1. Time Dependent Deformations
Properties depend on rate and duration of loading
Creep
Relaxation
Viscosity
Shrinkage
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2. Review: Elastic Behavior
Elastic material responds to load instantly
Material returns to original shape/dimensions when load is removed
Modulus of Elasticity = ds/de
Energy and strain are fully recoverable
Stress
Strain
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Stress – Strain Curve
Modulus of Toughness: Total absorbed energy before rupture
Modulus of Elasticity
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”.
The higher energy state of stress makes materials more susceptible to elevated temperature effects, which also agitate the atomic energy. Stress and temperature are interactive.
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6. Idealized Maxwell Creep Model
Maxwell proposed a model to describe this behavior, using two strain components:
Elastic strain, 1= /E
Creep strain, 
e 1=/E e
 = constant e2 
Maxwell model is a viscoelastic and can be thought of as a spring and dashpot in series. The spring constant in E and the dashpot constant is 1/n.  e1
time
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Creep Prediction
Creep can be predicted by using several methods
Creep Coefficient
creep/elastic
Specific Creep
creep/elastic
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8. Creep Behavior changes with Temperature
Strain
Tertiary
Secondary
Primary
High Temperature
Creep behavior can stabilize or be neglected at low temperatures for metals. However, at high temperature, metals can become viscous and fail through the onset of necking and rupture. Ni, Co, Cr alloying elements can improve the creep resistant at high temperatures. In hydrous materials, creep is primarily a function of water and capillary water stress, water loss and relative humidity.
Ambient Temperature
Time
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9. Creep Behavior changes with Stress
Time
Strain
Secondary
Primary
Tertiary
High Temperature
Low Stress
High Stress
Low stress levels at high temperatures may prevent viscous flow in metals. In hydrous materials, creep is related to stress level at all temps.
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Relaxation
Time dependent loss of stress due to sustained deformation
Stress
Strain to t
Relaxation Behavior
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11. Idealized Relaxation Model
Maxwell’s model can be used to mathematically describe relaxation by creating a boundary condition of ,
Maxwell model can be thought of as a spring and dashpot in series. The spring constant in E and the dashpot constant is 1/n.
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Plot of Relaxation 
time
 0
Exponential loss of stress.
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.
Shear strains and the rate of shear strain dominate the deformations of viscous flow.
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Viscous Behavior
Energy and strain are largely non-recoverable
Viscosity, h
h = t / dg/dt
shear strain rate = dg/dt
h is coefficient of proportionality between stress and strain rate
Shear Stress
Shear Strain
t, sec t0
dg/dt
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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 e0
e0-esh
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.
Portland cement, lime, gypsum, wood, organic fabrics are all susceptible to shrinkage. Prediction is usually exponential equation with a limit when water is no longer present.
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17. Summary of time dependent effects
Creep
Relaxation
Viscosity
Shrinkage
Temperature increases deformation
Microstructure of material
Atomic structure
Crystalline
Amorphous
Bonding
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