Fastener Hole Quality. Volume 1

Noronha, P. J.; Henslee, S.P.; Gordon, D. E.; Wolanski, Z. R.; Lee, B. G.

doi:10.21236/ada077859

Cited by 3 publications

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“…1. Experimental crack propagation curves from fastener hole specimens [ 1,7]. relationship derived for the constant amplitude loading, where the time is expressed in number of cycles.…”

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confidence: 99%

Markov Approximation to Fatigue Crack Size Distribution

Solomos¹,

Lucia²

1990

Fatigue Fract Eng Mat Struct

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The distribution of the crack size during the fatigue crack propagation phenomenon is investigated. A Markovian modeling of the crack is introduced through the fatigue crack growth law, and the associated Fokker-Planck equation is written while special care is devoted to specifying its boundary conditions. This equation is solved by the method of separation of variables and the sought distribution function is obtained in the form of a convergent infinite series. An illustrative example, demonstrating the applicability of the approach, shows satisfactory agreement between theoretical results and experimental data. NOMENCLATURE A = crack size b = crack growth law parameter a,, a, = initial, limit crack size Cov = covariance D ( . ) = p.d.f. correction factor E [ .] = mathematical expectation f ( . ) = crack transition time p.d.f. G(a) = probability current K, = integration constants Q ( . ) =crack growth rate law D, = random variable defining pulse amplitude Q* = crack growth law parameter R,, = autocorrelation of Y ( t ) S,, = spectral density function of Y ( t ) T(t) = functions of time qA(. 1 .) = transition probability density function of A t = time v = dummy integration variable w ( .) = unit height rectangular pulse X ( t ) = random process, pulse train model Y ( t ) = random process, the fluctuation part of X ( t ) Z ( z ) = functions of z z = transformed space variable for a ( t ) B = dispersion parameter of X ( t ) y = parameter related to Q( .) A = duration of pulse w( .) 6 = Dirac delta function, small increment 1 = eigenvalues p = mean of process X ( t ) pv = parameter of distribution of z v = arrival rate of the rectangular pulses w ( .) uv = parameter of distribution of z 5 = time lag w = circular frequency [ ( t ) = white noise process 457 458

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“…1. Experimental crack propagation curves from fastener hole specimens [ 1,7]. relationship derived for the constant amplitude loading, where the time is expressed in number of cycles.…”

mentioning

confidence: 99%