How to test materials

Measurement of material behavior

As blow molding and thermoforming are in general stretching (extensional) processes, we need to measure the stretching (extensional) behavior of the material at the typical processing temperatures and deformation rates to characterize the material.

Although the importance of extensional measurements is well recognized, there are relatively few data available because it is difficult to generate homogeneous extensional deformation field, especially for low viscosity materials. The basic problem is that without stationary boundaries it is difficult to control the deformation of a low viscosity material. Surface tension, gravity, and inertia conspire to change the deformation. A further problem arises from the large strains that are often required before stresses in memory materials can reach their steady straining limit. It is often not possible to reach a steady stress state before the sample ruptures or deforms nonuniformly. Many different methods have been tried to circumvent these problems and generate purely extensional deformation field. Here we present the most successful.

Methods generating true stress-strain curves

6.1.1 Uniaxial elongation

During the uniaxial elongation test, the tested specimen is deformed in just one direction, the remaining two directions are free:

Fig. 8: Uniaxial elongation

In Figure. 8, L₀ is an initial sample length, L_t is a sample length at time t and l₁(t) is an extension ratio in the direction of elongation, defined as

l₁(t) = L_t / L₀. (50)

Moreover, l₁(t) is an exponential function of time to obtain a steady uniaxial elongation:

, (51)

where is a strain rate in 1/s.

As the sample deforms, the corresponding force F generated in the material is measured. Using the measured forces F(t) and recorded l₁(t), the stress s(l₁(t)) at extension ratio l₁(t) is calculated:

(52)

where

A₀ is an initial sample cross-section area,

A(t) is a sample cross-section area at time t.

Obtained stress-strain curves are used for material model fitting described in section 7.

Uniaxial elongation experiments are complicated by problems appearing in a sample clamping (for example a tested sample is squeezed in clamps and nonuniform deformation appears). These problems can be overcome using special methods as rotating clamps. A tested sample can be also bond to a metal clip.

6.1.2 Lubricated compression

Lubricated compression generates purely equibiaxial extension deformation field. To eliminate shear between measuring heads and a tested sample, a lubricant is used. However, the lubricant is squeezed out from the gap between a sample and heads during the sample compression, and once there is not enough lubricant, the deformation is no longer equibiaxial. Then it is hard to determine whether a material shows strain hardening or there is not enough lubricant.

During a test, a tested sample is compressed at constant strain rate :

(53)

Force acting against the compression is measured and used to calculate true stress. The resulting stress-strain curve is used for material model fitting.

Fig. 9: Lubricated compression

6.1.3 Sheet stretching, multiaxial extension

Thin sheets can be pulled at their perimeter or inflated to give quite a variety of deformations. Meissner and co-workers developed a rotating clamp device for sheets of high viscosity liquids. This device enables various arrangements of rotating clamps so it is possible to measure equibiaxial, uniaxial, planar extension or any other combination of extensions. Schema of this device is in Figure 10. Rotating clamps (1 - 8) can be arranged.

Fig. 10: Sheet stretching device

Resulting stress / strain curves can be directly used for material parameters fitting.

 

6.2 Methods not generating true stress-strain curves

The methods described in sections 6.1 - 6.3 generate true stress-strain curves, which can be directly used for material model fitting. Now we will show some methods where the deformation is more complex and a simulation of the measuring process is necessary to estimate material model parameters (so called "inverse analysis").

6.2.1 Bubble inflation

This method can be said to be derived from thermoforming process, where at the beginning a flat sheet is inflated into a mold cavity. From this point of view, it is very similar to a real process.

A circular membrane is inflated to create a bubble. The bubble development in time is measured and recorded. Resulting data can be used for an inverse analysis to determine parameters of a material model.

Fig. 11: Bubble inflation

 

6.2.2 Deformation of a circular sample using a plug

This method can be said to be derived from plug assisted thermoforming, where at the beginning a flat sheet is pre-deformed using a plug. In this case, a plug is moving downwards during the tests at a constant speed. The corresponding force is measured and recorded along with the deformation. The resulting force vs. deformation curves at various temperatures and speeds of deformation can be used for an inverse analysis.

Fig. 12: Plug penetration test

6.2.3 Thermoforming / blow molding using a testing mold

This method is the most general, however, it is often very complicated to use an inverse analysis to obtain material parameters. How this method works ? A simple testing mold is used to prepare a product (thermoforming or blow molding process can be used). On this testing product, final thicknesses are measured. Now, an inverse analysis takes place. The testing process is simulated using different material parameters. The material parameters leading to a minimum sum of squares of differences between experimental and simulated values of thickness estimate the tested material behavior.