GPODT
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Can someone explain what is MPa√a exactly? I have never come across this..
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uberteknik
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(Original post by GPODT)
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Can someone explain what is MPa√a exactly? I have never come across this..
A long time since I covered this:

KIC = critical stress intensity factor for a mode I crack.

It's a measure of the materials resistance to crack growth. i.e. force needed to propagate an existing thin crack opening under normal tensile stress perpendicular to the crack (when KIC = fracture toughness).


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http://simscience.org/cracks/advanced/math1.html
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GPODT
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(Original post by uberteknik)
A long time since I covered this:

KIC = critical stress intensity factor for a mode I crack.

It's a measure of the materials resistance to crack growth. i.e. force needed to propagate an existing thin crack opening under normal tensile stress perpendicular to the crack (when KIC = fracture toughness).


Image
http://simscience.org/cracks/advanced/math1.html
Sorry if I wasn't clear enough, what I meant was how did they get the units MPa√m for Kic? The √m has confused me.
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Stonebridge
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(Original post by GPODT)
Sorry if I wasn't clear enough, what I meant was how did they get the units MPa√m for Kic? The √m has confused me.
It means square root of metre

So MPa√m has units

MPam½

Mega pascal √metre

This would come from the units in its defining equation.
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uberteknik
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(Original post by GPODT)
Sorry if I wasn't clear enough, what I meant was how did they get the units MPa√m for Kic? The √m has confused me.
As Stonebridge pointed out, \sqrt{m} is the remainder after factoring out \mathrm{Nm^{-2}} from the final equation definition for K_{IC}


E = \mathrm{Youngs \ modulus} = \frac{\sigma}{\epsilon} = \mathrm{Nm^{-2}}

G_c = \mathrm{Toughness} = \mathrm{Jm^{-2}} = \mathrm{Nm.m^{-2}} = \mathrm{Nm^{-1}}

EG_c = \mathrm{Nm^{-2}}.\mathrm{Nm^{-1}} = \mathrm{N^2m^{-3}}

K_{IC} = \sqrt{EG_c} = (\mathrm{N^2m^{-3}})^{\frac{1}{2}} = \mathrm{Nm^{\frac{-3}{2}}}


It's debatable that this is not a very intuitive form for the units (newtons per root metre cubed). I suspect because engineers are concerned more with application and convenience, a more memorable and intuitive unit factors out the exponent and reduces it to pascals root metre.

i.e. since:

\mathrm{Nm^{-2}} = \mathrm{pascals}

K_{IC} = \mathrm{Nm^{\frac{-3}{2}}} = \mathrm{Nm^{-2}.m^{\frac{1}{2}}} = \mathrm{Nm^{-2}\sqrt{m}}

\therefore K_{IC} = \mathrm{Pa{\sqrt{m}}}
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