Modulus of Elasticity Variation with Temperature: Designing Stainless Structures

Lub modulus ntawm elasticity - qhov ntsuas ntawm qhov hnyav npaum li cas ntawm cov khoom nyob rau hauv load - tsis yog tus lej tas raustainless hlau; Nws poob qis tsis tu ncua thaum kub nce, thiab qhov kev poob qis ncaj qha cuam tshuam ntau npaum li cas tus tswv cuab ntawm cov qauv deflects, nws ntxov npaum li cas buckles, thiab ntau npaum li cas tus qauv tsim muaj nyob rau hauv kev pabcuam. Rau ib qho stainless lossis npib tsib xee alloy qauv kev khiav hauj lwm saum qhov kub thiab txias ambient - txheej txheem piping, furnace support, pa systems, high -temperature vessels - siv ib chav tsev - kub modulus tus nqi thoob plaws hauv lub tsim yog ib qho kev ua yuam kev thiab qhov tshwm sim. Phau ntawv qhia no piav qhia tias vim li cas lub modulus ntog nrog qhov kub thiab txias, los ntawm ntau npaum li cas rau cov qib stainless hlau, thiab cov qauv tsim qauv yuav tsum muaj cov engineers account rau nws.

Dab tsi yog Modulus ntawm Elasticity, thiab Vim Li Cas Nws Hloov Nrog Kub?

Lub modulus ntawm elasticity (Young's modulus, E) ntsuas cov khoom siv tawv nqaij - nws tsis kam rau elastic deformation nyob rau hauv kev ntxhov siab - thiab nws txo qis thaum kub nce vim tias tshav kub ua rau lub zog atomic bonding zog uas muab cov khoom nws nruj rau thawj qhov chaw.

Hauv cov ntsiab lus yooj yim, qhov kev hloov pauv ntawm elasticity yog qhov piv ntawm kev ntxhov siab rau elastic strain: siv cov khoom hnyav, thiab cov khoom siv zog (siab dua E) deflects tsawg dua ib qho yooj yim dua (qis E). Ntawm qhov ntsuas atomic, qhov tawv tawv los ntawm lub zog ntawm cov hlau nplaum tuav cov atoms hauv lawv txoj haujlwm lattice. Raws li qhov kub thiab txias, atoms vibrate ntau zog thiab qhov nruab nrab qhov nruab nrab ntawm lawv loj hlob me ntsis, uas ua rau lub zog tsis muaj zog uas tiv thaiv elastic hloov.

Qhov tshwm sim yog cov khoom siv uas tseem coj tus cwj pwm elastically - nws tseem rov qab los rau nws cov qauv qub thaum unloaded - tab sis tiv taus deformation tsawg dua li nws tau ua nyob rau hauv chav tsev kub. Qhov no yog qhov tshwm sim txawv los ntawm kev tawm dag zog lub zog poob lossis nkag mus; Kev txo qis modulus cuam tshuam rau txhua tus qauv stainless hlau ua haujlwm kub, txawm tias ib qho kev thauj khoom zoo nyob rau hauv nws cov elastic ntau thiab deb ntawm kev nkag los lossis kev txhawj xeeb.

Ntau npaum li cas Modulus ntawm Elasticity ntawm Stainless Hlau txo qis thaum kub nce?

Standard austenitic stainless steels poob li ntawm 20-25% ntawm lawv chav-kub modulus los ntawm 600℃(1110℃F), thiab qhov kev poob ntawd yog maj mam thiab kwv yees es tsis yog ib qho kev tshwm sim tam sim ntawd, uas yog qhov tso cai rau nws mus tabulated thiab tsim nyob ib ncig ntawm kev ntseeg siab.

Cov ntaub ntawv siv tau luam tawm nyob rau hauv ASME Tshooj II-D thiab cov qauv thoob ntiaj teb sib npaug qhia cov qauv zoo ib yam thoob plaws qib: cov qauv qis qis qis thiab tsis tu ncua los ntawm chav tsev kub nce mus, tsis muaj qhov cuam tshuam tsis zoo ntawm qhov elasticity.

Qhov no du, zoo -tus cwj pwm poob qis yog ib qho laj thawj modulus txo yog qhov sib piv yooj yim rau kev tsim rau - tsis zoo li lub zog tawm los yog tus cwj pwm nkag, uas tuaj yeem sib txawv ntawm cov khoom siv hluav taws xob thiab cov khoom, cov modulus -kub kev sib raug zoo rau ib tsev neeg alloy tau zoo ib yam txaus uas tabulated qhov tseem ceeb yog suav hais tias txhim khu kev qha nyob rau hauv ib tug ntau yam ntawm cov khoom.

Tus neeg sawv cev modulus qhov tseem ceeb rau cov qib tsis sib xws thoob plaws ib qho kev nce siab - qhov kub thiab txias:

Table 1. Tus neeg sawv cev ntawm cov qauv ntawm elasticity (E) qhov tseem ceeb rau cov qib stainless hlau sib txawv ntawm qhov kub siab. Cov txiaj ntsig yog kev piav qhia thiab sib npaug; ib txwm lees paub tawm tsam tam sim no ntawm ASME Tshooj II-D, Ntu D, lossis cov khoom siv tshwj xeeb ua ntej siv rau hauv kev suav tsim.

Vim li cas thiaj li Qhov Kub Kub Txo Cov Modulus ntawm Elasticity ntawm Qib Atomic?

Modulus txo yog tsav los ntawm thermal expansion ntawm atomic lattice thiab nce atomic vibration amplitude, ob qho tib si uas tsis muaj zog ntawm interatomic bonding rog uas elastic rigidness nyob ntawm - tib lub cev mechanism ntawm tag nrho cov stainless thiab npib tsib xee alloy qib, txawm tias tus nqi poob nws txawv nrog alloy muaj pes tsawg leeg.

Elastic txhav yog qhov tseem ceeb ntawm kev ua haujlwm ntawm qhov nkhaus ntawm lub zog sib xyaw ua ke zoo - yuav ua li cas kom rov qab ua kom muaj zog nce ntxiv thaum atoms tau hloov pauv ntawm lawv qhov sib npaug. Ob qhov kub thiab txias-tsav los cuam tshuam qhov curvature: ua ntej, thermal expansion nce qhov nruab nrab atomic sib nrug, txav atoms ntxiv los ntawm qhov chaw siab tshaj ntawm qhov zoo; Thib ob, ntau dua thermal vibration amplitude ua tau zoo qhov nruab nrab ntawm kev sib koom ua ke ntawm ntau qhov chaw ntawm cov atomic tam sim no, feem ntau ntawm cov uas tsis tshua muaj nruj dua li txoj haujlwm sib npaug.

Alloying ntsiab lus uas ua rau kom muaj zog thiab lattice stability - npib tsib xee, molybdenum, thiab chromium nyob rau hauv ntau yam kev sib xyaw ua ke - tuaj yeem ua rau qeeb qeeb no, uas yog ib feem ntawm vim li cas npib tsib xee- nplua nuj alloys khaws ib feem ntau dua ntawm lawv chav- kub modulus ntawm ib qho kev nce siab ntawm cov hlau, txawm tias cov hlau tsis sib xws.

Lub Modulus qis ntawm Elasticity cuam tshuam li cas rau kev tsim qauv?

Ib qho kev txo qis ncaj qha nce elastic deflection nyob rau hauv ib qho load, txo qis qhov tseem ceeb buckling load ntawm compression cov tswv cuab, thiab txo qhov zaus ntawm cov qauv vibrating - txhais tau hais tias tus tswv cuab loj txaus ntawm chav tsev kub tuaj yeem ua rau hauv qab - txhav, nquag buckling, los yog resonance - rhiab heev thaum nws ncav cuag qhov kub thiab txias.

Peb qhov kev kuaj xyuas yog qhov nkag siab tshaj plaws rau kev txo qis. Deflection nyob rau hauv load yog inversely proportional rau E, yog li ib tug beam los yog yeeb nkab span uas ua tau raws li ib tug deflection txwv nyob rau hauv chav tsev kub tej zaum yuav tshaj nws nyob rau hauv siab kub txawm hais tias lub load thiab kev ntxhov siab tsis hloov. Elastic buckling muaj peev xwm ntawm txhua kab thiab nyias - cov plhaub phab ntsa yog ncaj qha proportional rau E, yog li tib qhov kev poob qis uas ua rau kom deflection kuj txo cov load uas tus tswv cuab compression ua tsis ruaj khov - ib qho tseem ceeb rau kev txhawb nqa rauv, nyias - cov hlab ntsha phab ntsa, thiab cov kav dej sib luag.

Ntuj zaus ntawm cov qauv vibrating yog proportional rau lub hauv paus square ntawm E, yog li cov cuab yeej rhiab heev rau resonance (piping yuav txaus-induced vibration, nyias vaj huam sib luag nyob ze ntawm rotating machinery) yuav hloov mus rau hauv ib tug ntau resonance ntau zaus thaum nws heats.

Cov qauv kuaj xyuas feem ntau cuam tshuam los ntawm kev txo qis modulus

Elastic deflection thiab sag ntawm kab teeb, yeeb nkab spans, thiab kev txhawb nqa nyob rau hauv sustained load.

Qhov tseem ceeb buckling load ntawm kab, nyias plhaub, thiab compression cov tswv cuab.

Ntuj zaus thiab resonance cwj pwm ntawm vibrating Cheebtsam.

Thermal stress calculations, qhov twg ib tug qis modulus ib feem offsets - tab sis tsis tshem tawm - kev ntxhov siab los ntawm restrained thermal expansion.

Dab tsi stainless hlau qib tuav Modulus zoo tshaj plaws ntawm qhov kub siab?

Duplex stainless steels pib nrog ib tug me ntsis siab dua chav tsev- kub modulus tshaj tus qauv austenitic qib thiab khaws cia ib tug piv los yog me ntsis zoo dua feem ntawm qhov nruj los ntawm lawv cov kev pab cuam ntau yam, thaum ferritic qib taug qab ze rau austenitic tus cwj pwm hauv qab lawv cov kev ua hauj lwm kub qab nthab; npib tsib xee-raws li alloys feem ntau tuav cov feem siab tshaj plaws ntawm chav tsev-temperature modulus ntawm qhov kub siab tshaj plaws.

Qhov feem pua ​​poob hauv modulus los ntawm chav tsev kub mus rau qhov ntsuas kub siab yog qhov dav zoo sib xws nyob rau hauv cov qauv stainless tsev neeg - feem ntau nyob rau hauv thaj tsam ntawm 20–30% los ntawm 600℃- vim hais tias lub hauv paus physics (lattic expansion thiab vibration) cuam tshuam rau tag nrho cov hlau -raws li thiab nickel{6}} raws li ib yam. Qhov sib txawv ntawm cov qhab nia yog li ntawd ntau ntxiv txog qhov pib thiab qhov ntsuas kub ntawm lub qab nthab ntau dua li qhov sib txawv ntawm qhov poob qis: duplex qib pib roughly 2-5% stiffer nyob rau hauv chav tsev kub tshaj austenitic qib, thiab npib tsib xee- hlau- chromium alloys txuas ntxiv usable degrees qhov kev pab cuam ntau tshaj ib puas degrees. Cov kev txwv cov tswv yim, uas tau tsav los ntawm lub zog thiab kev xav txog oxidation ntau dua li modulus ib leeg.

Modulus Reduction cuam tshuam li cas rau buckling thiab kem tsim ntawm qhov kub thiab txias?

Vim hais tias elastic tseem ceeb buckling load yog ncaj qha proportional rau modulus, ib tug 20% ​​txo nyob rau hauv E ntawm elevated kub ua roughly ib tug 20% ​​txo nyob rau hauv ib tug tseem ceeb buckling load rau tib tus tswv cuab geometry, uas yuav hloov ib kem los yog plhaub los ntawm ib tug txaus kev nyab xeeb margin ntawm chav tsev kub mus rau ib tug tsis txaus ib tug ntawm kev khiav hauj lwm kub yam tsis muaj kev hloov nyob rau hauv daim ntawv thov load.

Classical elastic (Euler) buckling kev sib raug zoo qhia txog qhov ncaj qha dependence:

Pᶄᵣ=π²EI / (KL)²

qhov twg Pᶄᵣ yog qhov tseem ceeb buckling load, E yog lub modulus ntawm elasticity ntawm kev khiav hauj lwm kub, Kuv yog tus tswv cuab lub sij hawm ntawm inertia, K yog qhov zoo qhov ntev, thiab L yog qhov ntev unbraced. Txhua lwm lo lus nyob rau hauv kab zauv no yog ib tug taag geometric los yog ciam teb - tej yam khoom, yog li qhov tseem ceeb buckling load txav nyob rau hauv ncaj qha feem rau modulus.

Qhov no yog vim li cas slender compression cov tswv cuab - rauv txhawb cov kab, nyias -cov hlab ntsha phab ntsa nyob rau hauv sab nraud siab, unbraced piping khiav - yuav tsum tau buckling checks ua nrog tus nqi modulus ntawm qhov tseeb ua hauj lwm kub, tsis yog chav tsev - kub tus nqi siv rau cov ntaub ntawv pov thawj. Kev siv chav - kub E hauv kev kuaj buckling ntawm cov qauv kub tsis yog -conservative thiab muaj peev xwm txhais tau tias overstate cov npoo muaj.

Yuav Ua Li Cas Tsim Codes Account rau Modulus Variation nrog Kub?

Cov qauv tsim loj yuav tsum tau nce siab - qhov ntsuas kub ntawm qhov ntsuas kub yuav tsum tau siv ncaj qha rau hauv kev xam tsim - ASME Tshooj II-D tabulates E piv rau qhov kub thiab txias los ntawm alloy rau cov cuab yeej siv siab, Eurocode 3 siv qhov kub thiab txias -nyob ntawm qhov txo qis rau kev siv cov qauv thiab hluav taws xob tsim, thiab cov khoom siv hlau tsis sib haum - cov khoom siv steel hlau. elevated - kub tsim tsis yog raws li ib chav tsev - kub modulus tus nqi.

Table 2. Kev sib piv ntawm qhov loj npaum li cas cov qauv tsim thiab cov qauv siv nyob rau qhov kub thiab txias - nyob ntawm cov qauv ntawm elasticity.

Txawm hais tias txawv cov qauv - ncaj qha tabulated qhov tseem ceeb piv rau qhov kub thiab txias - nyob ntawm qhov txo qis - tag nrho peb txoj hauv kev qhia tib qhov yuav tsum tau ua: lub modulus siv nyob rau hauv ib deflection, buckling, los yog txhav suav yuav tsum sib haum mus rau cov khoom siv qhov tseeb kev khiav hauj lwm los yog raug kub 3}, tsis yog nws qhov kub thiab txias.

Yuav Ua Li Cas Cov Kws Ua Haujlwm yuav kho cov qauv tsim rau kev nce siab -Tsuas Cov Qauv Stainless?

Cov kws ua haujlwm yuav tsum txheeb xyuas qhov ntsuas kub siab tshaj plaws rau txhua qhov kev kuaj xyuas, rub tus nqi sib xws ntawm cov lus siv code es tsis yog defaulting rau chav tsev kub, thiab re-khiav deflection, buckling, thiab zaus xam ntawm tus nqi ntawd - kho modulus txo raws li tus qauv kev tawm tswv yim, kev xaiv tsis pub dhau kev ntxhov siab.

Ib qho kev ua tiav rau kev sib koom ua ke ntawm kev txo qis hauv kev tsim qauv:

1. Tsim kom muaj kev tswj xyuas qhov kub thiab txiasrau txhua daim tshev - qhov no yuav txawv ntawm cov txheej txheem dej kub thiab yuav tsum muaj kev cuam tshuam qhov phem tshaj plaws - cov xwm txheej tsis tu ncua, tsis yog luv luv.

2. Rub qhov kub thiab txias - kho moduluslos ntawm cov lus siv tau (ASME II-D, Eurocode 3, lossis cov ntawv qhia txog kev tsim qauv tsis zoo) es tsis yog siv chav ntawv pov thawj- tus nqi ntsuas kub los ntawm daim ntawv qhia txog zeb.

3. Re- xyuas cov txwv deflectionsiv cov kev txo qis, txij li cov kev txwv tsis pub siv feem ntau yog thawj qhov kev kuaj xyuas kom tsis txhob muaj qhov kub thiab txias, txawm tias ua ntej lub zog margins dhau los ua kev txhawj xeeb.

4. Re-xyuas buckling muaj peev xwmrau ib qho slender los yog nyias -cov tswv cuab ntawm phab ntsa compression, siv cov kev txo qis ncaj qha rau hauv qhov sib npaug ntawm qhov tseem ceeb.

5. Document qhov kub thiab txiassiv rau txhua tus nqi modulus nyob rau hauv cov ntaub ntawv tsim, txij li tus qauv tsim uas tsim nyog ntawm ib qho kev ua haujlwm kub yuav tsis tsim nyog yog tias qhov kev pabcuam tiag tiag kub tom qab nce ntxiv.

Cov lus nug nquag

Puas yog modulus ntawm elasticity poob ua rau kev puas tsuaj mus tas li rau stainless hlau?

Tsis yog. Modulus txo yog qhov thim rov qab, elastic- qhov tshwm sim ntau yam - cov khoom siv rov ua dua nws chav- qhov kub thiab txias modulus thaum nws txias rov qab, tsis zoo li creep puas lossis metallurgical degradation, uas tuaj yeem mus tas li.

Puas yog modulus txo tib yam li qhov poob ntawm lub zog ntawm qhov kub thiab txias?

Tsis yog, lawv muaj feem cuam tshuam tab sis cov khoom sib txawv. Modulus tswj kev nruj thiab elastic deflection, thaum lub zog tawm los tswj qhov kev ntxhov siab ntawm qhov pib deformation mus tas li; ob qho tib si poob nrog qhov kub thiab txias, tab sis lawv tau nyeem los ntawm cov lus sib cais thiab siv rau hauv kev suav sib txawv.

Thaum twg qhov kub ntawm qhov kev txo qis modulus dhau los ua qhov kev txhawj xeeb tsim muaj txiaj ntsig?

Feem ntau cov engineers pib qhia meej txog kev txo qis ntawm kev hloov pauv ib zaug cov hlau kub kub siab tshaj li 150-200℃(300-390℃F), txij li hauv qab no qhov txo qis hauv chav- qhov kub thiab txias feem ntau yog me me txaus kom poob rau hauv cov qauv tsim qauv rau feem ntau cov qib stainless.

Puas yog nickel alloys ib txwm ua haujlwm zoo dua stainless hlau hauv kev tuav tswj?

Feem ntau yog ntawm qhov kub thiab txias, tab sis qhov ua tau zoo yog nyob ntawm qhov tshwj xeeb alloys raug muab piv thiab qhov kub thiab txias hauv nqe lus nug; ntawm qhov nruab nrab qhov kub siab qhov sib txawv ntawm qhov dej- xaiv austenitic stainless qib thiab nickel alloy yuav me me, nrog rau cov nickel alloy qhov zoo dua feem ntau tsav los ntawm lub zog thiab oxidation tsis kam ntawm qhov kub thiab txias tshaj stainless hlau qhov kev ua tau zoo.

Modulus ntawm elasticity puas tuaj yeem kuaj ncaj qha ntawm ib qho hauv -kev pabcuam?

Yog lawm, siv cov tswv yim xws li kev ntsuas ntsuas ntsuas ultrasonic lossis kev ntsuas kev sib txawv ntawm lub zog, txawm hais tias feem ntau cov hom phiaj tsim engineers cia siab rau cov cai tshaj tawm -tabulated qhov tseem ceeb rau cov alloy tshwj xeeb es tsis yog teb - kuaj modulus ncaj qha.