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On the effect of the backup plate stiffness on the brittle failure of a ceramic armor

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Abstract

The present investigation enquires the role of the backup plate mechanical properties in the brittle failure of a ceramic tile. It provides a full-field solution for the elastostatic problem of an infinite Kirchhoff plate containing a semi-infinite rectilinear crack (the tile) resting on a two-parameter elastic foundation (the backup plate) and subjected to general transverse loading condition. The backup plate is modeled as a weakly non-local (Pasternak type) foundation, which reduces to the familiar local (Winkler) model once the Pasternak modulus is set to zero. The same governing equations are obtained for a curved plate (shell) subjected to in-plane equi-biaxial loading. Fourier transforms and the Wiener–Hopf technique are employed. The solution is obtained for the case when the Pasternak modulus is greater than the Winkler modulus. Superposition and a two-step procedure are employed: First, an infinite uncracked plate subjected to general loading is considered; then, the bending moment and shearing force distribution acting along the crack line are adopted as the (continuous) loading condition to be fed in the solution for the cracked plate. Results are obtained as a function of the ratio of the Pasternak over the Winkler foundation stiffness times the tile flexural rigidity. It is established that the elastic foundation significantly affects the mechanical behavior of the elastic plate. In particular, the Winkler model substantially underestimates the stress state near the crack tip. Stress-intensity factors are determined, and they are employed as a guideline for increasing the composite toughness. The analytical solution presented in this paper may serve as a benchmark for a more refined numerical analysis.

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Authors and Affiliations

  1. Dipartimento di Ingegneria Enzo Ferrari, Università degli Studi di Modena e Reggio Emilia, Via Vignolese 905, 41125, Modena, Italy

    Andrea Nobili

  2. Dipartimento di Scienze e Metodi dell’Ingegneria, Università degli Studi di Modena e Reggio Emilia, Via Amendola 2, 42122, Reggio Emilia, Italy

    Enrico Radi

  3. Dipartimento di Economia e Tecnologia, Università degli Studi della Repubblica di San Marino, Via Salita Alla Rocca 44, 47890, San Marino, Republic of San Marino

    Luca Lanzoni

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  1. Andrea Nobili
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  2. Enrico Radi
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Correspondence to Andrea Nobili.

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Nobili, A., Radi, E. & Lanzoni, L. On the effect of the backup plate stiffness on the brittle failure of a ceramic armor. Acta Mech 227, 159–172 (2016). https://doi.org/10.1007/s00707-015-1412-5

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  • DOI: https://doi.org/10.1007/s00707-015-1412-5

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