Miner's rule of cumulative damage

When we by to assess the applicability of plastics pipes. we normally start with the longterm hoop strength diagram. Although of course known to everybody. I show Figure 1 to make clear that I wish to consider both mechanical (bursting) failure and chemical failure. For polyolefins pipes, the life time is sometimes limited by oxidation, rather than by bursting pressure. The degradation branch is usually called the third hranch. even when no knee has yet heen detected in the mechanical failure part of the diagram. This discussion will focus on polyolefins. that is, PE, PB. PP and PE-X. hut also applies to other polymers, such as PVC-U and PVC-C. 

This diagram, although empirical. has , proven to be very valuable when predicting life times under constant conditions. like 70~~110 barfor50 years. Butthosearenot very realistic conditions. However, the diagram is the key to accelerated testing. 

Heating systems have a cyclic pattern: high temperature in winter (from 70OC to 90'~). cold water in summer. and in spring and fall intermediate. Many potahle water systems log i have a cyclic day & night pattern. Other potable water systems require an occasional increase in temperature (higher than 70-C) for health reasons.

Predicting the life time under such varying conditions is more speculative than when applying constant conditions. Miner's rule is a means of making the necessary predictions, but is only a zero-order calculation. I will explain this later, but wish to state now already that in my opinion it is a conservative prediction. A next-order calculation will prohahly give longer life times