Reaction Rate Model for the Fatigue Strength of Wood
Keywords:
Absolute reaction rate, bending strength, creep rupture, Douglas-fir, duration of load, fatigue, frequency, sinusoidal load, strength, temperature, woodAbstract
In this paper, we consider the fatigue strength of wood structural members. That is, we develop a mathematical model for time-dependent strength under sinusoidal load. This work extends the model for time-dependent strength under constant load and ramp load derived previously by two of the authors. It is based on the statistical theory of the absolute reaction rate in a version favorably reviewed in the literature. Under the isothermal condition, the model predicts that the time at fracture is independent of stress frequency. The need to evaluate experimentally some of the model parameters that may depend on stress frequency indirectly through temperature changes is discussed.References
Bonfield, P. W., and M. P. Ansell. 1991. Fatigue properties of wood in tension, compression and shear. J. Mater. Sci. 26(17):4765-4773.nBurton, R. 1968. Vibration and impact. Dover Publications, Inc., New York, NY. Pp. 292-293.nCaulfield, D. F. 1985. A chemical kinetics approach to the duration-of-load problem in wood. Wood Fiber Sci. 17(4):504-521.nClouser, W. S. 1959. Creep of small wood beams under constant bending load. Report No. 2150, USDA, Forest Service, Forest Products Laboratory, Madison, WI.nColeman, B. D. 1956. Application of the theory of absolute reaction rates to the creep failure of polymeric filaments. J. Polymer Sci. 20:447-455.nColeman, B. D., and A. G. Knox. 1957. The interpretation of creep failure in textile fibers as a rate process. Textile Res. J. 5:393-399.nGerhards, C. C. 1977. Effect of duration and rate of loading on strength of wood and wood-based materials. Research Paper FPL 283, USDA, Forest Service, Forest Products Laboratory, Madison, WI.nGraham, P. H., C. N. Robinson, and C. B. Henderson. 1969. Analysis of dilatational failure of heterogeneous materials by reaction rate theory. Intl. J. Fracture Mech. 5(1):57-62.nHansen, A. C., and J. Baker-jarvis. 1990. A rate-dependent kinetic theory of fracture for polymers. Intl. J. Fracture 44(3):221-231.nHenderson, C. B., P. H. Graham, and C. N. Robinson. 1970. A comparison of reaction rate models for the fracture of solids. Intl. J. Fracture Mech. 6(1):33-40.nHsiao, C. C. 1966. Fracture. Physics Today. Pp. 49-53.nHsiao, C. C., and C. S. Ting. 1966. On deformation and strength. Proceedings, 1st International Conference on Fracture, Japan Society for Strength and Fracture 1:449-457.nHsiao, C. C., S. R. Moghe, and H. H. Kausch Von Schmeling. 1968. Time-dependent mechanical strength of oriented media. J. Appl. Phys. 39(8):3857-3861.nKozin, E., and J. L. Bogdanoff. 1990. Cumulative damage model for mean fatigue crack growth based on the kinetic theory of thermally activated fracture. Eng. Fracture Mech. 37(5):995-1010.nLiska, J. A. 1950. Effect of rapid loading on the compressive and flexural strength of wood. Report No. 1767, USDA, Forest Service, Forest Products Laboratory, Madison, WI.nLiu, J. Y., and E. L. Schaffer. 1991. Time-dependent mechanical strength of wood structural members. Proceedings, International Timber Engineering Conference, London. TRADA 4:164-171.nMoghe, S. R. 1971. International Conference on Mechanical Behavior of Materials. Society of Material Science, Japan 3:541.nMoghe, S. R., and L. Skolnik. 1986. Fatigue failure of fiber assemblies. J. Macromol. Sci. Phys. B25(4):487-504.nPai, G. A., S. K. Batra, and S. P. Hersh. 1991. Interpreting creep and fatigue failure of fibers via deformation kinetics. J. Appl. Polymer Sci.: Appl. Polymer Symp. 47:127-141.nRainville, E. D. 1960. Special functions. The MacMil-lan Co., New York, NY. Pp. 109, 114.nRegel, V. R., and A. M. Leksovsky. 1967. A study of fatigue within the framework of the kinetic concept of fracture. Intl. J. Fracture Mech. 5:99-109.nSchaffer, E. L. 1973. Effect of pyrolytic temperatures on the longitudinal strength of dry Douglas-fir. J. Testing Eval. JTEVA 1(4):319-329.nSchaffer, E. L. 1982. Influence of heat on the longitudinal creep of dry Douglas-fir. Pages 20-52 in R. W. Meyer and R. M. Kellogg, eds. Structural uses of wood in adverse environments. Society of Wood Science and Technology, Van Nostrand Reinhold Co., New York, NY.nTobolsky, A., and H. Eyring. 1943. Mechanical properties of polymeric materials. J. Chem. Phys. 11:125-134.nTsai, K. T., and M. P. Ansell. 1990. The fatigue properties of wood in flexure. J. Mater. Sci. 25:865-878.nWood, L. W. 1951. Relation of strength of wood to duration of load. Report No. R-1916, USDA, Forest Service, Forest Products Laboratory, Madison, WI.nYoungs, R. L., and H. C. Hilbrand. 1963. Time-related flexural behavior of small beams under prolonged loading. Forest Prod. J. 13(6):227-232.nZhurkov, S. N. 1965. Kinetic concept of the strength of solids. Intl. J. Fracture Mech. 1:311-323.n
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