A theoretical study of a thin-film delamination using shaft-loaded blister test: constitutive relation without delamination. (English) Zbl 1171.74377
Summary: This paper presents exact solutions for nonlinear large deflection of thin circular membrane loaded by a central point force using blister test with two types of boundary conditions and with or without residual stress cases. A comparison with existing solutions is presented, and a geometrically nonlinear finite element analysis (FEA) is conducted to verify our analytical solutions.
MSC:
| 74K35 | Thin films |
| 74R99 | Fracture and damage |
| 74G05 | Explicit solutions of equilibrium problems in solid mechanics |
| 74S05 | Finite element methods applied to problems in solid mechanics |
Keywords:
residual stress; shells and membranes; adhesion and adhesives; delamination; analytical solutionsReferences:
| [1] | Beck, A.; Grabmüller, H., Wrinkle-free solutions of circular membrane problems, Z. Angew. Math. Phys., 43, 481-504 (1992) · Zbl 0782.73035 |
| [2] | Bennett, S. J.; Devries, K. L.; Williams, L. M., Adhesive fracture mechanics, Int. J. Fract., 10, 1, 33-43 (1974) |
| [3] | Callegari, A. J.; Reiss, E. L., Nonlinear boundary value problems for the circular membrane, Arch. Ration. Mech. Anal., 31, 390-400 (1968) · Zbl 0179.54406 |
| [4] | Callegari, A. J.; Keller, H. B.; Reiss, E. L., Membrane buckling: a study of solution multiplicity, Comm. Pure Appl. Math., 24, 499-521 (1971) · Zbl 0218.73061 |
| [5] | Dannenberg, H., Measurement of adhesion by a blister method, J. Appl. Polym. Sci., 5, 125-134 (1961) |
| [6] | Föppl, A., Vorlesungen über Technische Mechanik Bd. 3 (1907), B.G. Teubner: B.G. Teubner Leipzig · JFM 47.0750.04 |
| [7] | Gent, A. N.; Lewandowski, L. H., Blowing-off pressures for adhering layers, J. Appl. Polym. Sci., 33, 1567-1577 (1987) |
| [8] | Guo, S.; Wan, K. T.; Dillard, D. A., A bending-to-stretching analysis of the blister test in the presence of tensile residual stress, Int. J. Solids Struct., 42, 9-10, 2771-2784 (2005) · Zbl 1096.74507 |
| [9] | Jennings, R. M.; Taylor, J. F.; Farris, R. J., Determination of residual stress in coatings by a membrane deflection technique, J. Adhes., 49, 57-74 (1995) |
| [10] | Jensen, H. M.; Thouless, M. D., Effects of residual stresses in the blister test, Int. J. Solids Struct., 30, 779-795 (1993) |
| [11] | Hencky, H., Über den Spannungszustand in kreisunden Platten, Z. Math. Phys., 63, 311-317 (1915) · JFM 45.1022.02 |
| [12] | Komaragiri, U.; Begley, M. R.; Simmonds, J. G., The mechanical response of freestanding circular elastic films under point and pressure loads, Trans. ASME J. Appl. Mech., 72, 203-212 (2005) · Zbl 1111.74486 |
| [13] | Lai, Y. H.; Dillard, D. A., A study of the fracture efficiency parameter of blister tests for films and coatings, J. Adhes. Sci. Technol., 8, 6, 663-678 (1994) |
| [14] | Lakes, R. S., Foam structures with a negative Poisson ratio, Science, 235, 1038 (1987) |
| [15] | Libai, A.; Simmonds, J. G., The Nonlinear Theory of Elastic Shells: One Spatial Dimension (1988), Academic Press: Academic Press Boston, 266-286 · Zbl 0644.73042 |
| [16] | Malyshev, B. M.; Salganik, R. L., The strength of adhesive joints using the theory of cracks, Int. J. Fract., 1, 114-128 (1965) |
| [17] | Schwerin, E., Ueber Spannungen und Formänderungen kreisringförmiger Membranen, Z. Techn. Phys., 12, 651-659 (1929) · JFM 55.0461.02 |
| [18] | Steigmann, D. J., Proof of a conjecture in elastic membrane theory, ASME J. Appl. Mech., 53, 955-956 (1986) · Zbl 0606.73077 |
| [19] | Su, Y. H.; Chen, K. S.; Roberts, D. C.; Spearing, S. M., Large deflection analysis of a pre-stressed annular plate with a rigid boss under axisymmetric loading, J. Micromech. Microeng., 11, 6, 645-653 (2001) |
| [20] | Thouless, M. D., Fracture mechanics for thin film adhesion, IBM J. Res. Dev., 38, 367-377 (1994) |
| [21] | Wan, K. T., Fracture mechanics of a shaft-loaded blister test-transition from a bending plate to a stretching membrane, J. Adhes., 70, 209-219 (1999) |
| [22] | Wan, K. T.; Liao, K., Measuring mechanical properties of thin flexible films by a shaft-loaded blister test, Thin Solid Films, 352, 167-172 (1999) |
| [23] | Wan, K. T.; Mai, Y. W., Fracture-mechanics of a new blister test with stable crack-growth, Acta Metall. Mater., 43, 11, 4109-4115 (1995) |
| [24] | Wan, K. T.; Guo, S.; Dillard, D. A., A theoretical and numerical study of a thin clamped circular film under an external load in the presence of residual stress, Thin Solid Films, 425, 150-162 (2003) |
| [25] | Weinitschke, H. J., Existenz- und Eindeutigkeitsssätze für die Gleichungen der kreisförmigen Membran, Meth. u. Verf. der Math. Physik, 3, 117-139 (1970) · Zbl 0219.73086 |
| [26] | Weinitschke, H. J., Stable and unstable axisymmetric solutions for membranes of revolution, Appl. Mech. Rev., 42, 11, Part 2, 289-294 (1989) · Zbl 0825.73292 |
| [27] | Williams, M. L., The continuum interpretation for fracture and adhesion, J. Appl. Polym. Sci., 13, 29-40 (1969) |
| [28] | Williams, J. G., Energy release rates for the peeling of flexible membranes and the analysis of blister tests, Int. J. Fract., 87, 265-288 (1997) |
| [29] | Yu, H.; Hutchinson, J. W., Delamination of thin film strips, Thin Solid Films, 423, 54-63 (2003) |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
