Experimental and numerical analysis of the heat generated by plastic deformation in quasi-static uniaxial tensile tests

Highlights

• Experimental and numerical analysis of the temperature rise in the quasi-static uniaxial tensile tests.

• The predicted temperature rise is almost independent of the selected heat transfer coefficients.

• Comparison between the Zehnder model and the Aravas model.

• Taylor–Quinney coefficient increases as the plastic deformation accumulates for the aluminium alloy AA6016-T4.

Abstract

This study evaluates the temperature variation observed in quasi-static uniaxial tensile tests, due to the heat generated by plastic deformation. The AA6016-T4 aluminium alloy was the material selected, considering different values of crosshead velocity (from 0.01 mm/s up to 1 mm/s). The temperature variation was also evaluated during the stress relaxation test. A finite element model of the uniaxial tensile test is presented, which takes into account the heat generated by plastic deformation, as well as the effect of the heat losses to the environment (convective heat transfer coefficient) and to the grips (interfacial heat transfer coefficient). The numerical results show that the predicted temperature variation is almost independent of the selected heat transfer coefficients. On the other hand, the temperature rise is influenced by the Taylor–Quinney coefficient. The comparison between experimental and numerical temperatures shows that the Zehnder model (increasing Taylor–Quinney coefficient) provides more accurate results than the Aravas model (decreasing Taylor–Quinney coefficient). Nevertheless, the evolution of the Taylor–Quinney coefficient defined by the Zehnder model assumes a constant value for the hardening coefficient, which does not fit the hardening behaviour observed for this aluminium alloy.

Introduction

In sheet metal forming processes, the blank temperature increases during the forming operation due to the heat generated by plastic deformation and by friction between the blank and the forming tools (Pereira and Rolfe, 2014). This is particularly relevant in mass production lines due to the periodic input of heat into the forming tools. In fact, the temperature variation produces changes both in the mechanical behaviour of the blank and particularly in the lubrication conditions, contributing to process variability (Hazra et al., 2011). Therefore, this phenomenon should be considered during the optimization of the process parameters, mainly in case of high strength steels and for high speed forming operations. Hence, the accurate numerical modelling of these forming processes requires a thermo-mechanical analysis, to account for the influence of the heat generated by plastic deformation.

Since the deformation process of metallic materials in the elastic regime leads to insignificant volume changes (lower than 1%), the temperature variation defined by the Joule–Thomson effect for solids is always slight (Kuo et al., 2005). In contrast, the plastic deformation generates a significant amount of heat (Farren and Taylor, 1925), which can lead to substantial temperature increases if the deformation process is fast (no time for heat exchange). Indeed, during plastic deformation, the mechanical energy is predominantly dissipated as heat, while the stored or latent energy remains in the material after removing the external loads (Hodowany et al., 2000). The first attempts to determine experimentally the fraction of plastic work converted into heat was carried by Taylor and Quinney (1934), using calorimetric methods. They found that the fraction of dissipated energy (also known as Taylor–Quinney coefficient) is about 90% for different metallic materials.

Some experimental studies show that the Taylor–Quinney coefficient may depend on the plastic strain and on the plastic strain rate. The study performed by Macdougall (2000) on an aluminium alloy shows that the Taylor–Quinney coefficient increases with the plastic strain, ranging roughly from 0.5 to 0.9, which is in agreement with the model developed by Zehnder (1991). An identical tendency was found by Rusinek and Klepaczko (2009) for TRIP steels, taking into account the phase transformation of austenite into martensite during plastic deformation. On the other hand, the influence of the plastic strain rate on the Taylor–Quinney coefficient was experimentally studied by Zhang et al. (2017), using the Kolsky bar with an infrared temperature measurement system. For the 7075-T651 aluminium alloy, they found that the Taylor–Quinney coefficient increases from 0.4 to 0.9 as the strain rate increases from 1100 to 4200 s⁻¹. Nonetheless, a different conclusion was obtained by Hodowany et al. (2000) for the 2024-T3 aluminium alloy, showing that the fraction of plastic work dissipated as heat is not sensitive to the strain rate over a range from 1 s⁻¹ to 3000 s⁻¹. Recently, the dependence of the Taylor–Quinney coefficient on the dynamic loading mode (tension, compression and shear) was experimentally studied by Rittel et al. (2017). The results show that identical coefficients are measured in tension, compression and shear, except for the commercially pure titanium, which is known to exhibit tension−compression asymmetry in its mechanical properties (Revil-Baudard et al., 2015).

In order to take advantage of the adiabatic conditions, high strain rate techniques (e.g. the Kolsky pressure bar) are commonly adopted to calculate the fraction of plastic work converted into heat, where the amount of heat generated is captured by infrared temperature measurements (Mason et al., 1994). Alternatively, hybrid approaches have been developed, combining experimental measurements with numerical analysis through inverse analysis (Zehnder et al., 1998). These approaches are particularly attractive in mechanical tests involving low and intermediate strain rates, i.e. loading under non-adiabatic conditions. The hybrid method developed by Pottier et al. (2013) combines full field measurements (strains and temperature) on heterogeneous tensile tests with numerical results of the thermo-mechanical finite element analysis. They use a Levenberg–Marquardt algorithm to optimize sequentially the mechanical parameters and the Taylor–Quinney coefficient.

The experimental techniques used for temperature measurement can be categorized into two groups: (i) contact and (ii) non-contact techniques. The temperature variations induced by plastic deformation are commonly measured using thermocouples (contact technique) or infrared thermography (non-contact technique) (Ait-Amokhtar et al., 2008). Compared to thermocouples, infrared thermography has the advantage of providing the thermal image of the surface under investigation, while thermocouples measure the temperature on a single point. Therefore, infrared thermography is commonly used to study local temperature variations, such as the ones associated with the Portevin–Le Chatelier effect of Al–Mg alloys (Ait-Amokhtar et al., 2008; Bernard et al., 2013). On the other hand, thermocouples can be inserted in the specimen, allowing the temperature measurement in hidden regions, which is very useful for some experimental studies (Pereira and Rolfe, 2014). Thermocouples spot welded on the specimen surface were reported to present a response time of about 10 milliseconds (Pandey and Chand, 2003), but response times of 10 microseconds can be attained in case of thermocouples embedded in the specimen (Rittel, 1998). Infrared thermography cameras have a response time between milliseconds and microseconds, for cameras based on thermal detectors and on quantum detectors, respectively (Carlomagno and Cardone, 2010). Finally, although the temperature measurement with both systems depends on the working conditions, infrared thermography also requires the calibration of the surface emissivity, which can change during plastic deformation (Hodowany et al., 2000). In order to minimize emissivity problems, the specimen surface is often painted with a high-emissivity graphic-black coating (Ait-Amokhtar et al., 2008; Bernard et al., 2013).

The purpose of this paper is to use temperature variation measurements from quasi-static uniaxial tensile tests to quantify the fraction of plastic work converted into heat. The accuracy of the numerical models that take into account the Taylor–Quinney coefficient as a function of plastic strain is evaluated. The material and the experimental setup of the quasi-static uniaxial tensile tests used are described in Section 2, while the experimental results are presented in Section 3. The proposed thermo-mechanical finite element model is presented in Section 4 including, both the heat generation and the heat losses that occur during the test. The comparison between numerical and experimental temperature results is performed in Section 5, highlighting the influence of the Taylor–Quinney coefficient on the predicted temperature. Section 6 contains the main conclusions of this study.