Question

# a brass sample has a yield strength of 345 MPa and a Young’s modulus of 103...

a brass sample has a yield strength of 345 MPa and a Young’s modulus of 103 GPa and is loaded to 370MPa, without necking, before being unloaded. Next, this same specimen is loaded to 300MPa. What is the strain resulting from this load?

For elastic deformation

ε(test) < ε(yield)

For plastic deformation

ε(test) > ε(yield)

In this case

When test load = 370 MPa

Yield strength = 345 MPa

Young’s modulus E = 103 GPa

For plastic deformation

ε(test) / ε(yield) > 1

( test load/E) / (Yield strength/E) > 1

(370/345) > 1

1.07 > 1

Since the deformation is plastic

strain resulting from 370 MPa = strain resulting from 345 MPa

= Yield strength / E

= 345 MPa / (103*10^3 MPa)

= 0.00335

When test load = 300 MPa

Yield strength = 345 MPa

Young’s modulus E = 103 GPa

For elastic deformation

ε(test) / ε(yield) <1

( test load/E) / (Yield strength/E) < 1

(300/345) < 1

0.869 < 1

Since the deformation is elastic

Strain resulting from 300 MPa =

= 300 MPa / (103*10^3 MPa)

= 0.00291

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