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

The stress-strain diagram for a ductile material (such as mild steel) illustrates the mechanical behavior under tensile loading. The curve is characterized by the following key points:

1. Limit of Proportionality: The point up to which stress is directly proportional to strain, following Hooke's Law.
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 a significant increase in load. It includes Upper and Lower yield points.
4. Ultimate Tensile Strength: The maximum stress on the engineering stress-strain curve, representing the peak load before necking begins.
5. Breaking/Fracture Point: The point at which the material finally ruptures.

Mohr's circle in three dimensions represents the state of stress at a point by considering all three principal stresses: σ1, σ2, and σ3, where σ1 ≥ σ2 ≥ σ3. In 3D, the stress state is defined by three individual circles plotted on the normal stress (σ) versus shear stress (τ) plane.

The three circles are constructed as follows:

• The largest circle has a diameter of (σ1 - σ3) and represents the maximum shear stress, which is equal to (σ1 - σ3) / 2.
• The other two circles have diameters of (σ1 - σ2) and (σ2 - σ3).
• All possible stress states at the point lie within the shaded region bounded by these three circles.

The diagram consists of the horizontal axis representing normal stress and the vertical axis representing shear stress. The three circles are nested, with the largest circle encompassing the two smaller ones. This graphical representation is essential for applying failure theories, such as the Tresca criterion, which identifies yielding when the maximum shear stress reaches a critical value.