Issue 28

M.Malnati, Frattura ed Integrità Strutturale, 28 (2014) 12-1 8; DOI: 10.3221/IGF-ESIS.28.02 17 understoodwhen thinking that in the present approach, when the stress point goes forth and back on a segment - from a point to a secondpoint and then back to the initial point - then two identical yield surfaces are created. Explicitly: if a S EQ -N curve is available in which N has the meaning of number of complete cycles (from peak to peak), then the damageD j associated to the yield surface ‘j’ calculatedwith the presentmethodwill be: D j = j 1 2N (21) whereN j is the number of cycles on the S EQ -N curve corresponding to  EQ,j . Using the Palmgren-Miner law, the total damageD at a given instant of the complete stress history is given by: D= j j D  (22) P RELIMINARYVALIDATIONOFTHEMETHODOLOGY he approach presented in this paper needs obviously at least firstly a robust numerical implementation and secondly a wide validation, by comparisonwith data coming from test or literature. This activity is in progress, in order to reach a comprehensive substantiation of themethodology. It is the intention of the author to present the complete results in a forthcoming publication. At the present time, the main purpose of the paper is to submit, in a first time, this methodology to the judgment of the community working in the field of the fatigue analysis and dealing with the necessity of treating complicated spectra and non-proportional loading in aHCFmultiaxial context. Nevertheless, a first important element of the validation process is presented here: the scope is to prove that for an uniaxial closed sequence having Variable Amplitude (VA) cycles, the present methodology is equivalent to a classical 1-D rainflow counting (see e.g. [1]) in the sense that the size  EQ of the yield surfaces is equal to the amplitude of the 1-D stress cycles extracted by the rainflow. This has been tested by comparison between the present procedure and the rainflow counting prescribed in [16]: namely, a set of 10 uniaxial stress sequences has been created, each one made of 50 stress points randomly generated with probability uniformly distributed between -100 and+100MPa. The stress points have been preliminarily discretized using a stepof 1MPa. The cycles extracted from both the rainflow procedure [16] and the present approach have been compared in terms of stress amplitude and they have been found to be strictly identical. The figure below gives for one of the sequences the stress points aswell as the cycles extractedwith the twomethods. Figure 5 : Stress points of a test-sequence and amplitude of extracted cycles. C ONCLUSIONS n the previous paragraphs a general approach for multiaxial HCF crack initiation assessment has been presented. As mentioned in the Preliminary validation of the methodology paragraph, its validation by comparison with available experimental data is inprogress andwill be enclosed in a future publication. T I