Chapter 11: Elasticity

Necking

a localized decrease in cross sectional area that causes a decrease in stress with an increase in strain

Spring constant (k)

a measure of the elasticity of the spring

Restoring force (F)

acts in the direction opposite the displacement of the oscillating body (F=-kx)

Shearing stress

alters only the shape of the body, leaving the volume unchanged; defined as the ratio of the shearing stress F/A to the shearing strain

Young's modulus

equals longitudinal stress over longitudinal strain; for materials whose length is much greater than the width or thickness, we are concerned with the longitudinal modulus of elasticity

Volume elasticity

not all deformations are linear; sometimes an applied stress F/A results in a decrease of volume; in such cases, there is a bulk modulus B of elasticity; B=volume stress/volume strain; the bulk modulus is negative because of the decrease in V

Inelastic body

one that does not return to its original shape after a deformation

Elastic body

one that returns to its original shape after a deformation

Modulus of elasticity

provided that the elastic limit is not exceeded, an elastic deformation (strain) is directly proportional to the magnitude of the applied force per unit area (stress); equals stress over strain

Stress

refers to the cause of a deformation; the ratio of an applied force F to the area A over which it acts

Strain

refers to the effect of the deformation; the relative change in the dimensions or shape of a body as the result of an applied stress

Fracture stress

stress in which the material fails

Ultimate strength

the greatest stress a body can experience without breaking or rupturing; if the stress exceeds the ultimate strength, the spring breaks

Elastic range

the linear proportion of the stress-strain curve. when the force is released, the material returns to its original dimensions

Elastic limit

the maximum stress a body can experience without becoming permanently deformed

Ultimate tensile strength

the maximum stress that the material can withstand; also defines the beginning of necking

Yield stress

the minimum stress that causes permanent deformation

Plastic range

the region of permanent deformation

Hooke's law

when a string is stretched, there is a restoring force that is proportional to the displacement; F=-kx; the spring constant k is a property of the spring given by: K=F/x