Calculating Ultimate Tensile Strength?

[semperfudge]

Homework Statement

A metal of cross-sectional area 3.22E-4 m2 is being tested in compression. At an engineering strain of 20%, the compression load of the sample is determined to be 25000lb. Calculate the true stress and true strain at that point. Assume sigma=A(epsilon)N where the strain hardening exponent N=0.35. Calculate the ultimate tensile strength assuming m=0.

Homework Equations

true stress = P/A
true strain = ln(1+e) where e=deltaL/L
m=d*ln(stress)/d*ln(strain rate)
ultimate tensile strength = Pmax/Ao
sigma = A(epsilon)^0.35

The Attempt at a Solution

So far I have calculated true strain epsilon to be 0.182 by substituting 0.2 into e. Then I calculated true stress to be P/A = (11205N)/(3.22E-4m2)=3.48E7 Pa. Now I don't know what do to calculate the ultimate tensile strength. I determined A=6.32E7 but now what?

 

[KataKoniK]

First, let's clarify the units of the given information. The cross-sectional area is given in square meters, but the load is given in pounds. We need to convert the load to Newtons, the standard unit of force in the SI system. 1 lb = 4.448 N, so the load of 25000 lb is equivalent to 111200 N.

Next, we can use the given equation for true stress, sigma = A(epsilon)^N, to solve for A. Plugging in the values we have, we get:

3.48E7 Pa = A(0.2)^0.35
A = 6.32E7 Pa

Now, we can use this value of A to calculate the ultimate tensile strength. The equation for ultimate tensile strength, Pmax/Ao, tells us that we need to find the maximum load, Pmax, and the original cross-sectional area, Ao. We already have Ao, which is 3.22E-4 m2. To find Pmax, we can use the given equation for true stress, sigma = A(epsilon)^N, and solve for Pmax. Plugging in the values we have, we get:

Pmax = sigma * Ao / (epsilon)^N
= (6.32E7 Pa) * (3.22E-4 m2) / (0.2)^0.35
= 2.18E8 Pa * m^2 / 0.59049
= 3.69E8 Pa * m^2

Finally, we can convert this to the appropriate units of pressure, which is Pascals. 1 Pa = 1 N/m2, so the ultimate tensile strength is:

Pmax = 3.69E8 Pa * m^2 = 3.69E8 N/m2 = 3.69E8 Pa

Therefore, the ultimate tensile strength is 3.69E8 Pa, or 369 MPa.