查看“︁弯曲模量”︁的源代码

'''弯曲模量'''（flexural modulus）<ref>{{Cite web |url=http://www.instron.com/wa/glossary/Modulus-in-Bending.aspx |title=Modulus in Bending |access-date=2015-06-02 |archive-date=2011-02-16 |archive-url=https://web.archive.org/web/20110216184542/http://www.instron.com/wa/glossary/Modulus-in-Bending.aspx }}</ref>為一[[力學]]名詞．是指在一材料弯曲變形，或是可能會彎曲的情形下[[應力]]和[[應變]]的比值。弯曲模量可以用弯曲測試（[[ASTM]] D 790）下應力應變曲線的斜率，其單位是面積面積下的力<ref>[http://www.makeitfrom.com/info/?about=Flexural_Modulus Flexural Modulus: Definition] {{webarchive|url=https://web.archive.org/web/20110821054420/http://www.makeitfrom.com/info/?about=Flexural_Modulus |date=2011-08-21 }}</ref>，弯曲模量是[[內含及外延性質|內含性質]]。

[[File:Flexural modulus measurement.png|thumb|upright=2.0|弯曲模量量測]]
右圖是一個長方形樑的三點測試，寬度為''w''，高度為''h''，''L''是外側兩個支持點之間的距離，''d''是因為在中間受力''F''而產生的形變，其弯曲模量為<ref>{{Cite web |url=http://www.engineersedge.com/strength_of_materials.htm |title=Strength of Materials - Mechanics of Materials |access-date=2015-06-02 |archive-date=2022-01-28 |archive-url=https://web.archive.org/web/20220128083801/https://www.engineersedge.com/strength_of_materials.htm }}</ref>：
:<math>
E_{\mathrm{bend}} = \frac {L^3 F}{4 w h^3 d}
</math>
針對線性的樑理論<math>
d = \frac {L^3 F}{48 I E } </math>
針對長方形的樑，<math> I = \frac{1}{12}wh^3 </math>

因此
<math>
E_{\mathrm{bend}} = E </math>（[[弹性模量]]）

若是[[各向同性]]材料（像是玻璃、金屬或是塑膠）上施加很小的應變。其彎曲[[弹性模量]]等於拉伸模量（[[杨氏模量]]）或是壓縮模量。不過若是像木材之類的各向異性材料，各模量不一定相等。[[複合材料]]（像纖維強化塑膠）<ref>{{Cite book |last=Tsai |first=S. W. |title=Composite Materials, Testing and Design |date=December 1979 |publisher=ASTM |isbn=9780803103078 |pages=247}}</ref><ref name=":0">{{Cite book|last=Askeland|first=Donald R.|url=https://www.worldcat.org/oclc/903959750|title=The science and engineering of materials|others=Wright, Wendelin J.|year=2016|isbn=978-1-305-07676-1|edition=Seventh|location=Boston, MA|pages=200|oclc=903959750|access-date=2024-04-09|archive-date=2021-05-31|archive-url=https://web.archive.org/web/20210531151448/https://www.worldcat.org/title/science-and-engineering-of-materials/oclc/903959750|dead-url=no}}</ref>或是生物組織<ref>{{Cite journal |last1=Chahine |first1=Nadeen O. |last2=Wang |first2=Christopher C-B. |last3=Hung |first3=Clark T. |last4=Ateshian |first4=Gerard A. |title=Anisotropic strain-dependent material properties of bovine articular cartilage in the transitional range from tension to compression |url=https://archive.org/details/sim_journal-of-biomechanics_2004-08_37_8/page/1251 |date=August 2004 |journal=Journal of Biomechanics |volume=37 |issue=8 |pages=1251–1261 |doi=10.1016/j.jbiomech.2003.12.008 |issn=0021-9290 |pmc=2819725 |pmid=15212931}}</ref>是二種或多種材料的異質組合，各自有其材料特質，因此其弯曲模量、拉伸模量及壓縮模量可能都不相同。

== 相關條目 ==
* {{link-en|彎曲強度|Flexural strength}}
* [[弹性模量]]

==參考資料==
{{Reflist}}

[[Category:材料科學]]
[[Category:彈性]]