Numerical study on local short-term heat treatments for joining by forming of high-strength 7xxx aluminum

7xxx aluminum alloys have very high specific strengths, making them interesting for manufacturing car bodies. However, the limited formability of the precipitation hardenable alloys in the artificially aged T6 temper is challenging for forming and joining processes. The pre-conditioning of aluminum sheets by a short-term retrogression is a promising approach to enhance the process limits of joining by forming technologies. In addition, localizing the heat treatment enables the control of the material flow. However, for a targeted material flow, a deeper understanding of the relation between the heat treatment layout and its influence on joining processes is needed, which can be achieved with the aid of numerical analyses. Therefore, within the scope of this work, an approach for the numerical simulation of locally limited heat treatment layouts for the control of the material flow of high-strength aluminum sheets in joining by forming process is shown. The investigations are conducted for the simulation software LS-DYNA and the innovative shear-clinching process. Process models for the local retrogression heat treatment of punch-sided AA7075 T6 and the subsequent shear-clinching as well as an approach to couple the individual models are presented. By performing a localized retrogression from the T6 temper, the radial material displacement of the upper sheet in the shear-clinching process can be reduced in comparison to joining AA7075 in the W temper. The control of the material flow in the joining process thereby causes the improvement of geometric features, which are critical for the joint strength.


Introduction
In order to reduce the energy consumption of vehicles, lightweight design is crucial.Regarding car bodies, high-strength steels, which allow the reduction of wall thicknesses and light alloys, which offer high specific strengths, substitute classical steel grades.Especially precipitation hardenable high-strength 7xxx aluminum alloys, which are mainly used in aviation, have come into focus of car manufacturers [1].However, manufacturing sheet metal assemblies, made from high-strength alloys, is challenging, as they have a generally limited formability when in an aged condition [2].This affects forming operations as well as joining by forming processes.
For manufacturing sheet metal components, mainly three different approaches are pursued to increase the formability of high-strength 7xxx aluminum alloys.These approaches are forming at elevated temperatures [3], hot form quenching [4], and W temper forming at room temperature [5].To improve the formability of high-strength aluminum alloys in joining by forming operations, two basic approaches are of importance.Joining operations can be conducted at elevated temperatures, too.Examples are the investigations of Lambiase [6], in which high-strength AA6xxx alloys were clinched after heating them to up to 300 °C and the self-pierce riveting of die-sided AA7075 T6, which was shown by Jäckel et al. [7].For magnesium sheets, clinching at elevated temperatures was shown by Hahn et al. [8].In general, heating of the sheets leads to reduced strength and increased ductility but makes their handling more difficult.Thus, joining after pre-conditioning is a promising approach.For precipitation hardenable aluminum alloys, the mechanical properties can be set by a heat treatment and joining can be conducted at room temperature afterwards.
For self-pierce riveting of die-sided AA7021 T4 as well as for clinching of punch-sided AA7075 T6, this approach was shown in [9].The sheets were heated via induction to 200 °C in case of AA7021 and to 250 °C in case of AA7075.The temperature was held for few seconds.Joining was then conducted at room temperature after cooling of the sheets.Due to the decrease of the material's strength, joining was possible without failure.
An innovative joining technology, which allows the joining by forming of dissimilar high-strength materials in a single-stage process is shear-clinching [10].During the joining sequence, the die-sided joining partner is indirectly cut and the upper sheet is drawn into the cut out hole and extruded to form an interlock.Therefore, on the die-side, ultra-high strength 22MnB5 can be joined [10].Yet, the process is limited by the properties of the upper joining partner as AA7075 in the artificially aged T6 temper cannot be joined without cracks [11].In [11], it was shown that a short-term retrogression prior to joining reduces the material's strength and enables the joining of high-strength AA7075 and highstrength steels.During retrogression heat treatment, hardenable aluminum alloys are annealed at temperatures higher than age-hardening temperature but lower than the solution heat treatment temperature [12], leading to the partial dissolution of precipitates.By localizing the heat treatment, the joint characteristics can be improved [11].However, the efficient design of suitable heat treatment layouts as well as the deeper understanding of the influence of the heat treatment on the material flow in mechanical joining processes require the use of numerical methods.
The first numerical model of the shear-clinching process was presented by Busse [13].Crucial for simulating the process is the modelling of the indirect shear-cutting of the die-sided joining partner.Busse [14] has used the software DEFORM 10.2 and the normalized Cockroft-Latham [15] damage criterion for the materials 22MnB5 and HCT600X.Müller [16] and Hörhold [17] presented numerical models of the process, using Simufact.Forming.For modelling the cutting of the lower sheet, both have used the normalized Cockroft-Latham damage criterion as well.The criterion requires the definition of a critical threshold value for the damage.Elements are deleted when this critical value is reached.The model must be calibrated for the process with a reverse numerical identification.Therefore, the determined values might not be suited for highly differing process conditions.
To allow the stress state dependent prediction of the cutting behavior of the die-sided sheet, Meschut and Otroshi [18] have shown a numerical model of the shear-clinching process for LS-DYNA using the GISSMO [19] damage criterion.For the GISSMO criterion, failure curves, which describe the critical strain in dependence of the triaxiality and of the Lode angle parameter, must be defined.For this purpose, the failure strain is determined for different stress states using various testing geometries.The extensive characterization of the failure behavior for self-pierce riveting of HX340LAD was shown by Otroshi in [20].The use of the GISSMO criterion for the numerical simulation of selfpierce riveting was also shown by Rusia [21] and Hofmann [22].The GISSMO criterion has therefore proven to be suitable for modelling joining by forming processes.However, non-linear strain paths as well as changing stress conditions during joining may still lead to errors regarding the prediction of failure.
Other aspects for modelling the process chain are the simulation of the heat treatment and the coupling of the thermal simulation and a subsequent forming operation.Kerausch [23] has presented the subsequent simulation of a local heat treatment and deep drawing with Abaqus and Autoform.In [7], Jäckel et al. have shown a 2D model for the thermalassisted joining in DEFORM 11.An approach for the modelling of locally varying material properties after pre-conditioning for the shear-clinching process was presented in [11].The upper sheet was divided into two bodies, which were then connected with a tied contact.Hereby, different properties can be assigned to the untreated and the heat-treated areas of the sheet.However, this approach does not allow the setting of property gradients and requires the manual assigning of temperature dependent material properties.Models for the continuous numerical simulation of local pre-conditioning and subsequent joining are not present.Thus, within the scope of this work, an approach for the numerical design of heat treatment layouts for the shearclinching of AA7075 T6 using LS-DYNA is shown.Individual simulation models for the heat treatment of the precipitation hardenable aluminum alloy and for shear-clinching are presented and validated with experimental data.The models are connected to continuously model the process chain.Finally, two different heat treatment layouts and their influence on the material flow during the joining sequence and the resulting joint formation are compared.

Materials
For the investigation, punch-sided AA7075 is shear-clinched with die-sided HCT780X and hot stamped 22MnB5.The aluminum alloy is originally in the F temper.The sheets are fully solution annealed for 15 min at 480 °C and quenched in water afterwards, achieving the W temper.After 7 d of natural ageing at room temperature, the sheets are artificially aged for 24 h at 120 °C (T6 temper).The heat treatment parameters were chosen according to [12].Natural ageing of at least 3 d prior to artificial ageing has proven to be beneficial for the maximum strength of AA7075 [24].
From the T6 temper, the material is softened by performing a laser-assisted short-term retrogression according to [25] in order to promote joinability.The heat treatment temperature is varied in five steps from 200 to 400 °C.For each temperature, the mechanical properties and the true stress-true strain curves are determined with uniaxial tensile tests pursuant to [26].The strain rate is set to 0.667%/s according to [27].The properties of the die-sided steels are also determined with uniaxial tensile tests and a strain rate of 0.4%/s with accordance to [28].Table 1 shows the mechanical properties of AA7075 in the W and the T6 temper and of the two die-sided sheet materials.
In the W temper, AA7075 has a distinctly lower strength and higher ductility than for the artificially aged T6 temper, promoting the formability of the alloy.The strength of diesided 22MnB5 is about twice as high as that of HCT780X.In contrast, the ductility is distinctly lower.Shear-clinching is conducted for all four possible material combinations with AA7075 on the punch side in order to validate the presented numerical model of the joining process.The W temper also serves as reference for the locally limited softening of AA7075 T6.
Figure 1 shows the true stress-true strain curves for the different materials and heat treatment conditions of AA7075.In [25], the effect of the retrogression heat treatment on the mechanical properties of AA7075 T6 and its flow behavior were discussed.Distinct softening occurs for retrogression at temperatures of 300 °C and higher.For lower temperatures, the mechanical properties and the flow behavior are comparable to the T6 temper [25].For 400 °C, the strength is similar to the W temper.
The determined true stress-true strain curves serve as input for modelling the material properties within the shear-clinching simulation.For this purpose, the true stress-true strain curves of AA7075 and 22MnB5 are approximated with the Hockett-Sherby model [29] in

Approximation Experimental Data
Fig. 1 True stress-true strain curves of used materials, retrogression heat treated AA7075 according to [25] order to allow their extrapolation for higher strains.In case of HCT780X, the approach by Swift [30] is used.

Setup for heat treatment
The retrogression heat treatment of AA7075 T6 is conducted with a diode laser Laserline LDM-3000.The laser has a maximum power of 3 kW and emits light with a wavelength of 900 to 1070 nm.The beam is either shaped with a zoom optics Laserline OTZ-2, which forms a rectangular spot with a width and length of 5 to 45 mm or with an optics Laserline OTS-5, which forms a circular spot with a diameter of 1.9 mm.Both optics are mounted to an industrial robot to realize flexible heat treatment layouts.The beam can either be stationary, which allows the setting of temperatures, heating rates and soaking times, or it can be moved across the specimen's surface, in which case the temperature and the scanning speed can be set.
The temperature of the radiated area is surveilled with a pyrometer, which is part of the laser control.For the optics OTZ-2, the laser power is controlled by the system depending on the measured temperature.For the optics OTS-5, the power-time curve is given and no temperature control is used.Due to the small laser spot of the OTS-5 optics, less than 5% of the maximum power is necessary for the heat treatment, which makes the temperaturebased process control more difficult leading to overshoot of the set temperature.In addition, the temperature of the whole specimen's top surface is recorded with a thermal camera FLIR SC7600 allowing the analyses of temperature distributions and local temperature-time curves.The specimen's top surface is sprayed with graphite to increase the absorption of the laser beam.For graphite, an emission coefficient of e = 0.95 is reached [31].

Setup for shear-clinching
The joining sequence can be divided into four principal steps (Fig. 2).After positioning and fixing the joining partners in the tool, the sheets are pressed into the die by the movement of the inner and the outer punch.The lower sheet is hereby indirectly cut, the upper sheet is drawn into the cut-out hole.When the anvil reaches its hard stop, the upper sheet is laterally extruded, which leads to the formation of an interlock.The cut-out slug remains within the tool during the joining sequence and is removed after retraction.
The setup, which is used for shear-clinching, is displayed in Fig. 3.The tool is installed in a universal testing machine Walter + Bai LFEM-300, which allows the application of a maximum testing force of 300 kN.For determining the punch force and displacement, the machine data is utilized.All active tool elements are mounted to individual carrier plates.The inner punch plate is connected with the outer punch plate via springs, which allows the relative movement of the punches in dependence of the process force.The blank holder plate and the outer punch plate are also connected via springs.Thus, the springs of the outer punch and of the blank holder are set up in series.The outer punch springs are pre-loaded with 29 kN and have a stiffness of 4600 N/mm.The blank holder springs are pre-loaded with 1 kN and have a stiffness of 1200 N/mm.
The die and the anvil are mounted to the base plate to which the outer punch plate and the inner punch plate are guided with guiding pillars.The die is slit, which allows the four lamellae to elastically deform during the process promoting the forming of an interlock.The anvil is also springloaded with a spring stiffness of 350 N/mm.Its displacement is limited by a hard stop, which defines the die depth.Within the scope of this work, the die depth is set to 1.8 mm.The counter force is necessary to enable the lateral material flow during the upsetting phase.
For the analysis, an inner punch with a diameter of d i = 5.4 mm is used.The outer punch has a conical shape

Blank holder Aluminium sheet
Steel sheet 3 Numerical modelling of short-term heat treatment assisted shear-clinching

Modelling of the heat treatment
For modelling the heat treatment, a 3D model is required (Fig. 4) in order to model the heat flow within the sheet, which is axisymmetric but not rotational symmetric.Thus, the laser beam has a differing distance to the specimen's edges.Energy is put into the surface by radiation.The heat is then conducted within the sheet plane and in thickness direction.Two different heat treatment layouts are to be analyzed namely a circular layout and a ring-shaped layout.
For the circular layout, the beam is stationary during the heat treatment.Thus, a quarter model of the process is sufficient as the definition of symmetry planes also allows the mirroring of thermal boundary conditions.In the xy-symmetry plane, the temperatures of the nodes are analyzed for the subsequent shear-clinching.Equal to the shear-clinching model, the mesh size within the xy-plane measures 0.05 mm.The length of the elements in z-direction is 0.2 mm.
In case of the ring-shaped layout, the beam is moved across the specimen.Thus, the whole sheet must be modelled.However, in order to save computation time, the quarter model, which is displayed in Fig. 4a is supplemented by a second part, which represents the rest of the sheet (Fig. 4b).Thus, two different mesh sizes can be used and the cutting plane, in which temperatures are analyzed for the subsequent shear-clinching simulation, is maintained.For the second body, a mesh size of 0.2 mm is used.By setting a heat transfer coefficient of α = 1,000,000 W/(m 2 • K), the two bodies behave like one.
A heat transfer coefficient of λ = 145 W/(m • K) and a specific heat capacity of c p = 862 J/(kg • K) are assumed for AA7075 [33].As boundary conditions, heat exchange by radiation and convection are considered.The specimen's top surface is sprayed with graphite.In accordance with [31], an emission coefficient of e = 0.95 is set.For the other surfaces, a coefficient of e = 0.3 is assumed.Within the real process, the specimens are placed on a holder with a surrounding overlap of 1 mm.Thus, heat can dissipate by conduction.This boundary condition is not modelled as the influence is estimated as minor due to the small overlap.
For the stationary laser beam, the heat input is modelled with *BOUNDARY_FLUX_SET.For this purpose, the power density of the laser has to be defined equaling the power divided by the irradiated area multiplied with an efficiency coefficient.A coefficient of 0.6 was found to be suitable, leading to good accordance with experimental data.The base power is scaled over the time, in order to set the desired heating rate, temperature and soaking time.Figure 5 shows the temperature-time curve for the middle of the specimens, where the maximum temperature is measured.The spot size was set to 8 × 8 mm 2 , the desired temperature to 400 °C, the heating rate to 100 K/s and the soaking time to 1 s.A very good accordance between the experiment and the simulation is achieved.Only for the cooling sequence, the simulation slightly overestimates the temperature.On the right side of Fig. 5, the temperature distribution at the end of the soaking time, which is marked in the diagram, is shown.The distribution also displays good accordance between the simulation and the experiment.It must be considered that the color scheme slightly differs due to the use of different software.
In case of the ring-shaped layout and the moving laser beam, the heat treatment is modelled with the keyword *BOUNDARY_FLUX_TRAJECTORY. In this keyword, a base energy input rate is defined, which is equal to the maximum power of the laser multiplied with the efficiency coefficient.Moreover, the velocity of the beam is set.The path of the laser is defined by additional nodes, which form the middle diameter of the irradiated ring.The energy input is scaled by a *LOAD_CURVE resulting in the actual power, which is necessary to reach the desired temperature.Figure 6 shows the maximum temperature-time curve for the surface of the specimen and the temperature distribution at a chosen point of time.For the displayed case, a temperature of 400 °C was aimed for.The beam moves with a speed of 2.5 mm/s.The ring has a middle diameter of 8 mm and is irradiated twice equaling a rotation angle of 720°.
Regarding the temperature-time curve, a satisfying accordance is achieved between the simulation and the experiment.The measured maximum temperatures are almost equal.However, at the beginning and at the end of the process, there are deviations of up to 50 °C regarding the maximum temperature at the surface, which can also be explained with errors caused by combusting graphite.However, for the marked position, a very good accordance is achieved during the heating phase.Yet, as can be deducted from the depicted temperature distribution, the heating of the non-irradiated surface is slightly overestimated, which leads to differences regarding the cooling behavior.

Modelling of shear-clinching process
For modelling the shear-clinching process, rotational symmetry of the process is considered and a 2D model is used (Fig. 7).Computing is done explicitly with time and mass scaling.The whole joining sequence is conducted within 0.01 s.Mass scaling results in added masses of approximately 50%.For computing the simulation, the SMP solver with double precision in the revision R12.0 is used.
All tool elements are defined as rigid bodies.The stiffness of the individual parts was determined with numerical simulations.Springs with according stiffness values are added to the shear-clinching simulation to model the elastic deformation behavior of the tool elements under load.The stiffness has a decisive influence on the maximum punch displacement, which has to be set, and on the resulting stress distribution in the deformed sheets.In case of the anvil, the part's stiffness also has an influence on the joint formation during the upsetting phase [34].Yet, stiffness of the carrier plates and the universal testing machine is not considered.Thus, the maximum punch displacement must be adapted within the simulation to s max = 3.2 mm.In comparison, a value of s max = 3.6 mm was set for the experiment.
The outer punch spring, the blankholder spring and the anvil springs must be modelled anyway.The stiffness of the springs and the stiffness of the actual parts are cumulated for the outer punch and the blankholder, whereby a series connection is assumed.For the anvil, two cases must be differed (Fig. 8).Before the anvil has reached its hard stop (Fig. 8a), only the stiffness of the spring is considered.When the anvil has reached its hard stop (Fig. 8b), parallel connection is assumed.However, due to the distinctly lower stiffness of the spring in comparison to the anvil itself, the spring stiffness can be neglected for case b.
For the die, stiffness in axial and radial direction is considered.As the die is slit, the four individual lamellas can elastically deform.Due to the assumption of rotational symmetry and the use of a 2D model, the individual opening of the lamellas is not possible in the numerical model.However, the radial stiffness of the lamellas was determined in a simulation according to [13] and is considered by the radial die spring.
Apart from the die, the element size measures 0.1 mm for the tools.As the load localizes on the cutting edge of the die during the cutting phase [35], the mesh of the die is slightly finer, measuring 0.05 mm.The mesh size of both sheets is 0.05 mm, too.2D r-adaptive re-meshing is activated, re-meshing the elements of the joining partners with a frequency of 0.0002 s.
For friction, a coefficient of µ = 0.3 is assumed, which has led to the best results.In [34], Müller has determined a friction coefficient of µ = 0.5 as suitable for the software Simufact Forming 12.0.However, in [17], Hörhold assumed a friction coefficient of µ = 0.25 for the contact of the lower sheet to the die and a coefficient of µ = 0.15 for the remaining contacts using Simufact.Forming 13 for her investigations.In [14], Busse has used coefficients of µ = 0.15 for the contact of the die and the lower sheet and µ = 0.12 for the other contacts.Busse has used the software DEFORM 10.2.Overall, a relatively large variety of friction coefficients has been utilized for modelling the shear-clinching process, indicating that the influence of this parameter on the numerical result is rather low.
When the temperature is not considered, materials are modelled with *MAT024-PIECEWISE_LINEAR_PLAS-TICITY.When the temperature is taken into account, the material *MAT255-PIECEWISE_LINEAR_PLASTIC_ THERMAL is used for the upper sheet.For the die-sided sheets, *MAT024-PIECEWISE_LINEAR_PLASTICITY is used in both cases.Either way, hardening behavior is described by an actual flow curve, which is defined with *DEFINE_LOAD_CURVE.The thermal properties of the parts are set with *MATT01-THERMAL_ISOTROPIC.
Damage is modelled with *MAT000-ADD_DAMAGE_ GISSMO and failure strain-triaxiality curves.The failure strain of AA7075 T6, 22MnB5 and HCT780X was determined for shear stress, uniaxial tensile stress and biaxial tensile stress.With the experimental data, failure strain-triaxiality curves have been approximated with the Hosford-Coulomb [36] model and the Excel solver using the least squares method.Figure 9 shows the derived curves.
For HCT780X, a distinctly higher failure strain is present for uniaxial tensile stress (η = 0.33) in comparison to the less ductile 22MnB5 and AA7075 T6 due to a higher influence of the Lode angle on the failure strain.In addition, for compressive stresses (η < 0), the failure strain distinctly increases.For the other two materials, the increase of the failure strain for compressive stresses is lower.This applies in particular for AA7075.Generally, the failure strains for all stress states are lower for 22MnB5 and AA7075 T6 than for HCT780X.Still, failure strains for 22MnB5 are slightly higher than for AA7075 T6.Yet, towards the biaxial state (η = 0.66), the failure strain-triaxiality curves are approaching each other.

Coupling of simulations
Depending on the heat treatment layout and the process control during the heat treatment, the mechanical properties of precipitation hardenable aluminum alloys and therefore property gradients in sheets can be set.Thus, there is a relationship between the local maximum temperature during the heat treatment and the resulting strength.This circumstance is used to couple the heat treatment simulation and the simulation of the shear-clinching process (Fig. 10).Despite the shear-clinching process being conducted at room temperature, the joining sequence is computed as thermomechanical simulation to model the influence of the heat treatment on the local properties of the punch-sided sheet.Apart from the upper sheet, which is heat treated, for all components a temperature of 20 °C, which equals the room temperature, is assumed.For the upper sheet, the temperatures are taken from the heat treatment simulation.
The mesh at the sectional plane A-A is equal to that of the upper sheet in the shear-clinching simulation.Within this plane, for each node, the temperature history is exported as ASCII-based text file.Using a self-developed Python script, the maximum temperature is determined for each node.The maximum temperature is then mapped to the nodes of the upper sheet in the shear-clinching simulation.While the nodes may differ regarding their identification number NID, the script identifies the nodes by their coordinates, which are equal due to the same mesh size and positioning.The keyword *INITIAL_TEMPERATURE_ SET is written in a text file and can be added to the input deck of the shear-clinching simulation.
For the upper sheet, the initial temperature of each node equals their maximum temperature during the heat treatment.To maintain the temperature profile throughout the whole joining sequence, the conductivity of the parts is set to λ = 0 W/(m • K) and the specific heat capacity to c p = 1E + 28 J/(kg • K).By the use of the material *MAT255-PIECEWISE_LINEAR_PLASTIC_THER-MAL, true stress-true strain curves are assigned to the individual nodes of the upper sheet in dependence of the present temperature.The curves were determined for the condition T6, which represents the condition at room temperature, as well as for retrogression annealed specimens, which were heat treated with 200, 250, 300, 350 and 400 °C [25].This approach allows the setting of strength gradients in dependence of the locally present temperature during the pre-conditioning of the sheets.

Process analysis for heat treatment conditions T6 and W
To validate the shear-clinching model and the determined damage values of the GISSMO criterion, the process is analyzed for AA7075 in the heat treatment conditions T6 and W. The validation of the process chain is conducted in the next step.Figure 11 shows the force-displacement curves for the four material combinations from the experiments and the simulations.The numerical simulation very well reflects the characteristic curve progressions of the shear-clinching process.For the combinations with die-sided 22MnB5, there is a distinct change of the curve's curvature between the drawing and the upsetting phases.In contrast, for HCT780X, the curvature does not change between the two phases.The punch displacement is set to 3.6 mm for the experiments.As the elastic deformation is considered only for the active tool elements, but not for the universal testing machine and the carrier plates of the tool, there are deviations regarding the stiffness of the numerical and the experimental setup.Since the lower stiffness of the experimental setup leads to a reduced actual punch travel, the punch displacement has been set to 3.2 mm for the simulation.Yet, it is obvious that for HCT780X, the numerical model represents the displacement at the cut of the lower sheet better than for 22MnB5.For both die-sided materials, the influence of the properties of the upper sheet on the cutting stroke s C is well represented.For 22MnB5, the cut of the lower sheet occurs at lower displacements for AA7075 T6 in comparison to the W temper.In contrast, for HCT780X, there is no distinct difference for the two heat treatment conditions.
The cutting force F C is in good accordance for 22MnB5.For HCT780X, the cutting force is slightly overestimated.Especially for the material combination with AA7075 W. As concerns the maximum joining force F max , there is the tendency that the force is underestimated, which may be explained with the reduced punch stroke.An exception is the combination AA7075 T6 / 22MnB5.However, the between experiment and simulation are less than 6%, which is considered as acceptable.On this basis, the numerical model should be further developed in the future in order to achieve an even higher accuracy.
Figure 12 shows the micro-sections and measured joint characteristics for both die-sided sheet materials and AA7075 in the W temper.For this heat treatment condition, AA7075 can be shear-clinched without failure.
For both die-sided joining partners, the numerical model shows good accordance regarding the joint geometry.The differing fracture behavior of the hot stamped 22MnB5 and the more ductile HCT780X is very well modelled.Regarding the characteristic features of the joint, the residual bottom thickness t b is lower in the numerical model.In contrast, the lower neck thickness t ln matches for both die-sided materials.The upper neck thickness t un coincides for HCT780X.For 22MnB5, deviations are slightly higher.Moreover, for 22MnB5, the fracture angle β is underestimated.Thus, the interlock f is also smaller in the simulation.For HCT780X, these features are well reflected by the simulation.The rollover height r and the fracture height b are in good accordance for 22MnB5.For HCT7800X, the rollover height r is slightly overestimated.Consequently, the fracture height b is underestimated by the simulation.For AA7075 T6, the upper sheet fails during joining [11].Thus, the characteristic features cannot be measured.Figure 13 shows micro-sections of the joints for punch-sided AA7075 T6 after the fracture of the upper sheet and at the end of the joining sequence.
For die-sided HCT780X, very good accordance regarding the joint geometry is achieved.The crack propagation of the upper sheet is equal to the experiment.In addition, the crack occurs at almost the same punch displacement.For 22MnB5, the crack of the upper sheet occurs at a higher punch displacement in the simulation.Moreover, due to the reduced rollover of the lower sheet in the simulation, the angle of the crack slightly differs from the experiment.Within the experiments, a varying crack propagation was observed for 22MnB5.The crack either propagates from the transition of the rollover and the fracture height to the radius of the inner punch or to the transition of the outer punch phase and the conus.In the simulation, the latter is the case.
Overall, the simulation model of the shear-clinching process shows a satisfying accordance with the experimental data.There are deviations regarding some geometrical features and the punch displacement.Due to the high process forces during joining, the elastic tool deformation has a high influence on the punch travel and the joint formation.Yet, only the stiffness of the active tool elements is considered within the numerical model causing deviations in comparison to the experiments.Still, the model correctly represents the influences of the heat treatment condition of AA7075 on the joining process and on the resulting joint geometry.It is therefore suited for the further analysis of the different heat treatment layouts.

Local heat treatment for the control of the material flow
Following, the influence of a locally limited retrogression on the material flow of AA7075 in the shear-clinching process is analyzed with the presented models.Figure 14 shows the distribution of the maximum temperature of the upper sheet for the two analyzed layouts after mapping them to the 2D shear-clinching simulation.Depending on the heat treatment layout, a different temperature gradient is set in the sheet.For the stationary beam and the central irradiation, the highest temperature is reached in the middle of the specimen.Towards the edge of the sheet, the maximum temperature declines.This leads to the gradual softening of the sheet in x-direction.In the middle of the sheet, softening is most pronounced, while the strength at the edge remains on a high level as only temperatures of circa 200 to 250 °C are reached.Thus, softening is only minor [25].
In contrast, for the moving beam and the ring-shaped layout, the highest temperature is situated at the top surface of the specimen at the irradiated diameter.A temperature gradient towards the lower surface, the specimen's middle and its edge is set.Thus, the area at the beam trajectory is softened the most.In comparison to the stationary beam, the specimen becomes warmer at the not irradiated area, which is due to the distinctly enhanced process time and the therefore enhanced overall energy input.Following, the influence of the heat treatment layout on the material flow and the joint formation are analyzed.
Figure 15 shows the experimental and numerical joint geometry for both layouts and die-sided 22MnB5.
Similar to the simulation of the W temper, the residual bottom thickness t b and the fracture angle β are smaller than in the experiments.In contrast, the lower neck thickness t ln is slightly larger, as the rollover r of the lower sheet is slightly underestimated.This applies for both layouts and indicates that the damage model has to be improved in the future.However, the simulation very well reflects the increase of the upper neck thickness t un and of the interlock f in comparison to the W temper.For the circular layout, the upper neck thickness t un is also slightly larger than for the ring-shaped layout.This effect of the heat treatment layout is also well reflected by the simulation.
Figure 16 shows the effect of the locally limited softening of AA7075 T6 on the material flow in comparison to joining AA7075 in the W temper.To set the W temper, the sheets are fully solution annealed in a furnace.Thus, they have homogeneous properties.
Within the cutting phase, the radial material flow of the upper sheet is reduced for the local heat treatment.This applies for both layouts.However, for the ring-shaped layout, the axial material flow in the area of the inner punch is enhanced in comparison to the circular design.In the drawing phase, there is also a distinct reduction of the radial material flow for the locally heat treated sheets.In contrast, for the W temper, there is a distinct radial material flow in the area of the outer punch conus present.The material flow in the lower neck area is almost equal for the three variations.The same applies for the material flow during upsetting.However, for the W temper, there is still a low radial material flow in the area of the outer punch conus present.
For the locally heat treated sheets, the areas, which were not softened, prevent the radial material flow during the joining sequence.As a result, the upper neck thickness t un and the interlock f, which are critical for the strength of shearclinched joints, become larger.The application of local heat treatments for AA7075 T6 therefore allows the control of the material flow in the joining process and the improved joint formation.
Figure 17 shows the experimental and numerical joint geometry for the two heat treatment layouts and die-sided HCT780X.The dual phase steel has a distinctly lower strength than hot stamped 22MnB5.
Similar to the simulation of the W temper, the residual bottom thickness t b is underestimated by the simulation while the lower neck thickness t ln is overestimated.Latter can be explained with the smaller rollover r in the simulation.However, the influence of the local heat treatment on the upper neck thickness t un and on the interlock f is very well reflected by the simulation.In comparison to the W temper, both features become larger.In addition, for the circular layout a slightly larger upper neck thickness t un is formed in comparison to the ring-shaped design.Figure 18 shows the effect of the locally limited softening of AA7075 During the cutting phase, there is no distinct difference regarding the occurring material flow for the three variants.In comparison to 22MnB5, the radial material displacement is vastly reduced, which is in good accordance with the findings in [32] for the software Simufact.Forming.For the drawing phase, a reduction of the radial material flow is achieved for the local softening of AA7075 T6 in comparison to the W temper.However, the effect is rather minor.For the upsetting phase, there is also only a minor influence of the heat treatment condition and the heat treatment layout on the material flow in the bottom area of the joint.Due to the increased material volume in the joining zone, the radial material flow in the bottom is reduced for the locally heattreated variations in comparison to the W temper.

Conclusions and outlook
Within the scope of this work, an approach for the numerical modelling of local pre-conditioning of precipitation hardenable 7xxx aluminum and subsequent mechanical joining is shown.Numerical models for the local heat treatment and for shear-clinching are presented and validated for different heat treatment conditions of AA7075, for two different heat treatment layouts and for two die-sided joining partners.From the investigations, the following conclusions are drawn: • The indirect shear-cutting of the die-sided joining partner in the shear-clinching process can be modelled with the GISSMO damage criterion, using the software LS-DYNA.In addition, failure of the upper sheet during the joining sequence can be predicted, too.For the presented model and the determined failure strain-triaxiality curves, a good accordance for the crack propagation in punch-sided AA7075 T6 was achieved.Yet, the damage model still needs further improvement, especially for modelling the crack propagation in die-sided hot stamped 22MnB5.
• A phenomenological material model is suitable for the continuous modelling of the retrogression of 7xxx aluminum and the subsequent joining process.By a thermomechanical coupled simulation of the joining process and the definition of adequate thermal boundary conditions, the set gradient of the temperature and therefore of the mechanical properties is maintained throughout the whole joining sequence, which is regarded as quasiwarm.• Shear-clinching of AA7075 in the fully solution annealed W temper is feasible for die-sided HCT780X and 22MnB5.The homogeneous softening of the upper sheet results in the enhanced radial material displacement during the joining process.• Local softening of AA7075 T6 is sufficient to ensure the joinability of the alloy in the shear-clinching process.Both, circular and ring-shaped layouts are possible heat treatment designs for rotational symmetric joining processes.The heat treatment layout allows the control of the material flow in the process.The effect of the layout and the resulting property gradients in the sheet on the resulting joint geometry are well reflected by the presented numerical models.• The influence of the heat treatment condition and of the applied heat treatment layout is higher for 22MnB5 than for HCT780X.Due to higher strength of the hot stamped 22MnB5, the radial material flow of the upper sheet is generally higher than for HCT780X.Thus, the locally limited softening has a stronger impact on the material flow.
Due to the large variety of possible heat treatment layouts and parameters, in future investigations, their influence on the material flow of hardenable 7xxx aluminum in shear-clinching process has to be analyzed in detail.In addition, the presented numerical models should be enhanced by the failure prediction of AA7075 T6 in dependence of the temperature during retrogression.Hereby, suitable heat treatment layouts and parameters can be designed efficiently and failure of the upper joining partner can be predicted without cost extensive trial and error.Yet, the damage model also needs further improvement for a better prediction of the joint geometry, especially regarding the fracture angle of the lower joining partner.
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Fig. 5
Fig. 5 Temperature-time curve and temperature distribution at the end of the soaking time for a stationary laser beam

Fig. 6 Fig. 7
Fig. 6 Temperature-time curve and temperature distribution at the marked time for a moving laser beam

Fig. 8
Fig. 8 Force flow for the anvil during a cutting and drawing and b upsetting

Fig. 11
Fig. 11 Process forces in dependence of the heat treatment condition of AA7075 and the die-sided joining partner

Fig. 12
Fig.12 Comparison of joint geometry for punch-sided AA7075 W

Fig. 13
Fig. 13 Comparison of joint geometry for punch-sided AA7075 in T6 temper

Fig. 14 Fig. 15
Fig. 14 Temperature distribution of the upper sheet after mapping of the nodal maximum temperature

Fig. 16 Fig. 17 Fig. 18
Fig. 16 Material flow in dependence of the heat treatment condition and layout for die-sided 22MnB5