Material Characterization of FGM Plates Using Elastic Waves and an Inverse Procedure

Abstract

A computational inverse procedure is presented for characterization of the material properties of functionally graded materials (FGMs) using the surface displacement response of the plate. Amodified hybrid numerical method is first developed combining some existing techniques to compute the wave field in an FGM plate for given material properties and their variation in the thickness direction. The modified HNM allows a linear variation of material properties in the element in the thickness direction. This is to reduce the number of elements needed to model the material variation of FGM. The modified HNM is proven more efficient than the original HNM. The high efficiency paves the way for inverse procedure. The reconstruction of the material properties of FGM plates is performed using an inverse procedure of nonlinear least squares method. Numerical examples are presented to demonstrate the present procedure for material characterization of FGM plates. The present procedure can recover accurately the material properties of an FGM with an initial guess of up to 40% off from their true values.

Keywords

material characterization functionally graded material elastic wave stress wave inverse procedure numerical simulation NDT

Get full access to this article

View all access options for this article.

References

1. M. Sasaki , Y. Wang T. Hirano and T. Hirai . 1989. Journal of ceramic society of Japan. (97)5, pp. 539-543. Design of SiC/C functionally gradient material and its propagation by chemical vapor deposition.

2. R. Watanabe and A. Kawasaki . 1990. Proceedings of the first international symposium on functionally gradient materials, Yamanouchi et al., Sendi, Japan. pp. 107-113. Overall view of the P/M fabrication of functionally gradient materials.

3. G. R. Liu , J. Tani and T. Ohyoshi . 1991. Transactions of the Japan society of mechanical engineers, 57(A), Number 535, pp. 131-142. Lamb waves in a functionally gradient material plates and its transient response. Part 1: Theory; Part 2: Calculation results.

4. G. R. Liu and J. Tani . 1992. Transactions of the Japan society of mechanical engineers 1992 58(A), Number 547, pp. 504-507 SH surface waves in functionally gradient piezoelectric material plates.

5. T. Ohyoshi , G. J. Sui and K. Miuro . 1996. Proceedings of the ASME Aerospace Division 52, pp. 101-106. Using of stacking model of the linearly inhomogeneous layers elements.

6. G. R. Liu , X. Han and K. Y. Lam . 1999. Composite Part B. 30, pp. 383-394. Stress waves in functionally gradient materials and its use for material characterization.

7. S. K. Datta , J. D. Achenbach and Y. S. Rajapakse . 1990. Elastic waves and ultrasonic nondestructive evaluation, North-Holland, Amsterdam.

8. D. E. Chimenti and A. H. Nayfeh . 1990. Journal of nondestructive evaluation. 9, pp. 51-69.Ultrasonic reflections and guided waves in fluid-coupled laminates.

9. A. K. Mal , M. R. Karim and Y. Bar-Cohen . 1992. International advance in nondestructive testing. 16, pp. 77-101, Determination of the dynamic elastic moduli of composite materials by leaky lamb wave experiment.

10.

10. Kim-Ho Lp , Ping-Cheung Tse and Tai-Cheung Lai 1998, Composite Part B. 29B, pp. 397-409, Material characterization for orthotropic shells using model analysis and Rayleigh-Ritz models.

11.

11. Y. C. Chu , A. D. Degtyar and S. I. Rokhlin . 1994. Journal of the acoustical society of America, 95(6), pp. 3191-3203, On determination of orthotropic material moduli from ultrasonic velocity data in non-symmetry planes.

12.

12. Y. C. Chu and S. I. 1994. Journal of the Acoustical Society of America, 95(1), 213-225, Stability of determination of composite moduli from velocity data in planes of symmetry for weak and strong anisotropies.

13.

13. Krishnan Balasubramaniam and Navin S. Bao . 1998. Composite Part B 29B, pp. 171-180, Inversion of composite material elastic constants from ultrasonic bulk wave phase velocity data using genetic algorithms.

14.

14. G. R. Liu , J. Tani , T. Ohyoshi and K. Watanabe . 1991. Journal of vibration and acoustics. 113, pp. 230-239. Transient waves in anisotropic laminated plates, Part 1: Theory; Part 2: Applications.

15.

15. G. R. Liu , K. Y. Lam and T. Ohyoshi . 1997. Composites Part B, 28B, pp. 667-677. A technique for analyzing elastodynamic responses of anisotropic laminated plates to line loads.

16.

16. G. R. Liu , K. Y. Lam and H. M. Shang . 1995. Composite Engineering 5(12), pp. 1489-1498. A new method for analyzing wave fields in laminated composite plates: Two-dimensional cases.

17.

17. Philiip E. Gill and Walter Murray . 1978 SIAM Journal for numerical analysis 15(5) Algorithms for the solution of the nonlinear least squares problem.

18.

18. E. H. Kerner . 1956. Proc. Phys. Soc., 63, pp. 808-813, The elastic and thermo-elastic properties of composite media.

19.

19. S. W. Tsai and T. H. Hahn . 1980. Introduction to composite materials, Technomic Publishing Co., Lancaster, PA