13th International Conference on Fracture June 16–21, 2013, Beijing, China -1- Determination of crack surface displacements for a radial crack emanating from a semi-circular notch using weight function method D H Tong, X R Wu* AVIC Beijing Institute of Aeronautical Materials , Beijing 10095 , China * Corresponding author: xueren.wu@gmail.com) Abstract A radial crack emanating from a semi-circular notch is of significant engineering importance. Accurate determination of key fracture mechanics parameters is essential for damage tolerance design and fatigue crack growth life predictions. The purpose of this paper is to provide an efficient and accurate closed-form weight function approach to the calculation of crack surface displacements for a radial crack emanating from a semi-circular notch in a semi-infinite plate. Results are presented for two load conditions: remote applied stress and uniform stress segment applied to crack surfaces. Based on a correction of stress intensity factor ratio, highly accurate analytical equations of crack surface displacements under the two load conditions are developed by fitting the data obtained by using the weight function method. It is demonstrated that the Wu-Carlsson closed-form weight functions are very efficient, accurate and easy-to-use for calculating crack surface displacements for arbitrary load conditions. The method will facilitate fatigue crack closure and other fracture mechanics analyses where accurate crack surface displacements are required. Keywords: Radial crack, Semi-circular notch, Dugdale strip-yield model, Crack surface displacement, Weight function method. 1. Introduction In fracture mechanics analysis and fatigue crack growth life predictions for structural components, the strip-yield model (modified Dugdale models) [1] have been employed for crack configurations like middle-crack tension [1-5] and compact specimens [6-8]. Reference [9] discussed the application of the model to analyze double radial cracks emanating from a circular hole. This crack configuration and a radial crack emanating from a semi-circular notch are among the most important crack types for aircraft structures. Stress intensity factors for such cracks under various loading conditions can be found in the literature [10-11]. However, crack surface displacements for various load conditions, preferably in analytical form, which are needed in crack-closure-based fatigue crack growth life prediction models and other fracture mechanics analyses, are rarely available. A modified Dugdale model is proposed by Newman [1]. The modification is to leave plastically deformed materials in the wake of the crack. The primary advantage in using this model is that the plastic-zone size and crack surface displacements are obtained by superposition of two elastic problems: a crack in a plate subjected to a remote uniform stress and a uniform stress applied over a segment of the crack surfaces. In the Newman model, crack surface displacements under remote applied stresses and a segment uniform pressure (partial loading) in the immediate wake of the crack tip are both required for calculating the crack opening stress, Sop. The accuracy of these displacements will significantly influence Sop, and further, fatigue crack growth rates. The motivation of the present paper is to explore an analytical approach, based on the closed-form weight functions, to the calculation of crack surface displacements for a radial crack emanating from a semi-circular notch in a semi-infinite plate. Results are presented for the two loading conditions: remote applied stress and uniform segment stress (partial load) applied to a segment of the crack surfaces. Based on a correction of stress intensity factor ratio, highly accurate analytical equations of the crack surface displacements are developed to fit the data from weight function
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