We investigate the load-indentation test on a brittle material when cone crack occurs. For this occurrence of defect, in an original way :
- we use the second gradient model of Rakotomanana-Ravelonarivo [1] in the frame of weak continuous media theory,
- we simply start with the static stress field of Boussinesq (a single force punctually applied normal to the brittle surface [2]),
- then we extend it with introduction of the vector of Cartan devoted to approximate the discontinuity due to the nucleation of rupture.
- the norm of the latter vector is a small perturbation parameter in the equations of equilibrium and the solution at the first order leads to a pragmatic semi-analytical study.
With simplifying assumptions, proper definition of the occurrence of decohesion [3][4] and use of hypergeometric functions, we focus our attention to trap the apex angle of the cone: the influence of Poisson's coefficient has a similar tendency as other previous data (spherical indentation [5] or punching test [6]).
[1]Rakotomanana-Ravelonarivo, Arch. Rat. Mech. Anal., 141 (1997) 199-236.
[2]Antonio-Tamarasselvame, Thesis report, ARED-Bretagne, Rennes, France, 2010.
[3]Buisson, Matériaux et Techniques, Vol.99 N°2 (2011) 163-168.
[4]Antonio-Tamarasselvame and Buisson, 20ième Congrès Français de Mécanique, Besançon, Session 24, 2011.
[5] Fett, Rizzi, Diegele, Engineering Fracture Mechanics, 71 (2004) 2551-2560,
[6] Selvadurai, Mechanics of cohesive-frictional materials, 5 (2000) 325-339.