Fatigue crack propagation in uniaxial loading and bending fatigue in 20 khz testing Mohamed Sadek PhD Student Karlstad university 2017-02-08
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
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.
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
Ultrasonic fatigue testing equipment System resonance frequency at 20 ±0,5 khz Specimen designed for 20 khz resonance frequency Appropriate for VHCFtesting. 10 9 cycles are reached in 14 hours! Oscillator Amplificationhorn Specimen Displacement Stress
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
- Experimental setup
- 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 20038 Hz. E-modulus = 210 GPa ν = 0,3 ρ = 7850 kg/m 3
- 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 0.0005 sec 10 load cycles
- 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
- 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 19 500 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.
- Frequency analysis 1. Modal analysis - ¼ symmetry - Crack surface interpenetration
- Frequency analysis 21000 20000 Resonance frequency, Hz 19000 18000 17000 16000 Experimental frequency Modal analysis - 1/4 symmetry 15000 0 0,001 0,002 0,003 0,004 0,005 0,006 0,007 Crack length, m
- 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
- Frequency analysis 21000 20000 Resonance frequency, Hz 19000 18000 17000 16000 Experimental frequency Modal analysis - 1/4 symmetry ENF - 1/4 symmetry 15000 0 0,001 0,002 0,003 0,004 0,005 0,006 0,007 Crack length, m
- 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.
- Frequency analysis All node at the top surface are constrained to keep the same vertical level at all time.
- Frequency analysis A rigid body is added to the model in order to block the crack surface from penetrating the symmetry plane.
- Frequency analysis Crack surface interpenetration vs No crack surface interpenetration
- Frequency analysis 21000 20000 Resonance frequency, Hz 19000 18000 17000 16000 15000 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
- 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
- Frequency analysis 21000 Resonance frequency, Hz 20000 19000 18000 17000 16000 15000 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
- K computation K I, MPa m^0.5 25 20 15 10 5 1/4 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
- K computation K I, MPa m^0.5 30 25 20 15 10 5 0 1/4 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
- 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) 2 2 4 + 7,1881( a / w) + 1,3693( a / w) 0,034 4 + 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
- K computation K I, MPa m^0.5 30 25 20 15 10 5 0 1/4 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.
- 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.
- Experimental results 1E-08 38MnSiV5 - Steel da/dn, m/cycle 1E-09 1E-10 1 10 100 K, MPa m^0.5
- Experimental results 1E-08 R = -1 da/dn, m/cycle 1E-09 1E-10 38MnSiV5 - Steel 50CrV4 - Steel 16MnCr5 - Steel 1 10 100 K, MPa m^0.5
- 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 1 10 100 K, MPa m^0.5
- Experimental results
Bending fatigue in 20 khz testing Determination of fatigue life at 10 8 cycles. Generating SN-data in the range 10 7-10 10 cycles. Tension-tension loading condition, R = 0,1.
Bending fatigue in 20 khz testing - FEM - modelling Specimen dimensions = (31,8 x 8 x 4) mm Resonance frequency = 19 996 Hz Distance between zero-nodes = 17,6 mm
Bending fatigue in 20 khz testing - FEM - modelling ¼ - Symmetry
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. 250 250 200 200 150 150 σ m [MPa] 100 50 σ m [MPa] 100 50 0 0 5 10 15 20 25 0 0 200 400 600 800 1000 1200 δ [m] F [N]
Bending fatigue in 20 khz testing - FEM - modelling 25 20 Displacement amplitude [µm] Stress amplitude [MPa] Bending stress amplitude - Displacement amplitude 300 Avg(σ a ) = 225 MPa Avg(δ) = 19,8 µm 15 200 M-factor: 10 5 100 225 19,8 =11,3 MPa/µm δ [µm] 0 0 0 0,0001 0,0002 0,0003 0,0004 0,0005 σ a [MPa] -5-10 -15-100 -200 Calibration with a displacement sensor: -20-25 Time [s] -300 V a = (U a - 42,26)/ 4,382
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 / 0,1997 250 22,1-4,59 306 1530 300 26,5-3,58 367 1836 350 31,0-2,57 428 2142 400 35,4-1,56 489 2448 450 39,8-0,56 550 2754 500 44,2 0,45 611 3060 550 48,7 1,46 672 3366 600 53,1 2,47 733 3672 650 57,5 3,48 794 3977 700 61,9 4,49 855 4283
Bending fatigue in 20 khz testing 3-point bending rig
Bending fatigue in 20 khz testing 3-point bending rig
Bending fatigue in 20 khz testing 3-point bending rig
Bending fatigue in 20 khz testing 3-point bending rig
Bending fatigue in 20 khz testing 3-point bending rig
Bending fatigue in 20 khz testing 3-point bending rig
Thank you for your attention!