{"id":7601,"date":"2022-08-03T13:52:29","date_gmt":"2022-08-03T12:52:29","guid":{"rendered":"https:\/\/www.nickzom.org\/blog\/?p=7601"},"modified":"2024-05-28T10:07:05","modified_gmt":"2024-05-28T09:07:05","slug":"how-to-calculate-and-solve-for-critical-fibre-length-composites","status":"publish","type":"post","link":"https:\/\/www.nickzom.org\/blog\/2022\/08\/03\/how-to-calculate-and-solve-for-critical-fibre-length-composites\/","title":{"rendered":"How to Calculate and Solve for Critical Fibre Length | Composites"},"content":{"rendered":"

The critical fibre length is illustrated by the image below. To calculate critical fibre length, three essential parameters are needed and these parameters are Critical Fibre Stress (\u03c3*f<\/sub>), Fibre Diameter (d)<\/strong> and Shear Yield Strength (\u03c4c<\/sub>).<\/strong><\/p>\n

\"\"<\/p>\n

The formula for calculating critical fibre length:<\/strong><\/h3>\n

lc<\/sub>\u00a0=\u00a0\u03c3*f<\/sub>d<\/sup>\/2\u03c4c<\/sub><\/p>\n

Where:<\/p>\n

lc<\/sub> = Critical Fibre Length
\n\u03c3*f<\/sub>\u00a0= Critical Fibre Stress
\nd = Fibre Diameter
\n\u03c4c<\/sub>\u00a0= Shear Yield Strength<\/p>\n

Let’s solve an example;
\nFind the critical fibre length when the critical fibre stress is 15, the fibre diameter is 3 and the shear yield strength is 10.<\/p>\n

This implies that;<\/p>\n

\u03c3*f<\/sub> = Critical Fibre Stress = 15
\nd = Fibre Diameter = 3
\n\u03c4c<\/sub> = Shear Yield Strength = 10<\/p>\n

lc<\/sub>\u00a0=\u00a0\u03c3*f<\/sub>d<\/sup>\/2\u03c4c<\/sub>
\nThat is, lc<\/sub>\u00a0=\u00a0(15)(3)<\/sup>\/2(10)<\/sub>
\nlc<\/sub>\u00a0=\u00a0(45)<\/sup>\/(20)<\/sub>
\nlc<\/sub> = 2.25<\/p>\n

Therefore, the\u00a0critical fibre length\u00a0<\/strong>is\u00a02.25 cm.<\/strong><\/p>\n

Calculating the Critical Fibre Stress when the Critical Fibre Length, the Fibre Diameter and the Shear Yield Strength are Given<\/strong><\/h3>\n

\u03c3*f<\/sub> = lc<\/sub> x 2\u03c4c<\/sub><\/sup> \/ d<\/sub><\/p>\n

Where:<\/p>\n

\u03c3*f<\/sub>\u00a0= Critical Fibre Stress
\nlc<\/sub> = Critical Fibre Length
\nd = Fibre Diameter
\n\u03c4c<\/sub>\u00a0= Shear Yield Strength<\/p>\n

Let’s solve an example;
\nGiven the critical fibre length as 24, the fibre diameter as 12 and the shear yield strength as 4. Find the critical fibre stress?<\/p>\n

This implies that;<\/p>\n

lc<\/sub> = Critical Fibre Length = 24
\nd = Fibre Diameter = 12
\n\u03c4c<\/sub> = Shear Yield Strength = 4<\/p>\n

\u03c3*f<\/sub> = lc<\/sub> x 2\u03c4c<\/sub><\/sup> \/ d<\/sub>
\n\u03c3*f<\/sub> = 24 x 2(4)<\/sup> \/ 12<\/sub>
\nThat is, \u03c3*f<\/sub> = 24 x 8<\/sup> \/ 12<\/sub>
\n\u03c3*f<\/sub> = 192<\/sup> \/ 12<\/sub>
\n\u03c3*f<\/sub> = 16<\/p>\n

Therefore, the\u00a0critical fibre stress\u00a0<\/strong>is\u00a016.<\/strong><\/p>\n

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

Calculating the Fibre Diameter when the Critical Fibre Length, the Critical Fibre Stress and the Shear Yield Strength are Given<\/strong><\/h3>\n

d = lc<\/sub> x 2\u03c4c<\/sub><\/sup> \/ \u03c3*f<\/sub><\/sub><\/p>\n

Where:<\/p>\n

d = Fibre Diameter
\nlc<\/sub> = Critical Fibre Length
\n\u03c3*f<\/sub>\u00a0= Critical Fibre Stress
\n\u03c4c<\/sub>\u00a0= Shear Yield Strength<\/p>\n

Let’s solve an example;
\nFind the fibre diameter when the critical fibre length is 20, the critical fibre stress is 32 and the shear yield strength is 12.<\/p>\n

This implies that;<\/p>\n

lc<\/sub> = Critical Fibre Length = 20
\n\u03c3*f<\/sub> = Critical Fibre Stress = 32
\n\u03c4c<\/sub> = Shear Yield Strength = 12<\/p>\n

d = lc<\/sub> x 2\u03c4c<\/sub><\/sup> \/ \u03c3*f<\/sub><\/sub>
\nd = 20 x 2(12)<\/sup> \/ 32<\/sub>
\nThat is, d = 20 x 24<\/sup> \/ 32<\/sub>
\nd = 480<\/sup> \/ 32<\/sub>
\nd = 15<\/p>\n

Therefore, the\u00a0fibre diameter\u00a0<\/strong>is\u00a015 cm.<\/strong><\/p>\n

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

Calculating the Shear Yield Strength when the Critical Fibre Length, the Critical Fibre Stress and the Fibre Diameter are Given<\/strong><\/h3>\n

\u03c4c<\/sub> = \u03c3*f<\/sub>d<\/sup> \/ lc<\/sub> x 2<\/sub><\/p>\n

Where:<\/p>\n

\u03c4c<\/sub>\u00a0= Shear Yield Strength
\nlc<\/sub> = Critical Fibre Length
\n\u03c3*f<\/sub>\u00a0= Critical Fibre Stress
\nd = Fibre Diameter<\/p>\n

Let’s solve an example;
\nGiven that the critical fibre length is 14, the critical fibre stress is 8 and the fibre diameter is 6. Find the Shear Yield Strength?<\/p>\n

This implies that;<\/p>\n

lc<\/sub> = Critical Fibre Length = 14
\n\u03c3*f<\/sub> = Critical Fibre Stress = 8
\nd = Fibre Diameter = 6<\/p>\n

\u03c4c<\/sub> = \u03c3*f<\/sub>d<\/sup> \/ lc<\/sub> x 2<\/sub>
\nSo, \u03c4c<\/sub> = (8)(6)<\/sup> \/ 14 x 2<\/sub>
\n\u03c4c<\/sub> = 48<\/sup> \/ 28<\/sub>
\n\u03c4c<\/sub> = 1.714<\/p>\n

Therefore, the\u00a0shear yield strength\u00a0<\/strong>is\u00a01.714.<\/strong><\/p>\n

How to Calculate Critical Fibre Length Using Nickzom Calculator<\/strong><\/h3>\n

Nickzom Calculator \u2013\u00a0The Calculator Encyclopedia<\/strong> is capable of calculating the critical fibre length.<\/p>\n

\n

To get the answer and workings of the critica fibre length 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\u00a0Critical Fibre Length<\/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 critical fibre length according to the respective parameter which is the Critical Fibre Stress (\u03c3*f<\/sub>), Fibre Diameter (d)<\/strong> and Shear Yield Strength (\u03c4c<\/sub>).<\/strong><\/p>\n

\"How<\/p>\n

Now, enter the values appropriately and accordingly for the parameters as required by the Critical Fibre Stress (\u03c3*f<\/sub>)<\/strong> is 15<\/strong>, Fibre Diameter (d)\u00a0<\/strong>is\u00a03<\/strong> and Shear Yield Strength (\u03c4c<\/sub>)<\/strong> is 10<\/strong>.<\/p>\n

\"How<\/p>\n

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

\"How<\/p>\n

As you can see from\u00a0the screenshot above,\u00a0Nickzom Calculator<\/strong>\u2013 The Calculator Encyclopedia solves for the critical fibre length and presents the formula, workings and steps too.<\/p>\n","protected":false},"excerpt":{"rendered":"The critical fibre length is illustrated by the image below. To calculate critical fibre length, three essential parameters…","protected":false},"author":5,"featured_media":15968,"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":[2131,2136,2133,60,2134,543,2135],"class_list":["post-7601","post","type-post","status-publish","format-standard","has-post-thumbnail","category-engineering","tag-composites","tag-critical-fibre-length","tag-critical-fibre-stress","tag-engineering","tag-fibre-diameter","tag-materials-and-metallurgical","tag-shear-yield-strength","cs-entry"],"yoast_head":"\nHow to Calculate and Solve for Critical Fibre Length | Composites<\/title>\n<meta name=\"description\" content=\"Learn the steps and the formula on How to Calculate and Solve for Critical Fibre Length. 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