Hooke’s law is the proportionality gives the relationship between elastic strain (ε) and stress (σ):
where ‘E’ is Young’s modulus of elasticity of the material.
The following power-law equation, known as Holloman-Ludwig equation, describes the material behavior in the plastic range:
Where ‘K’ is the strength coefficient, and n is the strain hardening exponent which can have values from n = 0 (perfectly plastic solid) to n = 1 (elastic solid). For most metals, n has values between 0.10 and 0.50.
A variation from the above power-law equation is also known as Ludwig equation
Where ‘σy‘ is the yield strength of the material. The true strain ε used in the above equation should actually be the plastic strain value, given by the following equation,
where elastic strains (εe) can be safely neglected because plastic strains are very large when compared to elastic strain values.