Abstract
The formalism of the earlier fatigue crack growth models is retained to account for multiscaling of the fatigue process that involves the creation of macrocracks from the accumulation of micro damage. The effects of at least two scales, say micro to macro, must be accounted for. The same data can thus be reinterpreted by the invariancy of the transitional stress intensity factors such that the microcracking and macrocracking data would lie on a straight line. The threshold associated with the sigmoid curve disappears. Scale segmentation is shown to be a necessity for addressing multiscale energy dissipative processes such as fatigue and creep. Path independency and energy release rate are monoscale criteria that can lead to unphysical results, violating the first principles. Application of monoscale failure or fracture criteria to nanomaterials is taking toll at the expense of manufacturing super strength and light materials and structural components. This brief view is offered in the spirit of much needed additional research for the reinforcement of materials by creating nanoscale interfaces with sustainable time in service. The step by step consideraton at the different scales may offer a better understanding of the test data and their limitations with reference to space and time.
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References
Adkins D E. A conversation about e-research and the supporting cyberinfrastructure. In: Forum to Consider the Implications for Research Libraries and Research Institutions, Washington, D.C., October 15, 2004
Chong K P. Research and challenges in nanomechanics, nanotechnology. In: Webcast, American Society of Mechanical Engineering, www.asme.org/nanowebcast, 2002
Roukes M. Plently of room, indeed. J Scientific Am, 2005, 13(1): 92–100
Sih G C. A blend of multiscaling and mesomechanics in higher engineering education. In: Proceedings of Symposium on Multi-/Inter-Disciplinary Engineering Education. Shanghai: East China University of Science and Technology Press, 2006. 45–59
Sih G C. Segmented multiscale approach by microscoping and telescoping in material science. In: Sih G C, ed. Multiscaling in Molecular and Continuum Mechanics: Interaction of Time and Size from Macro to Nano. Berlin: Springer, 2006. 259–89
USAF Damage Tolerance Design Handbook (section 5.3), Critique of J. C. Newman, Jr.“FAST-RAN II”-A fatigue crack growth structural analysis program, NASA Technical Memorandum, 1992. 104159
Jones R, Pitt S. On the frost dugdale law and the two parameter driving force for fatigue crack growth analysis. In: The 6th International Conference on Fatigue Damage of Structural Materials, Four Points Sheraton, Hyannis, Massachusetts, September 17–22, 2006
Newman J C, Wu X R, Venneri S L, et al. Small crack effects in high strength aluminum alloys. NASA Reference Publications, 1994. 1309
Private communication with Behrens Jr. B on Geometry and size effects for energetic materials for solid rocket propellants. Combustion Research Facility: Sandia National Laboratory, Livermore, California, November, 2002
Behrens Jr. B, Bulusu S. Thermal decomposition of energetic materials. 3. Temporal behaviors of rates of formation of the gaseous pyrolysis products from condensed-phase decomposition of 1,3,5-Trinitrohexahydro-S-Triazine. J Phys Chem, 1992, 96(22): 8877–8891
Sih G C, Tu S T. Why, where and when it becomes necessary to consider chemical reaction effect in mechanics. In: Sih G C, Tu S T, Wang Z D, eds. Fracture Mechanics and Applications: Structural Integrity and Materials Aging. Shanghai: East China University of Science and Technology Press, 2003. 1–19
Sih G C. Signal recognition of fatigue crack growth in bridgestructures connected to specimen behaviour. J Bridge Struct, 2006, 2(2): 133–145
Sih G C. Thermomechanics of solids: nonequilibrium and irreversibility. J Theor Appl Fracture Mech, 1988, 9(3): 175–98
Sih G C. Some basic problems in nonequilibriumthermomechanics. In: Sienietyez S, Salamon P, eds. Flow, Diffusion and Rate Processes. New York: Taylor and Francis, 1992. 218–247
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. J Theor Appl Fracture Mech, 2005, 43(1): 5–62
Sih G C, Tang X S. Singularity representation of multiscale damage due to inhomogeneity with mesomechanics consideration. In: Sih G C, Kermanidis Th B, PantelakisSp G, eds. Multiscaling in Applied Science and Emerging Technology. Patras, Greece: University of Patras Press, 2004. 1–15
Sih G C, Tang X S. Simultaneous occurrence of double micro/macro stress singularities for multiscale crack model. J Theor Appl Fracture Mech, 2006, 46(2): 1–14
Private communication with Bruemmer S M on Chemistry and microscopy of intergranular stress corrosion cracking in LWRs. Washington USA: Pacific Northwest National Laboratories (PNNL), June, 2005
Andresen P L, Yang L M. Characterization of the roles of electrochemistry, convection and crack chemistry in stress corrosion cracking. In: Proceedings of the Seventh International Symposium on Environmental Degradation of Materials in Nuclear Power Systems — Water Reactors. Houston: NACE International, 1995, 1: 579–96
Paris P C. The Growth of Cracks Due to Variations in Load. Dissertation for the Doctoral Degree. Bethlehem, Pennsylvania: Department of Mechanics, Lehigh University, 1962
Private communication with Molent L and Barter S on small crack size related to fatigue of combat structural integrity: Defence Science and Technology Organisation, Australia, August, 2006
Broek D, Schijve J. The influence of the mean stress on the propagation of fatigue cracks in aluminum alloy sheets. National Aeronautics and Astronautics Research Institute NLR-TN M.21111, Amsterdam, 1963. 1–57
Sih G C. Mechanics of Fracture Initiation and Propagation. The Netherlands: Kluwer Academic Publishers, 1991
Mast P W, Nash G E, Michopoulos J, et al. Characterization of strain induced damage in composites based on the dissipated energy density: Part I-Basic scheme and formulation; Part II-Composite specimens and naval structures; and Part III-General material constitutive relation. J Theor Appl Fracture Mech, 1995, 22(2): 71–125
Sih G C. Mechanics and physics of energy density and rate of change of volume with surface. J Theor Appl Fracture Mech, 1985, 4(3): 157–173
Sih G C. The role of surface and volume energy in the mechanisms of fracture. In: Balakrishnan V, Bottani E E, eds. Mechanical Properties of Solids: Plastic Instabilities. Singapore: World Scientific, 1985. 396–461
Sih G C, Lee Y D. Review of triaxial crack border stress and energy behaviour. J Theor Appl Fracture Mech, 1989, 12(1): 1–17
Patel A M. Growth of Small Fatigue Cracks in PH 13–8 Mo Stainless Steel. Georgia Institute of Tech. Res. Report, Neu RW (Adv.), www.me.gatech.edu/astm/research/akshay.html, 2005
Private communication with Farahmand B on virtual fatigue crack growth testing of Ti-6Al-4V, 4130 steel, 6061-T6, 7075-T73 and 2014-T6aluminum. Huntington Beach, USA: Boeing Integrated Defense System, Augusr, 2006
Sih G C. Introduction to a series on mechanics of fracture. In: Sih G C, ed. Methods of Analysis and Solutions of Crack Problems. Leyden, Netherlands: Nordhoff International Publishing, 1973. IX–XII
Cottrell A H. The Mechanical Properties of Matter. New York: Johm Wiley & Sons, 1964
Sih G C, Liu B. Mesofracture mechanics: A necessary link. J Theor Appl Fracture Mech, 2002, 37: 335–369
Sih G C. Signatures of rapid movement of electrons in valence band region: interdependence of position, time and temperature. J Theor Appl Fracture Mech, 2006, 45(1): 1–12
Sih G C. Irreconcilability of uni-axial test data for irreversibility of loading and unloading. J Theor Appl Fracture Mech, 2012, 62: 54–61
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Sih, G.C. From monoscale to multiscale modeling of fatigue crack growth: Stress and energy density factor. Sci. China Phys. Mech. Astron. 57, 39–50 (2014). https://doi.org/10.1007/s11433-013-5366-0
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DOI: https://doi.org/10.1007/s11433-013-5366-0