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Time Dependent Deformations
Properties depend on rate and duration of loading Creep Relaxation Viscosity Shrinkage
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Review: Elastic BehaviorElastic material responds to load instantly
Material returns to original shape/dimensions when load is removed
Modulus of Elasticity = d/d
Energy and strain are fully recoverableS
tress
Strain
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Modulus of Toughness: Total absorbed energy before rupture
Ductility: Ratio of ultimate strain to yield strain
Modulus of Resilience: Recoverable elastic Energy before yield
Modulus of Elasticity
Stress – Strain Curve
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Time dependent deformation under sustained loading
Creep
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Creep Behavior
Stress changes the energy state on atomic planes of a material.
The atoms will move over a period of time to reach the lowest possible energy state, therefore causing time dependent strain. In solids this is called “creep”.
In liquids, the shearing stresses react in a similar manner to reach a lower energy state. In liquids this is called “viscosity”.
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Idealized Maxwell Creep Model
Maxwell proposed a model to describe this behavior, using two strain components:
Elastic strain, 1= /E
Creep strain,
dt
d 2Rate Creep
time
= constant
dtt
0
2
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Creep Prediction
Creep can be predicted by using several methods
Creep Coefficientcreep/elastic
Specific Creepcreep/elastic
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Creep Behavior changes with Temperature
Time
Str
ain
Secondary
Pri
mary Tertiary
Ambient Temperature
High Temperature
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Creep Behavior changes with Stress
Time
Str
ain
Secondary
Pri
mary Tertiary
High Temperature
Low Stress
High Stress
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Time dependent loss of stress due to sustained deformation
RelaxationS
tres
sS
trai
n
to
t
t
Relaxation Behavior
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Idealized Relaxation ModelMaxwell’s model can be used to mathematically describe relaxation by creating a boundary condition of ,
dt
d
Edt
Edt
d t 10
0
tE
dtE
dtd tt
000
ln
0dt
d
Et
etE
00
ln
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Plot of Relaxation
= constant
time
Et
e
0
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Viscosity is a measure of the rate of shear strain with respect to time for a given shearing stress. It is a separating property between solids and liquids.Material flows from shear distortion instantly when load is applied and continues to deform
Higher viscosity indicates a greater resistance to flow
Solids have trace viscous effects As temperatures rise, solids approach melting point and
take on viscous properties.
Viscosity
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Viscous BehaviorEnergy and strain are largely non-recoverable
Viscosity, ddt
shear strain rate = ddt
is coefficient of proportionality between stress and strain rate
Shear Stress
Shear Strain
t, sec
t, sect0
ddt
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ShrinkageShrinkage deformations occur in hydrous materials
Loss of free water, capillary water, and chemically bound water can lead to a deduction of dimensions of a material
Organic materials like wood shrink and/or expand over time, depending on the ambient environmental conditions.
Hydrous materials like lime mortar shrink over time. The rate of shrinkage is largely related to relative humidity.
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Shrinkage MechanismThe loss of capillary water is accomplished by a variety of mechanisms
Heat Relative Humidity Ambient Pressure Stress (mathematically included in creep)
Shrinkage can also be related to the dehydration of hydrated compounds CaSO4*2H2O (gypsum) to CaSO4*½H2O or Ca(OH)2 to CaO. This type of dehydration is also accompanied with change in mechanical strength properties.
sh
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Summary of time dependent effects
CreepRelaxationViscosityShrinkage
Temperature increases deformation Microstructure of material
Atomic structure Crystalline Amorphous Bonding