## Dynamic Mechanical Analysis (DMA)

#### Definition

Dynamic Mechanical Analysis yields information on the mechanic properties under a small, mostly sinusoidal dynamic load as a function of temperature, time and/or frequency.

An applied mechanic load, i.e. tension or deformation, results in a corresponding response signal – deformation or tension - regarding amplitude and phase shift.

This results in a complex  modulus called E*, G* and K* depending on the deformation type.

• E*: Complex elasticity modulus
• G*: Complex shear modulus
• K*: Complex compression modulus

Dynamic Mechanical Analysis (DMA) is an indispensable tool for determining the visco-elastic properties of mainly polymer materials.

Functional Principle

#### Functional Principle

Dynamic Mechanical Analysis measures the visco-elastic properties of mostly polymer materials during a controlled temperature and/or frequency program.

During the test, a sinusoidal force (stress σ) is applied to the sample (Input). This results in a sinusoidal deformation (strain ε) (Output).

Certain materials, such as polymers, exhibit visco-elastic behavior; i.e., they show both elastic (such as an ideal spring) and viscous properties (such as an ideal dashpot). This visco-elastic behavior causes shifting of the corresponding stress and strain curves. The deviation is the phase shift δ.

The response signal (strain, ε) is split into an “in-phase” and an “out-of-phase” part by means of Fourier Transformation.

The results of this mathematical operation are the storage modulus E'(related to the reversible, “in-phase” response) and the loss modulus E''(related to the irreversible, “out-of-phase” response).

The loss factor tanδ is the ratio between the loss modulus and the storage modulus (tanδ = E''/E').

Generally, the storage modulus (E') refers to the material’s stiffness whereas the loss modulus (E'') is a measure for the oscillation energy transformed into heat. tanδ characterizes the mechanical damping or internal friction of a visco-elastic system.

#### Storage modulus (E´):

represents the material‘s stiffness and is proportional to the maximum stored work during stress.

#### Loss modulus (E´´):

is proportional to the work dissipated from the material during stress. It is a measure for the oscillation energy transformed into heat.

#### Loss factor (tanδ):

represents the mechanic damping or inner friction of a viscoelastic system. A high loss factor represents a high, non-elastic deformation part, a low loss factor a more elastic material.

#### Calculation of Modulus (simplified)

Young´s modulus  =  E*

Young's modulus can be calculated by dividing the tensile stress by the tensile strain:

where
E is the Young's modulus (modulus of elasticity)
F is the force applied to the object;
A0 is the original cross-sectional area through which the force is applied;
ΔL is the amount by which the length of the object changes;
L0 is the original length of the object.

#### Recommended Literature

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##### Characterizing High-Modulus Composites

For many decades, steel was the primary material used in the automotive industry. In more recent years, a shift toward electric motors has increased the popularity of lighter metals. Technological advancements make it necessary to continuously seek lighter and lighter materials, but without sacrificing the required stiffness over a broad temperature range. The key to reducing vehicular weight has been found in the use of fiber-reinforced polymers.

Application Literature

#### Application Literature

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