Presentation on theme: "Fatigue and Fracture Behavior of Airfield Concrete Slabs"— Presentation transcript:
1Fatigue and Fracture Behavior of Airfield Concrete Slabs FAA Center Annual Review – Champaign, IL, October 7, 2004Fatigue and Fracture Behavior of Airfield Concrete SlabsProf. S.P. Shah (Northwestern University)Prof. J.R. Roesler (UIUC)Dr. Bin MuDavid Ey (NWU)Amanda Bordelon (UIUC)
2Research Work Plan Finite Element Simulation of Cracked Slab Concrete slab complianceDevelop preliminary R-curve for concrete slabSmall-scale fracture parametersFatigue crack growth modelModel Validation
5Summary of ApproachThe load – crack length (compliance) response obtained from static loading acts as an envelope curve for fatigue loading.The condition KI = KIC can be used to predict fatigue failure.Fatigue crack growth rate has two stages: deceleration stage and acceleration stage.
6Static loading acts as an envelope curve for fatigue loading Static EnvelopeStatic loading acts as an envelope curve for fatigue loading(Subramaniam, K. V., Popovics, J.S., & Shah, S. P. (2002), Journal of Engineering Mechanics, ASCE 128(6): )
7The crack growth in deceleration stage is governed by R-curve. The crack growth in acceleration stage is governed by KI.
13KI Determination Calculation of KI: A modified crack closure integral Rybicki, E. F., and Kanninen, M. F., Eng. Fracture Mech., 9, , 1977.Young, M. J., Sun C. T., Int J Fracture 60, , 1993.acbdefElement-1Element-2Element-4Element-3Y, vX, uO’FcIf < 20% crack length, then accuracies are within 6% of the reference solutions.Finite element mesh near a crack tip
14Deflection vs. Crack Length Vertical displacement at the mid point of edge
15FEM Compliance Results Compliance and crack length
16Stress intensity factor and crack length KI vs Crack Length (a)Stress intensity factor and crack length
34Compliance, crack length and da/dN for T-4 Crack Growth for Slab T2Compliance, crack length and da/dN for T-4
35Fatigue Crack Growth Model Models for Slab-4, T2 & T4Accel.Decel.
36ChallengesNeed to calibrate material constants C1,n1, C2, n2 with slab monotonic data and small-scale resultsExplore other crack configurations modes (partial depth and quarter-elliptical cracks)Size Effect….
37Concrete Property Testing Test SetupTwo Parameter Fracture Model (KI and CTODc)Size Effect Law (KIf and cf)
38Concrete Material Property Setup Three Beam SizesSmallMediumLargeSizeDepthWidthLengthSpanNotch LengthNotch Width(mm)(in)162.52.461803.1535013.782509.84320.80.8230.11821505.90670027.5660023.62501.969110043.31100039.3783.33.281
39Large Beam LVDT notch Clip gauge CMOD 50 mm 50 mm S = 1 m D = 250 mm Initial crack length= 83 mm10 mmCMODW = 80 mmTop ViewLVDT
41Load vs. CMOD (Small Beam) Cast Date: Test Date:
42Load vs. CMOD (Large Beam) Cast Date: Test Date:
43Two Parameter Fracture Model Results Test #Dimensions (mm)ftcw/cda(mm)Eao/bac/bKsIcCTODc (mm)GsIc (N/m)bSbt(MPa)(GPa)(MPa m1/2)125062.58035.70.451927.30.3330.4171.1770.007250.73260015039.60.5381.7350.040276.083100039.40.4601.7880.032181.06437.928.00.5241.3140.025461.67546.10.5151.6990.029262.63634.00.4611.6930.035284.18Jenq and Shah
46Analysis of Slabs on Elastic Foundation using FM- Overview p = k0 * w * yApplied total load (P)rSlab on Elastic FoundationBeam on Elastic FoundationBeama0bPStLba0LFoundation
47Crack Growth Validation from Monotonic Slab Tests LoadCiCuKICCMODStatic Mode I SIFCompliance vs. crack length
48Future Direction Complete Monotonic Slab Testing** develop failure envelopeValidate for fatigue edge notch slabs**Validate for fully-supported beams**testing and FEMDevelop Partial-Depth Notch and Size EffectIncorporate small-scale fracture parameters into fatigue crack growth model
49Compliance vs. Crack Length for Fully Supported Beam λ4 (1 - e-λw cos (λ w)) = 3(k2 b w C) / (d2 q)λ2 / (e-λw sin (λ w)) = 3(q √(π a0) F(α0)) / (KIC b d2)λ = characteristic (dimension is length-1)w = ½ the length of load distributionk = modulus of subgrade reactionb = width of the beamC = Complianced = depth of the beamq = distributed loada0 = crack lengthF(α0) = α α α02 – 0.690αα0 = a0 / bKIC = Critical Stress Intensity Factor for Mode Iqwa0