Shear and Tensile Strengths 1

[DBCox]

Hello everyone,

I have searched and searched this site as well as the web for the relationship between shear and tensile strengths of metals. I typically use 1/2 of tensile to estimate the shear strength. However, I remember a professor telling us that there is a definate relationship that can be used to determine the shear strength of a metal if the tensile strength is known. It MUST be a metal, and it goes back to the 45 degree shear plane theory.

I want to say the relationship to tensile to shear is 1/sqrt(2) which is .707. This makes sense to me due to the geometry of the 45 degree shear plane, but I keep seeing this .577 factor pop up too. I cannot figure out where this is coming from. The .577 has something to do with the Mohr circle, but I am not as familiar with it, so I cannot reproduce this .577 result. Can someone do a quick derivation of this so I can stop thinking about it?

Thanks

 

[metengr]

The 0.577 factor does not apply to the ultimate tensile strength, it applies to the relationship between the tensile stress to cause yield and the shear stress to cause yield in metals. If you use the von Mises equation for predicting the equivalent stress to cause yield of metals, set the von Mises stress to cause yield = to the tensile yield stress (since in pure tension the other two principal stresses in the equation are 0).

Plug into the von Mises equation for the principal stress the shear yield stress (set the other two principal stresses equal to 0 because you can assume pure shear) and solve, you will obtain the following

shear stress to cause yield = tensile yield strength/sqrt (3)

 

[DBCox]

Metengr,

Thanks for the info. I see where it is coming from now (I think). The reason it is sqrt(3) rather than sqrt(2) is b/c of 3 principle stresses, correct? I was thinking 2d world, which is why I kept going back to 1/root2.

Thanks!

 

[TVP]

The ultimate shear strength is usually around 0.6*UTS. Perform a keyword search here at Eng-Tips for other discussions, etc.