13th International Conference on Fracture June 16–21, 2013, Beijing, China -1- A Periodic Array of Parallel Edge Cracks in a Functionally Graded Plate Subjected to Finite Cooling Rates Yuezhong Feng1,*, Zhihe Jin2 1 School of Mechanical Engineering, Purdue University, 47907, USA 2 Department of Mechanical Engineering, University of Maine, 04469, USA * Corresponding author: feng81@purdue.edu Abstract This work investigates the effects of cooling rate on the thermal fracture behavior of a functionally graded plate (FGM plate) with a periodic array of parallel edge cracks of alternating lengths. The thermal properties of the FGM are assumed to be continuous and piecewise differentiable functions of the coordinate in the plate thickness direction. A linear ramp function describes the rate of boundary temperature variation at the surfaces of the FGM plate. The integral equation method is used to analyze the thermal stress intensity factors (TSIFs) at the crack tips. The asymptotic solutions of TSIF are obtained using a closed form, short time solution of temperature field in the FGM plate. The effects of cooling rate and crack length ratio on the TSIF are examined using an Al2O3/Si3N4 FGM. Numerical results show that for given material gradation profile and crack morphology parameters, a lower cooling rate leads to a lower peak TSIF. For a given cooling rate, an appropriate material gradation profile reduces peak TSIFs. Finally, the variations of the TISF for the long and short cracks with the cooling rate and crack length ratio exhibit a complex pattern due to the interactions between the long and short cracks. Keywords functionally graded material, heat conduction, cooling rate, thermal stress intensity factor, periodic cracks 1. Introduction Functionally graded ceramics suffer multiple surface cracking when subjected to thermal shocks [1, 2]. These surface cracks greatly influence the thermal fracture behavior of the materials. FGMs with multiple surface cracks under thermal loading were considered by Rangaraj and Kokini [3], Han and Wang [4], and Jin and Feng [5]. Jin and Feng [6] further investigated thermal shock residual strength of an FGM with multiple surface cracks. The existing analytical and computational studies on multiple surface cracking in FGMs have assumed that the cracks have equal length. However, FGMs when subjected to thermal shocks may develop multiple cracks of unequal lengths as in the case of monolithic ceramics. An improved model is a periodic array of parallel cracks with alternating lengths. For monolithic ceramics, Nemat-Nasser et al. [7] considered a periodic array of parallel cracks with alternating lengths in a half plane and studied the stability problem of crack growth. Using a boundary element method and an energy release fracture criterion, Bahr et al. [8] studied the same crack geometry in a plate of finite thickness. Jin and Feng [9] considered an array of parallel edge cracks with alternating lengths in an elastic strip subjected to a thermal shock and presented detailed results on the effects of crack length ratio and crack spacing on the thermal stress intensity factors (TSIFs). For functionally graded ceramics, Feng and Jin [10, 11] investigated the effects of crack length ratio on the TSIFs at the tips of long and short cracks and thermal shock residual strength using a singular integral equation technique. All of the analytical studies above assume that the FGM specimens are subjected to a sudden cooling condition at their surfaces, i.e., the boundary temperature immediately attains the ambient temperature. In practical applications, however, the cooling rates on the material surfaces are finite.
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