Origins of strain localization in a silver-based flexible ink under tensile load

Abstract

Flexible electronics often employ composite inks consisting of conductive flakes embedded in a polymer matrix to transmit electrical signal. Recently, localized necking was identified as a cause of a substantial increase in normalized resistance with applied strain thereby adversely impacting electrical performance. The current study explores two possible contributing factors for the formation of such localization—ink surface roughness and local variations in silver flake volume fraction. Uniaxial tension experiments of a DuPont 5025 type ink are used to inform a constitutive model implemented using finite element method on different substrates. Surface roughness was modeled by sinusoidal variation in ink height, whose amplitude and wavelength are informed by experimental laser profilometry scan data. Local flake fraction variations obtained from experimental measurements before applying any strain, were modeled as local variations in the elastic modulus according to an inverse rule of mixtures between the silver flake and acrylic binder material properties. The study identified that the ink height roughness is the most impactful contributor to the subsequent strain localization. The substrate elastic properties impact the number and magnitude of localization bands, with the stiffer substrate delocalizing strain and averting catastrophic crack formation seen with a more compliant substrate. The model incorporating surface roughness closely matches experimental measurements of local strain across different substrates. The study can inform designers of the adverse impact of ink surface roughness on localization and subsequent detrimental increase of the resistance.