Test methodKinetics of stored and dissipated energies associated with cyclic loadings of dry polyamide 6.6 specimens
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.
Section snippets
Thermodynamic foundations of the heat equation
The framework of Thermodynamics of Irreversible Processes (Halphen and Nguyen (1975) [13]), is hereafter used to introduce the energy terms. Under the hypothesis of small deformations, the thermal, mechanical and microstructural states of the material are described by the following observable state variables: the absolute temperature T = αo, the total strain tensor ε = α1 and the set of internal variables {αk}k=1,…,m. The chosen thermodynamic potential is the specific Helmholtz free energy ψ = ψ
Experimental setup
The experimental setup used for conducting the thermomechanical tests is shown in Fig. 1. Samples were loaded using a MTS 810 hydraulic testing machine equipped with a load cell of ±25 kN. Temperature variations on one side and displacements on the other side of the sample were measured and captured simultaneously using a high resolution infrared focal plane array camera and a high resolution visible CCD camera, respectively.
Surface temperature fields corresponding to the rectangular gauge
Experimental results
The experimental study involved observation and analysis of the thermomechanical and energy properties of the PA6.6 dry matrix involved during cyclic fatigue tests. The investigations were essentially divided into two parts. The first part examined, at two different loading frequencies, the contribution of the stored and dissipated energies in the global energy balance. The second part focused on the localization of fatigue mechanisms using 2d full-field measurements through the heterogeneous
Concluding comments
Some aspects related to thermal and energy responses associated with PA6.6 dry specimens subjected to tensile-tensile tests were investigated in this work. The first aspect was the loading frequency dependence of energy balances. The investigations of energy stored during deformation indicated that the stored ratio was significantly smaller at low loading rates but remained high at high loading rates. In addition, it was shown that this ratio may take negative values at the last fatigue stages
Acknowledgements
The authors gratefully acknowledge Solvay Engineering Plastics for supporting this work and for providing material data and specimens. This work benefited from the financial support of the French Minister for Research (ANRT) and was performed in the framework of the European DURAFIP project.
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