Modal Origin of the Temperature-Dependent DMA Phase Shift in Polymer Beams

Dynamic mechanical analysis is widely used to characterize viscoelastic materials, yet the physical origin of the measured phase shift remains only partially understood for structurally extended specimens. Its standard interpretation typically assumes a single, effective phase shift between applied stress and strain. In this work, we investigate the temperature-dependent viscoelastic response of medical-grade acrylonitrile butadiene styrene (ABS) fabricated by fused filament fabrication and injection molding, combining DMA measurements, fractographic analysis, and analytical modeling. Rectangular beam specimens were subjected to three-point bending DMA over a temperature range spanning the glass transition region. The storage modulus, loss modulus, and phase shift were determined as functions of temperature and compared between manufacturing routes. While both materials exhibit nearly identical glass transition temperatures, the 3D-printed samples exhibit a modest reduction in storage modulus, reflecting microstructural heterogeneity introduced by the layer-wise fabrication process. Fractographic observations reveal characteristic interlayer features and microvoids that correlate with the observed mechanical response. To interpret the temperature-dependent phase shift, we develop a theoretical model of a damped vibrating beam in which each eigenmode contributes with its own phase shift. By introducing a temperature-dependent effective damping coefficient, the model’s mode-averaged phase shift reproduces the experimental DMA data with high accuracy. By linking DMA phase measurements to the mode dynamics of the tested structure, the proposed framework establishes DMA as a structure-sensitive dynamical probe and is applicable to a broad class of polymer, composite, and additively manufactured materials.