Staircase Test Method

5 Stress-Based Fatigue Analysis High Cycle Fatigue 

In the case of Fig. 5.16 with d =20 MPa and i = 8, the criterion d 2 8 = 16 MPa is not respected so that we have to use Eq. (5.41) or increase the number of tests. We may also define an interval confidence within the true mean value of the fatigue limit oy 50% will fall 

43) ta,v is the student parameter relative to the chosen level of confidence C = (1 — a), listed in Table 4.5. We may also evaluate the Lower Confidence level, LCL, relative to the wanted confidence 

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Always with the material of the previous sample problems, it has been run another experimental campaign to assess the fatigue limit of the carbon steel by the staircase test method. On the base of the S-N curves of Fig. 5.21 it has been chosen an initial stress amplimde of 225 MPa at a run out of 1,000,000 cycles and a step size d = 10 MPa. Twenty-six button hourglass specimens of 8 mm minimum diameter have been used aU having the same surface finish of the real work pieces to be built. The results of the testing campaign are shown in Fig. 5.24. Fourteen specimens failed and 12 run out at 1,000,000 cycles. Therefore, the low frequency event of run out has been selected for calculations. The characteristic quantities are iV = 12, A = 19 and B = 37 (see Eq. 5.37). 

Fig. 5.25 Fatigue limit at 10° cycles inferred by staircase test method, shown on the previously determined S-N diagrams...

T.W. Anderson et al, NAVORD Rept 65-46 (1946) described seven varieties of staircase method including the Bruceton test. Natrella (Ref 42a) also gives several References to other discussions of the up-and-down or staircase method of testing... 

Run-Down Method. A statistical testing procedure developed at Frankford Arsenal, Philadelphia (Ref 1) which produces a more complete frequency and probability of reaction curve than the Bruceton, up-and-down, or staircase methods (see under Impact, Initiation of Explosion by in Vol 7, 136-R to I37-L). Although a larger number of tests is used than in the latter procedures, the method makes possible a better evaluation of the distribution of the population. Starting at a level expected to be between 0%... 

The up-and-down method, also called the Bruceton or staircase method, is a widely used statistical procedure for the determination of the height at which 50% of the samples detonate or react and its standard deviation [17,18]. The advantages and disadvantages of the method are described elsewhere [18-20] basically the test gives a reliable 50% value but not a reliable standard deviation. The number of tests required at each height also has been investigated [21]. 

Fig. 5. T5rpical results of a dart-drop test using the staircase method of analysis (12). To convert J to ft-lbf, divide by 1.35. Courtesy of the Society of Plastics Engineers.

Impact tests were performed according to ASTM D5420 using the Gardner impact tester. This method is used to determine the energy to fracture rigid polymers. In our ease, the Bruceton staircase method (up and down) was performed. A minimum of 20 samples were tested for each condition. 

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