Experiments and Models for the Time Dependent Mechanics of Nanoscale Polymeric Structures and Nanocrystalline Metal Films

To date, micro and nanoscale experiments have been mostly focused on the length scale dependent mechanical behavior of nanostructures and nanostructured thin films but have not been able to address their time and rate dependence. This inefficiency stems from the use of high resolution electron microscopes which are slow imaging tools, and quite often are of detrimental effect to the integrity of polymeric materials. Optical methods have been revisited in the recent years and were modified to accommodate micro and nanoscale specimens in order to obtain high resolution deformations and their time evolution at time scales varying from microseconds to days [1-4]. This research, conducted at the University of Illinois, has developed new approaches to investigate the time-dependent mechanical behavior of metallic thin films for MEMS and polymeric nanostructures in an effort to understand the important deformation processes at small scales. The extended (internal) surfaces in nanocrystalline metal films and the large surface-to-volume ratios in polymeric nanostructures favor material transport mechanisms that are not important in bulk or large grain materials because they do not result in appreciable strains. On the contrary, in nanoscale polymeric fibers for instance such processes result in large material deformations and sustained ductilities in a large range of loading rates. This presentation will summarize experimental work conducted with polymeric nanofibers and nanocrystalline metals and some early modeling efforts to rationalize the measured time- and rate-dependent mechanical behavior.

Time-dependent Mechanics of Polymeric Nanofibers

Figure 1. Engineering stress-strain curves of PAN nanofibers at three strain rates. The curly brackets group the plots according to the engineering stress in the fiber during drawing [5].

Polymeric nanofibers have been of interest in the last two decades due to scalable manufacturing processes based on electrospinning. Although they are materials with clear time dependence, only recently their temporal mechanical behavior has been investigated in a relatively broad range of strain rates, varying from 10-4 to 200 s-1 [5,6] as the appropriate experimental tools have become available [1]. Using these experimental methods, the first creep experiments with nanoscale fibers were also conducted to determine simple viscoelastic laws which, when calibrated, could provide predictions for the rate-dependent response. At relatively low stresses (<40 MPa) compared to the yield strength (>100 MPa) of the nanofibers it has been shown that linear viscoelasticity may be applied and predictions of the strain evolution at slow strain rates could be made if the viscoelastic time constants were calculated as a function of the nanofiber diameter. This size effect was explained by extensive experiments with amorphous polymeric nanofibers, which have shown a strong dependence of the initial elastic stiffness and the yield and ultimate strengths on the nanofiber diameter. This behavior has been attributed to molecular orientation and density variations across the nanofiber thickness [6]. Additionally, it was found that the nanoscale size of the polymer fibers gives rise to enhanced ductility and strength: Contrary to macroscale trends, the reduction in the nanofiber ductility with the applied strain rate is rather small while the nanofiber strength increases significantly with the loading rate [6,7]. The reduced molecular confinement in nanofibrous structures can account for these effects. Finally, an unusual and interesting mechanical behavior of polymeric nanomaterials has been shown to take place in polymeric nanofibers when structural heterogeneity is present: strain rate experiments have shown a reversal in the rate dependency of the flow stress at slow (10-4 s-1) as opposed to 10-2 s-1, or higher, strain rates. At slow rates the stress riser effect of structural heterogeneity was mediated by stress relaxation contrary to faster strain rates where structural heterogeneity resulted in deformation localization and periodicity.

Strain Rate Behavior of Nanocrystalline Metallic Films

Equally interesting is the strain rate and creep response of nanocrystalline metallic films with grain sizes of 50 nm or smaller. Such films have received major attention in the recent years because of their large yield strength. Their small grain size promotes strengthening, which, in turn, results in high tensile strengths at the expense of reduced ductility and potentially toughness. An overlooked aspect of the mechanics of nanocrystalline metals is the increased strain rate sensitivity at reduced grain sizes and increased temperatures. The extended grain boundary network favors increased diffusion rates of defects and dislocations resulting in a significant and prolonged primary creep regime lasting for hours at pronounced primary creep rates [8]. This mechanical behavior has been the root cause for the long term performance degradation of metallic MEMS devices. Even when the latter are operated at otherwise elastic stresses, the appreciable primary creep rates result in considerable cumulative creep strain. The evolution of creep strain in nanocrystalline metals has been modeled via linear viscoelasticity in the past yielding satisfactory predictions [9]. More recently, such modeling based on creep experiments has provided predictions about the onset of plastic deformation at different strain rates [10]. Furthermore, relatively small increases in temperature have an equally significant, yet with opposite trends effects on the yield strength. At room temperature the effect of primary creep is evident in the mechanical response of films loaded at rates as high as 10-4 s-1. A small increase in temperature to 110°C further propels the effect of grain boundary induced creep affecting the mechanical response at rates as high as 10-1 s-1, which is faster that the rates encountered in most thin film applications. Finally, void nucleation, growth and microcracking have been shown to be rate dependent too demanding a three-dimensional description of damage nucleation and evolution. Experiments have shown that this evolution is dictated by the competition between creep/stress relaxation and the loading rate, which leads to a variety of failure modes due to distributed damage at slow strain rates, versus large void growth and localized damage at fast loading rates.