Question 5 of 7: TTT Diagram Reading for 1035 Steel; Maximum Crack Size in a Pressure Vessel

Question 5: TTT Diagram Reading for 1035 Steel; Maximum Crack Size in a Pressure Vessel (20 marks)

Question text not reproduced: the examination questions are © Engineers and Geoscientists BC. Open the official past paper (linked at the top of this page) to read the question, then follow the worked solution below.

Given. (a) The printed TTT diagram for 0.35%C (AISI/SAE 1035) steel, reproduced below. Temperature runs $300$–$1500^{\circ}$F on the left ordinate; time runs $50$ s to $100{,}000$ s logarithmically; and the right-hand ordinate is a hardness scale that ties each isothermal transformation temperature to the Brinell hardness of the fully transformed product. Reading the printed tick marks against the temperature gridlines gives

The transformation-start curve noses at $1100^{\circ}$F, $\approx100$ s; the transformation-finish curve noses at $1100^{\circ}$F, $\approx500$ s. $M_s$ sits on the $600^{\circ}$F gridline and $M_f$ on the $500^{\circ}$F gridline. (b) Low-alloy steel tank: $\sigma_y=600$ MPa, $K_{Ic}=120$ MPa$\cdot\sqrt{\text m}$, applied stress $=0.70\sigma_y$.

Find. (a)(i) Two microstructures that could give $400$ HB as-cast. (a)(ii) An isothermal-anneal time–temperature schedule reaching $\le250$ HB, with the hold temperature and hold time read off the diagram. (b) The critical crack size, and crack-detection methods.

Approach

(a) On this diagram hardness is read from the right-hand ordinate as a function of the temperature at which the austenite transforms, so a target hardness fixes a transformation temperature directly; the corresponding time is then read where that temperature line crosses the transformation-finish curve. An isothermal anneal is executed by austenitizing, cooling fast enough to miss the $100$ s nose, holding at the chosen temperature until the finish curve is crossed, then air-cooling. (b) is a direct application of the plane-strain fracture-mechanics relation $K_{Ic}=f\sigma\sqrt{\pi a_c}$ (geometry factor $f=1$, no factor given).

1. (a)(i) Where $400$ HB sits on the diagram. The right-hand scale puts $400$ HB on the $600^{\circ}$F line — which is also the $M_s$ line — and $500$ HB on the $500^{\circ}$F ($M_f$) line. Note what this rules out: the softest product the pearlite nose can give is $240$ HB at $1100^{\circ}$F, and even a $1000^{\circ}$F hold reaches only $300$ HB, so no pearlitic structure on this steel reaches $400$ HB. The $400$ HB casting must therefore have transformed at or below $600^{\circ}$F.
2. (a)(i) The two microstructures. (1) Bainite — specifically lower bainite, the fine ferrite/carbide aggregate formed isothermally just above $M_s$ at about $600^{\circ}$F, which the diagram's own hardness scale puts at exactly $400$ HB. Heavy or chilled sections of a casting that cool quickly past the nose but stall above $M_s$ produce it. (2) Martensite (untempered, with some retained austenite) — thin or mould-chilled sections that cool fast enough to miss the nose entirely and pass below $M_s=600^{\circ}$F transform martensitically; fully martensitic material reads $500$ HB on the same scale, so a section that is part martensitic and part bainitic/pearlitic averages the observed $400$ HB. Both are the classic as-cast "hard spots" that ruin machinability.
3. (a)(ii) Isothermal-anneal schedule — choosing the hold temperature. The hardness scale must read $\le250$ HB, so the transformation temperature must be at or above the point where the scale reads $250$. Interpolating the two bracketing ticks ($240$ HB at $1100^{\circ}$F and $300$ HB at $1000^{\circ}$F) gives $250$ HB at about $1083^{\circ}$F; any hold at or above that satisfies the specification. The natural choice is the nose temperature itself: $$\boxed{T_{\text{hold}} = 1100^{\circ}\text{F}\ (\approx 595^{\circ}\text{C}),\ \text{giving }240\ \text{HB} \le 250\ \text{HB}}$$ It is the fastest temperature at which the specification can be met — going higher for extra softness costs an order of magnitude or more in holding time.
4. (a)(ii) Hold time and the full cycle. At $1100^{\circ}$F the diagram's transformation-start curve is crossed at $\approx100$ s and the transformation-finish curve at $\approx500$ s, so the hold must last until the finish curve is passed: $$\boxed{t_{\text{hold}} \approx 500\ \text{s} \approx 8\ \text{min (hold 10 min for margin)}}$$ The complete cycle is therefore: austenitize at $\approx1550$–$1600^{\circ}$F (above the $A_3$/upper curve, which leaves the top of the diagram near $1500^{\circ}$F) and soak to full austenite; cool rapidly to $1100^{\circ}$F, fast enough that the cooling path stays left of the $100$ s start curve so no transformation occurs on the way down; hold isothermally at $1100^{\circ}$F for $\approx500$ s until transformation to $\alpha+\text{Ca}$ is complete; then air-cool to room temperature, during which nothing further transforms because the austenite is already fully consumed. The product is $240$ HB and readily machinable. The time–temperature chart this describes is drawn below.
5. (b) Minimum crack size that causes failure. The smallest flaw that will propagate unstably is the critical crack size $a_c$ — below it $K
6. (b) Crack-detection methods. Non-destructive evaluation (NDE) methods capable of resolving flaws at or below this size include: ultrasonic testing (pulse-echo, resolves internal flaws down to sub-millimetre size and gives depth information); radiography (X-ray/gamma, good for volumetric flaws, less sensitive to tight planar cracks unless aligned with the beam); magnetic-particle inspection (surface/near-surface cracks in ferromagnetic steels — directly applicable here); dye-penetrant inspection (surface-breaking cracks only, any material); and acoustic emission monitoring (detects active crack growth in service via the elastic waves it emits, rather than sizing a static flaw). For this ferromagnetic low-alloy tank, magnetic-particle inspection combined with ultrasonic thickness/flaw scanning is the typical in-service combination.