Dynamic Mechanical Analysis (DMA) for Glass Interlayers

What Is DMA?

Dynamic Mechanical Analysis is a characterisation method where a specimen is subjected to sinusoidal (oscillatory) deformation and the resulting stress response is measured. Because viscoelastic materials respond with a phase-shifted stress signal, DMA separates the response into an elastic component (energy stored) and a viscous component (energy dissipated).

For glass interlayer characterisation, DMA complements static relaxation tests. While relaxation gives G(t) directly in the time domain, DMA gives G′(ω) and G″(ω) in the frequency domain. Both contain the same information and are interconvertible via Fourier transforms.

Advantages of DMA over static tests

• Speed: a frequency sweep covering three decades takes minutes, not hours
• Precision: sinusoidal excitation with lock-in detection gives excellent signal-to-noise ratios
• Direct T_g determination: a single temperature ramp reveals the glass transition and any secondary transitions
• Damping characterisation: the loss factor tan(δ) is measured directly, which is critical for acoustic glazing applications

The Oscillatory Test Principle

In a DMA test, the specimen is deformed sinusoidally. The applied strain follows:

The phase shift δ is the key measurement. It quantifies the balance between elastic and viscous response:

Phase angle δ	G′ vs G″	Behaviour	Example
0°	G″ = 0	Ideally elastic	Glass, steel
0°–45°	G′ > G″	Viscoelastic solid	Interlayer below Tg
45°	G′ = G″	Crossover (sol-gel point)	Near Tg
45°–90°	G″ > G′	Viscoelastic liquid	Interlayer well above Tg
90°	G′ = 0	Ideally viscous	Water, thin oil

Output Quantities

The stress response is decomposed into an in-phase component (elastic) and an out-of-phase component (viscous) via the complex modulus:

Quantity	Symbol	Unit	Physical meaning
Storage modulus	G′	MPa	Elastic energy stored per deformation cycle. Characterises stiffness.
Loss modulus	G″	MPa	Energy irreversibly dissipated as heat per cycle due to internal molecular friction.
Complex modulus	|G*|	MPa	Total stiffness: ratio of stress to strain amplitude.
Loss factor	tan(δ)	—	Ratio G″/G′. Measures damping capability. Governs acoustic performance.

The Four Measurement Types

1. Amplitude sweep (strain sweep)

Purpose: determine the Linear Viscoelastic (LVE) range — the maximum strain at which the material response remains proportional to the input.

Procedure: frequency is held constant (typically 1 Hz); strain amplitude is increased step by step. Within the LVE range, G′ and G″ are constant (plateau region). Above the LVE limit, G′ decreases as the sample structure breaks down.

Why it matters: all subsequent DMA measurements must use a strain within the LVE range. Exceeding it invalidates the results — the measured moduli no longer represent the undisturbed material, and the Boltzmann superposition principle ceases to apply.

2. Frequency sweep

Purpose: characterise time-dependent viscoelastic behaviour.

Procedure: strain amplitude is held constant within the LVE range; angular frequency ω is varied (typically 0.01 to 100 rad/s). G′(ω), G″(ω), and tan(δ)(ω) are recorded at constant temperature.

Interpretation: high frequencies simulate short load durations (wind gusts); low frequencies simulate long load durations (permanent loads). A frequency sweep at one temperature is approximately equivalent to a relaxation test at the same temperature, with t ≈ 1/ω.

3. Temperature sweep (thermogram)

Purpose: determine thermal transitions, most importantly T_g.

Procedure: strain amplitude and frequency are held constant; temperature is ramped (e.g., −50°C to +100°C at 2–5°C/min). G′(T), G″(T), and tan(δ)(T) are recorded.

The thermogram reveals:

1. Glassy state (T << T_g): G′ ≈ 10³ MPa, tan(δ) < 0.1
2. Glass transition (T ≈ T_g): G′ drops steeply; G″ and tan(δ) peak
3. Rubber-elastic plateau (T > T_g): G′ stabilises at ~1 MPa; tan(δ) decreases
4. Flow region (T >> T_g): G′ drops further; viscous flow dominates

4. Time sweep (isothermal hold)

Purpose: monitor changes in material properties over time at constant conditions.

Procedure: temperature, strain amplitude, and frequency are all held constant. G′ and G″ are recorded over time. Used to verify thermal equilibrium, monitor curing or ageing, and detect structural changes.

Measuring Geometries for Interlayers

Geometry	Mode	Measures	Best for
Tension clamp (UXF)	Axial tension	E* (Young’s modulus)	Standalone interlayer films — used by Centelles et al. with RSA3
Solid Rectangular Fixture (SRF)	Torsion	G* (shear modulus) directly	Rectangular bars; avoids E-to-G conversion
Parallel plates (PP)	Shear	G* directly	Soft samples, gels, polymer melts
Three/four-point bending (TPB)	Flexure	E* (flexural modulus)	Rigid specimens; laminated glass assemblies

For standalone interlayer films, the tension clamp geometry is most practical. Centelles et al. (2021) used the RSA3 Dynamic Mechanical Analyser (TA Instruments) in tension mode, measuring E* and converting to G* via the Poisson ratio (ν ≈ 0.48 for PVB/ionomer).

For laminated glass assemblies, bending tests are used. Galic et al. (2022) tested laminated beams (500 × 100 mm, 5+0.76+5 mm glass-PVB-glass) in four-point bending, extracting the interlayer shear modulus from the measured deflection using the Wolfel-Bennison effective thickness model.

DMA vs Static Relaxation

Aspect	DMA (dynamic)	Static relaxation
Input signal	Sinusoidal: γ(t) = γ0 sin(ωt)	Step: γ(t) = γ0 · H(t)
Output	G′(ω), G″(ω), tan(δ)	G(t)
Domain	Frequency	Time
Decades per test	~3 (0.01–100 rad/s)	~3–4 (0.1–10,000 s)
Tg determination	Direct (temperature sweep)	Indirect (from WLF shift factors)
Prony series	Requires interconversion	Direct fit to G(t)

Exact interconversion via Fourier transforms

The relaxation modulus and dynamic moduli are connected by exact Fourier transform relations (Ferry, 1980, Ch. 3, Eq. 39–42):

For a Prony series, these integrals evaluate to the closed-form expressions:

Centelles et al. (2021) validated these interconversion formulas by fitting Prony series to relaxation data for seven interlayers and comparing the predicted G′(ω) and G″(ω) against independent DMA measurements. The agreement was excellent, confirming that either test method can serve as the starting point for complete viscoelastic characterisation.

DMA Results for Glass Interlayers

Centelles et al. (2021) measured dynamic master curves for seven interlayers at T₀ = 20°C. The loss tangent peak values reveal fundamental differences in material character:

Material	tan(δ) peak	log ω at peak (rad/s)	Interpretation
PVB BG-R20	1.28	1.27	Highest damping — best acoustic performance
Saflex DG-41	0.80	0.40	High damping (stiff PVB)
PVB ES	0.72	0.35	High damping (structural PVB)
SentryGlas	0.65	−2.16	Moderate damping; transition at very low frequency
EVALAM	0.11	−0.55	Low damping (already rubbery at 20°C)
EVASAFE	0.09	−0.76	Lowest damping
TPU	0.08	1.92	Very low damping

Standard PVB (BG-R20) is the best acoustic interlayer with tan(δ) = 1.28 at its peak. This is why acoustic laminated glass uses standard or modified PVB — the energy dissipation per cycle is maximum in the glass transition zone, which for standard PVB coincides with room temperature and audible frequencies.

SentryGlas shows its peak at very low frequency (log ω = −2.16 rad/s, equivalent to t ≈ 145 s). This means its glass transition occurs at timescales relevant to sustained structural loads, not to acoustic vibrations — consistent with its high T_g (≈ 55°C).

EVA and TPU have tan(δ) below 0.12 because they are already above their T_g at 20°C. The transition peak lies below the measured temperature range. These materials are poor dampers but provide consistent (if modest) structural coupling across all service temperatures.