Correct option is C
The Rankine theory states that failure occurs when the maximum principal stress in a material reaches the ultimate tensile or compressive stress of the material.
Applicable For:
Brittle materials (e.g., cast iron, ceramics)
Materials that fail suddenly without yielding
Shape of region - Square
The Tresca theory states that yielding begins when the maximum shear stress in a material reaches the shear stress at yield in a simple tension test.
Applicable For:
Ductile materials (e.g., mild steel, aluminum)
Accurate for metals that yield before fracture
Shape of region - Hexagon
St. Venant's theory proposes that failure (or yielding) occurs when the maximum principal strain in the material reaches the strain at yield point in a uniaxial tension test.
Applicable For:
Rarely used in modern engineering design
Of historical significance rather than practical relevance
Shape of region - Rhombus
The Von Mises theory states that yielding occurs when the distortion energy per unit volume in a material reaches the same value as at the yield point in uniaxial tension.
This theory is widely used for ductile materials, as it considers combined stresses and provides accurate predictions for onset of yielding.
Applicable For:
Ductile materials like mild steel, copper, aluminum
General-purpose failure theory in solid mechanics
Shape of region - Ellipse
