tikalsky – penn state university time dependent deformations properties depend on rate and...

Tikalsky – Penn State University

Time Dependent Deformations

Properties depend on rate and duration of loading Creep Relaxation Viscosity Shrinkage


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


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


Time dependent deformation under sustained loading

Creep


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”.


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


Creep Prediction

Creep can be predicted by using several methods

Creep Coefficientcreep/elastic

Specific Creepcreep/elastic


Creep Behavior changes with Temperature

Time

Str

ain

Secondary

Pri

mary Tertiary

Ambient Temperature

High Temperature


Creep Behavior changes with Stress

Time

Str

ain

Secondary

Pri

mary Tertiary

High Temperature

Low Stress

High Stress


Time dependent loss of stress due to sustained deformation

RelaxationS

tres

sS

trai

n

to

t

t

Relaxation Behavior


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


Plot of Relaxation

= constant

time

Et

e

0


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


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


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.


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


Summary of time dependent effects

CreepRelaxationViscosityShrinkage

Temperature increases deformation Microstructure of material

Atomic structure Crystalline Amorphous Bonding

tikalsky – penn state university time dependent deformations properties depend on rate and...

Documents