Prediction of Matrix Failure in Fibre Reinforced Polymer Composites

<table>Nonlinear stress-strain relationship. <svg height="15.4" id="M104" style="vertical-align:-3.3907pt" version="1.1" viewbox="0 0 14.7375 15.4" width="14.7375" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<g transform="matrix(.017,-0,0,-.017,.062,11.112)"><path d="M609 650l-19 -162l-30 -2q2 69 -14 94q-9 18 -28.5 26t-74.5 8h-88q-30 0 -37 -6.5t-12 -36.5l-41 -212h103q48 0 69 5.5t32 19t26 50.5h29l-40 -198h-30q2 58 -11.5 70.5t-85.5 12.5h-99l-30 -167q-17 -87 3 -101q18 -15 111 -15q59 0 89 7t54 27q8 7 15.5 16t16 21.5
l14 20.5t15 23.5t13.5 21.5l29 -10q-52 -129 -71 -163h-500l6 28q66 4 83 17.5t28 73.5l77 409q11 61 -0.5 75.5t-78.5 18.5l10 28h467z" id="x1D438"></path></g>
<g transform="matrix(.012,-0,0,-.012,10.8,15.187)"><path d="M244 607q0 -25 -15.5 -43t-37.5 -18q-19 0 -32 13t-13 35q0 21 15 41t39 20q20 0 32 -14t12 -34zM222 91q-29 -33 -79 -68t-75 -35q-13 0 -19 7.5t-6 31t10 65.5l62 253q5 26 -1 26q-21 0 -72 -43l-13 24q43 40 91 68t71 28q30 0 10 -78l-71 -274q-8 -30 3 -30
q16 0 76 48z" id="x1D456"></path></g>
</svg> = initial or nominal modulus, <svg height="11.9625" id="M105" style="vertical-align:-3.3907pt" version="1.1" viewbox="0 0 12.6375 11.9625" width="12.6375" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<g transform="matrix(.017,-0,0,-.017,.062,7.675)"><path d="M387 375q0 -16 -17 -31t-29 -15q-9 0 -12 13q-13 74 -80 74q-36 0 -61 -24.5t-25 -56.5t24 -51.5t68 -19.5q33 0 47 2l2 -7l-32 -42q-20 2 -54 2q-45 0 -74 -21.5t-29 -60.5q0 -41 28 -65.5t73 -24.5q78 0 145 67l17 -23q-33 -47 -84.5 -75t-111.5 -28q-70 0 -114.5 35.5
t-44.5 92.5q0 46 38 78t95 45v2q-35 10 -54.5 33t-19.5 52q0 55 53 88.5t122 33.5q67 0 98.5 -23.5t31.5 -49.5z" id="x1D700"></path></g>
<g transform="matrix(.012,-0,0,-.012,7.037,11.762)"><path d="M391 364q0 -28 -20.5 -53.5t-50 -43.5t-70 -34t-73.5 -25t-68 -17v-29q0 -48 20 -81t65 -33q73 0 157 76l16 -23q-107 -113 -221 -113q-21 0 -40.5 6.5t-39 22t-31.5 47t-12 75.5q0 69 33.5 139.5t95.5 114.5q77 55 143 55q42 0 69 -24.5t27 -59.5zM313 350
q0 26 -14.5 40.5t-37.5 14.5q-32 0 -44 -7q-82 -46 -104 -175q200 49 200 127z" id="x1D452"></path></g>
</svg> = elastic limit strain, <svg height="11.9625" id="M106" style="vertical-align:-3.39069pt" version="1.1" viewbox="0 0 20.5875 11.9625" width="20.5875" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<g transform="matrix(.017,-0,0,-.017,.062,7.675)"><path d="M387 375q0 -16 -17 -31t-29 -15q-9 0 -12 13q-13 74 -80 74q-36 0 -61 -24.5t-25 -56.5t24 -51.5t68 -19.5q33 0 47 2l2 -7l-32 -42q-20 2 -54 2q-45 0 -74 -21.5t-29 -60.5q0 -41 28 -65.5t73 -24.5q78 0 145 67l17 -23q-33 -47 -84.5 -75t-111.5 -28q-70 0 -114.5 35.5
t-44.5 92.5q0 46 38 78t95 45v2q-35 10 -54.5 33t-19.5 52q0 55 53 88.5t122 33.5q67 0 98.5 -23.5t31.5 -49.5z" id="x1D700"></path></g>
<g transform="matrix(.012,-0,0,-.012,7.037,11.762)"><path d="M518 50v-26q-32 -4 -77 -16l-37 -11t-33 -9l-6 6v71q-56 -42 -74 -52q-43 -25 -77 -25q-55 0 -89.5 36.5t-34.5 112.5v196q0 38 -6.5 48.5t-26.5 15.5l-28 6v23q19 1 72 7q59 9 71 11q-3 -31 -3 -145v-135q0 -113 88 -113q59 0 108 48v234q0 38 -8 49t-34 15l-36 6v23
q44 2 90 8q37 4 67 10v-334q0 -37 8.5 -47t38.5 -12z" id="x75"></path></g><g transform="matrix(.012,-0,0,-.012,13.403,11.762)"><path d="M238 0h-223v26q48 5 60 17t12 61v473q0 50 -10.5 60.5t-58.5 15.5v24q73 8 148 35v-608q0 -49 11.5 -61t60.5 -17v-26z" id="x6C"></path></g><g transform="matrix(.012,-0,0,-.012,16.283,11.762)"><path d="M298 36l-68 -35q-25 -13 -42 -13q-98 0 -98 119v290h-69l-4 11l28 29h45v72l65 67l14 -2v-137h113q8 -8 6 -21t-12 -19h-107v-256q0 -96 59 -96q29 0 61 17z" id="x74"></path></g>
</svg> = ultimate strain, and <svg height="12.325" id="M107" style="vertical-align:-3.39069pt" version="1.1" viewbox="0 0 23.225 12.325" width="23.225" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<g transform="matrix(.017,-0,0,-.017,.062,8.038)"><path d="M548 455q-32 -77 -74 -77q-37 0 -103 10l-3 -2q36 -30 48.5 -62t12.5 -80q0 -103 -75 -179.5t-175 -76.5q-70 0 -113 45t-43 128q0 115 83.5 200.5t209.5 85.5q31 0 77.5 -4t67.5 -4q36 0 62 30zM350 274q0 54 -17 86q-19 35 -57 35q-50 0 -90 -37.5t-59 -91.5t-19 -109
q0 -61 24.5 -96.5t65.5 -35.5q51 0 87.5 46.5t50.5 100.5t14 102z" id="x1D70E"></path></g>
<g transform="matrix(.012,-0,0,-.012,9.663,12.112)"><path d="M518 50v-26q-32 -4 -77 -16l-37 -11t-33 -9l-6 6v71q-56 -42 -74 -52q-43 -25 -77 -25q-55 0 -89.5 36.5t-34.5 112.5v196q0 38 -6.5 48.5t-26.5 15.5l-28 6v23q19 1 72 7q59 9 71 11q-3 -31 -3 -145v-135q0 -113 88 -113q59 0 108 48v234q0 38 -8 49t-34 15l-36 6v23
q44 2 90 8q37 4 67 10v-334q0 -37 8.5 -47t38.5 -12z" id="x75"></path></g><g transform="matrix(.012,-0,0,-.012,16.04,12.112)"><path d="M238 0h-223v26q48 5 60 17t12 61v473q0 50 -10.5 60.5t-58.5 15.5v24q73 8 148 35v-608q0 -49 11.5 -61t60.5 -17v-26z" id="x6C"></path></g><g transform="matrix(.012,-0,0,-.012,18.92,12.112)"><path d="M298 36l-68 -35q-25 -13 -42 -13q-98 0 -98 119v290h-69l-4 11l28 29h45v72l65 67l14 -2v-137h113q8 -8 6 -21t-12 -19h-107v-256q0 -96 59 -96q29 0 61 17z" id="x74"></path></g>
</svg> = ultimate stress.</table>

Journal of Engineering

Prediction of Matrix Failure in Fibre Reinforced Polymer Composites

Figure 9