1.5 Solids under stress

• k = W/x

  k = spring constant

  W = work done

  x = extension
• Hooke’s law:

  The tension in a spring or wire is proportional to its extension from its natural length, provided the extension is not too great.
• Crystal:

  A solid in which atoms are arranged in a regular array There is a long range order within crystal structures
• Crystalline solid:

  Solid consisting of a crystal, or of many crystals, usually arranged randomly. The latter is strictly a polycrystalline solid. Metals are polycrystalline.
• Amorphous solid:

  A truly amorphous solid would have atoms arranged quite randomly. Examples are rare. In practice we include solids such as glass or brick
• Polymeric solid:

  A solid which is made up of chain-like molecules.
• Ductile material:

  A material which can be drawn out into a wire. This implies that plastic strain occurs under enough stress.
• Elastic strain:

  This is strain that disappears when the stress is removed, that is the specimen returns to its original size and shape.
• Plastic (or inelastic) strain:

  This is strain that decreases only slightly when the stress is removed. In a metal it arises from the movement of dislocations within the crystal structure.
• Elastic limit:

  This is the point at which deformation ceases to be elastic
• Dislocations in crystals:

  Certain faults in crystals which (if there are not too many) reduce the stress needed for planes of atoms to slide. The easiest dislocation to picture is an edge dislocation: the edge of an intrusive, incomplete plane of atoms.
• Grain boundaries:

  The boundaries between crystals (grains) in a polycrystalline material.
• Ductile fracture (necking):

  The characteristic fracture process in a ductile material. The fracture of a rod or wire is preceded by local thinning which increases the stress.
• Brittle material:

  Material with no region of plastic flow, which, under tension, fails by brittle fracture
• Brittle fracture:

  This is the fracture under tension of brittle materials by means of crack propagation.
• Elastic hysteresis:

  When a material such as rubber is put under stress and the stress is then relaxed, the stress-strain graphs for increasing and decreasing stress do not coincide, but form a loop. This is hysteresis.
• Linear relationship; Hooke's Law

  F = kx
• Stress = F / A
• Strain = ∆l / l
• E = Stress (sigma) / strain (epsilon)
• E = Young's modulus, measured in Pa
• If a material is stretched beyond the elastic limit it deforms, exhibiting plastic strain