Discerning the Elasticity Modulus of Brittle Cast Iron from Test Data

• Illgresi
In summary, the poster is seeking help with a lab report on a tensile test. They have successfully determined the modulus for two samples (high carbon steel and aluminum) but are having trouble with the third sample, which they believe is cast iron. They are unsure how to calculate the Young's modulus for the cast iron sample as it does not have a linear portion on the stress/strain diagram. Another user suggests using the 0.2% strain as a reference point, and the poster later confirms that they have solved the problem using the secant modulus method.
Illgresi
Here goes try number two, the forum deleted my last post.

First time poster, so hopefully I'm following the rules, I do apologise if I'm not. I have a problem with my lab report, I would be very grateful if anyone could help. Thanks.

Homework Statement

I'm writing a tensile test lab report and have hit a snag along the way. We were given three unknown specimens and through analysis of the recorded data, are to make educated guesses as to what they are. I have all but confirmed the first two are high carbon steel and aluminium of some description. Young's modulus, UTS and 0.2% proof stress are all accurate. In the case of the third sample, my modulus is far below what I would expect (22.5 GPa). I am however, convinced it is cast iron due to a number of factors; the shape of the load/extension diagram, the uts/fracture stress and above all the fact that it smelled like cast iron.

Homework Equations

σ=F/A, ε=ΔL/L0, E=σ/ε

The Attempt at a Solution

My successful attempt at calculating the modulus for samples A and B was to take an average (mean) across the entire elastic region for both stress and strain, and using these values to calculate. Essentially creating a best fit line, which made sense given E is actually the gradient. It worked superbly for the first two samples; 206.6 GPa for the steel sample, and 68 GPa for the Aluminium.

The problem with the 'Cast Iron' sample, is that it doesn't have any apparent linear portion; it curves from the origin to the fracture point. I was hoping someone could provide some ideas what to do. Perhaps there is a special technique for materials of this type?

I have included a picture of the stress/strain diagram of sample B (Al) and Sample C ('cast iron') to illustrate what I mean.

FYI, the dotted lines represent 0.2% offset, as you can see, it is particularly accurate for Sample B.

Many, many thanks for any help.

sample B has a well-defined yield, compared with sample C. It is quite common, in non-linear cases like C to take an equivalent linear case, using the 0.002 strain as a reference point.

pongo38 said:
sample B has a well-defined yield, compared with sample C. It is quite common, in non-linear cases like C to take an equivalent linear case, using the 0.002 strain as a reference point.

Hi, thanks for the reply, although I don't quite follow.

I'm aware that using 0.2% proof stress is the done thing unless the material shows yield point behaviour. What I'm having difficulty with is calculating the Young's Modulus. As I state above, my figure of 22.5 GPa is more inline with Graphite than Cast Iron which is in the region of 170 GPa.

Thanks.

FYI, I've solved the problem.

Gray iron does not obey Hooke’s law, and the modulus in tension is usually arbitrarily determined as the slope of the line connecting the origin of the stress-strain curve with the point corresponding to 1 / 4 of the tensile strength (secant modulus).

Campbell, F. C.. Elements of Metallurgy and Engineering Alloys. p.463

Thank you for sharing your question with the community. I understand the importance of accurately determining the properties of materials, especially for engineering purposes. Based on the information provided, it seems that you have done a thorough analysis of the first two samples and have successfully determined their Young's modulus. However, you have encountered a challenge with the third sample, which you believe to be cast iron.

One possible explanation for the discrepancy in your calculated Young's modulus for the cast iron sample could be the presence of impurities or defects in the material. Cast iron is known for its brittleness and can contain non-metallic inclusions, which can affect its mechanical properties. This could explain the lack of a linear portion in your stress-strain curve.

In such cases, it may be helpful to consult with your instructor or a materials expert to determine if there are any special techniques or adjustments that can be made to accurately determine the modulus of brittle materials like cast iron. It may also be worth considering conducting additional tests or analyses to confirm your initial hypothesis that the third sample is indeed cast iron.

Overall, it is important to acknowledge any limitations or uncertainties in your data and to seek guidance when faced with challenges in your analysis. I wish you the best of luck with your lab report and hope that you are able to find a satisfactory solution for determining the elasticity modulus of brittle cast iron.

1. How is the elasticity modulus of brittle cast iron determined?

The elasticity modulus of brittle cast iron is typically determined through tensile testing, where a sample of the iron is pulled apart until it breaks. The resulting load and displacement data is then used to calculate the elasticity modulus.

2. What factors can affect the accuracy of the elasticity modulus calculation?

The accuracy of the elasticity modulus calculation can be affected by factors such as the quality and size of the sample, the testing method used, and any external influences or defects in the iron itself.

3. Can the elasticity modulus of brittle cast iron change over time?

Yes, the elasticity modulus of brittle cast iron can change over time due to factors such as aging, exposure to extreme temperatures, and mechanical stress. It is important to regularly test and monitor the elasticity modulus to ensure the integrity of the iron.

4. How is the elasticity modulus of brittle cast iron used in engineering applications?

The elasticity modulus of brittle cast iron is an important property used in engineering applications to determine the strength and durability of structures and components made from this material. It is also used in the design and analysis of various mechanical systems.

5. Are there any alternative methods for determining the elasticity modulus of brittle cast iron?

Yes, there are alternative methods for determining the elasticity modulus of brittle cast iron, such as ultrasonic testing and non-destructive testing. However, tensile testing is the most common and reliable method for accurately calculating the elasticity modulus.

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