Crack simulation models in variable amplitude loading - a review

L. C. H. Ricardo et alii, Frattura ed Integrità Strutturale, 35 (2016) 456-471; DOI: 10.3221/IGF-ESIS.35.52 Crack simulation models in variable amplitude loading - a review Luiz Carlos H. Ricardo Materials Technology Department, IPEN, University of São Paulo, Brazil, Instituto de Pesquisas Energéticas e Nucleares Av. Lineu Prestes 2242 - Cidade Universitária - São Paulo - SP BRASIL- CEP: 05508-000. Carlos Alexandre J. Miranda Nuclear Engineering Department, IPEN, University of Sao Paulo, Brazil, Instituto de Pesquisas Energéticas e Nucleares Av. Lineu Prestes 2242 - Cidade Universitária - São Paulo - SP BRASIL- CEP: 05508-000 ABSTRACT. This work presents a review of crack propagation simulation models considering plane stress and plane strain conditions. It is presented also a chronological different methodologies used to perform the crack advance by finite element method. Some procedures used to edit variable spectrum loading and the effects during crack propagation processes, like retardation, in the fatigue life of the structures are discussed. Based on this work there is no consensus in the scientific community to determine the best way to simulate crack propagation under variable spectrum loading due the combination of metallurgic and mechanical factors regarding, for example, how to select and edit the representative spectrum loading to be used in the crack propagation simulation. KEYWORDS. Fatigue; Crack propagation simulation; Finite element method; Retardation. INTRODUCTION T he most common technique for predicting the fatigue life of automotive, aircraft and wind turbine structures is Miner’s rule [1]. Despite the known deviations, inaccuracies and proven conservatism of Miner’s cumulative damage law, it is even nowadays being used in the design of many advanced structures. Fracture mechanics techniques for fatigue life predictions remain as a back up in design procedures. The most important and difficult problem in using fracture mechanics concepts in design seems to be the use of crack growth data to predict fatigue life. The experimentally obtained data is used to derive a relationship between stress intensity range (K) and crack growth per cycle (da/dN). In cases of fatigue loaded parts containing a flaw under constant stress amplitude fatigue, the crack growth can be calculated by simple integration of the relation between da/dN and K. However, for complex spectrum loadings, simple addition of the crack growth occurring in each portion of the loading sequence produces results that, very often, are more erroneous than the results obtained using Miner’s rule with an S-N curve. Retardation tends to cause conservative results using Miner’s rule when the fatigue life is dominated by the crack growth. However, the opposite effect generally occurs when the life is dominated by the initiation and growth of small cracks. In these cases, large cyclic strains, which might occur locally at stress raisers due to overload, may pre-damage the material and lower its resistance to fatigue. The experimentally derived crack growth equations are independent of the loading sequence and depend only on the stress intensity range and the number of cycles for that portion of the loading sequence. The central problem in the successful utilization of fracture mechanic techniques applied to the fatigue spectrum is to obtain a clear understanding of 456 L. C. H. Ricardo et alii, Frattura ed Integrità Strutturale, 35 (2016) 456-471; DOI: 10.3221/IGF-ESIS.35.52 the influence of loading sequences on fatigue crack growth [2]. Investigations covering the effects of particular interest, after high overload, in the study of crack growth under variable-amplitude loading in the growth rate region, called crack growth retardation, seem to have little interest nowadays. Stouffer & Williams [3] and other researchers show a number of attempts to model this phenomenon through manipulation of the constants and stress intensity factors in the Paris-Erdogan equation however little appears to have been done in the effort to develop a completely rational analysis of the problem. Probably, the only one reason that the existing models of retarded crack growth are not satisfactory is that these models are deterministic whereas the fatigue crack growth phenomenon shows strong random features. In addition, most of the reported theoretical descriptions of the retardation are based on data fitting techniques, which tend to hide the behavior of the phenomenon. If the retarding effect of a peak overload on the crack growth is neglected, the prediction of the material lifetime is usually very conservative [4]. Accurate predictions of the fatigue life will hardly become possible before the physics of the peak overload mechanisms is better clarified. According to the existing findings, the retardation is a physically very complicated phenomenon which is affected by a wide range of variables associated with loading, metallurgical properties, environment, etc., and it is difficult to separate the contribution of each of these variables [5]. CRACK PROPAGATION CONCEPTS I rwin [6,7] defines in his work a release energy rate G, which is a measure of the available energy, dП-potential of energy and A-crack area, to provoke crack propagation as shown in Eq. (1). The term rate as employed is not related to a derivate in relation to the time but is referred to a change in the potential energy rate in the crack area. Later, this quantity has been called K, and is used to characterize the stress state ("stress intensity") near a crack tip caused by a remote load or residual stress in isotropic and elastic bodies. The stress field in the crack tip is given by Eq. (2), G d dA  ij  K (2 r )1/2 f ij (  )  A2 g ij (  )  A3hij (  )r 1/2  ...... (1) (2) where K is the stress intensity factor; r and  are the distance from the crack tip and the angle between the crack tip and the plane of the crack, respectively; Ai is a constant of the material; fij (), gij () and hij() are functions of ..After years, the stress-intensity factors for a large number of crack configurations have been generated; and these have been collated into several handbooks (see, for example, Refs [8,9]). The use of K is meaningful only when small-scale yielding conditions exist. Plasticity and nonlinear effects will be covered in the next section. Because fatigue-crack initiation is, in general, a surface phenomenon, the stress-intensity factors for a surface- or corner-crack in a plate or at a hole, such as those developed by Raju and Newman [10,11], are solutions that are needed to analyze small-crack growth. Some of these solutions are used later to predict fatigue-crack growth and fatigue lives for notched specimens made of a variety of materials [12]. Frost and Dugdale [13] have evidenced that the size of the plastic zone increases in the same ratio that of the crack length. One can notice that the results of the equati (...truncated)