Time Dependent Deformations

1
Time Dependent Deformations

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

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

3
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
4
Creep

• Time dependent deformation under sustained
  loading

5
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.

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
?
?
e1
time
7
Creep Prediction

• Creep can be predicted by using several methods
• Creep Coefficient
• ?creep/?elastic
• Specific Creep
• ?creep/?elastic

8
Creep Behavior changes with Temperature
Strain
Tertiary
Secondary
Primary
High Temperature
Ambient Temperature
Time
9
Creep Behavior changes with Stress
10
Relaxation

• Time dependent loss of stress due to sustained
  deformation

11
Idealized Relaxation Model

• Maxwells model can be used to mathematically
  describe relaxation by creating a boundary
  condition of ,

12
Plot of Relaxation
e constant
13
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.

14
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

15
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.

16
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 CaSO42H2O (gypsum) to
  CaSO4½H2O or Ca(OH)2 to CaO. This type of
  dehydration is also accompanied with change in
  mechanical strength properties.

17
Summary of time dependent effects

• Creep
• Relaxation
• Viscosity
• Shrinkage
• Temperature increases deformation
• Microstructure of material
• Atomic structure
• Crystalline
• Amorphous
• Bonding