Stress-probability-time diagrams

By substituting Eq. (9.14) into Eq. (9.8), it is possible to construct stress-probability-time (SPT) diagrams. For example, SPT diagrams showing lifetime under constant stress for different levels of failure probability can be formulated, as shown schematically in Fig. 9.6. 

Figure 9.6 Schematic of stress-probability-time (SPT) diagram for a body under constant stress.

Stress-probability-time (SPT) diagrams incorporate the time dependence of strength into failure statistics. They give lifetime predictions. An illustration of the use of SPT diagrams is in bioceramrcs. 

These diagrams focus on the temporal or time relationships of operations and they can be used to solve resource allocation problems, to determine whether there is any potential for time stress, and to consider alternative work methods in the execution of a procedure. An example drawn from traditional industrial engineering methods is shown in Figure 4.7. The chart is used to analyze the interaction between people and equipment. As indicated in the summary portion of this chart, there is a high proportion of idle time which would probably indicate the use of alternative procedures in the execution of this task. The chart enables the analyst to see the relationships among the activities of the different components in planning such alternatives. 

An important requirement for any implant material is how long it will last. Because of the nature of failure of ceramic components it is not possible to provide a specific and definite lifetime for each individual implant. Rather we have to express failme in terms of probabilities. Figure 16.27 is an applied stress versus probability of time to failure (SPT) diagram for medical grade alumina. It shows that for a 30-year survival period with failure of no more than 1 in 100 components the maximum tensile stress that can be applied is limited to <200MPa. If stresses of... 

FIGURE 16.27 SPT diagram for medical grade AI2O3. The survival probability decreases with increasing stress and longer times. 

Fig. 14.12 shows the stress—strain—normalized resistance plot for the specimen with 12-mm notch spacing. We know that the nominal strain at fracture for the composite material is around 0.0147. Due to the notches, the strain concentration would be three times that of the smooth specimen. Thus any damage around the notch should start at one-third of the applied strain on the smooth specimen. This is indeed the case as seen in Fig. 14.13. A sharp change in the slope of the stress—strain curve is seen at a nominal strain of 0.005 = l/3eu- Before this knee the resistivity variation is nonlinear with respect to the applied strain. With the onset of damage at e = 0.005 (at the edges of the notches) a sharp increase in resistivity is seen. After this point the resistivity response is linear with the applied strain. Another jump in resistivity can be seen, probably due to damage initiation at the other notch, however, the stress—strain diagram does not detect this. After the second jump the sensor responds very...

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