Now, here is where the idea of case hardening comes in. Other shapes and loading geometries, including cylinders in torsion, also have the highest stresses at the surface and gradually decreasing (normal) stresses as you move to the core. Note that we have not talked about the shear stresses, which INCREASE as you go toward the neutral axis. That is for another day (see earlier blog on normal and shear stresses). The shear stresses are usually significantly lower than the normal stresses in bending, while in torsion they are similar to the normal stresses at any given location. They would never be higher than the normal stresses. So for that reason we are justified in just looking at the normal stresses for now. Figure 6 shows a “fake” situation (because the particular stress values that I have assigned to the case-hardened layers are unrealistic), which is again adequate for conceptual purposes.
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.
Many people check their case-hardened parts the easy way. They only do surface hardness tests. But what if instead of the red line shown above, we had the alternate dotted red line shown in Figure 7. In this case, the surface hardness is over that of the “GOOD GREEN” part, but it will still have issues in the interior layers. This series of graphs shows, conceptually, the importance of knowing not just the surface hardness but the characteristics of the hardness or strength profile for a case-hardened part in a critical application. The use of the hardness-profile-based “effective case depth” type of specification is one way to at least get a handle on this issue, even if we did not truly understand all the ramifications when the effective-case-depth test method was specified for the particular part.
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.