What is the thickness dependance of shear strength?

Question

I'm trying to find out how in-plane shear strength for a foam core panel changes based on thickness of the foam. The testing shear strength for EPS foam is 15 psi with a 1" thickness. Is there a governing equation for shear vs. thickness that I could use to approximate shear strength at 2", 4", 6", 8"?

Also would it be linear across different points on the stress/strain curve, or just at the rupture point?

Answer 1

There are at three types of shear on a material. These are;

1. Cutting shear

2. Longitudinal shear

3. Shear due to torsion

Since we are not talking about shafts, we deal only with the first two.

Cutting shear is the stress produced across the material by two opposite and equal forces. The shear stress is given by the formula;

(1). v = V/bd

Where;

v = the shear stress

V = the shear force

b = the width of the material

d = the thickness of the material

Cutting shear is assumed to be distributed evenly on the cross-sectional area of the material at the line of shear.

Longitudinal shear is the shear stress produced by bending which tends to split the material lengthwise. This type of shear is maximum at the neutral axis of the material. for a rectangular section, the neutral axis falls at the mid-thickness of the material. For a rectangular section, the maximum longitudinal shear stress is given by the formula;

(2). v = 1.5V/bd

Where;

v = shear stress

V = maximum value of the shear force

b = width of the material

t = thickness of the material

Longitudinal shear stress is maximum at the neutral axis and reduces to zero at the upper and lower faces of the beam.

The above formulas show how the thickness affects the shear stress.