EMA 4223 February 2007

Mechanical Behavior of Materials        Example Test 3B

Name ________________________ UFID # _________________

1. A polycrystalline metal has a plastic stress-strain curve that obeys the Hollomon-Ludwik equation,

s = K eⁿ. Determine n, knowing that the flow stresses of this material at 2% and 10% plastic deformation (offset) are equal to 180 MPa and 200 MPa, respectively.

2. You are traveling in an airplane. The engineer who designed it tells you that the wings are designed using von Mises’ criterion . Would you feel safer if she had told you that Tresca’s criterion would be used? Why?

3. Calculate the softening temperature for a soda-lime silica glass at which the viscosity is equal to 10^13.4 P if the activation energy for viscous flow is 2.5 kJ/ mole and the viscosity at 1000°C is 10¹⁴ P. [1 P = 0.1 Pa s}.

4. When tested at room temperature, a thermoplastic material showed a yield stress of 60 MPa in uniaxial tension and 80 MPa in uniaxial compression. Compute the tensile yield strength of this polymer when tested in a pressure chamber with superimposed hydrostatic pressure of 300 MPa. Remember there will be a contribution to hydrostatic stress from the uniaxial stress equal to s₀/3.

5. There are at least three theories for flow in biaxial loading. Sketch the graphical representation of these theories in biaxial loading using the principal stresses s₁ and s₂ as the axes. Identify the representation of the theories in the figure. Make it clear which is which in all quadrants.