Analysis of thermal stress intensity factors for cracked cylinders using weight function method. (English) Zbl 1231.74098
Summary: A general weight function was derived to evaluate the thermal stress intensity factors of a circumferential crack in cylinders. The weight function derived is valid for a wide range of thin- to thick-walled cylinders and relative crack depth. Closed-form stress intensity factor based on the weight function method was derived as a function of the Biot number and relative depth and various inner-to-outer radius ratios of cylinders. The accuracy of the analysis has been examined using the finite element method results and were compared to existing solutions for uniform loading in the literature for special geometries, indicating an excellent agreement.
MSC:
| 74F05 | Thermal effects in solid mechanics |
| 74R99 | Fracture and damage |
| 74S05 | Finite element methods applied to problems in solid mechanics |
Software:
ANSYSReferences:
| [1] | Murakami, Y., Stress Intensity Factors Handbook (1987), Pergamon Press: Pergamon Press New York |
| [2] | Tada, H.; Paris, P. C., The Stress Analysis of Cracks Handbook (1986), Del Research Corp.: Del Research Corp. Hellertown |
| [3] | Nied, H. F.; Erdogan, F., The elasticity problem for a thick-walled cylinder containing a circumferential crack, International Journal of Fracture, 22, 277-301 (1983) |
| [4] | Birinci, A.; Sukru Ozsahin, T.; Erdol, R., Axisymmetric circumferential internal crack problem of a thick-walled cylinder with inner and outer claddings, European Journal of Mechanics A/Solids, 25, 764-777 (2006) · Zbl 1100.74050 |
| [5] | Grebner, H., Finite element calculation of stress intensity factors for complete circumferential surface cracks at the outer wall of a pipe, International Journal of Fracture, 27, R99-R102 (1985) |
| [6] | Chen, Y. Z., Stress intensity factors in a finite length cylinder with a circumferential crack, International Journal of Pressure Vessels and Piping, 77, 439-444 (2000) |
| [7] | Zahoor, A., Closed form expressions for fracture mechanics analysis of cracked pipes, ASME Journal of Pressure Vessel Technology, 107, 203-205 (1985) |
| [8] | Mattheck, C.; Morawietz, P.; Munz, D.; Stamm, H., Comparison of different methods for the determination stress intensity factors of cracks in pipes with stress gradient, ASME Journal of Pressure Vessel Technology, 106, 209-213 (1984) |
| [9] | S.R. Mettu, R.G. Forman, Analysis of circumferential cracks in circular cylinders using the weight-function method, in: Fracture Mechanics: Twenty-Third Symposium ASTM STP 1180, Philadelphia, 1993, pp. 417-440.; S.R. Mettu, R.G. Forman, Analysis of circumferential cracks in circular cylinders using the weight-function method, in: Fracture Mechanics: Twenty-Third Symposium ASTM STP 1180, Philadelphia, 1993, pp. 417-440. |
| [10] | Liebster, T. D.; Glinka, G.; Burns, D. J.; Mettu, S. R., Calculating stress intensity factors for internal circumferential cracks by using weight functions, ASME High Pressure Technology, PVP-281, 1-6 (1994) |
| [11] | Jones, I. S.; Rothwell, G., Reference stress intensity factors with application to weight functions for internal circumferential cracks in cylinders, Engineering Fracture Mechanics, 68, 435-454 (2001) |
| [12] | Lee, H.-Y.; Kim, Y.-W.; Yun, B. I., Stress intensity factor solution for radial and circumferential cracks in hollow cylinders using indirect boundary integral, International Journal of Pressure Vessels and Piping, 69, 45-52 (1996) |
| [13] | Varfolomeyev, I. V.; Hodulak, L., Improved weight functions for infinitely long axial and circumferential cracks in a cylinder, International Journal of Pressure Vessels and Piping, 70, 103-109 (1997) |
| [14] | Varfolomeyev, I. V.; Petersilge, M.; Busch, M., Stress intensity factors for internal circumferential cracks in thin- and thick-walled cylinders, Engineering Fracture Mechanics, 60, 491-500 (1998) |
| [15] | Lynch, M. A.; Moreton, D. N.; Moffat, D. G., Limit loads for axially loaded cylinders having full circumferential cracks: experimental, analytical and numerical studies, Strain, 38, 89-103 (2002) |
| [16] | Meshii, T.; Watanabe, K., Closed form stress intensity factor of an arbitrarily located inner-surface circumferential crack in an edge-restraint cylinder under linear radial temperature distribution, Engineering Fracture Mechanics, 60, 519-527 (1998) |
| [17] | Meshii, T.; Watanabe, K., Closed-form stress intensity factor for an arbitrarily located inner circumferential surface crack in a cylinder subjected to axisymmetric bending loads, Engineering Fracture Mechanics, 59, 589-597 (1998) |
| [18] | Meshii, T.; Watanabe, K., Stress intensity factor for a circumferential crack in a finite-length thin to thick-walled cylinder under an arbitrary biquadratic stress distribution on the crack surfaces, Engineering Fracture Mechanics, 68, 975-986 (2001) |
| [19] | Meshii, T.; Watanabe, K., Stress intensity factor evaluation of a circumferential crack in a finite length thin-walled cylinder for arbitrarily distributed stress on crack surface by weight function method, Nuclear Engineering and Design, 206, 13-20 (2001) |
| [20] | Meshii, T.; Watanabe, K., Maximum stress intensity factor for a circumferential crack in a finite length thin-walled cylinder under transient radial temperature distribution, Engineering Fracture Mechanics, 63, 23-38 (1999) |
| [21] | Meshii, T.; Watanabe, K., Analytical approach to crack arrest tendency under cyclic thermal stress for an inner-surface circumferential crack in a finite-length cylinder, ASME Journal Pressure Vessel Technology, 123, 220-225 (2001) |
| [22] | Meshii, T.; Watanabe, K., Crack arrest analysis under cyclic thermal shock for an inner-surface circumferential crack in a finite-length thick-walled cylinder, Journal of Thermal Stresses, 25, 1121-1131 (2002) |
| [23] | Meshii, T.; Watanabe, K., Stress intensity factor of a circumferential crack in a thick-walled cylinder under thermal striping, ASME Journal of Pressure Vessel Technology, 126, 157-162 (2004) |
| [24] | Meshii, T.; Watanabe, K., Normalized stress intensity factor range solutions of an inner-surface circumferential crack in thin- to thick-walled cylinder under thermal striping by semi-analytical numerical method, Journal of Thermal Stresses, 27, 253-267 (2004) |
| [25] | Meshii, T.; Shibata, K.; Watanabe, K., Simplified method to evaluate upper limit stress intensity factor range of an inner-surface circumferential crack under steady state thermal striping, Nuclear Engineering and Design, 236, 1081-1085 (2006) |
| [26] | Nied, H. F.; Erdogan, F., Transient thermal stress problem for a circumferentially cracked hollow cylinder, Journal of Thermal Stresses, 6, 1-14 (1983) |
| [27] | Nied, H. F., Thermal shock in a circumferentially cracked hollow cylinder with cladding, Engineering Fracture Mechanics, 20, 113-137 (1984) |
| [28] | Jayadevan, K. R., Critical stress intensity factors for cracked hollow pipes under transient thermal loads, Journal of Thermal Stresses, 25, 951-968 (2002) |
| [29] | Jones, I. S., Impulse response model of thermal striping for hollow cylindrical geometries, Theoretical and Applied Fracture Mechanics, 43, 77-88 (2005) |
| [30] | Chang, K.-H.; Lee, C.-H., Behaviour of stresses in circumferential butt welds of steel pipe under superimposed axial tension loading, Materials and Structures, 42, 791-801 (2009) |
| [31] | Hetnarski, R. B.; Eslami, M. R., Thermal Stresses - Advanced Theory and Applications (2009), Springer · Zbl 1165.74004 |
| [32] | ANSYS Release 11.0, ANSYS, Inc, Canonsburg, PA, 2009.; ANSYS Release 11.0, ANSYS, Inc, Canonsburg, PA, 2009. |
| [33] | Banks-Sills, L., Application of the finite element to linear elastic fracture mechanic, ASME Applied Mechanic Review, 44, 447-461 (1991) |
| [34] | Bueckner, H. F., A novel principle for the computation of stress intensity factors, Zeitschrift fur Angewandte Mathematik und Mechanik, 50, 129-146 (1970) · Zbl 0213.26603 |
| [35] | Rice, J. R., Some remarks on elastic crack-tip stress fields, International Journal of Solid and Structures, 8, 751-758 (1972) · Zbl 0245.73083 |
| [36] | Glinka, G.; Shen, G., Universal features of weight functions for cracks in mode I, Engineering Fracture Mechanics, 40, 1135-1146 (1991) |
| [37] | Shen, G.; Glinka, G., Determination of weight functions from reference stress intensity factors, Theoretical and Applied Fracture Mechanics, 15, 237-245 (1991) |
| [38] | Fett, T.; Mattheck, C.; Munz, D., On the calculation of crack opening displacement from the stress intensity factor, Engineering Fracture Mechanics, 27, 697-715 (1987) |
| [39] | D.O. Harris, E.Y. Lim, Stress intensity factors for complete circumferential interior surface cracks in hollow cylinders, in: Proceedings of the Thirteenth National Symposium on Fracture Mechanics, ASTM-STP 743, 1981, pp. 375-386.; D.O. Harris, E.Y. Lim, Stress intensity factors for complete circumferential interior surface cracks in hollow cylinders, in: Proceedings of the Thirteenth National Symposium on Fracture Mechanics, ASTM-STP 743, 1981, pp. 375-386. |
| [40] | BS 7910, Guide on Methods for Assessing the Acceptability of Flaws in Metallic Structures, British Standards Institution, London, 1999.; BS 7910, Guide on Methods for Assessing the Acceptability of Flaws in Metallic Structures, British Standards Institution, London, 1999. |
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