Investigation of deformation and failure features in hot stamping of AA6082: Experimentation and modelling M. S. Mohamed, A. D. Foster, J. Lin, D. S. Balint* & T. A. Dean Department of Mechanical Engineering, Imperial College London, London SW7 2AZ, UK Abstract This paper introduces a set of coupled viscoplastic constitutive equations for deformation and damage in hot stamping and cold die quenching of AA6082 panel parts. The equation set can be used to predict viscoplastic flow and plasticity-induced damage of AA6082 under hot forming conditions. Deformation and damage depend upon a coupled set of evolving internal state variables, e.g. dislocation density, which in turn is affected by thermally-activated and deformation-dependent recrystallisation and recovery. A phenomenological description of damage is derived based on the expected physical scaling with temperature, strain and strain rate. The resulting equations were implemented in the commercial software ABAQUS via the user-defined subroutine VUMAT for carrying out forming process simulations. An experimental programme was designed, and specialised testing facilities developed for calibrating and validating the FE process modelling results. A good agreement between the process simulation and the experimental results has been achieved. This confirms that the physical dependencies in the constitutive equations are correctly formed, and that the equations and FE model can be calibrated and used for hot stamping of AA6082 panel parts. Further, forming process optimisation was carried out using the model to identify the optimal forming parameters for a basic panel part with a circular hole in the middle. The study concludes with a discussion of the potential impact of the constitutive model, experimental characterisation and modelling results on AA6082 panel parts manufacture. Keywords: Hot stamping; AA6082; viscoplasticity; damage model; formability; FE process modelling. * Corresponding Author: D.S. Balint; d.balint@imperial.ac.uk 1 1. Introduction The demand for aluminium alloys has increased in recent years in response to a growing need for lightweight structural metals. For example, using aluminium alloys (rather than steels) for reduced automobile weight is currently of great interest, primarily for lower CO2 emission and reduced fossil fuel consumption, per vehicle, but also for improved vehicle performance. Further reasons for the increased use of aluminium alloys in vehicles include their high strength to weight ratio and good recyclability, which are especially attractive features considering recent regulations aimed at reducing the negative impact automobiles have on the environment. Although aluminium alloys are currently used for a considerable number of components, the use of formed aluminium alloy sheet is still limited [1-4]. Most often, 6xxx series alloys are cold formed in the T4 (pre age hardened) condition, in which ductility, measured as strain to failure, may reach 0.2 [1, 3]. However, the T4 condition ductility is still significantly less than that of deep drawing sheet steel [3]. In converting a part to aluminium, a single sheet steel pressing may need to be redesigned as an assembly of several aluminium sub-parts to ensure production is possible; furthermore, springback of cold formed aluminium sheet and the stress relaxation that occurs during the artificial aging process may lead to geometric tolerance issues. For low production volume applications, such as high performance cars, superplastic forming has been used to overcome formability issues. While superplastic forming offers outstanding formability, the component must be formed at low strain rate and high temperature, significantly limiting production speed and increasing energy consumption; a single part may take as long as an hour to be formed, depending on the complexity and drawing depth required [1]. In addition, the state of the microstructure is critical for superplastic forming; specialized small-grained sheet alloys are required, at considerable cost. Superplastic forming may also lead to uneven thinning at part corners [1]. While superplastic forming has had a significant impact in niche markets, it is unsuitable for mass produced parts. Warm forming has been studied and tested for many years, as ductility can be improved for some grades of aluminium at elevated temperatures. Most often, the dies are heated to ensure a constant temperature during the deformation. Typical forming temperatures are in the range 150-300 °C. At temperatures greater than 300 °C, the tempered microstructure deteriorates, hence significant additional thermal processing would be required [1]. The gain in formability from raising the temperature is modest compared to the substantial additional complexity of heating the tooling and 2 blank, which is the principal reason warm forming has failed to become a widely used technology [3]. Hydroforming may be used as an alternative to cold deep drawing; it has an advantage over cold deep drawing for very low production runs, in that only one die is needed. It is also stated to provide better-than-average surface finish and higher formability [5]. Unlike tube hydroforming, in which adequate sealing can be achieved easily, sheet hydroforming requires the use of a rubber membrane to ensure the high pressure fluid does not escape [1, 5]. This affects reliability and complicates tooling. Again, the process has made little impact in the mass-production of sheet components from Al-alloys. By comparison, hot stamping processes do not require specialised alloy grades with particular microstructures, and can form parts at least as fast as cold forming and operate in a temperature range where Al has significantly enhanced ductility [1]. In hot stamping processes, the material is heated to the Solution Heat Treatment (SHT) temperature to enable the precipitates to be dissolved within the primary α-Al matrix. (Some intermetallic phases are not dissolved in the matrix during SHT.) Generally, for 6xxx series aluminium alloys, it is known that the ductility of the material is obtained from the SHT (T4 condition), and the strength is obtained from the aging process (T6 condition) [2, 4]. Thus, it is beneficial to complete the forming stage prior to age hardening in order to benefit from the gained ductility following the SHT. The temperature at which SHT is performed is an important parameter, since it leads to significant changes in the microstructure of the alloy, and if optimised may lead to an improved capacity to tolerate extensive plastic deformation without cracking, i.e. to an improved formability of the material. The main reasons for the SHT of AA6xxx alloys are: To obtain a uniform distribution of the alloying elements in solid solution [3,4]. To dissolve low melting point Mg2Si and Si particles, which cause hardening of the matrix during deformation [3, 4]. To transform β-AlFeSi phase particles to α-AlFeMnSi phase, which gives better formability [ 4]. A typical thermal history of a hot stamping process is shown in Figure 1. The aluminium alloy blank is heated to its solution heat treatment (SHT) temperature (e.g. 525 °C for AA6082) and then deformed between the cold die set directly after SHT. There are two reasons the formed part is held within the cold dies: one is to achieve rapid quenching to avoid the formation of coarse β phase 3 precipitates, particularly at grain boundaries, and the second is to avoid thermal distortion of the formed part during quenching. In order to identify proper forming conditions for sheet of a given aluminium alloy, the formability limit and ductile fracture initiation must be correctly predicted for the relevant sheet forming process; knowledge of the failure features is essential. The initiation of localized necking (which is thought to originate from instabilities caused by ductile fracture mechanisms) usually instigates the process of void nucleation and growth, and, in turn, determines the formability limit (the state of deformation just preceding failure) of sheet metal [7-9] It is well known that non-metallic inclusions and second phase particles play a fundamental role in the ductile fracture of metal alloys by acting as the source of voids in the material when the particles fracture or decohere from the matrix, which then grow by plastic deformation until final coalescence [4, 10]. The most common mode of void nucleation is the complete or partial interfacial decohesion of the second phase particles from the surrounding material [10]. The main objective of this study was to determine a set of constitutive equations for aluminium alloy AA6082, with the correct physical scaling relationships in terms of relevant internal state variables, for FE simulation of the hot stamping process, so that it is possible to predict the failure features and the formability of AA6082 under different forming rates. The constitutive equations can be calibrated so that they are valid over a wide range of strain rates and temperatures, hence can be used in simulations of panel part manufacture provided the bounds on strain rate and temperature in the real forming process do not appreciably exceed those used in the calibration. This is a significant step towards realistic part forming simulation with damage accurately predicted as a function of the forming conditions, without recourse to e.g. forming limit diagrams only applicable for a single temperature and strain rate. In order to characterise the failure features of the material and motivate the constitutive equation development, a test programme and the associated results are reported first. 2. Deformation and damage in solution heat treated Al-alloys Until recently, studies of damage mechanisms in aluminium alloys at high temperature have been focused largely on superplastic forming and creep processes. It has been found that high temperature causes grain boundary diffusion, which facilitates grain rotation and grain boundary sliding, both of which are more active when the grain size is small, temperature is high and 4 deformation rate is low, as in superplastic forming [11, 13]. However, grain rotation and grain boundary sliding are not restricted to these conditions and may be present to a lesser extent at faster forming rates and in alloys not capable of superplasticity. The relative displacement of grains resulting from rotation and boundary sliding is accommodated by the redistribution of matter within the mantle adjacent to grain boundaries [11, 12]. When this accommodating process is insufficient to meet the requirements of the deformation rate, stresses at the grain boundaries are not relaxed sufficiently and, consequently, cavities nucleate. When a cavity is present at a grain boundary (either nucleated during superplastic deformation or existing prior to the deformation), it grows by either superplastic diffusion processes or plastic deformation [11]. In creep-type deformation the occurrence or absence of grain boundary damage nucleation and growth is strongly sensitive to alloy composition and processing route [1, 13]. The damage reduces the real load bearing section and so accelerates creep, and this increases the rate at which damage grows. Under low stress, the damage is void-like; under high stress, the voids may link to form grain boundary cracks [13]. Metals can fracture by this mechanism alone, though it is more common for multiple damage mechanisms to interact, reducing ductility. Grain boundary damage formation is a kinetic phenomenon that, in metal forming, is linked strongly to the deformation rate. The influence of damage on deformation resistance and fracture mode for complex stress states depends critically on the damage nucleation and growth rates, which in a macroscopic sense will be controlled by material temperature, stress state and strain rate [10, 11]. As a general rule, ductile fracture results from the nucleation, growth and coalescence of damage. This failure mode occurs in metals provided the material is deformed to a sufficient degree for a given temperature and strain rate. In observing the failure surface in aluminium alloys, it is evident that damage initiation sites are usually associated with second phase particles or non-metallic inclusions [10]. The growth of damage in metals takes place by a combination of classical dislocation plasticity mechanisms, creep mechanisms and superplastic mechanisms, depending on the conditions of the deformation. In the sheet forming processes currently being developed for aluminium alloys, forming temperatures normally are above 0.6 of the melting temperature (Tm) and strain rates on conventional mass production presses being used are often high, e.g., up to 10 s-1 [14]. Due to the lack of appropriate evidence to demonstrate the damage features under hot metal forming conditions, a series of hot tensile tests have been carried out on AA6082 aluminium alloys for a 5 range of deformation temperatures and strain rates. In order to study and characterise the damage mechanism in AA6082 alloys at high temperature, metallographically prepared sections of fractured specimens, previously strained under uniaxial tension at various temperatures and strain rates, were analysed using a Scanning Electron Microscope (SEM). Small samples were cut from the tensile specimens from the necking region and ground parallel to the loading direction. The samples were then polished and etched using standard metallographic techniques. Figure 2 shows SEM micrographs in which typical features of the processes of (a) void nucleation due to inclusion/matrix decohesion at grain boundaries and (b) subsequent void growth can be seen for AA6082. In this instance, the test piece was deformed at 450 °C and a constant strain rate of 1 s-1. Figure 3 shows (a) voids starting to coalesce and (b) a large void opening, with the material close to final failure. In Figure 3, the test piece was deformed at 500 °C and a constant strain rate of 10 s-1. The first occurrences of damage are at large strains (relative to the total failure strain). Nucleation always occurs by debonding along particle/matrix interfaces at grain boundaries, as shown in Figure 2(a) (the inclusions themselves have been ejected from the metal matrix when polishing and etching the samples). Total debonding requires additional strain, at which point the microcavities or microvoids grow quickly with increasing tensile strain, as shown in Figure 3, then form macroscopic cavities or cracks leading to macroscopic fracture. 3. Experimental setup 3.1 Test material In all tests, the heat-treatable aluminium alloy AA6082 was used. It was originally supplied in large sheets with thickness of 2 mm in a T6 condition (subjected to SHT, quenched, stretched (3%) in the rolling direction, and artificially aged). The recommended T6 heat treatment for AA6082 is heating to 525 °C for 30 min [5], which ensures full dissolution of the alloying elements into the matrix, followed by an aging treatment consisting of heating to 190 °C for 9 hrs. This process is typical of commercial production of AA6xxx aluminium alloy sheet. AA6082 is commercially available and offers very good corrosion resistance, weldability and machinability, all of which are important for the post-processing of components after forming; it is considered to be a high-strength, heattreatable alloy having very good fatigue strength. 6 3.2 Ductility testing The parameters considered in investigating the high temperature flow response of AA6082 were the strain rate and deformation temperature. The objective of the tests was to understand the effect these parameters have on the strength and ductility of the aluminium alloy at elevated temperatures. For all the tests, the heat-treatable aluminium alloy AA6082 was used. In the manufacturing process, sheet is heated to the SHT temperature, and then transferred to a press for deformation. The transfer may take a few seconds, during which the sheet temperature decreases. A further decrease in temperature occurs during the forming process as heat transfers to the cold dies (see Figure 1). Tensile testing using a Gleeble system is widely used to investigate the effect of processing parameters (particularly, temperature and strain rate, both of which can be controlled very accurately) on the mechanical properties of materials. In the present work, tensile tests were carried out using a Gleeble 3800, which utilises electrical resistance heating, over a temperature range of 525-450 ºC in order to simulate the temperature variation that occurs in the sheet during the actual forming process. Specifically, the temperature profile shown in Figure 4 was used, in which the sheet samples were heated to the SHT temperature (525 °C), and subsequently either maintained at that temperature during deformation, or decreased and maintained at a lower temperature during deformation: 500 °C to simulate the loss of heat during transfer to the press in actual forming, or 450 °C to capture the lower bound on the temperature during actual forming. In order to control the heating rate, achieve the target SHT temperature and deformation temperature, a thermocouple was welded to the centre of the test piece to provide measured temperature feedback to the Gleeble. Rectangular dog bone shaped samples having thickness 2 mm, gauge length 50 mm, and width 12 mm, were used in the tests. The deformation process was conducted quickly, with times typically less than one second [1]. Inevitably, there is a range of strain rates within the sheet during actual forming, hence a broad range of strain rates were investigated (0.1 s-1 to 10 s-1). 3.2.1 The effect of strain rate The symbols in Figure 5 show the Gleeble tensile test results for AA6082 at different strain rates (0.1, 1.0 and 10 s-1) and a deformation temperature of 500 °C. The flow stress increases 7 significantly with increasing strain rate, which demonstrates the highly viscoplastic nature of the material at 500 °C. The ductility also increases with increasing strain rate, contrary to what is commonly observed of other materials. These results are in agreement with results published by Lassence, et al. [10] and El-Danaf, et al. [15, 16] for AA6082. It is proposed that the observed behaviour is due to the effect of grain growth within the aluminium matrix at lower strain rates, which would affect the ductility of the material in the way observed (large grains reduce the extent of grain boundary deformation effects, which improve ductility, as the total grain boundary area in the sample is less when the grain size is large). Grain boundary deformation effects (grain boundary sliding and rotation) are primarily diffusion controlled, hence rate (and temperature) limited, so the effect of increasing strain rate both encourages and inhibits ductility. However, the effect of a large grain size resulting from a lower strain rate likely offsets any gain in activation of grain boundary deformation effects associated with that lower strain rate. Towards the end of deformation the flow stress decreases due to damage softening which dominates until the final failure strain is achieved. 3.2.2 The effect of deformation temperature The symbols in Figure 6 show the Gleeble tensile test results for AA6082 at different deformation temperatures (525, 500 and 450˚C) and a strain rate of 1 s-1. The measured flow stress decreases with increasing temperature. This is typical of most metals, and is commonly a result of higher dislocation mobility (by affecting e.g. the Peierls barrier, phonon drag and the relative strength of obstacles to dislocation motion, etc.), activation of diffusion controlled processes such as grain boundary sliding and rotation and dislocation climb, as well as a generally more active recovery mechanism, all of which are thermally activated processes. In general, greater ductility can be expected with increased temperature, although this is not the case for all aluminium alloys (e.g. AA2024 exhibits much lower ductility at temperatures appreciably higher than about 450 ˚C, which is still below the SHT temperature for that alloy) and this can indeed be observed by comparing the tensile test results carried out at 450 ˚C to those at 500 ˚C. The results at 525 ˚C do not follow the trend with temperature, although the ductilities of the 500 ˚C and 525 ˚C tests are effectively indistinguishable given possible small error inherent in the stress and strain measurement; the lack of improvement in the ductility at 525 ˚C relative to 500 ˚C is likely a result of the significant necking experienced near final failure, which biases the measured strain and makes calculating the stress difficult as an accurate measure of the neck diameter at that stage of the deformation is not available. 8 Increased ductility implies that increased formability can indeed be achieved by forming at high temperature, hence more complicated components can be manufactured, with features such as large draw depths and sharp corners, and multi-part assemblies can be consolidated. Hence transferring the sheet from the furnace to the press is critical, in that it should be done quickly and with minimal opportunity for convective heat loss (e.g. the plane of the sheet should be parallel to the direction of transfer), and the forming process should also be carried out quickly to minimise the loss of heat to the dies. 3.3 Formability tests Experiments were designed to investigate the deformation and failure features of the hightemperature plastic flow of AA6082. To fully test hot stamping feasibility, a number of tests were carried out to investigate the expected primary factors, forming rate and deformation temperature, that influence the hot stamping process and the failure features of the material. 3.3.1 Test setup Tests were carried out using a 250 kN high-speed hydraulic press with a custom tool and die set for testing formability. . The die set which is shown in Figure 7 was designed to interrogate formability by stretching the sheet over a hemispherical punch, thereby imposing a difficult biaxial state of strain (i.e. radial and circumferential) on the sheet in contact with the die. The tool set, as shown in Figure 7, has four main parts: hemispherical punch, top and bottom blank holders, and gas springs. Light springs maintain separation between the top plate and blank holder plate, where the sheet is located, until the press stroke equals the initial separation, at which point the sheet is clamped between the blank holders (the much stiffer gas springs do not deflect appreciably until this occurs, but thereafter provide the clamping force on the sheet, which increases with increasing press stroke). The bottom blank holder was designed with a circumferential drawing bead, and corresponding recess in the top blank holder, to constrain the material from flowing into the die. The bottom blank holder was designed with four spring pins (diameter 5.5 mm) to mitigate temperature loss from the sheet into the bottom blank holder, after it is inserted and just prior to forming. Square samples of AA6082 with dimensions of 170 x 170 x 2 mm were cut from the supplied sheets. A 16 mm diameter hole was drilled in the centre of the sample, which allows the material to 9 flow over the punch more easily, and reduces the area of first contact between the punch and the sheet before the deformation begins, which mitigates local temperature reduction, particularly at slow forming rates. The test setup was used to form 80 mm diameter hemispherical cups from the square blanks under pure stretch conditions. First, the samples were heated to the SHT temperature, 525 °C, then transferred to the cold tool (resting on the spring pins attached to the bottom blank holder) within the press for forming. The transfer (horizontally) took a few seconds, during which the sheet temperature reduced slightly. A further decrease in temperature occurred during the forming process by heat transfer to the cold dies. During a hot stamping process, the hot blank will start to cool locally as soon as contact is made with the cold dies. Further, it was demonstrated in [2] that lubricant hastens the heat loss under moderate loading conditions. While the thermal conductivity of aluminium is high (typically 170 W/mK), the large surface area and thin section of the sheet causes local cold spots to form where contact is made with the cold die set [3]. In practice, forming took place at sheet temperatures ranging spatially, and with time, from 525 to 450 °C. To control the heating rate, SHT temperature, and deformation temperature, a thermocouple was welded to each workpiece. Once the blank was transferred to the press and rested on the bottom blank holder spring pins, the deformation was initiated by momentarily applying a blank holder pressure of approximately 3 MPa to crimp the material at the circumferential drawing bead, thereby ensuring that no material was drawn to produce a pure stretching condition. The press was then actuated, stretching the clamped blank over the punch. A lubricant consistent with that used in [3] was applied to the punch to reduce the friction, and, in turn, allow the material to stretch with minimal influence from a non-uniform friction stress on the underside of the sheet. Two types of forming tests were carried out: (i) Investigation of the failure features under fast (0.64 ± 0.01 m/s) and slow (0.166 ± 0.01 m/s) forming rates. In this case, the samples were deformed until failure occurred; (ii) Investigation of the degree of normalized thickness variation (t/t0) along the deformed part, where t is the instantaneous thickness and t0 is the original thickness. In this case, the samples were deformed to a state just prior to the onset of failure at the fast and slow forming rates. 10 3.3.2 Experimental results Two failure modes were observed in the hot stamping of AA6082 tests: (A) circumferential necking and subsequent tearing, occurring approximately halfway between the base and apex of the formed cup, and (B) radial necking and subsequent tearing, emanating from the central hole. Figures 8a and 8b show hot stamping experimental results for a deformation temperature of 470 ± 10 °C, punch stroke of 42 mm and forming rates of 0.64 ± 0.01 m/s and 0.166 ± 0.01 m/s, respectively. The following conclusions can be drawn from the experimental results: The failure mode of AA6082 under hot stamping depends on the forming rate. At a slow forming rate, failure occurred as a circumferential tear, preceded by necking at a middle height location on the formed cup. The time elapsed from when punch and sheet first come into contact until the end of forming is higher for a slower forming rate. This results in a higher temperature reduction in the region of contact, and, in turn, the part of the sheet in contact with the punch becomes stronger than the area not in contact with the punch. Hence, most of the stretching occurred in the part of the sheet not in contact with the punch because it was hotter and so had a higher ductility and lower flow stress; the eventual failure was initiated by necking resulting from excessive strain in a preferred circumferential location. A fast forming rate led to radial necking and tearing. Thinning of the sheet was maximal around the periphery of the central hole; radial thinning followed at a preferred location, and brought about the eventual ductile tearing of the sheet in that location. In contrast with the slow forming rate case, the central region of the sheet is in contact with the punch for a shorter time, causing a smaller temperature reduction. Therefore, provided the forming rate is sufficiently fast, the central region of the sheet in contact with the punch remains at a relatively high temperature, and so has a higher ductility and lower flow stress than the same region when the forming rate is slower. Hence, the central area of the sheet can be easily deformed, allowing ductile failure to occur in that location. It should be noted that if the sheet temperature were uniform and constant throughout the forming process, the strain in the central hole area would be higher, hence that is the preferred location of failure in the absence of sufficient cooling to cause failure to occur circumferentially, away from the central hole. Non-uniformity of the sheet temperature is exacerbated by a slower forming rate. While a nonuniform temperature profile can be useful in special cases, in general a uniform temperature is 11 desirable to ensure homogeneous deformation [1]; this is simplest to achieve by using a fast forming rate since heat transfer to the dies during the deformation process is kept to a minimum. AA6082 aluminium alloy shows little intrinsic strength at the SHT temperature and does not significantly strain harden when deformed. As a result, the low flow stress may not be sufficient to draw material into the die and across the die surface, leading to local thinning and low formability [1]. By increasing the forming rate, the deformation can occur at a higher temperature, at which the material has a stable microstructure and high ductility, but is still strong enough as a result of the fast forming rate to draw into the die. 4. Unified viscoplastic damage model Viscoplastic constitutive equations have been developed by many researchers for many engineering materials, and have been used to model a wide range of time-dependent phenomena, including strain rate effects, creep, recrystallisation, and recovery. In previous equations, hardening during viscoplastic deformation is dependent only on the accumulated plastic strain [12, 14, 17]. Recently, dislocation-based hardening constitutive equations have been developed [14, 17], in which the annihilation of dislocations (recovery) due to annealing and recrystallisation under hot forming conditions are taken into account. In order to simulate the hot stamping carried out in this study, a new set of coupled viscoplastic constitutive equations was developed to further account for the changes that occur in the material while forming at the SHT temperature. 4.1 Damage constitutive equations In hot metal forming processes, softening due to damage dominates the later stages of deformation, which decreases the flow stress as shown in Figures 5 and 6. Hence, this stage in the deformation is the most critical for accurately predicting hot formability. The hot deformation damage mechanism considered in this work is void nucleation and growth. According to the specific damage mechanism for AA6xxx which presented previously in section 2, the deformation rate is high and the deformation mechanism is combined between the grain boundary sliding and dislocation motion resulting in damage features appearing at the interface of the inclusion particularly at the grain boundaries. The damage mechanism for aluminium alloys in the current study is highly liked with that occurs at superplastic forming which is void nucleation and growth at the interface of the second phase and the matrix particularly at the grain boundary. A model proposed in [14] of damage in superplastically deforming materials (which occurs at grain boundaries in a manner similar to that shown in Figures 2 and 3 for hot deformation of AA6082) is adopted, where both 12 diffusion and plasticity (power-law) induced cavity expansion are modelled. The area fraction of damaged material is defined as, f d rd2 / l 2 , where rd is an effective cavity size that includes the radial extent of the diffusion zone, and l is the cavity spacing. It is a feature of the model that if rd l , cavity growth occurs purely by diffusion, and if rd is equal to the actual radial cavity size, then cavity growth occurs purely by power-law plasticity. Henceforth, the parameters rd and l are not explicitly required. Damage evolution is defined (as in [14]) by Equation (1), where the damage parameter f d 0 prior to deformation (the initial state of the material); when the damage parameter reaches a critical value, taken to be 0.7 in this study, the material is deemed to have failed: ( f d = D1 fd 1 e p2 + D2e p3 cosh D3e p d d d ) (1) where D1 and D2 are temperature-dependent parameters, and D3 , d1, d2, and d3 are material constants. The temperature dependent parameters D1 and D2 are given by Arrhenius equations [12]: 1 2 D1 D10 exp QD RgT D2 D20 exp QD (2) (3) RgT where, Rg is the universal gas constant, QD and QD are activation energies, and D10 and D20 are 1 2 material constants. 4.2 Viscoplastic damage constitutive equations For ductile metals and alloys at temperatures less than 0.4Tm, at which plastic deformation occurs by dislocation motion, the hardening relationship is conventionally described by a power law: K PN (4) where K is a stress constant and N is the strain-hardening exponent. When the temperature rises above 0.5Tm, thermally activated processes become significant and the flow stress depends on strain rate (replacing Equation (4)): 13 s = K e PN e Pm (5) where e P is the plastic strain rate and m is the strain rate-hardening exponent. The initial material has a yield stress k . The stress that leads to viscoplastic flow can be expressed as k , where the brackets indicate that only positive values are valid (i.e. the stress must exceed the yield point for consideration of viscoplastic flow to be meaningful). After sufficient plastic straining occurs, dislocation entanglement, pile-ups, etc., harden the material by an amount R ; the stress that leads to viscoplastic flow is reduced to R k . Thus the flow rule can be modified to depend directly on the isotropic hardening and initial yield stress. Equation (5) is replaced by: æs - R-kö eP = ç ÷ø K è n1 (6) which is the traditional power law viscoplastic flow formulation and K and n1 are material constants. Considering the effect of damage on viscoplastic flow, a set of unified viscoplastic damage constitutive equations can be assembled: æ s (1 - f d ) - R - k ö eP = ç ÷ K è ø n1 (7) R = 0.5Br -0.5 r (8) r = A(1- r ) e P - C r n 2 (9) ( f d = D1 fd 1 e p2 + D2e p3 cosh D3e p d d d E 1 fd T P ) (10) (11) The evolution of material hardening, R , is given by Equation (8), which is a function of the normalised dislocation density [4, 20-21] (through the coupling of the equations, the dislocation density and plastic strain affect each other), which is given by 0 / max 0 , where 0 is the initial dislocation density of the material, i.e. the normalized dislocation density varies from 0 14 (the initial state) to 1 (the dislocation network saturated state). Further details of the dislocation hardening formulation are given in [14, 17]. The parameters K, k, B, C and E are temperaturedependent material constants, and A, n1 and n2 are temperature-independent material constants (E is the Young’s modulus of the material). Equations (12-16) represent the Arrhenius equations for the temperature-dependent parameters [12]: K K0 exp QK RgT (12) k k0 exp Qk Rg T (13) B B0 exp QB Rg T (14) C C0 exp QC RgT (15) E E0 exp QE RgT (16) 5. Calibration of the constitutive equations One of the most difficult tasks encountered in developing viscoplastic constitutive equations is accurately determining the material constants from experimental data, valid over a range of temperatures and strain rates. The equation set has a total of 21 material constants K0, k0, B0, C0, E0, D10 , D20 , QK , Qk , QB , QC , QE , QD , QD , n1 n2 , A, d1, d2, d3 and D3. The tensile data obtained at 1 2 different temperatures and strain rates (Figures 5 and 6) were used to determine the material constants arising in the constitutive equations. The procedure used to determine the material constants consists of four steps: 1. Fit the equations (i.e. determine a set of values for the material constants) to the data obtained for different strain rates and a deformation temperature of 500 °C. 2. Fit the equations to the data obtained for a strain rate of 1 s-1 and deformation temperature of 450 °C by changing only the values of the temperature dependent parameters (i.e., for a fixed temperature, the activation energies and coefficients of temperature dependency are not required); values of the parameters that do not depend on temperature are retained from Step 1. This leads to a second set of independent temperature-dependent parameter values. 15 3. Using the Arrhenius equations for the temperature-dependent parameters as shown in Equations (2), (3) and (12)-(16), the values of the coefficients and activation energies in the temperature dependencies are determined from the two independent values of each temperature-dependent parameter obtained in Steps 1 and 2. 4. The last step is validating the values of the material constants obtained from the optimization. This was done in this study by using the parameter values determined by Steps 1-3 to predict the remaining data set (strain rate of 1 s-1 and deformation temperature of 525 °C); a good agreement indicates the parameter values are valid. More robust checking can be carried out by using the parameter values to predict further data sets not used in the optimization procedure. The optimization procedure described above was used to determine the material constants in the constitutive equations for AA6082, listed in Table 1. Table 1. Material constants in the viscoplastic damage constitutive equations for AA6082. B0 (MPa) k0 K0 (MPa) (MPa) QE (J/mol) QC (J/mol) QB (J/mol) Qk (J/mol) QK (J/mol) n1 n2 d1 11625. 8 6679 27687 5 1.8 1.2 QD QD2 (J/mol) (J/mol) E0 (MPa) C0 A 6408.4 119804 322.81 0.26 13 4.91 0.89 0.219 12986 3393.4 d2 d3 D1 D2 D3 1.0101 0.5 10.32 0 0 5.49E19 26.8 1 The constants in Table 1 were used to make the model predictions (curves) for stress versus strain shown in Figures 5 and 6, which demonstrate a good agreement between the model predictions and experimental results (symbols) for three different strain rates at a deformation temperature of 500 °C, and different deformation temperatures for a strain rate of 1 s-1, respectively. Figure 9 represents the relationship between the damage parameter and the true strain for different strain rates. The damage parameter is zero (undamaged) at the beginning of the deformation, and remains zero until damage initiates, at which point the damage parameter begins to rapidly increase as failure of the material is approached. In this way, the viscoplastic damage equations can be used to predict the viscoplastic deformation and ductile fracture of AA6082 in a hot stamping process, 16 i.e. failure of the material (hence the failure strain) can be identified by the damage parameter attaining a critical value, taken to be 0.7 for AA6082 in this study. 6. FE process modelling 6.1 FE model FE simulations of hemispherical cup forming at elevated temperatures were conducted for AA6082 aluminium alloy using the explicit FE code ABAQUS and the coupled temperature-displacement axisymmetric deformation mode. The sheet was meshed using axisymmetric quadratic elements, with four elements through the thickness to ensure bending could be captured, although the sheet deformation in the simulations is almost exclusively stretch. The viscoplastic equations for deformation and damage, as well as the equations for the temperature dependent parameters, were implemented via the Variable User MATerial (VUMAT) subroutine, programmed in FORTRAN. A schematic diagram of the coupled thermo-mechanical model with boundary conditions is shown in Figure 10. The blank holders and punch were modelled as elastic deformable parts to investigate the temperature and stress distributions in both the sheet specimen and tool. The physical and thermal properties used in the FE analysis are given in Table 2 [1]. Table 2. Physical and thermal properties used in the FE analysis [1]. Property Part Value die 7.85e-9 Units Tonne/mm3 Density blank 2.7e-9 die 5.1e8 blank 8.9e8 die 50 blank 170 mJ/Tonne·K Specific heat Thermal conductivity mW/mm·K 6.2 Process modelling procedure The first step in the FE process modelling procedure is application of the boundary conditions as shown in Figure 10. At the start of the simulation, the punch moves toward the sheet and first 17 contact occurs between the sheet and blank holders. A blank holder pressure of approximately 3 MPa is applied to ensure that no material draws in during the process, exactly as in the pure stretching experiments. In the fast forming rate case (0.64 m/s), the stroke applied is 50 mm occurring (with a linear ramp in time) over 0.08 s, and in the slow forming rate case (0.166 m/s), the stroke applied is 50 mm over 0.3 s. The first objective of the process simulation was an investigation into the failure features of AA6082 during hot stamping. This was accomplished by simulating under fast and slow forming rates until failure took place. The second objective of the process simulation was an examination of the spatial thickness gradient (in terms of normalized thickness t/t0) of the deformed cup under different forming rates at the point in forming just before failure took place; the latter is used to develop a so-called process window, a recommended region of processing parameters for successful forming, for the hot stamping process of AA6082 aluminium alloys under different forming rates. The process window was identified by running simulations with different forming rates and different punch strokes to identify the bounds on possible combinations that lead to successful part forming (i.e. without failure or unacceptable thinning). 7. Validation and computational results Figures 8a and 8b show contours of the damage parameter for the fast and slow forming rates, respectively. It can be observed that ductile failure is initiated at the location of localized necking, and that the location of localized necking is dependent on the forming rate. Figure 8a shows that, for the fast forming rate, necking occurs at the top of the cup around the central hole, and maximum damage is predicted in this area, consistent with the experimental observations. On the other hand, Figure 8b shows that in simulations with a slow forming rate, necking occurs in the middle region of the workpiece, circumferentially, also consistent with the experiments. Qualitatively, the simulations are in very good agreement with the experiments suggesting that the damage equation is correctly formulated. Figures 11a and 11b are direct comparisons of the experimental and simulated cup profiles, further confirming that the location of necking is the same in simulation and experiment, for both the fast and slow forming rates, respectively. The sheet was deformed at 470 ± 10 °C to a state prior to failure, but after the start of necking, requiring a punch stroke of 32 mm. Contours of plastic strain 18 are also shown for the simulation results in Figures 11a and 11b, where the largest plastic strain indicates the location of maximum thinning. Notably, the plastic strain is low in the mid-height circumferential region when the forming rate is fast, and in the vicinity of the hole when the forming rate is slow; in both cases, the plastic strain is low at the location of the drawing bead, indicating that very little drawing of material through the clamping location occurs in the simulations. The normalized thickness ( t / t0 ), where t0 is the initial sheet thickness, was measured for the experimental and simulated formed parts, compared in Figure 12. Solid symbols are the experimental results, with circles representing fast forming (0.64 m/s) and triangles slow forming (0.166 m/s), while the hollow symbols and solid curves are the simulation results and best fits to the simulation results, respectively, for the two forming rates. A third, intermediate forming rate (0.21 m/s) was simulated, given by the dashed line in the figure. Measurements were carried out for a number of tested specimens and cross sections, giving the error bars in the figure for the scatter in the measured data. There is a fairly good agreement between the experiments and simulations for both forming rates. The results in Figure 12 show quantitatively that the minimum value of t/t0 is at the central hole for the fast forming rate. On the other hand, for the slow forming rate, the thinnest location is shown to be at a middle height on the cup. Figures 8a, 8b, 11a, 11b and 12 confirm that the constitutive equations and FE model implementation are suitable for predicting deformation and failure features for hot stamping of AA6082 panel parts. Figure 12 shows that significant necking and damage are observed in the central hole and middleheight cup regions for the fast and slow forming rates, respectively, in the hot stamping of the cup component. Hence, it is expected that there exists a transition region in forming rate between the failure locations, which gives a more homogenous and uniform thickness in the formed part. At the transition forming rate, thinning may occur in the central hole and mid-height cup regions to a similar degree. The transition forming rate is the optimum forming rate for the hot stamping process. To determine the optimum forming rate, a series of FE simulations were carried out with forming rates ranging from 0.13 to 0.64 m/s. The simulations shown in Figure 12 by the dashed line for a rate of 0.21 m/s indicates the beginning of the transition to a circumferential failure mode. The thickness in the neck is greater for the 0.21 m/s case compared to the 0.166 m/s case. Further reduction of the forming rate towards 0.166 m/s gives a rapidly increasing thickness in the central hole region, and as 0.166 m/s is approached, the thinnest region moves to the middle height of the 19 cup. It is difficult to identify precisely the optimum forming rate, but 0.21 m/s was the most optimal forming rate simulated, which enabled the part to be formed with the most uniform thickness distribution and a higher drawing depth. At the optimal forming rate, the quality of the formed part can be improved, and localised necking occurs only at a much later stage in the drawing process. To explore this further, Figure 13 shows cross sections of the formed cups for simulations at different forming rates. Again, it can be observed that the failure mode is a circumferential tear when the forming rate is slow (0.13 m/s to 0.2 m/s). The transition to the central hole failure mode occurs between the forming rates of 0.2 m/s and 0.23 m/s; the thickness distribution of the 0.21 m/s forming rate is fairly uniform (as shown in Figure 12). For successful manufacture of a component using hot stamping, correctly choosing the process parameters is essential. The forming rate and drawing depth are the two most important parameters, which are studied in depth to define the process window for hot stamping of AA6082 aluminium alloy panel parts. To determine the process window, a series of FE simulations were carried out for different forming rates and drawing depths. To define a boundary point (delineating between failure and success) for a given forming rate, a simple bisection method was used. Simulations were carried out with a forming rate of 0.166 m/s as an example to describe the procedure. An initial guess for the drawing depth limit of 35 mm was used; the part was formed without failure (Simulation 1 in Figure 14). The next simulation was carried out with an increased drawing depth of 41.5 mm, selected according to previous experience to ensure failure would take place (Simulation 2 in Figure 14). From the first two simulation results, it can be concluded that the critical drawing depth for forming the part at a forming rate of 0.166 m/s is between 35 mm and 41.5 mm. The next simulation was carried out with a drawing depth of 38.25 mm, halfway between 35 mm and 41.5 mm (Simulation 3 in Figure 14); as failure did not occur, it can be concluded that the critical drawing depth must be between 38.25 mm and 41.5 mm. The process can be repeated until the critical drawing depth is identified to the required accuracy. In this case, it was found to be 38.65 mm; any drawing depth less than this can be formed at 0.166 m/s without failure taking place. This procedure produces a single point on Figure 15, corresponding to a forming rate of 0.166 m/s. Figure 15 shows the forming process window in terms of forming rate (ranging from 0.13 to 0.3 m/s) and drawing depth. The open and solid circles are simulation results where no failure occurred, and failure occurred, respectively. Hence, the boundary between the open and solid circles in Figure 15 is the formability limit curve; below the curve, quality parts can be formed. Figure 15 can be 20 regarded as an overall forming working diagram for hot stamping of AA6082 panel parts. (Pictures of tests corresponding to four different combinations of forming rate and drawing depth are shown, further indicating that good qualitative agreement was achieved between experiment and simulation). The failure region (above the forming limit curve) is divided into three parts: The transition region where the forming rate is optimal and the maximum drawing depth can be obtained with a nearly uniform part thickness, which is bounded on the left by a region where failure occurs circumferentially at a mid-height location on the formed cup, and on the right by a region where failure occurs at the central hole. Further, according to the known viscoplastic response of AA6082, a higher strain rate leads to higher ductility, which is different from the trend observed for most other materials. Therefore, the trend of the forming limit curve, shown in Figure 15, differs from what would be expected for a material that exhibits lower ductility at a higher strain rate, particularly at fast forming rates; the expectation for such a material, in the fast forming region, is given by the dashed line sketch in Figure 15. Conclusions A set of viscoplastic damage constitutive equations were developed and calibrated for AA6082. The equations and the procedure used to calibrate them were validated by comparing model predictions of tension and hemispherical punch forming to experimental results. The close agreement between the predictions and observations, particularly for the forming rate dependency of the failure mode in hot stamping, indicates that the calibrated equations have the correct physical scaling and can be used to accurately model the viscoplastic flow and damage behaviour of AA6082 up until failure. The hot stamping process is used to deform an AA6082 panel part. AA6082 is preferable alloys series for automotive applications due to medium strength with excellent corrosion resistance. However, this study can be achieved using in different aluminium alloys. An FE model employing a material model for viscoplastic flow and plasticity induced damage in AA6082. The model was used to define the process window for hot stamping of an AA6082 panel part with a central hole. Major conclusions drawn from this study are: The failure features of AA6082 in hot stamping of panel parts are forming rate dependent. For a fast forming rate, the failure mode is a radial tear emanating from the central hole on the formed cup. However, for a slow forming rate, the failure mode is a circumferential tear 21 at a mid-height location on the formed cup. The failure features were both predicted by FE simulations and experimentally observed. The forming process window for AA6082 hot stamping was determined by FE simulations, and was experimentally validated. The largest drawing depth and most uniform part thickness can be achieved with a forming rate of approximately 0.21 m/s. Physically based, alloy-specific material models, calibrated by experimental data, can be used with commercial FE software to successfully determine forming limit curves where otherwise many time consuming and costly tests would be needed. This approach constitutes a virtual metal forming process design procedure, which may be readily extended to other alloys if material models and data are available. Acknowledgement Financial support from the Engineering and Physical Sciences Research Council, UK, (EPSRC Grant No: EP/E00573X), and student support from the Egyptian Government, are gratefully acknowledged. References [1] A. Foster, M. Mohamed, J. Lin, T. Dean, An investigation of lubrication and heat transfer for a sheet aluminium Heat, Form-Quench (HFQ) process, Steel Res Int. 79-11-VII (2008), 133-140. [2] I. J. Polmear, Light Alloys-Metallurgy of the Light Metals, third Ed, London, 1995, 337-342. [3] M. Mohamed, A. D. Foster, J. Lin, Solution heat treatment in HFQ process, Steel Res Int. 7911-VII (2008), 160-167. [4] G. Mrówka-Nowotnik, J. Sieniawski, A. Nowotnik, Influence of heat treatment on the microstructure and mechanical properties of 6005 and 6082 aluminium alloys, Achievements in Materials and Manufacturing Engineering. 20 (1-2) (2005), 447-450. [5] F. Dohmann, Ch. Hartl, Hydroforming - a method to manufacture light-weight parts, J Mater Process Tech. 60 (1996) 669-676. [6] N. Abedrabbo, F. Pourboghrat, J. Carsley, Forming of AA5182-O and AA5754-O at elevated temperatures using coupled thermo-mechanical finite element models, Int J Plasticity. 23 (2) (2007), 841-875. [7] H. Takuda, et al, Prediction of forming limit in deep drawing of Fe/Al laminated composite 22 sheets using ductile fracture criterion, J Mater Process Tech. 60 (1-4) (1996), 291-296. [8] O. Fahrettin, L. Daeyong, Analysis of forming limits using ductile fracture criteria, J Mater Process Tech. (147) 2004, 397-404. [9] P. Brozzo, B. Deluca, and R. Redina, A new method for the prediction of formability limits in metal sheets, Biennial Conference of the International Deep Drawing Research Group, 7th. (1972). [10] D. Lassance, D. Fabrègue, F. Delannay, T. Pardoen, Micromechanics of room and high temperature fracture in 6xxx Al alloys, Prog Mater Sci. (52) (2007), 67-129. [11] J. Lin, Y. Liu and T. A. Dean, A Review on Damage Mechanisms Models and Calibration Methods under Various Deformation Conditions, Int J Damage Mech. 14 (2005), 299-319. [12] A.D. Foster, J. Lin, D.C.J. Farrugia, and T.A. Dean, Investigation into damage nucleation and growth for free-cutting steel under hot-rolling conditions, J Strain Anal Eng. 42(4) (2007), 227235. [13] A.C.F. Cocks, & M. F. Ashby, On creep fracture by void growth, Prog Mater Sc. 27, (1982), 189-244. [14] J. Lin, B.H. Cheong, X. Yao, Universal multi-objective function for optimising superplasticdamage constitutive equations, J Mater Process Tech. (125-126) (2002), 199-205. [15] A. El-Danaf, Ehab, A. AlMajid, Abdulhakim, Soliman, S. Mahmoud, Hot deformation of AA6082-T4 aluminium alloy, J Mater Sci. 43 (2008), 6324-6330. [16] A. El-Danaf, Ehab, S. Soliman, Mahmoud and A. AlMajid, Abdulhakim, Effect of Solution Heat Treatment on the Hot Workability of Al-Mg-Si Alloy, Mater Manuf Process. 24(6) (2009), 637- 643. [17] J. Lin, T.A. Dean, A Modelling of microstructure evolution in hot forming using unified constitutive equations, J Mater Process Tech. 167(2-3) (2005), 354-362. [18] A. Andrade-Campos, F. Neto da Silva and F. Teixeira-Dias, Modelling and numerical analysis of heat treatments on aluminium part, Int J Numer Meth Eng. (2006), 1–6 [19] M.K. Khraisheh, H.M. Zbib, C.H. Hamilton, A.E. Bayoumi, Constitutive modelling of superplastic deformation 1: theory and experiments, Int J Plasticity. 13 (1-2) (1997), 143–164. [20] M.A. Khaleel, H.M. Zbib, E.A. Nyberg, Constitutive modelling of deformation and damage in superplastic materials, Int J Plasticity. 17 (3) (2001), 277–296. [21] M.S. Mohamed, J. Lin, L. Wang, D. Balint, Hybrid forming processes for production of lightweight high strength automotive panel parts, International Heat Treatment & Surface Engineering. (4)(2010), 160-165 23 SHT (525°C) Temperature (°C) Transfer to the press Deformation Hold within cold dies Time (s) Figure 1 A schematic diagram showing a typical thermal history for hot stamping of AA6082 aluminum alloys. 24 Void nucleation by inclusion/matrix decohesion (at grain boundary) Loading direction (a) (b) Figure 2 SEM micrographs showing early features of the damage mechanism: (a) Void nucleation resulting from inclusion/matrix decohesion and (b) void growth in AA6082 deformed at 450 °C and a strain rate of 1 s-1. 25 (a) (b) Figure 3 SEM micrographs showing final features of the damage mechanism: (a) Voids beginning to coalesce and (b) a large void opening and the material close to final failure for AA6082 deformed at 500 °C and a strain rate of 10 s-1. 26 Deformation Temperature (°C) 525°C 500°C 450°C Time (sec) Figure 4 Temperature profile for the tensile test. 27 70 True Stress (MPa) 60 10 s-1 50 1 s-1 40 30 0.1 s-1 20 10 0 0 1.1 0.1 0.2 0.3 0.4 0.5 0.6 True Strain 0.7 0.8 0.9 1.0 Figure 5 Comparison of computed (solid curves) and experimental (symbols) stress–strain relationships for AA6082 deformed at a temperature of 500 °C for three different strain rates. 28 60 450 °C True Stress (MPa) 50 500 °C 40 525 °C 30 20 10 0 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 True Strain 0.8 0.9 1.0 1.1 Figure 6 Comparison of computed (solid curves) and experimental (symbols) stress–strain relationships for AA6082 deformed at a strain rate of 1 s-1 for three different deformation temperatures. 29 Die set top plate Die set blank holder plate blank holder plate Punch Stop ring Die set base plate Gas spring Punch support Die set support Rig base plate Figure 7 Tool and die set for testing formability. 30 Damage 0.7 0.64 0.60 0.53 0.14 0 (a) Fast forming rate Damage 0.7 0.64 0.60 0.53 0.14 0 (b) Slow forming rate Figure 8 Experimental results and FE formability simulation showing contours of the damage parameter for AA6082 sheet deformed at 470 ± 10 °C and a punch stroke of 42 mm: (a) Fast forming rate (0.64 ± 0.01 m/s) failure due to radial tearing from the central hole. (b) Slow forming rate (0.166 ± 0.01 m/s) failure due to circumferential tearing at a mid-height location. 31 0.7 10 s-1 0.6 1 s-1 Damage (fd) 0.5 0.1 s-1 0.4 0.3 0.2 0.1 0 0.5 0.6 0.7 0.8 0.9 1 1.1 True Strain Figure 9 Prediction of the damage parameter for AA6082 deformed at a temperature of 500 ºC for different strain rates. 32 Stroke Amplitude 43 (m/s) Top Blank Holder 8 Blank 2 R5 Movement of the Dies Blank Holding Pressure Bottom Blank Holder Y Hemispherical Punch X 40 Figure 10 FE model of the hemispherical punch formability test. 33 Maximum thinning Plastic Strain 0.65 0.54 0.44 0.33 0.23 0.11 0.01 (a) High forming rate Maximum thinning Plastic Strain 0.4 0.33 0.26 0.19 0.13 0.063 0.006 (b) Slow forming rate Figure 11 Comparison of the FE simulation deformed profile (with contours of plastic strain) and the cross section of the experimental deformed part for a punch stroke of 32 mm and forming rates of (a) 0.64 ± 0.01 m/s and (b) 0.166 ± 0.01 m/s. 34 0.64 m/s 0.166 m/s 1 1 0.9 0.9 0.21 m/s Normalized thickness (t/t0) 0.8 0.8 0.7 0.7 0.6 0.6 Zero position 0.5 0.5 0.4 0.4 0 0 5 5 10 10 15 15 20 20 25 25 30 30 35 35 40 40 Radial position (mm) Figure 12 Comparison of normalized thickness distribution of the FE simulations (hollow symbols and solid curves) and experiments for a punch stroke of 32 mm and forming rates of 0.64 ± 0.01 m/s and 0.166 ± 0.01m/s. 35 Damage 0.13 m/s 0.7 0.704 0.166 m/s 0.6 0.18 m/s 0.465 0.37 0.2 m/s 0 0.21 m/s 0.137 0 0.23 m/s 0.25 m/s 0.39 m/s Figure 13 Prediction of the failure features and maximum thinning of the deformed cup for different forming rates. 36 41.5 Forming rate = 0.166 m/s Punch Stoke (mm) 39.7 38.9 38.3 35 Damage 0.7 0.704 0.6 0.465 0.137 0 1 2 3 5 4 Simulation number Figure 14 Prediction of the formability limit for a forming rate of 0.166 m/s by simulating different deformation strokes. 37 Transition region 44 Circumferential failure Radial failure 42 2 40 Failure region Punch stroke (mm) 4 38 Forming rate = 0.166 ± 0.01m/s 5 Stroke = 42mm Forming rate = 0.64 ± 0.01 m/s Stroke = 42 mm 3 36 1 34 Forming region 32 30 Forming rate = 0.166 ± 0.01 m/s Stroke = 32 mm Forming rate = 0.32 ± 0.01 m/s Stroke = 32 mm 28 0.08 0.1 0.12 0.14 0.16 0.18 0.2 0.22 0.24 0.26 0.28 0.3 Forming rate (m/s) Figure 15 Forming process window (with select experimentally determined failure features shown) for hot stamping of AA6082 aluminium alloys. 38 39