Runout analysis in fatigue investigation

Abstract

Experiments to evaluate and validate processes of engineering and science are particularly important when the phenomena under investigation may be studied empirically, as can metal fatigue or medical injection dosages. Sometimes during an experiment, individual tests in a series are not completed, or must be suspended or interrupted, or are somehow damaged. Such test points are referred to as "suspended," or "censored points," or in the case of metal fatigue are simply called runouts. All these names refer to test specimens that do not fail under the same conditions as do other specimens or data points. In reliability and biometry, runout data are termed Type I censored observations. Inclusion of runouts in data analysis and interpretation can be problematic, and such ad hoc approaches as ignoring the runout observation or treating it as a failure can significantly affect estimation. Even when data are plotted and represented by a mathematical function utilizing least squares analysis to minimize data scatter about the "best fit" function, runouts and censored observations cause estimation problems because they cannot be incorporated directly into a leastsquares analysis procedure. This paper offers a methodology to help alleviate the problems presented by runouts and censored data. The methodology handles runouts and censored data by employing the maximum likelihood estimation (MLE) method to incorporate the censored data properly. The methodology is illustrated with an example problem.

Monotonic and fatigue behavior of five clinically relevant conventional and highly crosslinked UHMWPEs in the presence of stress concentrations

“…The data were fitted with the logarithmic transform of the mean relationship commonly used in failure analysis (Lawless, 2003; Sarkani et al, 2007): $$N=k{\sigma }^{-m}\text{therefore}\text{ln}N=-m\text{ln}\sigma +\text{ln}k$$ where N is the lifetime, σ is the axial engineering stress amplitude, and m and k are constants. As data is commonly presented in S-N diagrams the more familiar Basquin relationship (Dowling, 1999) is easily related to the mean relationship: $$\sigma =A{N}^b\text{therefore}b=-\frac{1}{m}\text{and}A=k^{-\left(\frac{1}{m}\right)}$$…”

“…Instead, the method of maximum likelihood estimation (MLE) with unbiased estimators was used, as is commonly done in reliability testing (Lawless, 2003; Sarkani et al, 2007). The advantage of using MLE is that censored data (runout) is considered, rather than using other approaches that are commonly used that either ignore or count runout as a failure point (Sarkani et al, 2007).…”

“…Instead, the method of maximum likelihood estimation (MLE) with unbiased estimators was used, as is commonly done in reliability testing (Lawless, 2003; Sarkani et al, 2007). The advantage of using MLE is that censored data (runout) is considered, rather than using other approaches that are commonly used that either ignore or count runout as a failure point (Sarkani et al, 2007). For this type of modeling the mean relationship is used in its log transform with the underlying failure distribution being a Weibull distribution at all applied stresses (Collins, 1993; Sarkani et al, 2007).…”

“…The advantage of using MLE is that censored data (runout) is considered, rather than using other approaches that are commonly used that either ignore or count runout as a failure point (Sarkani et al, 2007). For this type of modeling the mean relationship is used in its log transform with the underlying failure distribution being a Weibull distribution at all applied stresses (Collins, 1993; Sarkani et al, 2007). Coefficient of determination (R 2 ) values were calculated using the generalized definition of R 2 proposed by Nagelkerke (Nagelkerke, 1991).…”

Estudo do comportamento em fadiga de alto ciclo da liga Ti-13V-11Cr-3AI

“…Estes pontos são referenciados como 'suspensos', 'pontos censurados', ou no caso da fadiga, são chamados de runouts (SARKANI et al, 2007 iii) Foi realizada a análise gráfica resultando em uma resistência de 66 N/mm 2 .…”