• Korea-Australia Rheology Journal
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• v.15 no.3
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• pp.131-150
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• 2003

A new numerical algorithm of finite element methods is presented to solve high Deborah number flow problems with geometric singularities. The steady inertialess planar 4 : 1 contraction flow is chosen for its test. As a viscoelastic constitutive equation, we have applied the globally stable (dissipative and Hadamard stable) Leonov model that can also properly accommodate important nonlinear viscoelastic phenomena. The streamline upwinding method with discrete elastic-viscous stress splitting is incorporated. New interpolation functions classified as rational interpolation, an alternative formalism to enhance numerical convergence at high Deborah number, are implemented not for the whole set of finite elements but for a few elements attached to the entrance comer, where stress singularity seems to exist. The rational interpolation scheme contains one arbitrary parameter b that controls the singular behavior of the rational functions, and its value is specified to yield the best stabilization effect. The new interpolation method raises the limit of Deborah number by 2∼5 times. Therefore on average, we can obtain convergent solution up to the Deborah number of 200 for which the comer vortex size reaches 1.6 times of the half width of the upstream reservoir. Examining spatial violation of the positive definiteness of the elastic strain tensor, we conjecture that the stabilization effect results from the peculiar behavior of rational functions identified as steep gradient on one domain boundary and linear slope on the other. Whereas the rational interpolation of both elastic strain and velocity distorts solutions significantly, it is shown that the variation of solutions incurred by rational interpolation only of the elastic strain is almost negligible. It is also verified that the rational interpolation deteriorates speed of convergence with respect to mesh refinement.

• KSCE Journal of Civil and Environmental Engineering Research
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• v.6 no.3
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• pp.53-62
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• 1986

For the research on the fatigue fracture behavior in the welded joints of steel structures, base metal specimens and welded ones were selected, and the direct fatigue tests were carried out. Thereafter, fatigue-life (S-N) curves, plastic strain-number of cycles (${\varepsilon}_p$-N) curve, the extrapolated fatigue-life (${\varepsilon}_p$-$N_c$) curve, and da/dN-${\Delta}K$ curves were plotted. By these results the followings were obtained. It was shown that the ratio of fatigue strength at $2{\times}10^6$ cycles of the welded specimen to that of the base metal one was 0.6, and that 0.72 for the base metal and 0.65 for the welded one were the ratio of fatigue strength at $2{\times}10^6$ cycles to yielding stress. The S-N curve for the welded specimen was separated into two sections, the low gradient section and the steep section. As this result, it was shown that the more stress became to reduce, the more the reduction of fatigue strength became to be great. It was shown that fatigue strength at $2{\times}10^6$ cycles from this case was about 83 % of that from the S-N curve plotted with one section. It was thought that the reason was that weld flaw acted greatly on the fatigue strength within the low stress range. It was shown that at the instart of crack initiation plastic strain increased abrupt1y in the case of the welded specimen more than the case of the base metal specimen, and increased abruptly in the upper stress range in both cases. It was shown that the experimental constant ${\alpha}$, 0.42, in the base metal nearly accorded with Manson-Coffin's result, but this made a great difference with the case in the welded specimen. It was thought that it was due to the abrupt change of plastic strain and the influence of weld flaw.