I had posed this in the "It happened at the gun show" thread, but I decided to move it into its own thread since so many inquiring minds seemed to want to know.
Does making a "blood groove" on a knife make it stronger?
It's all about moment of intertia.
For example, consider the shear stress on a linear elastic circular bar (as a simplified example)
where D is the diameter, pi = 3.14159... and Iy is the moment of inertia:
Iy_solid = (pi * D^4)/64
Now, take that same bar and hollow it out, such that it has an inner diameter d:
Iy_hollow = (pi * D^4)/64 - (pi * d^4)/64 = [pi * (D^4 - d^4)]/64
It has been shown that maximum shear stress, tau_max, on a circular bar subject
to a maximum torque T_max is:
tau_max = (T_max*D)/Iy
So, let's say we want to reduct the weight of the circular bar by removing half of the material,
where A1 is the cross-sectional area of the circular bar before being hollowed out and A2 is
the cross-sectional area of the circular bar after being hollowed out:
A1 = (pi * D^2)/4
A2 = A1/2 = (pi * D^2)/4 - (pi * d^2)/4
((pi * D^2)/4)/2 = (pi * (D^2-d^2))/4
Thus, d = .7071 * D
Going back to moment of inertia,
Iy_solid = (pi * D^4)/64
and
Iy_hollow = [pi * (D^4 - d^4)]/64 = [pi * (D^4 - (.7071 * D)^4)]/64 = (pi * D^4)*3/256
Therefore, the ratio of moments is
Iy_solid / Iy_hollow = 1.333
And, since
tau_max = (T_max*D)/Iy
tau_max_solid/tau_max_hollow = .75
Therefore, a 50% reduction in weight only results in an 33.3% higher maximum shear stress.
The knife geometry would be more complicated, of course, but I kept it simple here for the purposes of illustration.
Yes, the solid shaft is stronger, given the same outer diameter.
However, a larger hollowed out shaft can be made that will bear just as much load as the solid shaft with a considerable weight savings.
That is why your car's drive shaft is hollow, bicycle frames are hollow, etc...
So, making a "blood groove" on a knife cannot possibly make it stronger, unless a larger knife was made with the groove material removed to make it comparable in weight to the smaller knife, in which case we would no longer be talking about the same knife.
If anything, the "blood groove" will introduce a stress concentration and make the knife weaker than just shaving off material from the blade to achieve the same weight.