# How would a carbon-fiber bone compare to a biological bone under common workloads?

I am wondering how to approach the problem of carbon-fiber based bone replacements. Considering a femur, what downsides would carbon-fiber have under the types of torsion, compression, wear-and-tear, etc.. experienced by a biological femur?

It would be great if you happen to consider any methods for countering downsides, if any. Question assumes production is not an issue but design is.

So let's look at the facts. The bones in your body are made from material which has a tensile strength of 150MPa, a strain to failure of 2% and a fracture toughness of 4MPa(m)½. For a structural material that's not good. We can make alloy steels that are ten times better in all three of those properties. But of course there are some other factors we need to take account of in order to make a valid comparison. Bone is less dense than metals and this is important because the weight of our bones strongly affects the energy needed to move around. To do a quantitative analysis we need to consider the geometry and loading on the structure. The major bones are mostly tubular in shape, loaded in compression and bending. So a rational comparison is to imagine tubes made from different materials, all having the same length and diameter, with their thicknesses adjusted to give them all the same weight. Putting in some typical dimensions and material properties we find that the stresses in a bone made from titanium alloy, for example, would be about 1.3 times higher than in a bone of the same weight, made from bone. But the titanium alloy is 5 times stronger so obviously its safety factor is much higher.

• Hi Garet, I would downvote because there is no specific physics question, or ironically, some might argue there are far too many of them for this Q and A. Sorry – user146020 Mar 22 '17 at 22:20
• np, Could you perhaps suggest a scope to reduce the range of questions? I attempted to do so by narrowing things to the shape and range of use that a femur experiences. mostly torsion and compression -- things like chemical effects of the biome were not expected. – Garet Claborn Mar 22 '17 at 22:55

It is assumed that bio-compatible / flexible resin systems would be used. As CFRP strength is more than natural bone stress in compression/bending it would be way better in function if considered separately..

That said rest is tough to satisfy..1) the direction of fiber is important if the Nature's function developed after so many thousands years of evolution if "reverse -engineering" is attempted artificially. 2) Local stiffness variation should be accurately known to be duplicated in fiber placement.

The diagram of bone structure & orientation shows disposition of (hollow sandwich) bone matter. Bone filaments run along $\pm 45^0$ in the middle of the Femur shaft as well as in the neck region above. Force enters normal at either end in the trabecular and condyle regions. Interface force resultant should be normal to transmitted force so as not to induce crack/delamination by weakness of interlaminar stresses and edge stress effects in laminated construction.

How would the prosthetic element be made?.. that is the more important question. Devil is in the detail.. or so one views design with composites. No over/undesign is permissible. Material should not be where it is not required without a functional requirement. Material should be placed in the right amount and and in the right direction.

As one possibility a carbon cloth with more layers at extremities should be rolled and inserted into a metal mould cavity and hot resin cured. A design/FEM analysis is needed after considering FMECA which are medically well known. Loads and their combination at neck of ball/socket/pelvis joint should be known. Torsional strength required at knee cap may need Silicone rich pockets for shock absorption in the vicinity of the two joints.

Downsides with carbon/graphite fiber composite depend upon conformance of the degree of stiffness in multiaxial stress distribution.

May be 3d printing of ceramics provides a better stress conduction path than using injection moulding or cloth moulding carbon/graphite for stiffness flexibility and grain direction control.

• thanks for the detailed answer! i leave questions up for a couple days for good measure, marked correct. for reference, I'm fascinated you offered a start to manufacturing method - thanks. I'll note that where you mention multiaxial stress, some papers suggest introducing veins with a high impurity and small grain size. Perhaps dip some of the cloths in an extra solution of some sort. – Garet Claborn Mar 25 '17 at 4:02
• [Chunni][2] I used to wonder cloth combination multiply twisted .. coiled coil steel ropes) addresses reqd design/fabn [2]: google.co.in/…: – Narasimham Mar 25 '17 at 12:57