If I had a piece of 3K twill carbon fiber 5"x1"x4mm, how thick of a piece of titanium (5"x1") would I need to have the approx equivalent strength? I assume the titanium piece would weigh more?
In the real industry they use UNI-directional carbon fiber .....3K carbon twill carbon is more for cosmetics then something useful for a more demanding task then knife handle .. ... Now , Strenght .......strenght has many face , on which one you think when you want to compare carbon with titanium ?
In what way do you want the Ti to be as strong as the CF?
As Natlek has pointed out strength is not a single term. There is breaking strength, bend resistance strength, puncture resistance ( bullet proof), wear resistance, etc.
There is no answer to your question without the parameters of your test.
It's actually not for a knife handle, but I couldn't think of a place with more knowledgeable people in this department. It's too hot for me to make knives over the summer so I took up flying (mostly crashing) racing drones. I was thinking of milling some arms out of titanium this winter if I could get the weight close. I think it could withstand more abuse than the carbon fiber ones. That and titanium has major cool factor.
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