Kinetics of stored and dissipated energies associated with cyclic loadings of dry polyamide 6.6 specimens

Abstract

An experimental protocol was developed to achieve complete energy balances associated with the low cycle fatigue (LCF) of dry polyamide 6.6 (PA6.6) matrix. The protocol uses two quantitative imaging techniques, infrared thermography (IRT) and digital image correlation (DIC). The first technique provides a direct estimate of heat sources, especially intrinsic dissipation and thermoelastic sources, using the local heat diffusion equation. The second technique gives access to the deformation energy by means of strain and stress assessments. Stresses were derived from strain measurements using a simplified local form of equilibrium equations. Both techniques were then successfully combined with the aim of quantifying various energies involved in the energy balance (e.g. deformation, dissipated and stored energies) and then to obtain an estimate of the Taylor-Quinney ratio.

From a thermomechanical modeling standpoint, the experimental results exhibit some interesting findings during the first few cycles. It was found that there was neither mechanical nor thermodynamic cyclic stability. From a mechanical standpoint, a significant ratcheting phenomenon characterized by accumulation of cyclic strain is classically observed. From a thermodynamic viewpoint, it was shown that the dissipated energy per cycle was always less than the mechanical energy that could be associated with the area of the hysteresis loop. This energy difference reflects the significant contribution of the stored energy associated, cycle by cycle, with the microstructural changes. Moreover, a 2d full-field measurement analysis highlighted hot spots occurring in the dissipation fields. The surface detection of these spots was thus correlated with those of the thermoelastic source with the aim of monitoring the fatigue damage accumulation in the region where the crack finally occurred.

Introduction

Semi-crystalline polymers represent an important class of materials which are now widespread in various industrial areas, such as the automotive industry. These engineering materials are of particular interest because of their remarkable advantages, notably regarding their low density, high deformability, toughness and long lifespan. Although academic and industrial research has enhanced knowledge on fatigue mechanisms in these thermo-hygro-sensitive materials, further insight is required on some issues concerning the understanding of i) dissipative and stored energy changes, ii) the influence of the loading frequency and iii) the localization of fatigue damage. One promising approach for addressing these issues is based on energy considerations. A combined description of mechanical and energy phenomena occurring during the deformation process may shed greater light on the behaviour of these polymeric materials (see e.g. Rittel (2000) [1], Rittel and Rabin (2000) [2]).

When a material is subjected to irreversible transformations, part of the mechanical energy expended in the deformation process is converted into heat, with the rest remaining stored in the material, thereby modifying its internal energy. Many interesting surveys on specific aspects of the stored energy can be found in the literature. The most significant developments that have taken place in the computation and interpretation of the stored energy were closely related to calorimetric procedures. Most research has been focused on temperature rise measurements to estimate variations in this energy using different experimental equipment, ranging from embedded thermocouples, microcalorimeters to infrared detectors. The earliest available references on the subject were focused on metal studies. Farren and Taylor (1925) [3] and Taylor and Quinney (1934) [4] were the first to build an apparatus to measure stored energy during the deformation of metallic materials¹ subjected to quasi-static monotonous tensile tests. Williams (1967) [5] and Leach (1970) [6] reviewed calorimetric methods in detail and assessed procedures and equipment for calorimetry applicable to the measurement of stored energy. Most investigations have focused on the Taylor-Quinney ratio, which expresses the fraction of the anelastic deformation energy rate irreversibly converted into heat, i.e. dissipated. In addition, these earliest works were limited by the fact that they were mostly carried out with standard and traditional measurement devices that could not reliably obtain high precision estimates of this ratio. However, with the introduction of high resolution infrared scanners in the early 1980s, extensive experimental studies rectified these deficiencies and assessed the Taylor-Quinney coefficient with greater accuracy (see e.g. Chrysochoos (1985) [7], Chrysochoos et al. (1989) [8], Mason et al. (1994) [9], Rittel (1999) [10], Rosakis et al. (2000) [11], Oliferuk et al., 2004 [12]).

In practice, thermal, displacement and stress fields are required for evaluating the various quantities involved in the energy balance. The most convenient imaging techniques for measuring these fields are infrared thermography and digital image correlation. The first technique provides thermal images, and the heat sources associated with the material deformation are directly assessed using the local heat diffusion equation. The second technique gives access to surface displacement fields from which strains and strain rates are derived. The deformation energy rate can thus be calculated through local measurement of stress and strain rate fields. Both non-contact quantitative imaging techniques can then be combined to establish energy rate balances.

In the present paper we document some findings pertaining to the thermomechanical behavior of PA6.6 dry matrix. Specifically, we used infrared and CCD cameras to simultaneously record, during cyclic loading, fields corresponding to temperature variations and displacement over the sample gauge part. We focused particularly on the energy balance form associated with the mechanical hysteresis loop. In particular, we obtained energy balances at two different loading frequencies, thus providing the deformation, dissipated and stored energy patterns. We finally derived time courses of the Taylor-Quinney ratio in order to quantify the relative importance of both dissipated and stored energy rates over each cycle. In addition, we used 2D analysis to highlight the existence of hot spots in dissipation fields. The location of these spots was correlated with those of the thermoelasticity and could be interesting for tracking the onset and propagation of local failure.

First, we present a very brief overview of the theoretical framework used to interpret the experiments.