• Support PF! Buy your school textbooks, materials and every day products Here!

Continuum Mechanics: Finding Plastic Strain

  • Thread starter lanew
  • Start date
13
0
1. Homework Statement

http://img683.imageshack.us/img683/7060/selection001l.png [Broken]


2. Homework Equations

[itex]\epsilon^{pl} = \epsilon - \epsilon^{el}[/itex]

[itex]\epsilon^{pl} = \epsilon - \frac{\bar{\sigma}}{E}[/itex]

[itex]r = \frac{\epsilon_w}{\epsilon_t}[/itex]


3. The Attempt at a Solution

I'm stuck trying to calculate [itex]\bar{\sigma}[/itex]. Can I just assume that [itex]\bar{\sigma} = \sigma[/itex] @ 104 s-1? If so, the axial plastic strain is calculated as follows:

[itex]\begin{align}
\epsilon_a^{pl} &= \epsilon_a - \frac{\bar{\sigma}}{E} \\
&= (0.10) - \frac{(66.1)}{(200*10^3)} \\
&= 0.09967
\end{align}[/itex]

and

[itex]\begin{align}
\epsilon_w^{pl} &= \epsilon_w - \frac{\bar{\sigma}}{E} \\
&= (-0.042) - \frac{(66.1)}{(200*10^3)} \\
&= -0.04233
\end{align}[/itex]

If this is correct I should be able to related the thickness by [itex]v[/itex], correct?

Also, as far as (b) goes, should I be using [itex]\sigma = k \epsilon^n \dot{\epsilon}^m[/itex]?
 
Last edited by a moderator:

Answers and Replies

114
2
[itex]\bar{\sigma}[/itex] might be intended to be taken as Von Mises (Von Mises is the only context where I've personally seen [itex]\bar{\sigma}[/itex]). So, for this uniaxial stress, you should (if I'm not mistaken) divide the value that you are using for [itex]\bar{\sigma}[/itex] by [itex]\sqrt{3}[/itex].

I'm not too familiar with this stuff, but I'm assuming that your table of strains and stresses are all beyond yield, and the higher strain rates are supposed to correlate with stronger material behavior (typos in the table?). Figured I'd take a look since you have no replies, but I'm no plasticity expert.
 

Related Threads for: Continuum Mechanics: Finding Plastic Strain

  • Last Post
Replies
2
Views
819
  • Last Post
Replies
2
Views
885
Replies
2
Views
2K
Replies
1
Views
1K
  • Last Post
Replies
0
Views
999
Replies
1
Views
490
Replies
0
Views
846
Top