IPL and Coffin Manson Relationship

In accelerated life testing analysis, thermal cycling is commonly treated as a low-cycle fatigue problem, using the inverse power law relationship. Coffin and Manson suggested that the number of cycles-to-failure of a metal subjected to thermal cycling is given by [28],

(11)

$images\8_7_11.gif$

where,

· N is the number of cycles to failure,

· C is a constant, characteristic of the metal,

· $images\yy.gif$ is another constant, also characteristic of the metal,

and

· $images\tri.gif$ T is the range of the thermal cycle.

This model is basically the inverse power law relationship, where instead of the stress, V, the range $images\tri.gif$ V is substituted into Eqn. (30). This is an attempt to simplify the analysis of a time-varying stress test by using a constant stress model. It is a very commonly used methodology for thermal cycling and mechanical fatigue tests. However, by performing such a simplification, the following assumptions and shortcomings are inevitable. First the acceleration effects due to the stress rate of change are ignored. In other words, it is assumed that the failures are accelerated by the stress difference and not by how rapidly this difference occurs. Secondly, the acceleration effects due to stress relaxation and creep are ignored.

Example

In this example the use of Eqn. (11) will be illustrated. This is a very simple example that can be repeated at any time. The reader is encouraged to perform this test.

Product: ACME Paper Clip Model 4456

Reliability Target: 99% at a 90% confidence after 30 cycles of 45°.

After consulting with our paper-clip engineers, the acceleration stress was determined to be the angle to which the clips are bent. Two bend stresses of 90° and 180° where used. A sample of six paper clips was tested to failure at both 90° and 180° bends with the following data obtained.

$images\8_71ex.gif$

The test was performed as shown in the next figures (a side-view of the paper clip is shown).

$images\degrees.gif$

Using the IPL lognormal model, determine whether the reliability target was met.

Solution

By using the IPL relationship to analyze the data, we are actually using a constant stress model to analyze a cycling process. Caution must be taken when performing the test. The rate of change in the angle must be constant and equal for both the 90° and 180° bends and constant and equal to the rate of change in the angle for the use life of 45° bend. Rate effects are influencing the life of the paper clip. By keeping the rate constant and equal at all stress levels, we can then eliminate these rate effects from our analysis. Otherwise the analysis will not be valid.

The data are entered and analyzed using ReliaSoft's ALTA.

$images\paperalta.gif$

The parameters of the IPL-lognormal model were estimated to be,

$images\op.gif$ = 0.198533,

K = 0.000012,

n = 1.856808.

Using the QCP, the 90% lower 1-sided confidence bound on reliability after 30 cycles for a 45° bend was estimated to be 99.6%, as shown below.

$images\paper-clip_qcp.gif$

This meets the target reliability of 99%.