Crack-Tip Stress Analysis at a Bi-Material Interface by Photoelastic, Isopachic and FEA

ABSTRACT

The paper investigates the stress state at the bi-material interface crack-tip by the Photoelastic and Isopachic methods and the Finite Element Analysis (FEA). The principal stresses at the bi-material interface crack-tip are theoretically determined using the combination photoelastic and isopachic fringes. The size and the shape of crack-tip isochro-matic and isopachic fringes, at a bi-material interface under static load, are studied. When the crack-tip, which is perpendicular to interface, is placed at the interface of the bi-material, the isochromatic and the isopachic fringes depend on the properties of the two materials. Thus, the isochromatic and the isopachic fringes are divided into two branches, which present a jump of values at the interface. The size of the two branches mainly depends on the elastic modulus and the Poisson’s ratio of the two materials. From the combination of the isochromatic and the isopachic fringes, the principal stresses σ_{1} and σ_{2} can be estimated and the contour curves around the crack-tip can be plotted. For the FEA analysis, the program ANSYS 11.0 was used. The bi-material cracked plates were made from Lexan (BCBA) and Plexiglas (PMMA).

The paper investigates the stress state at the bi-material interface crack-tip by the Photoelastic and Isopachic methods and the Finite Element Analysis (FEA). The principal stresses at the bi-material interface crack-tip are theoretically determined using the combination photoelastic and isopachic fringes. The size and the shape of crack-tip isochro-matic and isopachic fringes, at a bi-material interface under static load, are studied. When the crack-tip, which is perpendicular to interface, is placed at the interface of the bi-material, the isochromatic and the isopachic fringes depend on the properties of the two materials. Thus, the isochromatic and the isopachic fringes are divided into two branches, which present a jump of values at the interface. The size of the two branches mainly depends on the elastic modulus and the Poisson’s ratio of the two materials. From the combination of the isochromatic and the isopachic fringes, the principal stresses σ

Cite this paper

nullG. Papadopoulos, E. Bouloukou and E. Papadopoulou, "Crack-Tip Stress Analysis at a Bi-Material Interface by Photoelastic, Isopachic and FEA,"*Materials Sciences and Applications*, Vol. 2 No. 8, 2011, pp. 1027-1032. doi: 10.4236/msa.2011.28139.

nullG. Papadopoulos, E. Bouloukou and E. Papadopoulou, "Crack-Tip Stress Analysis at a Bi-Material Interface by Photoelastic, Isopachic and FEA,"

References

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[2] M. L. Williams, “Stress Singularities Resulting from Various Boundary Conditions in Angular Corners of Plates in Extension,” Journal of Applied Mechanics, Transactions ASME, Vol. 19, No. 4, 1952, pp. 526-528.

[3] M. L. Williams,“On the Stress at the Base of a Stationary Crack,” Journal of Applied Mechanics, Transactions ASME, Vol. 24, 1957, pp. 109-114.

[4] M. L. Williams, “The Stresses Around a Fault or Crack in Dissimilar Media,” Bulletin of the Seismological Society of America, Vol. 49, No. 2, 1959, pp. 199-204.

[5] A. R. Zak and M. L. Williams, “Crack Point Stress Singularities at a Bi-Material Interface,” Journal of Applied Mechanics, Vol. 30, 1963, pp. 142-143.

[6] J. W. Dally and T. Kobayashi, “Crack Arrest in Duplex Specimens,” International Journal of Solids and Structures, Vol. 14, No. 2, 1978, pp. 121-126. doi:10.1016/0020-7683(78)90048-3

[7] P. S. Theocaris and J. Milios, “Crack Propagation Velocities in Bi-Phase Plates under Static and Dynamic Loading,” Engineering Fracture Mechanics, Vol. 13, 1979, pp. 559-609.

[8] P. S. Theocaris and J. Milios, “Dynamic Crack Propagation in Composites,” International Journal of Fracture, Vol. 16, No. 1, 1980, pp. 31-51. doi:10.1007/BF00042384

[9] P. S. Theocaris, “The Mesophase Concept in Composites,” Springer-Verlag, Berlin Heidelberg, 1987.

[10] P. S. Theocaris and J. Milios, “Crack Arrest at a Bimaterial Interface,” International Journal of Solids and Structures, Vol. 17, No. 2, 1981, pp. 217-230. doi:10.1016/0020-7683(81)90077-9

[11] P. S. Theocaris, M. Siarova and G. A. Papadopoulos, “Crack Propagation and Bifurcation in Fibber-Composite Models: I Soft-Hard-Soft Sequence of Phases,” Journal of Reinforced Plastics and Composites, Vol. 5, No. 1, 1986, pp. 23-50. doi:10.1177/073168448600500104

[12] P. S. Theocaris and G. A. Papadopoulos, “Crack Propagation and Bifurcation in Fibber-Composite Models II: Hard- Soft-Hard Sequence of Phases,” Journal of Reinforced Plastics and Composites, Vol. 5, No. 2, 1986, pp. 120-140. doi:10.1177/073168448600500204

[13] E. E. Gdoutos, “Failure of a Bimaterial Plate with a Crack at an Arbitrary Angle to the Interface,” Fibber Science and Technology, Vol. 15, No. 1, 1981, pp. 27-40. doi:10.1016/0015-0568(81)90029-4

[14] E. E. Gdoutos and A. Giannakopoulou, “Stress and Failure Analysis of Brittle Matrix Composites, Part I: Stress Analysis,” International Journal of Fracture, Vol. 98, No. 3-4, 1999, pp. 263-277. doi:10.1023/A:1018354300645

[15] E. E. Gdoutos, A. Giannakopoulou and D. A. Zacharopoulos, “Stress and Failure Analysis of Brittle Matrix Composites. Part II: Failure Analysis,” International Journal of Fracture, Vol. 98, No. 3-4, 1999, pp. 279-291. doi:10.1023/A:1018386616575

[16] E. N. Theotokoglou, G. J. Tsamasphyros and C. P. Spyropoulos, “Photoelastic Study of a Crack Approaching the Bonded Half-Plates Interface,” Engineering Fracture Mechanics, Vol. 34, No. 1, 1989, pp. 31-42. doi:10.1016/0013-7944(89)90240-3

[17] C. P. Spyropoulos, E. N. Theotokoglou and G. J. Tsamasphyros, “Evaluation of the Stress Intensity Factors for a Crack Approaching the Bonded Half-plates Interface from Isopachics,” Acta Mechanica, Vol. 81, No. 1-2, 1990, pp. 75-89. doi:10.1007/BF01174557

[18] G. A. Papadopoulos, “Crack-Tip Caustics at a Bi-Material Interface,” International journal of Fracture, Vol. 98, No. 1-2, No. 3-4, 1999, pp. 329-342. doi:10.1023/A:1018617719180

[19] L. Marsavina and T. Sadowski, “Stress Intensity Factor for an Interface Kinked Crack in a Bi-material Plate Loading Normal to the Interface,” International journal of Fracture, Vol. 145, No. 3, 2007, pp. 22-43. doi:10.1007/s10704-007-9124-z

[20] L. Marsavina and T. Sadowski, “Effect of Biaxial Load on Crack Deflection Penetration at Bi-Material Ceramic Interface,” International journal of Fracture, Vol. 148, No. 1, 2007, pp. 79-84. doi:10.1007/s10704-008-9181-y

[21] M. M. Frocht, “Photoelasticity,” John Willey, New York, 1948.

[22] G. A. Papadopoulos, “Fracture Mechanics. The Experimental Method of Caustics and the Det-Criterion of Fracture,” Springer-Verlag, London, 1993.

[1] M. L. Williams, “Surface Stress Singularities Resulting from Various Boundary Conditions in Angular Corners of Plates under Bending,” Proceedings, First U.S. National Congress of Applied Mechanics, ASME, June 1952, pp. 325-329.

[2] M. L. Williams, “Stress Singularities Resulting from Various Boundary Conditions in Angular Corners of Plates in Extension,” Journal of Applied Mechanics, Transactions ASME, Vol. 19, No. 4, 1952, pp. 526-528.

[3] M. L. Williams,“On the Stress at the Base of a Stationary Crack,” Journal of Applied Mechanics, Transactions ASME, Vol. 24, 1957, pp. 109-114.

[4] M. L. Williams, “The Stresses Around a Fault or Crack in Dissimilar Media,” Bulletin of the Seismological Society of America, Vol. 49, No. 2, 1959, pp. 199-204.

[5] A. R. Zak and M. L. Williams, “Crack Point Stress Singularities at a Bi-Material Interface,” Journal of Applied Mechanics, Vol. 30, 1963, pp. 142-143.

[6] J. W. Dally and T. Kobayashi, “Crack Arrest in Duplex Specimens,” International Journal of Solids and Structures, Vol. 14, No. 2, 1978, pp. 121-126. doi:10.1016/0020-7683(78)90048-3

[7] P. S. Theocaris and J. Milios, “Crack Propagation Velocities in Bi-Phase Plates under Static and Dynamic Loading,” Engineering Fracture Mechanics, Vol. 13, 1979, pp. 559-609.

[8] P. S. Theocaris and J. Milios, “Dynamic Crack Propagation in Composites,” International Journal of Fracture, Vol. 16, No. 1, 1980, pp. 31-51. doi:10.1007/BF00042384

[9] P. S. Theocaris, “The Mesophase Concept in Composites,” Springer-Verlag, Berlin Heidelberg, 1987.

[10] P. S. Theocaris and J. Milios, “Crack Arrest at a Bimaterial Interface,” International Journal of Solids and Structures, Vol. 17, No. 2, 1981, pp. 217-230. doi:10.1016/0020-7683(81)90077-9

[11] P. S. Theocaris, M. Siarova and G. A. Papadopoulos, “Crack Propagation and Bifurcation in Fibber-Composite Models: I Soft-Hard-Soft Sequence of Phases,” Journal of Reinforced Plastics and Composites, Vol. 5, No. 1, 1986, pp. 23-50. doi:10.1177/073168448600500104

[12] P. S. Theocaris and G. A. Papadopoulos, “Crack Propagation and Bifurcation in Fibber-Composite Models II: Hard- Soft-Hard Sequence of Phases,” Journal of Reinforced Plastics and Composites, Vol. 5, No. 2, 1986, pp. 120-140. doi:10.1177/073168448600500204

[13] E. E. Gdoutos, “Failure of a Bimaterial Plate with a Crack at an Arbitrary Angle to the Interface,” Fibber Science and Technology, Vol. 15, No. 1, 1981, pp. 27-40. doi:10.1016/0015-0568(81)90029-4

[14] E. E. Gdoutos and A. Giannakopoulou, “Stress and Failure Analysis of Brittle Matrix Composites, Part I: Stress Analysis,” International Journal of Fracture, Vol. 98, No. 3-4, 1999, pp. 263-277. doi:10.1023/A:1018354300645

[15] E. E. Gdoutos, A. Giannakopoulou and D. A. Zacharopoulos, “Stress and Failure Analysis of Brittle Matrix Composites. Part II: Failure Analysis,” International Journal of Fracture, Vol. 98, No. 3-4, 1999, pp. 279-291. doi:10.1023/A:1018386616575

[16] E. N. Theotokoglou, G. J. Tsamasphyros and C. P. Spyropoulos, “Photoelastic Study of a Crack Approaching the Bonded Half-Plates Interface,” Engineering Fracture Mechanics, Vol. 34, No. 1, 1989, pp. 31-42. doi:10.1016/0013-7944(89)90240-3

[17] C. P. Spyropoulos, E. N. Theotokoglou and G. J. Tsamasphyros, “Evaluation of the Stress Intensity Factors for a Crack Approaching the Bonded Half-plates Interface from Isopachics,” Acta Mechanica, Vol. 81, No. 1-2, 1990, pp. 75-89. doi:10.1007/BF01174557

[18] G. A. Papadopoulos, “Crack-Tip Caustics at a Bi-Material Interface,” International journal of Fracture, Vol. 98, No. 1-2, No. 3-4, 1999, pp. 329-342. doi:10.1023/A:1018617719180

[19] L. Marsavina and T. Sadowski, “Stress Intensity Factor for an Interface Kinked Crack in a Bi-material Plate Loading Normal to the Interface,” International journal of Fracture, Vol. 145, No. 3, 2007, pp. 22-43. doi:10.1007/s10704-007-9124-z

[20] L. Marsavina and T. Sadowski, “Effect of Biaxial Load on Crack Deflection Penetration at Bi-Material Ceramic Interface,” International journal of Fracture, Vol. 148, No. 1, 2007, pp. 79-84. doi:10.1007/s10704-008-9181-y

[21] M. M. Frocht, “Photoelasticity,” John Willey, New York, 1948.

[22] G. A. Papadopoulos, “Fracture Mechanics. The Experimental Method of Caustics and the Det-Criterion of Fracture,” Springer-Verlag, London, 1993.