I. Introduction
The interaction between the semi-infinite crack and a neighboring
micro-crack has been studied by several researchers [1-3]. In this
paper, based on the strain energy, this study is devoted to determining
the influence of microcrack on the semi-infinite crack. During the
propagation of semi-infinite crack, the strain energy is mainly based on
the stress field found by H. Hamli benzahar [4]. The problem is
formulated by a brittle material of a thin thickness, cracked at the
end, having a microcrack varies around itself by an angle α and around d
the semi-infinite crack by an angle (see Figure 1). The cracked model is
subjected to a uniform load making opening of semi-infinite crack
according to the first mode of rupture (Mode I). Using the mathematical
approaches, the constraints and strains fields of a micro-crack and
semi-infinite crack are formulated by using of the complex potentials
theory [5]. The strain energy rate is defined as the energy released
during the cracking of a brittle or ductile material [6]. To
determine the evolution of the semi-infinite crack, several researchers
used the principle of J-integral [7-8]. Experimental and numerical
results show that macroscopic specimens which contain microscopic
defects producing local stress concentrations [9-10]. In brittle
materials, the failure is considered to be an energy-consuming
phenomenon, taking into account the energy state of the atoms before and
after cracking. [11]. This study is divided to two parts;
- The first part is devoted to the study of the orientation of the
microcrack around the semi-infinite crack according to the angle ,
whose strain energy is determined for each position of the microcrack.
- On the other hand, the orientation of the microcrack around itself
(according to the angle α) is studied in the second part.
According strain energy results, the positioning of the microcrack can
amplify, reduce and sometimes stop the propagation of the semi-infinite
crack.