Estimation of P‐S‐N curves in very‐high‐cycle fatigue: Statistical procedure based on a general crack growth rate model

Abstract

Extensive experimental investigations show that internal defects play a key role in the very‐high‐cycle fatigue (VHCF) response of metallic materials and that crack growth from internal defects can take place even if the stress intensity factor associated to the initial defect is below the threshold for crack growth. By introducing a reduction term in the typical formulation of the threshold for crack growth, the authors recently proposed a general phenomenological model, which can effectively describe crack growth from internal defects in VHCF. The model is able to consider the different crack growth scenarios that may arise in VHCF and is enough general to embrace the various weakening mechanisms proposed in the literature for explaining why crack can grow below the threshold. In the present paper, the model is generalized in a statistical framework. The statistical distributions of the crack growth threshold and of the initial defect size are put into the model. The procedure for the estimation of the Probabilistic‐S‐N curves and of the fatigue limit distribution is illustrated and numerically applied to an experimental dataset.

Very high cycle fatigue life and critical defect size: Modeling of statistical size effects

“…Two different large volumes with constant stress are highlighted in Figure 1: the first one, v i , is in a region with stress equal to 13.75% of the maximum stress; the second one, v j , is larger and in a region with larger stress (equal to 92.75% of the maximum stress). Volume v j is the one subjected to a larger stress and, according to the statistics of extremes, 17,33,51 is the one with larger probability of including a large defect. Therefore, if compared to v i , v j more probably contains the critical defect.…”

“…If volume v i is considered, then a given largest defect size , which is randomly extracted from , and a given local stress level s i must be taken into account to estimate the VHCF life associated to v i . Indeed, it is well known in the literature 16,17,32,51,52 that the VHCF life depends both on the stress amplitude and on the defect size. It is worth to note that, to simplify the statistical model, several approximations must be tolerated (e.g., defect shape and composition as well as three‐dimensional effects 53,54 at the initial defect are not taken into account).…”

A Study of Probabilistic Diagnosis Method for Three Kinds of Internal Combustion Engine Faults Based on the Graphical Model

“…The inertial force can be described as the combination of the reciprocating inertial force generated by the reciprocating mass with the centrifugal force generated by the rotating mass. As such, the prior probabilities can be described by the Probabilistic-S-N curve (P-S-N curve) of the material [30] based on the Bayesian theory. According to the probability model presented by Feng et al [31], the survival probability density function of a material parameter is…”

Methodology for assessment of statistical planning effects on the S‐N curve determination using Monte Carlo simulations

“…The great scatter of fatigue test results requires a special plan for the experiment. Many studies focused on fatigue properties were and still are being developed, such as Shen, 4 Pascual and Meeker, 5 Gope,6,7 Pinto et al, 8 Pascual, 9 Lorén and Lundström, 10 Paolino et al, 11 Pang et al, 12 Strzelecki and Sempruch 13,14 and Strzelecki and Tomaszewski, 15 and Paolino et al 16 In these researches, different practices and experimental plans were studied to obtain the S-N curves, as well as probabilistic methods were employed. The Monte Carlo simulation is an important statistical tool to analyze fatigue data, since fatigue life is probabilistic and not deterministic.…”