Microvoid coalescence

<h2 id="fracture-process">Fracture process</h2>
MVC proceeds in three stages: nucleation, growth, and coalescence of microvoids. The nucleation of microvoids can be caused by particle cracking or interfacial failure between <a href="/facts/Precipitation_hardening/hxe4lpBj">precipitate particles</a> and the matrix. Additionally, microvoids often form at grain boundaries or inclusions within the material.<a class="footnote-ref" id="fnref:1" href="#fn:1">1</a><a class="footnote-ref" id="fnref:2" href="#fn:2">2</a> Microvoids grow during plastic flow of the matrix, and microvoids coalesce when adjacent microvoids link together or the material between microvoids experiences <a href="/facts/Necking_(engineering)/wwG8GIav">necking</a>. Microvoid coalescence leads to fracture.<a class="footnote-ref" id="fnref:3" href="#fn:3">3</a> Void growth rates can be predicted assuming continuum plasticity using the Rice-Tracey model:<a class="footnote-ref" id="fnref:4" href="#fn:4">4</a><a class="footnote-ref" id="fnref:5" href="#fn:5">5</a>

 
 
 
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 ϵ
 
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 {\displaystyle \ln \left({\frac {\bar {R}}{R_{0}}}\right)=\int \limits _{0}^{\epsilon _{q}}A\left({\frac {3\sigma _{m}}{2\sigma _{ys}}}\right)d\epsilon _{v}^{p}}

where 
 
 
 
 A
 
 
 {\displaystyle A}
 
 is a constant typically equal to 0.283 (but dependent upon the stress triaxiality), 
 
 
 
 
 σ
 
 y
 s
 
 
 
 
 {\displaystyle \sigma _{ys}}
 
 is the <a href="/facts/Yield_Stress/mrSg02gW">yield stress</a>, 
 
 
 
 
 σ
 
 m
 
 
 
 
 {\displaystyle \sigma _{m}}
 
 is the <a href="/facts/Hydrostatic_stress/c5Id9Xq0">mean stress</a>, 
 
 
 
 
 ϵ
 
 q
 
 
 
 
 {\displaystyle \epsilon _{q}}
 
 is the equivalent Von Mises plastic strain, 
 
 
 
 
 R
 
 o
 
 
 
 
 {\displaystyle R_{o}}
 
 is the particle size, and 
 
 
 
 
 
 
 R
 ¯
 
 
 
 
 
 {\displaystyle {\bar {R}}}
 
 produced by the stress triaxality:

 
 
 
 
 
 
 R
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 1
 
 
 +
 
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 2
 
 
 +
 
 R
 
 3
 
 
 
 3
 
 
 
 
 {\displaystyle {\bar {R}}={\frac {R_{1}+R_{2}+R_{3}}{3}}}

<h2 id="fracture-surface-morphologies">Fracture surface morphologies</h2>
MVC can result in three distinct fracture morphologies based on the type of loading at failure. <a href="/facts/Tension_(physics)/waNGYp3a">Tensile loading</a> results in equiaxed dimples, which are spherical depressions a few micrometres in diameter that coalesce normal to the loading axis. <a href="/facts/Shear_stress/aWWnzIhE">Shear stresses</a> will result elongated dimples, which are parabolic depressions that coalesce in planes of maximum shear stress. The depressions point back to the crack origin, and shear influenced failure will produce depressions that point in opposite directions on opposing fracture surfaces. Combined tension and <a href="/facts/Bending/gxA8Pks1">bending</a> will also produce the elongated dimple morphology, but the directions of the depressions will be in the same direction on both fracture surfaces.

<h2 id="references">References</h2>

<ol>
<li id="fn:1">Askeland, Donald R. (January 2015). The science and engineering of materials. Wright, Wendelin J. (Seventh ed.). Boston, MA. pp. 236–237. ISBN 978-1-305-07676-1. OCLC 903959750.{{cite book}}: CS1 maint: location missing publisher (link) <a href="978-1-305-07676-1" target="_blank">978-1-305-07676-1</a> <a href="#fnref:1" class="footnote-back-ref">↩</a></li>
<li id="fn:2">Soboyejo, W.O (2003). Mechanical properties of engineered materials. Marcel Dekker. pp. 393–394. ISBN 0-203-91039-7. OCLC 54091550. <a href="0-203-91039-7" target="_blank">0-203-91039-7</a> <a href="#fnref:2" class="footnote-back-ref">↩</a></li>
<li id="fn:3">Hertzberg, Richard W. Deformation and Fracture Mechanics of Engineering Materials, Fourth Edition. John Wiley and Sons, Inc, Hoboken, NJ: 1996. <a href="#fnref:3" class="footnote-back-ref">↩</a></li>
<li id="fn:4">Soboyejo, W.O (2003). Mechanical properties of engineered materials. Marcel Dekker. pp. 393–394. ISBN 0-203-91039-7. OCLC 54091550. <a href="0-203-91039-7" target="_blank">0-203-91039-7</a> <a href="#fnref:4" class="footnote-back-ref">↩</a></li>
<li id="fn:5">Comprehensive structural integrity. Milne, I., Ritchie, R. O., Karihaloo, B. L. (1st ed.). Amsterdam: Elsevier/Pergamon. 2003. pp. 186–192. ISBN 978-0-08-049073-1. OCLC 190802556.{{cite book}}: CS1 maint: others (link) <a href="978-0-08-049073-1" target="_blank">978-0-08-049073-1</a> <a href="#fnref:5" class="footnote-back-ref">↩</a></li>
</ol>

Microvoid coalescence open-in-new

Microvoid coalescence