The bulge test: A comparison of the theory and experiment for isotropic and anisotropic films

A theoretical analysis was made of the deformation of foils in the biaxial “bulge test”. The relationship between stress and strain on the one hand and the pressure and height of the bulge on the other hand was established as a function of the Poisson's ratio and the crystal symmetry. For strains less than 1% Beams' formulae were found to be accurate to within 8%. The distribution of stresses and strains and the curvature throughout the bulge was also determined. Expressions for the biaxial elastic modulus Y[ hkl], measured from the slope of the stress-strain curve of a bulge test, were derived for (100), (110) and (111) crystallographic orientations of the film plane in cubic crystals. A bulge tester was constructed and stress-strain curves were obtained for copper and CuNi homogeneous foils. The measured biaxial moduli Y[111] for both copper and 50at.%CuNi foils having strong 〈111〉 texture were in excellent agreement with those calculated from the bulk alloy elastic constants. Satisfactory agreement was also found between measured and calculated values of Y[100] for films with a 〈100〉 texture.