Fatigue crack propagation in uniaxial loading and bending fatigue in 20 khz testing. Mohamed Sadek PhD Student Karlstad university

Transcription

1 Fatigue crack propagation in uniaxial loading and bending fatigue in 20 khz testing Mohamed Sadek PhD Student Karlstad university

2 EU - project Influence of cyclic frequency on fatigue strength and crack growth of engineering steels for demanding applications, FREQTIGUE. RFCS-funded. Participants: Karlstad University Centro Ricerche Fiat SPCA, CRFIAT Arcelormittal Maizierez Research SA, Arcelor Research Rheinische Westfalische Technische Hochschule Aachen, RWTH Aachen Universite de Paris Oeust-Nantarre la defence UPO, UPO Karlsruher Institut fur Technologie KIT, KIT KA Sidenor I + S

3 FREQTIGUE Main aim of the project is to analyze the influence of loading frequency on the fatigue strength and crack growth rates. Materials: High strength steels. 3 for bar specimens 3 for flat specimens 38MnSiV5 steel 50CrV4 steel 16MnCr5 steel M800HY steel CP1000 steel DP1180 steel Different loading frequencies: 25Hz, 150Hz, 1000Hz and 20 khz.

4 Outline Ultrasonic fatigue testing equipment Fatigue crack propagation testing at 20 khz - FEM-modelling - Frequency analysis - K-computation - da/dn vs K - results Bending fatigue at 20 khz - FEM-modelling - Stress calculations - Testing rig

5 Ultrasonic fatigue testing equipment System resonance frequency at 20 ±0,5 khz Specimen designed for 20 khz resonance frequency Appropriate for VHCFtesting cycles are reached in 14 hours! Oscillator Amplificationhorn Specimen Displacement Stress

6 Determination of fatigue crack growth rates and the crack tip stress intensity factor. da dn = C Two different loading conditions are used: 1) Tension-compression, R = -1. 2) Tension-tension, R = 0,1. ( K ) n

7 - Experimental setup

8 - Specimen FCG Specimen in 20kHz testing 1 mm notch depth 0,5 mm notch radius Mechanical symmetry at the crack plane. Variable thickness reduces the resonance length of the specimen. Resonance frequency calculated by FEM to Hz. E-modulus = 210 GPa ν = 0,3 ρ = 7850 kg/m 3

9 - FEM - modelling Numerical analysis - Abaqus CAE Data input: E = 210 GPa ν = 0.3 ρ = 7850 kg/m 3 ¼ - and ½ - symmetry 10 µm displacement, U 0 Static and dynamic analysis Dynamic analysis: 20kHz testing frequency sec 10 load cycles

10 - FEM - modelling - FE-meshing Volume partition is used for the area around the crack. Hexahedral mesh is used for the area close to the crack, and tetrahedral mesh is used for the rest of the sample. Crack length, a

11 - Frequency analysis As the crack propagates within the material the stiffness of the specimen decreases. This stiffness drop, decreases the system resonance frequency. Eventually, at around (a = 6mm), the frequency has dropped to the lower limit of the Ultrasonic system at Hz. Different FEM-models were used to predict the resonance frequency drop for a propagating crack. The combination of resonance frequency and crack length is used as input to the stress intensity calculations.

12 - Frequency analysis 1. Modal analysis - ¼ symmetry - Crack surface interpenetration

13 - Frequency analysis Resonance frequency, Hz Experimental frequency Modal analysis - 1/4 symmetry ,001 0,002 0,003 0,004 0,005 0,006 0,007 Crack length, m

14 - Frequency analysis 2. Effective natural frequency ¼ symmetry Modal analysis of a cracked beam. M. Chati, R rand and S. Mukherjee Account for the non-linear behavior of a beam with a breathing crack and correcting for the crack surface interpenetration. Effective Natural Frequency - ENF: ω 0 = 2ω 1ω 2 ω 1 +ω 2 ω 1 = frequency of a closed crack ω 2 = frequency of a open crack

15 - Frequency analysis Resonance frequency, Hz Experimental frequency Modal analysis - 1/4 symmetry ENF - 1/4 symmetry ,001 0,002 0,003 0,004 0,005 0,006 0,007 Crack length, m

16 - Frequency analysis 3. Pull and release method to obtain resonance frequency Two step simulation ¼ - symmetry: Step1 The top surface of the specimen is pulled in a static step to a certain displacement. Step2 The specimen is released from the displacement and is allowed to bounce back under a dynamic step. The time period of each cycle/bounce is measured and the frequency is then calculated. This model allows us to use different constraint in the model, e.g. surface contact properties.

17 - Frequency analysis All node at the top surface are constrained to keep the same vertical level at all time.

18 - Frequency analysis A rigid body is added to the model in order to block the crack surface from penetrating the symmetry plane.

19 - Frequency analysis Crack surface interpenetration vs No crack surface interpenetration

20 - Frequency analysis Resonance frequency, Hz Experimental frequency Modal analysis - 1/4 symmetry ENF - 1/4 symmetry "Pull and release"-method 0 0,001 0,002 0,003 0,004 0,005 0,006 0,007 Crack length, m

21 - Frequency analysis 4. Effective natural frequency (specimen+horn+oscillator) Modal analysis of the whole load train; specimen, horn and oscillator. ½ - symmetry along the length Implementation of the ENF approximation. ω 0 = 2ω 1ω 2 ω 1 +ω 2

22 - Frequency analysis Resonance frequency, Hz Experimental frequency Modal analysis - 1/4 symmetry "Pull and release"-method ENF - 1/4 symmetry ENF - 1/2 symmetry inc horn and osc 0 0,001 0,002 0,003 0,004 0,005 0,006 0,007 Crack length, m

23 - K computation K I, MPa m^ /4 symmetry - constant freq. 1/4 symmetry - ENF K- values calculated with static simulations are approximately 30% lower than the ones calculated with dynamic simulations. Static simulations 0 0 0,001 0,002 0,003 0,004 0,005 0,006 0,007 0,008 Crack length, m K-calculations at different crack lengths with different frequency dependencies

24 - K computation K I, MPa m^ /4 symmetry - constant freq. 1/4 symmetry - ENF 1/2 symmetry - inc. horn and osc - ENF Static simulations 0 0,001 0,002 0,003 0,004 0,005 0,006 0,007 0,008 K- values calculated with static simulations are approximately 30% lower than the ones calculated with dynamic simulations. By taking the whole load train into account a final K vs a -curve is obtained. Crack length, m K-calculations at different crack lengths with different frequency dependencies

25 - K computation The stress intensity is computed by FEM using static and dynamic analysis. Wu and Bathias, 1994 Ed K = U 0 π / a f ( a / w) 2 1 ν Calibrated geometry function - Dynamic: - Static: f ( a / w) = 6,0932( a / w) 3,0046( a / w) f ( a / w) = 1,2075( a / w) + 0,139( a / w) ,1881( a / w) + 1,3693( a / w) 0, ,4698( a / w) + 0,6074( a / w) 0,0073 The calibrated geometry function, f(a/w), is used to produce the calibrated K used at testing. 3 3

26 - K computation K I, MPa m^ /4 symmetry - constant freq. 1/4 symmetry - ENF 1/2 symmetry - inc. horn and osc - ENF Static simulations Calibrated DK 0 0,001 0,002 0,003 0,004 0,005 0,006 0,007 0,008 Crack length, m K-calculations at different crack lengths with different frequency dependencies K- values calculated with static simulations are approximately 30% lower than the ones calculated with dynamic simulations. By taking the whole load train into account a final K vs a - curve is obtained. The calibrated K starts at a = 0,001 m.

27 - Experimental procedure The displacement amplitude is calibrated against and controlled by the voltage input of the Ultrasonic Booster. The relationship between the displacement amplitude and the K-amplitude is computed by FEM. The amplitude is increased every 10 7 cycles by approximately 10% until crack initiation occurs. The crack is allowed to propagate stepwise about 0,5 mm each step, where the amplitude is decreased by approximately 10%. When K = K th is reached and no crack propagation occurs, the amplitude is increased stepwise in a similar manner as when decreased.

28 - Experimental results 1E-08 38MnSiV5 - Steel da/dn, m/cycle 1E-09 1E K, MPa m^0.5

29 - Experimental results 1E-08 R = -1 da/dn, m/cycle 1E-09 1E-10 38MnSiV5 - Steel 50CrV4 - Steel 16MnCr5 - Steel K, MPa m^0.5

30 - Experimental results 1,00E-07 R = 0,1 da/dn, m/cycle 1,00E-08 1,00E-09 1,00E-10 38MnSiV5 - Steel 50CrV4 - Steel 16MnCr5 - Steel K, MPa m^0.5

31 - Experimental results

32 Bending fatigue in 20 khz testing Determination of fatigue life at 10 8 cycles. Generating SN-data in the range cycles. Tension-tension loading condition, R = 0,1.

33 Bending fatigue in 20 khz testing - FEM - modelling Specimen dimensions = (31,8 x 8 x 4) mm Resonance frequency = Hz Distance between zero-nodes = 17,6 mm

34 Bending fatigue in 20 khz testing - FEM - modelling ¼ - Symmetry

35 Bending fatigue in 20 khz testing - FEM - modelling Static FEM simulations; δ = 2, 5, 10 and 20 µm σ m [MPa] = 0,1997 * F [N] The mean stress is controlled by the Force input during the experiments σ m [MPa] σ m [MPa] δ [m] F [N]

36 Bending fatigue in 20 khz testing - FEM - modelling Displacement amplitude [µm] Stress amplitude [MPa] Bending stress amplitude - Displacement amplitude 300 Avg(σ a ) = 225 MPa Avg(δ) = 19,8 µm M-factor: ,8 =11,3 MPa/µm δ [µm] ,0001 0,0002 0,0003 0,0004 0,0005 σ a [MPa] Calibration with a displacement sensor: Time [s] -300 V a = (U a - 42,26)/ 4,382

37 Bending fatigue in 20 khz testing R = σ mmm σ mmm = 0,1 σ m = σ a * 1,22 σ a [MPa] U a [µm] = σ a / 11,3 V a [V] = (U a - 42,26)/ 4,382 σ m [MPa] = σ a * 1,22 F m [N] = σ m / 0, ,1-4, ,5-3, ,0-2, ,4-1, ,8-0, ,2 0, ,7 1, ,1 2, ,5 3, ,9 4,

38 Bending fatigue in 20 khz testing 3-point bending rig

39 Bending fatigue in 20 khz testing 3-point bending rig

40 Bending fatigue in 20 khz testing 3-point bending rig

41 Bending fatigue in 20 khz testing 3-point bending rig

42 Bending fatigue in 20 khz testing 3-point bending rig

43 Bending fatigue in 20 khz testing 3-point bending rig

44 Thank you for your attention!