{"id":7617,"date":"2022-08-03T15:02:36","date_gmt":"2022-08-03T14:02:36","guid":{"rendered":"https:\/\/www.nickzom.org\/blog\/?p=7617"},"modified":"2024-05-28T10:07:26","modified_gmt":"2024-05-28T09:07:26","slug":"how-to-calculate-and-solve-for-total-composite-strength-composites","status":"publish","type":"post","link":"https:\/\/www.nickzom.org\/blog\/2022\/08\/03\/how-to-calculate-and-solve-for-total-composite-strength-composites\/","title":{"rendered":"How to Calculate and Solve for Total Composite Strength | Composites"},"content":{"rendered":"

The total composite strength is illustrated by the image below. If you want to calculate the total composite strength, four essential parameters are needed and these parameters are Strength of the Matrix (\u03c3m<\/sub>), Strength of the Fibre (\u03c3f<\/sub>), Volume Fraction of the Matrix (Vm<\/sub>)<\/strong> and Volume Fraction of the Fibre (Vf<\/sub>).<\/strong><\/p>\n

\"\"<\/p>\n

The formula for calculating total composite strength:<\/strong><\/h3>\n

\u03c3c<\/sub>\u00a0= \u03c3m<\/sub>Vm<\/sub>\u00a0+ \u03c3f<\/sub>Vf<\/sub><\/p>\n

Where:<\/p>\n

\u03c3c<\/sub>\u00a0= Total Composite Strength
\n\u03c3m<\/sub>\u00a0= Strength of the Matrix
\nAlso, \u03c3f<\/sub>\u00a0= Strength of the Fibre
\nVm<\/sub>\u00a0= Volume Fraction of the Matrix
\nVf<\/sub>\u00a0= Volume Fraction of the Fibre<\/p>\n

Let’s solve an example;
\nFind the total composite strength when the strength of the matrix is 6, the strength of the fibre is 12, the volume fraction of the matrix is 10 and the volume fraction of the fibre is 4.<\/p>\n

This implies that;<\/p>\n

\u03c3m<\/sub> = Strength of the Matrix = 6
\n\u03c3f<\/sub> = Strength of the Fibre = 12
\nVm<\/sub> = Volume Fraction of the Matrix = 10
\nVf<\/sub> = Volume Fraction of the Fibre = 4<\/p>\n

\u03c3c<\/sub>\u00a0= \u03c3m<\/sub>Vm<\/sub>\u00a0+ \u03c3f<\/sub>Vf<\/sub>
\nThat is, \u03c3c<\/sub> = (6)(10) + (12)(4)
\n\u03c3c<\/sub> = (60) + (48)
\n\u03c3c<\/sub>\u00a0= 108<\/p>\n

Therefore, the\u00a0total composite strength <\/strong>is 108 Pa.<\/strong><\/p>\n

Calculating the Strength of the Matrix when the Total Composite Strength, the Strength of the Fibre, the Volume Fraction of the Matrix and the Volume Fraction of the Fibre are Given<\/strong><\/h3>\n

\u03c3m<\/sub> = \u03c3c<\/sub> – \u03c3f<\/sub>Vf<\/sub><\/sup> \/ Vm<\/sub><\/sub><\/p>\n

Where:<\/p>\n

\u03c3m<\/sub>\u00a0= Strength of the Matrix
\n\u03c3c<\/sub>\u00a0= Total Composite Strength
\nAlso, \u03c3f<\/sub>\u00a0= Strength of the Fibre
\nVm<\/sub>\u00a0= Volume Fraction of the Matrix
\nVf<\/sub>\u00a0= Volume Fraction of the Fibre<\/p>\n

Let’s solve an example;
\nFind the strength of the matrix when the total composite strength is 40, the strength of the fibre is 10, the volume fractions of the matrix is 5 and the volume fractions of the fibre is 2.<\/p>\n

This implies that;<\/p>\n

\u03c3c<\/sub>\u00a0= Total Composite Strength = 40
\n\u03c3f<\/sub>\u00a0= Strength of the Fibre = 10
\nVm<\/sub>\u00a0= Volume Fraction of the Matrix = 5
\nVf<\/sub>\u00a0= Volume Fraction of the Fibre = 2<\/p>\n

\u03c3m<\/sub> = \u03c3c<\/sub> – \u03c3f<\/sub>Vf<\/sub><\/sup> \/ Vm<\/sub><\/sub>
\n\u03c3m<\/sub> = 40 – (10)(2)<\/sup> \/ 5<\/sub>
\nThat is, \u03c3m<\/sub> = 40 – 20<\/sup> \/ 5<\/sub>
\n\u03c3m<\/sub> = 20<\/sup> \/ 5<\/sub>
\n\u03c3m<\/sub> = 4<\/p>\n

Therefore, the\u00a0strength of the matrix\u00a0<\/strong>is\u00a04.<\/strong><\/p>\n

Read more:\u00a0How to Calculate and Solve for Total Load on Composite | Composites<\/a><\/p>\n

Calculating the Strength of the Fibre when the Total Composite Strength, the Strength of the Matrix, the Volume Fraction of the Matrix and the Volume Fraction of the Fibre are Given<\/strong><\/h3>\n

\u03c3f<\/sub> = \u03c3c<\/sub>\u00a0 – \u03c3m<\/sub>Vm<\/sub><\/sup> \/ Vf<\/sub><\/sub><\/p>\n

Where:<\/p>\n

\u03c3f<\/sub>\u00a0= Strength of the Fibre
\n\u03c3c<\/sub>\u00a0= Total Composite Strength
\nThen, \u03c3m<\/sub>\u00a0= Strength of the Matrix
\nVm<\/sub>\u00a0= Volume Fraction of the Matrix
\nVf<\/sub>\u00a0= Volume Fraction of the Fibre<\/p>\n

Let’s solve an example;
\nFind the strength of the fibre when the total composite strength is 50, the strength of the matrix is 4, the volume fractions of the matrix is 5 and the volume fractions of the fibre is 10.<\/p>\n

This implies that;<\/p>\n

\u03c3c<\/sub>\u00a0= Total Composite Strength = 50
\n\u03c3m<\/sub>\u00a0= Strength of the Matrix = 4
\nVm<\/sub>\u00a0= Volume Fraction of the Matrix = 5
\nVf<\/sub>\u00a0= Volume Fraction of the Fibre = 10<\/p>\n

\u03c3f<\/sub> = \u03c3c<\/sub>\u00a0 – \u03c3m<\/sub>Vm<\/sub><\/sup> \/ Vf<\/sub><\/sub>
\n\u03c3f<\/sub> = 50 – (4)(5)<\/sup> \/ 10<\/sub>
\nThat is, \u03c3f<\/sub> = 50 – 20<\/sup> \/ 10<\/sub>
\n\u03c3f<\/sub> = 30<\/sup> \/ 10<\/sub>
\n\u03c3f<\/sub> = 3<\/p>\n

Therefore, the\u00a0strength of the fibre\u00a0<\/strong>is\u00a03.<\/strong><\/p>\n

Calculate the volume fraction of the matrix when the total composite strength, the strength of the matrix, the strength of the fibre, and the volume fraction of the fibre are given<\/b><\/h3>\n

Vm<\/sub> = \u03c3c<\/sub> – \u03c3f<\/sub>Vf<\/sub><\/sup> \/ \u03c3m<\/sub><\/sub><\/p>\n

Where:<\/p>\n

Vm<\/sub>\u00a0= Volume Fraction of the Matrix
\n\u03c3c<\/sub>\u00a0= Total Composite Strength
\n\u03c3m<\/sub>\u00a0= Strength of the Matrix
\nThen, \u03c3f<\/sub>\u00a0= Strength of the Fibre
\nVf<\/sub>\u00a0= Volume Fraction of the Fibre<\/p>\n

Given an example;
\nFind the volume fractions of the matrix when the total composite strength is 30, the strength of the matrix is 3, the strength of the fibre is 5 and the volume fractions of the fibre is 3.<\/p>\n

This implies that;<\/p>\n

\u03c3c<\/sub>\u00a0= Total Composite Strength = 30
\n\u03c3m<\/sub>\u00a0= Strength of the Matrix = 3
\nAlso, \u03c3f<\/sub>\u00a0= Strength of the Fibre = 5
\nVf<\/sub>\u00a0= Volume Fraction of the Fibre = 3<\/p>\n

That is, Vm<\/sub> = \u03c3c<\/sub> – \u03c3f<\/sub>Vf<\/sub><\/sup> \/ \u03c3m<\/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

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

Calculating the Volume Fraction of the Fibre when the Total Composite Strength, the Strength of the Matrix, the Strength of the Fibre and the Volume Fraction of the Matrix are Given<\/strong><\/h3>\n

Vf<\/sub> = \u03c3c<\/sub> – \u03c3m<\/sub>Vm<\/sub><\/sup> \/ \u03c3f<\/sub><\/sub><\/p>\n

Where:<\/p>\n

Vf<\/sub>\u00a0= Volume Fraction of the Fibre
\n\u03c3c<\/sub>\u00a0= Total Composite Strength
\nAlso, \u03c3m<\/sub>\u00a0= Strength of the Matrix
\n\u03c3f<\/sub>\u00a0= Strength of the Fibre
\nVm<\/sub>\u00a0= Volume Fraction of the Matrix<\/p>\n

Let’s solve an example;
\nFind the volume fractions of the fibre when the total composite strength is 10, the strength of matrix is 2, the strength of the fibre is 4 and the volume fraction of the matrix is 3.<\/p>\n

This implies that;<\/p>\n

\u03c3c<\/sub>\u00a0= Total Composite Strength = 10
\n\u03c3m<\/sub>\u00a0= Strength of the Matrix = 2
\nThat is, \u03c3f<\/sub>\u00a0= Strength of the Fibre = 4
\nVm<\/sub>\u00a0= Volume Fraction of the Matrix = 3<\/p>\n

Vf<\/sub> = \u03c3c<\/sub> – \u03c3m<\/sub>Vm<\/sub><\/sup> \/ \u03c3f<\/sub><\/sub>
\nThat is, Vf<\/sub> = 10 – (2)(3)<\/sup> \/ 4<\/sub>
\nVf<\/sub> = 10 – 6<\/sup> \/ 4<\/sub>
\nThen, Vf<\/sub> = 4<\/sup> \/ 4<\/sub>
\nVf<\/sub> = 1<\/p>\n

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

How to Calculate the Total Composite Strength Using Nickzom Calculator<\/strong><\/h3>\n

Nickzom Calculator \u2013\u00a0The Calculator Encyclopedia<\/strong> is capable of calculating the total composite strength.<\/p>\n

\n

To get the answer and workings of the total composite strength 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 Total Composite Strength <\/b>under Composites<\/b><\/p>\n

\"\"<\/p>\n

The screenshot below displays the page or activity to enter your values, to get the answer for the total composite strength according to the respective parameter which is the Strength of the Matrix (\u03c3m<\/sub>), Strength of the Fibre (\u03c3f<\/sub>), Volume Fraction of the Matrix (Vm<\/sub>)<\/strong> and Volume Fraction of the Fibre (Vf<\/sub>).<\/strong><\/p>\n

\"\"<\/p>\n

Now, enter the values appropriately and accordingly for the parameters as required by the Strength of the Matrix (\u03c3m<\/sub>)<\/strong> is 6<\/strong>, Strength of the Fibre (\u03c3f<\/sub>)<\/strong> is 12<\/strong>, Volume Fraction of the Matrix (Vm<\/sub>)\u00a0<\/strong>is\u00a010<\/strong> and Volume Fraction of the Fibre (Vf<\/sub>)<\/strong> is 4<\/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\u2014The Calculator Encyclopedia can calculate the total composite strength and presents the formula, workings, and steps,<\/strong>\u00a0too.<\/p>\n","protected":false},"excerpt":{"rendered":"The total composite strength is illustrated by the image below. If you want to calculate the total composite…","protected":false},"author":5,"featured_media":15819,"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":[2131,60,543,2141,2140,2143,2142,2128],"class_list":["post-7617","post","type-post","status-publish","format-standard","has-post-thumbnail","category-engineering","tag-composites","tag-engineering","tag-materials-and-metallurgical","tag-strength-of-the-fibre","tag-strength-of-the-matrix","tag-total-composite-strength","tag-volume-fraction-of-the-fibre","tag-volume-fraction-of-the-matrix","cs-entry"],"yoast_head":"\nHow to Calculate and Solve for Total Composite Strength | Composites<\/title>\n<meta name=\"description\" content=\"Master the steps, formula, and parameters on How to Calculate and Solve for Total Composite Strength. 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