Jawaharlal Nehru Technological University Hyderabad B.Tech III MECHANICAL WORKING Previous Question Paper (October - 2020 - R16)

The uniform deformation energy method assumes that the total work done by the drawing force is equal to the internal energy of plastic deformation, neglecting friction and redundant work. For a wide sheet of initial thickness h0 being drawn to a final thickness h1, the stress state is considered plane strain.

The work done per unit volume is given by the integral of the flow stress with respect to the true strain:

Where the true strain ε is defined as ln(h0/h1). In the uniform deformation energy method, the drawing stress σ_d is equated to the work of deformation:

This model assumes that the entire sheet undergoes uniform deformation across its cross-section. The mechanics involve the application of a tensile force at the exit of the die, which pulls the material through the die opening. The stress acting on the element is primarily a longitudinal tensile stress, which must overcome the flow resistance of the material to achieve the required reduction in thickness.

Deformation velocity significantly influences the flow stress and the mechanical properties of the worked metal. The primary effects include:

• Strain Rate Sensitivity: As the deformation velocity increases, the strain rate increases. Most metals exhibit a higher flow stress at higher strain rates, a phenomenon known as strain rate sensitivity. This is particularly pronounced in hot working where the material behaves more like a viscous fluid.
• Adiabatic Heating: At high deformation velocities, the energy dissipated as heat cannot be conducted away quickly enough, leading to a local temperature rise in the workpiece. This adiabatic heating reduces the flow stress and can lead to non-uniform deformation or localized failure.
• Lubrication Performance: High velocities affect the thickness and stability of the lubricant film. In many processes, higher speeds can improve hydrodynamic lubrication, reducing friction, although extremely high speeds may lead to film breakdown due to thermal effects.
• Microstructural Evolution: Increased velocity alters the kinetics of dynamic recovery and recrystallization. In hot working, higher speeds may suppress dynamic recrystallization, leading to different grain structures compared to slow-speed deformation.
• Tool Life: Higher deformation velocities generally increase the rate of tool wear due to increased interface temperatures and higher contact pressures, necessitating advanced tool materials and cooling strategies.