Gina Cavallo
MANE 6940
June 3, 2014
1. Discuss briefly the key features of the following types of macroscopic mechanical behavior of
materials:
Linear Elasticity
Thermo-Elasticity
Viscoelasticity
Plasticity and Elasto-plasticity
Viscoplasticity/Creep
Damage/Fracture/Fatigue
Linear Elasticity
A linear elastic material will return back to its original shape after external loads cause
deformation on the object. The strain depends on the stress applied to the object and the
𝜎
behavior of these materials can be demonstrated by Hooke’s Law 𝜀 = 𝐸 .
The amount of displacement is linearly proportional to the applied forces. However, the rate at
which the forces are applied does not affect the deformation. This material builds strain energy
if a load is applied for a prolonged period of time.
Other Sources: http://solidmechanics.org/text/Chapter3_2/Chapter3_2.htm
Thermo-Elasticity
Thermoelasticity involves elasticity plus a temperature variable. An elastic material expands
when thermal energy is added to it. The additional stresses caused by thermal expansion need
to be taken into consideration when applying Hooke’s law. The equation to describe uni-axial
expansion from thermal energy is ΔL/L = 𝜀 = 𝛼(𝑇 − 𝑇𝑜) where 𝛼 is the thermal expansion
coefficient, To is the initial uniform temperature, and T is the final temperature at which the
material is heated. ΔL is the length by which the material expands .
Viscoelasticity
Viscoelasticity describes a linear elastic solid that remembers is deformation history. Viscoelastic
materials exhibit both elastic and viscous behavior when under deformation. They return to
their original shape, but it takes some time to do so. Therefore, the response to deformation of
these materials is time dependent. Viscoelasticity can be modeled by a system of springs and
dashpots, which are pistons that move inside a viscous fluid, a fluid that resists deformation
from shear or tensile stress. Also, unlike elastic materials, viscoelastic materials do not conserve
all of their energy under deformation. Some of this energy is dissipated. This behavior is called
hysteresis. Another property of a viscoelastic material is stress relaxation, when its stress
reaches an upper limit, then decreases with time under a constant strain.
Other Sources:
http://www.ewp.rpi.edu/hartford/~ernesto/Su2014/SMS/Notes/ch07.pdf
http://www.umich.edu/~bme332/ch7consteqviscoelasticity/bme332consteqviscoelasticity.htm
Plasticity and Elasto-plasticity
A plastic material initially deforms elastically under a load, but then at a certain threshold,
continues deforming at much smaller stresses and does not return to its original undeformed
state when the load is removed. The stress threshold at which the elastic deformation ends and
the plastic deformation begins can be called the critical value, σ0 ,and it can be found by a uniaxial tensile test of the specified material. The deformation is called elastoplastic if it includes
the elastic deformation in addition to a plastic deformation before the threshold.
Viscoplasticity/Creep
Viscoplasticity describes metals undergoing time dependent deformation at high temperatures
under a constant load. However, unlike viscoelastic materials, the material remains deformed
after the load is removed. The three variables involved in creep are temperature, time, and
stress. A creep test is performed by a tension test at constant load and temperature. The strain
vs time relationship is measured, and creates a creep curve. The creep curve typically has three
stages, primary creep, secondary creep, and tertiary creep. If the creep test is extended long
enough, the material will break. A common formula used to describe the stress-strain
relationship is 𝜀 𝑒𝑓𝑓 =A(σeff)n tm, where 𝜀 𝑒𝑓𝑓 and σeff are the effective creep strain and creep
stress, respectively. A,m,n are material properties which are determined by creep tests.
Other sources:
http://solidmechanics.org/text/Chapter3_8/Chapter3_8.htm
Damage/Fracture/Fatigue
Damage describes the mechanical deterioration that results in specimen failure. It occurs as
soon as external loading occurs. It is characterized by surface discontinuities or volume
discontinuities. The damage of a small volume of material can be described by the formula D
=dSD/dS where D = the damage, dS is the area of a section of the volume, and dSD is the portion
of this area with material defects such as cracks and voids. Fracture describes the failure of a
component when it can no longer bear an external monotonic load. Fatigue is the failure of a
component when it can no longer bear a cyclic load.