Method of Sections

Passivation is the process by which a material becomes 'passive,' meaning it is less affected by environmental factors such as corrosion. It involves the spontaneous formation of a very thin, non-reactive surface film that acts as a barrier, shielding the bulk material from further attack. This film is typically an oxide or nitride layer, a few nanometers thick.

A hydrostatic test is a specific type of proof test for pressure vessels like pipes, boilers, and gas cylinders. The vessel is filled with a nearly incompressible liquid, typically water, and pressurized to a specified test pressure. This method is preferred over pneumatic testing because it requires less energy release to achieve the same pressure, making it very significantly safer if a rupture occurs.

Concentrated solar power systems use mirrors or lenses to concentrate a large area of sunlight onto a receiver. The concentrated light heats a fluid, which then drives a heat engine (usually a steam turbine) connected to an electrical power generator. This method contrasts with photovoltaics, which convert light directly into electricity. CSP allows for thermal energy storage.

The principal stresses, \(\sigma_1\) and \(\sigma_2\), are the maximum and minimum normal stresses at a point, occurring on planes with zero shear stress. On Mohr's circle, these correspond to the two points where the circle intersects the horizontal (\(\sigma_n\)) axis. The maximum in-plane shear stress, \(\tau_{max}\), is equal to the radius of the circle, \(R\).

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.

Young's Modulus, denoted by E, quantifies a solid material's stiffness. It is the ratio of tensile stress (\(\sigma\)) to extensional strain (\(\epsilon\)) in the elastic (linear) region of the stress-strain curve. This relationship is defined by Hooke's Law: \(E = \frac{\sigma}{\epsilon}\). A higher modulus indicates a stiffer material, meaning more stress is required for a given amount of elastic deformation.

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.

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.

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.

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 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.