On the Strain Measurement for Thermoplastics with Bi-Axial Extensometer in Thermo-Mechanical Testing: A Case of Characterizing Temperature and Physical Aging Effects on Polycarbonate

Abstract

Background

Characterizing the mechanical behavior of materials at elevated temperatures is critical for the design and development of polymer systems for use in complex operating conditions. The commonly used Dynamic Mechanical Analysis (DMA) does not apply to the investigation of the three-dimensional properties of materials. A combination of a mechanical testing system and an environmental chamber with extensometer measurements is more suitable for this purpose. However, the bi-axial extensometer suffers errors in measuring strains in thermoplastic specimens at elevated temperatures due to its characteristics.

Objective

This brief technical note analyzes the source of measurement errors with an extensometer and proposes a robust and straightforward experimental procedure for three-dimensional mechanical testing at high temperatures.

Methods

Two temperature and physical aging effects characterization experiments on polycarbonate at 120 ${}^{\circ }\text {C}$ were performed as a case study. Thermal and penetration drifts were analyzed and corrected in the axial and transverse measurements.

Results

The corrected experimental results for the two tests are nearly identical, attesting to the reproducibility of the proposed procedure. Furthermore, the bulk-related strain computed using the corrected strain increases monotonically with time, consistent with the thermodynamic principle, thus demonstrating the reliability of experimental results.

Conclusions

The methodology described in this work can serve as a protocol to guide the three-dimensional thermo-mechanical testing with a bi-axial extensometer.

Appendix

Contact Between Extensometer Knife Edge and Specimen

For clarity and simplicity, suppose that the specimen is elastic. The knife edge of the extensometer was made of steel, which is much stiffer than the PC. Therefore, the contact between the knife edge and the specimen can be modeled as a contact between a rigid cylinder and a semi-infinite elastic body, which is the classical Hertz contact problem, and the closed-form solution has been given in textbooks [22]. In this problem, the semi-contact-width a can be expressed as:

$$\begin{aligned} a = \sqrt{\frac{4PR(1 - \nu ^2)}{\pi E}}, \end{aligned}$$

(4)

where E = 2300 MPa is the Young’s modulus and $\nu$ = 0.36 is the Poisson’s ratio of PC at room temperature. The compressive load per unit P can be measured by a piezoresistive force sensor, which is of 3.12 N/mm. The radius of knife edge R can be measured by Olympus™ SZX-12 stereo microscope and Evolution™ VF digital camera, which is of 0.045 mm. Therefore, the maximum stress can be computed as

$$\begin{aligned} p_{\max } = \frac{2P}{\pi a} = {241\,\mathrm{\text {M}\text {Pa}}}, \end{aligned}$$

(5)

which exceeds PC’s elastic strength of 60 MPa. This result demonstrates that the knife edge yields the PC specimen when the extensometer is mounted. Considering PC exhibit also viscoelasticity, thus, the continuous penetration in the transverse direction is induced simultaneously by the yielding and creep of PC.