Modulu na-agbatị agbatị

Igwe ngbanwe (nke mgbanwe dị ka modulus of elasticity ) bụ ndị nke mbụ nke ihe ma ọ bụ ihe na- achị nrụrụ ngbanwe (ya bụ, na-azụ nke na-na-adịgide adịgide) mgbe ụfọdụ ndụ na ya.

Nkọwa

Akọwapụtara modul nke ihe na-agbanwe agbanwe dị ka mkpọda nke ire ya na mpaghara nrụrụ ala: [1] Ihe siri ike ga-enwe modul ngbanwe dị elu. Modul nke na-agbanwe agbanwe nwere ụdị:

\delta \ {\stackrel {\text{def}}{=}}\ {\frac {\text{stress}}{\text{strain}}}

ebe ị bụ ike na-eme ka nrụrụ kewara site na mpaghara ebe a na-etinye ike na àgwà bụ oke nke ihe na ụfọdụ paramita agba nrụrụ na uru mbụ nke paramita ahụ.

Ebe ọ bụ na nje bụ a dimensionless quantity, nkeji nke $\delta$ ga-abụ otu ihe ahụ dị ka nkeji nke nrụgide. ^[1]

Elastic Constant na Moduli

Elastic na-agbanwe agbanwe bụ paramita dị iche iche na-achọpụta isi ike nke ihe na nzaghachi na-atụgharị ma bụrụ ihe dị mkpa n'ịkọwa adịghị na-agbanwe nke ihe. Ihe ndị a na-adịgide adịgide na-etolite ihe dị na matrix stiffness na tensor notation, nke na-ada ada na ada site na nha nha n'ahịrị na ihe anisotropic . A na-akpọkarị Cijkl, ebe i, j, k, na l bụ ntụzịaka nhazi, ihe ndị a na-agbanwe agbanwe dị mkpa maka ọchịchị otú si eme n'okpuru ibu dị iche iche. ^[2]

Ụdị modul na-agbanwe agbanwe

Ịkọwapụta ka a ga-esi tụọ nrụgide na nsogbu, gụnyere ntụzịaka, na-enye ohere ka akọwapụta ọtụtụ ụdị moduli na-agbanwe. Ndị mbụ anọ bụ:

Modules na-eto eto ( E ) na-akọwa nhịahụ na mkpakọ elasticity, ma ọ bụ ọchịchọ nke ihe na-agbanwe n'akụkụ axis mgbe a na-etinye ike megidere n'akụkụ axis; A kọwapụtara ya dị ka oke nrụrụ aka na nhụsi ike . A na-akpọkarị ya naanị dị ka modul na-agbanwe agbanwe .
Ọkpụkpọ mkpụkọ ma ọ bụ modulu nke siri ike ( G ma ọ bụ $\mu \,$ Lamé second parameter) na-akọwa ọchịchọ ihe na-akpacha ihe (nrụrụ ọdịdị na ụda olu mgbe nile) mgbe ndị agha na-emegide mere ya; A kọwapụtara ya dị ka nrụgide shiee n'ihi nsogbu nke shii . Modules shear bụ akụkụ nke mpụta nke viscosity .
Modules buru ibu ( K ) na-akọwa ngbanwe volumetric, ma ọ bụ ọchịchọ nke ihe na-emebi n'akụkụ niile mgbe ejiri otu n'otu n'otu n'akụkụ niile; A kọwapụtara ya dị ka nrụgide volumetric n'elu ụdị volumetric, ọ bụkwa ntụgharị nke mkpakọ . Nnukwu modul bụ ndọtị modul nke Young ruo akụkụ atọ.
Mgbanwe mgbanwe (E _flex ) na-akọwa ihe ihe ahụ na-eme mgbanwe mgbe emere ya obere oge .

Moduli abụọ ọzọ na- agbanwe bụ paramita mbụ Lamé, λ, na P-wave modulus, M, dị ka ejiri na atụnyere modulus nyere ntụnyere n'okpuru. Homogeneous na isotropic (yiri n'ụdị niile) ihe (sikedo) nwere ha (linear) elastic Njirimara n'ụzọ zuru ezu ezu saịtị na abụọ elastic moduli, na otu onye nwere ike họrọ ọ ụzọ ụzọ. Nyere ụdị moduli na- agbanwe agbanwe, agbatị ike ịgbakọ moduli ndị ọzọ dị ka usoro dị n'okpuru na njedebe nke ibe.

Mmiri inviscid iche iche n'ihi na ha akara ike ike ahia shiee, nke ihe na modul nke shear na-ihe efu. Nke a pụtakwara na modul nke Young maka otu a na-ese efu.

N'edemede ụfọdụ, a na-akpọ modulus nke ngbanwe dị ka ihe na-agbanwe agbanwe, ebe ọnụọgụ mgbanwe na-ezo aka dị ka modulus elasticity .

Ngụkọ Theory arụrụ arụ njupụta nke Modul Elastic

Theory Functional Density (DFT) na-enye ụzọ a ụkwụ na ya maka ọtụtụ ụdị moduli na-agbanwe agbanwe nke na-pụtara njiri mara dị iche iche nke omume ihe na mgbakasị usoro. Jiri ngwa DFT dị ka VASP, Quantum ESPRESSO ma ọ bụ ABINIT . N'ozuzu, na-eduzi ule iji hụ na-adabereghị na usoro usoro na ịdị ka n akara nke k-point mesh, ike ọkọ ụgbọ elu, na nha cell simulation..

Modulus Young (E) - tinye obere mgbanwe mgbanwe na oke lattice n'akụkụ otu axis wee gbakọọ nzaghachi nrụgide kwekọrọ na iji DFT. A na-agbakọ modul ntorobịa dị ka E = σ / ϵ, ebe σ bụ nrụgide na ϵ bụ nsogbu ahụ. ^[3]
1. Nhazi mmalite: Malite site na nhazi ahụ dị jụụ nke ihe. Atọm niile kwesịrị ịdị na steeti ike kacha nta (ya bụ, steeti ume kacha nta nwere ikike efu na atọm) tupu etinyere nrụrụ ọ bụla. ^[4]
2. Udiri Uniaxial na-abawanye: Tinye obere nsogbu na-abawanye na lattice kristal n'akụkụ otu axis. Nsogbu a na-abụkarị uniaxial, nke pụtara na ọ na-agbatị ma ọ bụ na-akpakọ lattice n'otu akụkụ ma na-edobe akụkụ ndị ọzọ mgbe niile ma ọ bụ oge.
3. Gbakọọ nrụgide: Maka nhazi ọ bụla nwere nsogbu, mee ngụkọ DFT iji gbakọọ nrụgide nrụgide na-akpata. Nke a gụnyere idozi nha Kohn-Sham iji chọta njupụta elektrọn steeti ala na ike n'okpuru ọnọdụ ọjọọ.
4. Usoro mgbakasị-nsogbu : Chee echiche mgbakasị ahụ gbakọọ na eriri etinyere iji mepụta usoro mgbakasị ahụ. Mkpọda nke mbụ, nke ahịrị akụkụ nke usoro a na-enye modul nke Young. Na mgbakọ na mwepụ, a na-agbakọ modulus nke Young site na iji usoro E = σ / ϵ, ebe σ bụ nrụgide na ϵ bụ nsogbu ahụ.
Shear Modulus (G)
1. Nhazi mmalite: Malite site na nhazi ahụ dị jụụ nke ihe. Atọm niile kwesịrị ịdị n'ọnọdụ ike kacha nta na-enweghị ike fọdụrụnụ . (ya bụ, opekempe ike steeti nwere ikike efu na atọm) tupu etinyere nrụrụ ọ bụla.
2. Ngwa ngwungwu Shear: Tinye obere mkpirisi nke nchara n'ihe. Akpụkpọ anụ na-abụkarị ihe ndị na-adịghị na diagonal na eriri eriri ahụ, na-emetụta ọdịdị ahụ mana ọ bụghị olu nke cell kristal. ^[5]
3. Mgbakọ nrụgide: Maka nhazi nke ọ bụla nwere nrụnye shear etinyere, mee ngụkọ DFT iji chọpụta ihe mgbakasị ahụ na-akpata.
4. Shear Stress vs. Shear Strain Curve : Kpebie nrụgide shiee gbakọọ megide eriri shiee etinyere maka mmụba ọ bụla. Mkpọda nke nrụgide nrụgide na mpaghara linear ya na-enye modul nke shear, G = τ / γ, ebe τ bụ nrụgide siri ike na γ bụ nke a na-etinye n'ọrụ.
Nnukwu Modul (K)
1. Nhazi mmalite: Malite site na nhazi ahụ dị jụụ nke ihe. Ọ dị mkpa na emeziwanye ihe ahụ n'ụzọ zuru oke, na-ahụ na mgbanwe ọ bụla na olu bụ naanị n'ihi nrụgide etinyere.
2. Mgbanwe olu: na-agbanwewanye ụda cell cell kristal, ma ọ bụ mpikota onu ma ọ bụ gbasaa ya. A na-emekarị nke a site n'ịkọba parampat lattice n'ụdị.
3. Gbakọọ nrụgide: Maka olu ọ bụla gbanwere, mee ngụkọ DFT iji chọpụta nrụgide achọrọ iji dowe olu ahụ. DFT na-enye ohere maka mgbako nke nrụgide nrụgide nke na-enye ihe nrịbama nke nrụgide dị n'ime.
4. Nrụgide-Volume Curve : Kpee nrụgide etinyere megide mgbanwe olu ga-apụta. Enwere ike gbakọọ modul dị ukwuu site na mkpọda nke mgbanaka a na mpaghara eriri ahịrị. A kọwapụtara modul dị ukwuu dị ka K = - VdVdP, ebe V bụ ụda mbụ, dP bụ mgbanwe nrụgide, na dV bụ mgbanwe na olu. ^[6]

Hụkwa

Ntụaka

↑ Beer (2009). Mechanics of Materials. McGraw Hill. ISBN 978-0-07-015389-9.
↑ Schreiber (1974). Elastic constants and their measurement. New York: McGraw-Hill. ISBN 978-0-07-055603-4.
↑ Alasfar (2022-01-18). "A Review on the Modeling of the Elastic Modulus and Yield Stress of Polymers and Polymer Nanocomposites: Effect of Temperature, Loading Rate and Porosity" (in en). Polymers 14 (3): 360. DOI:10.3390/polym14030360. ISSN 2073-4360. PMID 35160350.
↑ Hadi (2022-08-18). "DFT insights into the electronic structure, mechanical behaviour, lattice dynamics and defect processes in the first Sc-based MAX phase Sc2SnC" (in en). Scientific Reports 12 (1). DOI:10.1038/s41598-022-18336-z. ISSN 2045-2322. PMID 35982080.
↑ Ahmed (May 2023). "DFT based comparative analysis of the physical properties of some binary transition metal carbides XC (X = Nb, Ta, Ti)". Journal of Materials Research and Technology 24: 4808–4832. DOI:10.1016/j.jmrt.2023.04.147. ISSN 2238-7854.
↑ Choudhary (2018-07-12). "Elastic properties of bulk and low-dimensional materials using van der Waals density functional" (in en). Physical Review B 98 (1). DOI:10.1103/PhysRevB.98.014107. ISSN 2469-9950. PMID 32166206.

Ọgụgụ ọzọ

Hartsuijker (2001). Engineering Mechanics, Volume 2. Springer. ISBN 978-1-4020-4123-5.

De Jong (2015). "Charting the complete elastic properties of inorganic crystalline compounds". Scientific Data 2: 150009. DOI:10.1038/sdata.2015.9. PMID 25984348.

[1] Beer (2009). Mechanics of Materials. McGraw Hill. ISBN 978-0-07-015389-9.

[2] Schreiber (1974). Elastic constants and their measurement. New York: McGraw-Hill. ISBN 978-0-07-055603-4.

[3] Alasfar (2022-01-18). "A Review on the Modeling of the Elastic Modulus and Yield Stress of Polymers and Polymer Nanocomposites: Effect of Temperature, Loading Rate and Porosity" (in en). Polymers 14 (3): 360. DOI:10.3390/polym14030360. ISSN 2073-4360. PMID 35160350.

[4] Hadi (2022-08-18). "DFT insights into the electronic structure, mechanical behaviour, lattice dynamics and defect processes in the first Sc-based MAX phase Sc2SnC" (in en). Scientific Reports 12 (1). DOI:10.1038/s41598-022-18336-z. ISSN 2045-2322. PMID 35982080.

[5] Ahmed (May 2023). "DFT based comparative analysis of the physical properties of some binary transition metal carbides XC (X = Nb, Ta, Ti)". Journal of Materials Research and Technology 24: 4808–4832. DOI:10.1016/j.jmrt.2023.04.147. ISSN 2238-7854.

[6] Choudhary (2018-07-12). "Elastic properties of bulk and low-dimensional materials using van der Waals density functional" (in en). Physical Review B 98 (1). DOI:10.1103/PhysRevB.98.014107. ISSN 2469-9950. PMID 32166206.

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