{"id":5181,"date":"2021-03-08T16:51:17","date_gmt":"2021-03-08T15:51:17","guid":{"rendered":"https:\/\/www.nickzom.org\/blog\/?p=5181"},"modified":"2024-05-01T16:32:01","modified_gmt":"2024-05-01T15:32:01","slug":"how-to-calculate-and-solve-for-shear-modulus-of-rubber-fracture-mechanics","status":"publish","type":"post","link":"https:\/\/www.nickzom.org\/blog\/2021\/03\/08\/how-to-calculate-and-solve-for-shear-modulus-of-rubber-fracture-mechanics\/","title":{"rendered":"How to Calculate and Solve for Shear Modulus of Rubber | Fracture Mechanics"},"content":{"rendered":"

\"\"<\/p>\n

The image above represents shear modulus of rubber. To calculate shear modulus of rubber, three essential parameters are needed and these parameters are Density of Network Cross Links (N), Boltzmann’s Constant (KB<\/sub>)\u00a0<\/strong>and\u00a0Temperature (T).<\/strong><\/p>\n

The formula for calculating shear modulus of rubber:<\/strong><\/h3>\n

G = NKB<\/sub>T<\/p>\n

Where:<\/p>\n

G = Shear Modulus of Rubber
\nN = Density of Network Cross Links
\nKB<\/sub> = Boltzmann’s Constant
\nT = Temperature<\/p>\n

Let’s solve an example;
\nFind the shear modulus of rubber when the density of network cross links is 21, the boltzmann’s constant is 1.38064852E-23 and the temperature is 10.<\/p>\n

This implies that;<\/p>\n

N = Density of Network Cross Links = 21
\nKB<\/sub> = Boltzmann’s Constant = 1.38064852E-23
\nT = Temperature = 10<\/p>\n

That is, G = NKB<\/sub>T
\nG = (21)(1.38064852e-23)(10)
\nG = 2.89<\/p>\n

Therefore, the\u00a0shear modulus of rubber\u00a0<\/strong>is\u00a02.89e-23 Pa.<\/strong><\/p>\n

Read more:\u00a0How to Calculate and Solve for Shear Modulus | Mechanical Properties<\/a><\/p>\n

Calculating the Density of Network Cross Links when the Shear Modulus of Rubber, Boltzmann’s Constant and the Temperature are Given<\/strong><\/h3>\n

N = G<\/sup> \/ KB<\/sub>T<\/sub><\/p>\n

Where;<\/p>\n

N = Density of Network Cross Links
\nG = Shear Modulus of Rubber
\nKB<\/sub> = Boltzmann’s Constant
\nT = Temperature<\/p>\n

Let’s solve an example;
\nFind the density of network cross links when the shear modulus of rubber is 14, the boltzmann’s constant is 1.380e-23 and temperature is 4.<\/p>\n

This implies that;<\/p>\n

G = Shear Modulus of Rubber = 14
\nKB<\/sub> = Boltzmann’s Constant = 1.380e-23
\nT = Temperature = 4<\/p>\n

N = G<\/sup> \/ KB<\/sub>T<\/sub>
\nN = 14<\/sup> \/ 1.380e-23 x 4<\/sub>
\nSo, N = 14<\/sup> \/ 5.52e-23<\/sub>
\nN = 2.54e-23<\/p>\n

Therefore, the\u00a0network cross links\u00a0<\/strong>is\u00a02.54e-23.<\/strong><\/p>\n

Read more:\u00a0How to Calculate and Solve for Young’s Modulus | Fracture Mechanics<\/a><\/p>\n

Calculating the Temperature when the Shear Modulus of Rubber, the Density of Network Cross Links and the Boltzmann’s Constant are Given<\/strong><\/h3>\n

T = G<\/sup> \/ KB<\/sub>N<\/sub><\/p>\n

Where;<\/p>\n

T = Temperature
\nG = Shear Modulus of Rubber
\nN = Density of Network Cross Links
\nKB<\/sub> = Boltzmann’s Constant<\/p>\n

Let’s solve an example;
\nFind the temperature when the shear modulus of rubber is 20, the density of network cross links is 18 and the boltzmann’s constant is 1.380e-23.<\/p>\n

This implies that;<\/p>\n

G = Shear Modulus of Rubber = 20
\nN = Density of Network Cross Links = 18
\nKB<\/sub> = Boltzmann’s Constant = 1.380e-23<\/p>\n

T = G<\/sup> \/ KB<\/sub>N<\/sub>
\nT = 20<\/sup> \/ 1.380e-23 x 18<\/sub>
\nSo, T = 20<\/sup> \/ 2.48e-22<\/sub>
\nT = 8.06e-22<\/p>\n

Therefore, the\u00a0temperature\u00a0<\/strong>is\u00a08.06e-22.<\/strong><\/p>\n

Read more:\u00a0How to Calculate and Solve for Shear Modulus | Rock Mechanics<\/a><\/p>\n

How to Calculate and Solve for Shear Modulus of Rubber Using Nickzom Calculator<\/strong><\/h3>\n

Nickzom Calculator \u2013\u00a0The Calculator Encyclopedia<\/strong> is capable of calculating the shear modulus of rubber.<\/p>\n

To get the answer and workings of the shear modulus of rubber using the\u00a0Nickzom Calculator \u2013 The Calculator Encyclopedia.\u00a0<\/strong>First, you need to obtain the app.<\/p>\n

You can get this app via any of these means:<\/p>\n

Web<\/strong>\u00a0\u2013\u00a0https:\/\/www.nickzom.org\/calculator-plus<\/a><\/p>\n

To get access to the\u00a0professional\u00a0<\/strong>version via web, you need to\u00a0register<\/strong>\u00a0and\u00a0subscribe\u00a0<\/strong>for\u00a0NGN 2,000\u00a0<\/strong>per\u00a0annum<\/strong>\u00a0to have utter access to all functionalities.
\nYou can also try the\u00a0demo\u00a0<\/strong>version via\u00a0https:\/\/www.nickzom.org\/calculator<\/a><\/p>\n

Android (Paid)<\/strong>\u00a0\u2013\u00a0https:\/\/play.google.com\/store\/apps\/details?id=org.nickzom.nickzomcalculator<\/a>
\nAndroid (Free)<\/strong>\u00a0\u2013\u00a0https:\/\/play.google.com\/store\/apps\/details?id=com.nickzom.nickzomcalculator<\/a>
\nApple (Paid)<\/strong>\u00a0\u2013\u00a0https:\/\/itunes.apple.com\/us\/app\/nickzom-calculator\/id1331162702?mt=8<\/a>
\nOnce, you have obtained the calculator encyclopedia app, proceed to the\u00a0Calculator Map,\u00a0<\/strong>then click on\u00a0Materials and Metallurgical\u00a0<\/b>under\u00a0Engineering<\/strong>.<\/strong><\/p>\n

\"\"<\/p>\n

Now, Click on\u00a0Fracture Mechanics\u00a0<\/strong>under\u00a0Materials and Metallurgical<\/strong><\/p>\n

\"\"<\/p>\n

Now, Click on\u00a0Shear Modulus of Rubber\u00a0<\/strong>under\u00a0Fracture Mechanics<\/strong><\/p>\n

\"\"<\/p>\n

The screenshot below displays the page or activity to enter your values, to get the answer for the shear modulus of rubber according to the respective parameters which is the Density of Network Cross Links (N), Boltzmann’s Constant (KB<\/sub>)\u00a0<\/strong>and\u00a0Temperature (T).<\/strong><\/p>\n

\"How<\/p>\n

Now, enter the\u00a0<\/span>v<\/span>al<\/span>ue appropriately and accordingly for the parameter as required by the <\/span>Density of Network Cross Links (N)<\/strong>\u00a0is <\/span>21<\/strong>,<\/span> Boltzmann’s Constant (KB<\/sub>)<\/strong>\u00a0is <\/span>1.380e-23\u00a0<\/strong>and\u00a0<\/span>Temperature (T)<\/strong>\u00a0is <\/span>10<\/strong>.<\/span><\/p>\n

\"How<\/p>\n

Finally, Click on Calculate<\/span><\/p>\n

\"How<\/p>\n

As you can see from the screenshot above,\u00a0Nickzom Calculator<\/strong>\u2013 The Calculator Encyclopedia solves for the shear modulus of rubber and presents the formula, workings and steps too.<\/p>\n","protected":false},"excerpt":{"rendered":"The image above represents shear modulus of rubber. To calculate shear modulus of rubber, three essential parameters are…","protected":false},"author":5,"featured_media":14655,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_yoast_wpseo_opengraph-title":"","_yoast_wpseo_opengraph-description":"","_yoast_wpseo_twitter-title":"","_yoast_wpseo_twitter-description":"","_lmt_disableupdate":"","_lmt_disable":"","_sitemap_exclude":false,"_sitemap_priority":"","_sitemap_frequency":"","_yoast_wpseo_focuskw_text_input":"","csco_display_header_overlay":false,"csco_singular_sidebar":"","csco_page_header_type":"","footnotes":"","_members_access_role":[],"_members_access_error":""},"categories":[47],"tags":[873,1473,60,1469,543,1474,75],"class_list":["post-5181","post","type-post","status-publish","format-standard","has-post-thumbnail","category-engineering","tag-boltzmanns-constant","tag-density-of-network-cross-link","tag-engineering","tag-fracture-mechanics","tag-materials-and-metallurgical","tag-shear-modulus-of-rubber","tag-temperature","cs-entry"],"yoast_head":"\nHow 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