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Table 1 Mode II fracture toughness test geometries.

From: Mode II Fracture Toughness of Hybrid FRCs

Test geometries

Calculation equation

Dimensions mm

If h ≥ 2a, w ≥ πa. \( K_{IIc} = \frac{\sigma }{4}\left( {\pi a} \right)^{1/2} \)

If h ≥ 2a, w ≤ πa \( K_ {IIc} = \frac{\sigma }{4}w^{{{\raise0.5ex\hbox{$\scriptstyle 1$} \kern-0.1em/\kern-0.15em \lower0.25ex\hbox{$\scriptstyle 2$}}}} \)

Proposed by Reinhardt et al. (1997)

2h = 200

2a = 140, 120, 100

w = 100

Thickness = 100

\( K_{IIc}= \frac {5.11{\it {P}_Q}} {2{\it {BW}}}\left( {\pi a} \right)^{1/2} \)

Proposed by Watkins (1983) and Prokopski (1991)

Cube 150 mm

a = 45, 60, 75

w = 150

B = w − a

\( {K}_{IIc} {\mkern 1mu} = - \frac{{2{P}}}{{t}}\sqrt {\frac{\lambda }{{\pi R}}} \left\{ {\begin{array}{l} {B_{0} - \lambda ^{2} \left( {B_{0} + \frac{1}{2}B_{2} } \right) + \lambda ^{4} \left( { - \frac{1}{8}B_{0} + \frac{1}{4}B_{2} + \frac{3}{8}B_{4} } \right){\text{ }}} \\ { + \lambda ^{6} \left( {B_{0} - \frac{1}{{16}}B_{2} + \frac{1}{8}B_{4} + \frac{5}{{16}}B_{6} } \right)} \\ { + {\text{ }}\lambda ^{8} \left( { - \frac{{17}}{{64}}B_{0} + \frac{3}{8}B_{2} - \frac{5}{{128}}B_{4} + \frac{5}{{64}}B_{6} + \frac{{35}}{{128}}B_{8} } \right)} \\ \end{array} } \right\} \)

λ = a/R, and β: the notch inclination angle = 30°

B 0 = sin 2β, B2 = 2 [sin4β − sin2β], B4 = 3 [sin6β  − 2sin4β].

B 6 = 4 [sin8β − 3sin6β], B 8 = 5 [sin10β − 4sin8β].

Proposed by Irobe and Pen (1992)

β = 30°

R = 75

Thickness = 60

2a = 45, 60, 75

\( {K}_{IIc} = {Y}_{II} \sigma \sqrt {\pi a} \)

Proposed by Iosipescu (1967)

Prism 100 × 100 × 500

a = 30, 40, 50

Loaded span = 400