# Ultimate Tensile Strength

1. Nov 4, 2007

### pecosbill

1. The problem statement, all variables and given/known data

What is the ultimate tensile strength if necking begins at a true strain = 0.25 in a material whose stress strain curve obeys the relation:
sigma=120000(epsilon)^1/2 psi?

2. Relevant equations

3. The attempt at a solution

I'm kind of stumped on this. I really doesn't understand what's going on, but I know the answer is 116,700 psi.
1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

2. Nov 5, 2007

### Astronuc

Staff Emeritus
Is this the relationship after the yield point, i.e. does this apply after the material has yielded, and therefore has elastic strain of YS/E?

3. Nov 5, 2007

### pecosbill

yes, after necking begins. however, this is the only information i was provided with, no young's mod.

4. Nov 5, 2007

### pecosbill

this is the solution my teacher handed out in class today, but when i asked him about adding the yield strength, he forgot why he added it.

_____
TRANSLATE INTO S:
if volume is constant,
sigma=l/a=(V(0)L)*s/VL(0))

sigma=(L/L(0))s
ln(L/L(0))=E or L/L(0)=e^0.25

sigma(at UTS)=60000=se^0.25
s=60000*e^/0.25=46800 psi

s(uts)=s+s(yield)=46800+70000 psi=116800 psi

________
This solution cleared nothing up for me. I understand up to the very last line...that all makes sense to me. But why does he add yield strength, and where the hell does he get that value of yield strength from? It's not given in the problem, so I assume there is an easy way to calculate it from the information given?
I know this problem is really confusing, but if anyone can offer an explanation of the yield strength and where it came from, I'd appreciate it.

5. Nov 10, 2007

### Astronuc

Staff Emeritus
If the material was loaded to necking and then unloaded, the measured true strain is the the permanent strain, since the material unloads along a diagonal parallel with the elastic line.

The stress-strain relationship appears to be just the stress-strain relationship for plasic deformation beyond yield.

6. Nov 11, 2007