{"id":3111,"date":"2020-04-19T10:24:39","date_gmt":"2020-04-19T09:24:39","guid":{"rendered":"https:\/\/www.nickzom.org\/blog\/?p=3111"},"modified":"2024-03-31T06:45:15","modified_gmt":"2024-03-31T05:45:15","slug":"how-to-calculate-and-solve-for-flexural-strength-with-relation-to-volume-fraction-ceramics","status":"publish","type":"post","link":"https:\/\/www.nickzom.org\/blog\/2020\/04\/19\/how-to-calculate-and-solve-for-flexural-strength-with-relation-to-volume-fraction-ceramics\/","title":{"rendered":"How to Calculate and Solve for Flexural Strength with Relation to Volume Fraction | Ceramics"},"content":{"rendered":"

\"\"<\/p>\n

The image above represents Flexural strength with relation to volume in ceramics. To calculate flexural strength with relation to volume in ceramics, three essential parameters are needed and these parameters are Initial Stress (\u03c3o<\/sub>), Constant (n)<\/strong> and Volume fraction porosity (P).<\/strong><\/p>\n

The formula for calculating flexural strength with relation to volume:<\/p>\n

\u03c3fs<\/sub>\u00a0= \u03c3o <\/sub>exp (-nP)<\/p>\n

Where:<\/p>\n

\u03c3fs<\/sub>\u00a0= Flexural Strength
\n\u03c3o<\/sub>\u00a0= Initial Stress
\nn = Constant
\nP = Volume Fraction Porosity<\/p>\n

Let’s solve an example;
\nFind the flexural strength when the initial stress is 11, the constant is 8 and the volume fraction porosity is 22.<\/p>\n

This implies that;<\/p>\n

\u03c3o<\/sub> = Initial Stress = 11
\nn = Constant = 8
\nP = Volume Fraction Porosity = 22<\/p>\n

\u03c3fs<\/sub>\u00a0= \u03c3o <\/sub>exp (-nP)
\n\u03c3fr<\/sub> = (11)exp(-(8)(22))
\nThen, \u03c3fr<\/sub> = (11)exp(-176)
\n\u03c3fr<\/sub> = (11)(3.665e-77)
\n\u03c3fr<\/sub> = 4.032e-76<\/p>\n

Therefore, the\u00a0flexural strength\u00a0<\/strong>is\u00a04.032e-76 Pa.<\/strong><\/p>\n

Calculating the Initial Stress when the Flexural Strength, the Constant and the Volume Fraction Porosity are Given<\/strong><\/h3>\n

\u03c3o<\/sub> = \u03c3fr<\/sub><\/sup> \/ exp (-nP)<\/sub><\/p>\n

Where;<\/p>\n

\u03c3o<\/sub>\u00a0= Initial Stress
\n\u03c3fs<\/sub>\u00a0= Flexural Strength
\nn = Constant
\nP = Volume Fraction Porosity<\/p>\n

Let’s solve an example;
\nFind the initial stress when the flexural strength is 20, the constant is 10 and the volume fraction porosity is 8.<\/p>\n

This implies that;<\/p>\n

\u03c3fs<\/sub> = Flexural Strength = 20
\nn = Constant = 10
\nP = Volume Fraction Porosity = 8<\/p>\n

\u03c3o<\/sub> = \u03c3fr<\/sub><\/sup> \/ exp (-nP)<\/sub>
\n\u03c3o<\/sub> = 20<\/sup> \/ exp (-10 x 8)<\/sub>
\nThat is, \u03c3o<\/sub> = 20<\/sup> \/ exp (-80)<\/sub>
\n\u03c3o<\/sub> = 20<\/sup> \/ – 5.54e+34<\/sub>
\n\u03c3o<\/sub> = – 3.61e-34<\/p>\n

Therefore, the\u00a0initial stress\u00a0<\/strong>is\u00a03.61e-34.<\/strong><\/p>\n

Read more:\u00a0How to Calculate and Solve for Flexural Strength for Circular Cross-section in Defects | Ceramics<\/a><\/p>\n

Calculating the Constant when the Flexural Strength, the Initial Stress and the Volume Fraction Porosity are Given<\/strong><\/h3>\n

n = – (In \u03c3fr<\/sub><\/sup> \/ \u03c3o<\/sub><\/sub>) x 1<\/sup> \/ P<\/sub><\/p>\n

Where;<\/p>\n

n = Constant
\n\u03c3fs<\/sub>\u00a0= Flexural Strength
\n\u03c3o<\/sub>\u00a0= Initial Stress
\nP = Volume Fraction Porosity<\/p>\n

Let’s solve an example;
\nFind the constant when the flexural strength is 30, the initial stress is 10 and volume fraction porosity is 20.<\/p>\n

This implies that;<\/p>\n

\u03c3fs<\/sub> = Flexural Strength = 30
\n\u03c3o<\/sub> = Initial Stress = 10
\nP = Volume Fraction Porosity = 20<\/p>\n

n = – (In \u03c3fr<\/sub><\/sup> \/ \u03c3o<\/sub><\/sub>) x 1<\/sup> \/ P<\/sub>
\nn = – (In 30<\/sup> \/ 10<\/sub>) x 1<\/sup> \/ 20<\/sub>
\nThat is, n = – (In 3) x 0.05
\nn = – 1.098 x 0.05
\nn = – 0.0549<\/p>\n

Therefore, the\u00a0constant\u00a0<\/strong>is\u00a0– 0.0549.<\/strong><\/p>\n

Read more:\u00a0How to Calculate and Solve for Relationship between Modulus of Elasticity on Volume Fraction Porosity, E | Ceramics<\/a><\/p>\n

Calculating the Volume Fraction Porosity when the Flexural Strength, the Initial Stress and Constant are Given<\/strong><\/h3>\n

P = – (In \u03c3fr<\/sub><\/sup> \/ \u03c3o<\/sub><\/sub>) x 1<\/sup> \/ n<\/sub><\/p>\n

Where;<\/p>\n

P = Volume Fraction Porosity
\n\u03c3fs<\/sub>\u00a0= Flexural Strength
\n\u03c3o<\/sub>\u00a0= Initial Stress
\nn = Constant<\/p>\n

Let’s solve an example;
\nFind the volume fraction porosity when the flexural strength is 40, the initial stress is 2 and the constant is 12.<\/p>\n

This implies that;<\/p>\n

\u03c3fs<\/sub> = Flexural Strength = 40
\n\u03c3o<\/sub> = Initial Stress = 2
\nn = Constant = 12<\/p>\n

P = – (In \u03c3fr<\/sub><\/sup> \/ \u03c3o<\/sub><\/sub>) x 1<\/sup> \/ n<\/sub>
\nP = – (In 40<\/sup> \/ 2<\/sub>) x 1<\/sup> \/ 12<\/sub>
\nThen, P = – (In 20) x 0.05
\nP = – 2.99 x 0.05
\nP = – 0.1495<\/p>\n

Therefore, the\u00a0volume fraction porosity\u00a0<\/strong>is\u00a0– 0.1495.<\/strong><\/p>\n

How to Calculate Flexural Strength with Relation to Volume Fraction in Ceramics Using Nickzom Calculator<\/strong><\/h3>\n

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

To get the answer and workings of the flexural 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>for\u00a0NGN 1,500\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 & Metallurgical<\/strong>\u00a0<\/b>under\u00a0Engineering<\/strong>.<\/strong><\/p>\n

\"\"<\/p>\n

Now, Click on\u00a0Ceramics<\/strong>\u00a0<\/strong>under\u00a0Material & Metallurgical<\/strong><\/p>\n

\"\"<\/p>\n

Now, Click on Flexural Strength<\/strong>\u00a0<\/strong>under\u00a0Ceramics<\/strong><\/p>\n

\"\"<\/p>\n

The screenshot below displays the page or activity to enter your values, to get the answer for the flexural strength according to the respective parameters which are the Initial Stress (\u03c3o<\/sub>), Constant (n)<\/strong> and Volume fraction porosity (P).<\/strong><\/p>\n

\"How<\/p>\n

Now, enter the values appropriately and accordingly for the parameters as required by the Initial Stress (\u03c3o<\/sub>)<\/strong> is 8<\/strong>, Constant (n)<\/strong> is 11 <\/strong>and Volume fraction porosity (P)<\/strong> is 22<\/strong>.<\/p>\n

\"How<\/p>\n

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

\"How<\/p>\n

As you can see from the screenshot above,\u00a0Nickzom Calculator<\/strong>\u2013 The Calculator Encyclopedia solves for the flexural strength and presents the formula, workings and steps too.<\/p>\n","protected":false},"excerpt":{"rendered":"The image above represents Flexural strength with relation to volume in ceramics. To calculate flexural strength with relation…","protected":false},"author":5,"featured_media":13564,"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":[865,875,60,886,885,543,883],"class_list":["post-3111","post","type-post","status-publish","format-standard","has-post-thumbnail","category-engineering","tag-ceramics","tag-constant","tag-engineering","tag-flexural-strength-with-relation-to-volume-fraction","tag-initial-stress","tag-materials-and-metallurgical","tag-volume-fraction-porosity","cs-entry"],"yoast_head":"\nHow 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