**Abstract**

Cracks in engineering materials and structures can undergo different modes of deformation. This chapter presents a numerical and experimental approaches aimed to assess the fracture toughness and the Fracture behavior under tensile and shear loading of bioceramics based on commercial Alumina (Al2O3), synthesized Tricalcium phosphate (β-TCP). Conditioning was conducted at different percentages of TCP. After a sintering process at 1600°C for 1 hour, The Crack Straight Through Brazilian Disc were performed by image correlation during a mechanical test and numerical tests were carried out in order to find the angle where the pure mode II. A CDM based constitutive model was selected and implemented into a finite element code to study the damage of our bioceramics. The result of this combination was compared with the direction of crack propagation obtained experimentally. The directions of crack propagation found numerically were found in good agreement with those experimentally obtained by a mechanical test. Alumina-10 wt.% Tricalcium phosphate composites displayed the highest values of the fracture toughness. This value reached 8.76 MPa m1/2 MPa. The same optimal composition for the mode I and mode II stress intensity factor with maximum values of 7.6 MPa m1/2 and 8.45 MPa m1/2 respectively.

**Keywords:** Fracture, Modeling, Tensile loading, Shear loading
