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1 MSE200 Lecture 10 (CH ) Mechanical Properties II Instructor: Yuntian Zhu Objectives/outcoes: You will learn the following: Crack growth rate during fatigue. Fatigue life of cracked coponents. Stages of creep. Effect of stress and teperature on creep behavior. The Larsen-Miller paraeter.

2 Fatigue Crack Propagation Rate Notched specien used. Cyclic fatigue action is generated.

3 Stress & Crack Length Fatigue Crack Propagation. 2 1 When a is sall, da/dn is also sall. da/dn increases with increasing crack length. Increase in increases crack growth rate. da dn da dn = fatigue crack growth rate. = A K K = K ax -K in = r a A, = Constants depending on aterial, environent, frequency teperature and stress ratio.

4 Fatigue Crack Growth rate Versus K Log da = Log(A K ) dn = Log( K) + Log(A) Straight line with slope Liiting value of K below which there is no easurable Crack growth is called stress intensity factor range threshold K th

5 Fatigue Life Calculation da dn K K da dn 2 2 ( y a = A K = Y = = A y a Integrating fro initial crack size a 0 to final crack size a f at nuber of fatigue cycles N f a f a 0 a 2 da = A But Therefore Therefore y 2 dn Integrating and solving for N f N f = N f 0 (Assuing Y is independent of crack length) 2 a 2 ) 1 a 1 2 f a 2 0 Ay 2 (1 2 )

6 Creep in Metals Creep is progressive deforation under constant stress. Iportant in high teperature applications.

7 3 stages in creep Priary creep: creep rate decreases with tie due to strain hardening. Secondary creep: Creep rate is constant due to siultaneous strain hardening and recovery process. Tertiary creep: Creep rate increases with tie leading to necking and fracture. Creep rate is slope of the curve Steady state creep

8 Creep Test Metals are tested at constant stress at different teperature & constant teperature with different stress. High teperature or stress Mediu teperature or stress Low teperature or stress

9 Creep strength Creep strength: Stress to produce a creep rate of 10-5 %/h at a given teperature. Creep rate eans steady state creep rate

10 Creep Test (Cont..) Creep rupture test is sae as creep test but aied at failing the specien.

11 Larsen Miller Paraeter for Rupture creep Larsen Miller paraeter is used to represent creepstress rupture data. P(Larsen-Miller) = T[log t r + C] T = teperature(k), t r = stress-rupture tie h C = Constant (order of 20)

12 If two variables of tie to rupture, teperature and stress are known, 3 rd paraeter that fits L.M. paraeter can be deterined. Larsen Miller Paraeter P = T[log t r + 20] P is a function of stress

13 L.M. Diagra of several alloys/exaples Exaple: Calculate tie to cause rupture in gaa Titaniu aluinide at 40 KSI and F Fro fig, p = P = T[log t r + C] = ( ) (log t + 20) t=776 h

14 Creep rate is usually controlled by Diffusion of atos Factors affecting creep rate:

15 Hoework Exaple probles: 7.2, 7.3, 7.4, 7.5 Chapter 7: download fro website Reading assignent for next lecture on (after Test 2): Chapter

TestNian

TestNian Fatigue Damage Mechanism in Very High Cycle Regime Nian Zhou 2012.5.24 Fatigue Low cycle fatigue N f 10 5 cycles Strain-controlled fatigue High cycle fatigue N f f 10 5 cycles Stress-based fatigue Endurance