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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)

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Presentation on theme: "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)"— Presentation transcript:

1 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

2 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

3 Large-Scale Concrete Slab Tests

4 Typical S-N Curves for Concrete Fatigue

5  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

6 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): ) Static Envelope

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

8 Static and Fatigue Envelope

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

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

11 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

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

13 Calculation of K I: A modified crack closure integral Rybicki, E. F., and Kanninen, M. F., Eng. Fracture Mech., 9, , Young, M. J., Sun C. T., Int J Fracture 60, , 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

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

15 Compliance and crack length FEM Compliance Results

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

17 CMOD vs Crack Length

18 Processing Lab Fatigue Data Single pulse loading Tridem pulse loading

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

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

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

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

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

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

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

26 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

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

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

29 Slab-4 Normalized Compliance

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

31 T-2 Tridem Slab (T2)

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

33 T-4 Tridem Slab (T4)

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

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

36 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….

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

38 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)

39 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

40 Testing Apparatus Before Loading After Loading

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)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 ) Jenq and Shah

44 Size Effect Law Results Bazant et al

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

46 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

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

48 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

49 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 ) = α α α 0 2 – 0.690α  α 0 = a 0 / b  K IC = Critical Stress Intensity Factor for Mode I q w a0a0


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