Method for the evaluation of the service life under random loading based on the energy criterion of fatigue fracture

Abstract

We propose a method aimed at the assessment of the service life of structural elements under random loads based on the energy criterion of fatigue fracture and the model of cyclic deformation of materials after overloading. The possibility of determination of the maximum amplitude of stresses according to the number of loading cycles prior to fracture is substantiated. The results of evaluation of the service life under conditions of uniform stressed state are compared with the experimental data obtained by Swanson, Raikher spectral hypothesis of summation of defects, and linear hypothesis of summation. The dependence of the right-hand side of the linear hypothesis equation on the dispersion of the random loading process is established.Introduction. The service life of structural elements is, to a significant extent, determined by the spectrum of acting loads. In the stage of operation of a product, the loads are determined more precisely by recording the realizations of the force factor in time. The obtained realizations are processed by the methods of schematization of random processes. The methods of full cycles and "rain flow" are used especially extensively. The second method is often regarded as preferable because it allows one to form closed hysteresis loops. As a result of processing, we get the tables of differential repetition frequency of the loads characterizing the number of cycles of repetition of combinations of the amplitude and mean values. A method for the evaluation of the service life based on the energy fracture criterion was proposed for loads specified as indicated above in [1].In the stage of design, the loads can be found by the methods of statistical dynamics when the perturbing factor is analyzed in the probabilistic aspect. The random loading process is supposed to be stationary and normal with known spectral density and the distribution function of amplitudes of the force factor. In [2], a method for the evaluation of service life on the basis of the linear hypothesis of summation of fatigue defects is proposed within the framework of this approach. In [3], a hypothesis of spectral summation of defects is advanced and the comparison of the experimental and published data is realized. The results of calculations carried out according to the linear and spectral hypotheses either coincide or are sufficiently close. In [3], it is indicated that, for the Swanson experiment, the disagreement between the experimental data and numerical results is substantial. Indeed, in this case, the service life determined according to the numerical results is overestimated by about an order of magnitude.The aim of the present work is to develop a method aimed at the assessment of the service life under random loading realized under conditions of uniform stressed state on the basis of the energy approach to the process of fatigue fracture. Similar methods for the programmed, block, and biharmonic loads are proposed in [1,4,5].Theoretical Foundations. First, we consider some dependences typical of normal st...