It has been my practical experience as well as understanding that a heat treated or hardened piece if steel is certainly more rigid than the same steel in an annealed state. Please clarify how you distinguish between "stiffness" , "rigidity" and strength ?

From : Don Stackhouse

Sorry Walt, Mark is right on this one. Heat treated or otherwise hardened steel (such as the work hardening present in music wire) has essentially no effect on the stiffness of the material within the elastic range. Hardened tool steel has almost exactly the same stiffness in tension, compression and torsion as soft coat-hanger wire. What you probably perceived was a higher yield point, not a higher stiffness.

Let's review the meaning of some key material properties:

1. Ultimate stress: This is the stress level of the material at the point that the material breaks. There is a compressive and a tensile ultimate stress, as well as an ultimate stress in shear. The shear ultimate is what matters in the case of a torsionally loaded part.

2. Yield stress: This is the stress level at which the material begins to permanently stretch, bend or otherwise deform. At any stress level less than this, the material will spring back to its original shape when the load that's causing the stress is released. The range of stresses below the yield point is called the "elastic range". The yield stress is also sometimes called the "elastic limit". Unless you don't mind if the part ends up in a different shape than it was before the flight, you need to make certain that the operating stresses are completely within the elastic range.

Some materials do not have a clearly defined elastic limit. In those cases, the convention is usually to define the elastic limit as the point where the material has been permanently deformed by 2% of its original shape. Generally speaking, if such a material is deformed to that 2% stress level, it will not deform any further if later it is again stressed to less than that level. This is due to the effects of the residual stresses left behind from that first stressing event.

Other materials, such as most composites, have a yield stress that's equal to the ultimate strength. In other words, you can stretch them and stretch them and stretch them until they break, but up until that point they do not have any significant permanent deformation. For example, you can bend a straight piece of music wire into the shape of a landing gear strut. Attempting to do the same thing with a carbon fiber rod will get you nothing but frustration and a bunch of carbon splinters.

3. Elongation: This is how far the material stretches between the yield point and when it fractures upon reaching its ultimate stress, usually expressed as a percent of its original dimensions.

4. Toughness: This is usually measured by the amount of energy the material absorbs between its yield point and its ultimate strength. Its the product of the stretching than occurs times the accumulated force required to do that stretching, and so the units are those of work. Both the stiffness and the stretchability of the material are involved. A very stiff material could stretch very little before breaking and still have high toughness; a low stiffness material could be tough by having a lot of stretch before ultimately fracturing. Brittleness is the opposite of toughness.

For example, a piece of bubble gum is tougher than a saltine cracker. The cracker is stiffer, but stretches very little before breaking; its elongation is poor. Conversely, an old leather boot is tougher than the bubble gum. Even though its elongation is not as good as the bubble gum, it's stiffness is higher, and therefore it takes more energy to stretch it to failure.

5. Endurance limit: For fatigue, some materials, particularly iron alloys such as steels, have an "endurance limit". If you keep the stress level below this value (typically about 40% of the ultimate strength for most steels), the part will NEVER fail due to fatigue, even if you subject it to an infinite number of fatigue cycles.

Wood is an interesting material in this regard, since some data indicates that the endurance limit of wood is, at least in some cases, EQUAL to its ultimate strength. In other words, if it doesn't break the first time you take it to its maximum load, it's not going to break at all, ever. That's why the FAA only requires a max load test on wooden props for full-scale aircraft, unlike the extensive vibrations surveys and fatigue analyses required for metal props. Of course all this ignores the effects of aging and biological deterioration; for example, if it gets rotten, it could fail, but that's because the rot reduced its ultimate strength.

This sort of behavior is the exception. Most other materials, such as aluminum alloys, do not have a well defined endurance limit. No matter how low the load and stress, if you subject it to enough cycles (which could of course take centuries, which is why DC-3's are still flying so successfully today), it will eventually fail due to fatigue.

For heat treatable and otherwise hardenable materials, all of the above properties can be significantly changed by the hardening process.

4. Stiffness. This generally refers to how far the material deflects for a given amount of stress. Usually we talk about the stiffness in the elastic range, below the yield point, since the stiffness above the yield point (in what we call the "plastic range") usually changes as the material deforms. It is this stiffness in the elastic range that Mark and I are referring to.

Stiffness in tension and compression in the elastic range is usually measured as the "Elastic modulus", also called the "Young's modulus". For essentially ALL types of steels, regardless of heat treatment, it's almost exactly 30 million pounds per square inch. At high temperatures it decreases a bit. Stainless steels are slightly less, about 29.5 million psi, and nearly all aluminum alloys have an elastic modulus of 10 million psi.

That's right, a piece of hardened tool steel and a piece of 1020 steel coat hanger wire BOTH have an elastic modulus of 30 million psi.

Shear modulus measures stiffness in shear, and it's typically about 2/3 of the Young's modulus. Once again, for all steels it's almost exactly the same.

The yield strength and ultimate strength determine when the material will permanently deform or break. Your hardened steel torque rods for RADS linkages will be far more resistant to getting bent by things such as the flaps getting dragged on the ground during a touchdown.

However, for flutter and other stiffness-related phenomena (such as buckling failures), there will be a difference for different materials, such as using steel torque rods instead of brass or aluminum, but there will be exactly ZERO measurable difference due to switching from mild steel to hardened steel. If you're already using the stiffest material available, the only remaining options for improvement would be to add more material (using a larger diameter steel rod), or using the material you have more efficiently (such as using a larger diameter tube of the same weight, instead of the smaller rod; in torsion, the material in the center of a rod has no leverage, so it contributes little to the torsional stiffness).

v One other thing to be careful of is the difference between stiffness and stiffness-to-weight. The stiffness of most carbon fiber-epoxy per square inch of material is nowhere near as high as that of steel. A 1/8" diameter carbon rod, even with the fibers oriented for torsion, would be torsionally much less stiff than a 1/8" steel rod.

However, the stiffness-to-weight ratio of the carbon is much higher than steel. If you replaced a 1/8" diameter steel rod with a torsionally-oriented carbon fiber rod of the same WEIGHT, the carbon fiber rod would be stiffer. However, it would also be more than twice as big in diameter. Whether you could get an improvement from that approach would depend on whether you had enough room for the fatter rod. At that point you might also want to consider a steel tube.

For stiffness-critical structures, if space is the limiting factor, its usually best to go with the stiffest material available. If weight is the criteria and space is not a constraint, the best choice is probably the material with the best stiffness-to-weight ratio. For RADS, where the thickness available for the pocket in the control surface is usually the limiting factor (at least in most of our applications), steel is therefore probably the best choice.

Don Stackhouse
DJ Aerotech