Metals and Alloys

Heat treatment is a controlled sequence of heating a metal (steel) in the solid state to a definite temperature, holding (soaking) it there for a set time and then cooling at a chosen rate, in order to change its internal structure (grain size, phases) and so obtain the desired mechanical properties without changing its shape.

Principle

The properties of steel depend on its microstructure. When steel is heated above the critical temperature (about 723-910 C, depending on carbon), its structure changes to austenite (a solid solution of carbon in gamma-iron). On cooling, austenite changes into different structures according to the cooling rate:

Thus by controlling the heating temperature, soaking time and cooling rate, the structure and so the properties (hardness, strength, ductility, toughness) can be adjusted. The main processes are annealing, normalizing, hardening (quenching), tempering and surface hardening.

The main purposes of heat treatment of metals (steel) are:

1. To increase hardness and wear resistance (for example cutting tools and bearing surfaces) by quenching.
2. To soften the metal and improve machinability and cold working (annealing).
3. To improve strength and toughness, and to obtain a good combination of them (normalizing, tempering).
4. To relieve internal stresses caused by welding, casting, forging or cold working, preventing cracking and distortion.
5. To refine the grain size and make the structure uniform (homogeneous).
6. To increase ductility and malleability.
7. To harden only the surface and keep a tough core (case hardening).
8. To improve electrical and magnetic properties, and corrosion/heat resistance.
9. To remove gases and improve the structure of castings.

Annealing is a heat treatment in which steel is heated to a temperature above its upper critical point (about 30-50 C above, 723-910 C depending on carbon content), held (soaked) there for sufficient time, and then cooled very slowly, usually in the furnace itself.

Purposes

• Softens the steel and improves ductility and machinability.
• Relieves internal stresses and refines the grain.
• Gives a uniform structure (coarse pearlite and ferrite).

 Temp
  ^      _______  <- soak (above upper
  |     /       \    critical temp)
  |    /         \
  |   /           \___ slow furnace
  |  /                  cooling
  +-----------------------------> Time

Types: full annealing, process annealing (below the lower critical), stress-relief annealing, spheroidising and isothermal annealing.

Steel (and iron) is supplied in the market in the following commercial forms:

1. Bars: round, square and flat bars; deformed bars (TMT/Tor bars) of 6-40 mm diameter for reinforcement.
2. Structural sections: angles (L), channels (C), I-beams (ISMB), T-sections, H-sections, and hollow sections (square, rectangular, circular).
3. Plates and sheets: plain sheets, chequered plates, corrugated galvanised iron (CGI) sheets.
4. Wires: plain and binding wires, high-tensile wire and strands for prestressing, wire mesh and fabric.
5. Pipes and tubes: GI, black pipes, seamless and welded tubes.
6. Rails, rods and strips.
7. Castings and forgings: cast iron pipes, manhole covers and fittings; bolts, nuts, nails, rivets, screws, hooks.
8. Cables and ropes (wire ropes).

Normalizing is a heat treatment in which steel is heated to about 40-50 C above its upper critical temperature, soaked for a short period, and then cooled in still air (at room temperature).

• Faster cooling than annealing gives a finer, more uniform grain (fine pearlite) than annealing.
• Results in higher strength, hardness and toughness than annealed steel, and removes internal stresses from forging, rolling or casting.
• Used for structural steel, castings and forgings, and as a preparation before hardening.

Quenching is the rapid cooling of steel from a high temperature (the hardening temperature, above its upper critical point, 30-50 C above) by dipping it in a quenching medium such as water, brine, oil or air blast.

It prevents the austenite from changing into soft pearlite, and instead forms martensite, which is very hard and strong but brittle and has internal stress. Hence quenching is normally followed by tempering. The quenching speed depends on the medium (brine is fastest, then water, then oil).

Surface hardening (case hardening) is a heat treatment that makes the outer layer (case) of a steel part hard and wear resistant, while the inner core remains soft, tough and ductile. It is used for gears, cams, shafts, bearings and tools that need a hard surface to resist wear but a tough core to resist shock.

Methods

1. Carburising: low carbon steel is heated at about 900-950 C in a carbon-rich medium (charcoal, gas or liquid) so that carbon diffuses into the surface (0.5-2 mm); then quenched and tempered, giving a high-carbon hard case.
2. Nitriding: steel containing Al, Cr or Mo is heated at about 500-550 C in ammonia, forming very hard nitrides on the surface without quenching; little distortion.
3. Cyaniding / carbonitriding: heated in a molten cyanide salt bath so carbon and nitrogen enter the surface; quenched.
4. Flame hardening: the surface is heated with an oxy-acetylene flame and quenched immediately by water spray.
5. Induction hardening: the surface is heated by high frequency induced current, then quenched.

   Hard case (high carbon)
   +---------------------+
   |  ...............    |
   |  .  Tough, soft  .  |
   |  .     core      .  |
   |  ...............    |
   +---------------------+

Why mechanical treatment is done

Mechanical treatment (mechanical working) is the shaping of steel by applying force (hammering, rolling, drawing) to obtain the required shape and size, and to improve its properties.

• It gives the required shape and size (bars, sheets, sections, wires).
• It refines the grain and removes casting defects such as blow holes and porosity, increasing strength, toughness and density.
• It improves the surface finish and dimensional accuracy.
• Cold work raises yield strength and hardness (strain hardening).

Methods

A. Hot working (above the recrystallisation temperature, about 900-1200 C for steel):

1. Rolling: red-hot steel passes between rollers to make plates, sheets, bars and structural sections.
2. Forging: hammering or pressing hot steel into shape (bolts, hooks, crankshafts).
3. Extrusion: forcing hot metal through a die to give a long section.
4. Pressing/piercing: for pipes and hollow items.

B. Cold working (at room temperature or below recrystallisation temperature):

1. Cold rolling: for thin sheets with a smooth surface.
2. Drawing: a bar is pulled through a die to make wires and rods.
3. Bending, twisting (cold twisted deformed bars) and stretching.
4. Spinning, shearing, stamping and pressing.

• Metal: an element that is usually hard, lustrous, malleable and ductile, and a good conductor of heat and electricity, for example iron, copper, aluminium, zinc and lead. Metals are crystalline solids and form positive ions.
• Alloy: a mixture of a metal with one or more other metals or non-metals, formed by melting them together and solidifying, to obtain improved properties (strength, hardness, corrosion resistance). Examples: steel (iron + carbon), brass (copper + zinc), bronze (copper + tin).

Importance of steel in civil engineering

• High strength in tension and compression, with a high strength-to-weight ratio.
• Ductile, tough and elastic, so structures give warning before failure and absorb earthquake energy.
• Used as reinforcement in RCC, structural frames, bridges, roof trusses, towers, and for pipes, doors and windows.
• Easy to fabricate and join (welding, bolting), quick to erect, uniform quality, and recyclable.
• Needs protection from corrosion and fire.

Types of steel

A. By carbon content (composition)

B. By alloying elements

• Plain carbon steel: iron + carbon (with small Mn, Si).
• Alloy steel: with added Cr, Ni, Mo, V, Mn, etc., for special properties: stainless steel (Cr and Ni, corrosion resistant), high tensile steel (HTS), and tool steels.

C. By use / properties: structural steel, reinforcing steel (Fe 415, Fe 500), tool steel, stainless steel, and high strength low alloy steel.

Carbon is the main element that decides the strength and hardness of steel.

• As the carbon percentage increases (up to about 1%), the strength and hardness increase, as carbon forms hard iron carbide (cementite) with iron.
• Ductility, malleability, toughness and weldability decrease with more carbon.
• Carbon makes steel responsive to heat treatment (hardening by quenching).

Typical range is 0.05-1.5% carbon (below 2%); above 2% it becomes cast iron.

Tempering is the reheating of hardened (quenched) steel to a temperature below the lower critical point (150-650 C), holding it there, and then cooling in air or oil. It reduces the brittleness and internal stresses of martensite and increases toughness and ductility, with some loss of hardness.

 Temp
  ^
  |        ______ temper temp (150-650 C)
  |       /      \
  |      /        \ cool in air
  |     /          \
  +--------------------------> Time

Lower tempering temperature (150-300 C) retains hardness (cutting tools); higher (400-650 C) gives more toughness (springs, shafts).

Mechanical vs heat treatment

Annealing

Annealing is heating steel above the upper critical temperature, soaking, and cooling very slowly in the furnace to soften it, remove internal stresses and refine the grain.

Red shortness

Red shortness is the brittleness of steel at red-hot temperature (during hot working such as forging and rolling), causing cracks. It is caused by the presence of sulphur (forming low melting iron sulphide at the grain boundaries). It is reduced by adding manganese, which forms manganese sulphide, and by keeping sulphur low.

Mechanical treatment versus heat treatment

Isothermal annealing

Isothermal annealing is a variant of full annealing in which steel is heated above its upper critical temperature (austenitised), cooled rapidly to a temperature just below the lower critical point (about 600-700 C), held at this constant temperature until the austenite fully transforms to pearlite/ferrite, and then cooled in air.

 Temp
  ^
  |   ____ austenitise (A3 + 30-50 C)
  |  /    \
  |-/------\------------- A1 (723 C)
  | /       \_________
  |/    rapid cool  | hold (isothermal)
  |                 |_______ air cool
  +--------------------------> Time

It saves time compared with full annealing, gives uniform structure and good machinability, and is used for alloy steel forgings and castings.

Tempering

Tempering is the reheating of hardened (quenched) steel to a temperature below the lower critical point (150-650 C), holding it there, and then cooling in air or oil. It reduces the brittleness and internal stresses of martensite and increases toughness and ductility, with some loss of hardness.

 Temp
  ^
  |        ______ temper temp (150-650 C)
  |       /      \
  |      /        \ cool in air
  |     /          \
  +--------------------------> Time

Lower tempering temperature (150-300 C) retains hardness (cutting tools); higher (400-650 C) gives more toughness (springs, shafts).

Heat treatment is the controlled heating of a metal (steel) in the solid state to a definite temperature, soaking, and cooling at a chosen rate to change its structure and get the desired properties, without changing the shape.

Objectives

1. To increase hardness and wear resistance.
2. To soften the metal and improve machinability.
3. To improve strength, toughness and ductility.
4. To relieve internal stresses of casting, welding or cold working.
5. To refine grain size and make the structure uniform.
6. To harden only the surface (case hardening).

Isothermal annealing

Isothermal annealing is a variant of full annealing in which steel is heated above its upper critical temperature (austenitised), cooled rapidly to a temperature just below the lower critical point (about 600-700 C), held at this constant temperature until the austenite fully transforms to pearlite/ferrite, and then cooled in air.

 Temp
  ^
  |   ____ austenitise (A3 + 30-50 C)
  |  /    \
  |-/------\------------- A1 (723 C)
  | /       \_________
  |/    rapid cool  | hold (isothermal)
  |                 |_______ air cool
  +--------------------------> Time

It saves time compared with full annealing, gives uniform structure and good machinability, and is used for alloy steel forgings and castings.

Heat treatment of steel is heating it to a definite temperature, holding it there, and cooling at a chosen rate, to change the microstructure and obtain required properties (hardness, strength, ductility), without change of shape.

Isothermal annealing

Isothermal annealing is a variant of full annealing in which steel is heated above its upper critical temperature (austenitised), cooled rapidly to a temperature just below the lower critical point (about 600-700 C), held at this constant temperature until the austenite fully transforms to pearlite/ferrite, and then cooled in air.

 Temp
  ^
  |   ____ austenitise (A3 + 30-50 C)
  |  /    \
  |-/------\------------- A1 (723 C)
  | /       \_________
  |/    rapid cool  | hold (isothermal)
  |                 |_______ air cool
  +--------------------------> Time

It saves time compared with full annealing, gives uniform structure and good machinability, and is used for alloy steel forgings and castings.

Quenching

Quenching is the rapid cooling of steel heated above the upper critical temperature (30-50 C above), by dipping in water, brine or oil.

• Rapid cooling prevents formation of soft pearlite, and austenite changes into martensite, giving very high hardness and strength.
• The steel becomes brittle and has residual stress, so it is tempered afterwards.
• Cooling rate: brine > water > oil > air. High-carbon steel is hardened by quenching; low-carbon steel does not harden much.

 Temp
  ^
  |   ____  heat 30-50 C above A3
  |  /    |
  | /     | very rapid cooling
  |/      |  in water/oil
  |        \______
  +------------------------> Time
   Result: martensite (hard, brittle)

Principle of heat treatment

Steel properties depend on its microstructure. Heating above the critical temperature converts the structure to austenite; the rate of cooling then decides the final structure: slow cooling gives soft pearlite/ferrite, moderate cooling gives fine pearlite, and very fast cooling gives hard martensite. By controlling temperature, soaking time and cooling rate, the required properties are obtained.

Importance

• Adjusts hardness, strength, toughness and ductility to the use.
• Relieves internal stress and refines the grain.
• Improves machinability, wear resistance, and fatigue life.
• Allows a single steel to be used for many purposes.

Quenching

Quenching is the rapid cooling of steel heated above the upper critical temperature (30-50 C above), by dipping in water, brine or oil.

• Rapid cooling prevents formation of soft pearlite, and austenite changes into martensite, giving very high hardness and strength.
• The steel becomes brittle and has residual stress, so it is tempered afterwards.
• Cooling rate: brine > water > oil > air. High-carbon steel is hardened by quenching; low-carbon steel does not harden much.

Tempering

Tempering is the reheating of hardened (quenched) steel to a temperature below the lower critical point (150-650 C), holding it there, and then cooling in air or oil. It reduces the brittleness and internal stresses of martensite and increases toughness and ductility, with some loss of hardness.

 Temp
  ^
  |        ______ temper temp (150-650 C)
  |       /      \
  |      /        \ cool in air
  |     /          \
  +--------------------------> Time

Lower tempering temperature (150-300 C) retains hardness (cutting tools); higher (400-650 C) gives more toughness (springs, shafts).

Quenching and tempering together give a hard but tough steel (tools, springs, shafts).

Heat treatment

Heat treatment is the controlled heating of steel to a definite temperature, soaking, and cooling at a set rate to alter its structure and properties without changing shape.

Why it is necessary

• To get the required hardness, strength, toughness and ductility.
• To remove internal stresses and refine the grain.
• To improve machinability and wear resistance, and to harden surfaces.

Three methods

1. Annealing Steel is heated to about 30-50 C above the upper critical temperature, soaked, and cooled very slowly in the furnace. It gives soft, ductile steel with a coarse pearlite and ferrite structure, relieves stresses and improves machinability.

2. Normalizing Steel is heated about 40-50 C above the upper critical temperature, soaked briefly and cooled in still air. Faster cooling gives a finer grain, higher strength and toughness than annealing. Used for forgings, castings and structural steel.

3. Quenching (hardening) and tempering Quenching is the rapid cooling of steel heated above the upper critical temperature (30-50 C above), by dipping in water, brine or oil.

• Rapid cooling prevents formation of soft pearlite, and austenite changes into martensite, giving very high hardness and strength.
• The steel becomes brittle and has residual stress, so it is tempered afterwards.
• Cooling rate: brine > water > oil > air. High-carbon steel is hardened by quenching; low-carbon steel does not harden much.

After quenching, steel is tempered by reheating below 723 C (150-650 C) to reduce brittleness.

Copper is used for: electric wires, cables and bus bars (high electrical conductivity); water supply pipes and fittings, roof sheets and flashings (corrosion resistance); alloys such as brass and bronze; heat exchangers and boilers (thermal conductivity); and ornamental and roofing work.

Non-ferrous metals contain no (or very little) iron.

General properties

• Lighter, resist corrosion (do not rust), and good conductors of heat and electricity.
• Easy to cast, work and form, and non-magnetic.
• Generally weaker and costlier than steel.

Common metals and uses

Ferrous products (iron base)

Cast iron, wrought iron, mild steel, high carbon and alloy steels: reinforcement bars, structural sections, plates, pipes, columns, wires, nails, bolts, GI sheets.

• Merits: high strength, ductility, toughness, easy to weld and fabricate, recyclable, relatively cheap.
• Demerits: corrode (rust) and need painting/galvanising, heavy, lose strength in fire, magnetic.

Non-ferrous products

Aluminium, copper, zinc, lead, tin, brass, bronze: windows and doors, roofing, wires, pipes, fittings, flashing, galvanising, ornamental work.

• Merits: light, corrosion resistant, good conductors, easy to work, attractive appearance, low maintenance.
• Demerits: costly, lower strength than steel, aluminium has a lower stiffness and melting point, and some (lead) are toxic.

Alloy steels contain added elements (Cr, Ni, Mn, Mo, V, etc.) which improve properties that plain carbon steel cannot match. They are preferred because they give:

1. Higher strength and hardness, with good toughness.
2. Better corrosion resistance (stainless steel) and heat resistance.
3. Better wear and fatigue resistance.
4. Good response to heat treatment (deeper hardening).
5. Better weldability, machinability and magnetic or electrical properties for special uses.

So thinner and lighter members can be used, which saves weight and material despite higher cost.

Alloy steels are steels containing alloying elements, other than carbon, in enough quantities (usually above 1-2%) to give special properties.

Common alloy steels

Alloying improves strength, hardness, toughness, corrosion and heat resistance, but increases cost.

Metals used in modern civil engineering

1. Ferrous metals: cast iron (pipes, columns), wrought iron (gates, railings), and steel (mild steel, high tensile, stainless).
2. Non-ferrous metals: aluminium (windows, cladding), copper (wires, pipes), zinc (galvanising), lead (pipes, shielding), tin, and their alloys brass and bronze.

Why alloys are popular

Pure metals are usually too soft, weak or reactive for direct use. Alloying with other elements:

• increases strength, hardness and toughness (steel is stronger than pure iron; duralumin than aluminium);
• improves corrosion resistance (stainless steel, brass);
• improves workability, castability and lowers melting point;
• improves wear, heat and fatigue resistance;
• allows the properties to be adjusted by the proportion of elements, and may reduce cost.

Examples: steel (Fe + C), brass (Cu + Zn), bronze (Cu + Sn), duralumin (Al + Cu), stainless steel (Fe + Cr + Ni).

Uses

• Cast iron: pipes, columns, manhole covers, brackets, drainage fittings.
• Steel: reinforcement, structural frames, bridges, trusses, roofs, tanks.
• Aluminium: windows, doors, roof sheets, cladding, curtain walls, conductors.

Cast iron is an iron-carbon alloy containing 2–4.5% carbon (plus Si, Mn, S, P), made by remelting pig iron. It is hard and brittle, and it is cast into shape because it cannot be forged or rolled.

Manufacture

Pig iron is first produced in a blast furnace from iron ore, coke (fuel and reducing agent) and limestone (flux). Pig iron is then refined into cast iron in a cupola furnace.

1. Blast furnace: Charge of ore, coke and limestone is fed from the top; hot air blast enters near the bottom. Coke burns to give CO, which reduces the ore ($Fe_2O_3 + 3CO \rightarrow 2Fe + 3CO_2$). Limestone combines with silica impurities to form slag. Molten iron collects at the bottom and is tapped as pig iron.
2. Cupola furnace: A vertical cylindrical furnace lined with fire bricks. Pig iron, scrap iron, coke and limestone are charged in layers. An air blast through tuyeres burns the coke and melts the iron. The molten metal is tapped from the bottom, poured into moulds, and cooled to get castings.

   Charge (pig iron+scrap+coke+flux)
            |
        +---v---+
        |       |  <- Cupola
  Air ->|=======|  <- tuyeres
        |       |
        +---+---+
            |  Molten iron -> Mould
            v  Slag tapped separately

Types

Grey cast iron (flake graphite), white cast iron (carbon as cementite), malleable cast iron (annealed white iron), and nodular (SG) cast iron.

Properties

• Carbon content 2–4.5%; melting point about 1200 °C (lower than steel).
• Very high compressive strength (about 600–1000 N/mm²), but low tensile strength (about 150–250 N/mm²).
• Hard and brittle; fails suddenly with little elongation.
• Good fluidity when molten, so complex shapes can be cast.
• Cannot be welded easily, forged or rolled; can be machined (grey iron).
• Good wear resistance and vibration damping.
• Resists corrosion better than mild steel; specific gravity about 7.2–7.5.

Uses: pipes, manhole covers, columns, brackets, drain fittings, machine beds and railings.

Microscopic (microstructure) examination is the study of the internal structure of a metal under a microscope. A small sample is cut, ground, polished to a mirror finish, etched with a mild acid (e.g. nital, 2% nitric acid in alcohol) and viewed at 100–1000× magnification. It shows the phases, grain size and shape, which control the strength and hardness of the steel.

Microstructures of steel

1. Ferrite: Almost pure iron (about 0.02% C) in BCC form. Soft, ductile, weak, magnetic. Appears as light, white grains.
2. Cementite ($Fe_3C$): Iron carbide with 6.67% C. Very hard and brittle. Appears as white needles or plates.
3. Pearlite: A lamellar (layered) mixture of ferrite and cementite, with 0.8% C. Appears dark in an etched sample, like mother-of-pearl. Fairly strong and tough.
4. Austenite: Solid solution of carbon in FCC iron, stable above about 723 °C. Non-magnetic, soft, tough. Exists at room temperature only in special (stainless) steels.
5. Martensite: Supersaturated carbon in BCT iron, formed by rapid quenching of austenite. Needle-like, very hard and brittle.
6. Bainite: Fine mixture of ferrite and cementite formed by cooling at an intermediate rate. Harder than pearlite and tougher than martensite.
7. Troostite and sorbite: Tempered martensite products. Troostite is harder and finer; sorbite is tougher and less hard.

Low-carbon steel has ferrite + pearlite; 0.8% C steel is fully pearlite; high-carbon steel has pearlite + cementite.

Steel is an alloy of iron and carbon (up to about 1.5% C) that is the most important structural material in construction. Its properties depend on the carbon content and heat treatment.

• Strength: High strength in both tension and compression. Mild steel has yield strength about 250 N/mm²; HYSD (Fe 415/500) bars have 415–500 N/mm².
• Ductility: Mild steel stretches a lot before failure, giving warning. Ductility falls as carbon increases.
• Malleability and toughness: It can be rolled, forged and bent into shapes, and absorbs energy well.
• Hardness: Increases with carbon content and by quenching.
• Elasticity: Modulus of elasticity about $2 \times 10^5$ N/mm², nearly constant for all grades.
• Weldability: Good in low-carbon steel; poor when carbon exceeds about 0.3%.
• Density: About 7850 kg/m³.
• Fatigue resistance and homogeneity: Uniform material with predictable behaviour.
• Thermal and electrical conductivity: Good conductor; loses strength above about 400–500 °C.
• Corrosion: Rusts in moist air unless protected by paint, galvanising or alloying.
• Magnetic: Ordinary steel is magnetic (stainless austenitic grades are not).
• Recyclable.

Corrosion is the gradual destruction of a metal by chemical or electrochemical reaction with its environment (oxygen, moisture, acids, salts), converting it to oxides, hydroxides or salts. Rusting of iron is the common example.

Types of corrosion

1. Uniform (general) corrosion: Attack over the whole exposed surface at nearly equal rate, e.g. rusting of unprotected steel sheets.
2. Galvanic (bimetallic) corrosion: When two dissimilar metals are in contact in the presence of an electrolyte, the more active (anodic) metal corrodes, e.g. steel bolts in copper or brass fittings.
3. Pitting corrosion: Localised attack forming small deep holes, often by chlorides; dangerous because it is hard to detect.
4. Crevice corrosion: Occurs in narrow gaps (under washers, joints) where oxygen supply differs.
5. Stress corrosion cracking: Cracks under combined tensile stress and a corrosive environment.
6. Intergranular corrosion: Attack along grain boundaries, e.g. in poorly heat-treated stainless steel.
7. Erosion corrosion and atmospheric corrosion: Wear of protective film by flowing fluid; and rusting by humid or polluted air.

Methods of prevention

1. Protective coatings: Paint, varnish, bitumen, enamel, or oil/grease on the surface.
2. Metallic coatings: Galvanising (zinc), tinning, chromium or nickel plating, cladding.
3. Alloying: Using stainless steel (Cr, Ni) or weathering steel.
4. Cathodic protection: Connecting the structure to a more active metal (sacrificial anode such as Zn or Mg), or using an impressed current.
5. Proper design: Avoid crevices and contact of dissimilar metals, provide drainage, use insulation washers.
6. Environment control: Remove moisture, use dehumidifiers or corrosion inhibitors.
7. Concrete cover: For reinforcement, use dense concrete with adequate cover and low permeability.
8. Anodising or phosphating (for aluminium and iron surfaces).

Steel with 0.80% carbon is the eutectoid steel. Pearlite itself contains 0.80% C, so the steel is entirely pearlite.

Data: carbon in steel $C = 0.80\%$; carbon in pearlite $= 0.80\%$; carbon in cementite ($Fe_3C$) $= 6.67\%$. Carbon dissolved in ferrite is neglected (about 0.02%).

Pearlite

Cementite

Ferrite

Free (proeutectoid) ferrite is $100 - 100 = 0\%$, because all the ferrite and cementite are present together as lamellae in pearlite.

Answer: Pearlite = 100%; cementite = 11.99%; ferrite = 88.01% (all of the ferrite and cementite lie inside the pearlite).

The carbon is present as iron carbide ($Fe_3C$, cementite). Pearlite is the eutectoid mixture of ferrite and cementite containing 0.80% C, and the steel is hypo-eutectoid ($C < 0.80\%$), so it has free ferrite plus pearlite.

Data: $C = 0.33\%$; cementite has 6.67% C; pearlite has 0.80% C.

Cementite

Ferrite (total, free + in pearlite)

Pearlite

The rest, $100 - 41.25 = 58.75\%$, is free (proeutectoid) ferrite. The ferrite and cementite inside the pearlite are in the ratio 88.01 : 11.99.

Answer: Cementite = 4.95%; total ferrite = 95.05% (of which free ferrite = 58.75%); pearlite = 41.25%.

The carbon is present as iron carbide ($Fe_3C$, cementite). Pearlite is the eutectoid mixture of ferrite and cementite containing 0.80% C, and the steel is hypo-eutectoid ($C < 0.80\%$), so it has free ferrite plus pearlite.

Data: $C = 0.35\%$; cementite has 6.67% C; pearlite has 0.80% C.

Cementite

Ferrite (total, free + in pearlite)

Pearlite

The rest, $100 - 43.75 = 56.25\%$, is free (proeutectoid) ferrite. The ferrite and cementite inside the pearlite are in the ratio 88.01 : 11.99.

Answer: Cementite = 5.25%; total ferrite = 94.75% (of which free ferrite = 56.25%); pearlite = 43.75%.

The question gives no carbon content, so the common textbook case is taken: high strength steel is high carbon steel of eutectoid composition, 0.80% C. Pearlite holds 0.80% C and cementite holds 6.67% C (carbon dissolved in ferrite is neglected).

So the structure is 100% pearlite, made of about 88% ferrite and 12% cementite layers. Free ferrite is zero.

General method for any hypo-eutectoid steel with carbon $C$ (%): pearlite $= \dfrac{C}{0.80} \times 100$ and free ferrite $= 100 -$ pearlite. For example, for 0.60% C: pearlite $= 75\%$, free ferrite $= 25\%$.

Answer: Pearlite = 100%, with 88.01% ferrite and 11.99% cementite inside it (0.80% C steel).