Electrochemical Engineering

Appendix D: Mechanics of Materials

D.1 Stress and Strain

A material subjected to a uniaxial load will deform. If compressed, the length of the material is reduced; if placed under tension, the length increases. The deformation or linear strain of a material of length L is

(D.1)

where δ is the distance that the material deforms. Thus, this normal strain is a dimensionless quantity. Normal stress is simply the force of compression or tension in the material; and stress and strain are related with Young's modulus of elasticity:

(D.2)

This modulus is a property of the material and has units of pressure [Pa]. Figure D.1 shows the stress–strain relationship for a brittle and a ductile material. At low strain, the stress varies linearly, or said another way the modulus is constant. Furthermore, when the stress is relieved, the material returns to its original shape. Thus, Equation D.2 is equivalent to Hooke's law for a spring and describes proportional behavior. At some point the proportional limit is reached, above this strain the slope is no longer constant, but the behavior is still elastic, meaning that there is no permanent deformation. If the stress is excessive, the material can fail. For ductile materials, above the elastic limit the material continues to deform, but the ...