JNTU B.Tech III MECHANICAL WORKING Previous Question Paper (March - 2021 - R16/R18)

The stress-strain diagram for a ductile material (like mild steel) illustrates the mechanical behavior under tensile loading. The curve begins with a linear elastic region followed by plastic deformation until fracture.

1. Proportional Limit: The point up to which stress is directly proportional to strain (Hooke's Law holds).
2. Elastic Limit: The maximum stress the material can withstand without permanent deformation.
3. Yield Point: The stress level at which the material begins to deform plastically without an increase in load.
4. Ultimate Tensile Strength: The maximum stress on the engineering stress-strain curve.
5. Breaking/Fracture Point: The point where the material finally ruptures.

Mohr's circle in three dimensions represents the state of stress at a point by considering the three principal stresses: σ1, σ2, and σ3, where σ1 ≥ σ2 ≥ σ3. In 3D, the state of stress is defined by three circles rather than one.

The three circles are constructed on the σ-τ plane with diameters corresponding to the differences between the principal stresses:

The largest circle, with diameter (σ1 - σ3), encloses the other two circles. Any state of stress at the point, represented by normal and shear stress components on an arbitrary plane, must lie within the shaded region bounded by these three circles. The maximum shear stress is given by the radius of the largest circle:

This graphical representation is essential for applying failure theories, such as the Tresca criterion, which predicts yielding when the maximum shear stress reaches a critical value.