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Five primary mechanisms increase strength: (1) solid-solution strengthening from dissolved alloying atoms, (2) precipitation hardening from small coherent particles blocking dislocation motion, (3) grain-refinement (Hall-Petch) from smaller grains, (4) work-hardening from increased dislocation density, and (5) dispersion-strengthening from non-deformable particles. Combinations of these mechanisms are used in alloy design to maximize strength while maintaining ductility.
From plastic deformation and yielding, you know that a metal yields when dislocations begin moving through the lattice under an applied shear stress. The yield strength is therefore the stress required to move dislocations. Every strengthening mechanism exploits this by creating obstacles that impede dislocation motion — either by imposing elastic strain fields that resist dislocation approach, by placing physical barriers the dislocation must cut or bypass, or by simply increasing the density of dislocations until they jam each other. Understanding which mechanism is active tells you how to design the alloy and what temperature or processing limits apply.
Solid-solution strengthening places foreign atoms — either substitutional (similar size, sitting in lattice sites) or interstitial (small atoms like carbon squeezed between lattice sites) — throughout the matrix. These atoms distort the surrounding lattice, creating local strain fields. A passing dislocation interacts elastically with these strain fields: it must push through regions of lattice mismatch. Interstitial atoms (carbon in iron, nitrogen in steel) are especially potent because they create asymmetric, non-spherical distortions that interact with both edge and screw dislocations. The strength increment scales roughly as c1/2 for random solid solutions. Pure aluminum is soft; aluminum-magnesium alloys are considerably harder from Mg in solid solution, without any heat treatment.
Precipitation hardening (also called age hardening) introduces fine, coherent particles of a second phase by a sequence of solution treatment (dissolve all solute at high T), quench (trap it in supersaturated solution), and age (let fine precipitates nucleate and grow at intermediate T). When precipitates are small and coherent — lattice planes continuous across the particle-matrix interface — dislocations can shear through them but must do extra work to do so (cutting mechanism). When precipitates grow larger and become incoherent, dislocations loop around them and leave dislocation rings (Orowan bowing mechanism). Peak strength occurs at intermediate particle sizes where both mechanisms are equally difficult. Over-aging coarsens the particles past the optimal size, reducing strength. The 2xxx and 7xxx series aluminum alloys (used in aircraft structure) are classic precipitation-hardened systems.
Grain refinement works differently: grain boundaries are high-angle discontinuities in crystal orientation. A dislocation gliding in one grain cannot easily cross the boundary — it would have to change its Burgers vector and slip system to continue in the neighboring grain. Grain boundaries therefore act as barriers that cause dislocation pileups, raising the stress needed to propagate yielding. The Hall-Petch relation σ_y = σ_0 + k/√d encodes this: smaller grain diameter d means more boundaries per unit length and a higher yield stress. Grain refinement is unique among strengthening mechanisms in that it also improves fracture toughness, because smaller grains limit crack propagation. Fine-grained microstructures are achieved by controlled rolling, recrystallization treatments, or microalloying additions that pin grain boundaries.
Work hardening (strain hardening) occurs during deformation itself. As a metal is cold-worked, dislocation density increases from roughly 1010/m² (annealed) to 1015–1016/m² (heavily deformed). At these densities, dislocations interact strongly with one another: they form junctions, tangle, and pile up against each other. Each increment of additional deformation requires higher stress to move dislocations through this increasingly obstructed network — the metal hardens as it is worked. This is exploited in cold-drawing wire and forming sheet metal. The trade-off is reduced ductility: a heavily work-hardened metal has little remaining capacity for plastic deformation before fracture. Annealing restores ductility by allowing dislocations to annihilate and grain boundaries to migrate, returning the microstructure toward a lower-energy state.