Eyring Relationship Introduction

The Eyring model was formulated from quantum mechanics principles [9] and is most often used when thermal stress (temperature) is the acceleration variable. However, the Eyring relationship is also often used for stress variables other than temperature, such as humidity. The relationship is given by:

(1)

$images\7_1_1.gif$

where,

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

· V represents the stress level (temperature values in absolute units, i.e. degrees Kelvin or degrees Rankine)

· A is one of the model parameters to be determined,

and,

· B is another model parameter to be determined.

$images\f0rz3h0h.gif$

Fig. 1: Graphical look at the Eyring relationship (linear scale), at different life characteristics and with a Weibull life distribution.

The Eyring relationship is similar to the Arrhenius relationship. This similarity is more apparent if Eqn. (1) is rewritten in the following way:

$images\7_1_0.gif$

or,

(2)

$images\7_1_2.gif$

The Arrhenius relationship is given by:

$images\7_1_3.gif$

Comparing Eqn. (2) to the Arrhenius relationship, it can be seen that the only difference between the two relationships is the $images\1v.gif$ term in Eqn. (2). In general, both relationships yield very similar results. Like the Arrhenius, the Eyring relationship is plotted on a log-reciprocal paper.

$images\eyring.gif$

Fig. 2: Eyring relationship plotted on Arrhenius paper.