Presentation on theme: "Fatigue and Fracture Behavior of Airfield Concrete Slabs"— Presentation transcript:
1 Fatigue 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)
2 Research Work Plan Finite Element Simulation of Cracked Slab Concrete slab complianceDevelop preliminary R-curve for concrete slabSmall-scale fracture parametersFatigue crack growth modelModel Validation
5 Summary 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.
6 Static 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): )
7 The crack growth in deceleration stage is governed by R-curve. The crack growth in acceleration stage is governed by KI.
9 Crack growth during fatigue test (a) crack length vs. cycles (b) rate of crack growth
10 FEM Simulation of Cracked Slab Phase –1: Fatigue testStep 1FEM Simulation of Cracked SlabFEMC=C(a) and KI=KI(a)a
11 Experimental setup and FEM mesh Elastic support2000 mm1000 mmaSymmetric line200 mm100 mmUIUC setupFEM mesh with a=400 mm
12 FEM ContoursDeformation(a=400 mm)Node force(a=400mm)
13 KI 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
14 Deflection vs. Crack Length Vertical displacement at the mid point of edge
15 FEM Compliance Results Compliance and crack length
16 Stress intensity factor and crack length KI vs Crack Length (a)Stress intensity factor and crack length
34 Compliance, crack length and da/dN for T-4 Crack Growth for Slab T2Compliance, crack length and da/dN for T-4
35 Fatigue Crack Growth Model Models for Slab-4, T2 & T4Accel.Decel.
36 ChallengesNeed 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….
37 Concrete Property Testing Test SetupTwo Parameter Fracture Model (KI and CTODc)Size Effect Law (KIf and cf)
38 Concrete 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
39 Large 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
41 Load vs. CMOD (Small Beam) Cast Date: Test Date:
42 Load vs. CMOD (Large Beam) Cast Date: Test Date:
43 Two 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
46 Analysis of Slabs on Elastic Foundation using FM- Overview p = k0 * w * yApplied total load (P)rSlab on Elastic FoundationBeam on Elastic FoundationBeama0bPStLba0LFoundation
47 Crack Growth Validation from Monotonic Slab Tests LoadCiCuKICCMODStatic Mode I SIFCompliance vs. crack length
48 Future 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
49 Compliance 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