Analysis of stress fields for plane problem of periodic cracks in orthotropic composites

By introducing proper Westergaard's stress function,the stress fields for mode Ⅰ and Ⅱ problems of periodic cracks in orthotropic composites were analyzed using the complex variable function method and approach of undetermined coefficients.Firstly,the stress intensity factors(SIFs) at the crack tip for mode Ⅰ and Ⅱ problems were presented under symmetrical loadings and skew-symmetrical loadings at infinity.The analytic expressions of the stress fields are then induced by the SIFs.In addition,the stress fields are related to the material constants,which is the characteristic of orthotropic materials different from the isotropic materials.Due to the distribution of periodic cracks in an orthotropic plate,the SIFs are determined by the shape factor.The results show that the shape factor increases as the crack length becomes longer,but decreases as the crack spacing becomes larger.Especially,the present result can reduce to the case of the central crack in an orthotropic plate when the crack spacing tends to infinity.