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Fatigue and Fracture Behavior of Airfield Concrete Slabs Prof. S.P. Shah (Northwestern University) Prof. J.R. Roesler (UIUC) Dr. Bin Mu David Ey (NWU) Amanda Bordelon (UIUC) FAA Center Annual Review – Champaign, IL, October 7, 2004

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Research Work Plan 1. Finite Element Simulation of Cracked Slab 2. Concrete slab compliance 3. Develop preliminary R-curve for concrete slab 4. Small-scale fracture parameters 5. Fatigue crack growth model 6. Model Validation

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Large-Scale Concrete Slab Tests

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Typical S-N Curves for Concrete Fatigue

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The load – crack length (compliance) response obtained from static loading acts as an envelope curve for fatigue loading. The condition K I = K IC can be used to predict fatigue failure. Fatigue crack growth rate has two stages: deceleration stage and acceleration stage. Summary of Approach

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Static 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): 668-676.) Static Envelope

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The crack growth in deceleration stage is governed by R-curve. The crack growth in acceleration stage is governed by K I.

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Static and Fatigue Envelope

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Crack growth during fatigue test (a) crack length vs. cycles (b) rate of crack growth

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Step 1 Phase –1: Fatigue test FEM C=C(a) and K I =K I (a) FEM Simulation of Cracked Slab a

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Experimental setup and FEM mesh Elastic support 2000 mm 1000 mm a Symmetric line 200 mm 100 mm UIUC setup FEM mesh with a=400 mm

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Deformation (a=400 mm) Node force (a=400mm) FEM Contours

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Calculation of K I: A modified crack closure integral Rybicki, E. F., and Kanninen, M. F., Eng. Fracture Mech., 9, 931-938, 1977. Young, M. J., Sun C. T., Int J Fracture 60, 227-247, 1993. a c b d e f Element-1 Element-2 Element-4 Element-3 Y, v X, u O’ FcFc Finite element mesh near a crack tip If < 20% crack length, then accuracies are within 6% of the reference solutions. K I Determination

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Vertical displacement at the mid point of edge Deflection vs. Crack Length

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Compliance and crack length FEM Compliance Results

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Stress intensity factor and crack length K I vs Crack Length (a)

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CMOD vs Crack Length

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Processing Lab Fatigue Data Single pulse loading Tridem pulse loading

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Single Pulse Fatigue Loading (1 Cycle) Loading Unloading P max P min

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Tridem Pulse Fatigue Loading (1 Cycle) Loading L1 Loading L2 Loading L3 Unloading U1 Unloading U2 Unloading L3 P max P int P min

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Deflection vs. Number of Cycles (Single Pulse Slab 4)

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Deflection vs. Number of Cycles (Tridem Pulse Slab 7)

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Compliance Plots Loading vs. Unloading Compliance Single vs. Tridem Pulses Need to measure CMOD in future!!!

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Single Pulse Loading vs. Unloading Compliance Load vs Rebound Deflection for S4 Cycle 85529 Loading Compliance Unloading Compliance

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Single Pulse Compliance (Slab 9) P max = 96.9 kN P min = 67.7 kN N fail = 352

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Tridem Pulse Loading vs. Unloading Compliance Load vs Rebound Deflection for T4 Cycle 3968 Loading L1 Compliance Unloading U3 Compliance Unloading U1, Loading L2, Unloading L2 and Loading L3 Compliances

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Tridem Pulse Compliance (Slab 2) P max = 91.5 kN P min = 7.0 kN N fail = 61,184

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Tridem Pulse Compliance (Slab 4) P max = 90.7 kN P min = 7.5 kN N fail = 4,384

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Slab-4 Normalized Compliance

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Compliance, crack length and da/dN for Slab-4 Single Pulse Slab4

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T-2 Tridem Slab (T2)

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Compliance, crack length and da/dN for T-2 Crack Growth for Slab T2

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T-4 Tridem Slab (T4)

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Compliance, crack length and da/dN for T-4 Crack Growth for Slab T2

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Models for Slab-4, T2 & T4 Fatigue Crack Growth Model Accel. Decel.

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Challenges Need to calibrate material constants C 1,n 1, C 2, n 2 with slab monotonic data and small- scale results Explore other crack configurations modes (partial depth and quarter-elliptical cracks) Size Effect….

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Concrete Property Testing Test Setup Two Parameter Fracture Model (K I and CTOD c ) Size Effect Law (K If and c f )

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Concrete Material Property Setup Three Beam Sizes Small Medium Large Size DepthWidthLengthSpanNotch LengthNotch Width (mm)(in)(mm)(in)(mm)(in)(mm)(in)(mm)(in)(mm)(in) 162.52.461803.1535013.782509.84320.80.8230.118 21505.906803.1570027.5660023.62501.96930.118 32509.843803.15110043.31100039.3783.33.28130.118

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S = 1 m D = 250 mm 50 mm W = 80 mm Large Beam Initial crack length = 83 mm Clip gauge CMOD 50 mm notch LVDT Top View LVDT 10 mm CMOD

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Testing Apparatus Before Loading After Loading

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Load vs. CMOD (Small Beam) Cast Date: 06-14-04Test Date: 06-22-04

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Load vs. CMOD (Large Beam) Cast Date: 06-14-04Test Date: 06-22-04

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Two Parameter Fracture Model Results Test # Dimensions (mm)ftcftc w/c d a (mm) E a o /ba c /b K s Ic CTOD c (mm) G s Ic (N/m) b Sbt(MPa)(GPa) (MPa m 1/2 ) 125062.58035.70.451927.30.3330.4171.1770.007250.73 26001508035.70.451939.60.3330.5381.7350.040276.08 310002508035.70.451939.40.3330.4601.7880.032181.06 425062.58037.90.451928.00.3330.5241.3140.025461.67 56001508037.90.451946.10.3330.5151.6990.029262.63 610002508037.90.451934.00.3330.4611.6930.035284.18 Jenq and Shah

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Size Effect Law Results Bazant et al

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Partial Depth Crack Edge Notch Crack Quarter-Elliptical Crack a b c d Slab Tests

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Analysis of Slabs on Elastic Foundation using FM- Overview b a L Foundation p = k0 * w * y Applied total load (P) r b a0a0 L Foundation a0a0 b P S t L Slab on Elastic Foundation Beam on Elastic Foundation Beam

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CMOD Load K IC C i C u Static Mode I SIFCompliance vs. crack length Crack Growth Validation from Monotonic Slab Tests

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Future Direction Complete Monotonic Slab Testing** develop failure envelope Validate for fatigue edge notch slabs** Validate for fully-supported beams** testing and FEM Develop Partial-Depth Notch and Size Effect Incorporate small-scale fracture parameters into fatigue crack growth model

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Compliance vs. Crack Length for Fully Supported Beam λ 4 (1 - e -λw cos (λ w)) = 3(k 2 b w C) / (d 2 q) λ 2 / (e -λw sin (λ w)) = 3(q √(π a 0 ) F(α 0 )) / (K IC b d 2 ) λ = characteristic (dimension is length -1 ) w = ½ the length of load distribution k = modulus of subgrade reaction b = width of the beam C = Compliance d = depth of the beam q = distributed load a 0 = crack length F(α 0 ) = -3.035α 0 4 + 2.540α 0 3 + 1.137α 0 2 – 0.690α 0 + 1.334 α 0 = a 0 / b K IC = Critical Stress Intensity Factor for Mode I q w a0a0

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