Mechanical Properties of Solids Quiz

Hydraulic Stress and Volume Strain

• Hydraulic stress is the internal restoring force per unit area developed when a body is subjected to fluid pressure, counteracting the applied fluid forces.
• When removed from the fluid, the body restores its original shape and size.
• Volume strain is defined as the ratio of change in volume (∆V) to the original volume (V) and is dimensionless: (\Delta = \frac{\Delta V}{V}).

Hooke's Law

• Hooke's law states that for small deformations, stress is proportional to strain.
• Expressed as: stress ∝ strain or stress = k × strain, where k is the modulus of elasticity.
• Generally applicable to most materials but not valid for all.

Stress-Strain Curve

• A stress-strain curve plots the relationship between stress (force per unit area) and strain (fractional change in length) during tensile tests.
• Initially, stress and strain are linearly related (region O to A) where Hooke's law holds, indicating elastic behavior.
• Upon removing the load in the elastic region, the material regains original dimensions.

Yield Point and Permanent Deformation

• Beyond the yield point (B), the relationship between stress and strain becomes nonlinear, but the material can still return to its original dimensions after load removal.
• The yield point indicates the elastic limit and the yield strength (σy) of a material.
• Permanent deformation occurs when the load exceeds the yield strength, leading to plastic deformation, where original dimensions are not regained.

Ultimate Tensile Strength and Fracture

• The ultimate tensile strength (σu) is the maximum stress a material can withstand before failure, located at point D on the curve.
• Fracture occurs at point E; if ultimate strength and fracture points are close, the material is brittle; if far apart, it is ductile.

Material-Specific Behavior

• Stress-strain behaviors differ among materials.
• Rubber can be stretched significantly beyond its original length while returning to its shape, demonstrating its unique elastic properties.
• The stress-strain relationship for elastomeric tissues, such as those in the aorta, shows a large elastic region, indicating significant deformability without permanent change.