Thermodynamics of Phase Change from Solid to Liquid

Thermodynamics of Phase Change from Solid to Liquid P M V Subbarao Professor Mechanical Engineering Department I I T Delhi A shift from cutting to casting…. .

Mathematical Definitions of Strain • Strain is a second-order tensor related to the displacement u of two points. • Euler’s Tensor for small displacements of points(<10%) • Green-Lagrange tensor for large displacements of points: • Define T as the tangent linear transformation of point Q in initial configuration into a point Q’ in deformed configuration.

Mathematical Definitions of Stress • Stress, a second order tensor dual of the strain tensor. • Its contracted product by the strain rate tensor is the power involved in the manufacturing process. • Cauchy stress tensor for small displacements of points:

Equation of State in Tensor form for Solids • A solid work piece acts as house of generation of Strain field. • Two independent variable the strain field are stress and temperature.

Eo. S for LINEAR ELASTIC SOLIDS

Matrix form of models of linear elastic materials

Hypoelastic Solids • Also called as incremental elastic solids. • Their Eo. S always written in an incremental form of irreversible material equations:

Plastic Solids • Many important engineering materials (metals, polymers, soils) will have quite different mechanical behavior when their physical state comes on its load bearing capacity. • The material mostly lost its elastic characteristics. • This is called as plastic phenomena. • The size of this plastic range depends on the internal microstructure of the material.

Melting • Melting is a vibrational instability released when the root mean square amplitude of vibration reaches a critical fraction (10%) of the interatomic distance. • Several investigators attempted to calculate the critical temperature for different planes when this instability will appear. • The onset of melting of these particles is found to take place significantly below the bulk melting point. • This is called as Debye temperature.