Inverse Power Law Relationship Introduction

The inverse power law (IPL) model (or relationship) is commonly used for non-thermal accelerated stresses and is given by:

(1)

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where,

· L represents a quantifiable life measure, such as mean life, characteristic life, median life, B(x) life, etc.,

· V represents the stress level,

· K is one of the model parameters to be determined, (K > 0),

and,

· n is another model parameter to be determined.

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Fig. 1: The inverse power law relationship on linear scales at different life characteristics and with a Weibull life distribution.

The inverse power law appears as a straight line when plotted on a log-log paper. The equation of the line is given by:

(2)

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Plotting methods are widely used in estimating the parameters of the inverse power law relationship since obtaining K and n is as simple as finding the slope and the intercept on Eqn. (2).

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Fig. 2: Graphical look at the IPL relationship (log-log scale)

A Look at the Parameter n

The parameter n in the inverse power relationship is a measure of the effect of the stress on the life. As the absolute value of n increases, the greater the effect of the stress. Negative values of n indicate an increasing life with increasing stress. An absolute value of n approaching zero indicates small effect of the stress on the life, with no effect (constant life with stress) when n = 0.

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Fig. 3: Life vs. stress for different values of n.