View source for Ductility of thin metal films on polymer substrates modulated by interfacial adhesion

Fall 2010 Anna Wang

== References ==
Teng Li and Z. Suo, 'Ductility of thin metal films on polymer substrates modulated by interfacial adhesion'. ''International Journal of Solids and Structures'' '''44''', 1696-1705 (2007). 

=  Overview =
[[Image:wiki2_intro.jpg|300px|thumb|right|'''Figure 1.''' (a) a freestanding film elongates and ruptures as the halves move apart. (b) elongation and hence rupture is suppressed as the film is adhered to a substrate]]

Thin films are at the centre of macroelectronic components (such as thin-film solar cells and antennae) and provide a platform for creating such components on a massive scale. Presently, most macroelectronic devices use silicon or glass as a substrate but both of these are expensive and fragile. Flexible macroelectronics provide a more robust alternative, and use polymer as a substrate. 

Studies have suggested that the tensile behaviour of thin metal films on polymer substrates depends on the film’s adhesion to the substrate (Figure 1), although the rupture strains measured have varied greatly across these studies. This paper uses finite element simulations to look at the process by which a film ruptures during stress. In particular, the co-evolution of debonding at the metal/polymer interface and necking of a metal film during tensile stress is modelled. 

= Simulations =
The simulations used the following conditions: 
* Film: thickness = h, parameters for a weakly hardening metal
* Substrate: dimensions = 100h thick x 80h long, parameters for a steeply hardening polymer

The metal/polymer interface was modelled as an array of non-linear springs. 

Plane strain conditions were applied. An imperfection in the film was used to induce non-uniform deformation (V-shaped notched, 0.2h wide by 0.02h deep at the centre of the film). 

= Results =
[[Image:wiki2_norupture.jpg|300px|thumb|right|'''Figure 2.''' Rupture strain as a function of normalised stiffness for various interfacial strengths]]

[[Image:wiki2_sliding.jpg|300px|thumb|right|'''Figure 3.''' Rupture strain as a function of interfacial strength. For a given normalised interfacial stiffness, systems with higher interfacial shear strength (red) leads to a marked difference in rupture strains from systems with higher tensile strength (blue) and equal shear and tensile strength (black)]]

Three types of tensile behaviour were identified.

'''Type I:''' interface strength is low and interfacial displacement is high (eg ratio=normalised interfacial stiffness ~0.01). A single event of simultaneous debonding and film necking at the pre-existing notch occurred. The notch thinned at a strain of about 2%, rupture strain 4.6%

'''Type II:''' Interfacial strength and interfacial displacement are both intermediate (eg ratio ~10). Multiple necks formed but rupture only occurred at the pre-existing notch. The rupture strain is large (>60%) as each necking event contributes to the elongation of the metal film.

'''Type III:''' Interfacial strength is high and interfacial displacement is small (eg ratio ~200). Metal films deform to very large strains without debonding or rupture.

It was found that for high interfacial strengths, the increase in rupture strain increases substantially as the normliased interfacial sitffness increases (Figure 2).

Also, the effects of interfacial shear strength and interfacial tensile strength on rupture strain were compared (Figure 3). For a given normalised interfacial stiffness the rupture strain is more sensitive to interfacial shear strength (resulting in interfacial sliding) than the interfacial tensile strength (interfacial opening).

= Conclusions =
The studies agree well with previous studies on metal films/elastomer substrates, suggesting that the approximation that the metal/polymer interface acts like a set of springs is reasonable. Three regimes for tensile behaviour were identified, and the origin of the necking was found to be mainly attributed to interfacial sliding rather than opening.