Lecture 21 Creep ME 330 Engineering Materials Creep Curves Temperature and Stress Effects Creep Mechanisms Creep Resistance Read Chapter 15

Creep : Time/Temperature-Dependent, Constant Load  Constant load - usually static mechanical stresses below yield  “High” temperature  Amount of creep will depend on:  Magnitude of load application  Duration of load application  strain is time dependent  Temperature  Important time-temperature relations   Unload Hold  Creep Permanent deformation  creep  plastic deformation! Load yy

T < 0.3T m T > 0.4T m Creep strain,  time, t For steel: “High” Temperatures Metals: T > *T melt Ceramics: T > *T melt (some ~0.66*T melt ) Amorphous polymers: T > T g (or > 0.4*T melt ) Crystalline polymers: T > 0.4*T melt From: Ashby & Jones

Some Common Materials Ni & Ti alloys often used for turbine blades Room temperature (~300K) –For lead & tin, this is “high” –Steel shows no creep effects For ice, creep is a problem –Glaciers move!

Typical Creep Curve Constant temperature, load Creep strain,  time, t (log scale) Primary creep Elasticity Tertiary creep Secondary or Steady-state creep tt  trtr X Rupture

Regions of Creep DecreasingIncreasing Constant PrimaryTertiary Secondary Rate Hardening vs. Recovery Mechanisms Important Parameter Hardening Greater Recovery Greater Balanced Diffusion (in grains and along boundaries) Dislocation motion Hardening Dislocation interactions/ Frank Reed sources Grain boundary & particulate blocking dislocations Recovery Dislocation annihilation Same as before (more recovery) Rupture Grain Boundary separation Internal cracks, voids, cavities Neck (tension) Rupture lifetime, t r Short life Steady state creep rate, Long life  t

Temperature & Stress Effects Below the critical temperature, strain does not change with time As temperature or stress increases: –Elastic (instantaneous) portion of strain increases –Steady-state creep rate increases –Rupture lifetime decreases T    Creep strain,  time, t

Quantifying Stress Effects Often plot log(stress) vs. log(t r ) –Often non-linear Plot log of stress vs. log of inverse rupture time ( ) –Empirically found power-law relation works at a given T –K & n are material “constants” n is slope of straight line K will vary with temperature From: Dowling, Callister

Quantifying Temperature Effects Steady-state creep rate increases with temperature –Now plot inverse of temperature –An exponential curve fits the data in a linear fashion Short term tests can be used to predict long term behavior –Basis for “time-temperature superposition” Temp T = 1055 °C t r = 400 h T = 922 °C t r = 10,000 h Q c activation energy R gas constant

Steady-State Creep Model Time - Temperature - Stress parameters  Arrhenius type equation  K 2 : Constant  n: Creep index Will change depending on creep mechanism  Q c : Activation energy for creep Similar to activation energy for diffusion  R: Gas constant Bulk Diffusion n = 1 Power law creep n = 3 to 8

Basic Creep Behavior Creep Test: At fixed stress and temperature the strain increases with time : Stress Relaxation Test: At fixed strain and temperature the stress decreases with time:  t  t  t  t

Creep Mechanisms Stress-induced vacancy diffusion (Nabarro- Herring creep) –Bulk diffusion within grains Grain boundary diffusion (Coble creep) Grain boundary sliding –Must be accommodated by other mechanisms –Vacancy diffusion elongates grains, the sliding occurs to maintain grain continuity Dislocation creep –Diffusion controlled dislocation motion –Usually climb instead of glide That which is operative depends on the temperature, stress, and strain rate

Vacancy Diffusion During Creep Occurs within the core of the grains Mass transport changes shape of grains When temperatures are low, grain boundary diffusion takes over

Grain Boundary Diffusion Similar to before: mass transport changes shape of grain boundaries As boundaries change shape, forces grains to change as well

Grain Boundary Sliding Grain boundary sliding leads to cavitation Often accompanies diffusion processes From: Dowling

Dislocations Climb by Diffusion Climb force   Metals: deformation arises from dislocation motion  Dislocations are blocked and can’t move under the applied load  Dislocations diffuse to vacancies  Diffusion is enhanced at elevated T From: Ashby & Jones

 Dislocation creep - power law creep: Stress Dependence  Bulk diffusion - through the grains – (Nabarro-Herring creep):  Grain boundary diffusion (Coble Creep): Interesting point: Smaller grains have faster creep rates. Unfortunately, contradicts low temperature, tensile advantages predicted by Hall-Petch n =3 to 8, often 5

Deformation Maps From: Ashby & Jones

Actual Data vs. Deformation Map From: Ashby & Jones, Kurath

Creep Resistance Increase creep resistance by choosing material with: –High T m –High E –Larger grain size* –Solid-solution alloying –Dispersion hardening –Directional solidification –Single crystal structure

Non-metallic Materials Ceramics –Dislocation motion difficult –Diffusion difficult –As a result, ceramics have a good creep resistance Polymers –Very low melting point –Viscous flow - different mechanism –Important problem at room temperature

Ashby Plot From M F Ashby, Materials Selection in Mechanical Design, 1999

Dependencies –“High” Temperature Creep Curves –Primary, Secondary, Tertiary Creep –Steady-state creep & steady- state creep rate –Rupture & rupture time Temperature & Stress Effects –Trends with creep strain curves –Power-law relation –Arrhenius temperature dependence –Time-temperature equivalence –Steady-state creep model –Creep vs. stress relaxation tests New Concepts & Terms *Know concept, not definition Creep Extrapolation Methods –Temperature compensated time –Larson-Miller parameter –Sherby-Dorn parameter Creep Mechanisms –Stress induced vacancy diffusion –Grain boundary diffusion –Dislocation creep –Dislocation climb –Grain boundary sliding –Deformation map –Stress dependencies Creep Resistance