Biaxial bulge testing of thin films and foils Miroslav Cieslar Faculty of Mathematics and Physics Charles University, Prague Czech Republic J.L. Martin,

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Biaxial bulge testing of thin films and foils Miroslav Cieslar Faculty of Mathematics and Physics Charles University, Prague Czech Republic J.L. Martin, A. Karimi: EPFL Lausanne, Switzerland C. Fressengeas: LPMM, Université de Metz, France

Schedule Introduction to small structure testing Bulge test Applications –Recrystallization of thin foils –Plastic instabilities in Al foils –Plastic deformation of thin metallic films

Most common experimental methods Films adhered to substrate –Nanoindentation (hardness, modulus) –Microbeam bending (fatigue, bending) –Wafer curvature (biaxial strain, thermal fatigue) Free standing films –Tensile test (difficult sample preparation) –Microbeam bending –Biaxial bulge test

Industrial requirements for reliable biaxial tests Biaxial bulge test Testing of membranes in micro- and nano-devices Finstocks for heat exchangers

Spherical cap model Biaxial bulge test

Biaxial test with a constant fluid flow-rate Time [s] Stress [MPa]

Biaxial test under constant stress-rate Time [s] Stress-rate [MPa/s]

Examples Thin Al-Fe-Si foils (thickness 8.5  m) ElementFeSiCuMnMgZnTiAl wt. % bal.

Initial microstructure after homogenization 590 °C/30 min

Stress – strain curves obtained from bulge tests during prestraining and after annealing at indicated temperatures. Recrystallization of thin foils

Yield stress variation of predeformed aluminium foils with annealing temperature

Microstructure after predeformation and annealing 200 °Cinitial 380 °C 590 °C

Plastic instabilities in Al–Fe-Si foils

Instabilities after strain rate jump

Instabilities after an instant increase of stress by 3 MPa

Portevin – Le Chatelier effect?

Stress or strain oscillations?

Stability analysis Constitutive equation Evolution of perturbations Homogeneous solution

Stability analysis Instability grow The rate of perturbations growth  >0

Stability analysis Hill’s criterion For negative SRS For positive SRS  e ~  e n

Simulations Ring-shaped zone of localized intense strain rate

Simulations

Thin film plastic deformation Biaxial plastic deformation of Al thin films

Influence of temperature

Biaxial plastic deformation of Al thin films Creep-fatigue tests Variation of maximum strain with the number of cycles Deformation loops received during cycling

Deformation processes in Al-Zn-Mg- Cu thin films 4  m thin films from AA 7075 alloy