# Shear stress without fracture?

1. Mar 27, 2013

### risecolt

Material: PVC
E-modulus: 1300 N/mm^2
Poisson's ratio: 0.35
Applied shear force: 100 N
Resisting area: 28 mm^2

Shear modulus: E = 2G(1+v) --> G = E/(2(1+v)) = 1300/(2(1+0.35) = 481 N/mm^2

Does this mean that a force which can be applied to the area without fracturing is 481 N/mm^2 * 28 mm^2?

I just need to know. How can I use this information to calculate how much shear force the area can be exposed to?

Last edited: Mar 27, 2013
2. Mar 27, 2013

### SteamKing

Staff Emeritus
G is the ratio of shear stress to shear strain, analogous to E being the ratio of tensile stress to tensile strain.

In order to answer your question about maximum shear stress of PVC, you will have to find out more information about the material (e.g., max. tensile stress) The max. shear stress is usually expressed as a factor * ult. tensile stress for ductile materials like metals. For plastics like PVC, there may be a different relationship.

3. Mar 28, 2013

### risecolt

I have an equation for polymers which describes the relationship between the shear yield point and uniaxial yield point based on the Von Mises criterion:

τy = ( ((1+μ)/sqrt(3)) /sqrt(3) ) * σy

From a diagram plotted by a stress test, I have the value for uniaxial yield point σy; the point where the material becomes subject to plastic deformation.

μ is a material parameter which determines the change in yield point with respect to a change in pressure. But I'm not sure how I can acquire this parameter, nor can I find any tables for this parameter. Neither do I know the name of this parameter. Is it effective viscosity?