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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 recoverable

Stre

ss

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 loadingCreep

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Creep BehaviorStress 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,

dtd 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

Stra

in

Secondary

Prim

ary Tertiary

Ambient TemperatureHigh Temperature

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Creep Behavior changes with Stress

Time

Stra

in

Secondary

Prim

ary Tertiary

High Temperature

Low Stress

High Stress

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Time dependent loss of stress due to sustained deformation

RelaxationS

tress

Stra

in

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

dE

dtEdt

d t 100

tEdtEdtd tt

000

ln

0dtd

EtetE

0

0

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