The Mechanical Response of Freestanding Circular Elastic Films Under Point and Pressure Loads

[+] Author and Article Information
U. Komaragiri, M. R. Begley, J. G. Simmonds

Structural and Solid Mechanics Program, Department of Civil Engineering, University of Virginia, Charlottesville, VA 22904

J. Appl. Mech 72(2), 203-212 (Mar 15, 2005) (10 pages) doi:10.1115/1.1827246 History: Received May 23, 2003; Revised June 17, 2004; Online March 15, 2005
Copyright © 2005 by ASME
Your Session has timed out. Please sign back in to continue.


Maner,  K. C., Begley,  M. R., and Oliver,  W. C., 2004, “Nanomechanical Testing and Circular Freestanding Polymer Films With Sub-Micron Thickness,” Acta Mater.,52, pp. 5451–5460.
Espinosa,  H. D., Prorok,  B. C., and Fischer,  M., 2003, “A Methodology for Determining Mechanical Properties of Freestanding Thin Films and MEMS Materials,” J. Mech. Phys. Solids, 51, pp. 47–67.
Vernon,  T. J., Mackin,  T. J., and Begley,  M. R., 2003, “Fatigue Testing of Polymer Membranes,” Polym. Compos., (in press).
Sheplak,  M., and Dugundji,  J., 1998, “Large Deflections of Clamped Circular Plates Under Initial Tension and Transition to Membrane Behavior,” ASME J. Appl. Mech., 65, pp. 107–115.
Frakes,  J. P., and Simmonds,  J. G., 1985, “Asymptotic Solutions of the von Kármán Equations for a Circular Plate Under a Concentrated Load,” ASME J. Appl. Mech., 52, pp. 326–330.
Junkin,  G., and Davis,  R. T., 1972, “General Non-Linear Plate Theory Applied to a Circular Plate With Large Deflections,” Int. J. Non-Linear Mech., 7, pp. 503–526.
Timoshenko, S., and Woinowsky-Krieger, S., 1959, Theory of Plates and Shells, McGraw-Hill, New York.
Vlassak,  J. J., and Nix,  W. D., 1992, “A New Bulge Test Technique for the Determination of Young’s Modulus and Poisson’s Ratio of Thin Films,” J. Mater. Res., 7, pp. 3242–3249.
Poilane,  C., Delobelle,  P., Lexcellent,  C., Hayashi,  S., and Tobushi,  H., 2000, “Analysis of the Mechanical Behavior of Shape Memory Polymer Membranes by Nanoindentation, Bulging and Point Membrane Deflection Tests,” Thin Solid Films, 379, pp. 156–165.
Libai, A., and Simmonds, J. G., 1998, The Non-Linear Theory of Elastic Shells, 2nd ed., Cambridge University Press, Cambridge.
Hong,  S., Weihs,  T. P., Bravman,  J. C., and Nix,  W. D., 1990, “Measuring Stiffnesses and Residual Stress of Silicon Nitride Thin Films,” J. Electron. Mater., 19, pp. 903–909.
Wan,  K. T., Guo,  S., and Dillard,  D. A., 2003, “A Theoretical and Numerical Study of a Thin Clamped Circular Film Under an External Load in the Presence of a Tensile Residual Stress,” Thin Solid Films, 425, pp. 150–162.
Schwerin,  E., 1929, “Uber Spannungen und Formänderungen Kreisringförmiger Membranen,” Z. Tech. Phys. (Leipzig), 12, pp. 651–659.
Tsakalakos,  T., 1981, “Bulge Test: A Comparison of Theory and Experiment for Isotropic and Anisotropic Films,” Thin Solid Films, 75, pp. 293–305.
Voorthuyzen,  J. A., and Bergveld,  P., 1984, “The Influence of Tensile Forces on the Deflection of Circular Diaphragms in Pressure Sensors,” Sens. Actuators, 6, pp. 201–213.
Tabata,  O., Kawahata,  K., Sugiyama,  S., and Igarashi,  I., 1989, “Mechanical Property Measurement of Thin Films Using Load-Deflection of Composite Rectangular Membranes,” Sens. Actuators, A, 20, pp. 135–141.
Small,  M. K., and Nix,  W. D., 1992, “Analysis of the Accuracy of the Bulge Test in Determining the Mechanical Properties of Thin Films,” J. Mater. Res., 7, pp. 1553–1563.
Ziebart,  V., Paul,  O., Münch,  U., Schwizer,  J., and Baltes,  H., 1998, “Mechanical Properties of Thin Films From the Load Deflection of Long Clamped Plates,” J. Microelectromech. Syst., 7, pp. 320–328.
Ahmed,  M., and Hashmi,  M. S. J., 1998, “Finite Element Analysis of Bulge Forming Applying Pressure and In-Plane Compressive Load,” J. Mater. Process. Technol., 77, pp. 95–102.
Schellin,  R., Hess,  G., Kuhnel,  W., Thielemann,  C., Trost,  D., Wacker,  J., and Steinmann,  R., 1994, “Measurements of the Mechanical Behavior of Micromachined Silicon and Silicon-Nitride Membranes for Microphones, Pressure Sensors and Gas Flow Meters,” Sens. Actuators, A, 41–42, pp. 287–292.
Karimi,  A., Shojaei,  O. R., Kruml,  T., and Martin,  J. L., 1997, “Characterization of TiN Thin Films Using the Bulge Test and the Nanoindentation Technique,” Thin Solid Films, 308–309, pp. 334–339.
Shojaei,  O. R., and Karimi,  A., 1998, “Comparison of Mechanical Properties of TiN Thin Films Using Nanoindentation and Bulge Test,” Thin Solid Films, 332, pp. 202–208.
Ju,  B. F., Liu,  K.-K., Ling,  S.-F., and Ng,  W. H., 2002, “A Novel Technique for Characterizing Elastic Properties of Thin Biological Membrane,” Mech. Mater., 34, pp. 749–754.
Kaenel,  Y. V., Giachetto,  J.-C., Stiegler,  J., Drezet,  J.-M., and Blank,  E., 1996, “A New Interpretation of Bulge Test Measurements Using Numerical Simulation,” Diamond Relat. Mater., 5, pp. 635–639.
Bonnotte,  E., Delobelle,  P., Bornier,  L., Trolard,  B., and Tribillon,  G., 1997, “Two Interferometric Methods for the Mechanical Characterization of Thin Films by Bulge Tests. Application to Single Crystal of Silicon,” J. Mater. Res., 12, pp. 2234–2246.
Jayaraman,  S., Edwards,  R. L., and Hemker,  K. J., 1999, “Relating Mechanical Testing and Microstructural Features of Polysilicon Thin Films,” J. Mater. Res., 14, pp. 688–697.
Zheng,  D. W., Xu,  Y. H., Tsai,  Y. P., Tu,  K. N., Patterson,  P., Zhao,  B., Liu,  Q.-Z., and Brongo,  M., 2000, “Mechanical Property Measurement of Thin Polymeric-Low Dielectric-Constant Films Using Bulge Testing Method,” Appl. Phys. Lett., 76, pp. 2008–2010.
Yang,  J. L., and Paul,  O., 2002, “Fracture Properties of LPCVD Silicon Nitride Thin Films From the Load-Deflection of Long Membranes,” Sens. Actuators, A, 97–98, pp. 520–526.


Grahic Jump Location
Schematic illustration of the dimensions and variables used in the analysis of a thin circular film subjected to a point load
Grahic Jump Location
Parameter space delineating between regions of plate behavior (1), linear (or pre-stretched) membrane behavior (2), and nonlinear membrane behavior (3). Note that increasing pre-stretch and load (εo and P) corresponds to decreasing α and γ, respectively.
Grahic Jump Location
Load-deflection relationships for a thin film with several values of pre-stretch; the inset depicts where these cases fall in the behavior map given as Fig. 2
Grahic Jump Location
Boundaries in the behavioral map determined by comparing numerical and asymptotic solutions: the shaded regions correspond to load/pre-stretch combinations for which analytical solutions have less than 10% error
Grahic Jump Location
Illustration of combinations of load and pre-stretch for which asymptotic solutions are accurate: the shaded region represents the plate-to-membrane transition regime where no accurate analytical solution exists
Grahic Jump Location
Illustration of combinations of load and film thickness for which asymptotic solutions are accurate: the shaded region represents the plate-to-membrane transition regime where no accurate analytical solution exists
Grahic Jump Location
Illustration of combinations of load and film thickness for which small rotation assumptions are accurate: the shaded region represents combinations where small rotation membrane analytical solutions are accurate. For h/a∼0.075, there is no accurate small rotation analytical membrane result.
Grahic Jump Location
Universal results for cases with several pre-stretch illustrating transition from plate to membrane behavior




Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In