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For Ti–6Al–4V, use its own fracture toughness and yield stress inThe same unit-conversion formulas from part(i) apply. A feasible yield-limited screening interval requires $t_{\mathrm{yield}}<t_{\max }$, using consistent crack geometry and low-temperature properties.

High specific strength and corrosion resistance can be attractive, but cost, fabrication, joining and toughness must also be assessed. The label HCP is not a sufficient rule that every titanium alloy has the same sharp ductile-to-brittle transition as ferritic steel; actual low-temperature alloy and microstructural data are needed.

TODO: numerical thickness cannot be completed without the unavailable 2018 NST Data Book's Ti–6Al–4V property pair. No historical value or material-specific Arctic toughness is invented.

For high-strength steel, useAt fixed toughness, raising yield stress reduces $t_{\max }$ quadratically but reduces the required pressure thickness only linearly. Thus a higher-strength grade can have a worse leak-before-break screening margin. The relevant screening combination is $K_{IC}^2/{\sigma }_y$, since simultaneous satisfaction requiresUse measured low-temperature toughness and appropriate joining/environmental performance; strength alone does not establish suitability. The comparison also has to remain within the thin-wall approximation.

TODO: numerical thickness cannot be completed without the unavailable 2018 NST Data Book's high-strength-steel property pair. The four material rankings cannot be made numerically definitive from the exam PDF alone.

Steel is an iron-based alloy with controlled carbon content and impurities; its manufacture requires extracting iron from an ore and then adjusting the composition. In a modern plain-carbon classification, steel generally contains less than about $2\%$ carbon by mass, whereas pig iron is more carbon-rich. The historical practical contrast was with low-carbon wrought iron and readily cast but relatively brittle cast iron. Hardening by quenching is characteristic of suitable carbon-rich steels, but not every grade hardens in the same way.

Begin, for example, with an iron oxide ore. Preparation removes some earthy matter and, where appropriate, roasting expels moisture or converts a carbonate-bearing ore to oxide. A blast furnace receives the ore, coke and a flux such as limestone. The hot air blast sustains combustion of coke, generating heat and the carbon monoxide needed for much of the oxide reduction. Representative overall balances areCalcination of limestone provides calcium oxide. Combination with acidic gangue, represented by silica, gives a liquid slag:Actual slag is a multicomponent melt, rather than necessarily pure calcium silicate. The descending iron picks up carbon and other impurities and collects as molten pig iron. This first extraction product is not already finished steel.

Two important routes available in 1867 proceed from this stage. In the older indirect route, refining and puddling oxidize much of the carbon and remove slag-associated impurities to obtain wrought iron. Bars packed with charcoal are then heated for a prolonged period in the cementation process. Carbon enters the bars, giving blister steel; forging and welding can make shear steel, while melting suitable stock in covered crucibles produces more uniform crucible steel. The bar can acquire carbon through gas-mediated surface reactions and diffusion; the process should not be imagined as intact charcoal grains travelling through the iron.

In the Bessemer process, an air blast passes through molten pig iron in a converter. Oxidation of silicon, manganese and carbon supplies heat, while lowering the carbon content. Composition can be corrected by adding a controlled carbon- and manganese-bearing material such as spiegeleisen. Henry Bessemer's 1856 patent describes the central idea of maintaining the conversion by oxidizing constituents of the molten metal, without fuel for reheating during that stage.^[ref]

The early acidic converter demanded suitable feed: it did not solve removal of phosphorus from every ore. Later basic converter practice must not be silently imported into a December 1867 account. Final casting, working and heat treatment determine the steel microstructure and properties as well as composition. The useful manufacturing chain is therefore ore → extracted carbon-rich iron → controlled composition → worked and appropriately heat-treated steel.

The characteristic effect is an irradiation-induced upward shift of the ductile-to-brittle transition in ferritic steel. A component previously used above its transition can then fail by cleavage fracture at the same service temperature, with much less warning from plastic deformation.

Ferrite has a body-centered cubic lattice. At low temperature, dislocation glide becomes difficult enough that brittle crack propagation can precede substantial plastic relaxation. Irradiation hardening raises the yield strength by introducing obstacles to dislocation glide; the competition with cleavage fracture consequently shifts toward brittle failure. Austenite, with its face-centered cubic lattice, does not normally show this same sharp cleavage transition. This does not make austenitic steel immune to loss of ductility, helium embrittlement or other radiation damage in materials.

Examine the fracture surface for cleavage fracture facets and river patterns, and compare Charpy impact test energy-versus-temperature curves from exposed material and an unirradiated reference of the same composition and heat treatment. The reference is important: a low impact energy from one failed specimen cannot establish an irradiation-induced shift. Transition curves can also use lateral expansion or the proportion of ductile fracture appearance.^[ref]

A direct fracture toughness test over the transition region complements the Charpy impact test; the two measurements are not interchangeable. Combine these observations with exposure history, local temperature, microstructure and crack location. Brittle appearance supports the failure mechanism, while a measured transition shift and suitable controls support its attribution to irradiation.

Neutron capture by boron-10 can generate helium, leading to helium embrittlement, especially at elevated temperature. The relevant nuclear reaction isThe emitted alpha particle eventually becomes a helium atom in the metal. The product branch can also involve gamma emission, without changing this helium-producing balance. The production depends on boron isotopic content and the neutron energy spectrum; a thermal component is particularly relevant to this reaction.

Helium has very low solubility in steel and can be trapped at vacancies, interfaces and grain boundaries. Boron already segregated near grain boundaries can therefore create a locally unfavorable distribution of helium. Stabilized helium–vacancy clusters develop into bubbles or cavities. Under tensile stress, boundary cavities can grow and link, reducing ductility, fracture toughness and creep-rupture life through intergranular fracture. Early thin-foil observations and mechanical tests associated high-temperature ductility loss with helium-containing boundary bubbles and their coalescence.^[ref]

Irradiation temperature controls the transport and clustering of both helium and vacancies. At lower temperature, reduced long-range transport can retain small trapped clusters in the matrix. These can contribute to irradiation hardening, but extensive boundary-cavity growth is kinetically less favorable. At higher temperature, migration, cavity growth and material creep become faster, making intergranular fracture and loss of high-temperature ductility more likely. Trap distribution and prior microstructure can redistribute the gas, so there is no composition-independent critical temperature or universal monotonic law.

The mechanical-test temperature also matters. Material irradiated cold can become embrittled during subsequent hot testing or service when trapped gas and defects become mobile. Distinguish gas production during irradiation from the later conditions under which its mechanical consequences are expressed.

The key imbalance is preferential loss of self-interstitials to biased defect sinks, leaving a vacancy supersaturation that can feed void swelling. The initial displacement cascade creates both vacancies and self-interstitials, often in equal net numbers as Frenkel pairs; it need not create more vacancies than interstitials at birth.

Many nearby Frenkel pairs recombine. Others separate, become trapped or form dislocation loops. Surviving self-interstitials are usually much more mobile than vacancies over the relevant range. Dislocations also have an interstitial bias: their elastic interaction with defects makes them more efficient sinks for self-interstitials. Preferential interstitial removal to the dislocation structure can leave the mobile vacancy population above its thermal equilibrium value.

A minimal radiation damage rate theory makes the distinction explicit:Here $c_i,c_v$ are defect number densities, $G$ is the surviving mobile-pair production rate per volume, $K$ the recombination coefficient, $D_i,D_v$ the diffusion coefficients, and $k_i^2,k_v^2$ the respective sink strengths. The vacancy loss term includes thermal emission in an effective form. Equal production terms do not require equal steady populations or equal partitioning among sinks. This simplified model omits an explicit cluster-size distribution.

A stable cavity receiving a greater vacancy influx than interstitial influx and vacancy emission grows. Vacancies therefore condense into voids, producing void swelling. Helium can stabilize small cavity nuclei, but a growing vacancy void need not be a high-pressure gas bubble. Dislocation loops, precipitates and changes in the dislocation density evolve alongside the voids and modify the competing sink strengths.

There is no violation of atom conservation: atoms represented by removed self-interstitials have joined extended defects or surfaces, while the corresponding unfilled lattice volume can accumulate in cavities. The classic electron-microscope observations of cavities in irradiated type316 steel provide direct evidence for this microscopic basis of swelling.^[ref]

Irradiation softening occurs when irradiation removes pre-existing strengthening obstacles faster than it creates new ones. It is particularly plausible in an initially hardened alloy, rather than an initially soft annealed reference.

In a material strengthened by cold working, the starting dislocation density is high. Irradiation-generated point defects can assist dislocation climb, rearrangement and annihilation, reducing the contribution of work hardening. A schematic estimate iswhere $\mu$ is the shear modulus, $b$ the magnitude of the Burgers vector, ${\rho }_d$ the dislocation density, and the last two terms represent precipitate and irradiation-obstacle strengthening. It is an illustrative decomposition, not an exact additive law for every alloy. A sufficiently large decrease in the pre-existing contributions can exceed the increase in $\Delta {\sigma }_{\mathrm{irr}}$.

In a material strengthened by precipitation hardening, ballistic mixing can dissolve or disorder the original obstacles. Radiation-enhanced diffusion can change their composition or accelerate coarsening; increasing obstacle spacing can reduce strength. In an ordered alloy, irradiation-induced loss of order can also remove a strengthening contribution. None of these outcomes is inevitable: irradiation can instead create new strengthening precipitates.

The required conditions therefore include an appropriate initial microstructure, enough displacement dose to modify it, and a temperature and displacement dose rate at which obstacle removal or recovery can compete with new defect accumulation. Compare with an unirradiated specimen held for the same time at the same temperature to separate ordinary thermal aging from an irradiation effect.

A drop in yield strength or hardness need not restore ductility: cavities, helium embrittlement or localization of dislocation glide can coexist with softening. Conversely, an initially annealed steel may show strong irradiation hardening under the same exposure conditions.

Physical metallurgy connects the internal structure of metals and alloys to their properties and the processes used to change them. It studies crystal structures, crystal defects, phases and their transformations, including changes caused by deformation and heat treatment.

A controlled comparison heats samples of the same steel and cools them differently, then measures hardness and examines their microstructures. Differences in properties can then be related to phase formation and transformation history rather than to a change in overall chemical composition. This is why selecting an alloy and selecting its thermal/mechanical processing are coupled design decisions.^[ref]

Historical steel made by welding and forging suitable steel bars, often from blister steel.

A chromium-bearing steel whose protective surface film can confer corrosion resistance. Composition, microstructure and environment determine whether that protection persists.

Steel is an iron-based alloy family in which carbon and other alloying elements control structure and properties. It is not a single compound with one fixed carbon content.

Cooling and heat treatment change the distribution of phases and microstructural features. The same overall elemental composition can therefore give very different strength, hardness, and ductility depending on how the material was processed.

Steelmaking produces steel by controlling the carbon content, other alloying elements and unwanted constituents of iron. A blast furnace first produces carbon-rich pig iron; a basic oxygen furnace then refines the molten material by oxidation and composition adjustment. An electric arc furnace instead supplies heat electrically to melt a charge that can include recycled steel, direct reduced iron and pig iron.^[ref]

The distinction between iron extraction and steelmaking matters: converting an iron oxide to metallic iron and adjusting an existing iron-based alloy to the required composition are different tasks. The Bessemer process is an important historical example of refining pig iron by an air blast; modern basic oxygen steelmaking uses an oxygen supply rather than ordinary air.