530.352 Materials Selection

1. 530.352 Materials Selection Lecture #26 High Temperature Creep - II TuesdayNovember 15th, 2005

2. Sherby-Dorn Equation . ss = C n exp (- Qdiffusion / RT) Temperature dependence Stress dependence Constants Use this equation to calculate creep rate at any given or new stress or temperature !!

3. Example of creep based design: • Ni-base superalloys that are used for jet turbine applications exhibit Qcreep = 320 kJ/mol and n=5. • What is the creep rate at 925 oC and 350 MPa if C=1.7x10-7 and R=8.314 J/mol-oC ? • What would the creep rate be if the stress were increased by 25 MPa ? • What would the creep rate be if the temperature were increased by 25 oC ? • If your boss wanted to increase the operating temperature by 50 oC, how much would you have to decrease the stress to maintain the same creep rate ?

4. Creep rate; T=925 oC and s=350 MPa . ss = C n exp (- Q / RT) . ss = 1.7x10-7 3505 exp( -320,000/8.314 x 1198 K ) = 1.7x10-7x 5.25x1012x 11.1x10-15 = 10-8 sec-1

5. Is 10-8 sec-1 fast ? Is short for a service life but long for a graduate student -- must extrapolate from short tests to long times !!

6. . ss-1 = C 1n exp (- Q / RT1) . ss-2 = C 2n exp (- Q / RT2) Increasing by 25 MPa : . . 1 / 2 = (1/ 2 )n = (350/375)5 = 0.708 2 = 1.4 x 10-8 sec .

7. . ss-1 = C 1n exp (- Q / RT1) . ss-2 = C 2n exp (- Q / RT2) Increasing by 25 oC: 2 = 1.92 x 10-8 sec

8. . ss-1 = C 1n exp (- Q / RT1) . ss-2 = C 2n exp (- Q / RT2) Changing both T and s :

9. Creep Mechanisms (metals and ceramics) • Diffusion creep • Dislocation creep (power-law creep) • Stress Relaxation • Creep Fracture

10. Diffusion creep  grain boundary diffusiond  bulk crystal diffusion d 

11. climb glide climb glide Dislocation creep Diffusion assisted climb important: 1. Annihilation: poof ! 2. By passing obstacles:

12. Dislocation Climb:

13. Stress Relaxation . . total = el + pl = 0 so el = - pl el =  / E and pl = c = A n(@ cont. T) -n d = - AE dt 1-n | = - AE t |0 . . . . t s o p   el time time

14. Creep damage starts c tertiary creep time Tertiary creep :

15. Design against creep (metals) • Minimize T / Tmeltingto slow diffusion, climb, and creep. • Arrange for large grain sizes to slowdiffusion. • Use precipitates (oxide particles) and solid solutions to slow dislocations.

16. Creep in ceramics : • Very little dislocation motion - mostly diffusion creep or something else. • Glassy phases (oxides) that form at grain boundaries soften and high T and lead to grain boundary sliding.

17. Design against creep (ceramics) • Similar to metals, reduce diffusion and dislocation motion, but must also ... • Reduce/control grain boundary phases.

18. Creep Mechanisms (polymers) • Tg replaces Tm at the critical T and Tg is often close to RT !!! • Viscous flow is like creep: = C 1 exp (-Qv / RT) • Qviscous not QDiffusion, Qvicsous is Q slide lumpy molecules past one another • n = 1 for Newtonian viscous flow .

19. Design Against Creep (polymers) • Increased degree of cross-linking ->increased Tg and less creep. • High molecular weight -> high viscosity-> low creep rate. • Crystalline polymers better than glassy. • Add fibers or particles to make composites !!