Fatigue 7-1

Fatigue of Metals Metals often fail at much lower stress at cyclic loading compared to static loading. Crack nucleates at region of stress concentration and propagates due to cyclic loading. Failure occurs when cross sectional area of the metal too small to withstand applied load. Fatigue fractured surface of keyed shaft Figure 6.19 Fracture started here Final rupture (After “Metals Handbook,” vol 9, 8 th ed., American Society of Metals, 1974, p.389) 7-13

Fatigues Testing Alternating compression and tension load is applied on metal piece tapered towards center. Stress to cause failure S and number of cycles required N are plotted to form SN curve. (After H.W. Hayden, W.G. Moffatt, and J.Wulff, “The structure and Properties of Materials,” vol. III, Wiley, 1965, p.15.) Figure 6.20 Figure 6.23 Figure

Cyclic Stresses Different types of stress cycles are possible (axial, torsional and flexural). Mean stress = Stress amplitude = Stress range = Figure

Structural Changes in Fatigue Process Crack initiation first occurs. Reversed directions of crack initiation caused surface ridges and groves called slipband extrusion and intrusion. This is stage I and is very slow ( m/cycle). Crack growth changes direction to be perpendi- cular to maximum tensile stress (rate microns/sec). Sample ruptures by ductile failure when remaining cross-sectional area is small to withstand the stress. Persistent slip bands In copper crystal Figure 6.26 Courtesy of Windy C. Crone, University of Wisconsin 7-16

Factors Affecting Fatigue Strength Stress concentration: Fatigue strength is reduced by stress concentration. Surface roughness: Smoother surface increases the fatigue strength. Surface condition: Surface treatments like carburizing and nitriding increases fatigue life. Environment: Chemically reactive environment, which might result in corrosion, decreases fatigue life. 7-17

Fatigue Crack Propagation Rate Notched specimen used. Cyclic fatigue action is generated. Crack length is measured by change in potential produced by crack opening. Figure 6.27 (After “Metals Handbook,” Vol 8, 9 th ed., American Society of Metals, 1985, p.388.) 7-18

Stress & Crack Length Fatigue Crack Propagation. σ2σ2 σ1σ1 Δa ΔN Δa ΔN When ‘a’ is small, da/dN is also small. da/dN increases with inc- reasing crack length. Increase in σ increases crack growth rate. = fatigue crack growth rate. ΔK = K max -K min = stress intensity factor range. A,m = Constants depending on material, environment, frequency temperature and stress ratio. α f(σ,a) Figure

Fatigue Crack Growth rate Versus ΔK Straight line with slope m Limiting value of ΔK below Which there is no measurable Crack growth is called stress intensity factor range threshold ΔK th (After P.C. Paris et al. Stress analysis and growth of cracks, STP 513 ASTM, Philadelphia, 1972, PP Figure

Fatigue Life Calculation Integrating from initial crack size a 0 to final crack size a f at number of fatigue cycles N f Integrating and solving for N f (Assuming Y is independent of crack length) But Therefore 7-21

Fatigue Behavior of Nanomaterials Nanomaterials and Ultrafine Ni are found to have higher endurance limit than microcrystalline Ni. Fatigue crack growth is increased in the intermediate regime with decreasing grain size. Lower fatigue crack growth threshold K th observed for nanocrystalline metal.