xy yz zx 2 2 2 2 2 2 2 3 3 3                       (2) using proper components of the stress tensor: xx xy xz yx yy yz zx zy zz                     σ (3) In 1994 Preumont and Piefort [10] represent a breakthrough adapt of the von Mises criterion for determining the material fatigue directly in frequency domain. They propose to calculate of the power spectral density of equivalent von Mises stress directly in frequency domain as follow   EMS M G f f ( ) Trace ( )  Q G (4) However in the referenced paper [10] plane stress state was analysed presented method is well applicable also in spatial stress state with following power spectral density matrix:           xx xx xx yz yz xx yz yz G f G f f G f G f , , , ,            G      (5) defined according to vector of stress tensor components xx yy zz xy yz zx [ ]        S (6) and with von Mises coefficient matrix [11] T