Quantification of the influence of vertex singularities on fatigue crack behavior P. Hutar ˇ * , L. Náhlík, Z. Knésl Institute of Physics of Materials, Academy of Sciences of the Czech Republic, Z ˇ iz ˇkova 22, 616 62 Brno, Czech Republic article info Article history: Received 29 November 2007 Received in revised form 11 August 2008 Accepted 21 August 2008 Available online 1 October 2008 PACS: 02.40.Xx 46.50.+a 62.20.me 02.70.Dh Keywords: Vertex singularity Generalized stress intensity factor Stress singularity Fatigue crack V-notch abstract The effect of vertex singularity on fatigue crack behavior is presented in the article. The methodology based on generalized stress intensity factor and model of V-notch is used for reliable estimation of the fatigue crack growth rate in the area close to the free surface, where the effect of the vertex singularity is dominant. It is shown that decrease of the crack singularity exponent close to the vertex point leads to a decrease in the fatigue crack growth rate and contributes to a typical curved crack front observed exper- imentally for through crack. Ó 2008 Elsevier B.V. All rights reserved. 1. Introduction Due to the existence of vertex singularity at the point where the crack front intersects the free surface, singular stress distribution around the crack tip and the type of the singularity is changed [1–4]. In the interior of the structure the square root singularity is dominant and crack can be described using semi-analytic equa- tions of two-dimensional stress distribution around the crack tip. Contrary to this, at the free surface or in the boundary region close to a free surface vertex singularity is significant. The three-dimensional singular stress field near the point where the crack front intersects the free surface (vertex point) of an elastic body was investigated in large number of papers for e.g., Baz ˇant and Estenssoro [5], Benthem [6], Picu and Gupta [7]. According to their results, the power of the singularity is weaker than the classical value of 0.5. The singularity exponent induced by the free surface differs from 0.5 and depends on Poisson’s ratio m. Despite intensive effort to describe mathematically the stress distribution around the vertex singularity little has been done to explain the crack behavior near the free surface from the perspec- tive of fracture mechanics. The influence of vertex singularity on fatigue crack behavior is modelled and described in this paper. The physical consequences of the stress singularity exponent change are discussed. For esti- mation the fatigue crack behavior close to the free surface where the stress singularity is smaller than 1/2 the model of a V-notch and the concept of the generalized stress intensity factor [8,9] have been used. It is shown that the existence of vertex singularity con- tributes to slower fatigue crack propagation in regions near the free surface of the body. Generally, methodology suggested de- scribes the behavior of a fatigue crack with a complex singular behavior. 2. Numerical estimation of the stress singularity exponent To describe the behavior of a fatigue crack near the vertex point the stress distribution around the crack front has to be known. In the contribution the influence of the vertex singularity on stress field around crack front in the sense of linear elastic fracture mechanics has been assessed using a middle tension (MT) speci- men, see Fig. 1. The dimensions of the MT specimen were: specimen width 2b = 50 mm and a/W = 0.5. The thickness b of the specimen varied from 6 mm to 20 mm. Material properties were considered homog- enous and isotropic, defined by Young modulus E = 210 GPa and Poisson’s ratio m ranges from 0 to 0.5. Uniform applied tensile 0927-0256/$ - see front matter Ó 2008 Elsevier B.V. All rights reserved. doi:10.1016/j.commatsci.2008.08.009 * Corresponding author. E-mail address: hutar@ipm.cz (P. Hutar ˇ). Computational Materials Science 45 (2009) 653–657 Contents lists available at ScienceDirect Computational Materials Science journal homepage: www.elsevier.com/locate/commatsci