from the MASTER, in metallurgy and sword making....Kevin Cashen......
O.K. I hope I got somewhere in the vicinity of what these curves may look like. All I had in my books were comparison curves for iron or steel of varying carbon contents, not differing heat treatments, so I guessed. Please excuse inaccuracies, this graphic is not meant to represent any actual tests that I have performed not are they expected to be in the proper proportion to each other, but I think we may get the general idea from them. Those with experience with this sort of thing, please excuse any omissions or the minimizing of the dip between the proportional and yield limits that many materials exhibit, I am trying to keep this as simple as possible
This is my version of a compilation of three stress strain curves for the same steel having different heat treatments. The stress strain curve is a graphic representation of the numbers generated in a typical tensile test. In such a test a specimen is locked into a machine that pulls it with great force in opposite directions and measures the amount of that force for a given amount of deformation of the tested material.
There are two types of deformation represented here, elastic (temporary) and plastic (permanent). On the graph there are labeled various points of interest to our conversation.
a. Proportional limit. This is the limit of the range where the amount of load will be directly proportional to the amount of deformation. This also means that the deformation or strain will go way as soon a proportional amount of the load is removed so for our purposes, since in many materials the proportional limit closely coincides with the elastic limit, we will simply designate a. as the elastic limit as well.
b. Yield point. For our conversation this simply takes up where the Proportional limit left off, but in many materials there is some funky dips and curves in this area that make it a little more complicated that what my feeble mind wishes to deal with. The Yield point is when the deformation is no longer proportional to the load and will continue to increase even though no more load is applied. If this is hard to imagine in the sense of the tensile test, then think of putting weight on the end of a strip of iron. Eventually there will be enough weight that the iron will bend, and keep bending toward the floor even though no more weight is added; this is the yield point of that piece. Obviously this is no longer elastic deformation since the results are quite permanent, so this is now in the plastic deformation range.
c. Ultimate strength. This is the last straw, so to speak. When the material reaches this point, all it has left to do is failure. In brittle materials fracture occurs at the point of ultimate strength. In ductile materials c marks the point where heavy necking (not the type that steamed up your car windows in High School ) occurs right before fracture. There will be a drastic reduction in cross-section as large amounts of slip occurs at the point that the piece will come apart. Then next time you break a blade with a softer spine, notice the dip in the outside curve right at the point of fracture.
I have also divided the curves into 2 parts, that which falls to the left of the elastic limit being the elastic range, and the area to the right being the plastic range. The area covered in the curve in the plastic range describes the toughness of the material.
The plastic range is the one that is affect by heat treatment. You will notice all the lines to the left are straight, as they are governed by a constant known as Youngs modulus, which I will cover shortly. Since heat treatment affects the brittleness or toughness of the material, it is the plastic range where it is manifested. Hardening the steel pushes the yield point higher and the failure point closer to the yield point (i.e. it doesnt bend it breaks!). Tempering the steel widens the gap between the yield and failure point and allows for more plastic deformation before failure, but it will take much less to reach the yield point. Like all things in the universe, there is always a trade off, we simply cant have out metallurgical cake and eat it too.
The area in the elastic range is governed by a principle known as the modulus of elasticity or Youngs Modulus This modulus involves some heavy numbers and mathematical savvy so it is best simplified for dimwits like myself. For our purposes we can simplify the entire concept by dividing things by 1000 and describing this mess as the 30,000 lbs. of load required to elastically deform .001. Different materials will have differing modulus values, copper is 15 million (or 15,000 / .001) lead is only 2,500 /001. The point of all this is that the modulus of elasticity for steel is 30,000/ .001, and that is what it is, regardless of heat treatment. It is 30,000/ .001 for fully annealed steel and it is 30,000/ .001 for fully hardened steel. It is 30,000/ .001 for both the spine and the edge of a katana, as all of this falls to the left of the proportional limit.
This all translates out in the real world as steel having the same elastic resistance, in a given cross section, no matter what the heat treat. If we define flex as elastic deformation, that is not permanent and will return to its original shape when the load is removed, and bend as plastic deformation that is permanent when the load is removed. Then youngs modulus or modulus of elasticity applies to the flexing of steel, and the flex of that steel will be the same regardless of heat treatment.
Bending of steel will be affected by heat treatment. So how stiff or resistant to flex a blade can be is solely determined by the amount of steel there is to move. A thin blade will be easier to flex than a thick one. A thin blade will also be able to flex farther without taking a set due to what is going on in the cross section.
Think of the cross section of a blade, being flexed or bent, as a lever. To one side of the center, or fulcrum, are compressive forces (the inside of the curve) and on the opposite side are tensile forces. Simple physics tells you that the farther you get from the fulcrum the greater the forces can be exerted, so a thick blade will have more tensile forces exerted on that outer skin than a thin one, but the amount of material to be affect by youngs modulus will also increase. So basically all the stakes go up. A thinner blade of the same length will handle the flex better, but if you make the dimension entirely proportional then we are back to square one.
A quick look at the curves will show you that a person trying to display his heat-treating prowess by flexing a sword in front of you is showing you nothing more than the blade has a higher yield point. This could mean that it is HRC 45 or HRC 62! The only thing it definitely tells you is that it is thinner than blade that doesnt flex as well. In order to really determine anything about the heat treat, by this flexing, is to exceed the yield point, which means either a bent or broken blade.
Those most impressed with elastic deformation of blades are those who are used to having them bend too easily. In European blades this results from a poor quench or too aggressive tempering. Japanese blades are the two extremes in one blade, a spine that will easily reach the proportional limit and an edge that will have little room between yield and failure, but it all seems to equal out most times.
Enough on how much this stuff applies to us, and lets get into how irrelevant it can be. One of the paradoxes of modern sword and knife testing is the heavy emphasis on tensile strength toughness, with the main test being steady bending. This is most confusing since rarely will a knife or sword see these types of stress in use. This is why I pay much less attention to this type of testing and focus heavily on what large knives and swords will be subjected to- impact type testing. You dont gently pry things with swords- you hit things!
