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TECHNICAL PAPERS

Progressive Cracking of a Multilayer System Upon Thermal Cycling

[+] Author and Article Information
M. R. Begley

Department of Civil Engineering, University of Virginia, Charlottesville, VA 22904 e-mail: begley@virginia.edu

A. G. Evans

Materials Institute, Princeton University, Princeton, NJ 08540

J. Appl. Mech 68(4), 513-520 (Nov 07, 2000) (8 pages) doi:10.1115/1.1379529 History: Received December 22, 1999; Revised November 07, 2000
Copyright © 2001 by ASME
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References

Bree,  J., 1989, “Plastic Deformation of a Closed Tube due to Interaction of Pressure Stresses and Cyclic Thermal Stresses,” Int. J. Mech. Sci., 31, pp. 865–892.
Ponter,  A. R. S., and Cocks,  A. C. F., 1984, “The Incremental Strain Growth of an Elastic-Plastic Body Loaded in Excess of the Shakedown Limit,” ASME J. Appl. Mech., 51, pp. 465–470.
Ponter,  A. R. S., and Cocks,  A. C. F., 1984, “The Incremental Strain Growth of Elastic-Plastic Bodies Subjected to High Levels of Cyclic Thermal Loading,” ASME J. Appl. Mech., 51, pp. 470–474.
Megahed,  M. M., Ponter,  A. R. S., and Morrison,  C. J., 1984, “Experimental Investigations Into the Influence of Cyclic Phenomena of Metals on Structural Ratcheting Behavior,” Int. J. Mech. Sci., 26, pp. 625–638.
Megahed,  M. M., 1981, “Influence of Hardening Rule on the Elasto-Plastic Behavior of a Simple Structure Under Cyclic Loading,” Int. J. Mech. Sci., 23, pp. 169–182.
Bree,  J., 1968, “Incremental Growth due to Creep and Plastic Yielding of Thin Tubes Subjected to Internal Pressures and Cyclic Thermal Stresses,” J. Strain Anal., 3, pp. 122–127.
Bree,  J., 1967, “Elastic-Plastic Behaviour of Thin Tubes Subjected to Internal Pressure and Intermittent High-Heat Fluxes With Application to Fast-Nuclear-Reaction Fuel Elements,” J. Strain Anal., 2, pp. 226–238.
Jansson,  S., and Leckie,  F. A., 1992, “Mechanical Behavior of a Continuous Fiber-Reinforced Aluminum Matrix Composite Subjected to Transverse and Thermal Loading,” J. Mech. Phys. Solids, 40, pp. 593–612.
Beuth,  J. L., and Klingbeil,  N. W., 1996, “Cracking of Thin Films Bonded to Elastic-Plastic Substrates,” J. Mech. Phys. Solids, 44, pp. 1411–1428.
Begley, M. R., Evans, A. G., and Ambrico, J. M., 2001, “Cracking During Thermal Cycling of Thin Multilayers,” Proceedings of the International Congress on Fracture, Honolulu, HI.
Hutchinson,  J. W., and Suo,  Z., 1994, “Mixed-Mode Cracking in Layered Materials,” Adv. Appl. Mech., 29, pp. 64–191.

Figures

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Bree diagrams for a metal-matrix composite (left) and a two-bar model used for studying pressure vessels (right), illustrating the relationship between thermal loading, applied tensile loading, and regions of ratcheting and shakedown
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Schematic of a channeling crack in a multilayer deposited on an elastic substrate. The middle layer represents an elastic-plastic interconnect, while the top layer is representative of an elastic dielectric; N is the number of thermal cycles.
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Schematic of tri-layer system used to define the finite element model
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(a) Crack-opening as a function of stress in the dielectric (monotonic loading), for constant ratios of stress in the metal layer to stress in the dielectric. The result is also an upper bound estimate for the energy release rate. (b) Crack-opening (or upper bound estimate of the energy release rate) as a function of stress in the metal layer (monotonic loading), for constant ratios of stress in the metal layer to stress in the dielectric.
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Crack-opening as a function of stress in the metal layer for several values of stress in the dielectric (monotonic loading). The stress ratio during the loading stage (ΣR) is dictated by the ratio of Σ1 and Σ2.
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Crack-opening displacements at the surface of the dielectric as a function of time (or thermal cycles) for two representative cases; the cases are the same as those labeled in Fig. 7 and described in Table 2
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Crack-opening (or upper bound estimate of the energy release rate) as a function of time (or thermal cycles) for representative cases outlined in Table 2
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Fractional increase in crack opening from the first thermal cycle to the tenth thermal cycle, plotted as a function of total stress amplitude range in the metal layer
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Crack opening as a function of initial stress in the dielectric layer, for two scenarios. Because of the small difference in thermal expansion between the dielectric and substrate, the mean stress in the dielectric remains close to the initial value.
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Modified Bree diagram for a trilayer: (a) for moderate values of mean stress in the dielectric, (b) for high levels of mean stress in the dielectric

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