Evaluation of dynamic properties in ABS and PLA thermoplastics across frequency ranges

Abstract

Additively manufactured thermoplastics are increasingly employed in vibration-sensitive applications across the automotive, biomedical, and aerospace industries, where mechanical performance under dynamic loading is critical. This study provides a novel integration of Dynamic Mechanical Thermal Analysis (DMTA) with frequency response function (FRF) evaluation to capture the sub-glass-transition viscoelastic behaviour of 3D-printed ABS and PLA within 5–100 Hz range, a comparative approach not previously reported in the literature. The narrow 35–60 °C range was selected to focus on sub-Tg behaviour relevant to service conditions at which applications include vibration control in automotive panels, biomedical housings, and electronic enclosures. Unlike prior DMTA-only studies, this work combines FRF and DMTA to provide novel frequency-domain insights. The results reveal distinct thermomechanical responses: ABS demonstrates superior damping near its glass transition temperature due to its amorphous structure, whereas PLA exhibits stable stiffness and frequency-independent damping at lower temperatures, attributed to its semi-crystalline morphology. Key findings reveal that ABS exhibits a peak damping factor (tanδ ≈ 0.25) around 55 °C, while PLA maintains a higher storage modulus at lower temperatures (while PLA retains a storage modulus of ~ 1.2E + 08 Pa at 35 °C) but shows a sharp decline beyond 50 °C, limiting its use in thermally elevated conditions. These insights elucidate structure–property relationships in 3D-printed polymers and inform material selection for vibration-damping applications requiring thermal and frequency stability within sub-Tg operating regimes.

Supplementary Information

The online version contains supplementary material available at 10.1038/s41598-025-26846-9.

Introduction

Thermoplastics such as Acrylonitrile Butadiene Styrene (ABS) and Polylactic Acid (PLA) are widely used in vibration and acoustic control applications due to their favourable viscoelastic properties, processability, and damping capabilities^1–4. While their static mechanical properties are well-documented^5–7, their dynamic behaviour, particularly under varying temperature and frequency conditions, remains insufficiently explored, especially for 3D-printed forms where microstructure and porosity significantly affect performance. Although several studies have examined the mechanical properties of FDM polymers, limited work has focused on sub-Tg viscoelastic behaviour under frequency sweeps, particularly combining DMTA with FRF analysis.

ABS is an amorphous, petroleum-based thermoplastic^5,7 known for its toughness, impact resistance, and glass transition behaviour near 105 °C. Its internal morphology, comprising rubbery butadiene dispersed in a styrene-acrylonitrile matrix, enhances damping near Tg (the glass transition temperature)⁵, making it suitable for energy-dissipating components. PLA, in contrast, is a semi-crystalline, bio-based thermoplastic with high stiffness and low thermal stability^8,9. While it lacks ABS’s impact resistance, PLA’s rigidity and environmentally friendly profile⁸ make it attractive for applications requiring consistent dimensional stability and low-temperature damping, such as biomedical scaffolds and consumer product casings^10,11. ABS and PLA are widely utilised in additive manufacturing (AM), particularly through Fused Deposition Modelling (FDM), due to their thermal processability and geometric versatility. FDM operates by extruding thermoplastic filaments through a heated nozzle to build parts layer by layer based on a pre-defined CAD model¹², which is accepted as a low-cost and accessible option¹³.

However, the layer-by-layer nature of FDM introduces inherent anisotropy, interfacial weaknesses, and porosity due to incomplete fusion or void formation. Process parameters such as infill density, layer height, print orientation, and thermal history critically influence the microstructure and mechanical behaviour of the printed components. These morphological variations directly affect the viscoelastic and damping performance of polymeric parts under dynamic loading. Therefore, a comprehensive evaluation of their dynamic mechanical response is essential, particularly for applications involving cyclic or vibratory environments^14,15. For this reason, understanding their damping behaviour requires advanced testing techniques. Polymeric materials are usually assessed with the Dynamic Mechanical Thermal Analysis (DMTA) in terms of characterising their material and mechanical properties and providing precise data to characterise the properties of structures made of polymers^16,17. DMTA enables a nuanced understanding of material performance under operationally relevant dynamic conditions, making it indispensable for evaluating polymer-based components in vibration-sensitive applications such as automotive interiors, electronic housings, and biomedical devices. Unlike static mechanical testing, DMTA evaluates both the elastic and viscous components of deformation by applying sinusoidal stress or strain and analysing the phase lag between stress and strain responses.

Key viscoelastic parameters¹⁸ measured in DMTA include the storage modulus (), which represents the elastic (energy-storing) behaviour; the loss modulus (), which quantifies the viscous (energy-dissipating) component; and the loss factor (tanδ = /), a dimensionless measure of damping efficiency¹⁸. DMTA tests can be conducted in various modes, such as three-point bending, compression, tension, and shear, depending on the sample geometry and application. Standard test protocols include frequency sweeps, temperature ramps, strain sweeps, and isothermal tests, all designed to capture time–temperature superposition effects and molecular mobility transitions^4,19. Frequency sweeps conducted at fixed temperatures uncover the frequency sensitivity of damping behaviour, which is critical for vibroacoustic applications. In polymeric systems, especially amorphous and semi-crystalline thermoplastics like ABS and PLA, DMTA provides vital data for understanding dynamic stiffness, energy dissipation capacity, and thermal transitions^19–21.

Prior studies often examine temperature or frequency effects in isolation and overlook their interaction^22,23. Moreover, structure–property relationships in 3D-printed materials, particularly the influence of semi-crystalline versus amorphous morphologies, require further clarification. This study investigates the dynamic mechanical behaviour of 3D-printed ABS and PLA over a temperature range of 35–60 °C and a frequency range of 5–100 Hz, and questions the frequency response of these materials and structures printed out using these materials. This range corresponds to operational conditions in applications such as automotive interiors, electronics housings, and medical devices, where polymer structures are exposed to moderate heating and cyclic loading. The selected range avoids thermal degradation while capturing key transitions at sub-Tg (glassy transition region temperature).

The aim of this study is to compare the sub-Tg viscoelastic behaviour of 3D-printed ABS and PLA through DMTA and FRF analysis, with emphasis on vibration-damping applications. The primary objective of this study is to systematically evaluate and compare the frequency- and temperature-dependent viscoelastic behaviour of 3D-printed ABS and PLA through DMTA and FRF analysis, with emphasis on their suitability for vibration-sensitive applications. Recent studies on sustainable additive manufacturing, such as recycled Rigid PU/PLA composites²², and hybrid PLA-based composites with natural fibres²³, further demonstrate the potential of filament extrusion for tailoring thermomechanical and acoustic properties. These works provide a broader context for evaluating damping and stiffness in PLA- and ABS-based systems. To enhance the scientific significance, this study integrates both DMTA and frequency response function (FRF) analysis, thereby extending conventional modulus-based evaluations toward dynamic system-level insights. This combined approach provides novelty by linking viscoelastic parameters to vibration-relevant performance, which has not been previously reported for 3D-printed ABS and PLA.

Material characterisation testing procedure for the polymers (ABS and PLA)

To fabricate the test specimens required for this study, additive manufacturing via fused deposition modelling (FDM) was employed using polymeric thermoplastic filaments. FDM is a widely utilised 3D printing technique due to its cost-effectiveness, ease of use, and capacity for fabricating complex geometries with customisable parameters^24,25. All samples were produced using an Ultimaker S3 printer, which is selected for its high-resolution capabilities and compatibility with engineering-grade filaments. The 3D models were designed using computer-aided design (CAD) software and exported in STL format^12,26. The slicing process for the 3D printing was carried out using Ultimaker Cura (Version 4.10), a software developed by Ultimaker B.V. (https://ultimaker.com/software/ultimaker-cura), which converts the geometry into machine-readable G-code while allowing for precise control over key printing parameters. A standard nozzle diameter of 0.25 mm was used, with filament diameters of 2.85 mm. FDM process parameters included a nozzle temperature of 200 °C (PLA) and 230 °C (ABS), bed temperature of 80 °C, and printing speed of 50 mm/s. Test specimens were printed in a rectangular geometry of 20 mm × 10 mm × 10 mm. The 65% infill ratio was elected to balance porosity and mechanical stability, consistent with prior studies that demonstrated increasing stiffness and strength with higher infill density in FDM-printed PLA and ABS specimens²⁷. The chosen infill level provides a balance between mechanical integrity and material efficiency, reflecting practical manufacturing scenarios. The controlled printing parameters, including infill percentage, nozzle temperature, and layer resolution, were kept constant across all samples to ensure comparability in dynamic mechanical testing.

Following fabrication, the mass of each 3D-printed specimen was measured using a high-precision analytical balance with an accuracy of ± 0.001 g to ensure reliable data for subsequent density calculations. These values reflect the influence of both material type and internal structure (65% infill) on the effective density of the printed parts. All test specimens were directly fabricated via FDM 3D printing without additional cutting or fibre processing. The PLA specimen exhibited an average mass of 1.8 g, while the ABS specimen recorded a slightly higher mass of 1.9 g, as summarised in Table 1. The density values were re-verified, with PLA measured at 1.24 g/cm³ and ABS at 1.05 g/cm³, in agreement with reported literature values^28–32.

Table 1.

Material properties of the 3D-printed and the DMTA testing applied samples.

	ABS (Acrylonitrile Butadiene Styrene)	PLA (Polylactic Acid)
Total Mass [g]	1.9	1.8
Poisson’s Ratio [-]	0.35	0.35
Mass Density [kg/m3]	1050	1240

Dynamic Mechanical Thermal Analysis (DMTA) was conducted using a Metravib Xpander VA 2000 viscoanalyser (see Fig. 1), to evaluate the viscoelastic behaviour of the 3D-printed PLA and ABS samples. The testing protocol was designed to systematically investigate frequency-dependent and temperature-sensitive mechanical responses. DMTA tests were performed in a three-point bending configuration according to ASTM D4065³³, using the printed specimens of 20 × 10 × 10 mm with a span length of 15 mm, allowing for consistent volume estimates across all test specimens. FRF curves were derived from DMTA output by computing the ratio of dynamic displacement to force across frequency sweeps. Temperature was ramped from 35 °C to 60 °C at a controlled rate of 5 °C/min, allowing thermal equilibrium to be achieved at each setpoint. At each isothermal condition, frequency sweeps were performed across the range of 5–100 Hz, enabling characterisation of the materials’ dynamic stiffness and damping behaviour. Key viscoelastic parameters were extracted, including: Storage modulus (), representing elastic stiffness; Loss modulus (), indicating energy dissipation; Loss factor (tanδ), quantifying damping efficiency.

Fig. 1.

The DMTA test machine ready-to-test form of the machine.

The instrument was calibrated prior to each experimental run to minimise systematic error. All measurements were conducted under identical environmental conditions. To ensure consistency, repeated scans were performed on the same specimen, and deviations between consecutive runs remained within ~ 3%. While multiple replicates were not available for this study, the low variability observed across repeated measurements suggests that the results are representative of the material behaviour within the tested range.

The excitation parameters were maintained within the linear viscoelastic regime, with the applied dynamic stress amplitude fixed at 0.001 Pa and the corresponding strain amplitude limited to 0.0001 as stated in the standard procedure for DMTA testing, ASTM D4065³³. These infinitesimal deformation levels ensured that the material response remained free from non-linear effects and structural damage during testing. Additionally, the collected data provided insight into temperature-dependent transitions, such as the glass transition region, and the material’s resistance to dynamic deformation under operational frequency and temperature ranges. This information is critical for assessing the suitability of PLA and ABS in vibration-sensitive applications under varying thermal conditions.

Results

This paper presents the results from dynamic and thermal analysis of the 3D-printed thermoplastic samples to evaluate their mechanical and viscoelastic properties under certain conditions via DMTA testing. This research provides valuable information about how the 3D-printed structures behave under dynamic loading when the atmospheric conditions are changeable under sub-Tg conditions and what their mechanical properties are as newly adapted materials.

The experimental results are presented in terms of storage modulus (), loss modulus (), and the loss factor (tanδ), which collectively characterise the material’s stiffness and damping behaviour. The storage modulus, representing the elastic (recoverable) component of the complex modulus, reflects the ability of the material to store mechanical energy while ability of the material to resist cyclic loading^32,34. In contrast, the loss modulus quantifies the energy dissipated as heat during cyclic loading, indicating internal friction and molecular motion³⁵. The damping efficiency is expressed by the loss factor (tanδ), calculated as the ratio of  to  (Eq. 1). These viscoelastic parameters, obtained through Dynamic Mechanical Thermal Analysis (DMTA), provide critical insights into the performance of 3D-printed PLA and ABS under dynamic thermal and frequency conditions^16,36. All numerical analyses and curve fitting were performed using MATLAB R2023b (MathWorks Inc.).

1

Figures 2 and 3 provide insight into the storage modulus of two material samples under specific testing conditions. Figure 2 illustrates the storage modulus (E′) of ABS samples measured across a frequency range of 5–100 Hz under six distinct temperature conditions (35 °C to 60 °C). The storage modulus exhibits a positive correlation with frequency at all tested temperature levels. This trend is consistent with the viscoelastic behaviour of thermoplastics, where higher excitation frequencies reduce the time available for molecular relaxation, thereby resulting in a stiffer response. As temperature increases, a progressive reduction in storage modulus is observed. This behaviour reflects the thermally induced softening of ABS as it approaches its glass transition region. The stiffness decline is more pronounced at temperatures above 50 °C, highlighting the increasing molecular mobility within the amorphous domains of the polymer matrix. At 35 °C, the storage modulus reaches approximately 1.48 GPa and remains the highest across the frequency range, whereas at 60 °C, it decreases to approximately 1.26 GPa, indicating a 15% reduction in stiffness due to thermal effects. The data also demonstrate that while frequency enhances stiffness, temperature remains the dominant factor influencing the modulus magnitude. This figure underscores the interplay between temperature and frequency in governing the dynamic mechanical performance of ABS. Such insights are critical for applications where thermomechanical stability and dynamic load-bearing capability are essential, such as in automotive interiors, consumer electronics, and lightweight structural components.

Fig. 2.

Storage Modulus of ABS under varying temperature and frequency.

Fig. 3.

Storage Modulus of PLA under varying temperature and frequency.

Figure 3 presents the storage modulus () of PLA samples measured across a frequency range of 5–100 Hz at discrete temperature levels from 35 °C to 60 °C. The results demonstrate that PLA exhibits a consistently decreasing storage modulus with increasing temperature, a behaviour that aligns with the thermal softening of polymer chains as the material approaches and surpasses its glass transition temperature (Tg ≈ 55–60 °C). At 35 °C, PLA maintains the highest stiffness (~ 1.3 GPa), while at 60 °C, the modulus drops sharply to below 200 MPa, indicating severe softening and loss of structural integrity at elevated temperatures. In terms of frequency dependence, PLA shows modest increases in storage modulus with increasing frequency at each temperature level. This trend is expected in viscoelastic materials, as higher frequencies limit molecular relaxation and enhance the elastic response, which results in stiffening and higher storage modulus levels. However, the magnitude of frequency sensitivity is relatively low, particularly at lower temperatures, suggesting stable stiffness performance under dynamic loading. The semi-crystalline nature of PLA contributes to its high stiffness at sub-Tg temperatures, where crystalline domains act as reinforcing elements. However, once the temperature exceeds Tg, these domains lose coherence, resulting in rapid stiffness degradation. This behaviour restricts PLA’s effective use to low- to moderate-temperature applications, particularly where dimensional stability and mechanical performance are critical. These results highlight PLA’s suitability for applications requiring stiffness and consistent elastic performance at lower temperatures and moderate frequencies, such as biomedical devices, packaging, and low-temperature vibration-isolating components. However, its limited thermal stability underscores the need for modification or reinforcement for use in high-temperature or load-bearing environments.

Figure 4 illustrates the variation of loss modulus () of ABS samples as a function of frequency (5–100 Hz) at discrete isothermal conditions between 35 °C and 60 °C. The loss modulus characterises the energy dissipated as heat due to internal friction during cyclic loading and is a critical indicator of damping performance in viscoelastic materials. Across all temperatures, ABS exhibits a positive correlation between frequency and loss modulus, indicating enhanced energy dissipation at higher excitation rates. This behaviour is attributed to the reduced time available for molecular rearrangement under rapid cyclic deformation, resulting in increased internal friction and hysteresis loss. A distinct observation is the increasing trend in loss modulus with rising temperature, especially up to 55 °C, after which the values tend to stabilise or marginally decrease. This trend is consistent with the approach to glass transition temperature (Tg ≈ 105 °C for ABS), where molecular mobility increases, facilitating greater segmental motion and frictional energy loss²¹. Notably, at 60 °C, ABS demonstrates the highest loss modulus, suggesting enhanced damping capability at elevated but sub-Tg conditions. However, the variability seen at higher frequencies may reflect microstructural relaxation limits or thermal softening onset. Moreover, the convergence of data at higher frequencies across temperatures suggests that frequency becomes the dominant factor over temperature in defining damping behaviour beyond a certain threshold. This reinforces the relevance of ABS in dynamic environments, such as automotive interiors, vibration isolators, or consumer electronics, where moderate thermal loads and broad excitation frequencies coexist. In summary, ABS shows temperature- and frequency-sensitive damping characteristics, with enhanced loss modulus near elevated temperatures, reinforcing its suitability for applications requiring effective energy dissipation under varying thermal and dynamic conditions.

Fig. 4.

Loss Modulus change in ABS by varying temperature and frequency impacts.

The variation in the loss modulus () of PLA across the studied frequency and temperature ranges (Fig. 5) provides insight into its energy dissipation behaviour under dynamic loading. At 35–45 °C, PLA shows relatively low but stable E″ values (~ 2.5–3.0 × 10⁷ Pa), with only a modest increase of ~ 10–15% as frequency rises from 5 to 100 Hz. This limited frequency dependence is consistent with its semi-crystalline morphology, where crystalline regions constrain chain mobility and reduce viscous energy dissipation. At 55 °C and above, however, E″ increases by nearly 35% compared to its baseline at 35 °C, accompanied by greater variability. This behaviour reflects the onset of thermal softening near the glass transition temperature (Tg ≈ 55–65 °C). While amorphous domains exhibit enhanced relaxation and higher energy loss per cycle, the absence of a sharp E″ peak indicates that crystalline domains suppress large-scale relaxation, producing a broad and less pronounced transition than observed in amorphous polymers like ABS. From an application standpoint, PLA’s relatively low and temperature-stable loss modulus below 50 °C highlights its suitability for stiff, frequency-stable components (e.g., electronic housings, medical prototypes), whereas the ~ 35% rise in E″ near Tg reflects reduced damping efficiency and limits its use in high-temperature or vibration-isolation applications.

Fig. 5.

Loss Modulus change in PLA by varying temperature and frequency impacts.

The loss factor (tanδ) of ABS, defined as /, provides a direct measure of damping efficiency under cyclic loading. As shown in Fig. 6, ABS exhibits a distinct tanδ peak (~ 0.25) in the 50–55 °C range, coinciding with its glass transition (Tg ≈ 50–60 °C). Below Tg, polymer chains remain in a rigid glassy state, limiting molecular relaxation and energy dissipation. As temperature approaches Tg, increased chain mobility in the amorphous domains enhances internal friction, leading to a ~ 60–70% rise in tanδ relative to its baseline at 35 °C. The sharp peak reflects the amorphous morphology of ABS, where the absence of crystalline constraints allows for a rapid transition between glassy and rubbery states. Beyond 55 °C, tanδ decreases as the material softens and energy dissipation declines due to excessive chain mobility and reduced modulus. The relatively high tanδ peak compared to typical thermoplastics underscores ABS’s strong damping potential, making it suitable for vibration control in thermally dynamic environments, such as automotive interiors, consumer electronics, and structural damping components operating near Tg.

Fig. 6.

Loss Factor change of ABS for temperature ranges of 35–60 ᵒC.

Figure 7 displays that PLA shows a broad, temperature ranges of 35–60 °C, shallow peak in loss factor, with the maximum value reaching approximately 0.15 around 55–60 °C, which aligns with the onset of its glass transition temperature (Tg). Unlike ABS, PLA’s semi-crystalline structure restricts extensive molecular mobility, leading to a broader and more gradual transition in tanδ. The crystalline domains within PLA act as physical cross-links, inhibiting the free movement of chain segments and thereby limiting energy dissipation, even as the amorphous regions approach their Tg. This suppressed molecular relaxation contributes to a lower peak value and a flatter loss factor curve, indicating a more stable but less efficient damping behaviour. At lower temperatures (35–45 °C), PLA exhibits relatively consistent and low tanδ values, suggesting that the material maintains its structural stiffness with minimal damping. This frequency-independent and thermally stable damping behaviour makes PLA suitable for low-temperature vibroacoustic applications where dimensional stability and long-term performance are prioritised over peak energy dissipation. However, above 55 °C, the tanδ curve begins to flatten and decline, indicating the onset of thermal softening and loss of damping effectiveness, likely due to the breakdown of crystalline integrity and increased segmental mobility in the amorphous regions²⁹. Overall, while PLA does not provide the same peak damping efficiency as ABS, its broad and steady loss factor profile makes it attractive for applications requiring predictable damping across a range of operating frequencies, particularly in biomedical devices, electronic enclosures, or structural components where thermal and vibrational stability are required below 60 °C.

Fig. 7.

Loss Factor change of PLA for temperature ranges of 35–60 ᵒC.

In addition to the graphical representation of storage modulus, loss modulus, and loss factor, the key viscoelastic parameters are summarised in Table 2. For ABS, the storage modulus remained in the order of 10⁹ Pa, while the loss modulus reached a peak of 5.02E + 07 Pa at 55 °C, corresponding to a tanδ maximum of 0.228 at 55 °C. PLA, in contrast, exhibited an order-of-magnitude lower stiffness and damping values, with a storage modulus in the range of 10⁹ Pa and a maximum loss modulus of 2.15E + 08 Pa. Its tanδ peak was measured at 0.15 at 55 °C. These values provide a direct comparison of the stiffness-damping trade-offs between the two thermoplastics, highlighting ABS’s superior damping near Tg and PLA’s stable elastic response at lower temperatures. At higher temperatures, isolated tanδ values exceeding unity were occasionally observed. These anomalies are attributed to instrumental sensitivity and are not considered representative of the material response. Therefore, only consistent and physically meaningful values are reported in Table 2.

Table 2.

Summary of key viscoelastic parameters for ABS and PLA obtained from DMTA. Mean values are averaged across the frequency range (5–100 Hz) at each temperature. Peak values correspond to maximum damping efficiency points.

Material	Temperature Range (ᵒC)	E′ (Pa, mean)	E′′ (Pa, mean)	tanδ (mean)	E′′ (Pa, peak)	tanδ (peak)
ABS	35–60	1.38E + 09	3.15E + 07	2.28E-02	5.02E + 07 at 55 ᵒC	3.75E-02 at 55 ᵒC
PLA	35–60	1.03E + 09	7.57E + 07	1.45E-01	2.15E + 08 at 60 ᵒC	9.98E-01 at 60 ᵒC

Dynamic mechanical analysis of 3D-printed ABS and PLA highlights their distinct viscoelastic profiles for vibration-sensitive applications. FRF captures dynamic displacement and force ratio, while DMTA directly measures phase lag. Trends from both align qualitatively. PLA’s higher storage modulus at lower temperatures, driven by its semi-crystalline structure, suits applications requiring stiffness and dimensional stability, such as biomedical devices and consumer electronics. ABS, with its elevated loss modulus and tanδ peak near 50–55 °C, demonstrates superior damping near its glass transition, making it preferable for thermally dynamic environments like automotive interiors or impact-absorbing components. These findings support material selection based on specific thermal and vibrational demands.

Frequency response function (FRF) analysis – based on DMTA data

In order to complement the DMTA results, a frequency response function (FRF) model was developed using the frequency-dependent viscoelastic moduli (storage and loss modulus) and the loss factor data for both PLA and ABS samples. The analysis was conducted for two representative temperature levels, which are the highest level (60 ᵒC) and the lowest level (35 ᵒC), within the frequency range of 5 to 100 Hz. The FRF analysis was developed by processing DMTA frequency sweep data to extract amplitude and phase relations between applied load and displacement. This approach complements modulus-based analysis by representing energy transfer in the frequency domain.

According to Fig. 8, at 60 °C, the FRF amplitude for PLA was observed to be higher than that of ABS, suggesting a reduced stiffness or increased damping behaviour. The phase angle for PLA varied between − 60° and − 25°, indicating a strong viscoelastic response. In contrast, ABS exhibited phase angles close to 0°, reflecting a nearly elastic behaviour with minimal energy dissipation. The loss factor (tanδ) for PLA ranged from 1.5 to 0.5, decreasing with frequency, while ABS remained nearly zero, confirming its weak damping capacity at elevated temperatures. Therefore, applications in high temperature levels require careful selection of damping materials³⁷.

Fig. 8.

Frequency response analysis for varied material properties at 60 °C.

As seen from Fig. 9 provides information for the results of materials at 35 °C; both materials showed similar FRF amplitude profiles and phase angles around − 1°, implying primarily elastic responses. However, the loss factor values increased with frequency for both materials, from approximately 0.015 at low frequencies up to 0.04 at 100 Hz, indicating frequency-activated damping. Interestingly, ABS showed slightly higher damping than PLA at higher frequencies under this temperature condition.

Fig. 9.

Frequency response analysis for varied material properties at 35 °C.

The integration of Frequency Response Function (FRF) analysis complements conventional DMTA by capturing the dynamic behaviour of ABS and PLA under harmonic excitation. FRF reveals phase lag, amplitude response, and energy dissipation beyond static modulus data, offering valuable insight into material performance in vibration-sensitive applications. This is especially critical at elevated temperatures, where damping behaviour changes significantly. The combined DMTA–FRF approach enhances the understanding of real-world thermo-mechanical responses, supporting material selection for applications such as automotive panels, electronic enclosures, and structural components subjected to dynamic and thermal loads.

Discussion

A direct comparative analysis highlights that ABS exhibits superior damping performance near its glass transition, whereas PLA demonstrates greater stiffness and frequency stability at sub-Tg conditions. This distinction provides a novel perspective on tailoring polymer selection for vibration-sensitive applications.

The DMTA results confirm that both ABS and PLA exhibit frequency-dependent stiffening, a typical feature of viscoelastic polymers. The storage modulus (E′) for both materials increases with frequency, consistent with the time–temperature superposition principle, reflecting reduced relaxation times at higher oscillation rates. ABS consistently maintains higher absolute E′ values compared to PLA, yet its modulus shows marked thermal softening as the temperature approaches the sub-Tg regime, highlighting a progressive loss of stiffness and potential compromise of structural integrity under elevated thermal loads. PLA, although exhibiting lower E′ values overall, demonstrates improved thermal stability within the studied sub-Tg window. This behaviour can be attributed to its semi-crystalline morphology, where crystalline domains act as reinforcing elements that constrain molecular mobility and delay modulus degradation.

Beyond 50 °C, however, PLA undergoes a sharp reduction in E′, suggesting disruption of crystalline order and the onset of thermal softening. Despite this decline, PLA’s frequency-dependent response remains relatively stable, which makes it suitable for applications requiring dimensional stability and rigidity under mild thermal and vibrational conditions. Conversely, ABS shows a steeper and more progressive decline in modulus with temperature, underlining the need for reinforcement or hybridisation strategies when targeting load-bearing or thermally dynamic applications.The loss modulus (), representing viscous dissipation, increases with frequency for both materials but is significantly more pronounced in ABS, particularly between 50 and 60 °C. This trend reflects increased molecular mobility near Tg and supports the suitability of ABS for energy-dissipating applications in thermally dynamic environments. PLA displays consistently lower  values, with minimal frequency and temperature sensitivity, limiting its damping performance but favouring stability.

The damping efficiency, as reflected by the loss factor (tanδ), peaks at ~ 0.25 for ABS near 55 °C, indicating enhanced energy dissipation near Tg. PLA shows a broader tanδ peak (~ 0.15), suggesting a more stable but less efficient damping response. Measured tanδ ranges for PLA (~ 0.12–0.18) and ABS (~ 0.20–0.27) are consistent with previous reports, where PLA typically exhibits tanδ values in the range of ~ 0.12–0.15³⁸, and ABS generally shows higher damping factors under comparable conditions³⁹. These distinctions imply that ABS is more appropriate for dynamic environments requiring active vibration attenuation, whereas PLA is better suited for static or low-dynamic-load applications where mechanical predictability is critical, such as biomedical housings or low-frequency electronic enclosures.

The FRF model is complementary to DMTA, providing additional insights into phase lag and resonance trends. While not intended as a strict validation tool, FRF strengthens the interpretation of the experimental viscoelastic data. Overall, the observed viscoelastic trends emphasise the importance of temperature and frequency as design parameters in thermoplastic-based functional components. The distinct behaviours of ABS and PLA support their targeted use in vibration-sensitive applications, with ABS favoured for high-damping, high-temperature environments, and PLA for rigid, frequency-stable conditions. While this study focuses on ABS and PLA as benchmark FDM polymers, the methodology developed here—particularly the integration of FRF with DMTA—provides a scalable framework that can be applied to advanced or composite materials in future studies.

Conclusion

This study presents a comparative assessment of the dynamic mechanical behaviour of 3D-printed ABS and PLA under varying thermal (35–60 °C as sub-Tg ranges) and frequency (5–100 Hz) conditions using DMTA. The study concludes that ABS provides superior damping efficiency in thermally dynamic environments due to its pronounced tanδ peak, while PLA offers greater stiffness and dimensional stability at lower temperatures, making it more suitable for structural or biomedical applications. While ABS tanδ peak reaches ~ 0.25, PLA storage modulus drop more than 40% beyond 55 °C. This supports the dynamic thermal fluctuations in the material properties.

This research demonstrates the complementary use of DMTA and FRF for evaluating sub-Tg viscoelastic behaviour of 3D-printed polymers, underscoring the importance of frequency-domain evaluations in material selection for vibration-sensitive design. These findings offer practical guidance for applying ABS and PLA in additively-manufactured systems and suggest directions for future research, including material reinforcement, advanced modelling (e.g., Maxwell-based fitting), and structural characterisation techniques such as SEM and DSC to deepen understanding of viscoelastic performance. Another limitation of this study is that DMTA measurements were performed on single specimens due to restricted material availability and equipment access. Consequently, standard deviations and error bars could not be reported. Nevertheless, the testing instrument (Metravib Xpander VA2000) ensures a reproducibility within ± 3% based on calibration standards, which constrains the expected variability. Future studies will include multiple replicates (n ≥ 3) to provide a robust statistical assessment of the viscoelastic properties.

Supplementary Information

Below is the link to the electronic supplementary material.

Abbreviations

ABS

Acrylonitrile Butadiene Styrene

PLA

Polylactic Acid

FDM

Fused Deposition Modelling

DMTA

Dynamic Mechanical Thermal Analysis

FRF

Frequency Response Function

SEM

Scanning Electron Microscopy

DSC

Differential Scanning Calorimetry

ASTM

American Society for Testing and Materials

STL

Stereolithography

CAD

Computer-aided Design

AM

Additive Manufacturing

Tg

Glass Transition Temperature

E’

Storage Modulus

E’’

Loss Modulus

tanδ

tan delta

Author contributions

Dr Demiryurek studied, conducted all the research, wrote and editted all the work shared in this manuscript.

Data availability

The datasets used and/or analysed during the current study are available from the corresponding author on reasonable request.

Declarations

Competing interests

The authors declare no competing interests.