**1. Introduction**

Recently, the technology of tissue engineering has widely known in substantial advancements and innovations. This technology is a discipline to restoring the task of various organs through the regeneration and also develop novel synthetic biomaterials. It is being investigated and applied in most organ systems, restoring the function of various tissues and organs, such as heart valves, blood vessels and orthopedic implants, among many others [1–3]. Cracks and flaws which certainly exist in the sample reduce in a significant way the load-bearing capacity and then

cause the substitute to break [4, 5]. The fracture toughness and stress intensity factor have been proposed to express the critical stress states in the vicinity of the crack tip, in the aim to analyze crack initiation and propagation [5].

Calcium phosphate bioceramics, with its excellent biological properties, such as biocompatibility and osteconductivity and its outstanding mechanical properties, including hardness, low density and its inertness at high temperature, is widely known as a suitable candidate for biomaterials. Despite their advantages, Calcium phosphates bioceramics exhibit very low toughness which limits their overall applications [6]. The challenge of increasing the toughness of bioceramic has been a key motivation in the field of biomaterials research. In this pursuit of improving toughness, β-tricalcium phosphate (β-Ca3(PO4)2) (β-TCP) are often used due to its outstanding biological responses to physiological environments [7]. The introduction of Alumina (Al2O3) toughening agent increased the toughness of the tricalcium phosphate composite.

Alumina has been widely studied due to its high wear resistance, fracture toughness and strength as well as relatively low friction without forgetting its bioinertness [8].

In recent investigation, Barkallah et al. [9] have been concerned with the Alumina - Tricalcium phosphate composites with different percentages. These Al2O3/β-TCP composites have shown a good combination of elastic modulus (76 GPa), tensile strength (27 MPa), compressive (173 MPa) and flexural strength (66 MPa) but this biomaterial has never been investigated the stress intensity factors in Crack Straight Through Brazilian Disc specimen, under tensile and shear loading and their crack's initiation and its propagation. Those parameters of the developed composites should be evaluated.

In fact, there are three basic fracture propagation modes (**Figure 1**): Mode I (opening mode), Mode II (in-plane shear mode), and mixed mode [10]. In pure mode I loading, any two respective points along the notch faces open relative to the notch bi-sector line without any sliding. Under pure mode II, the two respective points along the notch faces slide relative to the notch bi-sector line without any opening and the tangential stress along the bi-sector line is zero. Any combination of mode I and mode II deformation is called mixed mode loading. The shear stress along the bi-sector line is zero for only the loading is pure mode I [11].

#### **Figure 1.**

*Basic modes known in fracture mechanics: (a) tensile opening (mode I), (b) In-plane shear (mode II) and (c) out-of-plane shear (mode III).*

### *Combination of Numerical, Experimental and Digital Image Correlation for Mechanical… DOI: http://dx.doi.org/10.5772/intechopen.99357*

Many different test specimens have been proposed in the past for brittle or quasi-brittle materials for determining the mode I, II fracture toughness for various engineering materials [12–14]. The centrally cracked Brazilian disc specimen has been used by many researchers to study mode I and mode II fracture mechanics in different brittle materials [11, 14].

Because of the brittleness of Biomaterials based on ceramics, the study of the contact problem with external objects is important. However, ceramics and bioceramics are inherently brittle. This characteristic leads, in particular, to a wide variation in the material strength. A CDM based constitutive model have been developed to study the damage of our bioceramics and thanks to this model, the numerical modeling of the damage behavior of bioceramics during a mechanical test is reported. This modeling is essential for a better understanding of fracture mechanisms of bioceramics [15].

On the other hand, in the last 20 years, digital image correlation (DIC) has shown that it is a valuable non-contact technique for measuring kinematic fields during a mechanical test [16, 17]. In order to account for the maximum load, it is crucial to work with local displacements at the damage progress zone.

In this chapter, we present a damage model in combination with finite element technique that can help automatize the damage progress fracture in an efficient manner. Our work was undertaken to evaluate the mechanical behavior of the combination of commercial alumina with synthetic Tricalcium phosphate as bone substitute material. To achieve this purpose, we study the stress intensity factor KI under tensile stress (mode I rupture) and stress intensity factor KII under shear stress (mode II rupture experimentally and theoretically using modified Brazilian test. The samples were also characterized by scanning electron microscopy (SEM).
