Critical Examination of the Use of Coherent Gradient Sensing in Measuring Fracture Parameters in Functionally Graded Materials

Abstract

Specific relations for out-of-plane deformation near crack tips of linearly graded materials are introduced and used with the optical method of coherent gradient sensing (CGS) to interpret experimentally obtained fringes. Stress intensity factors are thus derived and used to reconstruct synthetic fringes that are then compared to experimental ones. An error function is used with sets of 2-6 terms in the asymptotic solution to gage the incremental accuracy contributed by using these additional terms with the experimental results. The study reveals the necessity of using up to the sixth higher-order term to obtain a precise agreement between the analytical solution and the experimental interferograms. Specimen configurations with cracks consecutively positioned at the stiffer, and then at the more compliant end of the gradient are used. Distinct features of the interferograms indicate the benefits of having the crack on the compliant side of the elastic modulus variation.

Keywords

optical mapping nonhomogeneity linear gradient crack tip deformation CGS

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References

Messler, R. W. Jr. , Jou, M. and Orling, T. T. (1990). A Model for Designing Functionally Gradient Material Joints , Welding Research Supplement, 74(5): 160-167 .

Dao, M. , Gu, P. , Maewal, A. and Asaro, R. J. (1997). A Micromechanical Study of Residual Stresses in FGMs , Acta Mater., 45(8): 3265-3276 .

Koizumi, M. and Niino, M. (1995). Overview of FGM Research in Japan , MRS Bull., 20(1): 19-21 .

Atkinson, C. and List, R. D. (1978). Steady State Crack Propagation into Media with Spatially Varying Elastic Properties , Int. J. Eng. Sci., 16(10): 717-730 .

Delale, F. and Erdogan, F. (1983). The Crack Problem for a Nonhomogeneous Plane , J. Appl. Mech., 50(3): 609-614 .

Eischen, J. W. (1987). Fracture of Nonhomogeneous Materials , Int. J. Fract., 34: 3-22 .

Honein, T. and Herrmann, G. (1997). Conservation Laws in Nonhomogeneous Plane Elastostatics , J. Mech. Phys. Solids, 45(5): 789-805 .

Rousseau, C.-E. and Tippur, H. V. (2000). Compositionally Graded Materials with Cracks Normal to the Elastic Gradient , Acta Mater., 48(16): 4021-4033 .

Marur, P. R. and Tippur, H. V. (2000). Dynamic Response Of Bimaterial and Graded Interface Cracks Under Impact Loading , Int. J. Fract., 103(1): 95-109 .

10.

Westergaard, H. M. (1939). Bearing Pressures and Cracks , J. Appl. Mech., 6(5): A49-A53 .

11.

Parameswaran, V. and Shukla, A. (1999). Crack-tip Stress Fields for Dynamic Fracture in Functionally Gradient Materials , Mech. Mat., 31(9): 579-596 .

12.

Jain, N. , Rousseau, C.-E. and Shukla, A. (2004). Crack Tip Stress Fields in Functionally Graded Materials with Linearly Varying Properties , Theoretical Appl. Fract. Mech., 42(2): 155-170 .

13.

Erdogan, F. (1995). Fracture Mechanics of Functionally Graded Materials , Comp. Eng., 5(7): 753-770 .

14.

Tippur, H. V. , Krishnaswamy, S. and Rosakis, A. J. (1992). A Coherent Gradient Sensor for Crack Tip Deformation Measurements: Analysis and Experimental Results , Int. J. Fract., 48(3): 193-204 .

15.

Xu, L. , Tippur, H. V. and Rousseau, C.-E. (1999). Measurement of Contact Stresses using Real-time Shearing Interferometry , Opt. Eng., 38(11): 1932-1937 .

16.

Golub, G. H. and Kahan, W. (1965). Calculating the Singular Values and Pseudo-inverse of a Matrix , SIAM J. Num. Anal., 2(2): 205-224 .

17.

Rousseau, C.-E. (2000). Evaluation of Crack Tip Fields and Fracture Parameters in Functionally Graded Materials, PhD Dissertation, Auburn University.

18.

Whitney, J. M. , Daniel, I. M. and Pipes, R. B. (1984). Experimental Mechanics of Fiber Reinforced Composite Materials, SEM Monograph No. 4, Prentice Hall, Inc., NJ .

19.

Tippur, H. V. , Krishnaswamy, S. and Rosakis, A. J. (1991). Crack Tip Deformation Field Measurements using Coherent Gradient Sensing , SPIE, 1554A: 176-191 .