AC Circuit Generalization of Ohm’s Law

Ductility is a measure of a material's ability to undergo significant plastic deformation before rupture, often quantified by percent elongation or percent reduction in area. Ductile materials, like steel, show a long plastic region on their stress-strain curve. Brittleness is the opposite; brittle materials, like ceramics or cast iron, fracture with little to no plastic deformation.

Hydrogen embrittlement (HE) is a process where metals, most notably high-strength steels, become brittle and fracture following exposure to hydrogen. Atomic hydrogen diffuses into the metal lattice and reduces its ductility and load-bearing capacity. Key proposed mechanisms include Hydrogen-Enhanced Decohesion (HEDE), which weakens atomic bonds, and Hydrogen-Enhanced Localized Plasticity (HELP), which facilitates dislocation motion and localized failure.

The Hall-Héroult process is the major industrial method for smelting aluminum. It involves dissolving alumina (aluminum oxide, Al₂O₃) in molten cryolite (Na₃AlF₆) and electrolyzing the molten salt bath. Aluminum metal is deposited at the cathode, while oxygen from the alumina reacts with the carbon anode, producing carbon dioxide. This process made aluminum widely available and affordable.

Exothermic welding, also known as thermite welding, is a technique that uses the superheated molten metal from an aluminothermic reaction to create a strong, permanent molecular bond between metal components. The process is self-contained, requiring no external power source. It is most famously used to join sections of railway track into continuous welded rail, creating a smoother and more durable track.

The properties of an oxy-acetylene flame are controlled by the volumetric ratio of oxygen to acetylene. A neutral flame (ratio ≈ 1.1:1) is standard for steel welding. A carburizing or reducing flame (ratio 1.1:1) has excess oxygen, is hotter, and is used for braze-welding.

A proof test is a form of stress testing where a structure or component is subjected to a load greater than its normal service load, but less than its expected failure load. The purpose is to demonstrate fitness for use and screen for manufacturing defects without causing damage to a properly manufactured item, thus verifying its structural integrity.

Yield strength, or the yield point, is the stress at which a material begins to deform plastically. Prior to the yield point, the material deforms elastically and will return to its original shape when the applied stress is removed. Once the yield point is passed, some fraction of the deformation will be permanent and non-reversible. It marks the limit of elastic behavior.

The chloralkali process is an industrial method for the electrolysis of sodium chloride (NaCl) solution, known as brine. It is the primary source for producing chlorine (Cl₂), sodium hydroxide (NaOH), and hydrogen (H₂), which are essential commodity chemicals. Modern methods use a membrane cell to separate the anode and cathode products, ensuring high purity and efficiency.

An empirical formula that describes how the available capacity of a battery decreases as the rate of discharge increases. The law is stated as \(C_p = I^k t\), where \(C_p\) is the capacity at a one-ampere discharge rate, \(I\) is the discharge current, \(t\) is the discharge time, and \(k\) is the Peukert constant, specific to the battery type. It quantifies the inefficiency at high loads.

Oxy-acetylene welding uses a flame produced by the combustion of acetylene (\(C_2H_2\)) with pure oxygen. The reaction occurs in two stages. The primary reaction in the inner, white-hot cone is incomplete, producing carbon monoxide and hydrogen: \(2C_2H_2 + 2O_2 \rightarrow 4CO + 2H_2\). These hot gases then react with atmospheric oxygen in the outer envelope, completing the combustion.

Oxy-fuel cutting, or flame cutting, severs ferrous metals by a rapid, exothermic oxidation process. First, a preheating flame raises the steel's surface to its kindling temperature (approx. 870 °C or 1600 °F). A high-pressure jet of pure oxygen is then directed at the spot, initiating a chemical reaction, \(3Fe + 2O_2 \rightarrow Fe_3O_4\), which forms molten iron oxide (slag) and releases heat.