JMatPro計(jì)算原理探討課件

JMatPro計(jì)算原理探討動(dòng)態(tài)物理模型的建立強(qiáng)大的金屬材料數(shù)據(jù)庫廣泛且經(jīng)實(shí)驗(yàn)驗(yàn)證的計(jì)算結(jié)果JMatPro計(jì)算原理探討Modellingpropertiesandbehaviour:JMatPro材料性能模擬：JMatProModellingpropertiesandbehav

3.1ThermodynamicCalculations:Background熱動(dòng)力學(xué)計(jì)算原理BasicequationfortheGibbsEnergyofamulti-componentSolutionPhase多元合金固溶相吉布斯自由能基本方程Gibbsenergyofpurecomponents純組元的吉布斯自由能Idealentropy理想狀態(tài)下的焓Interactionterms(Basedonpairwiseinteractions)相互作用項(xiàng)（基于兩兩之間相互作用）3.1ThermodynamicCalculatio3.2PhaseTransformationKinetics:Model相轉(zhuǎn)變動(dòng)力學(xué)模型:(用于鋼的)

GeneralEquationforTTTcalculationisafterKirkaldyetal.(TTT計(jì)算的一般方程：Kirkaldyetal.)=2(G-1)/2,isanempiricalcoefficient,GistheASTMgrainsize,Disaneffectivediffusioncoefficient,Tistheundercooling,qisanexponent3.2PhaseTransformationKine

dependentontheeffectivediffusionmechanismandxisthefractiontransformed.(=2(G-1)/2,是一個(gè)經(jīng)驗(yàn)系數(shù)，G是晶粒尺寸，D是有效擴(kuò)散系數(shù)，T是過冷度，q是一個(gè)取決于有效擴(kuò)散機(jī)制的指數(shù)。X是轉(zhuǎn)變的百分?jǐn)?shù))dependentontheeffective3.2.1Martensitictransformations馬氏體轉(zhuǎn)變

3.2.1Martensitictransformat3.2.2PhaseTransformations(TTT/CCTdiagrams)相轉(zhuǎn)變（TTT/CCT相圖）CalculatedTTTdiagramsforU720andU720LIwithexperimentalresultsofKeefeetal.superimposed.對(duì)U720和U720LI所計(jì)算的TTT曲線與Keefeetal.的實(shí)驗(yàn)結(jié)果比較3.2.2PhaseTransformationsCa3.2.3PhaseTransformations(g/gcoarsening)相轉(zhuǎn)變（γ/γ晶粒的長大

）晶粒的計(jì)算長大率與實(shí)驗(yàn)得到的長大率的比較3.2.3PhaseTransformations(g3.2.2PhaseTransformations(TTT/CCTdiagrams)相轉(zhuǎn)變（TTT/CCT相圖）7183.2.2PhaseTransformations7CalculatedTTTdiagramforthesinglecrystalalloyRR2071withexperimentalresultsofRaeatal.superimposed3.2.2PhaseTransformations(TTT/CCTdiagrams)相轉(zhuǎn)變（TTT/CCT相圖）RR2071合金計(jì)算的TTT曲線與Raeatal.的實(shí)驗(yàn)結(jié)果的比較CalculatedTTTdiagramforthe3.3BackgroundtoPropertyCalculations物理/熱物理性能計(jì)算背景知識(shí)PropertyofaSolutionPhase固溶相性能Propertyofpurecomponents純組元時(shí)的性能Interactionterms(Basedonpairwiseinteractions)相互作用項(xiàng)（基于相與相兩兩之間相互作用）

3.3BackgroundtoPropertyCa3.4MechanicalProperties機(jī)械性能Twotypesofstrengtheningmechanismaretreated.

可考慮兩種強(qiáng)化機(jī)制Solidsolutionstrengthening.固溶強(qiáng)化Particlestrengthening.第二相粒子強(qiáng)化3.4MechanicalPropertiesTwo3.4.1MechanicalProperties(PrecipitationHardening)機(jī)械性能（析出強(qiáng)化）Theyieldstrengthofanalloyhardenedbyg’particlescanbegivenbytheequationbelowforsmallparticles微小γ‘粒子對(duì)合金的屈服強(qiáng)度的強(qiáng)化效果可用以下方程來衡量YS0andYS1=yieldstressofthematrixandalloyM=Taylorfactor b=burger’svector3.4.1MechanicalPropertiesA=shapedependentconstant d=ppt.diameterτ

=linetensionofadislocation f=volfractionγ'γ=APBenergyYS0和YS1=晶格屈服強(qiáng)度和合金屈服強(qiáng)度M=泰勒系數(shù) b=柏氏矢量A=形狀因子常量d=析出粒子直徑τ=位錯(cuò)的線張力 f=γ‘體積分?jǐn)?shù)γ=APB能量A=shapedependentconstant Forlargerparticlestheequationbelowcanbeused

對(duì)于大尺寸的粒子，強(qiáng)化效果用下面方程來衡量ω=constantthataccountsforrepulsionofdislocationswithintheprecipitates(essentiallyanempiricallyadjustableparameter).ω=一個(gè)表明析出物內(nèi)部位錯(cuò)間斥力的常數(shù)（實(shí)質(zhì)上是一個(gè)經(jīng)驗(yàn)系數(shù)）3.4.1MechanicalProperties(PrecipitationHardening)機(jī)械性能（析出強(qiáng)化）Forlargerparticlestheequat3.4.2MechanicalProperties機(jī)械性能屈服強(qiáng)度的計(jì)算值與實(shí)驗(yàn)值的比較3.4.2MechanicalProperties屈服強(qiáng)3.4.3ComparisonofMechanicalPropertiesforNi-basedSuperalloys鎳基超合金機(jī)械性能實(shí)驗(yàn)與計(jì)算值的比較3.4.3ComparisonofMechanica3.4.4AgeingResponseofaNi-basedSuperalloy(combiningcoarseningandpptnhardening)鎳基超合金時(shí)效效應(yīng)（綜合晶粒長大和析出強(qiáng)化）3.4.4AgeingResponseofaNi3.5HighTempMechanicalProperties(creep)高溫機(jī)械性能（蠕變）GeneralCreepEquation蠕變一般方程A=Materialconstant D=effectivediffusioncoeffSFE=stackingfaultenergy G=shearmodulusb=burger’svector σ=appliedstressσo=backstress E=Young’smodulusm=3 n=creepexponent3.5HighTempMechanicalPropeA=材料常數(shù) D=有效擴(kuò)散系數(shù)SFE=層錯(cuò)能 G=剪切模量b=柏氏矢量 σ=外加應(yīng)力σo=背應(yīng)力 E=楊氏模量m=3 n=蠕變指數(shù)A=材料常數(shù) D=有效擴(kuò)散3.5.1HighTempMechanicalProperties(creep)高溫機(jī)械性能（蠕變）蠕變率的計(jì)算值與實(shí)驗(yàn)值的比較3.5.1HighTempMechanicalProAsrupturestrengthisanalternativedesigncriterioninmanypracticalcases,thecalculationprocedurehasbeenextendedtoincludethispropertybyusinganinverserelationshipbetweenstressrupturelifeandsecondarycreeprate在許多實(shí)際情況中，斷裂強(qiáng)度是一個(gè)可供選擇的設(shè)計(jì)標(biāo)準(zhǔn)。我們的軟件現(xiàn)在已經(jīng)能夠計(jì)算蠕變強(qiáng)度，這是通過利用蠕變斷裂應(yīng)力與蠕變率的對(duì)立關(guān)系間接得到的。3.5.2HighTempMechanicalProperties(creep)高溫機(jī)械性能（蠕變）AsrupturestrengthisanalteComparisonbetweenexperimentalandcalculated1000hrrupturestrengthsforvariouswroughtNi-basedsuperalloys3.5.3HighTempMechanicalProperties(creep)高溫機(jī)械性能（蠕變）成分不同的各種鎳基超合金1000小時(shí)斷裂強(qiáng)度實(shí)驗(yàn)值與計(jì)算值的比較。ComparisonbetweenexperimentaComparisonbetweenexperimentalandcalculatedrupturelifeforvarioussinglecrystalsuperalloys3.5.4HighTempMechanicalProperties(creep)高溫機(jī)械性能（蠕變）各種單晶超合金斷裂壽命的實(shí)驗(yàn)值與計(jì)算值的比較。ComparisonbetweenexperimentaThecreepcalculationshavebeencombinedwiththeearlierlowtemperatureyieldstresscalculationstomodeltheflowstressofNi-basedsuperalloysatraisedtemperatures.蠕變計(jì)算已經(jīng)綜合了早期低溫屈服應(yīng)力計(jì)算，用來模擬鎳基超合金隨溫度升高時(shí)的流體應(yīng)力。3.6HighTempMechanicalProperties高溫機(jī)械性能ThecreepcalculationshavebeThedecayinRTyieldstresswithiswellmatchedusinganequationofthefollowingtype高溫情況下，室溫屈服應(yīng)力的衰減與下面方程所給出的結(jié)果相吻合。

whereαandβareconstantsdirectlyrelatedtoσRTandthevalueofQ,whichisdeterminedempiricallythroughregressionanalysis.3.6HighTempMechanicalProperties高溫機(jī)械性能ThedecayinRTyieldstressw在這里，α和β都是與室溫強(qiáng)度σRT

和激活能Q值直接相關(guān)的常量。Q值的大小一般是通過回歸分析憑經(jīng)驗(yàn)來確定的。在這里，α和β都是與室溫強(qiáng)度σRT和激活能Q值直接相關(guān)的Asthetemperatureisraisedtohighlevelsthealloywillyieldviacreepwhenthestrainrateofthemechanicaltestisequaltoorslowerthanthecreeprateatthetestingtemperature.當(dāng)溫度升到較高的檢測(cè)溫度下，試驗(yàn)機(jī)的拉伸速率等于或小于蠕變速率時(shí)，合金將發(fā)生蠕變屈服。Thiscanbecombinedwiththepreviousrelationship3.6HighTempMechanicalProperties高溫機(jī)械性能AsthetemperatureisraisedttogivemechanicalpropertiesfromRTtothemeltingpoint把蠕變效應(yīng)和其它因素結(jié)合起來，這樣我們就可以給出從室溫到材料熔點(diǎn)區(qū)間范圍內(nèi)材料的機(jī)械性能。togivemechanicalpropertiesComparisonbetweenexperimentalandcalculatedyieldstressforNimonic75and105asafunctionoftemperature.3.6HighTempMechanicalProperties高溫機(jī)械性能75和105鎳基合金實(shí)驗(yàn)與計(jì)算情況下強(qiáng)度隨溫度的變化的比較ComparisonbetweenexperimentaComparisonbetweenexperimentalandcalculatedyieldstressatforvariouswroughtsuperalloysandpureNibetweenRTand1000oC.不同質(zhì)量百分?jǐn)?shù)的超合金以及純鎳在室溫和1000oC時(shí),屈服應(yīng)力的實(shí)驗(yàn)與計(jì)算值的比較3.6HighTempMechanicalProperties高溫機(jī)械性能Comparisonbetweenexperimenta3.7更多計(jì)算原理信息3.7更多計(jì)算原理信息3.7更多計(jì)算原理信息D:\ProgramFiles\JMatPro-4.0\docs\pdfwww.sentesoftware.co.ukAboutus-Profile

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3.7更多計(jì)算原理信息JMatPro計(jì)算原理探討動(dòng)態(tài)物理模型的建立強(qiáng)大的金屬材料數(shù)據(jù)庫廣泛且經(jīng)實(shí)驗(yàn)驗(yàn)證的計(jì)算結(jié)果JMatPro計(jì)算原理探討Modellingpropertiesandbehaviour:JMatPro材料性能模擬：JMatProModellingpropertiesandbehav

3.1ThermodynamicCalculations:Background熱動(dòng)力學(xué)計(jì)算原理BasicequationfortheGibbsEnergyofamulti-componentSolutionPhase多元合金固溶相吉布斯自由能基本方程Gibbsenergyofpurecomponents純組元的吉布斯自由能Idealentropy理想狀態(tài)下的焓Interactionterms(Basedonpairwiseinteractions)相互作用項(xiàng)（基于兩兩之間相互作用）3.1ThermodynamicCalculatio3.2PhaseTransformationKinetics:Model相轉(zhuǎn)變動(dòng)力學(xué)模型:(用于鋼的)

GeneralEquationforTTTcalculationisafterKirkaldyetal.(TTT計(jì)算的一般方程：Kirkaldyetal.)=2(G-1)/2,isanempiricalcoefficient,GistheASTMgrainsize,Disaneffectivediffusioncoefficient,Tistheundercooling,qisanexponent3.2PhaseTransformationKine

dependentontheeffectivediffusionmechanismandxisthefractiontransformed.(=2(G-1)/2,是一個(gè)經(jīng)驗(yàn)系數(shù)，G是晶粒尺寸，D是有效擴(kuò)散系數(shù)，T是過冷度，q是一個(gè)取決于有效擴(kuò)散機(jī)制的指數(shù)。X是轉(zhuǎn)變的百分?jǐn)?shù))dependentontheeffective3.2.1Martensitictransformations馬氏體轉(zhuǎn)變

3.2.1Martensitictransformat3.2.2PhaseTransformations(TTT/CCTdiagrams)相轉(zhuǎn)變（TTT/CCT相圖）CalculatedTTTdiagramsforU720andU720LIwithexperimentalresultsofKeefeetal.superimposed.對(duì)U720和U720LI所計(jì)算的TTT曲線與Keefeetal.的實(shí)驗(yàn)結(jié)果比較3.2.2PhaseTransformationsCa3.2.3PhaseTransformations(g/gcoarsening)相轉(zhuǎn)變（γ/γ晶粒的長大

）晶粒的計(jì)算長大率與實(shí)驗(yàn)得到的長大率的比較3.2.3PhaseTransformations(g3.2.2PhaseTransformations(TTT/CCTdiagrams)相轉(zhuǎn)變（TTT/CCT相圖）7183.2.2PhaseTransformations7CalculatedTTTdiagramforthesinglecrystalalloyRR2071withexperimentalresultsofRaeatal.superimposed3.2.2PhaseTransformations(TTT/CCTdiagrams)相轉(zhuǎn)變（TTT/CCT相圖）RR2071合金計(jì)算的TTT曲線與Raeatal.的實(shí)驗(yàn)結(jié)果的比較CalculatedTTTdiagramforthe3.3BackgroundtoPropertyCalculations物理/熱物理性能計(jì)算背景知識(shí)PropertyofaSolutionPhase固溶相性能Propertyofpurecomponents純組元時(shí)的性能Interactionterms(Basedonpairwiseinteractions)相互作用項(xiàng)（基于相與相兩兩之間相互作用）

3.3BackgroundtoPropertyCa3.4MechanicalProperties機(jī)械性能Twotypesofstrengtheningmechanismaretreated.

可考慮兩種強(qiáng)化機(jī)制Solidsolutionstrengthening.固溶強(qiáng)化Particlestrengthening.第二相粒子強(qiáng)化3.4MechanicalPropertiesTwo3.4.1MechanicalProperties(PrecipitationHardening)機(jī)械性能（析出強(qiáng)化）Theyieldstrengthofanalloyhardenedbyg’particlescanbegivenbytheequationbelowforsmallparticles微小γ‘粒子對(duì)合金的屈服強(qiáng)度的強(qiáng)化效果可用以下方程來衡量YS0andYS1=yieldstressofthematrixandalloyM=Taylorfactor b=burger’svector3.4.1MechanicalPropertiesA=shapedependentconstant d=ppt.diameterτ

=linetensionofadislocation f=volfractionγ'γ=APBenergyYS0和YS1=晶格屈服強(qiáng)度和合金屈服強(qiáng)度M=泰勒系數(shù) b=柏氏矢量A=形狀因子常量d=析出粒子直徑τ=位錯(cuò)的線張力 f=γ‘體積分?jǐn)?shù)γ=APB能量A=shapedependentconstant Forlargerparticlestheequationbelowcanbeused

對(duì)于大尺寸的粒子，強(qiáng)化效果用下面方程來衡量ω=constantthataccountsforrepulsionofdislocationswithintheprecipitates(essentiallyanempiricallyadjustableparameter).ω=一個(gè)表明析出物內(nèi)部位錯(cuò)間斥力的常數(shù)（實(shí)質(zhì)上是一個(gè)經(jīng)驗(yàn)系數(shù)）3.4.1MechanicalProperties(PrecipitationHardening)機(jī)械性能（析出強(qiáng)化）Forlargerparticlestheequat3.4.2MechanicalProperties機(jī)械性能屈服強(qiáng)度的計(jì)算值與實(shí)驗(yàn)值的比較3.4.2MechanicalProperties屈服強(qiáng)3.4.3ComparisonofMechanicalPropertiesforNi-basedSuperalloys鎳基超合金機(jī)械性能實(shí)驗(yàn)與計(jì)算值的比較3.4.3ComparisonofMechanica3.4.4AgeingResponseofaNi-basedSuperalloy(combiningcoarseningandpptnhardening)鎳基超合金時(shí)效效應(yīng)（綜合晶粒長大和析出強(qiáng)化）3.4.4AgeingResponseofaNi3.5HighTempMechanicalProperties(creep)高溫機(jī)械性能（蠕變）GeneralCreepEquation蠕變一般方程A=Materialconstant D=effectivediffusioncoeffSFE=stackingfaultenergy G=shearmodulusb=burger’svector σ=appliedstressσo=backstress E=Young’smodulusm=3 n=creepexponent3.5HighTempMechanicalPropeA=材料常數(shù) D=有效擴(kuò)散系數(shù)SFE=層錯(cuò)能 G=剪切模量b=柏氏矢量 σ=外加應(yīng)力σo=背應(yīng)力 E=楊氏模量m=3 n=蠕變指數(shù)A=材料常數(shù) D=有效擴(kuò)散3.5.1HighTempMechanicalProperties(creep)高溫機(jī)械性能（蠕變）蠕變率的計(jì)算值與實(shí)驗(yàn)值的比較3.5.1HighTempMechanicalProAsrupturestrengthisanalternativedesigncriterioninmanypracticalcases,thecalculationprocedurehasbeenextendedtoincludethispropertybyusinganinverserelationshipbetweenstressrupturelifeandsecondarycreeprate在許多實(shí)際情況中，斷裂強(qiáng)度是一個(gè)可供選擇的設(shè)計(jì)標(biāo)準(zhǔn)。我們的軟件現(xiàn)在已經(jīng)能夠計(jì)算蠕變強(qiáng)度，這是通過利用蠕變斷裂應(yīng)力與蠕變率的對(duì)立關(guān)系間接得到的。3.5.2HighTempMechanicalProperties(creep)高溫機(jī)械性能（蠕變）AsrupturestrengthisanalteComparisonbetweenexperimentalandcalculated1000hrrupturestrengthsforvariouswroughtNi-basedsuperalloys3.5.3HighTempMechanicalProperties(creep)高溫機(jī)械性能（蠕變）成分不同的各種鎳基超合金1000小時(shí)斷裂強(qiáng)度實(shí)驗(yàn)值與計(jì)算值的比較。ComparisonbetweenexperimentaComparisonbetweenexperimentalandcalculatedrupturelifeforvarioussinglecrystalsuperalloys3.5.4HighTempMechanicalProperties(creep)高溫機(jī)械性能（蠕變）各種單晶超合金斷裂壽命的實(shí)驗(yàn)值與計(jì)算值的比較。ComparisonbetweenexperimentaThecreepcalculationshavebeencombinedwiththeearlierlowtemperatureyieldstresscalculationstomodeltheflowstressofNi-basedsuperalloysatraisedtemperatures.蠕變計(jì)算已經(jīng)綜合了早期低溫屈服應(yīng)力計(jì)算，用來模擬鎳基超合金隨溫度升高時(shí)的流體應(yīng)力。3.6HighTempMechanicalProperties高溫機(jī)械性能ThecreepcalculationshavebeThedecayinRTyieldstresswithiswellmatchedusinganequationofthefollowingtype高溫情況下，室溫屈服應(yīng)力的衰減與下面方程所給出的結(jié)果相吻合。

whereαandβareconstantsdirectlyrela