start-ver=1.4 cd-journal=joma no-vol=43 cd-vols= no-issue= article-no= start-page=1 end-page=7 dt-received= dt-revised= dt-accepted= dt-pub-year=2009 dt-pub=200901 dt-online= en-article= kn-article= en-subject= kn-subject= en-title= kn-title=Crystal rotation behavior with fatigue crack propagation in copper films en-subtitle= kn-subtitle= en-abstract= kn-abstract=Using a fatigue testing method by which fatigue cracks can be initiated and propagated in a film adhered to cover an elliptical through-hole in a base plate subjected to push-pull cyclic loads, annealed copper films with the thickness of 100μm and those reduced the thickness from the 100μm to 50μm by an electro-polishing were fatigued under a constant stress amplitude with a stress ratio of zero. The crystal rotation behavior with the fatigue crack propagation was investigated by measuring the crystal orientation around the fatigue crack initiated from the notch root before and after fatigue testing, using EBSD (Electron Back-scatter Diffraction) method. Then, the change of crystal orientation with fatigue testing was evaluated quantitatively from the misorientation between the crystal orientation matrix on the same point obtained before and after fatigue testing. As a result, the angle of the crystal rotation obtained from the region showing the high fatigue crack propagation rate was larger than that obtained from the region showing the low fatigue crack propagation rate for the film with the thickness of 100μm, while the fatigue crack propagated faster in the film with the thickness of 50μm than that with the thickness of 100μm regardless of the small crystal rotation angles with the fatigue testing for the film with the thickness of 50μm. en-copyright= kn-copyright= en-aut-name=ShimizuKenichi en-aut-sei=Shimizu en-aut-mei=Kenichi kn-aut-name= kn-aut-sei= kn-aut-mei= aut-affil-num=1 ORCID= en-aut-name=ToriiTashiyuki en-aut-sei=Torii en-aut-mei=Tashiyuki kn-aut-name= kn-aut-sei= kn-aut-mei= aut-affil-num=2 ORCID= en-aut-name=IshidaKoki en-aut-sei=Ishida en-aut-mei=Koki kn-aut-name= kn-aut-sei= kn-aut-mei= aut-affil-num=3 ORCID= affil-num=1 en-affil= kn-affil=Division of Industrial Innovation Sciences The Graduate School of Natural Science and Technology, Okayama University affil-num=2 en-affil= kn-affil=Division of Industrial Innovation Sciences The Graduate School of Natural Science and Technology, Okayama University affil-num=3 en-affil= kn-affil=Uchiyama Manufacturing Corp. END start-ver=1.4 cd-journal=joma no-vol=40 cd-vols= no-issue=1 article-no= start-page=1 end-page=8 dt-received= dt-revised= dt-accepted= dt-pub-year=2006 dt-pub=200601 dt-online= en-article= kn-article= en-subject= kn-subject= en-title= kn-title=Fatigue Crack Propagation Behavior Bent from Precrack under Mixed-Mode Conditions - Noting the Crack-Surface Contact due to a Compressive Residual Stress along a Precrack - en-subtitle= kn-subtitle= en-abstract= kn-abstract=A testing for bent fatigue crack propagation under mixed-mode conditions was carried out using fatigue and annealed slant precracks with different slant angles, β ,defined as the angle between loading and precrack directions in a rectangular plate. As a result, bent fatigue crack from the fatigue precrack with β =45deg. propagated under mixed-mode conditions with mode II stress intensity factor (K(II))(est) evaluated from the discontinuous displacement measured along the crack. On the other hand, bent fatigue crack from the fatigue precrack with β =60deg. and from the annealed precracks with both slant angles of β =60deg. and β =45deg. propagated under the mode I behavior. This was because the compressive residual stress near the fatigue precrack caused contact to each other between the upper and the lower surfaces of the precrack with the smaller slant angle β . Furthermore, the fatigue crack propagation rates indicated almost the same relationship for all the data, using the mixed-mode effective stress intensity factor (K(M))(est), calculated from the discontinuous displacement measured along the bent fatigue crack. en-copyright= kn-copyright= en-aut-name=MaYouLi en-aut-sei=Ma en-aut-mei=YouLi kn-aut-name=馬有理 kn-aut-sei=馬 kn-aut-mei=有理 aut-affil-num=1 ORCID= en-aut-name=ShimizuKenichi en-aut-sei=Shimizu en-aut-mei=Kenichi kn-aut-name=清水憲一 kn-aut-sei=清水 kn-aut-mei=憲一 aut-affil-num=2 ORCID= en-aut-name=ToriiTashiyuki en-aut-sei=Torii en-aut-mei=Tashiyuki kn-aut-name=鳥居太始之 kn-aut-sei=鳥居 kn-aut-mei=太始之 aut-affil-num=3 ORCID= affil-num=1 en-affil= kn-affil=The Graduate School of Natural Science and Technology, Okayama University affil-num=2 en-affil= kn-affil=Division of Industrial Innovation Sciences The Graduate School of Natural Science and Technology, Okayama University affil-num=3 en-affil= kn-affil=Division of Industrial Innovation Sciences The Graduate School of Natural Science and Technology, Okayama University END start-ver=1.4 cd-journal=joma no-vol=42 cd-vols= no-issue=1 article-no= start-page=104 end-page=109 dt-received= dt-revised= dt-accepted= dt-pub-year=2008 dt-pub=200801 dt-online= en-article= kn-article= en-subject= kn-subject= en-title= kn-title=Fatigue Crack Propagation Evaluated by Electric Resistance and Ultrasonics in Copper Film Bonded to Base Metal with Resin en-subtitle= kn-subtitle= en-abstract= kn-abstract=As model specimens of surface film-bonded materials, pure copper films with a thickness of 100μm were bonded to the surface of steel base with epoxy resin, where the tensile residual stress was measured by an X-ray on the surface copper film. The distribution of initial electric resistance was measured on both copper film and base specimen by a direct current potential drop technique. As a result, there was a good agreement between the measured and theoretical values. From the fatigue testing results, it was shown that the measured electric resistance increased with the fatigue crack length on the copper film, which was almost equal to the theoretical value calculated for a central slit in a plate with finite width. This was probably because the fatigue crack was opened due to the tensile residual stress on the film even under unloading condition. In addition, the internal crack length during fatigue was examined by ultrasonic testing for the film-bonded specimen. As a result, there was a difference in the fatigue crack length between the surface copper film and the inner base. en-copyright= kn-copyright= en-aut-name=DonghuiMA en-aut-sei=Donghui en-aut-mei=MA kn-aut-name= kn-aut-sei= kn-aut-mei= aut-affil-num=1 ORCID= en-aut-name=ToriiTashiyuki en-aut-sei=Torii en-aut-mei=Tashiyuki kn-aut-name= kn-aut-sei= kn-aut-mei= aut-affil-num=2 ORCID= en-aut-name=ShimizuKenichi en-aut-sei=Shimizu en-aut-mei=Kenichi kn-aut-name= kn-aut-sei= kn-aut-mei= aut-affil-num=3 ORCID= en-aut-name=MatsubaAkira en-aut-sei=Matsuba en-aut-mei=Akira kn-aut-name= kn-aut-sei= kn-aut-mei= aut-affil-num=4 ORCID= affil-num=1 en-affil= kn-affil=Graduate student, Graduate School of Natural Science and Technology, Okayama University affil-num=2 en-affil= kn-affil=Graduate School of Natural Science and Technology, Okayama University affil-num=3 en-affil= kn-affil=Graduate School of Natural Science and Technology, Okayama University affil-num=4 en-affil= kn-affil=Hiroshima Prefectural Technology Research Institute END start-ver=1.4 cd-journal=joma no-vol=50 cd-vols= no-issue=1 article-no= start-page=85 end-page=99 dt-received= dt-revised= dt-accepted= dt-pub-year=2008 dt-pub=200801 dt-online= en-article= kn-article= en-subject= kn-subject= en-title= kn-title=Imaginary Quadratic Fields whose Exponents are Less Than or Equal To Two en-subtitle= kn-subtitle= en-abstract= kn-abstract=

We give a necessary condition for an imaginary quadratic field to have exponent less than or equal to two. Further we discuss relations of this condition with other necessary conditions studied by Möller and Mollin, and conjecture that these conditions are equivalent.

en-copyright= kn-copyright= en-aut-name=ShimizuKenichi en-aut-sei=Shimizu en-aut-mei=Kenichi kn-aut-name= kn-aut-sei= kn-aut-mei= aut-affil-num=1 ORCID= affil-num=1 en-affil= kn-affil=Senior High School en-keyword=imaginary quadratic field kn-keyword=imaginary quadratic field en-keyword=class number kn-keyword=class number en-keyword=exponent kn-keyword=exponent en-keyword=split prime kn-keyword=split prime END