Originally posted on my disabled blog LoneArtisan.com

The comparison between carbon fiber and other exotic materials is always inevitable. For this reason, of course, titanium couldn’t be out of the list but, is it really stronger than carbon fiber? Well, as always, this is not a so simple question to answer because carbon fiber is not an isotropic material, as I had explained in this article. This means that engineering plays a far more important role in carbon fiber parts than their metal counterparts.

Theoretically, carbon fiber can be as much as 3 times stronger than titanium when stress is aligned with its fibers. However, when stress is 45° off-axis, it can be almost 3 times weaker. In real-world applications, carbon fiber can be as much as 2 times stronger than titanium when advanced computational engineering and manufacturing are employed.

To understand exactly why engineering is important, we must have a good look on the properties of both materials. Since I don’t want to write a general treatise on composite materials and alloys, I will focus this article on the tensile strength, but it will be enough for you to reach the right conclusions.

Tensile strength

Ultimately, all discussions about what material is stronger lead to tensile strength. To understand it, we must imagine a rod pulled by a force along its axis. As a small force is applied, the rod just elongates a bit and returns to the original size when the force ceases to exist. If we pull the rod with more and more force, at some point it will deform permanently, and we call this a plastic deformation. In this case, the rod will never have its original size again, even when the force is completely drawn. However, if it is pulled by an even stronger force, it will eventually break.

So, as you can see, there are three main force regimes here. For engineering, in most cases, the first regime is the most important, though. There are two important parameters here. First, the Young module, which dictates how much the rod elongates when a force is applied. This can be understood as stiffness since something stiff needs a lot of force to cause elongation.

The second parameter is called the yield strength, and it says how much force the rod can take before it deforms permanently. As you can imagine, for most engineering applications, when a part goes into plastic deformation, it is often considered damaged and must be replaced. A third parameter, also important, is the ultimate tensile strength, and it is the maximum force our rod can bear before it breaks.

So, when comparing the tensile strength of different materials, we generally talk about those three parameters: Young’s module, yield strength, and ultimate tensile strength. However, they only tell half the story, because they don’t take the dimensions of the rod into account. All those modules are properties of the material, not the part, in this case, our theoretical rod.

To calculate exactly how much force our rod can stand, we must know how thick it is. In more technical terms, we must know its cross-sectional area. So, in theory, every material can stand the same forces, but some will be thicker than others. This means that the amount of material needed to make strong enough parts varies according to the material.

This is where density enters the game. Some materials have very high yield and young modulus, but are also rather dense, like steel. Others, such as aluminum, are not so strong, but they are less dense, which translates into lighter parts that can take the same stress. So, when we compare materials, we must always take into account how much they are going to weigh.

Titanium alloys properties

Parts are never made of a pure element. Usually, there are other elements in the recipe, which improve the properties and also the price of the material. In this article, I will consider the two most common titanium alloys, the Grade 5 6Al-4V the Grade 9 3Al/2.5V.

Grade 5, which has 6% Aluminum and 4% Vanadium in its composition is mostly used in aerospace applications. It has a density of 4.5 g/cm³, yield strength of 900 MPa, Young modulus of 100 GPa, and ultimate tensile strength of 925 MPa. Those are the mean acceptable values for this alloy.

Grade 9, on the other hand, uses 3% Aluminum and 2.5% Vanadium in the mix and is mostly used in bike frames, for example, due to its better weldability. It has a density of 4.48 g/com³, yield strength of 530 MPa, a Young modulus of 100 GPa, and ultimate tensile strength of 620 MPa. Don’t bother too much about all those numbers, we are putting them in a table below.

Carbon fiber properties

At the other side of the ring, we have carbon fiber. However, it is a bit more complicated to understand tensile strength in this case because it depends on the direction that the force is applied. Since carbon fiber is composed of a carbon fabric, which is a textile of carbon fibers, it can afford different forces at different directions.

Although it is quite strong in the direction of the fibers, it is a lot weaker when the forces are off-axis. A standard carbon fiber fabric has the fibers aligned in two directions, at 0 and 90°, as in the picture below. Those are the strongest directions. At 45°, the material properties are quite worse.

The density of standard carbon fiber is about 1.6 g/cm³. At 0 and 90°, it has an ultimate tensile strength of 600 MPa and Young Modulus of 70 GPa. At 45° the ultimate tensile strength is 110 MPa and Young Modulus 17 MPa. You can find this data here. As you are going to notice, carbon fiber doesn’t have a yield strength. The reason is that it doesn’t have a plastic deformation regime. Carbon fiber will just break if forces are higher than the yield strength limit. Below is a table comparing the main paramaters of titanium alloy Grade 5, Grade 9 and standard carbon fiber.

	Titanium Grade 5	Titanium Grade 9	Carbon fiber
Density (g/cm³)	4.5	4.48	1.6
Yield strength (MPa)	900	530	–
Ultimate Tensile Strength (MPa)	925	620	600 (0 and 90°), 110 (45°)
Young Modulus (GPa)	100	100	70 (0 and 90°), 17 (45°)

Density and tensile strength

And that’s where the answer to whether carbon fiber or titanium is stronger really lies. Although the yield strength of Grade 9 and carbon fiber are very similar, the density of carbon fiber is about 2.8 times smaller. For sake of simplicity, let’s define the strength-to-weight ratio the Yield strength divided by the density for titanium alloys, and ultimate tensile strength by density for carbon fiber. For grade 5, this number is 20, for grade 9 it is around 12 and, for carbon fiber, it is roughly 37. So, when we take into account the weight of the part, carbon fiber is 1.85 times stronger than grade 5 titanium and 3.1 times stronger than grade 9.

Things change quite a bit, however, when we compare the yield strength at 45°. Since this number doesn’t change for a metal alloy, they stay the same. However, for carbon fiber it drops to 6.9. At this condition, grade 5 titanium is 2.9 times stronger than carbon fiber, and grade 9 is 1.7 times. So, as you can see, the answer varies a lot depending on the direction of the stress.

Density and stiffness

Let’s have a look now at stiffness. In the same fashion, the stiffness-to-weight ratio of grade 5 titanium is 22.2. The grade 9 is also 22.2. Carbon fiber at 0 and 90° is 43.7, but at 45° it is just 10.6. So, again, carbon fiber is far superior when stresses are applied in the direction of the fibers, but a lot weaker at 45°.

And the final answer is…

It depends, of course. What a blog post it would be without an it-depends-answer? The question here is that we must take into account that the strength of carbon fiber depends a lot on the direction of the fibers, and this is dictated by how the fabric is laid on the part. I always stress this a lot in my articles, but carbon fiber is as strong as it is well-engineered.

Also, we must always have into account that, in most parts as bike frames, for example, forces are far from distributed uniformly through the parts, and engineers must always keep room from failure, as a safety measure. In this case, they must be a lot more careful with carbon fiber, which always means a weight penalty. It is always better be heavier than sorry. So, they must bulk up some portions to make sure the part will meet the required loads.

It is really hard to give an accurate answer just by having a look at a materials properties table, though. So, for a real-world comparison, let’s have a look at some very nice bike frames. A very light titanium bike frame weighs 2.6 lbs (1176 g), while a carbon fiber Specialized S-Works Aethos weighs just 1.3 lbs (588g). So, that nails the question for me, and carbon fiber is definitely stronger than titanium, both by numbers and by real life. In this case, since both frames are designed to support the same stresses, it can be assumed that carbon fiber is 2 times stronger than titanium.

As an ending comment, Specialized states that they use supercomputers to design the frame to eliminate what they call ‘lazy fibers’, which are those that are not taking any force. So, as I always say, carbon fiber is as strong as its engineering. The last note is that all this discussion is for ambient temperature applications. For high temperature, such as turbines, carbon fiber is not a suitable material.