Heterogeneity

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Heterogeneity of the strain distribution

Determination of heterogeneity in the tensile test

A prerequisite for determining heterogeneity or strain heterogeneity in the tensile test is the use of a laser extensometer (angle or parallel scanner) to determine the local strain distribution in the plane-parallel part of the multipurpose test specimen. The differences determined in the local strain behaviour (Fig. 1) suggest that a heterogeneity value should be defined as a new material parameter for polymer testing on the basis of these strain values. Figure 1 shows the maximum (red line) and minimum (black line) local strain, with the integral strain between reflectors 1 to 26. The 2D representation of a polyamide ( abbreviation: PA) material with 13 reflectors in Fig. 2, for example, is used to calculate the heterogeneity from the ASCII data.

Fig. 1:

Local 3D strain distribution of an ABS material in a tensile test

Fig. 2:

Local 2D strain distribution of a PA material in the tensile test

If the maximum and minimum strain is determined from Fig. 2 in relation to time or strain, independent of the location of occurrence, and the integral strain is also calculated (Fig. 3), then the heterogeneity is the difference between the maximum and minimum strain in relation to the integral strain in the test specimen volume. The following equation is used to determine the heterogeneity H:

H={\frac {\epsilon _{l_{max}}-\epsilon _{l_{min}}}{\epsilon _{i}}}

(1)

Fig. 3:

Maximum and minimum local and integral strain of a PA material

As the initial range of the heterogeneity function at very small strains results in a de facto division ‘0/0’, similar to the calculation of the Poisson's ratio, the heterogeneity is related to the registered maximum, resulting in a representation of H_rel normalised to 1 as a function of time or integral strain (Fig. 4) (Eq. 2):

H_{rel}={\frac {H(t)}{H_{max}}}

(2)

Fig. 4:

Heterogeneity function of plastics

In the range of valid heterogeneity values, there is often a critical point at which the heterogeneity increases again after the minimum. This point corresponds to the accumulation of damage and hybrid methods of plastic diagnostics. When the fracture occurs, the fracture heterogeneity H_{B_rel} can then be specified as a characteristic value, which allows a simple comparison of different material states.

Application of heterogeneity

The primary field of application for the material parameter heterogeneity is structurally or morphologically heterogeneous materials in which changes in the deformation or damage mechanism are indicated by the heterogeneity function, provided there is sufficient sensitivity. If different PA 6 materials with different glass fibre contents (see also: ashing method) are welded together, as is common in the automotive industry, and test specimens are prepared from the plates (Fig. 5), these can be characterised using laser extensometry in the tensile test.

Fig. 5:

Welding of PA 6-GF10 and GF30 sheets and preparation of test specimens

If the base materials PA 6-GF10, PA 6-GF20 and PA 6-GF30 are also analysed using laser extensometry, the heterogeneity functions are obtained as a function of the integral strain as shown in Fig. 6. The fracture heterogeneity is below 0.2 for all PA 6 modifications and the critical increases occur comparatively late in the non-linear viscoelastic range (see: elasticity), which is also determined using the hybrid methods of plastics diagnostics.

Fig. 6:

Heterogeneity function and fracture heterogeneity of the base materials

If identical materials are welded together, the conventional weld factor can be used as a quotient between the strength of the weld seam and the base material. In the case of dissimilar welding partners, this weld seam parameter cannot be used, as there are two base materials with different strengths. In this case, it is advisable to use the heterogeneity as a basis for comparing the welds. As can be seen in Fig. 7, the functions are at a significantly higher level and the fracture heterogeneities reach values between 0.5 and 0.8 depending on the combination of welding partners. The critical point of the increase in the heterogeneity function, i.e. the onset of damage (see also: micro-damage limit), is shifted to smaller strains, which was validated by simultaneous measurement of the acoustic emission.

Fig. 7:

Heterogeneity function of the welded PA 6 materials

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Determination of heterogeneity in the tensile test

Application of heterogeneity

See also