Which statement best characterizes a Bingham plastic?

Which statement best characterizes a Bingham plastic?

• A. A Newtonian fluid with constant viscosity
• B. A fluid that yields under stress and then flows with a nonlinear relation between shear stress and shear rate
• C. A fluid that yields under stress and then flows with a linear relation between shear stress and shear rate
• D. A fluid with shear-thinning behavior without a yield stress

Answer: (C)

Bingham plastics resist deformation until a finite yield stress is exceeded, and after that they flow with a linear relationship between shear stress and shear rate. This is captured by tau = tau_y + mu_p * gamma_dot, where tau_y is the yield stress and mu_p is the plastic viscosity. Below the yield stress, there’s no flow; above it, increasing shear stress produces flow at a rate proportional to the applied stress. This linear post-yield behavior distinguishes them from Newtonian fluids (constant viscosity with no yield stress), from fluids that yield but have nonlinear post-yield relations, and from shear-thinning fluids that have no yield stress. Hence, the statement describing yielding followed by linear post-yield flow best characterizes a Bingham plastic.

Bingham plastics resist deformation until a finite yield stress is exceeded, and after that they flow with a linear relationship between shear stress and shear rate. This is captured by tau = tau_y + mu_p * gamma_dot, where tau_y is the yield stress and mu_p is the plastic viscosity. Below the yield stress, there’s no flow; above it, increasing shear stress produces flow at a rate proportional to the applied stress. This linear post-yield behavior distinguishes them from Newtonian fluids (constant viscosity with no yield stress), from fluids that yield but have nonlinear post-yield relations, and from shear-thinning fluids that have no yield stress. Hence, the statement describing yielding followed by linear post-yield flow best characterizes a Bingham plastic.