Abstract
Traditional open or closed-cell stochastic elastomeric foams have wide-ranging applications in numerous industries: from thermal insulation, shock absorbing/gap-filling support cushions, packaging, to light-weight structural and positional components. Recent developments in 3D printing technologies by direct ink-write have opened the possibility of replacing stochastic foam parts by more controlled printed micro-structures with superior stress-distribution and longer functional life. For successful deployment as mechanical support or structural components, it is crucial to characterize the response of such printed materials to long-term external loads in terms of stress-strain behavior evolution and in terms of irreversible structural and load-bearing capacity changes over time. To this end, here we report a thermal-age-aware constitutive model for a 3D printed close-packed foam structure under compression. The model is based on the Ogden hyperfoam strain-energy functional within the framework of Tobolsky two-network scheme. It accurately describes experimentally measured stress-strain response, compression set, and load retention for various aging times and temperatures. Through the technique of time-temperature-superposition the model enables the prediction of long-term changes along with the quantification of uncertainty stemming from sample-to-sample variation and measurement noise. All aging parameters appear to possess the same Arrhenius activation barrier, which suggests a single dominant aging mechanism at the molecular/network level.
Highlights
Traditional open or closed-cell stochastic elastomeric foams have wide-ranging applications in numerous industries: from thermal insulation, shock absorbing/gap-filling support cushions, packaging, to light-weight structural and positional components
When we optimized all six parameters to fit the observed stress-strain response under uniaxial compression, we found that the two β parameters are nearly zero, which is consistent with our findings that under compression without any transverse confinement there is almost no lateral bulging for compression levels of ~42%
In this paper we described the development of a thermal-age-aware constitutive model for a 3D printed foam under long-term compressive strains
Summary
The foam specimen used in this work was additively manufactured using the method described previously[8]. The noise in the resulting data (Fig. 3), especially at lower temperatures is likely more due to not achieving complete equilibrium because of slow system relaxation (i.e., long relaxation times) rather than sample differences in equilibrium properties In spite of this limitation, there are clear trends in the plots, which can be used to build an aging model with long-term predictions. Time and temperature dependence of: compression set (CS); load retention (LR); Shear modulus μ10 of the original network; and shear modulus μ11 of the induced network Each point in these graphs are obtained by optimized fitting of the experimental stress-strain response with the Ogden + Tobolsky model at each time and temperature, averaged over two samples for each isotherm. The Arrhenius-based smooth margins are (rightly) not influenced by such noise
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