{"id":7634,"date":"2022-08-04T06:20:35","date_gmt":"2022-08-04T05:20:35","guid":{"rendered":"https:\/\/www.nickzom.org\/blog\/?p=7634"},"modified":"2024-05-28T10:09:55","modified_gmt":"2024-05-28T09:09:55","slug":"how-to-calculate-and-solve-for-ratio-of-load-of-fibre-to-matrix-composites","status":"publish","type":"post","link":"https:\/\/www.nickzom.org\/blog\/2022\/08\/04\/how-to-calculate-and-solve-for-ratio-of-load-of-fibre-to-matrix-composites\/","title":{"rendered":"How to Calculate and Solve for Ratio of Load of Fibre to Matrix | Composites"},"content":{"rendered":"

The ratio of load of fibre to matrix is illustrated by the image below. To calculate ratio of load of fibre to matrix, four essential parameters are needed and these parameters are Elastic Modulus of the Fibre (Ef<\/sub>), Elastic Modulus of the Matrix (Em<\/sub>), Volume Fraction of the Fibre (Vf<\/sub>)<\/strong> and Volume Fraction of the Matrix (Vm<\/sub>).<\/strong><\/p>\n

\"\"<\/p>\n

The formula for calculating ratio of load of fibre to matrix:<\/strong><\/h3>\n

F(f\/m)<\/sub>\u00a0=\u00a0Ef<\/sub>Vf<\/sub><\/sup>\/EmVm<\/sub><\/p>\n

Where:<\/p>\n

F(f\/m)<\/sub>\u00a0= Ratio of Load of Fibre to Matrix
\nEf<\/sub>\u00a0= Elastic Modulus of the Fibre
\nEm<\/sub>\u00a0= Elastic Modulus of the Matrix
\nVf<\/sub>\u00a0= Volume Fraction of the Fibre
\nVm<\/sub>\u00a0= Volume Fraction of the Matrix<\/p>\n

Let’s solve an example;
\nFind the ratio of load of fibre to matix when the elastic modulus of the fibre is 14, the elastic modulus of the matrix is 10, the volume fraction of the fibre is 6 and the volume fraction of the matrix is 2.<\/p>\n

This implies that;<\/p>\n

Ef<\/sub> = Elastic Modulus of the Fibre = 14
\nEm<\/sub> = Elastic Modulus of the Matrix = 10
\nVf<\/sub> = Volume Fraction of the Fibre = 6
\nVm<\/sub> = Volume Fraction of the Matrix = 2<\/p>\n

F(f\/m)<\/sub>\u00a0=\u00a0Ef<\/sub>Vf<\/sub><\/sup>\/EmVm<\/sub>
\nThat is, F(f\/m)<\/sub>\u00a0=\u00a0(14)(6)<\/sup>\/(10)(2)<\/sub>
\nF(f\/m)<\/sub>\u00a0=\u00a0(84)<\/sup>\/(20)<\/sub>
\nF(f\/m)<\/sub> = 4.2<\/p>\n

Therefore, the\u00a0ratio of load of fibre to matrix\u00a0<\/strong>is\u00a04.2.<\/strong><\/p>\n

Calculating the Elastic Modulus of the Fibre when the Ratio of Load of Fibre to Matrix, the Elastic Modulus of the Matrix, the Volume Fraction of the Fibre and the Volume Fraction of the Matrix are Given<\/strong><\/h3>\n

Ef<\/sub> = F(f\/m)<\/sub> x Em<\/sub>Vm<\/sub><\/sup> \/ Vf<\/sub><\/sub><\/p>\n

Where:<\/p>\n

Ef<\/sub>\u00a0= Elastic Modulus of the Fibre
\nF(f\/m)<\/sub>\u00a0= Ratio of Load of Fibre to Matrix
\nEm<\/sub>\u00a0= Elastic Modulus of the Matrix
\nVf<\/sub>\u00a0= Volume Fraction of the Fibre
\nVm<\/sub>\u00a0= Volume Fraction of the Matrix<\/p>\n

Let’s solve an example;
\nFind the elastic modulus of the fibre when the ratio of load of fibre to matrix is 20, the elastic modulus of the matrix is 4, the volume fraction of the matrix is 2 and the volume fraction of the fibre is 12.<\/p>\n

This implies that;<\/p>\n

F(f\/m)<\/sub> = Ratio of Load of Fibre to Matrix = 20
\nEm<\/sub> = Elastic Modulus of the Matrix = 4
\nVf<\/sub> = Volume Fraction of the Fibre = 12
\nVm<\/sub> = Volume Fraction of the Matrix = 2<\/p>\n

Ef<\/sub> = F(f\/m)<\/sub> x Em<\/sub>Vm<\/sub><\/sup> \/ Vf<\/sub><\/sub>
\nEf<\/sub> = 20 x (4)(2)<\/sup> \/ 12<\/sub>
\nSo, Ef<\/sub> = 20 x 8<\/sup> \/ 12<\/sub>
\nEf<\/sub> = 160<\/sup> \/ 12<\/sub>
\nEf<\/sub> = 13.33<\/p>\n

Therefore, the\u00a0elastic modulus of the fibre\u00a0<\/strong>is\u00a013.33<\/strong><\/p>\n

Read more:\u00a0How to Calculate and Solve for Critical Fibre Strength for Composite | Composites<\/a><\/p>\n

Calculating the Elastic Modulus of the Matrix when the Ratio of Load of Fibre to Matrix, the Elastic Modulus of the Fibre, the Volume Fraction of the Fibre and the Volume Fraction of the Matrix is Given<\/strong><\/h3>\n

Em<\/sub> = Ef<\/sub>Vf<\/sub><\/sup> \/ F(f\/m)<\/sub> x Vm<\/sub><\/sub><\/p>\n

Where:<\/p>\n

Em<\/sub>\u00a0= Elastic Modulus of the Matrix
\nF(f\/m)<\/sub>\u00a0= Ratio of Load of Fibre to Matrix
\nEf<\/sub>\u00a0= Elastic Modulus of the Fibre
\nVf<\/sub>\u00a0= Volume Fraction of the Fibre
\nVm<\/sub>\u00a0= Volume Fraction of the Matrix<\/p>\n

Let’s solve an example;
\nFind the elastic modulus of the matrix when the ratio of load of fibre to matrix is 18, the elastic modulus of the fibre is 12, the volume fraction of the fibre is 14 and the volume fraction of the matrix is 8.<\/p>\n

This implies that;<\/p>\n

F(f\/m)<\/sub> = Ratio of Load of Fibre to Matrix = 18
\nEf<\/sub> = Elastic Modulus of the Fibre = 12
\nVf<\/sub> = Volume Fraction of the Fibre = 14
\nVm<\/sub> = Volume Fraction of the Matrix = 8<\/p>\n

Em<\/sub> = Ef<\/sub>Vf<\/sub><\/sup> \/ F(f\/m)<\/sub> x Vm<\/sub><\/sub>
\nEm<\/sub> = (12)(14)<\/sup> \/ 18 x 8<\/sub>
\nThen, Em<\/sub> = 168<\/sup> \/ 144<\/sub>
\nEm<\/sub> = 1.167<\/p>\n

Therefore, the\u00a0elastic modulus of the matrix\u00a0<\/strong>is\u00a01.167<\/strong><\/p>\n

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

Calculating the Volume Fraction of the Matrix when the Ratio of Load of Fibre to Matrix, the Elastic Modulus of the Fibre, the Elastic Modulus of the Matrix and the Volume Fraction of the Fibre are Given<\/strong><\/h3>\n

Vf<\/sub> = F(f\/m)<\/sub> x Em<\/sub>Vm<\/sub><\/sup> \/ Ef<\/sub><\/sub><\/p>\n

Where:<\/p>\n

Vf<\/sub>\u00a0= Volume Fraction of the Fibre
\nF(f\/m)<\/sub>\u00a0= Ratio of Load of Fibre to Matrix
\nEf<\/sub>\u00a0= Elastic Modulus of the Fibre
\nEm<\/sub>\u00a0= Elastic Modulus of the Matrix
\nVm<\/sub>\u00a0= Volume Fraction of the Matrix<\/p>\n

Let’s solve an example;
\nFind the volume fraction of the fibre when the ratio of load of fibre to matrix is 7, the elastic modulus of the fibre is 20, the elastic modulus of the matrix is 4 and the volume fraction of the matrix is 6.<\/p>\n

This implies that;<\/p>\n

F(f\/m)<\/sub> = Ratio of Load of Fibre to Matrix = 7
\nEf<\/sub> = Elastic Modulus of the Fibre = 20
\nEm<\/sub> = Elastic Modulus of the Matrix = 4
\nVm<\/sub> = Volume Fraction of the Matrix = 6<\/p>\n

Vf<\/sub> = F(f\/m)<\/sub> x Em<\/sub>Vm<\/sub><\/sup> \/ Ef<\/sub><\/sub>
\nThat is, Vf<\/sub> = 7 x (4)(6)<\/sup> \/ 20<\/sub>
\nVf<\/sub> = 168<\/sup> \/ 20<\/sub>
\nVf<\/sub> = 8.4<\/p>\n

Therefore, the\u00a0volume fraction of the fibre\u00a0<\/strong>is\u00a08.4<\/strong><\/p>\n

Calculating the Volume Fraction of the Fibre when the Ratio of Load of Fibre to Matrix, the Elastic Modulus of the Fibre, the Elastic Modulus of the Matrix and the Volume Fraction of the Matrix are Given<\/strong><\/h3>\n

Vm<\/sub> = Ef<\/sub>Vf<\/sub><\/sup> \/ F(f\/m)<\/sub> x Em<\/sub><\/sub><\/p>\n

Where:<\/p>\n

Vm<\/sub>\u00a0= Volume Fraction of the Matrix
\nF(f\/m)<\/sub>\u00a0= Ratio of Load of Fibre to Matrix
\nEf<\/sub>\u00a0= Elastic Modulus of the Fibre
\nEm<\/sub>\u00a0= Elastic Modulus of the Matrix
\nVf<\/sub> = Volume Fraction of the Fibre<\/p>\n

Let’s solve an example;
\nFind the volume fraction of the matrix when the ratio of load of fibre to matrix is 10, the elastic modulus of the fibre is 16, the elastic modulus of the matrix is 6 and the volume fraction of the fibre is 8.<\/p>\n

This implies that;<\/p>\n

F(f\/m)<\/sub> = Ratio of Load of Fibre to Matrix = 10
\nEf<\/sub> = Elastic Modulus of the Fibre = 16
\nEm<\/sub> = Elastic Modulus of the Matrix = 6
\nVf<\/sub> = Volume Fraction of the Fibre = 8<\/p>\n

Vm<\/sub> = Ef<\/sub>Vf<\/sub><\/sup> \/ F(f\/m)<\/sub> x Em<\/sub><\/sub>
\nThen, Vm<\/sub> = (16)(8)<\/sup> \/ 10 x 6<\/sub>
\nVm<\/sub> = 128<\/sup> \/ 60<\/sub>
\nVm<\/sub> = 2.13<\/p>\n

Therefore, the\u00a0volume fraction of the matrix\u00a0<\/strong>is\u00a02.13<\/strong><\/p>\n

How to Calculate the Ratio of Load of Fibre to Matrix With Nickzom Calculator<\/strong><\/h3>\n

Nickzom Calculator \u2013\u00a0The Calculator Encyclopedia<\/strong> is capable of calculating the ratio of load of fibre to matrix.<\/p>\n

\n

To get the answer and workings of the ratio of load of fibre to matrix 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\u00a0Ratio of Load of Fibre to Matrix<\/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 ratio of load of fibre to matrix according to the respective parameter which is the Elastic Modulus of the Fibre (Ef<\/sub>), Elastic Modulus of the Matrix (Em<\/sub>), Volume Fraction of the Fibre (Vf<\/sub>)<\/strong> and Volume Fraction of the Matrix (Vm<\/sub>).<\/strong><\/p>\n

\"\"<\/p>\n

Now, enter the values appropriately and accordingly for the parameters as required by the Elastic Modulus of the Fibre (Ef<\/sub>)<\/strong> is 14<\/strong>, Elastic Modulus of the Matrix (Em<\/sub>)<\/strong> is 10<\/strong>, Volume Fraction of the Fibre (Vf<\/sub>)\u00a0<\/strong>is\u00a06<\/strong> and Volume Fraction of the Matrix (Vm<\/sub>)<\/strong> is 2<\/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 ratio of load of fibre to matrix and presents the formula, workings and steps too.<\/p>\n","protected":false},"excerpt":{"rendered":"The ratio of load of fibre to matrix is illustrated by the image below. To calculate ratio of…","protected":false},"author":5,"featured_media":15970,"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":[2131,2145,2144,60,543,2147,2142,2128],"class_list":["post-7634","post","type-post","status-publish","format-standard","has-post-thumbnail","category-engineering","tag-composites","tag-elastic-modulus-of-the-fibre","tag-elastic-modulus-of-the-matrix","tag-engineering","tag-materials-and-metallurgical","tag-ratio-of-load-of-fibre-to-matrix","tag-volume-fraction-of-the-fibre","tag-volume-fraction-of-the-matrix","cs-entry"],"yoast_head":"\nHow to Calculate and Solve for Ratio of Load of Fibre to Matrix | Composites<\/title>\n<meta name=\"description\" content=\"Learn the step by step guide, workings, and formula on How to Calculate and Solve for Ratio of Load of Fibre to Matrix in Composites.\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/www.nickzom.org\/blog\/2022\/08\/04\/how-to-calculate-and-solve-for-ratio-of-load-of-fibre-to-matrix-composites\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"How to Calculate and Solve for Ratio of Load of Fibre to Matrix | Composites\" \/>\n<meta property=\"og:description\" content=\"Learn the step by step guide, workings, and formula on How to Calculate and Solve for Ratio of Load of Fibre to Matrix in Composites.\" \/>\n<meta property=\"og:url\" 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