Empfehlungen für die statistische Abschätzung des Zeit‐und Dauerfestigkeitsverhaltens von Stahl

Abstract

The introduction of recommendations for the proper application of elementary statistical methods to the planning of fatigue testing procedures and the subsequent analysis of the experimental data into international standards is probably imminent. Consequently, the inclusion in national specifications and standards seems to be only a question of time. This paper gives some basic guidelines of such recommendations dealing in detail with one of the most elementary methods which is aiming at the realization of so-called "statistically ascertained" Wohlerdiagrams. Therein, graphical explanations are preferred to computational ones. Additionally, the arc sine @transformation which until now has proved to be an outstanding evaluation method with special regard to engineering purposes, is reviewed. Both, the computational and the graphical way of evaluation are discussed and affiliated probability papers are given.

Arc sine % MathType!MTEF!2!1!+-% feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaaOaaaeaaca% WGqbaaleqaaaaa!36DD!\[\sqrt P \] transformation - an effective tool for graphical and numerical evaluation of planned W�hler experiments

“…Extended explanations of this transformation that can be traced back to Fisher [4], who employed it for variance stabilization to a problem in genetics, are given in the statistical literature [5][6][7][8][9]. Simplified numerical examples for evaluation of such results can be found among others in [1,11]. A considerable number of quite intensive research papers [12][13][14][15][16][17][18] revealed an entire series of advantages by using the arc sine V~ transformation for evaluation of fatigue test results.…”

“…The significance of the scatter and it's expected variations with the applied stress amplitude give grounds for statistical planning and evaluation of the fatigue tests [1][2][3]. In general these diagrams are determined by a rather arbitrary process of curve fitting through a relatively small number of points which present results of individual fatigue tests and are obtained as 'line of best fit'.…”

“…In view of the fact that a generally accepted distribution function of the fatigue strength is not known till today, the experimental data are commonly evaluated using one of several competing statistical models such as Gaussian distribution, Weibull or extreme value function, and arc sine x/P transformation [1]. Some of these models allow an extrapolation down to the estimates S(P = 0percent) in the transition range or N(P = 0percent) in the range of finite life, respectively, which cannot be directly ascertained experimentally.…”

Einfluß der Oberflächenbeschaffenheit auf die Schwingfestigkeit von Aluminium‐Druckguß

“…Die Diagramme enthalten ebenfalls die Geraden fur 50% Bruchwahrscheinlichkeit im Zeitfestigkeitsgebiet, sowie die Dauerfestigkeitswerte fur 5%, 50% und 95% Bruchwahrscheinlichkeit als horizontale Geraden im Ubergangsgebiet. Die zugrundeliegende statistische Auswertung erfolgte nach dem arcsin p-Verfahren [16].…”