Spontaneous formation and morphology of telephone cord blisters in thin films: the Ω formulae

Telephone cord blisters (TCBs) are frequently observed in film/substrate material systems. They nucleate and propagate forward with wavy boundaries between the film and the substrate. The current study views the problem from a completely new angle: It is discovered that the spontaneous formation and morphology of TCBs in thin films under biaxial compressive residual stresses can be accurately explained and determined by assuming the existence of a pocket of energy concentration (PEC) instead of the existence of a separation of critical size. For the first time, completely-analytical formulae—the ‘Ω formulae’—are derived for the two local morphology parameters of TCBs of any shape, that is, width and height, and for the two global morphology parameters of TCBs of sinusoidal shape, that is, the wavelength and transverse amplitude. Mechanical conditions are also given for the first time for the formation of TCBs. Predictions for the four morphology parameters of the developed theory agree very well with extensive experimental results. In addition, by reversing the calculation, the residual stress and the film/substrate interface fracture toughness are also accurately determined from measurements of the TCB morphology parameters.