A Novel Grip Design for High-Accuracy Thermo-Mechanical Tensile Testing of Boron Steel under Hot Stamping Conditions

Current global emission regulations are driving automotive industries to improve fuel efficiency and reduce CO₂ emissions of their vehicles, while passenger safety guidelines are forcing the car manufacturers to increase the level of passenger safety by increasing crashworthiness. Achieving both environmental and safety norms simultaneously is a major challenge for car manufacturers, since the two goals impose conflicting requirements, reduced weight and increased strength, on vehicle design [1]. To meet the mandatory regulations in both aspects, use of thin ultra-high-strength steel (UHSS), for body and chassis parts, is a solution for auto manufacturers. Manufacture of lightweight components made of UHSS in traditional cold stamping is limited by poor formability and excessive spring-back of the work-piece material. To overcome these drawbacks, hot stamping technology has been developed in the recent decade and is now widely used [2, 3].

Figure 1(a) shows the temperature profile of a work-piece in a typical hot stamping process of press hardening steel. The work-piece initially has a ferrite and pearlite microstructure and is heated to above the austenite transformation temperature (usually about 900 °C in production) and held for few minutes to achieve the austenite phase throughout its volume. Then the blank is quickly transferred from the furnace to the cold stamping tool, and is deformed into the required shape, while being rapidly quenched (>27 °C/s) within the tools to produce a final product predominately with a martensitic phase [4].

To design a robust efficient hot stamping process, finite element simulations are used. A series of advanced unified visco-plastic constitutive material models have been proposed [5‐9] for hot stamping simulation which address many time-dependent material mechanisms, for example, diffusion, recovery, recrystallization and grain growth. The metallurgical evolutions result in the force required for plastic deformation being time and deformation speed/strain rate, dependent [10]. Material mechanical property data used in these models has been obtained from tensile tests in which test-pieces undergo the temperature profile of the form shown in Fig. 1(b). In order to characterise properties of boron steel for hot stamping condition, rapid heating, soaking, and cooling of a test-piece must be an integral part of a uniaxial tensile test; therefore, conventional hot uniaxial testing which is operated in an oven or furnace is unsuitable. Performing uniaxial tests in the Gleeble Materials-Simulator can be considered as means of achieving suitable test conditions, since the machine can rapidly heat and cool a test-piece at any stage in the temperature cycle. In complex stamping, material is subjected to complex loading paths. The Gleeble-based test methodology can be used for both uniaxial and bi-axial testing. A novel biaxial testing system for use in Gleeble testing machine has been developed for practical hot stamping conditions [11].

In a Gleeble, heating a test-piece to the target temperature is done by direct electrical resistance heating through the grips at each end, but test-piece temperature is not uniform along its gauge length due to heat loss to the water cooled copper jaws, through which power is supplied, supporting the grips, as shown in Fig. 2(a). An overview of temperature distributions along uniaxial test-pieces found in the literature [12‐14] is shown in Fig. 2(b). For large temperature gradients, the metallurgical state of the middle part of a test-piece could be austenite and the ends, near the grips, ferrite [15]. And ferrite can be softer than austenite for certain temperature ranges [16]. Thus strain could be greater in the ferrite and non-uniform deformation along a test-piece result in calculation of erroneous stress-strain data, for use in simulations. A systematic analysis of error can be found in reference [17].

Extensive research and development of modified test-piece geometry and grips, has been undertaken to reduce thermal gradients in tensile test-pieces. For example, Walsh et al. showed that, longer jaw separation, higher test temperature, smaller test-piece diameter, and lower test-piece thermal diffusivity, enhance temperature uniformity. Any measure that reduces thermal conductivity at the jaw will promote the constant temperature region [18]. Brown, et al. simulated the effect of heat transfer co-efficient of grip material on thermal behaviour of test-pieces. Their study indicated that grips influence the rate of diffusive heat loss and the temperature distributions within a test-piece [19]. Norris et al. simulated the thermal behaviour of various Gleeble test-pieces to optimize a Gleeble test-piece design and found that the temperature gradient and the magnitude of this gradient dependent on the gripping material used [20]. Zupan et al. and Karanjgaokar et al. conducted thermo-mechanical tensile tests with micro machined metal samples using electrical resistance heating and observed non-uniform strain due to significant temperature gradients within a gauge length [21, 22].

Lindeman et al. proposed a technique for applying direct resistance heating current to particular locations in test-pieces and substantially reduced thermal gradients [23]. Ferguson et al. suggested an apparatus that provides enhanced self-resistive test-piece heating when used in a conventional thermo-mechanical material testing system for greater temperature uniformity throughout a test-piece [15]. Shen et al. concluded that the primary factor influencing uniform temperature, is the free span between jaws [24]. Li et al. proposed a set of stainless steel grips integrated with grooves and textured surface to reduce the contact area between the grips and dog-bone shaped work-piece with large parallel length (80 mm), to reduce temperature gradients. Uniformity of temperature was improved and an effective gauge length of 14 mm with temperature gradient less than 10 °C was achieved; however, with the gauge width of 8 mm, the ratio of (effective gauge length / gauge width) was less than 2 and apparently a better temperature uniformabity is desired [25]. Abspoel et al. proposed a new test-piece design, which can achieve equal current density by adding a pair of shunt connections, in order to achieve a uniform temperature along the test-piece [26]. Ganapathy et al. analysed the design and found that Abspoel test-piece was able to achieve a uniform temperature over the 30 mm gauge length (with the gauge width of 10 mm), and thus obtained a better uniform strain distribution over the test-piece gauge length [14]. However, the test-piece is in complex geometry without test standards to refer to; at the same time, the set-up is complicated and time-consuming. To address the aforementioned problems, the main aim of this paper is to design and develop a set of novel grips which enables a simple tensile test-piece design to be used to achieve uniform temperature through resistance heating, on a Gleeble, under hot stamping conditions.

To overcome the limitations of the existing conventional grips used for thermo-mechanical uniaxial tests, a novel set of grips, for hot tensile testing on a Gleeble have been developed. A schematic illustrating the concept of the self-resistance heating grips is shown in Fig. 3(a). The concept of the grips that hold the test-piece is that they do not rapidly loose heat to the copper jaws. Thus they are made of electrically non-conducting and heat insulating material so that electrical current to heat the test-piece can no longer pass directly from the copper jaws, through metal grips to the test-piece, as in the conventional design. Instead, a conductor of the electrical supply, from copper jaw to test-piece is made of a network of long branches of small cross-sectional area that are wrapped around the grips. Thus, while the electrical supply still heats the test-piece, heat generated due to the raised resistance of the conductor heats the grips also and because the grips are poor conductors of heat, little is lost to the water cooled grips, as in the conventional set-up. More electrical energy is supplied to generate higher heat energy; second, the heat loss to water cooled jaws from test-piece is reduced. Both concepts are further discussed, which leads to the detailed design, in the following subsections. The quantitative relation of design parameters and heat generation/loss is analysed.

To refine the proposed grip design, Finite element modelling of coupled Thermal-Electric analysis was simulated using ABAQUS/Standard along with user defined temperature feedback control subroutine called ‘UAMP’. Coupled thermal-electric finite element simulation was conducted for heating, soaking and cooling of the steel test-piece at specific rates. The Finite element model is shown in Fig. 4(a). Due to the symmetric feature of the design and current flow, only a quarter of the set-up is simulated. The boundary conditions considered for the thermal-electric simulation are shown in Fig. 4(b). The electric current was input at one end of the grips and the mid length of the test-piece was specified as having zero electric current potential. Heat loss from the test-piece to the grips by conduction and to the atmosphere by convection (h = 20 W/m ² − K) were considered in the simulation. The test-piece was in perfect contact with insulation at the interface and hence the interfacial heat transfer co-efficient was not considered; also, the contact heat transfer coefficient at the interface of test-piece and grips has little effect on the uniform zone [24]. The test-piece geometry used in this study is shown in Fig. 6(a). Test-piece geometry was selected to keep the longest jaw separations within existing Gleeble stroke and also to maintain minimum possible surface contact area with the nonconductive solid block.

Temperature dependent thermal properties considered in the simulation are listed in Tables 1 and 2. Carbon steel and stainless steel properties, used for the electrical network were obtained from relationship given in Appendix 2. The given relationship is valid for all types of carbon steels irrespective of steel phases [27]. Defining the electrical conductivity and density as a function of temperature does not have a significant effect on the predicted temperature fields [30] and hence they are kept constant as given in Table 3. The test-piece and grips were discretized with 4-node linear coupled thermal-electrical tetrahedron (DC3D4E) elements to capture the thermal and mechanical gradients in the gauge section.

Control of the temperature profile as shown in Fig. 6(b), performed in real tests by the thermocouple fixed at the test-piece centre, through controlling the amplitude of input current, was simulated through the user-defined subroutine, UAMP. The temperature difference between the prescribed and simulated temperature profiles at the middle of the test-piece for every time increment were calculated during the simulation as in eq. (3), and input current was varied according to eq. (4) and (5). Detailed information about UAMP along with Abaqus/standard is given in [11, 30].

\( {T}_i^p \) and \( {T}_i^s \) are the prescribed and simulated temperatures at each time increment, α is a coefficient that remains constant according to the corresponding time interval as shown in Table 4, which was defined by iteration until the simulated temperature profile matched the required heating cycle and calibrated with experimental temperature profile as shown Fig. 6(b). β is a constant coefficient, and its value is 0.001. The correction term, ΔI, is then multiplied by the current used (I _i − 1) in the previous time increment.

Finite element simulation was performed with three different electrical conductor materials namely, stainless steel, copper and carbon steel, all of which have different electrical and thermal properties. For each material, three cross-sectional areas were considered. Due to available working space and feasibility, only thickness of the conductor was varied while the width was kept constant at 3 mm as shown in Fig. 3(b). Three different cross-sectional areas were 3 mm², 4.5 mm² and 6 mm², which were achieved by only changing the thickness of the network arms to 1 mm, 1.5 mm and 2 mm respectively.

Finite element simulation was carried out to validate the proposed concept and based on the simulation results, a new grip arrangement as shown in Fig. 3 was fabricated to conduct the experiments. The results of both Finite element simulation and experiments are discussed in detail below.

To achieve fully austenitic microstructure throughout the test-piece and uniform temperature within the effective gauge region, an electrical conductor with appropriate material and cross-sectional area is required. In this study, design of the conductor was assisted by Finite element simulation to validate the new grip design. However finite element simulation is time consuming to design and choose the conductor material with respect to the test material type and its gauge section. Therefore an analytical relationship has been derived, relating test-piece and electrical conductor. This relationship can help choice of appropriate material with suitable cross-sectional area, for a given test material type and gauge section geometry. The equivalent electrical circuit diagram with real electrical conductor design is shown in Fig. 11(a) and (b).

Using Kirchhoff’s law and assumptions made based on the Finite element simulation results, the relationship has been derived between the electrical conductor and test-piece which is detailed in Appendix. 1. The derived correlation is described in equation (10).

Where ‘F’ is the resistivity ratio of electrical conductor to test-piece; ‘H’ is the ratio of specific heat of conductor to test-piece; ‘G’ is the ratio between cross-sectional area of electrical conductor to test-piece; and ‘D’ is the ratio between density of electrical conductor to test-piece. Where ρ _C  , Ac , C _C  , D _C  , T _C are resistivity, cross-sectional area, specific heat, density and temperature of the conductor, respectively, and ρ _S  , A _S  , C _S  , D _S  , T _S are resistivity, cross-sectional area, specific heat, density and temperature of test-piece, respectively.

For the given test material and its parallel section, the selection of the material and the cross-sectional area needs to be based on equation (10) and must fulfil the heating rate condition given in equation (12) for a successful, and uniform temperature thermo-mechanical test. If the ratio of heating rate of electrical conductor ( \( \dot{T} \) _C ) to the heating rate of test-piece ( \( \dot{T} \) _S ) is greater than 2, then the electrical conductor will reach its melting point due to overheating as discussed in appendix. 1.

If the test material is changed from steel to aluminium, it is strongly recommended to avoid stainless steel electrical conductor. Electrical resistivity of stainless steel is approximately 25 times higher than the aluminium, which will increase the ratio of heating rate of coonductor to test-piece by 10. This will result in overheating of electrical conductor before reaching the test-piece soaking temperature, subsequently may result in electrical current cut off during the test., Hence use of electrical conductor made with steel or copper material is recommended for aluminium test material.

Based on Finite element simulation, a new design of grip was fabricated for Gleeble uniaxial thermo-mechanical testing. The design was practically tested using boron steel test-pieces for test in which test-pieces were heated to the austenite range and then air cooled to deformation temperature and the results were compared with those obtained using conventional grips. An analytical method was developed as an effective tool to determine grip design parameters. From this work the following conclusions have been drawn:

The innovative design of the new grips developed in this study enables uniaxial tensile testing under hot stamping conditions to be performed in a simpler way resulting in more accurate results than obtainable from existing test methods. The concept of self-resistance heating grips, which ensures better uniformity of temperature fields in test-pieces, can also be applied for tests under complex tension conditions, such as biaxial tensile.