Pub Date : 1989-11-01DOI: 10.1016/0001-6160(89)90333-7
W.W. Mullins
An estimate is made of the geometrical rate constant G3 in the parabolic grain growth law d〈r〉2/dt = kG3 in three dimensions, where 〈r〉 is the average volume-equivalent grain radius and where k = -un/K is a positive constant in which un is the local boundary velocity along an outward pointing normal and K is the local mean curvature (positive for a sphere). The parabolic law follows from the above velocity rule and a hypothesis of statistical self-similarity of the structure. The estimate is based on (l) a theorem deduced from the preceeding assumptions, (2) an approximate formula for the rate of change of the volume of a given grain, (3) a model of polyhedral geometry and (4) the experimental data of Hull on separated β-brass grains. We estimate G3 = 0.5 ± 0.l. Comparison with previous estimates is made.
对三维抛物线型晶粒生长规律d < r > 2/dt = kG3中的几何速率常数G3进行了估计,其中< r >为平均体积等效晶粒半径,k = -un/ k为正常数,其中un为沿向外指向法线的局部边界速度,k为局部平均曲率(对球面为正)。根据上述速度规律和结构的统计自相似假设,可以得到抛物线定律。该估计是基于(1)从上述假设推导出的定理,(2)给定晶粒体积变化率的近似公式,(3)多面体几何模型和(4)赫尔对分离β-黄铜晶粒的实验数据。我们估计G3 = 0.5±0.1 l。与以前的估计数作了比较。
{"title":"Estimation of the geometrical rate constant in idealized three dimensional grain growth","authors":"W.W. Mullins","doi":"10.1016/0001-6160(89)90333-7","DOIUrl":"10.1016/0001-6160(89)90333-7","url":null,"abstract":"<div><p>An estimate is made of the geometrical rate constant <em>G</em><sub>3</sub> in the parabolic grain growth law <em>d</em>〈<em>r</em>〉<sup>2</sup>/<em>dt</em> = <em>k</em><em>G</em><sub>3</sub> in three dimensions, where 〈r〉 is the average volume-equivalent grain radius and where <em>k</em> = -<em>u</em><sub><em>n</em></sub>/<em>K</em> is a positive constant in which <em>u</em><sub><em>n</em></sub> is the local boundary velocity along an outward pointing normal and <em>K</em> is the local mean curvature (positive for a sphere). The parabolic law follows from the above velocity rule and a hypothesis of statistical self-similarity of the structure. The estimate is based on (l) a theorem deduced from the preceeding assumptions, (2) an approximate formula for the rate of change of the volume of a given grain, (3) a model of polyhedral geometry and (4) the experimental data of Hull on separated β-brass grains. We estimate <em>G</em><sub>3</sub> = 0.5 ± 0.l. Comparison with previous estimates is made.</p></div>","PeriodicalId":6969,"journal":{"name":"Acta Metallurgica","volume":"37 11","pages":"Pages 2979-2984"},"PeriodicalIF":0.0,"publicationDate":"1989-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/0001-6160(89)90333-7","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"91095905","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 1989-11-01DOI: 10.1016/0001-6160(89)90336-2
B.D. Flinn, M. Rühle , A.G. Evans
The toughening of Al2O3 by Al has been investigated, using electron microscopy to provide in sit measurements of the microstructural parameters that govern ductile ligament toughening. The results are used to compare the measured toughness with values calculated for ligaments that exhibit limited debonding during ductile rupture. Good agreement confirms that toughening is dominated by the plastic work expended in the ductile rupture of ligaments stretched between the crack surfaces. Furthermore, it is demonstrated that in situ measurements are needed to assign the appropriate flow stress, because of the occurrence of coupled precipitation/solution hardening, and to ascertain the extent of the plastic stretch.
{"title":"Toughening in composites of Al2O3 reinforced with Al","authors":"B.D. Flinn, M. Rühle , A.G. Evans","doi":"10.1016/0001-6160(89)90336-2","DOIUrl":"10.1016/0001-6160(89)90336-2","url":null,"abstract":"<div><p>The toughening of Al<sub>2</sub>O<sub>3</sub> by Al has been investigated, using electron microscopy to provide <em>in sit</em> measurements of the microstructural parameters that govern ductile ligament toughening. The results are used to compare the measured toughness with values calculated for ligaments that exhibit limited debonding during ductile rupture. Good agreement confirms that toughening is dominated by the plastic work expended in the ductile rupture of ligaments stretched between the crack surfaces. Furthermore, it is demonstrated that <em>in situ</em> measurements are needed to assign the appropriate flow stress, because of the occurrence of coupled precipitation/solution hardening, and to ascertain the extent of the plastic stretch.</p></div>","PeriodicalId":6969,"journal":{"name":"Acta Metallurgica","volume":"37 11","pages":"Pages 3001-3006"},"PeriodicalIF":0.0,"publicationDate":"1989-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/0001-6160(89)90336-2","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84530414","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 1989-11-01DOI: 10.1016/0001-6160(89)90332-5
H.C. Cao, B.J. Dalgleish, H.E. Dève, C. Elliott, A.G. Evans, R. Mehrabian, G.R. Odette
A cylindrical test specimen for evaluating the toughening of brittle intermetallics by ductile reinforcements has been evaluated. A processing procedure capable of producing specimens has been devised, using HIPing, and a method for the tensile testing of the specimen has been established. Results are presented for γ-TiAl reinforced with Nb and a Ti-33 at.% Nb alloy. The toughening imparted by these materials is interpreted in terms of their strength, ductility and interface reactions, as well as loss of constraint mediated by the extent of debonding along the reaction product layers. Finally, the results are compared with those previously obtained on actual composites.
{"title":"A test procedure for characterizing the toughening of brittle intermetallics by ductile reinforcements","authors":"H.C. Cao, B.J. Dalgleish, H.E. Dève, C. Elliott, A.G. Evans, R. Mehrabian, G.R. Odette","doi":"10.1016/0001-6160(89)90332-5","DOIUrl":"10.1016/0001-6160(89)90332-5","url":null,"abstract":"<div><p>A cylindrical test specimen for evaluating the toughening of brittle intermetallics by ductile reinforcements has been evaluated. A processing procedure capable of producing specimens has been devised, using HIPing, and a method for the tensile testing of the specimen has been established. Results are presented for γ-TiAl reinforced with Nb and a Ti-33 at.% Nb alloy. The toughening imparted by these materials is interpreted in terms of their strength, ductility and interface reactions, as well as loss of constraint mediated by the extent of debonding along the reaction product layers. Finally, the results are compared with those previously obtained on actual composites.</p></div>","PeriodicalId":6969,"journal":{"name":"Acta Metallurgica","volume":"37 11","pages":"Pages 2969-2977"},"PeriodicalIF":0.0,"publicationDate":"1989-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/0001-6160(89)90332-5","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87602760","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 1989-11-01DOI: 10.1016/0001-6160(89)90326-X
T. Muschik, W. Gust, S. Hofmann, B. Predel
Auger electron spectroscopy has been used to study indium grain boundary segregation in symmetric «110å tilt boundaries and randomly oriented boundaries in bicrystals as well as polycrystals of NiIn containing 0.l–1.4 at. % In. Quench-induced non-equilibrium segregation of In, caused by fluxes of In vacancy complexes to the interfaces, influenced the results for quenching temperatures above 1000–1100 K. A careful analysis of sputtering profiles supplied additional informations for the discussion with respect to current models of QINS. From the equilibrium segregation behaviour for the symmetric boundaries both the segregation enthalpies (ΔHse = 38 ± 3 kJ/mol and ΔHseg = 39 ± 3 kJ/mol) and the mean segregation entropy [ΔSseg = (0 ± 0.5)R] have been determined for the first time. The segregation free energy for 970 K is ΔGseg = 50 ± 5 kJ/mol for the polycrystals. The symmetric atomic arrangement along the tilt boundaries is assumed to be responsible for the low segregation entropy.
{"title":"The temperature dependence of grain boundary segregation in NiIn bicrystals studied with auger electron spectroscopy","authors":"T. Muschik, W. Gust, S. Hofmann, B. Predel","doi":"10.1016/0001-6160(89)90326-X","DOIUrl":"10.1016/0001-6160(89)90326-X","url":null,"abstract":"<div><p>Auger electron spectroscopy has been used to study indium grain boundary segregation in symmetric «110å tilt boundaries and randomly oriented boundaries in bicrystals as well as polycrystals of NiIn containing 0.l–1.4 at. % In. Quench-induced non-equilibrium segregation of In, caused by fluxes of In vacancy complexes to the interfaces, influenced the results for quenching temperatures above 1000–1100 K. A careful analysis of sputtering profiles supplied additional informations for the discussion with respect to current models of QINS. From the equilibrium segregation behaviour for the symmetric boundaries both the segregation enthalpies (<em>ΔH</em><sub>se</sub> = 38 ± 3 kJ/mol and <em>ΔH</em><sub>seg</sub> = 39 ± 3 kJ/mol) and the mean segregation entropy [<em>ΔS</em><sub>seg</sub> = (0 ± 0.5)<em>R</em>] have been determined for the first time. The segregation free energy for 970 K is <em>ΔG</em><sub>seg</sub> = 50 ± 5 kJ/mol for the polycrystals. The symmetric atomic arrangement along the tilt boundaries is assumed to be responsible for the low segregation entropy.</p></div>","PeriodicalId":6969,"journal":{"name":"Acta Metallurgica","volume":"37 11","pages":"Pages 2917-2925"},"PeriodicalIF":0.0,"publicationDate":"1989-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/0001-6160(89)90326-X","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81613577","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 1989-11-01DOI: 10.1016/0001-6160(89)90346-5
N.K. Sinha
A grain size dependent rheological model is presented for high temperature creep that is capable of predicting both primary and tertiary as well as secondary creep. Primary and tertiary creep rate are shown to be strongly influenced by grain size, whereas secondary or minimum creep rate is rather insensitive to it. During the primary creep stage creep rate increases with decreasing grain size, but the reverse is true in the tertiary or accelerating range. An increase in grain size also dictates decrease in the time to reach minimum creep rate concomitant with a decrease in strain. The model is based on intragranular dislocation creep enhanced by grain-facet size cracks produced during deformation by the embrittlement process that is caused by an intergranular sliding mechanism. Incorporation of the kinetics of microcracking activity is the foundation of the theory.
{"title":"Microcrack-enhanced creep in polycrystalline material at elevated temperature","authors":"N.K. Sinha","doi":"10.1016/0001-6160(89)90346-5","DOIUrl":"10.1016/0001-6160(89)90346-5","url":null,"abstract":"<div><p>A grain size dependent rheological model is presented for high temperature creep that is capable of predicting both primary and tertiary as well as secondary creep. Primary and tertiary creep rate are shown to be strongly influenced by grain size, whereas secondary or minimum creep rate is rather insensitive to it. During the primary creep stage creep rate increases with decreasing grain size, but the reverse is true in the tertiary or accelerating range. An increase in grain size also dictates decrease in the time to reach minimum creep rate concomitant with a decrease in strain. The model is based on intragranular dislocation creep enhanced by grain-facet size cracks produced during deformation by the embrittlement process that is caused by an intergranular sliding mechanism. Incorporation of the kinetics of microcracking activity is the foundation of the theory.</p></div>","PeriodicalId":6969,"journal":{"name":"Acta Metallurgica","volume":"37 11","pages":"Pages 3107-3118"},"PeriodicalIF":0.0,"publicationDate":"1989-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/0001-6160(89)90346-5","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82524821","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 1989-11-01DOI: 10.1016/0001-6160(89)90331-3
R. Gerling, F.P. Schimansky, R. Wagner
Specimens of amorphous Fe40Ni40P20 exposed to neutron-irradiation and subsequently annealed at different temperatures are shown to undergo a similar phase separation into amorphous P-enriched and P-depleted regions as occurs in specimens annealed without prior irradiation. Whilst the radius (∼ 3.2 nm) of the P-rich regions is independent of whether the specimen has been irradiated or not, the onset of phase separation occurs for irradiated samples at lower temperatures; under identical annealing conditions the volume fraction of P-rich clusters is much larger in irradiated FeNiP than in un-irradiated material. The faster phase separation kinetics are a consequence of the irradiation-induced excess volume which allows for an increased mobility of individual atoms.
{"title":"Radiation-enhanced phase separation in amorphous Fe40Ni40P20","authors":"R. Gerling, F.P. Schimansky, R. Wagner","doi":"10.1016/0001-6160(89)90331-3","DOIUrl":"10.1016/0001-6160(89)90331-3","url":null,"abstract":"<div><p>Specimens of amorphous Fe<sub>40</sub>Ni<sub>40</sub>P<sub>20</sub> exposed to neutron-irradiation and subsequently annealed at different temperatures are shown to undergo a similar phase separation into amorphous P-enriched and P-depleted regions as occurs in specimens annealed without prior irradiation. Whilst the radius (∼ 3.2 nm) of the P-rich regions is independent of whether the specimen has been irradiated or not, the onset of phase separation occurs for irradiated samples at lower temperatures; under identical annealing conditions the volume fraction of P-rich clusters is much larger in irradiated FeNiP than in un-irradiated material. The faster phase separation kinetics are a consequence of the irradiation-induced excess volume which allows for an increased mobility of individual atoms.</p></div>","PeriodicalId":6969,"journal":{"name":"Acta Metallurgica","volume":"37 11","pages":"Pages 2961-2967"},"PeriodicalIF":0.0,"publicationDate":"1989-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/0001-6160(89)90331-3","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86331627","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 1989-11-01DOI: 10.1016/0001-6160(89)90344-1
T.Y. Hsu (Xu Zuyao), Zhou Xiaowang
The driving forces for various possible reactions within the bainitic transformation temperature range of Cu 40 at.% Zn alloy have been calculated. The results show that because of the occurrence of β→β′ ordering transition within the temperature range, the driving forces ΔGβ′→α′ and ΔGβ′→β′+α increase inversely with decreasing temperature, with ΔGβ′→α′ > 0 and ΔGβ′→β′+α < 0. Moreover, the equilibrium temperature T0 of the two phases β′ and α′ is far below the experimental Bs for alloys of various compositions. Therefore, the bainitic transformation in CuZn alloys can only proceed as that of diffusional reaction β′→β1′+α.
{"title":"Thermodynamics of the bainitic transformation in a CuZn alloy","authors":"T.Y. Hsu (Xu Zuyao), Zhou Xiaowang","doi":"10.1016/0001-6160(89)90344-1","DOIUrl":"10.1016/0001-6160(89)90344-1","url":null,"abstract":"<div><p>The driving forces for various possible reactions within the bainitic transformation temperature range of Cu 40 at.% Zn alloy have been calculated. The results show that because of the occurrence of β→β′ ordering transition within the temperature range, the driving forces <em>ΔG</em><sup><em>β</em>′→<em>α</em>′</sup> and <em>ΔG</em><sup><em>β</em>′→<em>β</em>′+<em>α</em></sup> increase inversely with decreasing temperature, with <em>ΔG</em><sup><em>β</em>′→<em>α</em>′</sup> > 0 and <em>ΔG</em><sup><em>β</em>′→<em>β</em>′+<em>α</em></sup> < 0. Moreover, the equilibrium temperature <em>T</em><sub>0</sub> of the two phases β′ and α′ is far below the experimental <em>B</em><sub>s</sub> for alloys of various compositions. Therefore, the bainitic transformation in CuZn alloys can only proceed as that of diffusional reaction <em>β</em>′→<em>β</em><sub>1</sub>′+<em>α</em>.</p></div>","PeriodicalId":6969,"journal":{"name":"Acta Metallurgica","volume":"37 11","pages":"Pages 3095-3098"},"PeriodicalIF":0.0,"publicationDate":"1989-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/0001-6160(89)90344-1","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"52988471","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 1989-11-01DOI: 10.1016/S0001-6160(89)80001-X
J.A. Walsh , K.V. Jata , E.A. Starke Jr
Ductile fracture studies have been conducted on four high purity AlCuMgZr (2134 type) alloys containing 0, 0.31. 0.61 and 1.02 wt% Mn in the under and overaged conditions having similar yield strengths. The second phase particle content, i.e, Mn rich dispersoids and Mn containing large particles, increased with increasing Mn content. In both aging conditions maximum ductility and toughness were observed for the 0.31% Mn alloy and minimum values were observed for the 1.02% Mn alloy, The largest void content or damage accumulation due to void nucleation and growth at any strain level occurred in the 1.02% Mn alloy, consistent with ductility values. The 0.31% Mn alloy showed the highest ductility in both aging conditions, Although the void volume fractions for the 0.31% Mn alloy were similar to those of the 1.02% Mn alloy, accumulation occurred at higher strains. The void nucleation and growth data and microstructural analysis suggest that the 0.31% Mn additions provide sufficient submicrometer Mn-dispersoids to homogenize slip without producing large Mn-rich primary particles which decrease ductility. Ductility was observed to decrease with increasing triaxial constraint which increased void volume fraction and void growth rates. However, the degree of triaxiality had little or no effect on the nucleation rate of voids.
{"title":"The influence of Mn dispersoid content and stress state on ductile fracture of 2134 type Al alloys","authors":"J.A. Walsh , K.V. Jata , E.A. Starke Jr","doi":"10.1016/S0001-6160(89)80001-X","DOIUrl":"10.1016/S0001-6160(89)80001-X","url":null,"abstract":"<div><p>Ductile fracture studies have been conducted on four high purity Al<img>Cu<img>Mg<img>Zr (2134 type) alloys containing 0, 0.31. 0.61 and 1.02 wt% Mn in the under and overaged conditions having similar yield strengths. The second phase particle content, i.e, Mn rich dispersoids and Mn containing large particles, increased with increasing Mn content. In both aging conditions maximum ductility and toughness were observed for the 0.31% Mn alloy and minimum values were observed for the 1.02% Mn alloy, The largest void content or damage accumulation due to void nucleation and growth at any strain level occurred in the 1.02% Mn alloy, consistent with ductility values. The 0.31% Mn alloy showed the highest ductility in both aging conditions, Although the void volume fractions for the 0.31% Mn alloy were similar to those of the 1.02% Mn alloy, accumulation occurred at higher strains. The void nucleation and growth data and microstructural analysis suggest that the 0.31% Mn additions provide sufficient submicrometer Mn-dispersoids to homogenize slip without producing large Mn-rich primary particles which decrease ductility. Ductility was observed to decrease with increasing triaxial constraint which increased void volume fraction and void growth rates. However, the degree of triaxiality had little or no effect on the nucleation rate of voids.</p></div>","PeriodicalId":6969,"journal":{"name":"Acta Metallurgica","volume":"37 11","pages":"Pages 2861-2871"},"PeriodicalIF":0.0,"publicationDate":"1989-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/S0001-6160(89)80001-X","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80064155","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 1989-11-01DOI: 10.1016/0001-6160(89)90323-4
H. Kawazoe , T. Takasugi , O. Izumi
Slip behavior in cyclic-deformation has been studied using the α-β brass two-phase bicrystals, the phase-interface plane of which is parallel to the stress axis. Tension-compression tests were performed at room temperature under constant total strain amplitude of ±0.4%. Different slip patterns were developed in the vicinity of the interface at opposite surfaces of the α phase, while the patterns in the β phase were almost similar. It was thought that the behavior in β reflects its intrinsic monocrystalline property in response to the external stress. On the other hand, different slip behavior in α was interpreted in terms of the effect due to elastic strain incompatibility at the interface as given by Hook and Hirth [Acta metall.15, 535 (1967)]. The effect due to elastic strain incompatibility was shown to be more significant in cyclic straining.
{"title":"Cyclic deformation of α-β brass two-phase bicrystals—I. Slip behavior","authors":"H. Kawazoe , T. Takasugi , O. Izumi","doi":"10.1016/0001-6160(89)90323-4","DOIUrl":"10.1016/0001-6160(89)90323-4","url":null,"abstract":"<div><p>Slip behavior in cyclic-deformation has been studied using the α-β brass two-phase bicrystals, the phase-interface plane of which is parallel to the stress axis. Tension-compression tests were performed at room temperature under constant total strain amplitude of ±0.4%. Different slip patterns were developed in the vicinity of the interface at opposite surfaces of the α phase, while the patterns in the β phase were almost similar. It was thought that the behavior in β reflects its intrinsic monocrystalline property in response to the external stress. On the other hand, different slip behavior in α was interpreted in terms of the effect due to elastic strain incompatibility at the interface as given by Hook and Hirth [<em>Acta metall.</em><strong>15</strong>, 535 (1967)]. The effect due to elastic strain incompatibility was shown to be more significant in cyclic straining.</p></div>","PeriodicalId":6969,"journal":{"name":"Acta Metallurgica","volume":"37 11","pages":"Pages 2883-2894"},"PeriodicalIF":0.0,"publicationDate":"1989-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/0001-6160(89)90323-4","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79555208","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 1989-11-01DOI: 10.1016/0001-6160(89)90342-8
Zhou Xiaowang, T.Y. Hsu (Xu Zuyao)
For both the solid solutions α and β, composed of Cu and Zn, approximated by the regular solutions, the interaction parameters Eα and Eβ of components in the a and β phases are calculated with the experimental activities. By the application of lattice stability parameters ΔGCuβ→α and ΔZnβ→α of Cu and Zn, which are obtained from the phase diagram of CuZn system in this paper, a general formula for ΔGβ→α is derived. On the basis of Inden formula for the change of free energy ΔGβ→β′ in the β→β′ ordering transition, it is proposed, through discussing the critical temperature Tc of ordering and ordering degree as a function of temperature, that the theoretical maximum ordering degree can not be obtained for an alloy with given composition. The maximum ordering degree attained is approximately independent of composition for alloys with XZn = 0.35–0.65, so an approximate equation for ordering degree as a function of temperature is suggested. This equation is used to calculate the and phase boundaries of CuZn system, and the results are in good agreement with the phase diagram.
{"title":"Thermodynamics of the α- and β-phases equilibria and ordering in CuZn system","authors":"Zhou Xiaowang, T.Y. Hsu (Xu Zuyao)","doi":"10.1016/0001-6160(89)90342-8","DOIUrl":"10.1016/0001-6160(89)90342-8","url":null,"abstract":"<div><p>For both the solid solutions α and β, composed of Cu and Zn, approximated by the regular solutions, the interaction parameters <em>E</em><sup><em>α</em></sup> and <em>E</em><sup><em>β</em></sup> of components in the a and β phases are calculated with the experimental activities. By the application of lattice stability parameters <em>ΔG</em><sub>Cu</sub><sup><em>β</em>→<em>α</em></sup> and <em>Δ</em><sub>Zn</sub><sup><em>β</em>→<em>α</em></sup> of Cu and Zn, which are obtained from the phase diagram of CuZn system in this paper, a general formula for <em>ΔG</em><sup><em>β</em>→<em>α</em></sup> is derived. On the basis of Inden formula for the change of free energy <em>ΔG</em><sup><em>β</em>→<em>β</em>′</sup> in the β→β′ ordering transition, it is proposed, through discussing the critical temperature <em>T</em><sub>c</sub> of ordering and ordering degree as a function of temperature, that the theoretical maximum ordering degree can not be obtained for an alloy with given composition. The maximum ordering degree attained is approximately independent of composition for alloys with <em>X</em><sub>Zn</sub> = 0.35–0.65, so an approximate equation for ordering degree as a function of temperature is suggested. This equation is used to calculate the <span><math><mtext>α</mtext><mtext>(α + β′)</mtext></math></span> and <span><math><mtext>β′</mtext><mtext>(α + β′)</mtext></math></span> phase boundaries of CuZn system, and the results are in good agreement with the phase diagram.</p></div>","PeriodicalId":6969,"journal":{"name":"Acta Metallurgica","volume":"37 11","pages":"Pages 3085-3090"},"PeriodicalIF":0.0,"publicationDate":"1989-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/0001-6160(89)90342-8","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74706400","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}