Materials
Materials science links a material's internal structure — atoms, crystals, and phases — to the mechanical, thermal, and chemical properties engineers select for. The FE tests standard property values, crystal-structure geometry, phase diagrams, and thermal behavior, blending memorized facts with short calculations.
Mechanical properties and the stress–strain curve
A tensile test produces a stress–strain curve whose initial straight portion has slope equal to the modulus of elasticity (Young's modulus): about 200 GPa for structural steel and 70 GPa for aluminum. The proportional limit ends elastic behavior; the yield strength marks the onset of permanent deformation; the ultimate strength is the peak stress. Ductile materials (like mild steel) stretch substantially and neck before fracture, giving warning; brittle materials (like cast iron or ceramics) fracture with little plastic deformation. Toughness is the area under the whole curve, hardness a surface's resistance to indentation.
Thermal behavior and thermal stress
Materials expand when heated by δ = α·L·ΔT, where α is the coefficient of thermal expansion. A 10 m steel bar with α = 12×10⁻⁶ /°C heated 50°C grows δ = 12×10⁻⁶·10·50 = 6×10⁻³ m = 6 mm. If expansion is restrained, thermal strain becomes thermal stress σ = E·α·ΔT — the reason bridges use expansion joints, rails leave gaps, and pipelines add loops. Thermal conductivity and specific heat round out thermal selection, mattering wherever heat must be conducted or stored.
Crystal structures and packing
Metals crystallize on repeating lattices. A body-centered cubic (BCC) cell has an atom at each corner plus one in the center, 2 atoms per cell, a coordination number of 8, and an atomic packing factor (APF) of 0.68. A face-centered cubic (FCC) cell adds atoms on each face, giving 4 atoms per cell, coordination number 12, and a denser APF of 0.74 — the tightest packing possible for equal spheres, shared by hexagonal close-packed (HCP). APF is the fraction of the cell volume actually occupied by atoms. These numbers explain why FCC metals like copper and aluminum tend to be more ductile than BCC metals.
Phase diagrams and the lever rule
A binary phase diagram maps which phases exist at a given temperature and composition. In a two-phase region, the lever rule gives the fraction of each phase from the tie line: the weight fraction of one phase equals the opposite-arm length over the total tie-line length. For an alloy at 40 wt% B between an α phase at 20 wt% B and liquid at 60 wt% B, the liquid fraction is (40 − 20)/(60 − 20) = 0.5. Reading composition and phase amounts off a diagram is a reliable FE task.
Phase transformations and the iron–carbon system
A eutectic reaction is the isothermal transformation, on cooling, of a single liquid into two distinct solid phases simultaneously (L → α + β) at a fixed eutectic composition and temperature. The iron–carbon diagram anchors ferrous metallurgy: alloys are classified as steels below about 2.0 wt% carbon and as cast irons above it, because higher carbon changes the phases that form and the material's brittleness. Heat treatments such as annealing, quenching, and tempering exploit these transformations to tune strength, hardness, and ductility.
Failure, corrosion, and selection
Beyond static overload, materials fail by fatigue under repeated cyclic loading (below the static strength, initiated at stress concentrations), by creep under sustained load at high temperature, and by corrosion. Corrosion is an electrochemical process — galvanic attack occurs when dissimilar metals contact in an electrolyte, the more active metal acting as the sacrificial anode, the principle behind cathodic protection. Material selection ultimately balances strength, stiffness, weight, cost, corrosion resistance, temperature capability, and manufacturability against the demands of the application.
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