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AAE552-Session11

AAE552-Session11 - AAE 552 Spring 2009 A F Grandt AAE 552...

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AAE 552 Spring 2009 – A. F. Grandt 1 1 AAE 552: Nondestructive Evaluation of Structures and Materials A. F. Grandt, Jr. Professor of Aeronautics and Astronautics Purdue University W. Lafayette, IN 47907 Session 11 – 6 February 2009 2 Contact Information Alten F. (Skip) Grandt, Jr. Email: [email protected] Telephone: Office: 765-494-5141 Home: 765-463-4276 FAX: 765-494-0307 Course webpage accessed at: http://www.itap.purdue.edu/tlt/blackboard 3 AAE 552 Session 11 6 February 2009 Last Time: Overview LEFM Fracture example Fatigue crack growth Today: LEFM determination of Inspection intervals Damage Tolerant concepts Proof testing 4 Assignment Please read Textbook : Skim Chapter 3 Read 16.5 – 16.6 Read 4.3 5 Fracture Toughness Criterion Geometry Crack length Remote Stress t tan cons ) a ( a K c = = β π σ Material Criterion correlates coupon fracture with structure Note : are limitations and thickness effects associated with crack tip plasticity – discuss later 6 Fatigue Crack Growth Criterion Objective : Determine a criterion that specifies cyclic growth of pre-existent cracks Relate cyclic load, crack size, geometry, material Correlate lab tests with structure Evaluate materials Approach : Assume that the cyclic stress intensity factor controls fatigue crack growth rate Verify experimentally
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AAE 552 Spring 2009 – A. F. Grandt 2 7 Correlate Rate da/dN vs K 2a 2a Log K Log da/dN K th K c = K P B √π a K = ∆σ√π σ√π a Crack Length (a) Number of Cycles (N) da dN a* da dN Crack Length (a) Number of Cycles (N) 8 da/dN - K is Material Property Log K Log da/dN K th K c K = ∆σ ( π a) 1/2 β (a) geometry stress crack length Material da/dN = F( K) 9 Compute Fatigue Life N f a o , a f = initial, final crack sizes F(K) = function of: cyclic stress: ∆σ ∆σ , R, . . . crack geometry: β (a) crack length: a material N da F K f a a o f = ( ) da dN F K = ( ) ∆σ ∆σ time σ 2a ∆σ 10 Example 3.2 Life Calculation a Crack σ σ ∆σ = constant time σ Given : Edge crack in wide plate Initial crack a i Final crack a f Cyclic stress ∆σ ∆σ ∆σ = constant da/dN = C K m Find : cyclic life N f 11 Model da/dN - K Curve Fit data with models such as: da dN C K m = da dN C K R K K m c = - - ( ) 1 C, m, K c are empirical constants R = min/max stress Many other models Paris Forman Log K Log da/dN K th K c da/dN = F ( K) 12 Solution Example 3.2 [ ] = = da C K da C a m m a a a a o f o f 112 . σ π N f ( 29 ( 29 [ ] N C m a a f m f m o m = - - - - 1 112 1 5 1 5 1 5 . . . . σ π K a = σ π 112 . da dN C K m = Note: Solution only for edge crack with Paris Law
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AAE 552 Spring 2009 – A. F. Grandt 3 13 Cycle-by-Cycle Life Calculation Compute cycle-by-cycle growth of crack length a a current = a prior + da/dN current da/dN current = F(K current ) * “Retardation” term K current 2245 σ current ( π a prior ) 1/2 β (a prior ) Sum for all cycles in spectrum Applied Stress σ Cycles N Prior N ( σ N , a N ) Current N+1 ( σ N+1 , a N+1 ) 14 Cycle-by-Cycle Algorithm
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