Research On Stress Singularities About V-notch And Interface In Orthotropic Materials

In this paper, based on the fundamental equations of the two-dimensional linear elasticity for orthotropic materials, the general solution of the displacement method for orthotropic materials is derived by introducing the displacement function. According to this general solution, and employing the coordinate transformation and the eigenequation expansion method, displacement and singular stress fields near the singular point in orthotropic materials are presented in closed form expressions. When the two characteristic parameters of orthotropic materials are all equal to 1, the above displacement and singular stress fields are degenerated into the corresponding fields in isotropic materials. From these presented expressions, the fruits of the study in this paper are obtained as follows:(1) A symmetric V-notch in orthotropic materials is analyzed theoretically for the stress singularity at the notch tip. The eigenequations about the stress singularity, and the displacement and singular stress fields near the notch tip are acquired directly. It is found that the orders of the stress singularity at the notch tip in orthotropic materials are related not only to the angle of the V-notch, but also to the material properties, which being different to isotropic materials.(2) An asymmetric V-notch in orthotropic materials is analyzed theoretically for the stress singularity at the notch tip. The eigenequations about the stress singularity, and displacement and singular stress fields near the notch tip under various boundary conditions are presented explicitly.(3) For three match cases of the characteristic parameters of orthotropic materials, an interface corner of orthotropic bi-materials with an arbitrary joining angle is analyzed theoretically. The eigenequations about the stress singularity, and the displacement and singular stress fields near the interface corner are also explicitly established for the symmetric and anti-symmetric deformation modes, respectively. The results can be also applied to the interface corners in orthotropic/isotropic bi-materials and isotropic/isotropic bi-materials.(4) An interface edge of the orthotropic/isotropic bi-materials with an arbitrary wedge angle for the orthotropic material, which is a common geometry in the strengthened engineering, is analyzed theoretically. The eigenequation as well as the displacement and singular stress fields near the interface edge are derived directly. The relations between the singular stresses near the interface edge of the orthotropic/isotropic bi-material and the wedge angle as well as the material property of the orthotropic material are discussed in details.(5) A simple and effective numerical approach is developed to calculate the orders of the stress singularity and the related stress intensity factors for one and two stress singularities by using the results of an ordinary numerical analysis, and the associated formulae are presented for the numerical calculation. The approach can be used in engineering analysis conveniently, and the stress intensity factors evaluated by this method are very accurate.(6) To verify the correctness of the abovementioned theoretical analyses, the stress singularities at the V-notch tips, interface corners, and interface edges of orthotropic materials are analyzed numerically by Patran & Nastran code (MSC Corporation), based on the displacement finite element method. The analytical results are compared with the related numerical ones, respectively; it is found that they coincide with each other very well.