Stress-Strain Relationship

Hooke’s law is the proportionality gives the relationship between elastic strain (ε) and stress (σ):

σ = E.ε

Where ‘E’ is Young’s modulus of elasticity.

The following power-law equation, known as Holloman-Ludwig equation, describes the material behavior in the plastic range:

σ = K.εⁿ

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.

σ = σ_y + K.εⁿ

Where ‘σ_y‘ is the yield strength of the material. The true strain (ε) used in the above equation should be the plastic strain value, given by the following equation,

ε_p = ε – ε_e ≈ ε

where elastic strains ‘ε_e‘ can be safely neglected because plastic strains are enormous when compared to elastic strain values.

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