Young's modulus

{{Short description|Mechanical property that measures stiffness of a solid material}}

File:Stress strain ductile.svg for a material under tension or compression.]]

Young's modulus (or the Young modulus) is a mechanical property of solid materials that measures the tensile or compressive stiffness when the force is applied lengthwise. It is the modulus of elasticity for tension or axial compression. Young's modulus is defined as the ratio of the stress (force per unit area) applied to the object and the resulting axial strain (displacement or deformation) in the linear elastic region of the material.

Although Young's modulus is named after the 19th-century British scientist Thomas Young, the concept was developed in 1727 by Leonhard Euler. The first experiments that used the concept of Young's modulus in its modern form were performed by the Italian scientist Giordano Riccati in 1782, pre-dating Young's work by 25 years.The Rational mechanics of Flexible or Elastic Bodies, 1638–1788: Introduction to Leonhardi Euleri Opera Omnia, vol. X and XI, Seriei Secundae. Orell Fussli. The term modulus is derived from the Latin root term modus, which means measure.

Definition

Young's modulus, $E$ , quantifies the relationship between tensile or compressive stress $\sigma$ (force per unit area) and axial strain $\varepsilon$ (proportional deformation) in the linear elastic region of a material:{{cite book |last=Jastrzebski |first=D. |title=Nature and Properties of Engineering Materials |publisher=John Wiley & Sons, Inc |year=1959 |edition=Wiley International}}

$E = \frac{\sigma}{\varepsilon}$

Young's modulus is commonly measured in the International System of Units (SI) in multiples of the pascal (Pa) and common values are in the range of gigapascals (GPa).

Examples:

Rubber (increasing pressure: large length increase, meaning low $E$ )
Aluminium (increasing pressure: small length increase, meaning high $E$ )

=Linear elasticity=

A solid material undergoes elastic deformation when a small load is applied to it in compression or extension. Elastic deformation is reversible, meaning that the material returns to its original shape after the load is removed.

At near-zero stress and strain, the stress–strain curve is linear, and the relationship between stress and strain is described by Hooke's law that states stress is proportional to strain. The coefficient of proportionality is Young's modulus. The higher the modulus, the more stress is needed to create the same amount of strain; an idealized rigid body would have an infinite Young's modulus. Conversely, a very soft material (such as a fluid) would deform without force, and would have zero Young's modulus.

=Related but distinct properties=

Material stiffness is a distinct property from the following:

Strength: maximum amount of stress that material can withstand while staying in the elastic (reversible) deformation regime;
Geometric stiffness: a global characteristic of the body that depends on its shape, and not only on the local properties of the material; for instance, an I-beam has a higher bending stiffness than a rod of the same material for a given mass per length;
Hardness: relative resistance of the material's surface to penetration by a harder body;
Toughness: amount of energy that a material can absorb before fracture.
The point E is the elastic limit or the yield point of the material within which the stress is proportional to strain and the material regains its original shape after removal of the external force.

Usage

Young's modulus enables the calculation of the change in the dimension of a bar made of an isotropic elastic material under tensile or compressive loads. For instance, it predicts how much a material sample extends under tension or shortens under compression. The Young's modulus directly applies to cases of uniaxial stress; that is, tensile or compressive stress in one direction and no stress in the other directions. Young's modulus is also used in order to predict the deflection that will occur in a statically determinate beam when a load is applied at a point in between the beam's supports.

Other elastic calculations usually require the use of one additional elastic property, such as the shear modulus $G$ , bulk modulus $K$ , and Poisson's ratio $\nu$ . Any two of these parameters are sufficient to fully describe elasticity in an isotropic material. For example, calculating physical properties of cancerous skin tissue, has been measured and found to be a Poisson’s ratio of 0.43±0.12 and an average Young’s modulus of 52 KPa. Defining the elastic properties of skin may become the first step in turning elasticity into a clinical tool.{{Cite journal |last1=Tilleman |first1=Tamara Raveh |last2=Tilleman |first2=Michael M. |last3=Neumann |first3=Martino H.A. |date=December 2004 |title=The Elastic Properties of Cancerous Skin: Poisson's Ratio and Young's Modulus |url=https://www.ima.org.il/FilesUploadPublic/IMAJ/0/52/26480.pdf |journal=Israel Medical Association Journal |volume=6 |issue=12 |pages=753–755|pmid=15609889 }} For homogeneous isotropic materials simple relations exist between elastic constants that allow calculating them all as long as two are known:

: $E = 2G(1+\nu) = 3K(1-2\nu).$

=Linear versus non-linear=

Young's modulus represents the factor of proportionality in Hooke's law, which relates the stress and the strain. However, Hooke's law is only valid under the assumption of an elastic and linear response. Any real material will eventually fail and break when stretched over a very large distance or with a very large force; however, all solid materials exhibit nearly Hookean behavior for small enough strains or stresses. If the range over which Hooke's law is valid is large enough compared to the typical stress that one expects to apply to the material, the material is said to be linear. Otherwise (if the typical stress one would apply is outside the linear range), the material is said to be non-linear.

Steel, carbon fiber and glass among others are usually considered linear materials, while other materials such as rubber and soils are non-linear. However, this is not an absolute classification: if very small stresses or strains are applied to a non-linear material, the response will be linear, but if very high stress or strain is applied to a linear material, the linear theory will not be enough. For example, as the linear theory implies reversibility, it would be absurd to use the linear theory to describe the failure of a steel bridge under a high load; although steel is a linear material for most applications, it is not in such a case of catastrophic failure.

In solid mechanics, the slope of the stress–strain curve at any point is called the tangent modulus. It can be experimentally determined from the slope of a stress–strain curve created during tensile tests conducted on a sample of the material.

=Directional materials=

Young's modulus is not always the same in all orientations of a material. Most metals and ceramics, along with many other materials, are isotropic, and their mechanical properties are the same in all orientations. However, metals and ceramics can be treated with certain impurities, and metals can be mechanically worked to make their grain structures directional. These materials then become anisotropic, and Young's modulus will change depending on the direction of the force vector.{{Cite journal| last1=Gorodtsov |first1=V.A. |last2=Lisovenko |first2=D.S. |date=2019 |title=Extreme values of Young's modulus and Poisson's ratio of hexagonal crystals|journal=Mechanics of Materials |language=en |volume=134 |pages=1–8 |doi=10.1016/j.mechmat.2019.03.017 |bibcode=2019MechM.134....1G |s2cid=140493258 }} Anisotropy can be seen in many composites as well. For example, carbon fiber has a much higher Young's modulus (is much stiffer) when force is loaded parallel to the fibers (along the grain). Other such materials include wood and reinforced concrete. Engineers can use this directional phenomenon to their advantage in creating structures.

Calculation

Young's modulus is calculated by dividing the tensile stress, $\sigma(\varepsilon)$ , by the engineering extensional strain, $\varepsilon$ , in the elastic (initial, linear) portion of the physical stress–strain curve:

$E \equiv \frac{\sigma(\varepsilon)}{\varepsilon}= \frac{F/A}{\Delta L/L_0} = \frac{F L_0} {A \, \Delta L}$

where

$E$ is the Young's modulus (modulus of elasticity);
$F$ is the force exerted on an object under tension;
$A$ is the actual cross-sectional area, which equals the area of the cross-section perpendicular to the applied force;
$\Delta L$ is the amount by which the length of the object changes ( $\Delta L$ is positive if the material is stretched, and negative when the material is compressed);
$L_0$ is the original length of the object.

=Force exerted by stretched or contracted material=

Young's modulus of a material can be used to calculate the force it exerts under specific strain.

: $F = \frac{E A \, \Delta L} {L_0}$

where $F$ is the force exerted by the material when contracted or stretched by $\Delta L$ .

Hooke's law for a stretched wire can be derived from this formula:

: $F = \left( \frac{E A} {L_0} \right) \, \Delta L = k x$

where it comes in saturation

: $k \equiv \frac {E A} {L_0} \,$ and $x \equiv \Delta L.$

Note that the elasticity of coiled springs comes from shear modulus, not Young's modulus. When a spring is stretched, its wire's length doesn't change, but its shape does. This is why only the shear modulus of elasticity is involved in the stretching of a spring. {{citation needed|date=April 2021}}

=Elastic potential energy=

The elastic potential energy stored in a linear elastic material is given by the integral of the Hooke's law:

: $U_e = \int {k x}\, dx = \frac {1} {2} k x^2.$

now by explicating the intensive variables:

: $U_e = \int \frac{E A \, \Delta L} {L_0}\, d\Delta L = \frac {E A} {L_0} \int \Delta L \, d\Delta L = \frac {E A \, {\Delta L}^2} {2 L_0}$

This means that the elastic potential energy density (that is, per unit volume) is given by:

: $\frac{U_e} {A L_0} = \frac {E \, {\Delta L}^2} {2 L_0^2} =\frac{1}{2} \times \frac {E\, {\Delta L}}{L_0} \times \frac {\Delta L}{L_0} = \frac {1}{2} \times \sigma(\varepsilon) \times \varepsilon$

or, in simple notation, for a linear elastic material: $u_e(\varepsilon) = \int {E \, \varepsilon}\, d\varepsilon = \frac {1} {2} E {\varepsilon}^2$ , since the strain is defined $\varepsilon \equiv \frac {\Delta L} {L_0}$ .

In a nonlinear elastic material the Young's modulus is a function of the strain, so the second equivalence no longer holds, and the elastic energy is not a quadratic function of the strain:

: $u_e(\varepsilon) = \int E(\varepsilon) \, \varepsilon \, d\varepsilon \ne \frac {1} {2} E \varepsilon^2$

Examples

Image:SpiderGraph YoungMod.gif

Young's modulus can vary somewhat due to differences in sample composition and test method. The rate of deformation has the greatest impact on the data collected, especially in polymers. The values here are approximate and only meant for relative comparison.

class="wikitable sortable" style="text-align:center;"

|+Approximate Young's modulus for various materials

!Material

! data-sort-type="number" |Young's modulus (GPa)

! data-sort-type="number" |Megapound per square inch (M psi){{Cite web|title=Unit of Measure Converter|url=http://www.matweb.com/tools/unitconverter.aspx|access-date=May 9, 2021|website=MatWeb}}

!Ref.

style="text-align:left;" |Aluminium (₁₃Al)

|68

|9.86

|{{Cite web|title=Aluminum, Al|url=http://www.matweb.com/search/DataSheet.aspx?MatGUID=0cd1edf33ac145ee93a0aa6fc666c0e0|access-date=May 7, 2021|website=MatWeb}}{{Cite book |last=Weast |first=Robert C. |title=CRC Handbook of Chemistry and Physics |publisher=CRC Press |year=1981 |isbn=978-0-84-930740-9 |edition=62nd |location=Boca Raton, FL |doi=10.1002/jctb.280500215}}{{Cite book|last=Ross|first=Robert B.|title=Metallic Materials Specification Handbook|publisher=Chapman & Hall|year=1992|isbn=9780412369407|edition=4th|location=London|doi=10.1007/978-1-4615-3482-2}}{{Cite book|last1=Nunes|first1=Rafael|url=http://sme.vimaru.edu.vn/sites/sme.vimaru.edu.vn/files/volume_2_-_properties_and_selection_nonf.pdf|title=Volume 2: Properties and Selection: Nonferrous Alloys and Special-Purpose Materials|last2=Adams|first2=J. H.|last3=Ammons|first3=Mitchell|last4=Avery|first4=Howard S.|last5=Barnhurst|first5=Robert J.|last6=Bean|first6=John C.|last7=Beaudry|first7=B. J.|last8=Berry|first8=David F.|last9=Black|first9=William T.|publisher=ASM International|year=1990|isbn=978-0-87170-378-1|edition=10th|series=ASM Handbook|display-authors=3}}{{Cite book|last=Nayar|first=Alok|title=The Metals Databook|publisher=McGraw-Hill|year=1997|isbn=978-0-07-462300-8|location=New York, NY}}{{Cite book |title=CRC Handbook of Chemistry and Physics|publisher=CRC Press|year=1999|isbn=978-0-84-930480-4|editor-last=Lide|editor-first=David R.|edition=80th|location=Boca Raton, FL|chapter=Commercial Metals and Alloys}}

style="text-align:left;" |Amino-acid molecular crystals

|21–44

|3.05–6.38

|{{Cite journal |last1=Azuri |first1=Ido |last2=Meirzadeh |first2=Elena |last3=Ehre |first3=David |last4=Cohen |first4=Sidney R. |last5=Rappe |first5=Andrew M. |last6=Lahav |first6=Meir |last7=Lubomirsky |first7=Igor |last8=Kronik |first8=Leeor |display-authors=3 |date=November 9, 2015 |title=Unusually Large Young's Moduli of Amino Acid Molecular Crystals |url=http://www.sas.upenn.edu/rappegroup/publications/Papers/Azuri15p13566.pdf |journal=Angewandte Chemie |edition=International |publisher=Wiley |volume=54 |issue=46 |pages=13566–13570 |doi=10.1002/anie.201505813 |pmid=26373817 |via=PubMed |s2cid=13717077}}

style="text-align:left;" |Aramid (for example, Kevlar)

|70.5–112.4

|10.2–16.3

|{{Cite web|date=2017|title=Kevlar Aramid Fiber Technical Guide|url=https://www.dupont.com/content/dam/dupont/amer/us/en/safety/public/documents/en/Kevlar_Technical_Guide_0319.pdf|access-date=May 8, 2021|website=DuPont}}

style="text-align:left;" |Aromatic peptide-nanospheres

|230–275

|33.4–39.9

|{{Cite journal|last1=Adler-Abramovich|first1=Lihi |last2=Kol|first2=Nitzan |last3=Yanai|first3=Inbal |last4=Barlam|first4=David |last5=Shneck|first5=Roni Z. |last6=Gazit|first6=Ehud |last7=Rousso |first7=Itay|display-authors=3 |date=December 17, 2010 |title=Self-Assembled Organic Nanostructures with Metallic-Like Stiffness |journal=Angewandte Chemie |edition=International|publisher=Wiley-VCH |publication-date=September 28, 2010 |volume=49 |issue=51 |pages=9939–9942 |doi=10.1002/anie.201002037 |pmid=20878815|s2cid=44873277 }}

style="text-align:left;" |Aromatic peptide-nanotubes

|19–27

|2.76–3.92

|{{Cite journal |last1=Kol |first1=Nitzan |last2=Adler-Abramovich |first2=Lihi |last3=Barlam |first3=David |last4=Shneck |first4=Roni Z. |last5=Gazit |first5=Ehud |last6=Rousso |first6=Itay |display-authors=3 |date=June 8, 2005 |title=Self-Assembled Peptide Nanotubes Are Uniquely Rigid Bioinspired Supramolecular Structures |url=https://pubs.acs.org/doi/full/10.1021/nl0505896 |journal=Nano Letters |location=Israel |publisher=American Chemical Society |volume=5 |issue=7 |pages=1343–1346 |bibcode=2005NanoL...5.1343K |doi=10.1021/nl0505896 |pmid=16178235 |via=ACS Publications|url-access=subscription }}{{Cite journal |last1=Niu |first1=Lijiang |last2=Chen |first2=Xinyong |last3=Allen |first3=Stephanie |last4=Tendler |first4=Saul J. B. |display-authors=3 |date=June 6, 2007 |title=Using the Bending Beam Model to Estimate the Elasticity of Diphenylalanine Nanotubes |url=https://pubs.acs.org/doi/full/10.1021/la7010106 |journal=Langmuir |publisher=American Chemical Society |volume=23 |issue=14 |pages=7443–7446 |doi=10.1021/la7010106 |pmid=17550276 |via=ACS Publications|url-access=subscription }}

style="text-align:left;" |Bacteriophage capsids

|1–3

|0.145–0.435

|{{cite journal|last1=Ivanovska|first1=Irena L.|last2=de Pablo|first2=Pedro J. |last3=Ibarra |first3=Benjamin |last4=Sgalari |first4=Giorgia |last5=MacKintosh |first5=Fred C. |last6=Carrascosa |first6=José L. |last7=Schmidt |first7=Christoph F. |last8=Wuite |first8=Gijs J. L. |display-authors=3 |date=May 7, 2004 |editor-last=Lubensky |editor-first=Tom C. |title=Bacteriophage capsids: Tough nanoshells with complex elastic properties|journal=Proceedings of the National Academy of Sciences of the United States of America |publisher=The National Academy of Sciences |volume=101 |issue=20 |pages=7600–7605 |bibcode=2004PNAS..101.7600I |doi=10.1073/pnas.0308198101|pmc=419652|pmid=15133147|doi-access=free}}

style="text-align:left;" |Beryllium (₄Be)

|287

|41.6

|{{Cite book|last1=Foley|first1=James C.|title=Powder Materials: Current Research and Industrial Practices III|last2=Abeln|first2=Stephen P.|last3=Stanek|first3=Paul W.|last4=Bartram|first4=Brian D.|last5=Aikin|first5=Beverly|last6=Vargas|first6=Victor D.|publisher= John Wiley & Sons, Inc.|year=2010|isbn=978-1-11-898423-9|editor-last=Marquis|editor-first=Fernand D. S.|location=Hoboken, NJ|pages=263|chapter=An Overview of Current Research and Industrial Practices of be Powder Metallurgy|doi=10.1002/9781118984239.ch32|display-authors=3}}

style="text-align:left;" |Bone, human cortical

|14

|2.03

|{{Cite journal|last1=Rho|first1=Jae Young|last2=Ashman|first2=Richard B.|last3=Turner|first3=Charles H.|date=February 1993|title=Young's modulus of trabecular and cortical bone material: Ultrasonic and microtensile measurements |url=https://www.sciencedirect.com/science/article/abs/pii/002192909390042D|journal=Journal of Biomechanics|publisher=Elsevier |volume=26 |issue=2 |pages=111–119|doi=10.1016/0021-9290(93)90042-d|pmid=8429054|via=Elsevier Science Direct|url-access=subscription}}

style="text-align:left;" |Brass

|106

|15.4

|{{Cite web|title=Overview of materials for Brass|url=http://www.matweb.com/search/DataSheet.aspx?MatGUID=d3bd4617903543ada92f4c101c2a20e5 |access-date=May 7, 2021|website=MatWeb}}

style="text-align:left;" |Bronze

|112

|16.2

|{{Cite web|title=Overview of materials for Bronze|url=http://www.matweb.com/search/datasheet.aspx?MatGUID=66575ff2cd5249c49d76df15b47dbca4|access-date=May 7, 2021 |website=MatWeb}}

style="text-align:left;" |Carbon nitride (CN₂)

|822

|119

|{{Cite journal |last1=Chowdhury |first1=Shafiul |last2=Laugier |first2=Michael T. |last3=Rahman |first3=Ismet Zakia |date=April–August 2004 |title=Measurement of the mechanical properties of carbon nitride thin films from the nanoindentation loading curve |journal=Diamond and Related Materials |volume=13 |issue=4–8 |pages=1543–1548 |bibcode=2004DRM....13.1543C |doi=10.1016/j.diamond.2003.11.063 |via=Elsevier Science Direct}}

style="text-align:left;" |Carbon-fiber-reinforced plastic (CFRP), 50/50 fibre/matrix, biaxial fabric

|30–50

|4.35–7.25

|{{cite web|last=Summerscales|first=John|date=September 11, 2019|title=Composites Design and Manufacture (Plymouth University teaching support materials)|url=https://www.fose1.plymouth.ac.uk/sme/MATS347/MATS347A2%20E-G-nu.htm#E|access-date=May 8, 2021 |website=Advanced Composites Manufacturing Centre|publisher=University of Plymouth}}

style="text-align:left;" |Carbon-fiber-reinforced plastic (CFRP), 70/30 fibre/matrix, unidirectional, along fibre

|181

|26.3

|{{Cite web|last=Kopeliovich|first=Dmitri|date=June 3, 2012|title=Epoxy Matrix Composite reinforced by 70% carbon fibers |url=http://www.substech.com/dokuwiki/doku.php?id=epoxy_matrix_composite_reinforced_by_70_carbon_fibers|access-date=May 8, 2021|website=SubsTech}}

style="text-align:left;" |Cobalt-chrome (CoCr)

|230

|33.4

|{{Cite book|last1=Bose|first1=Susmita|title=Materials for Bone Disorders|last2=Banerjee|first2=Dishary|last3=Bandyopadhyay|first3=Amit|publisher=Academic Press|year=2016|isbn=978-0-12-802792-9|editor-last=Bose|editor-first=Susmita|pages=1–27|chapter=Introduction to Biomaterials and Devices for Bone Disorders|doi=10.1016/B978-0-12-802792-9.00001-X|editor-last2=Bandyopadhyay|editor-first2=Amit}}

style="text-align:left;" |Copper (Cu), annealed

|110

|16

|{{Cite web|title=Copper, Cu; Annealed|url=http://www.matweb.com/search/DataSheet.aspx?MatGUID=9aebe83845c04c1db5126fada6f76f7e|access-date=May 9, 2021|website=MatWeb}}

style="text-align:left;" |Diamond (C), synthetic

|1050–1210

|152–175

|{{Cite book|title=Synthetic Diamond: Emerging CVD Science and Technology|publisher= Wiley |year=1994 |isbn=978-0-47-153589-8|editor-last=Spear|editor-first=Karl E.|pages=315|issn=0275-0171|editor-last2=Dismukes|editor-first2=John P.}}

style="text-align:left;" |Diatom frustules, largely silicic acid

|0.35–2.77

|0.051–0.058

|{{cite journal |last1=Subhash |first1=Ghatu |last2=Yao |first2=Shuhuai |last3=Bellinger |first3=Brent |last4=Gretz |first4=Michael R. |date=January 2005 |title=Investigation of mechanical properties of diatom frustules using nanoindentation |journal=Journal of Nanoscience and Nanotechnology |publisher=American Scientific Publishers |volume=5 |issue=1 |pages=50–56 |doi=10.1166/jnn.2005.006 |pmid=15762160 |via=Ingenta Connect}}

style="text-align:left;" |Flax fiber

|58

|8.41

|{{Cite journal |last1=Bodros |first1=Edwin |last2=Baley |first2=Christophe |date=May 15, 2008 |title=Study of the tensile properties of stinging nettle fibres (Urtica dioica) |journal=Materials Letters |volume=62 |issue=14 |pages=2143–2145 |citeseerx=10.1.1.299.6908 |doi=10.1016/j.matlet.2007.11.034 |bibcode=2008MatL...62.2143B |via=Elsevier Science Direct}}

style="text-align:left;" |Float glass

|47.7–83.6

|6.92–12.1

|{{Cite web|date=February 16, 2001|title=Float glass – Properties and Applications|url=https://www.azom.com/properties.aspx?ArticleID=89|access-date=May 9, 2021|website=AZO Materials}}

style="text-align:left;" |Glass-reinforced polyester (GRP)

|17.2

|2.49

|{{Cite web|last=Kopeliovich|first=Dmitri|date=March 6, 2012|title=Polyester Matrix Composite reinforced by glass fibers (Fiberglass)|url=http://www.substech.com/dokuwiki/doku.php?id=polyester_matrix_composite_reinforced_by_glass_fibers_fiberglass|access-date=May 7, 2021|website=SubsTech}}

style="text-align:left;" |Gold

|77.2

|11.2

|{{cite web|url=http://www.matweb.com/search/DataSheet.aspx?MatGUID=d2a2119a08904a0fa706e9408cddb88e|title=Gold material property data|website=MatWeb|accessdate=September 8, 2021}}

style="text-align:left;" |Graphene

|1050

|152

|{{Cite journal|last1=Liu|first1=Fang|last2=Ming|first2=Pingbing|last3=Li|first3=Ju|date=August 28, 2007|title=Ab initio calculation of ideal strength and phonon instability of graphene under tension|url=http://li.mit.edu/A/Papers/07/Liu07.pdf|journal=Physical Review B|publisher=American Physical Society|volume=76|issue=6|page=064120|doi=10.1103/PhysRevB.76.064120|bibcode=2007PhRvB..76f4120L|via=APS Physics}}

style="text-align:left;" |Hemp fiber

|35

|5.08

|{{Cite journal|last1=Saheb|first1=Nabi|last2=Jog|first2=Jyoti|date=October 15, 1999|title=Natural fibre polymer composites: a review|journal=Advances in Polymer Technology|publisher= John Wiley & Sons, Inc.|volume=18|issue=4|pages=351–363|doi=10.1002/(SICI)1098-2329(199924)18:4<351::AID-ADV6>3.0.CO;2-X|doi-access=free}}

style="text-align:left;" |High-density polyethylene (HDPE)

|0.97–1.38

|0.141–0.2

|{{Cite web|title=High-Density Polyethylene (HDPE)|url=https://polymerdatabase.com/Commercial%20Polymers/HDPE.html|access-date=May 9, 2021|website=Polymer Database|publisher=Chemical Retrieval on the Web}}

style="text-align:left;" |High-strength concrete

|30

|4.35

|{{Cite book|last=Cardarelli|first=François|title=Materials Handbook: A Concise Desktop Reference|publisher= Springer-Verlag|year=2008|isbn=978-3-319-38923-3|edition=2nd|location=London|pages=1421–1439|chapter=Cements, Concrete, Building Stones, and Construction Materials|doi=10.1007/978-3-319-38925-7_15}}

style="text-align:left;" |Lead (₈₂Pb), chemical

|13

|1.89

style="text-align:left;" |Low-density polyethylene (LDPE), molded

|0.228

|0.0331

|{{cite web|title=Overview of materials for Low Density Polyethylene (LDPE), Molded|url=http://matweb.com/search/DataSheet.aspx?MatGUID=557b96c10e0843dbb1e830ceedeb35b0|access-date=May 7, 2021|website=MatWeb}}

style="text-align:left;" |Magnesium alloy

|45.2

|6.56

|{{Cite web|title=Overview of materials for Magnesium Alloy|url=http://www.matweb.com/search/DataSheet.aspx?MatGUID=4e6a4852b14c4b12998acf2f8316c07c|access-date=May 9, 2021|website=MatWeb}}

style="text-align:left;" |Medium-density fiberboard (MDF)

|0.58

|{{cite web|date=May 30, 2020|title=Medium Density Fiberboard (MDF)|url=http://www.makeitfrom.com/data/?material=MDF|access-date=May 8, 2021|website=MakeItFrom}}

style="text-align:left;" |Molybdenum (Mo), annealed

|330

|47.9

|{{Cite web|title=Molybdenum, Mo, Annealed|url=http://www.matweb.com/search/datasheet.aspx?matguid=ef57c33963404798ad0301a05692312a|access-date=May 9, 2021|website=MatWeb}}

style="text-align:left;" |Monel

|180

|26.1

style="text-align:left;" |Mother-of-pearl (largely calcium carbonate)

|70

|10.2

|{{cite journal|author=Jackson|first1=Andrew P.|last2=Vincent|first2=Julian F. V.|last3=Turner|first3=R. M.|date=September 22, 1988|title=The mechanical design of nacre|journal=Proceedings of the Royal Society B|publisher=Royal Society|volume=234|issue=1277|pages=415–440|bibcode=1988RSPSB.234..415J|doi=10.1098/rspb.1988.0056|issn=0080-4649|eissn=2053-9193|via= The Royal Society Publishing|s2cid=135544277}}

style="text-align:left;" |Nickel (₂₈Ni), commercial

|200

|29

style="text-align:left;" |Nylon 66

|2.93

|0.425

|{{Cite web|date=2011|title=Nylon® 6/6 (Polyamide)|url=https://www.polytechindustrial.com/products/plastic-stock-shapes/nylon-66|access-date=May 9, 2021|website=Poly-Tech Industrial, Inc.}}

style="text-align:left;" |Osmium (₇₆Os)

|525–562

|76.1–81.5

|{{cite journal|author=Pandey|first1=Dharmendra Kumar|last2=Singh|first2=Devraj|last3=Yadawa|first3=Pramod Kumar|date=April 2, 2009|title=Ultrasonic Study of Osmium and Ruthenium|url=http://www.technology.matthey.com/pdf/91-97-pmr-apr09.pdf|journal=Platinum Metals Review|publisher=Johnson Matthey|volume=53|issue=4|pages=91–97|doi=10.1595/147106709X430927|access-date=May 7, 2021|via=Ingenta Connect|doi-access=free}}

style="text-align:left;" |Osmium nitride (OsN₂)

|194.99–396.44

|28.3–57.5

|{{Cite web|last1=Gaillac|first1=Romain|last2=Coudert|first2=François-Xavier|date=July 26, 2020|title=ELATE: Elastic tensor analysis|url=http://progs.coudert.name/elate/mp?query=mp-973935|access-date=May 9, 2021|website=ELATE}}

style="text-align:left;" |Polycarbonate (PC)

|2.2

|0.319

|{{Cite web|title=Polycarbonate|url=https://designerdata.nl/materials/plastics/thermo-plastics/polycarbonate|access-date=May 9, 2021|website=DesignerData}}

style="text-align:left;" |Polyethylene terephthalate (PET), unreinforced

|3.14

|0.455

|{{Cite web|title=Overview of materials for Polyethylene Terephthalate (PET), Unreinforced|url=http://www.matweb.com/search/DataSheet.aspx?MatGUID=a696bdcdff6f41dd98f8eec3599eaa20|access-date=May 9, 2021|website=MatWeb}}

style="text-align:left;" |Polypropylene (PP), molded

|1.68

|0.244

|{{Cite web|title=Overview of Materials for Polypropylene, Molded|url=http://www.matweb.com/search/DataSheet.aspx?MatGUID=08fb0f47ef7e454fbf7092517b2264b2|access-date=May 9, 2021|website=MatWeb}}

style="text-align:left;" |Polystyrene, crystal

|2.5–3.5

|0.363–0.508

|{{Cite web|title=Young's Modulus: Tensile Elasticity Units, Factors & Material Table|url=https://omnexus.specialchem.com/polymer-properties/properties/young-modulus|access-date=May 9, 2021|website=Omnexus|publisher=SpecialChem}}

style="text-align:left;" |Polystyrene, foam

|0.0025–0.007

|0.000363–0.00102

|{{cite web|date=August 2019|title=Technical Data – Application Recommendations Dimensioning Aids|url=https://www.styrodur.com/portal/streamer?fid=1225078|access-date=May 7, 2021|website=Stryodur|publisher=BASF}}

style="text-align:left;" |Polytetrafluoroethylene (PTFE), molded

|0.564

|0.0818

|{{Cite web|title=Overview of materials for Polytetrafluoroethylene (PTFE), Molded|url=http://www.matweb.com/search/datasheet_print.aspx?matguid=4d14eac958e5401a8fd152e1261b6843|access-date=May 9, 2021|website=MatWeb}}

style="text-align:left;" |Rubber, small strain

|0.01–0.1

|0.00145–0.0145

style="text-align:left;" |Silicon, single crystal, different directions

|130–185

|18.9–26.8

|{{cite journal|author=Boyd|first1=Euan J.|last2=Uttamchandani|first2=Deepak|year=2012|title=Measurement of the Anisotropy of Young's Modulus in Single-Crystal Silicon|journal=Journal of Microelectromechanical Systems|publisher=Institute of Electrical and Electronics Engineers|volume=21|issue=1|pages=243–249|doi=10.1109/JMEMS.2011.2174415|issn=1057-7157|eissn=1941-0158|via=IEEE Xplore|s2cid=39025763}}

style="text-align:left;" |Silicon carbide (SiC)

|90–137

|13.1–19.9

|{{Cite web|date=February 5, 2001|title=Silicon Carbide (SiC) Properties and Applications|url=https://www.azom.com/properties.aspx?ArticleID=42|access-date=May 9, 2021|website=AZO Materials}}

style="text-align:left;" |Single-walled carbon nanotube

|data-sort-value="1000"| $>$ 1000

|data-sort-value="140"| $>$ 140

|{{Cite journal |last1=Forró |first1=László |last2=Salvetat |first2=Jean-Paul |last3=Bonard |first3=Jean-Marc |last4=Bacsa |first4=Revathi Ramachandran |last5=Thomson |first5=Neil H. |last6=Garaj |first6=Slaven |last7=Le |first7=Thien-Nga |last8=Gaál |first8=Richard |last9=Kulik |first9=Andrzej J. |last10=Ruzicka |first10=Barbara |last11=Degiorgi |first11=Leonardo |display-authors=3 |date=January 2002 |editor-last=Thorpe |editor-first=Michael F. |editor2-last=Tománek |editor2-first=David |editor2-link=David Tománek |editor3-last=Enbody |editor3-first=Richard J. |title=Electronic and Mechanical Properties of Carbon Nanotubes |url=https://www.researchgate.net/publication/226537355 |journal=Science and Application of Nanotubes |series=Fundamentals Materials Research |location=Boston, MA |publisher=Springer |pages=297–320 |doi=10.1007/0-306-47098-5_22 |isbn=978-0-306-46372-3 |via=ResearchGate}}{{cite journal|author=Yang|first1=Yi-Hsuan|last2=Li|first2=Wenzhi|date=January 24, 2011|title=Radial elasticity of single-walled carbon nanotube measured by atomic force microscopy|journal=Applied Physics Letters|publisher=American Institute of Physics|volume=98|issue=4|page=041901|bibcode=2011ApPhL..98d1901Y|doi=10.1063/1.3546170}}

style="text-align:left;" |Steel, A36

|200

|29

|{{Cite web|date=July 5, 2012|title=ASTM A36 Mild/Low Carbon Steel|url=https://www.azom.com/article.aspx?ArticleID=6117|access-date=May 9, 2021|website=AZO Materials}}

style="text-align:left;" |Stinging nettle fiber

|87

|12.6

style="text-align:left;" |Titanium (₂₂Ti)

|116

|16.8

|{{Cite web|title=Titanium, Ti|url=http://www.matweb.com/search/datasheet.aspx?MatGUID=66a15d609a3f4c829cb6ad08f0dafc01|access-date=May 7, 2021|website=MatWeb}}{{Cite book|title=Materials Properties Handbook: Titanium Alloys|publisher=ASM International|year=1994|isbn=978-0-87-170481-8|editor-last=Boyer|editor-first=Rodney|location=Materials Park, OH|editor-last2=Welsch|editor-first2=Gerhard|editor-last3=Collings|editor-first3=Edward W.}}

style="text-align:left;" |Titanium alloy, Grade 5

|114

|16.5

|{{Cite web|last=U.S. Titanium Industry Inc.|date=July 30, 2002|title=Titanium Alloys – Ti6Al4V Grade 5|url=https://www.azom.com/article.aspx?ArticleID=1547|access-date=May 9, 2021|website=AZO Materials}}

style="text-align:left;" |Tooth enamel, largely calcium phosphate

|83

|12

|{{cite journal|author=Staines|first1=Michael|last2=Robinson|first2=W. H.|last3=Hood|first3=J. A. A.|date=September 1981|title=Spherical indentation of tooth enamel|journal=Journal of Materials Science|publisher=Springer|volume=16|issue=9|pages=2551–2556|bibcode=1981JMatS..16.2551S|doi=10.1007/bf01113595|via=Springer Link|s2cid=137704231}}

style="text-align:left;" |Tungsten carbide (WC)

|600–686

|87–99.5

|{{Cite web|date=January 21, 2002|title=Tungsten Carbide – An Overview|url=https://www.azom.com/properties.aspx?ArticleID=1203|access-date=May 9, 2021|website=AZO Materials}}

style="text-align:left;" |Wood, American beech

|9.5–11.9

|1.38–1.73

|{{Cite book|last1=Green|first1=David W.|url=https://www.fpl.fs.fed.us/documnts/fplgtr/fplgtr113/ch04.pdf|title=Wood Handbook: Wood as an Engineering Material|last2=Winandy|first2=Jerrold E.|last3=Kretschmann|first3=David E.|publisher=Forest Products Laboratory|year=1999|location=Madison, WI|pages=4–8|chapter=Mechanical Properties of Wood|archive-url=https://web.archive.org/web/20180720153345/https://www.fpl.fs.fed.us/documnts/fplgtr/fplgtr113/ch04.pdf|archive-date=2018-07-20}}

style="text-align:left;" |Wood, black cherry

|9–10.3

|1.31–1.49

style="text-align:left;" |Wood, red maple

|9.6–11.3

|1.39–1.64

style="text-align:left;" |Wrought iron

|193

|28

|{{Cite web|date=August 13, 2013|title=Wrought Iron – Properties and Applications|url=https://www.azom.com/article.aspx?ArticleID=9555|access-date=May 9, 2021|website=AZO Materials}}

style="text-align:left;" |Yttrium iron garnet (YIG), polycrystalline

|193

|28

|{{Cite journal|last1=Chou|first1=Hung-Ming|last2=Case|first2=E. D.|date=November 1988|title=Characterization of some mechanical properties of polycrystalline yttrium iron garnet (YIG) by non-destructive methods|journal=Journal of Materials Science Letters|volume=7|issue=11|pages=1217–1220|doi=10.1007/BF00722341|via=SpringerLink|s2cid=135957639}}

style="text-align:left;" |Yttrium iron garnet (YIG), single-crystal

|200

|29

|{{Cite web|title=Yttrium Iron Garnet|url=http://deltroniccrystalindustries.com/deltronic_crystal_products/yttrium_iron_garnet|access-date=May 7, 2021|website=Deltronic Crystal Industries, Inc.|date=December 28, 2012}}

style="text-align:left;" |Zinc (₃₀Zn)

|108

|15.7

|{{Cite web|date=July 23, 2001|title=An Introduction to Zinc|url=https://www.azom.com/properties.aspx?ArticleID=602|access-date=May 9, 2021|website=AZO Materials}}

style="text-align:left;" |Zirconium (₄₀Zr), commercial

|95

|13.8

References

External links

[http://www.matweb.com/ Matweb: free database of engineering properties for over 175,000 materials]
[http://www-materials.eng.cam.ac.uk/mpsite/interactive_charts/stiffness-cost/NS6Chart.html Young's Modulus for groups of materials, and their cost]

Category:Elasticity (physics)

Category:Physical quantities

Category:Structural analysis

Young's modulus

Definition

=Linear elasticity=

=Related but distinct properties=

Usage

=Linear versus non-linear=

=Directional materials=

Calculation

=Force exerted by stretched or contracted material=

=Elastic potential energy=

Examples

See also

References

Further reading

External links