Stiffness and Material Behaviour primer (Pt I)

August 21 — 2012

Part 1 of 3

Words by: Joe Graney, SCB Engineering

This is the first of a three-part article about a topic that comes up quite a bit: stiffness. It was going to be two parts, but it was getting out of hand in length. There's a lot to cover, so we're breaking it into three parts:

Part 1 will concentrate on definitions of terms and explain why stiffness is a sought after characteristic.
Part 2 will discuss the fundamentally different behaviors of metals and polymers and why that matters.
Part 3 will be more bicycle specific, how stiffness is measured and stuff like that.

Jumping right in, here are some definitions so we're all reading from the same hymnal:

Stiffness is the resistance of "elastic deformation". The key here is "elastic", which means that once a force is applied to a thing, changing its original shape, the thing will spring back to the original shape after the force isn't applied anymore.
Strength is the resistance to "permanent deformation". It maybe not be broken in two, but it's a different shape, like it's bent, buckled or stretched out.
Fracture is actually breaking or cracking something.
Toughness is resistance to fracture.

Stiffness on a Bike

Stiffness on a bike frame (assume a hardtail for clarity) is going to come primarily from two sources. The first is the size and shape of the tubing, the second is the material itself. Take two tubes that are exactly the same diameter and wall thickness, with one in carbon fiber and one in aluminum, and bend them. The aluminum one, no matter what alloy, can only be made stiffer by making the tube diameter larger, or by increasing the wall thickness. The stiffness comes from the atoms in the metal being attracted to one another, and the metal is a uniform material. Alloys, like the 7000, 6000, 2000 designations you see used on different products, are used to change strength - but they can't change stiffness. Hydro-forming doesn't change it, forging all the bits together in one piece doesn't change it, butting doesn't change it. Those things can affect strength, but don't affect stiffness.

The carbon fiber tube, however, can have its stiffness values change dramatically by changing how the fibers are oriented. In a tube with 10 layers of carbon plies, the layers can be arranged differently to get a different combination of stiffness in different directions. Additionally, the fiber itself is available in different stiffness or "modulus". The plies can be arranged in different directions, with different modulus', resulting in hundreds and thousands of combinations of tube behaviors - all while keeping the diameter and wall thickness constant. That's great, but a lot of those combinations are going to suck for making a bike, because you can have something that is very stiff, but not strong (not good for a bike), or strong but not tough (also not great), or tough but not stiff (might not break but will suck to ride). It's a complicated balance, and one of the reasons why carbon fiber bikes can't all be judged as the same, as if its "black metal".

Frame Stiffness

I've been asked a number of times if a frame can get "too stiff". If we're talking about suspension mountain bikes, I don't think this is a concern. The notion of "too stiff" probably stems from motorcycle road-racing design and the science of "tuned chassis flex", which is how a motorcycle frame engineers intentionally build a certain amount of flex into their designs. It came about from the fact that motorcycles spend a great deal of time at high angles in cornering, but that just doesn't happen with mountain bikes.

Every time we've created a stiffer frame ride quality has increased. A lot of deflection pinging you around when you're trying to hold a line through a rock garden makes it harder to keep your bike handling predictably and pointed where you want. The amount of deflection also contributes to the "feel" a rider has for the terrain. Less deflection allows you to better consciously or unconsciously "feel" traction and control limits; thus allowing you to ride faster because, by definition, you are in control. When a metal bike flexes (this is true for metal wheels and forks, not only for metal frames) when traveling through rough terrain, it behaves like an un-damped spring, which flexes back without absorbing any energy. That's all you get with a metal - just a spring and no damper. If the suspension (both the frame's way of pushing the spring-damper, and the spring-damper unit itself) is working properly, it has the function of isolating terrain input. That means you don't get tossed around when hitting rocks because the suspension is absorbing some of that energy. Having a stiff frame decreases the amplitude of deformation which allows you to more confidently ride rough terrain without un-damped inputs that knock you off line. Ever land sideways on a flexy bike and feel like it got loaded up and springs back? That's what I'm talking about. That same scenario plays out on a smaller scale all the time off-road - every off-angle rock, turn, bump and root.

Simply put, stiffness gives you more control which lets you go faster.

The "feel" of carbon

In the second part of this series we'll discuss how polymeric materials different from metals fundamentally in their reaction to stresses and deflection. Its pretty heady stuff, but the "feel" of carbon is something that anyone who's ridden it knows is unique, and what makes carbon reinforced structures desirable for some applications beyond the weight or strength implications.

Previous Next Post Links