Analysis of a pull-out test with real specimen geometry. Part I: matrix droplet in the shape of a spherical segment

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Abstract
We compared two models of the pull-out specimen – the ‘equivalent cylinder’ and the platelet models in which the matrix droplet is represented as a set of thin parallel disks with the diameters varying along the embedded fiber to approximate the real droplet shape. Analytical expressions for the profiles of the fiber tensile stress and the interfacial shear stress have been derived for the matrix droplet in the shape of a spherical segment, including the effects of residual thermal stresses and interfacial friction. Using these expressions, we analyzed the process of crack initiation and propagation in the platelet model and investigated the effect of the specimen shape on the force–displacement curves. The interfacial stress near the loaded fiber end in the platelet model is higher than in the equivalent cylinder model, which gives rise to earlier crack initiation and smoother shape of the force–displacement curve. As a result, the calculated interfacial shear strength values may be underestimated by 10–20%, if the equivalent cylinder is used instead of the real droplet shape. A method of correction to the equivalent cylinder model in order to avoid this underestimation is proposed.