Research program
Methods for fatigue resistance evaluation of notched structural components under multiaxial loading
University Co-ordinator
Università degli Studi di PARMA -
INGEGNERIA CIVILE, DELL'AMBIENTE, DEL TERRITORIO E ARCHITETTURA - PARMA(PR)
Research Unit Leader
Andrea CARPINTERI
Description
The fatigue life evaluation of a notched structure subjected to multiaxial loading can be performed by applying methods based on the so-called critical plane approach. According to such an approach, the fatigue failure assessment is performed in a plane where the amplitude or the value of some stress components or a combination of them attains its maximum. Alternatively, the position of the critical plane may be correlated with that of the principal stress axes, since it has long been recognised that principal stress directions influence fatigue phenomena. On the other hand, the principal stress directions under fatigue loading are generally time-varying and, therefore, averaged principal stress directions should be considered by deducing them, for example, through appropriate weight functions. Aim of the present research project is to develop a criterion which correlates the critical plane orientation with the weighted mean principal stress directions. Then, the fatigue failure assessment of a notched structure can be performed by considering a combination of normal and shear stress components acting on the critical plane. In more detail, the research objectives are summarised in the following.OBJECTIVE No. 1 (1st year, 1st semester)Development of a criterion for multiaxial cyclic loading with a constant amplitude, in the high-cycle regime. Such a criterion will analyse the stress state at a "hot spot" of the structural component being considered. The averaging procedure of the time-varying principal stress directions will allow us to analyse even the case of nonproportional loading (e.g. out-of-phase loading, asynchronous loading, complex loading paths). The orientations of both dominant fatigue fracture plane and critical plane (verification plane) can be correlated with the weighted averaged principal stress directions. Amplitude and mean value of stress components acting on the critical plane can be defined and used to perform fatigue failure assessment. In particular, a nonlinear combination of the amplitude of the shear stress and of the maximum value of the normal stress acting on the critical plane might be considered. The multiaxial condition of fatigue limit should be first analysed. Accordingly, the safety domain against fatigue failure, described in the diagram of the shear stress amplitude against the maximum normal stress related to the critical plane, can be built up.By employing the classical Basquin relationship, the above criterion will be used to evaluate also fatigue life (in the high-cycle regime) under generic multiaxial loading conditions.Experimental results available in the literature should be used to thoroughly validate the criterion. Such experimental data are mainly related to smooth specimens made up of hard metals (for these materials, the ratio between the endurance limit under fully reversed torsion and that under fully reversed bending ranges from 0.58 and 1), whereas test loading conditions include: bending and torsion (round bar specimens), push-pull and internal pressure (tubular specimens), biaxial normal loading (cruciform specimens). The basic multiaxial loading being considered will concern synchronous sinusoidal in-phase and out-of-phase plane stress states with or without mean stresses, although experimental data for more complex constant amplitude cyclic loading conditions will also be examined. Some experimental tests will be performed by the Unit of Parma to integrate the experimental data available in the literature.OBJECTIVE No. 2 (1st year, 2nd semester)The aim will be to extend the above criterion to complex multiaxial loading conditions. In particular, variable amplitude loading should be considered. The essential issue of how cycles should be identified and damage computed for each cycle in a complex loading history will be addressed. By introducing a suitable cyclic counting method and a damage model, fatigue evaluation will be performed. Relevant experimental data available in the literature (including random loading) will be processed in order to verify the reliability of the proposed criterion. Some experimental tests will be performed by the Unit of Parma to integrate the experimental data available in the literature.OBJECTIVE No. 3 (2nd year, 1st semester)The aim will be to extend the criterion to the low-cycle fatigue regime. By considering normal and shear stresses acting on the critical plane, total strain energy density per cycle can be calculated. In such a way, a combined criterion based on the critical plane approach and the energy approach can be developed. The use of energy-based parameters to perform fatigue evaluation will allow us to take into account the influence of plastic deformations. Note that such parameters will be related to a specific plane (the critical plane previously defined). The above energy-based criterion will be applied under constant amplitude multiaxial loading (e.g. sinusoidal synchronous plane stress states). Some experimental data concerning low-cycle fatigue will be considered to validate the model. Some experimental tests will be performed by the Unit of Parma to integrate the experimental data available in the literature.OBJECTIVE No. 4 (2nd year, 2nd semester)Within the framework of the original stress-based approach, an attempt to tackle fatigue evaluation using non-local concepts will be performed. Accordingly, fatigue failure assessment will be carried out by considering the stress state not only in a single point but in a finite region of a structural component. In such a way, stress gradient effects, which are well-known to influence fatigue strength, will be included in the modelling. Such stress gradient conditions can originate from the loading conditions or the presence of notches (note that notches generate multaxial stress states in the notch neighbourhood even in uniaxially loaded structural components). A comparative analysis of experimental results showing the influence of stress gradient on fatigue behaviour will be undertaken. For instance, according to the proposed non-local approach, fatigue limit for smooth bars under combined normal and shear stresses should theoretically change depending on the stress gradient generated by the acting normal stress (zero stress gradient for traction, constant stress gradient for plane bending or rotating bending). Furthermore, the actual stress field near the notch should be considered to define the size of the finite volume (of material) used for fatigue evaluation. Hence, as has experimentally been observed, the predicted fatigue strength of a notched structural component should turn out to be dependent on the stress gradient, conversely to what would be predicted according to the local criterion (see Objective No. 1).Finally, some stress and strain analyses on mechanical and civil structural components, typically prone to fatigue failures, will be undertaken through numerical models. Then, by applying the proposed criterion, iso-fatigue life contours will be determined.
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