time-dependent plasticity occuring at stresses below the flow stress and at temperatures in excess of Tm/3

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primary: decreasing creep rate as disloation microstructure develops to reduce strain rate

secondary: equilibrium is established between deformation and recovery mechanisms to maintain a steady state strain rate

tertiary: increasing creep rate as the effective cross section reduces leading to failure

define the following creep data:

creep strength

creep life

minimum creep rate

stress rupture life

creep strength: stress to produce nominal strain in a given time

creep life: time to nominal strain at given stress and temperature

min creep rate: f(stress, temperature) tests are long and expensive

rupture life: time to break the specimen at particular stress and temperature (quick, cheap, inaccurate strain measurements)

considers time to rupture and minimum creep rate and states it is a constant

assumes that the bulk of life is in phase 2

it allows one to estimate the creep life of a material by extrapolating higher termpature data to much longer times at lower temperatures thereby accelerating the creep test

t-time to rupture, Q-activation energy for creep, C-constant

Herring-Nabarro: occurs when stresses are too low for dislocation motion can be activated and at high temperatures where diffusion is fast. atoms can move through bulk

desired to have small grain sizes because there is a L^-1/2 dependence on grain size

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Coble: at lower temperatures the main diffusion path is along grain boundaries therefore compared with Herring Nabarro, D is replaced with grain boundary diffusivity.  additionally there is a greater dependence on L due to path

Creep deformation maps

what is the effect of work hardening on these maps

shows under what conditions certain creep mechanisms will occur.  also has contours of constant strain rate

with work-hardening:

1. yield stress is higher
2. diffusional creep dominates to higher stresses (dislocations are inhibited by small grains)

1. power law creep: very strong dependence on stress, usually due to the glide of dislocations which is limited by climb of them around obstacles
2. pipe diffusion
3. power law breakdown: stresses overcoming activation energy, reaching realm of plasticity

• use FCC alloys
• high melting point materials
• increase grain size or elongate grains in direction of tensile stress
• add grain boundary precipitates to prevent slididng
• dispersion hardening

Ni based superalloys

• diffusion creep is reduced by producing elongated grains with minimal transverse boundaries
• FCC structure
• strain minimized during thermal cycling

the formation of voids, microcracks

these are usually at the site of grain boundaries or precipitate boundaries

similar to miner's law

exposure is broken into intervals at a particular stress and temperature for which the rupture time is known from tests directly

Describe the use of damage parameters

what is the effect of grain size

failure begins at the onset of void/crack formation

a damage parameter can therefore relate the initial area and the effective area (area lost to voids) to then develop values for the effective stress and Young's modulus

large grain size means a longer time before tertiary.  useful because you may want to delay the onset of final failure

fatigue + creep : this is a possibility at high temperatures

what equation models this and what are some of the cases that involve material behavior

this can be modeled by miner + robinson's laws

if there is no itneraction, the lifetimes are unchanged by damaage of the other sort

linear addition leads to direct correlation betweent miner's and robinson and these can be added

if tehre is strong interaction, the lifetimes for both creep and fatigure are much shorter

1. blunting of crack tip by creep>>reduce fatigue damage rate
2. cutting of grain boundary porosity>>increase growth rate of pores
3. increasing dislocation density>>decrease primary creep
4. increase in dislocation density>>icnrease creep rate