Question 9

[1 mark] Simple familiar

Topic guidesPremiumTopic guide 12 · Reading a stress–strain diagram Topic guide 12 · Worked example: 2025 Question 9

Game planPremium5.3 Read a stress–strain diagram

The question

A stress–strain diagram for four aluminium alloys is shown.

Four stress–strain curves from the origin for aluminium alloys W, X, Y and Z, each in its own line style, with stress on the vertical axis and strain on the horizontal axis. W, a thick grey dotted curve, rises steeply, bends over and keeps climbing slowly to the highest stress, ending far to the right. X, a dashed curve, yields a little higher than W and runs above it through the middle of the graph, then W crosses it and X turns down and ends earlier. Y, a dash-dot curve, rises most steeply, yields lower and stays almost flat before ending in the middle of the graph. Z, a fine dotted line, rises at a shallow slope to a bend and then climbs slowly to the furthest strain of all, staying well below the others. — Figure based on Fig 2 in Owolabi, G. et al. (2019), Fatigue Responses of Three AA 2000 Series Aluminum Alloys, Journal of Materials Science and Chemical Engineering, 7, 32–48, CC BY 4.0.

Which aluminium alloy has the greatest toughness?

That is it. Step through the hints below to see why. In 2025, 71.6% of Queensland students chose (A).

Not quite. X runs above W through the middle of the graph, so it looks bigger. W then crosses it, keeps climbing and runs on after X has turned down and stopped. X ends up with about three quarters of W’s area. In 2025, 14.9% of Queensland students chose (B).

Not quite. Y has the steepest start, so it is the stiffest, but it yields low and stays flat, and it stops before W. Its area is about half of W’s. In 2025, 3.2% of Queensland students chose (C).

Not quite. Z stretches furthest, so it is the most ductile, but it stays far below W the whole way. Its area is only about half of W’s. In 2025, 9.9% of Queensland students chose (D).

Pick an alloy (QCAA tells them apart by line style)

Trace along the curve

Rank the four curves by

Toughness is the energy a material absorbs before it breaks, the area under the whole curve from the origin to fracture.

$$\begin{gathered}\text{toughness}\\=\text{area under the curve}\end{gathered}$$

Match each letter to its line style first. W is the thick dotted curve, X dashed, Y dash-dot and Z the fine dotted line. W and X cross, so follow the style through the crossing.

Area needs height and length together. W ends at the highest stress and runs further than X and Y. Only Z runs further, and Z stays far lower.

X’s lead over W in the middle is a thin sliver, worth about 1% of W’s area on QCAA’s figure. The part of W beyond the end of X is worth about 23%.

Measured from QCAA’s figure, with W’s area as 100%:

$$\begin{gathered}\text{W}=100\%\quad\text{X}\approx74\%\\\text{Z}\approx52\%\quad\text{Y}\approx51\%\end{gathered}$$

W encloses the most area, so it has the greatest toughness.

Toughness is the area under the curve. W ends at the highest stress and runs further along the strain axis than X and Y, so it encloses the most area. Only Z runs further, and Z stays far lower.

(A)

How Queensland students answered in 2025

(A)

71.6%

(B)

14.9%

(C)

3.2%

(D)

9.9%

The most common wrong answer was (B), X. It runs above W through the middle of the graph, and this is the only QCAA stimulus so far in which curves cross. Judge the whole area, not the part where one curve looks higher. Stress-strain diagrams are reduced content in the 2025 syllabus, yet one appeared in every paper from 2020 to 2025.

Only mark this done when you could do it without help. Reading the solution does not count.

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Question wording and any figures are from the 2025 QCAA Engineering external assessment, © State of Queensland (QCAA) 2025, licensed under CC BY 4.0, and have been adapted, except where a third-party source is named. Tangent Tuition is not affiliated with the QCAA.

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