A Frequency Response Method for Calculating Stress Intensity Factors Due to Thermal Striping Loads

Abstract

When incompletely mixed hot and cold fluid streams pass adjacent to the surface of a component or a structure, they can cause thermal fatigue damage. An analytical model, based on linear elastic fracture mechanics and the frequency response method, is presented for the assessment of thermal fatigue damage. Various shapes of surface temperature-time histories, represented by their power spectral densities, are examined. The model is compared with an alternative method based on the impulse response method and good agreement is found. This kind of thermal fatigue is of particular concern in various types of nuclear reactors and rapid shut-downs of hot plant. The model proposed is intended as an engineering design tool and has been developed as a computer code known as "TBL". NOMENCLATUREF,-F., = Buchalet and Bamford "Influence Functions" F,(fi), F2(P) = dimensionless functions in small crack analysis fo = upper frequency in the power spectral density (PSD) G(w, a), J(w, a) = transfer function components h = plate thickness H(w, a) = stress intensity response function 11, I, =weighted integrals of P and Q respectively over the crack M ( x ) = weight function Kni,, K,,,, K,, = the minimum, maximum and rms values of the stress intensity factor (SIF) m,, rn2 = polynomials in the Bueckner weight function P, Q, R, S = real and imaginary partitions of A(o, x ) p = dimensionless through thickness coordinate S,(o, a) = PSD of the stress intensity factor &(w) = power spectral density of surface temperature signal T, , , , T, , = the maximum and rms values of the surface temperature T(x, t), T, = the temperature function and its time averaged mean t = time x = through-thickness coordinate a = coefficient of linear expansion A = range K = thermal diffusivity I, = reciprocal of attenuation length v = Poisson's ratio u(x, t ) = stress function a, coo = angular frequency and upper bound respectively in the PSD ao, p, SZ = dimensionless factors in small crack analysis

Asymptotic and numerical study of a surface breaking crack subject to a transient thermal loading

“…This geometry may be used in modelling short surface-breaking cracks which frequently arise in thermal striping [11]) The SIF is plotted as a function of crack depth for three striping frequencies, 0.0625Hz, 1Hz and 6.25Hz. These frequencies are typical of the range encountered in an experimental thirty-minute real time sample taken from an experimental rig [1]. This is a 0.2-scale air model of the Prototype Fast Reactor above core region which used to operate at Dounreay.…”

“…In practice, it is useful to look at the dimensioned SIF as function of crack depth at various striping frequencies. Such calculations have been carried out using the weight function method in [1][2][3][4][5][6]. One area in which thermal striping is a potential problem is in the region above the core in Fast Reactors.…”

“…Apart from the finite element method, other approaches, developed to assess the thermal fatigue damage caused by such temperature fluctuations, have been based on the frequency response method [1][2][3][4] and the impulse response method [4][5][6]. The analysis of realistic, temporally random striping is possible using these methods.…”

“…Structures exposed to such temperature fluctuations can suffer thermal fatigue damage. This problem has been discussed in [1][2][3][4][5][6][7][8][9][10][11][12]. For an engineering component containing a defect and situated in such a flow, the stress intensity factor (SIF), associated with the defect, will fluctuate in response to the imposed component surface temperature fluctuations.…”

Trapping of a crack advancing through an elastic lattice

“…The temperature fluctuation on the exterior boundary may occur as a result of the incomplete mixing of fluids at different temperatures. A structure in the presence of such a temperature distribution can undergo thermal fatigue damage (Jones & Lewis, 1994, 1996Movchan & Jones, 2006). Thermal striping has been observed in the above-core region of fast breeder reactors that are cooled by liquid sodium, where large temperature differences exist between the sodium emerging from the core and sub-breeder assemblies.…”