Stress Loading

The discussion of accelerated life testing analysis thus far has included the assumption that the stress loads applied to units in an accelerated test have been constant with respect to time. In real life, however, different types of loads can be considered when performing an accelerated test. Accelerated life tests can be classified as constant stress, step stress, cycling stress, random stress, etc. These types of loads are classified according to the dependency of the stress with respect to time. There are two possible stress loading schemes, loadings in which the stress is time-independent and loadings in which the stress is time-dependent. The mathematical treatment, models and assumptions vary depending on the relationship of stress to time. Both of these loading schemes are described next.

Stress is Time-Independent (Constant Stress)

When the stress is time-independent, the stress applied to a sample of units does not vary. In other words, if temperature is the thermal stress, each unit is tested under the same accelerated temperature, e.g. 100° C, and data are recorded. This is the type of stress load that has been discussed so far.

Fig. 8: Graphical representation of time vs. stress in a time-independent stress loading.

This type of stress loading has many advantages over time-dependent stress loadings. Specifically:

Most products are assumed to operate at a constant stress under normal use.
It is far easier to run a constant stress test (e.g. one in which the chamber is maintained at a single temperature).
It is far easier to quantify a constant stress test.
Models for data analysis exist, are widely publicized and are empirically verified.
Extrapolation from a well-executed constant stress test is more accurate than extrapolation from a time-dependent stress test.

Stress is Time-Dependent

When the stress is time-dependent, the product is subjected to a stress level that varies with time. Products subjected to time-dependent stress loadings will yield failures more quickly and models that fit them are thought by many to be the “holy grail” of accelerated life testing. The cumulative damage model, available in ALTA 7 PRO, allows you to analyze data from accelerated life tests with time-dependent stress profiles.

The step-stress model [ 31] and the related ramp-stress model are typical cases of time-dependent stress tests. In these cases, the stress load remains constant for a period of time and then is stepped/ramped into a different stress level where it remains constant for another time interval until it is stepped/ramped again. There are numerous variations of this concept.

Fig. 9: Graphical representation of the step-stress model.

Fig. 10: Graphical representation of the ramp-stress model.

The same idea can be extended to include a stress as a continuous function of time.

Fig. 11: Graphical representation of a constantly increasing (or progressive) stress model.

Fig. 12: Graphical representation of a completely time-dependent stress model.

A Summary of Accelerated Life Testing Analysis is presented next.

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