Lecture 14 Fatigue & Creep in Engineering Materials (Chapter 8) Chapter 8-1
Fatigue Fatigue = failure under applied cyclic stress. specimen compression on top bearing bearing motor counter flex coupling tension on bottom Stress varies with time. -- max key parameters are S, m, and cycling frequency m min S time Key points: Fatigue... --can cause part failure, even though max < y. --responsible for ~ 90% of mechanical engineering i failures. Chapter 8-2
Fatigue: Definitions Symmetric Asymmetric Random Chapter 8-3
Fatigue: Definitions Chapter 8-4
Types of Fatigue Behavior Fatigue limit, S fat : --no fatigue if S < S fat mplitude unsafe case for steel (typ.) S = stress a S fat safe 10 3 10 5 10 7 10 9 N = Cycles to failure For some materials, there is no fatigue limit! S = stress amplitude safe unsafe 10 3 10 5 10 7 10 9 N = Cycles to failure case for Al (typ.) Chapter 8-5
Ex: Fatigue in 7075-T6 Aluminum Alloy Chapter 8-6
Rate of Fatigue Crack Growth Crack grows incrementally da dn K m ~ typ. 1 to 6 a Failed rotating shaft -- crack grew even though K max < K c -- crack grows faster as increases crack gets longer loading freq. increases. increase in crack length per loading cycle crack origin Chapter 8-7
Fatigue Failure in Ductile Materials (Aluminum) Chapter 8-8
Fatigue Failure in Brittle Material Chapter 8-9
Importance of Mean Stress Chapter 8-10
Improving Fatigue Life 1. Impose compressive surface stresses (to suppress surface cracks from growing) S = stress amplitude N = Cycles to failure Adapted from Fig. 8.24, Callister & Rethwisch 8e. near zero or compressive m moderate tensile m Larger tensile m --Method 1: shot peening shot put surface into compression --Method 2: carburizing C-rich gas 2. Remove stress concentrators. bad bad better better Adapted from Fig. 8.25, Callister & Rethwisch 8e. Chapter 8-11
Effect of Surface Compressive Stresses Chapter 8-12
Effect of Surface Compressive Stresses Hardened Case depth by Carburization (or Nitriding) In compression Micro-indentation marks Chapter 8-13
Environmental Effects Thermal cycle..stress cycle..thermal fatigue. Chapter 8-14
Creep Sample deformation at a constant stress ( ) vs. time 0 t Primary Creep: slope (creep rate) decreases with time. Secondary Creep: steady-state i.e., constant slope / t) Tertiary Creep: slope (creep rate) increases with time, i.e. acceleration of rate. Adapted from Fig. 8.28, Callister & Rethwisch 8e. Chapter 8-15
Creep: Temperature Dependence Occurs at elevated temperature, T > 0.4 T m (in K) tertiary primary secondary elastic Chapter 8-16
Secondary Creep Strain rate is constant at a given T, -- strain hardening is balanced by recovery s strain rate material const. K 2 n stress exponent (material parameter) Q c exp RT applied stress activation energy for creep (material parameter) Strain rate 200 increases 100 with increasing T, 40 Stress s (MPa) 20 10 427ºC 538ºC 649ºC 10-2 10-1 1 Steady state creep rate (%/1000hr) s Chapter 8-17
Material constant depending on creep mechanism A better & more informative Creep Equation Activation energy for Self-diffusion Grain size Applied stress m & b depend on the creep mechanism Chapter 8-18
Mechanisms of Creep The mechanism of creep depends on temperature and stress. The various methods are: Bulk diffusion (Nabarro-Herring creep) Dislocation climb -here the strain is actually accomplished by climb Climb-assisted glide here the climb is an enabling mechanism, allowing dislocations to get around obstacles Grain boundary diffusion (Coble creep) Thermally activated glide e.g., via cross-slip Chapter 8-19
Mechanisms of Creep Things to know Dislocations related creep.. m = 4-6, and b = 0. It has a strong dependence on the applied stress and no grain size dependence. Nabarro-Herring Creep (Bulk Diff n)..m = 1, andb b = 2. Atoms diffuse through the lattice causing grains to elongate along the stress axis; it creep has a weak stress dependence and a moderate grain size dependence. Coble Creep (Grain boundary diffusion). m = 1, and b = 3Atoms 3. diffuse along grain boundaries to elongate the grains along the stress axis. This causes Coble creep to have a stronger grain size dependence than Nabarro-Herring creep. Here, Q(grain boundary diffusion) < Q(self diffusion), Coble creep occurs at lower temperatures than Nabarro-Herring creep. Thermally activated glide e.g., via cross-slip Chapter 8-20
Creep Failure Failure: along grain boundaries. g.b. cavities applied stress Chapter 8-21
Creep Failure in S-590 Alloy fig_08_31 Chapter 8 -
Prediction of Creep Rupture Lifetime Estimate rupture time S-590 Iron, T = 800ºC, = 20,000 psi 100 psi) Time to rupture, t r T(20 logtr ) L data for S-590 Iron 12 16 20 24 28 10 3 L (K-h) 20 10 1 Str ress (10 3 temperature function of applied stress time to failure (rupture) ( 1073 K)(20 logt ) r 24x10 3 Ans: t r = 233 hr Chapter 8-23
Estimate the rupture time for S-590 Iron, T = 750ºC, = 20,000000 psi Solution: Time to rupture, t r T (20 log tr ) L temperature function of applied stress time to failure (rupture) re) ( 1023 K)(20 log t ) ( r r Ans: t r = 2890 hr 3 24x10 data for S-590 Iron 12 16 20 24 28 10 3 L (K-h) 100 20 10 1 Stre ess (10 3 psi) Chapter 8-24
To Increase Creep Rupture Resistance: 1) Use large grain size material, highly directions grains or a single crystal. 2) Use heavy alloying (grain boundary drag, dislocation drag etc.) 3) Use high melting point material 4) Use high modulus of elasticity material Make sure it s justifiable ($$$$$...) Chapter 8-25
SUMMARY Engineering materials not as strong as predicted by theory Flaws act as stress concentrators that cause failure at stresses lower than theoretical values. Sharp corners produce large stress concentrations and premature failure. Failure type depends on T and : -For simple fracture (noncyclic and T < 0.4T m), failure stress decreases with: - increased maximum flaw size, - decreased T, - increased rate of loading. - For fatigue (cyclic : -cycles to fail decreases as increases. - For creep (T > 0.4T m ): - time to rupture decreases as or T increases. Chapter 8-26
ANNOUNCEMENTS Reading: Study chapter 8 thoroughly. Study the solutions of Chapter 8 problems very well. Do not memorize but try understanding the concepts behind the solutions Chapter 8-27