Fatigue Crack Propagation Fatigue Crack Growth • Once a crack is present in a material, it will tend to grow under the influence of cyclic loading. • The crack may be initiated by fatigue, or may be pre-existing from manufacture, or may be caused by an impact, or similar event (e.g., a thermal shock.) • The crack will grow to a critical length then fracture of the component will occur. Driving Force for Crack Growth • The driving force for crack growth is the range in the stress intensity factor during cycling. K f (a/W) a max min for R 0 max for R 0 Cyclic Loading max min mean 2 range max min max min Rotating Machinery amplitude 2 min StressRatio, R max Airframes, Bridges, Tanks, etc, Crack Growth Rate, da/dN 1 < 2 1 Crack Length, a ac1 X 2 ac2 X da/dN2 da/dN1 ao Cycles, N log(da/dN) A Threshold Region Slow Growth da dN m Paris Region A(K) m Stable Growth log(K) Paris Law Fast Fracture Region Rapid-unstable Growth Crack Growth Rates and Microstructural Features Fractographic Evidence of Crack Growth fatigue striations 10 mm Fatigue Striations in Al-alloy: 5 small cycles between overloads Crack Growth direction Crack Growth Mechanisms No Load Load reduced Slip Loaded No Load Max Load Loaded again Model for Crack Growth 4 6 2 1 5 7 Crack Propagation Life, Np Total fatigue life is the sum of the crack initiation life and the crack propagation (growth) life. Nf Ni N p For some components, where stress levels are high and/or the critical crack size is small, the crack propagation life is neglected in design. For other structures, including pressure vessels, ship structures, transport aircraft, etc. the crack growth life may be a substantial component of total life. ac da Np m a o A(K) Limits of Integration • The initial crack length, ao, is usually either found by inspection or a reasonable minimum size of crack is assumed for the analysis. • The critical crack size is found from: 2 1 Kc ac f (a/W) max • Where max is the maximum stress. (it’s not the stress range) Procedure for Constant Amplitude Crack Growth life Calculation • Obtain appropriate crack growth rate data for material, environment and stress ratio • Determine starting crack size, ao • Determine critical crack size, ac • Determine K for starting crack size, ao. If K< Kth then crack will not grow • If K> Kth then integrate to get crack growth life. (Can conservatively use Paris Law, if appropriate) General Paris Law Solution for Np ac da Np A f (a/W) ao a ) m Special Case: m=3; f(a/W) constant=Y 2 1 1 Np A ( ) Y 3/ 2 3 3 ao ac General Solution: • A more general solution will include the actual growth rate data in the threshold and near-threshold region. • If the starting crack size is relatively small, this will represent a major portion of growth life, so it may be un-economical to neglect it. • The life in the fast fracture region is generally neglected. Use this data carefully. Try it! • A fatigue crack 1.5 mm long has been discovered in a main wing spar of a CC-130 Hercules undergoing structural tear down and inspection. Given the loading, material and geometry shown, estimate the number of flying hours to fracture, and comment on the results. 7075-T73511 al alloy Kc (6mm) = 40 MPam Sy = 455 MPa A = 1.3x10-10 m/cycle m=3 Y = 1.27 (assume constant) S Crack a Section A-A Through Spar (inches) 10 Loading R 0.133 75 Stress (MPa) 75 10 0 time 100 cycles=1 flying hour OK... ac da Np a o A( Y a ) m • ao = 1.5 mm, find ao 2 2 1 Kc 1 40 ac YS 1.27( 75 ) 0.0561m (56.1mm) max Stress Range, = max-min = (75 - 10) MPa = 65 MPa For m=3, Y constant: 2 1 1 Np A3 / 2 ( )3 Y 3 ao ac 2 1 1 Np 10 3 / 2 3 1.3x10 ( 65 ) ( 1.27 ) 0.0015 3 0.0561 106000 cycles 1hr 106000 cycles 1060 flight hrs 100cycles Crack Growth Curve 95000 cycles 5 mm at half life! at half length! a/ac =15% N/Np =89% Comments & Observations • There is a substantial period of crack growth for this component. The fatigue crack can be monitored, inspected, and the component can be replaced or repaired after 500 more hours of operation. • Half-life (factor of safety on life) is a safer criterion than length, because cracks grow too rapidly as they become longer.