Modulus ntawm elasticity yog lub cev muaj nuj nqis uas ua rau tus cwj pwm elastic ntawm cov khoom siv thaum lub zog sab nraud raug siv rau nws hauv ib qho kev taw qhia. Tus cwj pwm elastic ntawm cov khoom txhais tau tias nws deformation hauv cheeb tsam elastic.
Keeb kwm ntawm kev kawm ntawm elasticity ntawm cov ntaub ntawv
Lub cev txoj kev xav ntawm lub cev elastic thiab lawv tus cwj pwm nyob rau hauv kev ua ntawm sab nraud quab yuam tau txiav txim siab nthuav dav thiab kawm los ntawm tus kws tshawb fawb Askiv ntawm xyoo pua 19th, Thomas Young. Txawm li cas los xij, lub tswv yim ntawm elasticity tau tsim rov qab rau xyoo 1727 los ntawm Swiss mathematician, physicist thiab philosopher Leonhard Euler, thiab thawj qhov kev sim uas muaj feem xyuam rau lub modulus ntawm elasticity tau ua nyob rau hauv 1782, uas yog, 25 xyoo ua ntej ua hauj lwm ntawm Thomas Jung., los ntawm Venetian mathematician thiab philosopher Jacopo Ricatti.
Thomas Young qhov txiaj ntsig yog qhov tseeb tias nws tau muab txoj kev xav ntawm elasticity ib lub ntsej muag niaj hnub zoo nkauj, uas tom qab ntawd tau ua raws li qhov yooj yim thiab tom qab ntawd ua rau Hooke txoj cai.
Lub cev ntawm elasticity
Txhua lub cev muaj cov atoms, nruab nrab ntawm lub zog ntawm kev nyiam thiab kev tawm tsam. Qhov sib npaug ntawm cov zog no yoglub xeev thiab parameters ntawm cov teeb meem nyob rau hauv muab tej yam kev mob. Lub atoms ntawm lub cev muaj zog, thaum tsis tseem ceeb sab nraud quab yuam ntawm nro los yog compression yog siv rau lawv, pib hloov, tsim ib tug quab yuam nyob rau hauv cov kev taw qhia thiab sib npaug ntawm qhov loj, uas nyhav rov qab cov atoms rau lawv thawj lub xeev.
Nyob rau hauv cov txheej txheem ntawm xws li hloov chaw ntawm atoms, lub zog ntawm tag nrho lub cev nce. Kev sim qhia tau hais tias ntawm cov kab mob me me lub zog yog proportional rau square ntawm cov hom no. Qhov no txhais tau hais tias lub zog, ua ib tug derivative nrog rau lub zog, hloov mus rau proportional rau thawj lub zog ntawm lub zog, uas yog, nws nyob ntawm linearly rau nws. Teb cov lus nug, dab tsi yog qhov modulus ntawm elasticity, peb tuaj yeem hais tias qhov no yog qhov coefficient ntawm proportionality ntawm lub zog ua rau lub atom thiab deformation uas lub zog no ua rau. Qhov dimension ntawm Young's modulus yog tib yam li qhov dimension ntawm siab (Pascal).
Elastic limit
Raws li cov ntsiab lus, cov qauv ntawm elasticity qhia tias yuav tsum muaj kev ntxhov siab npaum li cas rau cov khoom kom nws deformation yog 100%. Txawm li cas los xij, tag nrho cov khib nyiab muaj qhov txwv elastic sib npaug li 1% strain. Qhov no txhais tau hais tias yog siv lub zog tsim nyog thiab lub cev deformed los ntawm tus nqi tsawg dua 1%, tom qab qhov kev txiav tawm ntawm lub zog no, lub cev rov qab zoo li qub thiab qhov ntev. Yog tias siv zog ntau dhau, qhov deformation tus nqi siab tshaj 1%, tom qab kev txiav tawm ntawm sab nraud quab yuam, lub cev yuav tsis rov qab nws qhov qub qub. Nyob rau hauv rooj plaub tom kawg, ib tug hais txog lub hav zoov ntawm ib tug residual deformation, uas yogpov thawj tias qhov elastic txwv ntawm cov khoom tau dhau lawm.
Young's modulus in action
Txhawm rau txiav txim siab cov qauv ntawm elasticity, nrog rau kom nkag siab txog kev siv nws, koj tuaj yeem muab piv txwv yooj yim nrog lub caij nplooj ntoos hlav. Ua li no, koj yuav tsum coj lub caij nplooj ntoos hlav hlau thiab ntsuas thaj tsam ntawm lub voj voog uas nws cov coils tsim. Qhov no yog ua tiav siv cov qauv yooj yim S=πr², qhov twg n yog pi sib npaug rau 3.14 thiab r yog lub vojvoog ntawm lub caij nplooj ntoos hlav.
Tom ntej, ntsuas qhov ntev ntawm lub caij nplooj ntoos hlav l0 yam tsis muaj kev thauj khoom. Yog hais tias koj dai ib qho load ntawm huab hwm coj m1 rau lub caij nplooj ntoos hlav, ces nws yuav nce nws qhov ntev mus rau ib qho nqi l1. Lub modulus ntawm elasticity E tuaj yeem xam raws li kev paub ntawm Hooke txoj cai los ntawm cov mis: E=m1gl0/(S(l 1-l0)), qhov twg g yog lub caij nplooj zeeg dawb acceleration. Nyob rau hauv cov ntaub ntawv no, peb nco ntsoov tias tus nqi ntawm deformation ntawm lub caij nplooj ntoos hlav nyob rau hauv lub elastic cheeb tsam yuav zoo heev tshaj 1%.
Kev Paub Tus Hluas tus qauv tso cai rau koj los kwv yees tus nqi ntawm deformation nyob rau hauv qhov kev txiav txim ntawm ib qho kev ntxhov siab. Hauv qhov no, yog tias peb dai lwm pawg m2 rau lub caij nplooj ntoo hlav, peb tau txais tus nqi hauv qab no ntawm tus txheeb ze deformation: d=m2g / (SE), qhov twg d - txheeb ze deformation hauv cheeb tsam elastic.
Isotropy thiab anisotropy
Modulus ntawm elasticity yog tus yam ntxwv ntawm cov khoom uas piav txog lub zog ntawm kev sib raug zoo ntawm nws cov atoms thiab molecules, txawm li cas los xij ib qho khoom muaj peev xwm muaj ntau qhov sib txawv ntawm Young's moduli.
Qhov tseeb yog tias cov khoom ntawm txhua qhov khoom nyob ntawm nws cov qauv sab hauv. Yog hais tias cov khoom zoo ib yam nyob rau hauv tag nrho cov lus qhia spatial, ces peb tab tom tham txog cov khoom siv isotropic. Cov khoom zoo li no muaj cov qauv zoo sib xws, yog li qhov kev txiav txim ntawm ib qho kev quab yuam sab nraud nyob rau hauv cov lus qhia sib txawv ntawm lawv ua rau tib cov tshuaj tiv thaiv los ntawm cov khoom. Tag nrho cov ntaub ntawv amorphous yog isotropic, xws li roj hmab lossis iav.
Anisotropy yog qhov tshwm sim uas tshwm sim los ntawm kev vam khom ntawm lub cev ntawm cov khoom lossis cov kua ntawm kev coj ua. Tag nrho cov hlau thiab alloys raws li lawv muaj ib los yog lwm yam siv lead ua lattice, uas yog, ib qho kev txiav txim, tsis yog ib tug chaotic kev npaj ntawm ionic cores. Rau cov ntaub ntawv zoo li no, lub modulus ntawm elasticity nws txawv nyob ntawm seb lub axis ntawm kev ua ntawm sab nraud kev nyuaj siab. Piv txwv li, hlau nrog cubic symmetry, xws li txhuas, tooj liab, nyiaj, refractory hlau, thiab lwm yam, muaj peb yam Young's moduli.
Shear modulus
Kev piav qhia ntawm cov khoom elastic ntawm txawm tias ib qho khoom siv isotropic tsis xav tau kev paub txog ib tus Hluas modulus. Vim hais tias, ntxiv rau qhov nro thiab compression, cov khoom siv tuaj yeem cuam tshuam los ntawm shear stresses lossis torsional stresses. Hauv qhov no, nws yuav hnov mob txawv rau sab nraud quab yuam. Los piav qhia txog elastic shear deformation, ib qho piv txwv ntawm Young's modulus, shear modulus, lossis modulus ntawm elasticity ntawm ob hom yog qhia.
Txhua cov ntaub ntawv tiv thaiv shear stresses tsawg dua nro lossis compression, yog li tus nqi shear modulus rau lawv yog 2-3 npaug tsawg dua tus nqi ntawm Young's modulus. Yog li, rau titanium, uas nws Young's modulus yog sib npaug rau 107 GPa, lub shear modulus yogTsuas yog 40 GPa, rau cov hlau cov duab no yog 210 GPa thiab 80 GPa, feem.
Modulus ntawm elasticity ntawm ntoo
Ntoo yog cov khoom siv anisotropic vim ntoo fibers yog taw qhia raws ib qho kev taw qhia. Nws yog nyob ntawm cov fibers uas lub modulus ntawm elasticity ntawm ntoo yog ntsuas, vim nws yog 1-2 txiav txim ntawm qhov loj me me hla cov fibers. Kev paub txog Young's modulus rau ntoo yog qhov tseem ceeb thiab raug coj mus rau hauv tus account thaum tsim cov vaj huam sib luag ntoo.
Qhov tseem ceeb ntawm cov qauv ntawm elasticity ntawm ntoo rau qee hom ntoo muaj nyob rau hauv cov lus hauv qab no.
| Tree view | Young's modulus in GPa |
| Laurel tsob ntoo | 14 |
| Eucalyptus | 18 |
| Cedar | 8 |
| Spruce | 11 |
| Pine | 10 |
| Oak | 12 |
Nws yuav tsum raug sau tseg tias qhov txiaj ntsig tau muab tuaj yeem sib txawv txog li 1 GPa rau ib tsob ntoo tshwj xeeb, txij li nws cov Young's modulus cuam tshuam los ntawm qhov ntom ntawm cov ntoo thiab kev loj hlob.
Shear moduli rau ntau hom ntoo yog nyob rau hauv thaj tsam ntawm 1-2 GPa, piv txwv li, rau ntoo thuv nws yog 1.21 GPa, thiab rau ntoo qhib 1.38 GPa, uas yog, ntoo xyaum tsis tiv thaiv shear stresses. Qhov tseeb no yuav tsum tau coj mus rau hauv tus account nyob rau hauv kev tsim cov ntoo load-bearing lug, uas yog tsim los ua hauj lwm nyob rau hauv nruj nro los yog compression.
Elastic yam ntxwv ntawm cov hlau
Thaum muab piv nrog cov Young's modulus ntawm ntoo, qhov nruab nrab qhov tseem ceeb ntawm cov nqi no rau cov hlau thiab alloys yog qhov kev txiav txim siab ntau dua, raws li qhia hauv cov lus hauv qab no.
| Metal | Young's modulus in GPa |
| Bronze | 120 |
| Copper | 110 |
| Steel | 210 |
| Titanium | 107 |
| Nickel | 204 |
Elastic zog ntawm cov hlau uas muaj lub cubic syngony tau piav qhia los ntawm peb qhov elasticity. Cov hlau xws li tooj liab, npib tsib xee, txhuas, hlau. Yog hais tias ib tug hlau muaj ib tug hexagonal syngony, ces 6 qhov tas mus li twb xav tau los piav txog nws cov yam ntxwv elastic.
Rau cov tshuab hlau, Young's modulus yog ntsuas nyob rau hauv 0.2% strain, raws li cov txiaj ntsig loj tuaj yeem tshwm sim hauv cheeb tsam inelastic.
