Engineering Science 1021A/B Lecture Notes - Lecture 17: Viscosity, Activation Energy
17 May 2018
School
Department
Professor
Viscoelastic Behavior
For the load:
•
The strain response can be:
○
Viscous Flow
Materials like polymers deform by viscous flow
The particles flow past each other by shear
○
•
Viscous flow is described by Newton's law:•
Shear strain rate is equal to the shear stress divided by the viscosity
○
In terms of normal stress and strain:
○
Newtonian and other Fluids
Creep
Creep: time dependent deformation of a material subjected to a constant stress
Usually lower than yield stress
○
•
Only significant when the temperature is greater than !"#$
%
$
%: melting temperature on an absolute scale
○
•
A creep test measures strain as a function of time at a constant stress and temperature•
Stress & Temperature Effects
At any temperature, dislocations will move if a large enough stress is applied•
During the recovery phase of the annealing process, dislocations were able to rearrange
themselves due to the increased thermal energy
•
Increasing the deformation temperature allows dislocations to move under a lower
applied stress
•
Increasing the stress or temperature has the same effect on the creep behaviour:
Initial strain increases
○
Steady-state creep rate increases
○
Rupture life is decreased
○
Creep behaviour depends on stress and temperature
§
○
•
The Creep Test
The data from a creep test is plotted as strain vs. time•
•
Secondary creep: constant creep rate
○
•
Steady-State Creep Rate
Empirical relationships describe the steady-state creep rate:
For a specific temperature:
&'and (are material constants□
§
○
For any temperature:
&)and *+are constants
*+: activation energy for creep
®
□
§
○
○
•
The results from a series of creep tests can be plotted on a stress-rupture curve•
Find the time to rupture at ,-./0if the stress is .!1234
5#!!1678
§
○
What is the maximum service temperature of a component that must last
9!:!!!167s @1,!1MPa
;#</0 = > = ,-./0
§
> 5 ,<!/0
§
○
•
The Science Behind Creep
Diffusion
High temperature deformation occurs at lower applied stress because of the increased
thermal energy of the atoms/molecules
•
The average energy of an atom at temperature ($) is ?@$
Some atoms have more, while other have less
○
•
The probability than an atom has an energy greater than some value, A, is described by
the Maxwell-Boltzmann equation
•
Creep Mechanisms
Diffusional Flow
At low stress, you only get diffusion as a creep mechanism•
Diffusion alone is enough to cause a shape change
○
•
Atoms diffuse in response to the elastic strains caused by an applied stress
Atoms physically move in response to the applied stress
○
•
Smaller grains result in a short path for the atoms to travel
Creep rate increases
○
○
○
•
Damage & Failure: Tertiary Creep
Local diffusion of atoms will cause voids to grow on boundaries that are perpendicular to
the applied stress
Reduced area
○
Increases local stress
○
Accelerated creep strain
○
Fracture
○
•
•
Dislocation Climb
At higher stress, dislocations motion contributes significantly to creep deformation•
Barriers to dislocation motion can be overcome by dislocation climb•
Diffusion erodes the extra half plane of an edge dislocation, permitting the obstacle to be
passed
•
•
•
•
Thermal Activation of Dislocations
Increasing the temperature can provide the additional energy required to move pinned
dislocations
•
Deformation Mechanism Maps
Displays mechanical response as a function of stress and temperature, showing the regime
in which each mechanism operates
○
•
Improving Creep Resistance
•
Creep
Viscoelastic Behavior
For the load:
•
The strain response can be:
○
Viscous Flow
Materials like polymers deform by viscous flow
The particles flow past each other by shear
○
•
Viscous flow is described by Newton's law:•
Shear strain rate is equal to the shear stress divided by the viscosity
○
In terms of normal stress and strain:
○
Newtonian and other Fluids
Creep
Creep: time dependent deformation of a material subjected to a constant stress
Usually lower than yield stress
○
•
Only significant when the temperature is greater than !"#$
%
$
%: melting temperature on an absolute scale
○
•
A creep test measures strain as a function of time at a constant stress and temperature•
Stress & Temperature Effects
At any temperature, dislocations will move if a large enough stress is applied•
During the recovery phase of the annealing process, dislocations were able to rearrange
themselves due to the increased thermal energy
•
Increasing the deformation temperature allows dislocations to move under a lower
applied stress
•
Increasing the stress or temperature has the same effect on the creep behaviour:
Initial strain increases
○
Steady-state creep rate increases
○
Rupture life is decreased
○
Creep behaviour depends on stress and temperature
§
○
•
The Creep Test
The data from a creep test is plotted as strain vs. time•
•
Secondary creep: constant creep rate
○
•
Steady-State Creep Rate
Empirical relationships describe the steady-state creep rate:
For a specific temperature:
&'and (are material constants□
§
○
For any temperature:
&)and *+are constants
*+: activation energy for creep
®
□
§
○
○
•
The results from a series of creep tests can be plotted on a stress-rupture curve•
Find the time to rupture at ,-./0if the stress is .!1234
5#!!1678
§
○
What is the maximum service temperature of a component that must last
9!:!!!167s @1,!1MPa
;#</0 = > = ,-./0
§
> 5 ,<!/0
§
○
•
The Science Behind Creep
Diffusion
High temperature deformation occurs at lower applied stress because of the increased
thermal energy of the atoms/molecules
•
The average energy of an atom at temperature ($) is ?@$
Some atoms have more, while other have less
○
•
The probability than an atom has an energy greater than some value, A, is described by
the Maxwell-Boltzmann equation
•
Creep Mechanisms
Diffusional Flow
At low stress, you only get diffusion as a creep mechanism•
Diffusion alone is enough to cause a shape change
○
•
Atoms diffuse in response to the elastic strains caused by an applied stress
Atoms physically move in response to the applied stress
○
•
Smaller grains result in a short path for the atoms to travel
Creep rate increases
○
○
○
•
Damage & Failure: Tertiary Creep
Local diffusion of atoms will cause voids to grow on boundaries that are perpendicular to
the applied stress
Reduced area
○
Increases local stress
○
Accelerated creep strain
○
Fracture
○
•
•
Dislocation Climb
At higher stress, dislocations motion contributes significantly to creep deformation•
Barriers to dislocation motion can be overcome by dislocation climb•
Diffusion erodes the extra half plane of an edge dislocation, permitting the obstacle to be
passed
•
•
•
•
Thermal Activation of Dislocations
Increasing the temperature can provide the additional energy required to move pinned
dislocations
•
Deformation Mechanism Maps
Displays mechanical response as a function of stress and temperature, showing the regime
in which each mechanism operates
○
•
Improving Creep Resistance
•
Creep
Viscoelastic Behavior
For the load:•
The strain response can be:
○
Viscous Flow
Materials like polymers deform by viscous flow
The particles flow past each other by shear
○
•
Viscous flow is described by Newton's law:
•
Shear strain rate is equal to the shear stress divided by the viscosity
○
In terms of normal stress and strain:
○
Newtonian and other Fluids
Creep
Creep: time dependent deformation of a material subjected to a constant stress
Usually lower than yield stress
○
•
Only significant when the temperature is greater than !"#$
%
$
%: melting temperature on an absolute scale
○
•
A creep test measures strain as a function of time at a constant stress and temperature•
Stress & Temperature Effects
At any temperature, dislocations will move if a large enough stress is applied•
During the recovery phase of the annealing process, dislocations were able to rearrange
themselves due to the increased thermal energy
•
Increasing the deformation temperature allows dislocations to move under a lower
applied stress
•
Increasing the stress or temperature has the same effect on the creep behaviour:
Initial strain increases
○
Steady-state creep rate increases
○
Rupture life is decreased
○
Creep behaviour depends on stress and temperature
§
○
•
The Creep Test
The data from a creep test is plotted as strain vs. time•
•
Secondary creep: constant creep rate
○
•
Steady-State Creep Rate
Empirical relationships describe the steady-state creep rate:
For a specific temperature:
&'and (are material constants□
§
○
For any temperature:
&)and *+are constants
*+: activation energy for creep
®
□
§
○
○
•
The results from a series of creep tests can be plotted on a stress-rupture curve•
Find the time to rupture at ,-./0if the stress is .!1234
5#!!1678
§
○
What is the maximum service temperature of a component that must last
9!:!!!167s @1,!1MPa
;#</0 = > = ,-./0
§
> 5 ,<!/0
§
○
•
The Science Behind Creep
Diffusion
High temperature deformation occurs at lower applied stress because of the increased
thermal energy of the atoms/molecules
•
The average energy of an atom at temperature ($) is ?@$
Some atoms have more, while other have less
○
•
The probability than an atom has an energy greater than some value, A, is described by
the Maxwell-Boltzmann equation
•
Creep Mechanisms
Diffusional Flow
At low stress, you only get diffusion as a creep mechanism•
Diffusion alone is enough to cause a shape change
○
•
Atoms diffuse in response to the elastic strains caused by an applied stress
Atoms physically move in response to the applied stress
○
•
Smaller grains result in a short path for the atoms to travel
Creep rate increases
○
○
○
•
Damage & Failure: Tertiary Creep
Local diffusion of atoms will cause voids to grow on boundaries that are perpendicular to
the applied stress
Reduced area
○
Increases local stress
○
Accelerated creep strain
○
Fracture
○
•
•
Dislocation Climb
At higher stress, dislocations motion contributes significantly to creep deformation•
Barriers to dislocation motion can be overcome by dislocation climb•
Diffusion erodes the extra half plane of an edge dislocation, permitting the obstacle to be
passed
•
•
•
•
Thermal Activation of Dislocations
Increasing the temperature can provide the additional energy required to move pinned
dislocations
•
Deformation Mechanism Maps
Displays mechanical response as a function of stress and temperature, showing the regime
in which each mechanism operates
○
•
Improving Creep Resistance
•
Creep
Document Summary
The particles flow past each other by shear. Shear strain rate is equal to the shear stress divided by the viscosity. Creep: time dependent deformation of a material subjected to a constant stress. Only significant when the temperature is greater than 0. 4% A creep test measures strain as a function of time at a constant stress and temperature. At any temperature, dislocations will move if a large enough stress is applied. During the recovery phase of the annealing process, dislocations were able to rearrange themselves due to the increased thermal energy. Increasing the deformation temperature allows dislocations to move under a lower applied stress. Increasing the stress or temperature has the same effect on the creep behaviour: The data from a creep test is plotted as strain vs. time ge. The data from a creep test is plotted as strain vs. time. The results from a series of creep tests can be plotted on a stress-rupture curve.
