Tensile Components Example

Tensile Components Example

A tensile component of a landing gear was put through an accelerated reliability test to determine whether the life goal would be achieved under the designed-in load. Fifteen units, N=15, were tested at three different shock loads. The component was designed for a peak shock load of 50 kips with an estimated return of 10% of the population by 10,000 landings. Using the inverse power law lognormal model, determine whether the design life was met.

Failure, in Cycles	Shock Load, kips
1855	73
2158	73
2425	73
2736	73
3206	73
614	95
770	95
781	95
890	95
1055	95
152	128
162	128
173	128
209	128
216	128

Solution

The data were entered into ALTA, and the following estimates were obtained for the parameters of the IPL-lognormal model:

[math]\displaystyle{ \begin{align} Std=\ & 0.179080 \\ K=\ & 8.953055E-13 \\ n=\ & 4.638882 \end{align} }[/math]

The probability plot at each test stress level (73 kips, 95 kips and 123 kips) was then obtained, as shown next.

Probability plots at different shock loads.

In this plot, it can be seen that there is a good agreement between the data and the fitted model. The probability plot at a use stress level of 50 kips is shown next.

The probability plot at a use stress level of 50 kips.

Using the Use Level Probability plot, the cycles-to failure for a 10% probability of failure can be estimated. From the plot, this time is estimated to be [math]\displaystyle{ T(Q=0.10=10%)\approxeq 12,000 }[/math] landings. Another way to obtain life information is by using a Life vs. Stress plot. Once a Life vs. Stress plot is selected, the 10% unreliability (probability of failure) line must be plotted. To do this, click Life Lines... in the plot panel and and select the 10% Unreliability box (or enter 10 in one of the boxes and select the box) in the Specify Life Lines window, as shown next.

In the following plot, the 10% unreliability line is plotted (the first line from the left). For a stress of 50 psi (X-axis) and for the 10% unreliability line, the cycles-to-failure can be obtained by reading the value on the Y-axis. Again, [math]\displaystyle{ T(0.1)\approxeq 12,000 }[/math] landings.

Median Life line (right) and 10% unreliability line (left) vs. stress.

However, a more accurate way to obtain such information is by using the Quick Calculation Pad (QCP) in ALTA. Using the QCP, the life for a 10% probability of failure at 50 kips is estimated to be 11,669.1 cycles (or landings), as shown next.

The design criterion of 10,000 landings is met.