Calculating Ultimate Tensile Strength?

In summary, we calculated the true stress and true strain for a metal sample under compression, and then used those values to determine the ultimate tensile strength of the sample. We also converted the load from pounds to Newtons and clarified the units for each given value.
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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?
 
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  • #2


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.
 

Related to Calculating Ultimate Tensile Strength?

1. What is ultimate tensile strength (UTS)?

UTS is the maximum amount of stress that a material can withstand before breaking or fracturing. It is a measure of a material's ability to resist tensile forces, or pulling apart.

2. How is UTS calculated?

UTS is typically calculated by dividing the maximum load applied during a tensile test by the original cross-sectional area of the material. This results in a unit of stress, such as pounds per square inch (psi) or megapascals (MPa).

3. What factors can affect UTS?

There are several factors that can affect UTS, including the type of material, its composition and microstructure, temperature, and the presence of defects or imperfections. The manufacturing process and any external forces applied to the material can also affect its UTS.

4. Why is UTS important?

UTS is an important measure in engineering and materials science because it helps determine the strength and durability of a material. It is used to ensure that materials can withstand the expected stresses and forces in different applications, from building structures to manufacturing equipment.

5. How is UTS used in material selection?

When selecting a material for a specific application, UTS is one of the factors that engineers and scientists consider. A higher UTS indicates a stronger material that can withstand greater tensile forces and is less likely to fail under stress. However, other properties such as ductility, hardness, and cost must also be taken into account in the material selection process.

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