### Strain Hardening Behavior Exercise - Example Answers

What is the value of flow stress at strain = 1?

** ***s* = *K*

*s* = *K*.

On the stress-strain plot a value of *n* can be set and different values of *K* tried. It will be seen that the value on the stress axis for strain = 1 is equal to the value of *K* chosen.

A more easily seen answer can be obtained by by setting a value for *K* and trying various values of *n*.

Which material parameter, *K* or *n*, has a larger effect on material strength?

For example, using a value of *e* = 2

with *K* = 200 MPa

for *n* = .2 the flow stress is about 225 MPa

for *n* = .4 the flow stress is about 250 MPa

a ( 250 - 225 ) / 225 change of 11%

with *n* = .4

for *K* = 200 MPa the flow stress is about 250 MPa

for *K* = 400 MPa the flow stress is about 575 MPa

a ( 575 - 250 ) / 250 change of 130%

Answering this question requires defining "strength" and deciding on a method for comparing values of strength. One possibility is to define strength as the flow stress at a particular value of strain and ask, does doubling the value of *K* or *n* have a larger effect on flow stress?

If the value of *K* is doubled, by how much does the flow stress change?

The effect of doubling the value of *K* at *n* = .4 and *e* = 2 was determined above.

with *n* = .2 and *e* = 2

for *K* = 200 MPa the flow stress is about 250 MPa

for *K* = 400 MPa the flow stress is about 525 MPa

a ( 575 - 250 ) / 250 change of 130%

If the value of *n* is halved, by how much does the flow stress change?

Again, flow stress depends on *K* and *e* as well as on *n* so the answer will vary with the values of *K* and *e* at which the comparison is made.

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© 2001 by Barney E. Klamecki. All rights reserved