It is usual for the effect of temperature on the facture toughness of steel to show a lower shelf at low temperatures, then as the temperature increases to exhibit a rapid rise (a transition region) and then level off at an upper shelf. With further temperature increase the upper shelf slowly decreases until at high temperatures the decrease accelerates as the steel softens. It would be great to have an equation that describes as many of these trends a possible. In particular the data I have are for austenitic stainless steel weld metal and casting, which contain delta ferrite.
I have more experience with aluminum alloys but I suppose different fracture mechanisms become active at different temperatures and equations for those fracture mechanisms can be mixed as a function of temperature.
It certainly would!
The simple solution, at least to the classic transition zone, is to curve-fit a hyperbolic tangent or logistic function. As a description of the data such sigmoidal functions can work well, but they don't inform as to why changes are happening. For that reason I usually prefer at least a mechanistically-informed phenomenological model, even if a fully mechanistic one is out of reach.
A step on the way is provided by the various impact-tensile-toughness relationships. Jones is good for the lower-shelf into the transition and is fairly universal for ferritics. There are various upper-shelf correlations, but they seem much more material dependent.
For ferritic steels - and I think back to the early days of PWR and work on A533B / A508cl3 - it took three intersecting energy lines, all decreasing with temperature, to model a Charpy curve. They are probably all exponential, but linear worked well enough for the brittle modes (intergranular and cleavage). Sometimes a term to allow for crack nucleation vs crack growth was needed - but I never fully bottomed that effect out. The ductile mode seemed OK on a single exponential curve for the dynamic regime of Charpy, but for slower strain rates an extra term is needed when climb effects become important. A similar approach should work for 'real' toughness data and should cover all the effects we see.
The problem with austenitics is that they do not show the same sort of transition - the change is usually much smoother with temperature. They do, however, show big changes in properties with precipitation of carbides and intermetallics. It's an area I'm working in at present.
I attach a paper that I put into Baltica 2007 with a bit of the PWR work in it. Kim Wallin had a good paper in the same conference (I can send it to you privately if you wish).
Best wishes
Thanks John. Wrought stainless steels which are fully austenitic do tend to be ductile at all temperatures that I am interested in RT to ~600degC. However, the weld metal or castings contain 6-12% delta ferrite, which in the unaged condition can give a brittle to ductile transition a lower temperatures. This makes the RT data very scattered as some welds/castings are fully on the upper shelf, whereas others can be a little way down the transition. Things get a whole lot worse in thermally aged (500-600degC and above for 10k-100khrs) weld and castings, were the delta-ferrite transforms to carbides and intermetallics that form in the delta-ferrite stringers/dendrites. The transition region moves to higher temperatures and the upper shelf drops as more and more intergranular failure takes place, until eventually intergranular failure at these carbides and intermetallics dominates at all temperatures.
I am gathering a lot of data on one particular weld metal and plan to fit a suitable phenomenological equation to the data when I have enough. My question was motivated to gather views on the best models so thanks for you contribution much appreciated. The logistic model would be a useful sigmoidal model to try for the lower shelf to upper shelf transition. I would then need to reduce the upper shelf with temperature and build in the effect of ageing, which I was thinking of trying to build in the Avrami equation to scale the logistic model and move the transition to higher temperatures. Should be fun, but I need more data before I do it. The testing is planned but I always find it best to have a model in mind when designing the test matrix.
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