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
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Methods under Various Deformation Conditions, Int J Damage Mech. 14 (2005), 299-319.
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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