{"id":7574,"date":"2022-08-03T12:49:51","date_gmt":"2022-08-03T11:49:51","guid":{"rendered":"https:\/\/www.nickzom.org\/blog\/?p=7574"},"modified":"2024-05-28T10:06:26","modified_gmt":"2024-05-28T09:06:26","slug":"how-to-calculate-and-solve-for-modulus-of-elasticity-of-composites-upper-bound-composites","status":"publish","type":"post","link":"https:\/\/www.nickzom.org\/blog\/2022\/08\/03\/how-to-calculate-and-solve-for-modulus-of-elasticity-of-composites-upper-bound-composites\/","title":{"rendered":"How to Calculate and Solve for Modulus of Elasticity of Composites Upper Bound | Composites"},"content":{"rendered":"

The modulus of elasticity of composites upper bound is illustrated by the image below. To calculate modulus of elasticity of composites upper bound, four essential parameters are needed and these parameters are Modulus of Elasticity of the Matrix (Em<\/sub>), Modulus of Elasticity of the Particle (Ep<\/sub>), Volume Fraction of the Matrix (Vm<\/sub>)<\/strong> and Volume Fraction of the Particle (Vp<\/sub>).<\/strong><\/p>\n

\"\"<\/p>\n

The formula for calculating modulus of elasticity of composites upper bound:<\/strong><\/h3>\n

Ec(u)<\/sub>\u00a0= Em<\/sub>Vm<\/sub>\u00a0+ Ep<\/sub>Vp<\/sub><\/p>\n

Where:<\/p>\n

Ec(u)<\/sub>\u00a0= Modulus of Elasticity of Composites Upper Bound
\nEm<\/sub> =Modulus of Elasticity of the Matrix
\nAlso, Ep<\/sub> = Modulus of Elasticity of the Particle
\nVm<\/sub> = Volume Fractions of the Matrix
\nVp<\/sub> = Volume Fractions of the Particle<\/p>\n

Let’s solve an example;
\nFind the modulus of elasticity of composites upper bound when the modulus of elasticity of the matrix is 4, the modulus of elasticity of the particle is 7, the volume fractions of the matrix is 2 and the volume fractions of the particle is 6.<\/p>\n

This implies that;<\/p>\n

Em<\/sub> =Modulus of Elasticity of the Matrix = 4
\nEp<\/sub> = Modulus of Elasticity of the Particle = 7
\nVm<\/sub> = Volume Fractions of the Matrix = 2
\nVp<\/sub> = Volume Fractions of the Particle = 6<\/p>\n

Ec(u)<\/sub>\u00a0= Em<\/sub>Vm<\/sub>\u00a0+ Ep<\/sub>Vp<\/sub>
\nThen, Ec(u)<\/sub> = (4)(2) + (7)(6)
\nEc(u)<\/sub> = (8) + (42)
\nEc(u)<\/sub> = 50<\/p>\n

Therefore, the\u00a0modulus of elasticity of composites upper bound\u00a0<\/strong>is\u00a050 Pa.<\/strong><\/p>\n

Calculating the Modulus of Elasticity of the Matrix when the Modulus of Elasticity of Composites Upper Bound, the Modulus of Elasticity of the Particle, the Volume Fraction of the Matrix and the Volume Fraction of the Particle are Given<\/strong><\/h3>\n

Em<\/sub> = Ec(u)<\/sub> – Ep<\/sub>Vp<\/sub><\/sup> \/ Vm<\/sub><\/sub><\/p>\n

Where:<\/p>\n

Em<\/sub> =Modulus of Elasticity of the Matrix
\nEc(u)<\/sub>\u00a0= Modulus of Elasticity of Composites Upper Bound
\nAlso, Ep<\/sub> = Modulus of Elasticity of the Particle
\nVm<\/sub> = Volume Fractions of the Matrix
\nVp<\/sub> = Volume Fractions of the Particle<\/p>\n

Let’s solve an example;
\nFind the modulus of elasticity of the matrix when the modulus of elasticity of composites upper bound is 40, the modulus of elasticity of the particle is 10, the volume fractions of the matrix is 5 and the volume fractions of the particle is 2.<\/p>\n

This implies that;<\/p>\n

Ec(u)<\/sub> = Modulus of Elasticity of Composites Upper Bound = 40
\nEp<\/sub> = Modulus of Elasticity of the Particle = 10
\nVm<\/sub> = Volume Fractions of the Matrix = 5
\nVp<\/sub> = Volume Fractions of the Particle = 2<\/p>\n

Em<\/sub> = Ec(u)<\/sub> – Ep<\/sub>Vp<\/sub><\/sup> \/ Vm<\/sub><\/sub>
\nEm<\/sub> = 40 – (10)(2)<\/sup> \/ 5<\/sub>
\nThat is, Em<\/sub> = 40 – 20<\/sup> \/ 5<\/sub>
\nEm<\/sub> = 20<\/sup> \/ 5<\/sub>
\nEm<\/sub> = 4<\/p>\n

Therefore, the\u00a0modulus of elasticity of the matrix\u00a0<\/strong>is\u00a04.<\/strong><\/p>\n

Read more:\u00a0How to Calculate and Solve for Modulus of Elasticity of Composites Lower Bound | Composites<\/a><\/p>\n

Calculating the Modulus of Elasticity of the Particle when the Modulus of Elasticity of Composites Upper Bound, the Modulus of Elasticity of the Particle, the Volume Fraction of the Matrix and the Volume Fraction of the Particle are Given<\/strong><\/h4>\n

Ep<\/sub> = Ec(u)<\/sub> – Em<\/sub>Vm<\/sub><\/sup> \/ Vp<\/sub><\/sub><\/p>\n

Where:<\/p>\n

Ep<\/sub> = Modulus of Elasticity of the Particle
\nEc(u)<\/sub>\u00a0= Modulus of Elasticity of Composites Upper Bound
\nAnd then, Em<\/sub> =Modulus of Elasticity of the Matrix
\nVm<\/sub> = Volume Fractions of the Matrix
\nVp<\/sub> = Volume Fractions of the Particle<\/p>\n

Let’s solve an example;
\nFind the modulus of elasticity of the particle when the modulus of elasticity of composites upper bound is 50, the modulus of elasticity of the matrix is 4, the volume fractions of the matrix is 5 and the volume fractions of the particle is 10.<\/p>\n

This implies that;<\/p>\n

Ec(u)<\/sub> = Modulus of Elasticity of Composites Upper Bound = 50
\nEm<\/sub> =Modulus of Elasticity of the Matrix = 4
\nVm<\/sub> = Volume Fractions of the Matrix = 5
\nVp<\/sub> = Volume Fractions of the Particle = 10<\/p>\n

Ep<\/sub> = Ec(u)<\/sub> – Em<\/sub>Vm<\/sub><\/sup> \/ Vp<\/sub><\/sub>
\nEp<\/sub> = 50 – (4)(5)<\/sup> \/ 10<\/sub>
\nSo, Ep<\/sub> = 50 – 20<\/sup> \/ 10<\/sub>
\nEp<\/sub> = 30<\/sup> \/ 10<\/sub>
\nEp<\/sub> = 3<\/p>\n

Therefore, the\u00a0modulus of elasticity of the particle\u00a0<\/strong>is\u00a03.<\/strong><\/p>\n

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

Calculating the Volume Fraction of the Matrix when the Modulus of Elasticity of Composites Upper Bound, the Modulus of Elasticity of the Matrix, the Modulus of Elasticity of the Particle and the Volume Fraction of the Particle are Given<\/strong><\/h3>\n

Vm<\/sub> = Ec(u)<\/sub> – Ep<\/sub>Vp<\/sub><\/sup> \/ Em<\/sub><\/sub><\/p>\n

Where:<\/p>\n

Vm<\/sub> = Volume Fractions of the Matrix
\nEc(u)<\/sub>\u00a0= Modulus of Elasticity of Composites Upper Bound
\nEm<\/sub> =Modulus of Elasticity of the Matrix
\nAlso, Ep<\/sub> = Modulus of Elasticity of the Particle
\nVp<\/sub> = Volume Fractions of the Particle<\/p>\n

Given an example;
\nFind the volume fractions of the matrix when the modulus of elasticity of composites upper bound is 30, the modulus of elasticity of the matrix is 3, the modulus of elasticity of the particle is 5 and the volume fractions of the particle is 3.<\/p>\n

This implies that;<\/p>\n

Ec(u)<\/sub> = Modulus of Elasticity of Composites Upper Bound = 30
\nEm<\/sub> =Modulus of Elasticity of the Matrix = 3
\nAnd then, Ep<\/sub> = Modulus of Elasticity of the Particle = 5
\nVp<\/sub> = Volume Fractions of the Particle = 3<\/p>\n

That is, Vm<\/sub> = Ec(u)<\/sub> – Ep<\/sub>Vp<\/sub><\/sup> \/ Em<\/sub><\/sub>
\nVm<\/sub> = 30 – (5)(3)<\/sup> \/ 3<\/sub>
\nSo, Vm<\/sub> = 30 – 15<\/sup> \/ 3<\/sub>
\nVm<\/sub> = 15<\/sup> \/ 3<\/sub>
\nVm<\/sub> = 5<\/p>\n

Therefore, the\u00a0volume fraction of the matrix\u00a0<\/strong>is\u00a05.<\/strong><\/p>\n

Calculating the Volume Fraction of the Particle when the Modulus of Elasticity of Composites Upper Bound, the Modulus of Elasticity of the Matrix, the Modulus of Elasticity of the Particle and the Volume Fraction of the Matrix are Given<\/strong><\/h3>\n

Vp<\/sub> = Ec(u)<\/sub> – Em<\/sub>Vm<\/sub><\/sup> \/ Ep<\/sub><\/sub><\/p>\n

Where:<\/p>\n

Vp<\/sub> = Volume Fractions of the Particle
\nEc(u)<\/sub>\u00a0= Modulus of Elasticity of Composites Upper Bound
\nEm<\/sub> =Modulus of Elasticity of the Matrix
\nThen, Ep<\/sub> = Modulus of Elasticity of the Particle
\nVm<\/sub> = Volume Fractions of the Matrix<\/p>\n

Let’s solve an example;
\nFind the volume fractions of the particle when the modulus of elasticity of composites upper bound is 10, the modulus of elasticity of matrix is 2, the modulus of elasticity of the particle is 4 and the volume fraction of the matrix is 3.<\/p>\n

This implies that;<\/p>\n

Ec(u)<\/sub> = Modulus of Elasticity of Composites Upper Bound = 10
\nEm<\/sub> =Modulus of Elasticity of the Matrix = 2
\nAlso, Ep<\/sub> = Modulus of Elasticity of the Particle = 4
\nVm<\/sub> = Volume Fractions of the Matrix = 3<\/p>\n

So, Vp<\/sub> = Ec(u)<\/sub> – Em<\/sub>Vm<\/sub><\/sup> \/ Ep<\/sub><\/sub>
\nVp<\/sub> = 10 – (2)(3)<\/sup> \/ 4<\/sub>
\nThat is, Vp<\/sub> = 10 – 6<\/sup> \/ 4<\/sub>
\nVp<\/sub> = 4<\/sup> \/ 4<\/sub>
\nVp<\/sub> = 1<\/p>\n

Therefore, the\u00a0volume fractions of the particle\u00a0<\/strong>is\u00a01.<\/strong><\/p>\n

How to Calculate Modulus of Elasticity of Composites Upper Bound Using Nickzom Calculator<\/strong><\/h3>\n

Nickzom Calculator \u2013\u00a0The Calculator Encyclopedia<\/strong> is capable of calculating the modulus of elasticity of composites upper bound.<\/p>\n

\n

To get the answer and workings of the modulus of elasticity of composites upper bound using the Nickzom 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>to 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><\/p>\n

Apple (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<\/div>\n

<\/p>\n

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

\"\"<\/p>\n

Now, Click on\u00a0Modulus of Elasticity of Composites Upper Bound<\/strong>\u00a0under Composites<\/b><\/p>\n

\"\"<\/p>\n

The screenshot below displays the page or activity to enter your values, to get the answer for the modulus of elasticity of composites upper bound according to the respective parameter which is the Modulus of Elasticity of the Matrix (Em<\/sub>), Modulus of Elasticity of the Particle (Ep<\/sub>), Volume Fraction of the Matrix (Vm<\/sub>)<\/strong> and Volume Fraction of the Particle (Vp<\/sub>).<\/strong><\/p>\n

\"\"<\/p>\n

Now, enter the values appropriately and accordingly for the parameters as required by the Modulus of Elasticity of the Matrix (Em<\/sub>)<\/strong> is 4<\/strong>, Modulus of Elasticity of the Particle (Ep<\/sub>)<\/strong> is 7<\/strong>, Volume Fraction of the Matrix (Vm<\/sub>)\u00a0<\/strong>is\u00a02<\/strong> and Volume Fraction of the Particle (Vp<\/sub>)<\/strong> is 6<\/strong>.<\/p>\n

\"How<\/p>\n

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

\"How
\n\"How<\/p>\n

As you can see from\u00a0the screenshot above,\u00a0Nickzom Calculator<\/strong>\u2013 The Calculator Encyclopedia can calculate the modulus of elasticity of composites upper bound and presents the formula, workings and steps too.<\/p>\n","protected":false},"excerpt":{"rendered":"The modulus of elasticity of composites upper bound is illustrated by the image below. To calculate modulus of…","protected":false},"author":5,"featured_media":15966,"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":""},"categories":[47],"tags":[2131,60,543,2130,2126,2127,2128,2129],"class_list":["post-7574","post","type-post","status-publish","format-standard","has-post-thumbnail","category-engineering","tag-composites","tag-engineering","tag-materials-and-metallurgical","tag-modulus-of-elasticity-of-composites-upper-bound","tag-modulus-of-elasticity-of-the-matrix","tag-modulus-of-elasticity-of-the-particle","tag-volume-fraction-of-the-matrix","tag-volume-fraction-of-the-particle","cs-entry"],"yoast_head":"\nHow 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