Materials Science and Methods Calculating the resistance of a grain boundary against fatigue crack growth by the STRONG-approach Michael Marx*, Alain Franz Knorr, Florian Schaefer • Initiation of artificial micro-cracks • Interaction crack – grain boundary • FIB-tomography • Analytical description (Tanaka) • STRONG Technique FATIGUE 2014 Melbourne, Australia, March2014 Introduction Grain boundary in front of the crack tip: grain boundaries block dislocation motion and emission: less dislocations at the same ∆K => smaller CTSD => reduced crack growth fluctuating crack propagation rate crack stop possible Introduction Objectives: Influence of microstructure on fatigue 1. identify the crack initiation process in correlation with the microstructure phase I: where do cracks initiate? (BAD) 2. identify the mechanisms of the undisturbed crack propagation phase II: how fast does a crack grow? 3. identify the mechanisms of the crack propagation through microstructural barriers phase III: what determines the resistance of a grain boundary against crack growth? (GOOD) further objectives: 4. improving the calculation of fatigue life by considering the mechanisms 5. making materials fatigue resistant Initiation of artificial micro-cracks Crack initiation with a FIB notch Interaction crack – grain boundary Tested materials: material load Frequency R-ratio amplitude Initial crack in-situ tomography length mild steel 300 MPa 5 Hz -0,1 40 µm - Al 7075-T7 230 MPa 2 Hz -1 30 µm - UFG nickel 350 MPa 2 Hz -1 100 µm - DS superalloy 300 MPa 5 Hz - 0,1 100 µm - CG-CMSX4 300 MPa 5 Hz - 0,1 100 µm - Interaction crack – grain boundary Example 1: Aluminum alloy Al7075 - T7 cracks grow always perpendicular to the loading direction in stage II COD / µm distance to the grain boundary / µm Interaction crack – grain boundary Example 1: Aluminum alloy Al7075 - T7 crack interacting with a grain boundary: enlargement of COD can this be used to determine the resistance of a grain boundary against fatigue crack growth? Interaction crack – grain boundary Example 3: mild steel artificial crack growing through a grain boundary in stage I (left) and growing together with natural crack (right): several cracks are blocked by the boundary Interaction crack – grain boundary Example 3: mild steel cracks with misorientations of more than 20° do not pass the boundary Interaction crack – grain boundary Influences on the interaction: - crack length and distance to the grain boundary => FIB-notch - angle between grain boundary and surface? - active slip systems? => 3-dimensional information needed! 3D- model (Zhai)* driving force: surface-energy: minimal tilt angle β minimal twist angle α quantify the Zhai-model by local 3D-measurement => FIB tomography * T. Zhai et al.: International Journal of Fatigue 27 (2005) 1202-1209 FIB-tomography 3D reconstruction of the crack by the slice and view technique material: nickel based superalloy FIB-tomography Orientation of the grains and the active slip planes are known ϕ1 Φ ϕ2 -3° 60° 93° α1 α2 α3 14° 40° 29° (ī ı ı) (ı ī ı) (ı ı ı) ϕ1 Φ ϕ2 91° 83° -4° Interaction crack – grain boundary Example 5: polycrystalline CMSX-4 - large misorientation angle - but: no stopping, just deceleration Analytical description Quantifying the crack propagation: 2. for a slip band with grain boundary 2 a) plastic zone blocked by the grain boundary (Blocked Slip Band, BSB): ( ) βΔτ 2 2τ * a c 2 1/2 ΔCTSD = c − a + 2 ln πA π A a 2τ * a β = 1− arccos πΔτ c 2 b) plastic zone spread in the neighboring grain (Propagating Slip Band, PSB): resulting shear-stress τ* determined by τ1 and τ2 of both grains: 2τ * a c τ * −τ * ΔCTSD = 2 ln + 2 2 g(a; c, d) π A a π A g(a; c, d) = d ⋅ ln 1Tanaka c 2 − d2 + c 2 − a 2 c −d − c −a 2 2 2 2 − a ⋅ ln a c 2 − d2 + d c 2 − a 2 a c 2 − d2 − d c 2 − a 2 K., Akiniwa Y., Nakai y., Wei R.P.: Engineering Fracture Mechanics, Vol.24, 803-819, 1986 Analytical description Quantifying the crack propagation: for a slip band with grain boundary and different distances between notch tip and grain boundary W. Schaef, M. Marx: A numerical description of short fatigue cracks interacting with grain boundaries, Acta Mater. 60 (2012) 2425–2436 Interaction crack – grain boundary Quantifying the crack propagation: for a blocked slip band (BSB) Can not be described quantitatively Interaction crack – grain boundary Influences on the interaction: - crack length and distance to the grain boundary => FIB-notch - angle between grain boundary and surface? - active slip systems? => 3-dimensional information needed! 3D- model (Zhai)* driving force: surface-energy: minimal tilt angle β minimal twist angle α quantify the Zhai-model by local 3D-measurement => FIB tomography * T. Zhai et al.: International Journal of Fatigue 27 (2005) 1202-1209 Interaction crack – grain boundary Interaction crack – grain boundary step depth distance / [µm] /[µm] 0 0,0 1 16,0 2 46,8 3 54,9 4 64,4 5 84,4 6 95,4 7 104,8 8 120,8 9 134,7 10 153,0 11 173,2 24,8 30,5 Grain B 28,2 27,5 20,2 9,3 5,8 0,0 11,3 ------- Grain A STRONG-technique Slip Transfer Resistance Of Neigbouring Grains M crack plane n N STRONG-technique M crack plane n N STRONG-technique STRONG-technique STRONG-technique STRONG-technique STRONG-technique Ω 1 T 1 cos ∙ cos STRONG-technique Ω GB orientation well known! 1 T 1 cos ∙ cos Ω , 1 T 1 cos Ω , 1 T 1 cos 0,5° ∙ cos 15,1° Ω11,11 = 0,03 => slip transfer ∙ cos STRONG-technique if ε is unkown Ω is Ω(ε) GB orientation well known! Ω11,11 = 0,03 => slip transfer STRONG-technique if ε is unkown Ω is Ω(ε) GB orientation well known! ° , Ω11,11 = 0,03 => slip transfer ° STRONG-technique if ε is unkown Ω is Ω(ε) GB orientation well known! ° , Ω11,11 = 0,03 => slip transfer ° STRONG-technique if ε is unkown Ω is Ω(ε) GB orientation well known! ° Ω11,11 = 0,03 => slip transfer ° STRONG-technique if ε and δ is unkown Ω is Ω(ε, δ) GB orientation well known! , Ω11,11 = 0,03 => slip transfer , STRONG-technique if ε and δ is unkown Ω is Ω(ε, δ) GB orientation well known! , Ω11,11 = 0,03 => slip transfer , STRONG-technique Conclusions Influence of different grain boundaries in various materials on crack propagation can be observed qualitatively and quantitatively Crack path and grain boundary can be reconstructed in 3D by FIB tomography and serial sectioning The possibility for a continuous crack path determines the resistance of a grain boundary against crack propagation The crack propagation through grain boundaries can by described quantitatively by the model of Tanaka The STRONG-technique is tested to be used to identify strong and weak grain boundaries Acknowledgements Prof. Dr. Horst Vehoff Dr. Christian Holzapfel Dipl.-Ing. Anne Wölfing This work is supported by DFG and is gratefully acknowledged
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