Characterization of strain bursts in high density polyethylene by means of a novel nano creep test

Highlights

• Exact determination of the activation energy for strain bursts.

• First observation of negative strain bursts and oscillations after a strain burst.

• Plastic deformation already at stresses <1% of the yield stress.

• Deformation at low stress (strain bursts) is governed by the mobility of dislocations.

• For marked plastic flow additional dislocations must be mechanically generated.

Abstract

Recent nanoindentation experiments have shown that in semi-crystalline polymers, strain bursts emerge during creep experiments. A shortcome of nanoindentation is that due to the inhomogeneous stress field, a critical stress for the onset of strain bursts cannot be determined, and the resolution of the method seems to be limited. Since the strain bursts in polymers are in the nm range, an extremely high resolution in deformation measurement is necessary. Such a resolution is provided by modern solid state rheometers having a resolution < 10⁻⁶ rad. With such a facility, in this work single strain bursts in PE-HD have been investigated in creep mode at stresses as low as < 0.5 MPa. As the strain bursts only occur rarely, hundreds of creep experiments were carried out and evaluated statistically. Through variation of the temperature and the stress, the activation energy for the strain bursts was determined as 0.65 (±0.06) eV. In addition, negative strain bursts (contrary to the direction of deformation) with an activation energy of 0.49 (±0.08) eV and post-oscillations after strain bursts could be observed for the first time. In summary the new method represents a powerful tool for a quantitative characterization of strain bursts and gives a new insight to dislocation kinetics in semi-crystalline polymers.

Introduction

In several semi-crystalline polymers it was found that the deformation of the crystalline phase is governed by the generation and motion of crystal defects - namely dislocations - especially at deformations within the extended plastic regime (Young, 1974; Shadrake and Guiu, 1976; O'Kane and Young, 1995; Argon et al., 2005; Nikolov and Raabe, 2006; Rozanski and Galeski, 2013). Although the importance of dislocations for the plastic deformation in many semi-crystalline polymers is beyond dispute (Galeski, 2003; Galeski and Regnier, 2009; Bartczak and Galeski, 2010) and the deformation behaviour can be well described by micromechanical models (Ayoub et al., 2010; Uchida and Tada, 2013; Shojaei and Li, 2013; van Dommelen et al., 2017), the kinetic mechanisms of dislocations remain widely unclear.

While diffraction methods like the Multi-Reflection X-Ray Profile Analysis (MXPA) (Ungár and Borbély, 1996; Kerber et al., 2011) and texture measurements (Lee et al., 1993; Galeski, 2003) as well as neutron diffraction (Brown et al., 2007), can be considered as highly phase selective, the situation is more complex for mechanical experiments as they register an overlap of effects originating from the crystalline as well the amorphous phase. Nevertheless, for analysing the nature, mobility and annihilation of defects, the determination of activation volumes and energies from mechanical tests seems indispensable for the understanding and identification of the molecular processes controlling elastic properties, strength and ductility.

The first attempts to investigate the deformation behaviour of the crystalline phase independent of the amorphous phase were made by Rabinowitz and Brown (1967). They observed the onset of plastic deformation in the crystalline phase of high density polyethylene (PE-HD) at a stress of 0.18 MPa by cyclic tension experiments in the micro-strain region with high-resolution strain measurement (strain sensitivity of 10⁻⁶). Due to the enormous demands on the measuring accuracy and the lack of commercially available measuring systems, no further investigations on polymers in the microstrain range were carried out over several decades. Only recent developments like the nanointendation (Schuh, 2006; VanLandingham et al., 2001) enable a new approach.

From metals it is known that under certain conditions the flow of deformation can be jerky, which means that the macroscopic deformation curve exhibits significant jumps (strain bursts). Uchic (Uchic et al., 2004) showed that the deformation of small cylindrical nickel single crystals, with a diameter of some μm, occurs almost exclusively through strain bursts. The jumps become smaller with increasing sample size and they disappear for macroscopic specimens. Type of deformation (tension or compression) and crystal orientation have also an influence to the strain burst characteristics (Kim et al., 2012).

The cause of strain bursts in metals are usually dislocation avalanches (Zaiser, 2006). In metallic glasses, shear banding and martensitic transformations can also cause strain bursts (Tong et al., 2016). Since the deformation of the crystalline phase in many semi-crystalline polymers is dislocation controlled (Galeski, 2003; Bartczak and Galeski, 2010), strain bursts should also emerge.

The first evidence for strain bursts in a polymer was found by Li and Ngan (2010) with nanoindentation creep experiments on PE-HD. With some estimations, based on experimental data, they could determine an activation energy of 0.22 eV for the plastic deformation of the crystalline phase. Further comprehensive experiments were reported by Zare Ghomsheh et al. (Zare Ghomsheh et al., 2015; Zare Ghomsheh, 2018) where an influence of the loading rate and the applied load on the number and the height of bursts could be verified.

However, nanoindentation creep experiments have several limitations.

• The stress field is strongly inhomogeneous (Kermouche et al., 2008), which requires some assumptions and estimations for the evaluation of the activation energy.

• The sample volume tested is very small, and local effects can play a role.

Therefore, an alternative test method would be desirable, which does not suffer from these disadvantages.

In semi-crystalline polymers, the dislocation path length is limited by the lamella thickness and therefore strain bursts can only be of the order of the lamella thickness. In order to verify single strain bursts in polymers, the resolution of the deformation measurement must be in the nm scale. In addition, the deformation rate in the amorphous phase should be not too large. The greater the creep rate in the amorphous phase, the more difficult to detect a single strain burst. A possibility could be a creep experiment above the glass transition temperature $T_g$ with very small loadings in the microstrain region (finite strain near the origin about 10⁻⁶). Thereby the soft amorphous phase deforms continuously with very small creep rates (few nm/s), while the deformation in the crystalline phase runs jerky over strain bursts (some nm in typically 0.1 s). This would allow to distinguish the deformation in the amorphous phase from that of the crystalline phase and to study the mechanisms of plastic deformation in the crystalline phase independently.

An important aspect is the application of a homogeneous stress field over a large specimen volume. Thus the occurrence of strain bursts becomes more likely. The separation of deformations in the amorphous and crystalline phase is only possible at very low stresses. If the stress exceeds a critical value, strain bursts do not occur as a single event. So they cannot be separated from the deformation of the amorphous phase. In addition, a too high deformation rate in the amorphous phase can make the detection of individual strain bursts impossible, as the rate may exceed the ones observed during strain bursts. Since strain burst in semi-crystalline polymers cause deformations of several nm (Li and Ngan, 2010), a nm resolution in the deformation measurement is required. The requirement on the temperature stability during a measurement is very high. On the one hand temperature fluctuations can influence the strength of the amorphous phase on the other hand the deformation caused by low thermal fluctuations is, due to the large thermal expansion coefficient of polymers, much higher than the required deformation resolution for strain measurements. For instance in PE-HD (linear expansion coefficient $\alpha =2\cdot {10}^{-4}$ 1/K) a temperature increase of 0.1 °C causes, at a length of 10 mm, a length change of 200 nm. Therefore, a very good temperature stability during the measurement is required. In order to address this problem, a torsional loading with a pure shear deformation is more appropriate. In this load case, volume changes from temperature fluctuations do not play a critical role, since a volume change in a rotationally symmetric specimen does not cause torsional deformations. Furthermore a pure shear stress enables easy determination of the stress in the sliding plane.