Experimental and Theoretical Assessment of Brittle Fracture in Engineering Components Containing a Sharp V-Notch

Abstract

A criterion was proposed to predict brittle fracture in engineering components containing sharp V-shaped notches and subjected to mixed mode I/II loading. The criterion, called SV-MTS, was developed based on the maximum tangential stress (MTS) criterion proposed originally for analyzing crack problems. The curves which are obtained from the SV-MTS criterion could be used conveniently to predict the fracture resistance and also the notch bifurcation angle in sharp V-notched components under pure mode II and also mixed mode loading. To evaluate the validity of the proposed criterion, a set of fracture tests were conducted on a new test specimen, called sharp V-notched Brazilian disc (SV-BD), under mixed mode loading conditions. It is shown that the experimental results obtained from PMMA specimens are in very good agreement with the curves of SV-MTS criterion.

Appendix

The functions f _if (θ) and g _if (θ) used in the stress distribution around a sharp V-notch [18]:

$$ \left\{ {\begin{array}{*{20}{c}} {{f_{rr}}(\theta )} \\{{f_{\theta \theta }}(\theta )} \\{{f_{r\theta }}(\theta )} \\\end{array} } \right\} = \left[ {\begin{array}{*{20}{c}} {{{{\left\{ {\cos (m\theta ) + \frac{{(2 + n)}}{n}\frac{{\sin ({{{\omega \,m}} \left/ {2} \right.})}}{{\sin ({{{\omega \,n}} \left/ {2} \right.})}}\cos (n\theta )} \right\}}} \left/ {{\sigma_{\theta \theta }^I(\theta = 0)}} \right.}} \hfill \\{{{{\left\{ { - \cos (m\theta ) + \frac{m}{n}\frac{{\sin ({{{\omega \,m}} \left/ {2} \right.})}}{{\sin ({{{\omega \,n}} \left/ {2} \right.})}}\cos (n\theta )} \right\}}} \left/ {{\sigma_{\theta \theta }^I(\theta = 0)}} \right.}} \hfill \\{{{{\left\{ { - \sin (m\theta ) + \frac{{\sin ({{{\omega \,m}} \left/ {2} \right.})}}{{\sin ({{{\omega \,n}} \left/ {2} \right.})}}\sin (n\theta )} \right\}}} \left/ {{\sigma_{\theta \theta }^I(\theta = 0)}} \right.}} \hfill \\\end{array} } \right] $$

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$$ \left\{ {\begin{array}{*{20}{c}} {{g_{rr}}(\theta )} \\{{g_{\theta \theta }}(\theta )} \\{{g_{r\theta }}(\theta )} \\\end{array} } \right\} = \left[ {\begin{array}{*{20}{c}} {\left\{ {\sin (p\theta ) + \frac{{(2 + q)}}{p}\frac{{\sin ({{{\omega \,p}} \left/ {2} \right.})}}{{\sin ({{{\omega \,q}} \left/ {2} \right.})}}\sin (q\theta )} \right\}/\sigma_{r\theta }^{II}(\theta = 0)} \hfill \\{\left\{ { - \sin (p\theta ) + \frac{{\sin ({{{\omega \,p}} \left/ {2} \right.})}}{{\sin ({{{\omega \,q}} \left/ {2} \right.})}}\sin (q\theta )} \right\}/\sigma_{r\theta }^{II}(\theta = 0)} \hfill \\{\left\{ {\cos (p\theta ) - \frac{q}{p}\frac{{\sin ({{{\omega \,p}} \left/ {2} \right.})}}{{\sin ({{{\omega \,q}} \left/ {2} \right.})}}\cos (q\theta )} \right\}/\sigma_{r\theta }^{II}(\theta = 0)} \hfill \\\end{array} } \right] $$

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