Time Dependent Deformations
Properties depend on rate and duration
of loading
Creep
 Relaxation
 Viscosity
 Shrinkage

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Review: Elastic Behavior
Elastic material responds to load instantly
Modulus of Elasticity = ds/de
Stress
Material returns to original
shape/dimensions when load is removed
Strain
Energy and strain are fully recoverable
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Stress – Strain Curve
Modulus of
Elasticity
Modulus of Toughness:
Total absorbed energy
before rupture
Modulus of Resilience:
Recoverable elastic
Energy before yield
Ductility: Ratio of
ultimate strain to
yield strain
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Creep
Time dependent deformation under sustained
loading
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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:


s
e 1s/E
Creep Rate 
s

e
e2

de 2
dt
e2 
s
  dt
0
Elastic strain, e1= s/E
Creep strain,
t
e1
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s = constant

s
time
Creep Prediction
Creep can be predicted by using several
methods

Creep Coefficient
ecreep/eelastic

Specific Creep
ecreep/selastic
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Primary
Strain
Temperature
Secondary
Tertiary
Ambient Temperature
Time
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Primary
Strain
Creep Behavior changes with
Stress
High Temperature
Secondary
Tertiary
Low Stress
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Time
Relaxation
Time dependent loss of stress due to
sustained deformation
Strain
Relaxation Behavior
Stress
t
t
to
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Idealized Relaxation Model
Maxwell’s model can be used to mathematically
describe relaxation by creating a boundary
condition of ,
de
dt
 0
d s
0
 
dt  E
t

0
ds
s
ln
t

0
t
dt   
0
s
s0
 

1 ds
s
dt  
 
 
E dt

s
E

E

dt  ln
s
s0
 
t  s  s 0e
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E

 Et

t
Plot of Relaxation
s
s  s 0e
 Et

s0
time
e = constant
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Viscosity
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.
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Viscous Behavior
Energy and strain are largely non-recoverable
Shear
Stress
Viscosity, 
  t / dg/dt
t, sec
shear strain rate = dg/dt
Shear
Strain
dg/dt
t0
t, sec
 is coefficient of proportionality between stress and
strain rate
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Shrinkage
Shrinkage 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 Mechanism
e
0
The 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.
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e0esh
Summary of time dependent
effects
Creep
Relaxation
Viscosity
Shrinkage


Temperature increases deformation
Microstructure of material
 Atomic structure
 Crystalline


Amorphous
Bonding
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