Capillarity and wetting phenomena : drops, bubbles, pearls, by Pierre-Gilles de Gennes

By Pierre-Gilles de Gennes

The examine of capillarity is in the middle of a veritable explosion. what's provided this is no longer a complete evaluate of the newest examine yet fairly a compendium of ideas designed for the undergraduate scholar and for readers drawn to the physics underlying those phenomena.

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84. The manufacturing processes associated with these ultra-high strength steels are such that high-quality materials and well-controlled construction procedures are employed throughout, so that the likelihood of obtaining unanticipated stresses, which would lead to premature yielding, is relatively small. There is, therefore, a case for reducing the safety factor (based on yield) to improve safety with respect to fast fracture. 94 is so high that the most stringent precautions would need to be taken during manufacture to avoid failure by yield.

A turbine disc in an aero-engine would have a shorter design life in years, but probably more cycles (take-off/landing) per day. 6 mm. Hence, a o which is just greater than the expected low-amplitude cycles are insignificant. = 500 is approximately 14 r~Nm-3/2 for a ly above the threshold, AK th . 7 mm by "on-off" stresses before the "vi brati on" stress produces a stress i ntens i ty which exceeds the threshold value. 18 x 10 4 cycles, so that the contribution from "vibration" stresses is, indeed, small.

Now consider a loading sequence in which blocks 24 of stress levels 0i (i = 1,2,3,4, ... iods xi' During the first block, at stress 01' the crack grows from a o to a l and the period taken, xl' is given by (Io1/Co l P) where 101 is the integral of equation (11) between limits a o and a l . From equation (14), the life, xf(l)' at stress 01 is (IOf/CG1P), so that xl/Xf(l) = Iol/I of ' At stress G2' the crack grows from al to a 2 in a period x2 = (I 12 / Co and x2/x f (2) = I 12 1I 0f ' In general, x/xf(i) = I(i-l),/I of and, writing this as a summation, l) Iol/Iof + I12/Iof + I23/ I of + (l/I of ) (Io1 + 112 + 123 + ...

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