Originally published 5/3/2003
Sooner or later, if you’re discussing frame materials, one of the pocket protector wearing crowd starts using words and concepts a lot of cyclists aren’t really familiar with. I figured it’s better to give the whole story rather than just bits and pieces and hopefully help you better understand what goes into a designing and building a bike frame and the differences in materials. I’m going to give you the straight poop here, no this material is better than that, just the facts.
The first question to ask your self is, “what do I want in a bicycle frame?”
I’ll take a poke at it: you want what we all want. We want a frame that achieves some sort of dynamic homeostasis. We want something that is lightweight on the road to Sestrieres, rigid when we’re sprinting like Cipo, compliant when we’re old and the miles long, strong like a bull, durable like tractor, and safe as a babe in his mother’s arms. Am I right?
First some definitions — be aware that many of these are not necessarily the “textbook” definitions, but rather ones that I’ve tried to simplify for easier understanding or put in the context of bike frames.
PSI – Pounds per Square Inch. A value based on a unit of area.
KSI – 1 KSI equals 1,000 PSI.
MSI – 1 MSI equals 1,000,000 PSI.
Ultimate Tensile Strength (UTS): Bike geeks are always talking about how strong a bike material is and without fail, the Tensile Strength or UTS of the material is brought into play like some star witness to prove a case. It’s really not as important as yield strength but they are related and UTS is always the bigger number. Anyway, UTS is the maximum load sustained by a material prior to failure and is divided by its cross sectional area. It is expressed as a stress per unit of area, e.g., PSI, KSI, or MSI.
Here are some reference numbers:
- The best post-weld treated and aged Al used in frames have a tensile around 68KSI (68,000 PSI.).
- 3/2.5 Ti has a tensile around 90KSI.
- 6/4 Ti is typically 120-130KSI.
- 4130 (Chromo) steel is around 90-125KSI
- Foco/Zero/853/Platinum and their ilk can reach 200+KSI.
Yield Strength: A value assigned to a material based just beyond its elastic limit where it takes a permanent set. Typically expressed as a stress per unit of area. More important than UTS when talking about bike frames.
Elongation: The plastic extension of a material at failure and is expressed as the change in the original gauge length divided by its original length. This is then expressed as a percentage. The lower the elongation percentage, the more brittle the material. Often referred to as ductility. The elongation for frame materials range from around 8 to 30%.
Density: The weight of a material by volume. Some examples:
- Aluminum frame materials have a density of around .98 lb/in^3.
- Ti frame materials have a density of around .162 lb/in^3.
- Steel frame materials have a density of around .281 lb/in^3.
Stress (S): A force per unit of area. For instance, 100 PSI (pounds per square inch).
Strain: A measure of a body’s deformation when it is subjected to a stress or elongation per unit length.
Deformation: Changes in form produced by external forces or loads that act on non-rigid bodies.
Fatigue: This one gets bandied about a lot. Simply put, fatigue is the deterioration of a material subjected to repeated applied stress. An easy way to demonstrate fatigue is to use a steel paperclip and bend it back and forth till it breaks. You’ll notice that you have to bend it severely a number of times to break it. Bending a paperclip like that is demonstrating fatigue on a rapid and severe scale as you’re grossly surpassing the yield strength of the material. If you were to limit the bending of the clip so that it always returned to its original shape, you’d be at it a long, long time – maybe forever. Eventually it will break, IF you exceed the fatigue limit of the material. A material’s fatigue limit is typically well below its elastic limit, the elastic limit being where a material will not return to its original shape after release of the load and what a materials yield strength is based on.
Fatigue Limit: Now we’re getting to the meat and potatoes. The fatigue limit of a material is a stress value that will not cause failure of a material regardless of number of applied cycles. To determine the fatigue limit of a material it is stressed with various values for a number of cycles until failure occurs. Stress values are then reduced and the process repeats until no failure occurs regardless of the number of stress cycles or they stop counting. This results in a stress-cycle (S-N) diagram and typically will show a curve plotting material failures and then a sharp bend at a stress value where failure no longer occurs regardless of the number of stress cycles. That point where no more failures occur is the material’s fatigue limit.
Now, steel and titanium have a fatigue limit, and aluminum does not, i.e., no bend in its curve, no fork in the family tree. Aluminum keeps failing regardless of the applied stress, it does however take more and more cycles to achieve failure at lower stress levels. Achieve failure? Is that an oxymoron? This is why you don’t see aluminum frames that are both very light and very old and also why you should carefully read any “lifetime” warranty on aluminum bikes and note where it mentions that is doesn’t cover failures due to “fatigue” which is precisely how it will fail.
A simple, yet very important, caveat: surface defects, scratches, notches, heavy corrosion, anything that can cause a stress riser/concentration can greatly reduce the fatigue limit of a material.
Elasticity: The ability of a material to return to its original dimensions after the removal of stresses.
Elastic Limit: The limit of stress within which the deformation completely disappears after the removal of the stress.
Modulus of Elasticity (E): The ratio of stress to strain within the elastic limit. It is actually based on a stress value required to make a material double its length. Since most metals in their solid state would break long before they were ever stretched to double their length, it serves as unit of measurement reference. For example, steel has an E of approximately 30.1MSI (30,100,000 pounds per sq-in.), so if the material has a yield strength of, say, 30KSI (30,000 PSI), then it would elongate .001″ at yield. Some pertinent examples:
- The Modulus of Elasticity (E) of aluminum is about 10.1MSI
- The E of Ti is about 16MSI.
- The E of Steel is about 30MSI.
Inertia: The property of matter that causes it to resist any change in its motion; based on mass.
Moment of Inertia: MOI is related to the required force acting at a specific distance from an axis to displace one unit of area by one unit of length around the axis. Simply, it is a measure of the resistance offered by an object to rotational forces about an axis. For any given material, the greater the MOI, the greater the force required to deform the object around an axis. The equation to determine moment of inertia of a hollow tube is 0.78539(R^4-r^4) with “R” being the outside radius and “r” being the inside radius. The 0.78539 is the result of Pi over 4. I wish I knew how to type all the mathematical characters. In the context of bike tubes, both the wall thickness and diameter affect a tube’s strength. The greater the diameter of the tube or the greater its wall thickness or both, the greater its resistance to an applied stress.
Polar Moment of Inertia: The sum of the moments of inertia about any two axes at right angles to each other in the plane of the area and intersecting at the pole.
Those definitions and numbers are just a reference for the casual reader as they apply to bicycle frames. What it really means to bike frames is how they’re used to define the mechanical characteristics and design requirements of a material used in complex structures and said structures response to applied stress. This is where design and design stress comes in.
To properly design a product, you have to know a little about the stresses it will encounter during its life cycle and from there, hopefully, identity its maximum stress or permissible/design stress. In terms of bike frames, any material in addition to that required to provide the required life cycle at the design stress is realized as extra weight. This is not always a bad thing, you don’t want to harm anyone, and a good design should tolerate occasional loads above the design load without failure – this is a safety factor. The safety factor is based on the material’s UTS, yield strength, fatigue strength, ductility, the magnitude of loads, the operating conditions and environment, and of course any stress inducing manufacturing processes.