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溶接学会論文集 Vol. 13 (1995), No. 3

ISIJ International
belloff
オンライン版ISSN:
冊子版ISSN: 0288-4771
発行機関: JAPAN WELDING SOCIETY

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キーワードランキング

21 Nov. (Last 30 Days)

溶接学会論文集 Vol. 13 (1995), No. 3

A Chart Method to Determine Necessary Preheat Temperature in Steel Welding

Nobutaka YURIOKA, Tadashi KASUYA

pp. 347-357

DOI:

10.2207/qjjws.13.347

抄録

Preheating is carried out to avoid cold cracking in steel welding. The occurrence of cold cracking is considered to be governed by accumulating diffusible hydrogen, welding residual stresses and hardness at the crack initiation site. The hydrogen accumulating at the crack site depends on the initial diffusible hydrogen content in weld metal, the weld heat input and the wall thickness. The local residual stress is governed by the weld metal yield strength, the joint restraint and the notch stress concentration factor. The HAZ hardness is influenced by the steel chemical composition, the weld heat input and the plate (wall) thickness.
These influential factors affect cold cracking independenly or in an interacted manner. It must be, thus, difficult to predict the necessary preheat temperature by a theoretical method or simple formulae. The method presently proposed is completely based on the empirical results by y-groove weld cracking tests. The present method determines the necessary preheat temperature through the charts describing the following respective effects : 1) steel composition ; 2) diffusible hydrogen content of weld metal ; 3) weld heat input ; 4) wall thickness ; 5) weld metal yield strength ; 6) joint restraint. As to the steel composition, this method uses CEN carbon equivalent that preferably assesses weldability of a wide variety of steels. Also, this method considers a logarithmic dependence of the weld metal hydrogen and the analysis of hydrogen diffusion in a weld has proved that the hydrogen effect on cold cracking must be logarithmic.

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超高エネルギー密度電子ビームの発生と深溶込み溶接への適用

富江 通雄, 阿部 信行, 加藤 豊, 荒田 吉明

pp. 358-364

DOI:

10.2207/qjjws.13.358

抄録

An urtra-high voltage electron beam heat source with an electron gun employing 11-stage electromagnetic accelerating units was developed. The characteristics of the electron beam were studied and a strongly focused electron beam with an ultra-high average beam power density of 160-170 kW/mm2 using a beam power of 140-180 kW was successfully generated. Applicability of 500 kV ultra-high voltage electron beam to welding was investigated and it was found that this beam enabled a penetration depth of max 240 mm in flat position welding with a beam power of 180 kW and a welding speed of 6.7 mm/s, allowing a narrow weld bead to be produced with high efficiency.

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超高エネルギー密度電子ビームの発生と深溶込み溶接への適用

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薄鋼板における溶接欠陥と溶接品質評価

齊藤 亨, 一山 靖友

pp. 365-370

DOI:

10.2207/qjjws.13.365

抄録

Influence of chemical elements of base material has been investigated on interface quality of flash weld. Bend test of welds was carried out for 43 kinds of sheet steels which included solid solution strengthened, dual phase and precipitation hardened high strength steels up to 590 MPa.
Fractography anlysis indicated that cracks at weld interface were caused by oxide inclusions. Aluminum, silicon and manganese were major elements of the inclusion, and whose influence were determined to be strong as 10:1:0.01 in the order. Carbon was also proved to affect cracking at interface by reducing ductility of weld. Equivalent formula was experimentally established for the influence of those elements on interface cracking.
The ordinary bend test was proved to be used as a simple and reliable method in quantitative evaluation of the interface quality of flash weld, while notch bend test showed higher ability in the evaluation than that.

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アプセット開始前後の溶接現象と欠陥発生との相関性の考察

齊藤 亨, 一山 靖友

pp. 371-377

DOI:

10.2207/qjjws.13.371

抄録

Variation in welding process which would cause instability of weld quality have been examined for flash welding of sheet material using about 3 mm thick steel sheets. Welding current, voltage and displacement of platen travel were recorded and photographs of arc between specimen ends were taken by streak photograph technique for the period from final flash-stage through initial upset-stage.
When observed at any fixed point, maximal time interval between flashing was determined to be over 100 ms. Such long interval was analyzed to cause oxidation and decreased temperature at the point and to result in deteriorated interface quality. Quick platen movement in initial upset-stage, so called "Initial upset displacement", was proved to be under the influence both of flashing during final flash-stage and voltage phase of power source at the moment of upset starting.

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アプセット現象の解析と溶接品質向上へのアプセット位相制御法の提案

齊藤 亨, 一山 靖友

pp. 378-383

DOI:

10.2207/qjjws.13.378

抄録

Initial stage of upset was investigated. The welding machine for experiment was designed so that platen movement for upsetting can be initiated at any desired voltage phase of AC power source. The voltage phase of AC power source at the instant of platen movement for upsetting, named "upsetting point", showed significant influence on weld interface quality. The quality was best at the phase round 90 degree and worst at round 0 (or 180) degree. Good relasionship was observed between the phase and the quality. The influence of upsetting point control on weld interface quality was proved to be greater than that of duration of upset current by conventional current density, i.e. less than 80 A per square millimeter.

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鉄粉添加フラックスを用いた大入熱サブマージアーク溶接の溶融池現象と適正溶接条件

阪口 修一, 山口 忠政, 中野 善文

pp. 384-389

DOI:

10.2207/qjjws.13.384

抄録

The effect of the addition of iron powder to agglomerated flux on welding performance and the optimum welding conditions for high heat input welding were investigated. The main conclusions obtained follow :
(1) The addition of iron powder to flux increases the deposition rate and improves welding operability.
(2) The arc of leading electrode was generated at a lower point of molten metal between leading and trailing electrodes rather than at its top. The penetration depth was influenced by the ratio of the area of groove to that of molten metal on which leading arc is generated.
(3) The cross sectional profile of the bead was influenced by the current ratio of the trailing electrode to that of the leading. The optimum ratio for avoiding weld defects ranged between 0.70 and 0.80.
(4) The flux containing iron powder together with the selection of optimum welding conditions enabled the tandem wire one pass submerged arc welding for 60 mm thick plates.

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鉄粉添加フラックスを用いた大入熱サブマージアーク溶接の溶融池現象と適正溶接条件

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SUS304Lステンレス鋼とチタンとの拡散接合

大橋 修, 頴娃 一夫, 入江 宏定

pp. 390-394

DOI:

10.2207/qjjws.13.390

抄録

The aims of this study are first to investigate the relationship between diffusion welding parameters and joint quality of SUS304L stainless steel to titanium, and secondary to develop a bonding method to get good joints using a heat treatment in a vacuum for surface control. The equipment used consists of an ultra high vacuum welding chamber and an surface analysis chamber with Auger device.
The strength of joints increased using higher welding pressure and finer surface roughness at diffusion welding of SUS304L stainless steel to tianium. The heat treatment of specimens in a vacuum caused dissociation of surface oxides and contaminants. Bond formation at the contact area depended on the disappearance of the surface film.
Therefore, a new bonding process where specimens were heated in a vacuum prior to bonding was developed, unlike the conventional bonding process where the joint region was heated after the bonding surfaces are brought into contact. This bonding method produced the sound joint when specimens were heated at the suitable temperature.

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SUS304Lステンレス鋼とチタンとの拡散接合

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プラズマアーク粉体アロイング法によるAl合金表面へのTiC粒子アロイング層形成条件の検討

松田 福久, 中田 一博, 徐 昌済, 橋本 武典

pp. 395-403

DOI:

10.2207/qjjws.13.395

抄録

The effect of alloying conditions on the formation of alloyed layer on A5083 aluminum alloy surface has been investigated by using plasma transferred arc (PTA) process with TiC as powder alloyed material.
As process parameters, electrode polarity, kind of shielding gas, plasma arc current, powder feeding rate and travel speed were discussed.
The alloying conditions were 100-250 A in plasma arc current, 100-1000 mm/min in travel speed, 5-15 g/min in powder feeding rate with different combination of polarity and shielding gas, namely DCEN-Ar, AC-Ar and DCEN-He.
Alloyed layer with smooth surface can be easily obtained by PTA process with DCEN-He and AC -Ar, but was difficult with DCEN-Ar because molten pool surface was covered with thick oxide film which prevented smooth injection of TiC powder into molten pool.
Higher arc current and lower travel speed made easy to form the alloyed layer.
Injection efficiency (ratio of the gained TiC amount in alloyed layer to TiC amount fed) increased with the increase of a surface area of molten pool and reached almost 100% in DCEN-He.
Volume fraction of TiC in alloyed layer increased with the increase of plasma arc current and powder feeding rate, but was likely to saturate to a limited value.
It was made clear that DCEN-He was the most superior process to show the wider optimum range of alloying conditions even at high travel speed of 500 mm/min and large injection efficiency and volume fraction of TiC than AC-Ar and DCEN-Ar.
This beneficial effect of DCEN-He in PTA process was consider to high temperature of molten pool surface about 1000°C in DCEN-He, which was much higher in AC-Ar of about 700°C, because this high temperature of molten pool enabled the smooth injection of TiC particle into molten Al pool due to good wettability between TiC particle and molten Al.

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Ni3(Si,Ti)金属間化合物のNi基ろうによるろう付

渡辺 健彦, 大原 圭司, 柳沢 敦, 小沼 静代

pp. 404-410

DOI:

10.2207/qjjws.13.404

抄録

The Ni3, (Si, Ti, Hf) intermetallic compound full of the promise as a heat-resistant and anti-sulfuric acid material was preliminarily brazed using commercial Ni-based filler metals, and some properties of the joints were examined. According to the preliminary examination, a new Ni-based filler metal was developed to improve the characteristics of the joint. The results obtained in this study are as follows:
The commercial filler metals which contain some contents of boron or phosphorous to decrease the melting point can not provide us sound brazed joints due to the formation of brittle phases in the bonded interlayer.
A Ni based filler metal added some contents of copper as an element to decrease the melting point instead of boron or phosphorous was successfully developed, and it enables us to make sound brazed joints of which the tensile shear strength is approximately equal to that of the base metal.
And the joints brazed with this filler metal also exhibit excellent corrosion resistance to sulfuric acid solution.

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Ni3(Si,Ti)金属間化合物のNi基ろうによるろう付

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ベリリウム銅とステンレス鋼の拡散接合

益本 広久, 西尾 一政, 浅田 明弘, 加藤 光昭, 迎 静雄

pp. 411-417

DOI:

10.2207/qjjws.13.411

抄録

Diffusion bondings of commercial copper-beryllium alloys of Cu-0.5 mass%Be and Cu-2 mass%Be alloys to an austenitic stainless steel SUS304 were carried out in a vacuum. Ni foil and Cu foil were used as an insert metal. Influences of the bonding conditions of bonding temperature, bonding time and the insert metal on the bondability have been investigated. And also an effect of artificial agings on the joint strength of the joints has been studied. Main results obtained are as follows;
(1) On the direct bonding of copper-beryllium alloy to stainless steel, bonding was impossible when the ratio of bonding temperature to solidus temperatures of Cu-0.5 mass%Be and Cu-2 mass%Be alloys Tg/TSLwas less than 0.78 and 0.82, respectively. However, the joint strength increased abruptly with rising the ratio.
(2) The joint strength of the joints with Cu foil was higher by about 100 MPa than that of the direct bonds at the bonding condition of 830°C×3.6 ks. The tensile fracture of the joint of Cu-0.5 mass%Be alloy to SUS304 with Ni foil was occurred in the copper alloy base metal. However, the joint strength of the joint of Cu-2 mass%Be alloy to SUS304 with Ni foil was the same value as that of the direct bond because of development of voids in the diffusion layer between the copper alloy and Ni foil.
(3) When the joint of Cu-0.5 mass%Be ally to SUS304 with Cu foil or without the insert metal were aged, the joint strength was higher than that of the as-bonded, but the joint strength of the joint with Ni foil was higher value of 540 MPa. Though the direct bond of Cu-2 mass%Be alloy to SUS304 fractured at the bond interface during solution heat treatment, but the joint strength of the joint with Cu foil was higher value of 520 MPa.

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残留抵抗比による銅より線と黄銅端子圧着接合部の評価

藤巻 裕彦, 鷹合 徹也, 佐野 一仁

pp. 418-423

DOI:

10.2207/qjjws.13.418

抄録

A procedure for estimating the qualities in the crimping interface of the terminal and stranded copper conductor applying residual resistance ratio (RRR) measurements is proposed.
According to the RRR measurements of crimping interface the press oil was not detrimental to the qualities of the interface as ascertained by supplementary EPMA analysis results. Crimping conditions of the crimping interface were more sensitive to the variations of the RRR value than those of working strain conditions during the crimping process of the terminal and stranded wire.
The measurements of the RRR were also more susceptible to the variation of the electric contact qualities of the crimping interface than the measurements of the contact resistance for the specimens measured subsequently to the aging treatment of the crimping interface.
High quality of the welded interface with heat pressure was also confirmed applying the present RRR measurements.

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残留抵抗比による銅より線と黄銅端子圧着接合部の評価

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減圧プラズマ溶射被覆材のクリープ特性に及ぼす予熱の影響

本多 啓三, 千田 格, 斉藤 正弘, 石渡 裕, 深倉 壽一, 小林 紘二郎

pp. 424-431

DOI:

10.2207/qjjws.13.424

抄録

The effect of preheating on rupture properties of substrate coated by low pressure plasma spraying was investigated in this study. Creep-rupture specimens of Ni-base superalloy, Mar-M247 were coated after preheating at several temperature ranges. Especially, a relationship between preheating temperature and microstructures of sprayed substrates was discussed. The results are summarized as follows.
(1) Creep properties of Mar-M247, as a substrate, coated with CoCrA1Y were kept at the level of as cast material when preheated at the range of 1073-1173 K in low pressure plasma spraying.
(2) The substrates of specimen coated after preheated at the range of 1473-1573 K were severely damaged in rupture life, strain and reduction of area. It is considered that liquation induced by high preheating in low pressure plasma spraying should occur and grow on the solidification grain boundaries of substrate. Consequently, creep properties were deteriorated, because of opening the grain boundaries during cooling period.
(3) The mechanism of liquation and opening on the grain boundaries was deduced as the following. At first, selective decomposition of tungsten carbide in complex carbides is brought by heat. Simultaneously, carbon is dissolved around the grain boundaries which is one of elements decreasing melting point. After spraying, cooling shrinkage makes opening of solidification grain boundaries.

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減圧プラズマ溶射被覆材のクリープ特性に及ぼす予熱の影響

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摩擦肉盛法による表面硬化層の形成に関する研究

篠田 剛, 岡本 真弥, 武本 聡, 加藤 喜久, 冷水 孝夫

pp. 432-437

DOI:

10.2207/qjjws.13.432

抄録

Although there have been proposed and applied several surfacing technologies, no appropriate process was appeared to coat 1 mm thickness layer on substrate. This paper deals with the fundamental approach to establish friction surfacing as a technique to coat a hard layer -1 mm thick.
Experiments clarify the effect of operating parameters on surface quality using conventional friction welding machine equipped sliding stage. Material was selected a martensitic stainless steel with 1C-17Cr as a coated material, and a low carbon structural steel as a substrate.
A stable hardened coated layer was obtained with dimensions of 20 mm width and 1 mm thickness. No dilution was observed in this process. Hardness values reached around 500 to 600 Hv in as-coated condition. Dimensions of coated layer are depended on friction speed (rotating speed) of coated material, and lower friction speed can make thicker and wider coatings. Deposition speed is slightly less than those of conventional arc welding processes under the conditions of this experiment.

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摩擦肉盛法による表面硬化層の形成に関する研究

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高強度鋼溶接継手の疲労強度とその支配因子

渡辺 修, 松本 重人, 中野 善文, 斉藤 良行

pp. 438-443

DOI:

10.2207/qjjws.13.438

抄録

The fatigue strength of mild and high strength steel plates and their welded joints is studied with respect to stress concentration factor (Kt) and welding residual stress. The fatigue strength of high strength steel is higher than that of mild steel when Kt is less than 3, though the effect of strength on fatigue strength becomes smaller as Kt increases. The fatigue strength of welded joint of high strength steel, however, is similar to that of mild steel in the case that K2 is 1.68. The tensile residual stress in the welded joints of high strength steels is higher than that of mild steel. The effect of stress concentration factor on fatigue strength and the existence of higher welding residual stress in the higher strength steel welded joint conclude that the welding residual stress has a predominant effect on the fatigue strength of the welded joint of high strength steel.

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腐食ピットを有する摩擦圧接継手の疲労破壊特性

大植 義夫, 中山 英明, 向井 喜彦, 小川 恒一

pp. 444-449

DOI:

10.2207/qjjws.13.444

抄録

Studies on fatigue behavior of friction welded butt joints composed of similar carbon steel in ordinary atmospheric environment have revealed that the fatigue strength of the joint is higher than that of the base metal, but the joint shows the larger scatter of fatigue lives. On the other hand, results of corrosion fatigue tests on the joint carried out in artificial seawater indicated that, (1) the corrosion fatigue strength of the joint was almost the same as that of the base metal in long life region, (2) scatter of the corrosion fatigue lives of the joint bacame smaller with the increase in fatigue life in comparison with the case of base matal specimen, and (3) above mentioned characteristics were governed by corrosion pits preferentially generated near the weld interface.
The main aim of the present study is to clarify the cause of the fatigue strength reduction by corrosion pits. For this purpose the joint and base metal specimens were immersed in artificial seawater at stress free condition to generate corrosion pits, and rotating bending fatigue tests were carried out on the specimens with corrosion pits near weld interface in ordinary atmospheric environment. Reference data were also obtaind by using specimens without corrosion pits. Results of the study clearly indicated that the corrosion pits near the weld interface decreased the fatigue strength of the joint. Fatigue strength reduction due to the corrosion pits was well correlated with the hardness at fracture site. Furthermore, the fatigue strength reduction factor took considerablely high value for the specimen immersed in artificial seawater during long time, which suggests that the other detrimental factor such as grain boundary corrosion gives the effect to decrease the fatigue strength of the joint with corrosion pits. Additionally, effect of corrosion pits on the fatigue strength reduction was discussed by replacing tentatively with the effect of circumferential notch.

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腐食ピットを有する摩擦圧接継手の疲労破壊特性

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圧縮負荷を受けるTiN被覆材の皮膜破壊評価法

深井 利嗣, 小川 真吾, 竹本 幹男

pp. 450-455

DOI:

10.2207/qjjws.13.450

抄録

Evaluation method of film fracture of TiN coatings doposited by CVD and PVD was investigated under compressive load to estimate adhesive strength of the film which is important to apply ceramic coatings to instruments in engineering use. The proposed method consisted of corrosion potential monitoring and acoustic emission (AE) monitoring. The results obtained in this study are summarized as follows:
(1) Corrosion potential shift due to film fracture was recognized at higher substrate strain in CVD coatings having higher adhesive strength than in PVD coatings having lower adhesive strength.
(2) AE signal due to film fracture was also recognized at higher substrate strain in CVD coatings than in PVD coatings.
(3) Critical substrate strain at film fracture initiation estimated by corrosion potential measurement and AE monitoring methods correlated quantitatively with adhesive strength of CVD and PVD coatings.

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圧縮負荷を受けるTiN被覆材の皮膜破壊評価法

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炭素鋼同種摩擦圧接継手の腐食疲労強度特性の接合方式依存性について

大植 義夫, 中山 英明, 向井 喜彦, 小川 恒一

pp. 456-462

DOI:

10.2207/qjjws.13.456

抄録

Though friction welded butt joints have come into wider use machine elements and structural members, valid evaluation method of the joint performance, especially under service load conditions, has not been established yet. The reliability of this type of joint has been supported only by empirical knowledge accumulated up to the present. In order to clarify the fatigue behaviors of the joint, we have carried out a series of fatigue tests on several sorts of friction-welded butt joints in ordinaly atmospheric environment, and have revealed that the fatigue strength of the joint is higher than that of the base metal, but the lives show the large scatter. Evaluation of corrosion fatigue behavior of frictionwelded joints is also an urgent issue, because some of the joints are practically used in corrosive environments.
The main aim of this study is to reveal the relationship between the fiber flow conditions near the weld interface of the joint and their corrosion fatigue resistance. For this purpose, a series of experiments was carried out on four friction-welded butt joint specimens composed of a similar structural carbon steel fabricated by different friction welding conditions. This study covers following four phases : (1) Dependence of fiber flow conditions on friction welding procedure, (2) corrosion responce of the four joints fabricated by different friction welding procedures, (3) fatigue strength behavior of joints with corrosion pits in ordinaly atmospheric environment, and (4) corrosion fatigue resistance of respective joint.
The results of this study revealed that the corrosion fatigue resistance of the joint was well correlated with the fiber flow conditions of the joint; many and deep corrosion pits were generated on the surface area intersecting the fiber flow and the notch effect of the corrosion pits resulted in the reduction of fatigue strength. In other words, joint specimen wishout the surface area intersecting the fiber flow shows excellent corrosion fatigue performance.

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炭素鋼同種摩擦圧接継手の腐食疲労強度特性の接合方式依存性について

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ばり付鋼材摩擦圧接継手の疲れ強さに及ぼす圧接条件の影響

長谷川 正義

pp. 463-469

DOI:

10.2207/qjjws.13.463

抄録

The effect of flash on fatigue strength of friction welded joints are examined by means of rotating bending fatigue test, using as-welded joint specimens of hot and cold drawn mild steel round bar.
The following experimental results were obtained ;
(1) Fatigue strength of hot and cold drawn steel decreased with the increase of upset pressure.
(2) In welded joints with flash, fatigue cracks were initiated at toe of flash.
(3) Effect of upset pressure on fatigue strength was remarkable, but effect of friction pressure and total loss were slightly.
(4) Toe radius of flash decreased with the increase of upset pressure and toe angle increased with the increase of this pressure. Therefore, it was considered that the main cause of the decrease of fatigue strength was stress concentration of toe of flash.
(5) In the case of hot drawn steel, fatigue strength of the joint under any welding condition was recovered up to that of base metal, when flash was removed. In the case of cold drawn steel, however, that was not recovered, even when flash was removed.
(6) Fatigue strength of cold drawn steel joints was remarkably decreased, when fatigue failure occurred in duplicate zone of stress concentration and softening. Therefore, this material required sufficient care, when friction welding condition was selected.

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ばり付鋼材摩擦圧接継手の疲れ強さに及ぼす圧接条件の影響

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単層および多層すみ肉溶接残留応力の測定

上田 幸雄, 麻 寧緒, 王 雅生, 古木 良一

pp. 470-478

DOI:

10.2207/qjjws.13.470

抄録

In this paper, a new method for the measurement of 3-dimensional residual stresses in fillet welds is developed using inherent strain, which is considered a source of residual stresses. As a procedure of the new method, firstly the inherent strains are determined from a few of measured elastic strains with the aid of a proposed inherent strain distribution function, then residual stresses are computed by performing elastic analysis when inherent strains are applied to the weld joints.
In the actual measurement, when three kinds of specimens T, Ly and Lz are cut from a fillet weld, the measuring method is called TLyLz-method ; when only one piece of specimen T is cut from the weld, the measuring method is called T-method.
Respectively using TLyLz-method and T-method, 3-dimenional residual stresses distributed on the transverse sections of a single-pass and a multipass T-type fillet welds are measured. The residual stresses measured by TLyLz-method and T-method show a good coincidence with the ones directly measured on the surfaces of the welded joints.

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単層および多層すみ肉溶接残留応力の測定

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電磁プラズマ加速アークジェットのセラミックコーティングへの応用

田原 弘一, 安井 利明, 加賀谷 洋一, 吉川 孝雄

pp. 479-484

DOI:

10.2207/qjjws.13.479

抄録

A magneto-plasma-dynamic (MPD) arcjet generator, in which plasma generated is accelerated by the electromagnetic interaction between the discharge current and the magnetic field induced by it, is a simple, efficient, and reliable device suitable for material processing. A quasi-steady MPD arcjet was studied to examine fundamental operational characteristics and plasma features. The MPD arcjet was operated for discharge currents of 3-25 kA with working gases of Ar, H2, N2 and NH3. Three different discharge modes of diffuse, spot and gross erosion existed in the MPD arc, and a qualitative explanation of their nature was presented. As a result, the MPD arcjet was found to produce high-velocity, high-temperature, high-density, large-area plasmas. For applications of MPD arcjets to ceramic coatings, an ablation-type MPD arcjet with a cathode covered with ceramic materials was developed. In 100-shot operations for Ar at 5-10 kA, the ablation rates of the ceramic covers ranged from 1.1 to 7.5 mg/shot. The MPD plasma spraying showed that a dense uniform ceramic film with above 1200 Vickers hardness was deposited. From the XPS spectra, the peak area ratio of Si/Al for the coating film almost equaled that for the raw ceramic material, and the valence numbers of Al and Si did not change. Consequently, the MPD arcjet was found to have a high potential for material processing.

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電磁プラズマ加速アークジェットのセラミックコーティングへの応用

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