Deformation of solids

Stress

The force per unit area causing deformation

Strain

A measure of the amount of deformation caused by stress

Stress

Stress = Force/Area Unit= Pa

Stress is not the same as pressure

Stress applies at the internal level whereas pressure applies externally to the surface of objects

Stress question

Tensile stress

Occurs when outward forces along the length of an object cause the object to increase in length because atoms are pulled further apart

Compressive stress

The opposite of tensile strength. Inward forces along the object length tend to decrease the length of an object because the atoms are pushed closer together

Volume stress

Changes the volume of an object. It occurs due to uniform pressure on all sides of the object that results in the object being compressed but retaining the same shape

Stress= Delta P

Shear stress

Changes the shape of an object but not it’s dimensions. It occurs when different forces act across the object at different points, warping or deforming the object as the atoms are forced sideways.

Stress= force / area

Tensile and compressive strength

Strain is a measure of the amount of deformation caused by stress.

Strain = change in l length/initial length

Strain = delta L / L

Volume and shear strain

Volume strain = change in volume/ initial volume

Volume strain = delta V/ V

Shear strain = displacement / height = x/h

Factors that affect strain

1. The type of material. qualified by a constant of proportionality

2. The materials dimensions; length, volume, area

3. Applied force / pressure

Bulk modulus

For a sufficiently small volume stress, stress and strain are proportional.

Stress= -B strain

B=-stress/strain = delta P / delta v/v

B = bulk modulus is a measure of the stiffness of a material, how easy it is to compress

Shear modulus

For a sufficiently small shear stress, stress and strain are proportional.

Stress= S strain

S= Stress/Strain = F/A / x/h

S= shear modulus is a measure of the stiffness of a material, how easy it is to shear

Young’s modulus

For a sufficiently small tensile or compressive stress, stress and strain are proportional

Stress= E strain

E= stress/strain = F/A / deltah/h

E= Young’s modulus is a measure of the stiffness of a material, how easy it is to stretch or compress

Young’s modulus formula rearrangement

Stress strain graph under tensile strength

Young’s, shear and bulk moduli

Can be used to predict the behavior of a material when subjected to a force

Strain question

Young’s modulus question