Abstract
A common phenomenon of fatigue test data reported in the open literature such as S-N curves exhibits the scatter of points for a group of same specimens under the same loading condition. The reason is well known that the microstructure is different from specimen to specimen even in the same group. Specifically, a fatigue failure process is a multi-scale problem so that a fatigue failure model should have the ability to take the microscopic effect into account. A physically-based trans-scale crack model is established and the analytical solution is obtained by coupling the micro- and macro-scale. Obtained is the trans-scale stress intensity factor as well as the trans-scale strain energy density (SED) factor. By taking this trans-scale SEDF as a key controlling parameter for the fatigue crack propagation from micro- to macro-scale, a trans-scale fatigue crack growth model is proposed in this work which can reflect the microscopic effect and scale transition in a fatigue process. The fatigue test data of aluminum alloy LY12 plate specimens is chosen to check the model. Two S-N experimental curves for cyclic stress ratio R=0.02 and R=0.6 are selected. The scattering test data points and two S-N curves for both R=0.02 and R=0.6 are exactly re-produced by application of the proposed model. It is demonstrated that the proposed model is able to reflect the multiscaling effect in a fatigue process. The result also shows that the microscopic effect has a pronounced influence on the fatigue life of specimens.
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References
Miner M A. Cumulative damage in fatigue. J Appl Mech, 1945, 12(3): A159–A164
Paris P C. The growth of cracks due to variations in load. Dissertation for the Doctoral Degree. Bethlehem: Lehigh University, USA, 1962
Sih G C. Multiscaling in Molecular and Continuum Mechanics: Interaction of Time and Size from Macro to Nano. Berlin: Springer, 2006
Sih G C. Multiscale Fatigue Crack Initiation and Propagation of Engineering Materials: Structural Integrity and Microstructural Worthiness. Berlin: Springer, 2008
Jones R, Caims K, Baker J, et al. A study of the effect of CPCs on fatigue crack propagation in a representative fuselage lap joint specimen. Eng Fract Mech, 2012, 87: 1–82
Benedetti M, Fontanari V, Santus C, et al. Notch fatigue behaviour of shot peened high-strength aluminum alloys: Experiments and predictions using a critical distance method. Int J Fatigue, 2010, 32: 1600–1611
Schmidt F, Rheinfurth M, Horst P, et al. Multiaxial fatigue behaviour of GFRP with evenly distributed or accumulated voids monitored by various NDT methodologies. Int J Fatigue, 2012, 43: 207–216
Ma Y E, Staron P, Fischer T, et al. Size effects on residual stress and fatigue crack growth in friction stir welded 2195-T8 aluminum-Part I: Experiments. Int J Fatigue, 2011, 33: 1417–1425
Hong Y S, Zhao A G, Qian G A, et al. Fatigue strength and crack initiation mechanism of very-high-cycle fatigue for low alloy steels. Metall Mater Trans A, 2012, 43: 2753–2762
Sun C, Lei Z, Xie J, et al. Effects of inclusion size and stress ratio on fatigue strength for high-strength steels with fish-eye mode failure. Int J Fatigue, 2013, 48: 19–27
Zeng R C, Han E H, Ke W, et al. Influence of microstructure on tensile properties and fatigue crack growth in extruded magnesium alloy AM60. Int J Fatigue, 2010, 32: 411–419
Jang C H, Cho P Y, Kim M, et al. Effects of microstructure and residual stress on fatigue crack growth of stainless steel narrow gap welds. Mater Design, 2010, 31: 1862–1870
Bernarda J D, Jordonb J B, Lugo M, et al. Observations and modeling of the small fatigue crack behavior of an extruded AZ61 magnesium alloy. Int J Fatigue, 2013, 52: 20–29
Ghonem H. Microstructure and fatigue crack growth mechanisms in high temperature titanium alloys. Int J Fatigue, 2010, 32: 1448–1460
Vipul K G, Richard P G, Sean R A. Diffraction characterization of microstructure scale fatigue crack growth in a modern Al-Zn-Mg-Cu alloy. Int J Fatigue, 2012, 42: 131–146
Sih G C, Tang X S. Dual scaling damage model associated with weak singularity for macro-scopic crack possessing a micro-/meso-scopic notch tip. Theor Appl Fract Mech, 2004, 42: 1–24
Tang X S, Sih G C. Weak and strong singularities reflecting multiscale damage: micro-boundary conditions for free-free, fixed-fixed and free-fixed constraints. Theor Appl Fract Mech, 2005, 43: 5–62
Sih G C, Tang X S. Simultaneous occurrence of double micro/macro stress singularities for multiscale crack model. Theor Appl Fract Mech, 2006, 46: 87–104
Sih G C, Tang X S. Asymptotic micro-stress field dependency on mixed boundary conditions dictated by micro-structural asymmetry; Mode I macro-stress loading. Theor Appl Fract Mech, 2006, 46: 1–14
Tang X S, Sih G C. Equilibrium mechanics model of multiscaling by segmentation: asymptotic solution for macro-meso-micro damage in anti-plane shear deformation. Theor Appl Fract Mech, 2005, 44: 1–15
Sih G C, Tang X S. Triple scale segmentation of non-equilibrium system simulated by macro-micro-atomic line model with mesoscopic transitions. Theor Appl Fract Mech, 2005, 44: 116–145
Sih G C, Tang X S. Form-invariant representation of fatigue crack growth rate enabling linearization of multiscale data. Theor Appl Fract Mech, 2007, 47: 1–14
Editorial Board. Practical Handbook of Engineering Materials (Vol. 3) (In Chinese). Beijing: Chinese Standard Press, 1988. 92–144
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Tang, X. Scatter of fatigue data owing to material microscopic effects. Sci. China Phys. Mech. Astron. 57, 90–97 (2014). https://doi.org/10.1007/s11433-013-5333-9
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DOI: https://doi.org/10.1007/s11433-013-5333-9