If we assume that the outer layers are hardest, either because they have been more richly carburized or more quickly cooled (or both), we can look at two cases represented by the red dashed line and the green dotted line. The green dotted line is showing us at all locations that the strength of the part is higher than the stress value. This part is robust. It should not crack (if we are assuming that the strength shown is a fatigue strength appropriate to the number of expected service cycles). The red dashed line, however, crosses the stress curve. The portions of the part that are associated with the red locations under the blue line are thus seen to be inadequate to the demands of the service conditions. Going back to our hypothetical beam then, the areas at the surface and in the very center of the beam would be OK. Those at positions between approximately 1.2 and 2.8 inches from the centerline form two layers – above and below the centerline of the beam – that “have issues,” as the quality people in the automotive world like to say. It is not a good design, to say the least.
Please note that the issue of potential subsurface “failure zones” is discussed on page 143 of a book by Geoffrey Parrish, published by ASM in 1980, The Influence of Microstructure on the Properties of Case-Carburized Components. There are also newer editions of this book. As he also notes, we have not addressed the presence of residual stresses, which in properly carburized steel increase the useful service stress level at a given hardness. There are multiple other issues not addressed. But with the availability of finite element analysis for stress-distribution modeling, it will be interesting to see if more people take a more quantitative approach to specifying case-hardened steel hardness profiles.
Finally, Figure 7 can explain the popularity of requiring case AND core hardness and effective case-depth measurements to be within a specified range (for more critical components) to keep some sort of control of uniformity of parts that go out the door.