caa a22 4500 397572344 CHVBK 20180308164845.0 cr unu---uuuuu 161202e199611 xx s 000 0 eng 10.1093/qjmam/49.4.545 doi (NATIONALLICENCE)oxford-10.1093/qjmam/49.4.545 CRITICAL LOAD FOR A MODE-1 CRACK REINFORCED BY BRIDGING FIBRES [Elektronische Daten] [N. V. MOVCHAN, J. R. WILLIS] A long matrix crack in a unidirectional fibre-reinforced composite, perpendicular to the fibre direction and subjected to Mode-1 loading, is considered. The intact composite material is modelled as homogeneous linearly elastic and the bridging fibres are replaced by restraining tractions acting on the crack surfaces. The problem is formulated in terms of a hypersingular integral equation with respect to the relative crack-face separation and contains a small parameter multiplying the integral term. Two limiting cases, related to the maximal opening in the middle of the crack before fibres break and to the maximal opening at the ends of the region where fibres are broken, are analysed. The asymptotic solution of the problem is constructed with the use of a matched expansions technique. The values of applied load, corresponding to these two limiting situations, are estimated. This necessitates consideration of new boundary layers in the middle of the crack, even in the case when no fibres have broken. © Oxford University Press Articles nationallicence MOVCHAN N. V. School of Mathematical Sciences, University of Bath Bath BA2 7 AY) aut WILLIS J. R. Department of Applied Mathematics and Theoretical Physics, University of Cambridge Silver Street, Cambridge CB3 9EW) aut The Quarterly Journal of Mechanics and Applied Mathematics Oxford University Press 49/4(1996-11), 545-564 0033-5614 49:4<545 1996 49 qjmamj https://doi.org/10.1093/qjmam/49.4.545 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1093/qjmam/49.4.545 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- MOVCHAN N. V. School of Mathematical Sciences, University of Bath Bath BA2 7 AY) aut NATIONALLICENCE 700 1- WILLIS J. R. Department of Applied Mathematics and Theoretical Physics, University of Cambridge Silver Street, Cambridge CB3 9EW) aut NATIONALLICENCE 773 0- The Quarterly Journal of Mechanics and Applied Mathematics Oxford University Press 49/4(1996-11), 545-564 0033-5614 49:4<545 1996 49 qjmamj Metadata rights reserved CC BY-NC-4.0 http://creativecommons.org/licenses/by-nc/4.0 nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-oxford