Sunday, February 9, 2014

Multicausal failures

We all are aware of failures that are caused by a single event. From the point o view of engineering these are lucky cases, since controlling these events, the failure can be prevented. Engineering project usually assumes this hypothesis for this purpose. For example, the maximum stress level of a structure is calculated based on the yield or fracture stress of the individual components, some parts in airplanes are designed such that the cyclic stress intensity factor does not exceed the fatigue threshold level measured in a Paris plot.
There are, however, cases in which the failure is caused by multiple critical events happening in series or in parallel simmutaneously or not. The most famous example was the fire in the Kiss club in Santa Maria-RS, Brazil, last year. The causes ranged from corrupt city officials and firemen, who alloed the place to open without minimal safety conditions, greed by the owners, which led to bad material's selection of the foam used for acoustic insulation,which produced HCN when burnt, and the stupidity of the band members, who lit inappropriate fireworks in a closed space. Any of these events, if they were avoided, would prevent the tragedy too.This went surely through the mind of all people involved, but they surely decided that the probability of everything going wrong in the right sequence in the right time was too low to consider. The tragedy is there to prove they were wrong.
In fracture as Prof. Bažant teaches, this leads to two different failure propability distributions. In case of a single critical event (as in cleavage), the probability is described by the Weibull distribution. In the case the failure is a consequence of infinite individual critical events, like ductile fracture by microvoid coalescence, this leads to the gaussian distribution. There are also intermediate cases. The point here is to remind that multicausal failures do exist. They require nonlinear thinking by the engineer, who is forced to consider not only what could go wrong, but also in which sequence and in which time.
Worse, as I repeat to exhaustion to my students, when you decrese the probability of the unicausal failure, the multicausal failure becomes increasingly more probable.

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