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
