Advancements in extrusion and drawing: a review of the contributes by the ESAFORM community

The die is the main tool involved in the extrusion process that is used to shape the final profile by the flowing of the material throughout its opening. Die design represents a key step in the process optimization since it strongly affects not only the die lifetime itself but also the profile quality and the overall process productivity. During its service life, die is subjected to critical thermal and mechanical loads that can lead to different types of failures mechanisms. In 2006, Mousoulis et al. [1] studied the premature failure of the mandrel part of an H13 die, designed to produce 40.000 kg of an aluminum profile but that fractured after only 500 kg. The authors realized only visual and microscopic inspections of the die and they gained the conclusion that fracture was caused by shearing stress in weak section thus evidencing an incorrect dimensioning of the mandrel ribs. In 2010 Irgens et al. [2] analyzed the effect of the insertion of a shadowing tongue with the aim to reduce the load acting on the main tongue used in case of U-shaped or semi-hollow profiles geometries. Authors evidenced by means of numerical simulations with DEFORM 2D code a decrease of more than 30% of local stress, even if accompanied by an increase of the overall extrusion force. In the same year, Reggiani et al. [3] compared two different numerical codes in terms of predictability of the stress level induced in a die during operation and proved the need of advanced constitutive models of the tool steel for a reliable estimation of die life and damage, as that proposed by the same authors in 2011 [4]. In 2021, Lechner et al. [5] performed an experimental–numerical (DEFORM 2D code) campaign aimed at investigating the level of residual plastic deformation (die deflection) in the proximity of the die bearings during high temperature CW024A copper extrusion. In this work, four tool materials (hot work tool steel 1.2367 and CS1, Ni-based 718, Co-Cr Stellite 1 alloy) were compared concluding that Ni-based alloy was the most suitable for the specific application. In addition to withstanding of the severe process loads, the die must be designed with the aim of generating sound profiles (defect-free, with high mechanical properties, within the required tolerances) and to guarantee the required level of productivity. Thus, many contributions reported in literature have been focused on the investigation of the effect of die geometric variables on these two process issues. In 2009, Donati et al. [6] experimentally tested the effect of four different pocket shapes, two different profile thicknesses and two extrusion speeds on the material flow inside the die showing a significant impact on the profile exiting velocities, especially at high speed (Fig. 1). Afterwards, in 2012, the same authors investigated and compared different strategies in balancing material flow during direct extrusion of an AA6082 hollow profile [7]. In more details, two different strategies were evaluated, one by the use of bearings, the other by the use of porthole area and position to correct and balance the flow. It was proved that the latter solution provided not only longest profiles but also less critical conditions in terms of surface quality, but with the counterbalanced effect of generating seam welds very far from bridge position thus being potential critical for final profile applications. In 2015, Negendank et al. successfully proposed an innovative axially moveable stepped mandrel to manufacture tailored aluminum (AA6060) [8] and magnesium (AZ31) [9] profiles with variable wall thickness in order to control the profile cross section dimension according to the expected loads applied during technical application. Accounting for the influence of the die elastic deformation on the product quality as consequence of the pressure applied by the material under deformation, in 2017 Biba et al. [10] developed in QForm VX a novel integrated numerical approach that couples the FE model of the material flow with the deformation and temperature distribution in the die. Recently, with the aim of finding solutions capable of simultaneously optimizing the die life, the quality of the product (avoiding thermally induced defects) and productivity, several works have been focused on the numerical and experimental investigation of die cooling. In 2014, Holker et al. [11] manufactured a novel die design concept with inner cooling channel by Selective Laser Melting (SLM) as well as by Layer Laminated Manufacturing additive technologies. The study used water as cooling media and revealed the potential of the solution in increasing the productivity of 300% for an AA7075 alloy. The cooling improved also the surface quality of the profile furthermore reducing the formation of coarse grains on profile surface. Following these results, in 2020 Pelaccia et al. [12] manufactured an H13 insert with a cooling channel by SLM, successfully testing its performances during the extrusion of aluminum AA6063 and magnesium ZM21 alloys cooled with liquid nitrogen. In addition, an innovative numerical model was developed in COMSOL Multyphisics coupling the extrusion process simulation with nitrogen cooling, showing error less than 7.5% if compared to experimental data. The model was then validated by the same authors on an industrial complex AA6060 profile cooled by liquid nitrogen flowing into a channel milled on the mating mandrel-die face [13]. The experimental–numerical matching returned again a very good agreement and encouraged the use of the model for a rapid channel redesign in order to attain a more thermal-balanced and productive die configuration.

Proper temperature control is fundamental during the entire extrusion process, as the material properties, the final microstructure and the profile shape are strictly connected to the management of the thermal problem. Several studies have been carried out in the past years for the investigation of the temperature distribution on the material during the process. In 2005, Moe et al. [14] carried out an experiment for the evaluation of the temperature distribution on AA6060 billets heated through electromagnetic induction before the extrusion process. The induction heating of billets was simulated by the finite element code Ansys to compare the results with experimental ones. Cooling subsequent to extrusion is also a crucial aspect of the process. In this context, Jäger et al. [15], in 2009, investigated the quenching process effected directly behind the die after curved profile extrusion (CPE). A forced air quench system was tested on extrusion of thin wall tubes in EN AW-6082 aluminum alloy. In 2010, Bikass et al. [16] studied through numerical simulation only the shape distortion due to non-uniform and asymmetric cooling by using Abaqus/Standard software in the extrusion of an AA 6082 aluminum alloy rectangular profile. In the same year, Farjad Bastani et al. [17] analyzed the isothermal extrusion process of aluminum by the use of the 3D finite element software Altair HyperXtrude and the 2D finite element software ALMA2π. They provided the best combination of process parameters and the so called “isothermal maps” for each phase of the press cycle (Fig. 2).

The extrusion of heavy metal (i.e. copper or steel) involves high forming temperatures and high flow stresses. Semi-solid extrusion could be an alternative forming process due to the reduced flow stress. It combines the advantages of conventional casting and forging: forming has to take place in the semi-solid state, followed by a slidification step. In 2007, Neag et al. [18] carried out backward extrusion tests to examine the rheological behavior of a semi-solid Al-Si hypoeutectic alloy. With a mixed experimental–numerical method, by using the finite element code FORGE, they showed that Norton-Hoff model is insufficient to describe some characteristics of the semi-solid behavior. Two years later, Knauf et al. [19] studied the semi-solid extrusion applied to a ledeburitic cold working steel billet of X210CrW12. The experiments were performed by changing the main process parameters to detect their influence on the extruded products concerning chemical composition, microstructure and mechanical properties (Fig. 3).

Among the main difficulties for the development of a reliable numerical model of the hot extrusion process, the definition of the friction conditions at the material-tool interface plays a significant role. In 2005, Logé et al. [20] developed a small-scale extrusion method for the experimental determination of friction forces between the container and the billet. This method was applied to the extrusion of Zircaloy-4 (Zy-4) bars and tubes, while the rheological behavior of the material has been identified from uniaxial compression tests. Comparing the experimental activity with the numerical simulation by means FORGE finite element code, they identified a modified Coulomb law for an improved description of the friction at the billet-mandrel interface.

Few years later, in 2014, Sanabria et al. [21] investigated the friction boundary conditions during the extrusion process by using a new axial friction test, developed at the Research and Development Centre of UT Berlin. They studied the tribological behavior of aluminum alloy AA6060 and Magnesium alloy AZ31 against hot working steel 1.2344. The friction boundary conditions such as temperature, normalized normal stress and relative sliding speed were investigated and, in addition, the tested specimens were analyzed with OLM (Omnipresent Localization Microscopy) to investigate the variation in thickness of the shear zone and microstructure. The same experimental axial friction test was carried out in 2020 by the same authors [22], in order to investigate the thermo-mechanical behavior of the magnesium alloy AZ31B, to improve the constitutive modelling up to high strains (ε > 1). Moreover, friction tests were numerically simulated applying the FEM-based software DEFORM 2D. The Zener-Hollomon (Z-H) as well as the Hansel-Spittel (H–S) constitutive models, based on experimental data from hot compression tests, were evaluated during the simulations. From the comparison between experimental tests and simulation, a new strain-dependent multifunction model (SDM) was proposed.

As any manufacturing process, also extrusion is characterized by a proper set of defects that are intrinsically related to the process set up (seam welds, charge welds and coring) or caused by an improper selection of process parameters (streaks, chevron cracks, tears and others). Among the former set, seam (longitudinal) welds are generated during the extrusion of hollow sections due to the material split around the legs of the mandrel and the subsequent re-joint to produce a continuous profile. This material behavior implies that any hollow profile, for each leg, is affected by welds that extend all long the entire profile length, thus explaining the wide literature on the topic. In details, published works on the topic have been focused on three main research lines: investigation on the effect of process and die-design parameters on welds quality, set up of novel testing experimental methods and development of advanced numerical models.

In 2005, Donati and Tomesani [23] tested samples extracted by H-shape AA 6082 profiles extruded with different die geometries and process parameters. The authors proved the influence of the welding chamber height and pressure for the achievement of sound welds. Moreover, it was also verified that elongation at fracture in tensile tests is the parameter most sensitive to welding conditions inside the die. The latter criterion was then used by the same authors, in 2007, to assess the better performances of blade shaped if compared to square shaped legs in the extrusion of an AA 6060 round tube [24]. Conversely, blade legs were most sensitive to creep failure mechanism in relation to the higher mean stress, as numerical assessed by the DEFORM 3D code. The level of achieved pressure and radial elongation at fracture in a bulge test was used in 2012 by Segatori et al. [25] to test a new die for magnesium ZM21 alloy designed to increase, by a more uniform strain, the production rate. In 2005, Ghiotti et al. [26] proposed a novel experimental procedure able to reproduce, at laboratory scale on a Gleeble machine, the welding of two streams in the typical industrial operating conditions of the extrusion process in terms of temperatures and normal-pressure-on-equivalent strain ratio. A different testing method has been set up by Valberg et al. in 2011 [27] to assess the seam weld quality based on a mandrel expansion test. In 2020, Dariusz and Pawel [28] developed an original device that shear and compress two alloy samples in a working movement under comparable conditions that occurs in the welding chambers. With fast computers and powerful programs developed in the first decade of 2000, the trend was mainly focused on investigating the extrusion seam welding by FEA, in order to predict actual state variables. Bonding mechanics in an AA6082-T6 aluminum profile were numerically and experimentally analyzed by Buffa et al. in 2007 and results discussed in terms of analogies with friction stir welding (FSW) solid state bonding [29]. In 2009 Ceretti et al. [30] presented a novel numerical approach able to simulate the real welding of the streams to avoid the persistent contact of the mesh elements, thus promoting a deeper understanding of the mechanism (Fig. 4). The model was used to investigate different die geometric configuration, corroborating the conclusion drawn by Donati and Tomesani in 2005 [23] on the impact of the welding chamber height on the seam welds formation.

Khan, Valberg and co-authors have done a significant contribution in the knowledge advancement of welds mechanisms in the extrusion process from 2009 to 2012. Important and in-depth information on how streams flow inside the mandrel ports [31] and on how this flow is affected by parameters like the shape of the legs (blade/pointed vs square) [32, 33] and port size [34] was gained by detailed analysis of numerical simulations (DEFORM code) and/or by comparing numerical outcomes with experimental data of visioplascticity (grid pattern analysis) (Fig. 5).

In 2012, Schwane et al. proposed a novel numerical method for the evaluation of the position and quality of seam welds in AA6082 profiles [35] and to account for a gas pocket in the welding chamber [36] by means of steady-state FEM simulations performed with the Altair HyperXtrude code. Accounting for the process complexity and the difficulties to manage all the involved variables, Gagliardi et al. [37], in 2017, suggested to adopt the Taguchi/ANOVA techniques in order to reduce the required number of simulations for the evaluation of the influence of twelve geometric variables on two selected responses (load and pressure in the welding chamber). As previously highlighted, other than seam welds, also charge welds (front-end) and coring (back-end) defects are intrinsically related to the extrusion process mechanism. Differently from seams, charge welds, generated due to the billet-to-billet interaction, affect only the new-old billet transition zone of the profile. However, a further difference is that charge welds are usually marked by much lower mechanical properties than the base material due to the interface contamination, thus requiring to be discarded for critical applications. Coring defect, instead, caused by the inflow of contaminated skin of the billet toward the core during the extrusion cycle, can be avoided if a proper discard length is selected for each billet. In 2020, Valberg et al. [38] applied FEM (DEFORM 3D code) and experimental grid pattern analyses to deeply investigate how contaminated skin inflow occurs and how subsurface layers flow behave with respect to the history of deformation. In the same year, Negozio et al. [39] simulated, with Altair HyperXtrude code, two industrial profiles made of AA6063 and AA 6082 aluminum alloys to predict front end and back-end defects and compared the achieved results also with the theoretical models available in literature to evaluate pros and cons of each approach.

In the last decades, lightweight alloys increasingly gained industrial interest in the almost all industrial sectors including automotive and aerospace. The mechanical properties are deeply affected by the microstructure, and consequently, research activities became of increasing interest in order to investigate the influence of process parameters on the grain size evolution and to develop microstructure prediction models. These activities challenged the lightweight alloys research community, in particular for the study of the microstructural behavior of aluminum and magnesium alloys. Concerning magnesium alloys, in 2010 and 2011, Gall et al. [40, 41] studied the effect of different extrusion temperatures on the microstructure of AZ31 plate profiles, in order to investigate the influence of the anisotropy on the mechanical proprieties. The authors found that the anisotropy is linked to the developed texture, which allows the activation of specified deformations modes in defined directions. In 2011, Ge et al. [42] studied the grain size evolution of AZ31B and ZM21 alloys during hot compression and laboratory-scale extrusions for the understanding of the influence of billet pre-heating temperature and strain rates on the recrystallized grain size. In 2018, Jaehnke et al. [43] combined and integrated the extrusion and the equal channel angular pressing (ECAP) in a single extrusion die, in order to decrease the anisotropy and the strength differential effect (SDE) through modification of the texture compared to conventional extrusion process. In 2019, Tomovic-Petrovic [44] studied the effect of Ni on the mechanical properties and formability of AZ91 alloy, combining experimental investigations and FEM analysis during extrusion trials. Concerning aluminum alloys, studies were performed comparing experimental investigations with the results of FEM simulations. In 2006 and in 2009, Fitta et al. [45] integrated into commercial FEM codes a physical model based on dislocation density, subgrain size and misorientation angle and they studied the influence of the substructure on the static recrystallization of a AA2024 alloy. In 2008, Krumphals et al. [46] carried out extrusions of AA6082 profiles and the data obtained were used to validate an integral finite element model and to assess the relative importance of the extrusion parameters on the microstructure of the profile. The use of the FEM for the investigation of the microstructure evolution was also made by Parvizian et al. in 2010 [47], with the aim of demonstrating the sensitivity of the grain size of an extruded AA6060 profile to processing conditions (Fig. 6).

In 2011, Segatori et al. [48] compared the experimental results of extrusions made at different process conditions of an AA6082 profile to the results of FEM analysis, thus proving that there is no influence of process temperature and ram speed on the dynamic grain evolution. In 2007, Sanabria et al. [49] carried out sticking friction experiments to understand the impact of temperature and sliding speeds on the sub-surface deformation and microstructure of a AA6060 alloy. The authors found that a severe deformation occurs below the friction surface, which is distinguished to the adjacent slightly deformed dendritic grains and quantified the thickness evolution of the high shear deformation zone.

In the aluminum extrusion sector, FEM codes have become one of the most important tools for process and product optimization. The complexity of the process, the high extrusion ratio and, consequently, the long simulation times with pure FEM lagrangian approach, led to an evolution over the years of the numerical tools and methodologies to gain accurate solving capabilities at reduced computational times. Different numerical approaches and methodologies have been proposed over the years in order to study the issues of the process or to exceed the limit of existing numerical model. In 2008, Koopman et al. [50] used an Eulerian approach combined to the smooth original coordinate function with the aim to study the die filling and the flow front at the die exit (Fig. 7). The experimental–numerical comparison with the extrusion of AA6063 round profiles showed a quite good matching in terms of flow front although no die deflection was taken into account.

In 2009, Alfaro et al. [51] proposed the simulation of round tube profile with the Natural Element Method (NEM) to investigate the formation and the quality of the seam welds. The comparison with the real experimental test confirmed the good prediction of the welding behavior during the extrusion process. In 2007, Abrinia and Makaremi [52] studied the three-dimensional problem of the extrusion of elliptical profile using the upper bound theory. The analysis of shaped sections with larger dimensions than the initial billet was performed by varying the extrusion ratio, the die length, the friction condition and the shape complexity. W. Two years later, Assad et al. [53] studied the boundary conditions applied on bearing corner nodes to satisfy the flow conservation condition in the Eulerian formulation. Again in the years 2008 and 2009, Ertürk et al. [54, 55] proposed a modification of the phenomenological Cazacu and Barlat model to consider the strain rate and the temperature dependency on flow behavior of magnesium alloys. Indeed, due to the hexagonal closed packed crystallographic structure, the magnesium alloys show mechanical anisotropy and tension–compression asymmetry if compared with aluminum alloys. The coefficients of the model were calibrated for ZEK 100 magnesium alloy by means of hot compression test, then the flow stress law was implemented into the commercial software Abaqus/Explicit to simulate an indirect extrusion of a round bar. Several works were presented about the study of the extrusion process in terms of material flow, thermal field and die deflection with the aim to present the improvement of FEM codes as supporting tools for the process design in the industrial framework. In 2010, Donati et al. [56] compared six different FEM codes in the simulation of two overlapped AA6082 U-shape profiles: one with fully supported opening, the other with partially supported opening. The experimental–numerical comparison showed a good codes prediction in terms of thermal field and extrusion load, but some limits emerged in terms of die deflection prediction (Fig. 8). In 2011 and 2012, Biba et al. [57, 58] showed the increased accuracy of the software QForm Extrusion by taking into account the influence of the die deformation on the material flow through the die. The comparison with different experimental case studies showed that the die deformation causes the alteration of the bearing area and the friction condition, thus influencing the material flow. In 2017, Kronsteiner et al. [59] compared the Update Lagrangian method (DEFORM code) with the Arbitrary Lagrangian Eulerian method (LS-DYNA software) for the extrusion process of AA6082 tube profiles. One of the major advantages of the ALE method concerns the overcoming of the contact problem of the mesh elements in the welding chamber obtained through the preparation of Eulerian mesh elements representative of the billet, the die and the extruded profile already at the beginning of the simulation.

Finally, some works were focused on the virtual optimization of the extrusion process, testing a large number of variables in an automatic way. In 2010, Caseiro et al. [60] used three different optimization methods to design an integrally stiffened panel (ISP) subjected to buckling for aircraft applications. The simulation of the buckling was performed by means of Abaqus software. The algorithm based on a Hybrid Differential Evolution and Particle Swarm Optimization attained the lower values for the cross-sectional area, leading to the better ratio between the buckling load limit and the structure weight. In 2013, Siegbert et al. [61] tried out an optimization framework on the extrusion of L-shaped profile using the balancing of the exit profile velocity as objective function. The geometry parametrization allowed to test different geometry features based on die maker experiences in automatic way.

Together with friction, the definition of accurate flow stress data is a critical task for the development of reliable numerical simulations. Flow stress data can be characterized by means of different testing method (tensile test, compression test, torsion tests) in the temperature, strain and strain rate range of the process under analysis. The hot torsion test allows to obtain the material flow characterization at high temperature, strain and strain rate typical of the hot extrusion process, overcoming the limits of the other tests especially in terms of achievable maximum strain. In 2011, Donati and El Mehtedi [62] characterized the flow stress of AA6082 by means of hot torsion test: four different alloys belonging to the 6082 nominal standards were tested to analyze the differences in terms of flow stress behavior influenced by differences in chemical composition, evidencing that is not possible to identify a single flow stress behavior for the whole AA6082 class. In addition, the procedure to obtain the parameters for sinhyperbolic flow stress to be implemented within the FEM codes is presented and discussed. In 2012, Bruni and El Mehtedi [63] presented a new multivariable regression analysis starting from the hot torsion characterization of ZEK 200 magnesium alloy in the temperature range of 150–450 °C. The division of the temperature range into two classes (150 °C-300 °C and 300 °C-450 °C) made it possible to obtain a better accuracy over the experimental data respect to the regression with a single temperature range (150–450 °C) thanks to the reduction of the parameters in the equation.

The main challenge in hot metal extrusion is achieving an equal exit speed in all sections of the profile. Indeed, complex interactions between die design, friction conditions and material viscosity usually produce an unbalanced exit speed thus generating different types of defects (surface tears, thinning of the profile and aesthetic defects) that severely limit the productivity of the process. The interaction of these phenomena is too complex to be modeled with analytical approaches and only the development of reliable FEM simulations has allowed to investigate this specific aspect. In order to evaluate the accuracy of the simulation on this issue, several articles have focused their attention on the experimental investigations and simulations of the metal flow during metal extrusion. In 2006, Valberg et al. [64] used a commercial FEM code (DEFORM code) to analyze the indirect hot extrusion of AA6082 alloy. Important information on the metal flow were achieved by comparing the numerical results with the grid patterns in the butt after experimental tests. The studies on the extrusion of the AA6082 continued in the following years, from 2010 to 2017, thus consolidating the knowledge on the reliability of FEM simulations with DEFORM software of the process (Fig. 9) [65‐67].

In 2006, Hansson [68] investigated the numerical prediction of the process load thus comparing experimental measurements made on the extrusion of stainless-steel round bars with the results of the FEM simulations using the Lagrangian code MSC.Marc. In 2007, Koopman et al. [69] compared the metal flow obtained by experimental tests on the extrusion of aluminum billets with the results of FEM simulation (software DiekA) integrated with a method for determining the frontlines inside the container and the die based on the steady-state velocity field. In 2005, Manninen et al. [70] studied the flash formation during OFHC (Oxygen-Free High thermal Conductivity) copper with Conform extrusions under different process conditions, developing an analytical model validated with FE-analysis using the Abaqus/Explicit code. In 2005, Wajda et al. [71] examined changes in temperature and pressure during strip extrusion of AA6060, providing information useful for the development of thermo-mechanical models of material flow. In the same year, Baron et al. [72] developed a numerical model into a commercial FEM code, which consists of the pre- and postprocessor PEP and the solver LARSTRAN/SHAPE, validated by comparing the results of the simulation to the data acquired during experimental extrusion tests on a ZM21 alloy. In 2009, Pathak et al. [73] studied the material modelling combined to the die and process design of rod extrusion of γ iron, using the finite element analysis (MSC Software) to find and test the optimized design, evaluating the stress, strain distributions and load requirements. In 2010, Valberg [74] described the importance of tracking back profile points during direct and indirect extrusions by means of a new approach that he named as “emptying diagrams”. In 2011, Y.A. Khan et al. [75] carried out extrusions with different portholes sizes and used the grid pattern technique to characterize the metal flow of AA6005 alloy. The results were compared to the outputs of 3D simulations using DEFORM software thus further proving the importance and the reliability of the grid pattern technique to characterize the boundary conditions of real experiments. In 2012, J. Kandis et al. [76] experimentally investigated the two-hole extrusion of two alloy, AA6063 and AA7108, and compared the results with FEM metal flow analysis using the DEFORM code. In 2013 and 2014, Khorasani et al. [77, 78] highlighted the differences between the theoretical velocity field obtained by Avitzur model and the one simulated by DEFORM code on direct, indirect and friction assisted extrusion. The velocity field was also studied by Valberg et al. [79], in 2014: the authors conducted an accurate FEM analysis with DEFORM code to understand the metal flow in case of asymmetric portholes. In 2016, Kronsteiner et al. [80] presented an innovative non-destructive method for the analysis the metal flow of an AA6082 through the use of a billet copper coating and subsequent computed tomography analyses. In 2018, Chen et al. [81] simulated a AA6063 alloy extrusion using the Altair HyperXtrude software of an asymmetric die and validated the results with experiments thus proving the reliability of the code. Moreover, the scheme of the die correction and optimization were discussed. In 2018, Galliac et al. [82] studied the production route of Zirconium alloy cladding tubes for nuclear applications. Manufacturing route was optimized by modelling of hot extrusion and cold pilgering processes with FORGE software. The cladding tubes non-acceptance ratio coming from surface defects was reduced by the mastering of the microstructure and surface quality of the extruded tubes, together with the optimization of the pilgering tools geometry. In 2018 and 2019, Valberg et al. [83, 84] investigated the metal flow and temperature conditions during industrial size extrusions of AA7108 alloy at different process parameters using FEM analysis (DEFORM code). In 2021, Habans et al. [85] developed a numerical model of the hot extrusion process using the FEM code FORGE NxT with experimental data from literature and used it to assess the feasibility of the extrusion of a large seamless hexagonal 9% Cr—1% Mo steel tube.

The topic deals with the development of hybrid structural components with the aim to exploit the combination of advantageous mechanical, physical or chemical properties of various materials within a single component. The papers presented during the ESAFORM conferences can be divided based on the different objectives to be achieved with the co-extrusion process: the co-extrusion of bilayer billet to obtain different properties in the core and in the surface, the co-extrusion of a mixture powder, the lateral angular co-extrusion to realize hybrid steel-aluminum tube and the co-extrusion of billet reinforced with continuous/discontinuous steel element to increase the mechanical strength of lightweight components (Fig. 10).

In 2021, Chen et al. [86] studied a process chain of compound casting and co-extrusion of AA7075/6060 bilayer billets to obtain hybrid components with strength in the core (AA7075) and good corrosion resistance in the shell (AA6060). Compared to the as-cast components, the hot extrusion ones showed high homogenization of the interfacial bonding, reduced voids and higher shear bonding strength (from 93.8 MPa to 145.9 MPa). In 2013, Negendank et al. [87] studied the indirect co-extrusion of assembled billets with the core in AZ31 magnesium alloy and the shell in AA6060 or AA6082 aluminum alloys. The macroscopic observation of the coextruded rods provided a good surface quality independent from the investigated extrusion ratios (R = 24:1 and R = 41:1). The crack generation at the interface seemed to be caused by the different material flow velocities between the core and the shell as suggested by the FEM analysis of the process realized with DEFORM code. Finally, the push out test showed shear strength higher for higher extrusion ratio (an average of 65 MPa against an average of 36 MPa). In 2006, Sliwa [88] analyzed the metal flow in the co-extrusion of PbSb3 (core) and pure Pb (sleeve) using flat, conical and convex dies. The results showed that the use of convex die led to more homogenous flow of the layers of the composite material. In a different context, Negendank et al. [89], in 2021, tested the extrusion of a mixture of pure aluminum powder and graphene nano platelets (GPN) in contents of 0.5%, 1.0% and 1.5%. The powder mixtures, produced with EIRICH mixer, resulted in homogenous GNP dispersion. The surface quality of the extruded rods decreased with increasing GNP content but increased for higher extrusion ratios. In addition, the use of conic die resulted in better surface quality compared with the flat face die. In their works from 2017 to 2020, Thürer, Behrens et al. [90‐92] realized hybrid tubes on an industrial scale with the core in AISI 5120 steel or in 20MnCr5 and the shell in AA6082 aluminum alloy by using the lateral angular co-extrusion (LACE). The steel tube was inserted into the extrusion die at an angle of 90 °C to the extrusion direction, where it was covered by the aluminum. The obtained profile was very straight with no significant diameter changes, no waviness and no microscopic gaps in the aluminum-steel interface. The break-up of the initial oxide layer present on the aluminum was required to obtain a close bond to the steel. The pre-heating of the steel seemed to be necessary to establish the bonding during the LACE process. The validation of the numerical model of the LACE process by means of commercial software FORGE NxT was also presented in [91, 92]. In the years 2011 and 2012, Foydl et al. [93, 94] performed a co-extrusion process, where E295GC steel reinforcement elements were inserted into convectional AA6060 and AA6082 aluminum billets. Different shapes, dimensions and positions of the steel reinforcement were tested. It was found that the position of the reinforcements was influenced by the initial position in the billet, their length and the extrusion ratio, but not by the extrusion speed and the temperature of the billet. In addition, the forging of the co-extruded components was proved for the continuously reinforced products with X10CrNi18-8 wires. About the high reinforcing volume with steel wires, Pietzka et al. [95], in 2013, tested the extrusion of AA6060 alloys billets reinforced with X10CrNi18-8 wires fed through the bridges of a special porthole die. The paper reported the results in testing different die design and different strengthening strategy. A profile with a reinforcing volume of 13.5% was successfully manufactured and a first process window for this co-extrusion process was assumed.

The great interest in the recycling of material scraps, especially due to the high energy required to obtain primary aluminum, has led to several works presented during the ESAFORM conferences on the hot chip extrusion. A great deal of material is lost within the production cycle of mechanical components realized by chip removal process. Chip is a kind of scrap difficult to recycle by conventional re-melting process with an average material loss of 20–50% due to the contamination with oxides and machining oil. In addition, the high-energy consumption of the melting process may suggest the investigation of the recycling of the chips directly by hot extrusion, which requires only the 10% of the energy required by the re-melting. In 2010, Güley et al. [96] used material scraps in AA1050 in the shape of small pins and chips in AA6060 resulting from a turning operation to extrude a full rectangular profile (20 × 5 mm2) at 500 °C (Fig. 11). Chips and pins were preliminary degreased then cold compacted in cylindrical billet shape: a mixture of chips and pins and only 6060 chips were tested. The tensile test evidenced the same true stress-true strain curve for 6060 chips and the as-cast billet, while an intermediate strength between the value of source materials was found with the AA6060-AA1050 mixture billets.

In 2017 and 2018, Paraskevas et al. [97, 98] performed the recycling of AA6060 machining chips within the industrial production line, extruding a single solid profile bar (101.0 × 10.1 mm2) at 480 °C, after the degreasing and the cold compaction of the scraps. In the first work [97], the authors used a 2-porthole die and the tensile tests showed 32% of improved ductility and 40% of lower strength compared to the cast-based reference profile due to the coarser microstructure obtained. Instead, in the second work [98], the use of 4-porthole die introduced additional plastic strain into the profile and thus, higher grain refinement, higher mechanical strength, less ductility, enhanced solid state bonding/welding and less surface defects. The limit of the study is related to the introduction of additional plastic strain in the profile by means of porthole dies that normally is extruded through a simple flat die. In 2016, Buffa et al. [99] investigated the recycling of AZ31 magnesium alloy chips through the Friction Stir Extrusion. The combination of the ram pressure and the die rotation produced both the heat and the pressure to compact and extrude the scraps as a consolidated rod. Six different conditions were tested, varying the tool rotation speed (300, 500 and 700 rpm) and the extrusion ratio (5 and 3,57) as reported in Fig. 12. The higher tool rotation speed generated sound extruded rod with a mechanical resistance of about 80% of the base material. In this context, El Mehtedi et al. [100], in 2018, used the Friction Stir Extrusion to recover AA1099 machining chips. The numerical analysis with the commercial software DEFORM 3D and the experimental trials confirmed that a high rotational speed (1000 rpm in this case) was necessary to produce a sound round profile.

In 2012, Widerøe and Welo [101] analyzed the material flow of AA6060 granulate (3 mm of diameter and 8 mm of length) in a screw extruder using a contrast material. The rotation of the screw (10 rpm) guaranteed the compaction of the granulate, while the extrusion began when the pressure increased for the filling of the extrusion chamber. The results showed that the newly fed granulate first displaced material in the center of the screw channel, pushing pre-existing material further down the channel towards the extrusion chamber. The dead zones were mainly identified at the bottom of the screw channel and in the corners of the extrusion chamber. In the following year, Widerøe et al. [102] developed a new testing machine to characterize in a simplified manner the process parameters of the screw extruder in terms of rotational speed, extrusion load and temperatures for achieving sound profiles.

The manufacturing of lightweight components for support structures in the automotive and construction fields represents an interesting challenge for engineering researchers and technicians. In this context, the production of curved profiles is required due to geometric and aerodynamic specific requirements. Especially in the automotive field, these requirements can be extremely strict and difficult to be achieved by using the conventional bending procedures. Consequently, the definition of new or improved manufacturing techniques combined with controlling methods were investigated by some researchers and presented at ESAFORM. In 2007, Chatti and Kleiner [103] investigated innovative procedures, for the production of straight and curved profiles, developed at the Institute of Forming Technology and Lightweight Construction (IUL) of the University of Dortmund. Among these new procedures, methodologies for bending of profiles made by tailor rolled blanks, of tailored tubes and the curved profile extrusion were presented and analyzed in order to understand their applicability, feasibility and the improvements in terms of achievable product requirements. In the same year, Moe et al. [104] studied optical measurements techniques to be used for the in-line shape control in combination with the internal pressure during pure bending experiments on a AA6060 alloy material. The use these techniques, based on white light stripe projection, allowed to analyze the onset of sagging, buckling and spring-back phenomena.

The need to replicate, or predict, the evolution of processing conditions in cold forming operations has produced a wide literature on the use of numerical methods for process analysis. Since the first edition of the conference, the most investigated numerical methods have been upper bound techniques and FEM analyses, being the latter the one with greatest application over the years. In 2005, Ma and Barnett [105] presented an approximate upper bound solution for forward extrusion through a rotating conical die. The authors developed a model that took into account the material twisting inside the container and the circumferential slippage at the tool/workpiece interface thus providing coherent trends on extrusion load reduction but the paper lacked to validate the results over specific experimental verifications. In 2005, Skakun et al. [106] applied the upper bound model and the FEM approach through MSC Marc Software in the radial extrusion of an Aluminum gear section under different gear flank configurations. The authors compared the extrusion load predicted by the two approaches with experimental results and they found a reasonable agreement between upper bound and FEM with experimental data but the UB method evidenced a great discrepancy in the final stage of corners filling. Two years later, Pepelnjak et al. [107] applied FEM code Abaqus in the analysis of the inner race component of a constant velocity joint to be produced by the sequence inverse extrusion and fine coining in a near-net-shape approach. The influence of tool redesign was analyzed to evaluate the robustness of the forming process in order to stabilize the production around the mean value of prescribed narrow shape tolerances on a 1/12 section of the component. The loading conditions of the dies was experimentally and numerically investigated by Plancak et al. in 2006 [108] during the backward extrusion of a C15 steel. A pin load cell was radially placed in direct contact with forming materials and the acquired data were compared at different workpiece locations and punch strokes with numerical simulations performed by Abaqus/Explicit code. Authors found that radial stress in the die was well predicted by numerical analyses (error consistently below 10%) and that it was not constant and fixed since it always reached a maximum value below the instantaneous position of the punch. In 2009, Plancak et al. [109] applied the FEM code Simufact Forming in the backward extrusion of an involute gear-profile made by C1121 (low carbon steel) characterized by means of the Rastegaev upsetting test. FE results showed fair agreement with experimental results (Fig. 13) despite the scattered trend of the latter related to the frequent remeshing steps.

The comparison among analytical models and FEM predictions was investigated also in 2012 by Khorasani and Valberg [110] in the extrusion of an Al alloy for two different die geometries and in different friction conditions. It was found that the formulae reported in Altan book [111] and the one proposed by Aviztur [112] are less accurate than FEA analysis with DEFORM 2D code since formulae requires simplifying assumptions deeply influencing the predicted extrusion load. In 2007, Gronostajski and Hawryluk [113] introduced the issue that numerical simulations cannot be validated only on the basis of processing load and proposed to use plastic similarity condition in order to evaluate and compare material flow during metal forming processes. In particular, they characterized different waxes composition to be compared to lead under different forming conditions and concluded that plastic similarity conditions enable an easy and quick qualitative and quantitative matching of the material flow. In 2011, Merklein et al. [114] used Simufact.Forming code to analyze the forward extrusion of a 1.0501 low carbon steel, not only as comparison to experimental data, but also for the optimization of the hardness of the final product. Indeed, geometrical features of the die (namely local deformation ratio, shoulder radius and opening angle) were varied in order to evidence the effect on the final effective strains and consequently on the product surface hardness. Austen et al. [115] presented in 2014 a paper on the reduction of the forming force of car’s battery pack cell housing by means of DoE and FEM simulations The researchers used the Simufact.Forming code for 2D simplified simulations of the component under a wide range of variants involving punch’s head configuration, seam geometries, distance between seams and other geometrical tool features thus showing that the shoulder length was the most significant factor. Furthermore, the paper demonstrated that forming force can be reduced by around 20% when optimal geometrical features were selected. In 2018, two papers explained that numerical simulation provides a more reliable product development in industry: Saby et al. [116] investigated the forming process of nickel-based sparkplug electrode by means of coupled thermo-mechanical simulation in order to reduce die wear whilst Gortan [117] used the same thermo-mechanical approach in order to optimize the forward extrusion of a 16MnCr5 steel under single or double stage forming sequence. A specific type of cold backward extrusion is used in the production of cans and cups. In 2008, Abrinia and Gharibi [118] applied the FEM and the upper bound approaches in order to investigate the effect of the punch shape on the process load and can wall thicknesses. A greater accuracy of the FEM method through Abaqus code was found in the comparison with experimental data and the authors also found that an optimal reduction of axial and lateral forces can be obtained with a proper selection of the punch head fillet and slope (Fig. 14). In 2017 and 2018, Henry and Liewald proposed an innovative backward cup extrusion process able to realize the cup piercing phase within a single forming stroke. In [119] the process was analyzed by means of DEFORM 2D code in order to identify the optimal punch shape and in [120] the process was validated through further numerical simulations and experimental trials on three different steel (16MnCrS5, C10C and 42CrMo4).

Friction during cold forming process is a topic widely investigated by ESAFORM researchers not only for a better understanding of its effect on processing conditions but also in order to identify more reliable lubricants or to evaluate the effect of specific tailored coating on tools. In 2007, Abdollahi and Dehghani [121] developed the Matroll software able to provide several local processing parameters, including the friction coefficients (COF) during cold rolling process. The authors studied aluminum cold rolling on a four-high reversing mill and the COF provided by software was found well aligned with data previously reported in literature although the authors missed to validate the values in their experimental campaign. In 2008, Zhang et al. [122] presented the preliminary results of the activity of the WP3 workshop within the “VIF-Virtual Intelligent Forging” network aimed at providing a better understanding of the friction conditions during cold forging. In particular four University labs were involved in the study in order to compare by means of FEM simulations (FORGE software) the local friction conditions of an industrial process (cold extrusion of an AISI 1010 steel bar covered by phosphate layer and soap) with the local conditions of four different frictional tests (forward extrusion, double cup extrusion, upsetting-sliding tests and T-shape compression as reported in Fig. 15). A comparison of the tests on maximum pressure, maximum equivalent strain and new surface generation was realized and it was found that it is not possible to ensure similar contact conditions for each test and industry experiments simultaneously so a subsequent frictional test experimental campaign was planned in order to investigate which contact parameter has the greater influence on friction.

In 2014, Muller et al. [123] investigated the friction conditions during long sliding distance between workpiece and tools after multiple strokes and with different tools surface finishing by means of the sliding compression test. The authors evidenced the importance of the retained lubricant in the different conditions and the positive effect obtained with pre-lubricated tools. In 2017, two papers aimed at demonstrating the positive effect of surface functionalization for the achievement of a dry lubrication condition. Hild et al. [124] evaluated the tribological interaction between surface textured specimens and the tools in fully dry conditions (forward extrusion of 42CrS4 steel workpiece over X155CrMoV12 tools) while Teller et al. [125] investigated the effect of SAM (self-assembled-monloyares obtained by octadecylphosphonic acid) tools treatment on AISI D2 and AISI H11 during pure aluminum (Al99,5%) compression-torsion wear tests. In the same year Gortan [126] observed that during several cold forming processes, including forward extrusion, temperatures may rise above 200 °C and contact pressures may exceed 2500 MPa. The author proposed an adaptive friction model able to reduce simulations errors from 18.6% (constant friction coefficient of 0.063) to 3.3% during the cold forward extrusion of C4C carbon steel. In 2020, Costa et al. [127] investigated the influence of friction models (Tresca friction factor and constant tau) in the simulation of the cold forward extrusion of an AA6082 under different lubricants (MoS2 and Soap) by means of the DEFORM 2D code. The authors evidenced that when low friction conditions are present (m < 0.1) both approaches provided good agreement with experimental data while at higher frictional conditions (m > 0.1) the constant tau approach provided better results. Finally in 2019, Idegwu et al. [128] evaluated the efficiency of different non-edible vegetable oils (Mango, water-melon, African cherry and avocado peer seeds) as lubricants during ECAP in comparison with SAE40 mineral based lubricant. Different ram speeds were tested during the deformation of an AA6063 alloy. The authors found that mango and avocado oils showed greatest potential and possibility of replacing mineral oil as industrial lubricant under all the tested ram speed being mango oil performing best, followed by SAE40, then avocado, with cherry and watermelon given the least load reducing capability.

The material damage evaluation in metal forming process is of great importance in order to understand and predict the onset of some defects like the chevron cracks. Indeed, when workpiece formability is exhausted or when the material is subject to a severe tensile stress state, cracks may originate and grow during processing stages. The following papers have experimentally and numerically investigated the prediction of the damage accumulation by means of fracture criterion. In 2009, Labergere et al. used numerical simulations (Abaqus/Explicit software) to successfully predict chevron shaped cracks in cold extrusion of 100Cr6 steel by coupling thermo-elasto-viscoplastic constitutive equations with a ductile damage model [129]. In 2013, Terhorst et al. [130] investigated a hybridized solid forward extrusion process able to prevent the onset of chevron cracks on an AISI1055 steel by means of an adequate workpiece pre-heating, a tailored online heating or a combination of both. Along the centerline of the extruded part, highest temperatures were obtained within the most tapered shaft, the location at which chevron cracks are most likely to occur. Compared to the preheating of the wrought material prior to extrusion, as usually applied in warm forming, the proposed hybridized forming process reached higher temperatures in crack-relevant areas with the same energy input. As consequence, the proposed hybridized solid forward extrusion process allowed a predefined temperature-induced increase in deformability with less energy input. In relation to the paper’s achievement the same main author [131], in 2016, proposed an extension of the normalized Cockroft-Latham criterion by adding a temperature dependency to the critical damage value. Conventionally FE approaches using C-L criterion and element deletion adopt a constant value of the critical damage value. This approach may lead to an inaccurate prediction of chevron crack location and shape when high temperature ranges are involved in the forming process. The authors implemented within DEFORM 2D code a temperature dependent critical damage value through user routine and validated it through experiments on a AISI 1055 forward extrusion campaign. Figure 16 shows that, with different workpiece starting temperature, the prediction of the best chevron crack shape occurs at different critical values. A polynomial fitting was regressed by the authors and implemented in the FE simulation as material propriety thus allowing the prediction of the defect onset in a wider range of processing temperatures.

In 2019, Hearing presented two papers based on material damage modelling. In the first [132], the author investigated the effect of damage on the product performance of forward rod extruded parts. An experimental approach using automated energy dispersive X-ray spectroscopy (EDX) particle analysis in scanning electron microscopy (SEM) was used to successfully quantify the void area fraction and to obtain information on ductile damage. The method was applied on forward rod extrusion of 16MnCrS5 workpieces with varying extrusion strains and shoulder opening angles for the determination of the influence of the stress state on damage evolution. In forward rod extrusion different load paths can be realized. These load paths are characterized by scalar values describing the evolution of triaxiality during forming. The load path was described by the strain-weighted and the maximum triaxiality. The technique showed to be useful to quantify the damage state of parts, formed using various extrusion parameters. It was shown, that the triaxiality during forming is the main influencing factor for damage accumulation. Counterintuitively, higher strains do not inevitably lead to more damage. By varying the shoulder opening angles it was possible to produce parts with identical extrusion strains but different courses of triaxiality. The quantification method (SEM) proved the correlation between triaxiality and ductile damage and was verified by density measurements. It was observed, that the mean strain-weighted triaxiality describes the total volume change of a pre-existing void. A negative strain-weighted triaxiality leads to a decrease of the void area fraction. The maximum triaxiality is better suited to describe void nucleation. The results indicated that a certain threshold of the maximum triaxiality value must be exceeded for voids to nucleate. It was noted that voids below a certain threshold size are not considered. In [133] the authors illustrated the new idea to characterize material flow stress to high strains by the use of specimens obtained by forward rod extrusion. In the core of such specimens a deviatoric tension-loading was present, which is superposed by an adjustable hydrostatic pressure. Various damage levels were hence possible in the extrudate. Conducting tensile and upsetting tests with the pre-strained specimens both the influence of a load reversal as well as the material weakening through ductile damage on the resulting flow curve was explored. The results were utilized not only to identify flow curves of materials up to high strains (ε > 1.7), but also to get new insights into the plastic material behavior, which can be used for generating or adapting new damage models as well as kinematic hardening models under cold forging conditions. The proposed method was first assessed by means of analytical and numerical methods and then validated experimentally, by the example of the typical cold forging steel 16MnCrS5.

Residual stress together with strain hardening and material damage are phenomena to be kept under control in the manufacturing of cold metal formed parts. In 2008, Statharas et al. [134] showed that residual stresses originate during cold forming processes and subsequent machining phases can be the source of premature failure of a rotary cold working die for paper cutting made by AISI D2 tool steel. In 2021, Franceschi et al. [135] investigated the role of the ejection phase of a component on the residual stresses after a forward cold extrusion process for the austenitic stainless steel AISI 316L. Experimentally, the samples were cold extruded and the residual stresses were measured in the depth through chemical material removal and X-ray diffraction. The process was also investigated through FE simulation with a combined hardening material model. A new system consisting of an active die was used in the experimental conventional cold extrusion processes and it influenced the pre-stress applied on the die during the process through the movement of four drawing cushions. This is reached through an increase of the pre-stress, which leads to compressive axial and tangential residual stresses in the near-surface region. On the other side, a decrease of the pre-stress has a detrimental effect on the axial and tangential residual stresses. The simulations could qualitatively reproduce the profile of the residual stresses found with X-ray diffraction. The ejection phase had a positive effect on the residual stresses also in the conventional technology. It was determined that the residual stresses on the surface cannot be enhanced above a definite value through the active die. Above a certain limit of pre-stress during ejection, the residual stresses tend to high tensile values. The reason for this behavior was analyzed through FE simulations. In 2007, Rossi et al. [136] evaluated the through thickness residual stresses distribution in the walls and in the corners of a cold-formed open section made of a material presenting a non-linear hardening behavior. To get results as close as possible to the reality, the complete process was modelled, including coiling and uncoiling of the sheet before the cold bending of the corner itself. The elastic spring-back after flattening as well as after final shaping were also taken into account. The material was supposed to be anisotropic and to obey to Hill's quadratic yield surface and the subsequent plastic flow rule. Nonlinear hardening behavior was taken into account in the calculations. The results confirmed a complex distribution of flexural stresses and show good agreement with measurements collected in literature.

Sever Plastic Deformation (SPD) processes are used to increase the mechanical properties by producing grain refinement at room temperature trough high process strains. Between those processes, the Equal-Channel Angular Pressing (ECAP) is one of the most used due to the possibility of introducing large amounts of simple shear into metallic billets maintaining their initial cross sections.

In 2008, Beygelzimer et al. [137] carried out an experimental study of the Twist Extrusion (TE) of several alloys and compare it to the ECAP process in terms of deformation behavior. In 2009, Meyer et al. [138] investigated the strength, ductility and impact toughness of the AZ31B magnesium alloy after ECAP process, with the aim to achieve an optimal and homogeneous texturing thus preventing the component to present anisotropy on the mechanical properties. In the same year, Moradi et al. [139], studied the mechanical properties of A356 aluminum alloy produced by ECAP (Fig. 17) paying attention to the effect of different heat treatments such as annealing, solution, quenching and pre/post-aging. In 2009, Olejnik et al. [140] studied the feasibility of hydrostatic extrusion (HE) of UFG AA1070, performing a sequence of ECAP and HE processes. The authors found that the sequence of operations is capable of producing high-strength, medium ductility UFG materials. In 2010, Sabirov et al. [141] verified the advantages of producing AA6061 and AA6063 components with an innovative variation of the conformal ECAP technique called ECAP with parallel channel (ECAP-PC). In 2016, Bergmann et al. [142] performed tests to investigate the Gradation Extrusion in order to increase the mechanical properties of the commercially pure Ti using this new approach as an alternative to the ECAP.

Micro forming technologies have gained an increasing interest for the production of small metallic parts. For small production batch, machining can be the correct choice but, for the production of large quantities, forming technologies are more appropriate due to their high production rate. In this context, research activities have been carried out to investigate and solve the issues related to small scale extrusion process. In 2008, Geißdörfer et al. [143] investigated the possibility of using an ultrafine grained (UFG) metal for micro-extrusion. For this purpose, the material used was the UFG version of the pure copper, produced by severe plastic deformation (8 passes of ECAP at room temperature). The authors compared force, grain flow, shape representation and surface quality of the micro-components and assessed the benefit of using UFG structure of the metals formed. In 2009, Olejnik et al. [144] carried out experiments for the production of micro-cups of UFG Al 1070 and normal grain Al 1050 using the backward extrusion process at room temperature (Fig. 18).

In 2010, the FE simulation using Abaqus/Explicit software was used by Rosochowska et al. [145] to optimize the extrusion process configuration for the production of conical pin of Al 1070. In the following year, Berti et al. [146] performed experimental tests based on hydrostatic micro-extrusion at room temperature of billets in low carbon steel and commercially pure copper. The authors detected the effect of pressure and duration of the process on extrusion length.

In 2019, Sanabria et al. [147] carried out backward extrusions of bimetallic aluminum-copper (EN AW-1080A and Cu-ETP) and studied the friction conditions and material flow by comparing the experimental results with the FEM simulations (DEFORM code). Multiple fractures of the copper sleeve were observed in the experimental investigation, and these failures were caused by the increase of the flow stress ratio between copper and aluminum at high temperature. Moreover, the investigations showed that cold aluminum core and hot copper sleeve would reduce the flow stress ratio and lead to a more uniform material flow. In the same year, Görtan and Yaldız [148] performed a numerical investigation of the temperature, material flow, surface enlargement and contact normal stress behavior on the joint surface during co-extrusion of EN AW-6082 T6 and C10 using finite element analysis within the Abaqus/Explicit software. Three different die openings angle were simulated, and the results showed that the channel angle has no influence on the maximum temperatures on the aluminum side, but a strong influence on the steel surface maximum temperatures. Moreover, it was proved that part and die geometries have significant effect on the contact stresses and no influence on the surface enlargement on the contact interface.

In 2006, A.A.S. Akbari Mousavi and Feizi [149] investigated the effect of ultrasonic vibration on the steel forward extrusion process using the Abaqus/Explicit code, comparing the results with conventional cold forward extrusion. The authors studied the effect of extrusion speed, vibration amplitude and friction conditions on the extrusion force and found that it can be reduced by decreasing the extrusion speed or by increasing the amplitude of ultrasonic vibration only if the ram velocity is lower than a critical value. In 2007, Rosochowska and Rosochowski [150] performed FE simulations using the Abaqus software of the ultrasonic backward extrusion of aluminum billets in order to investigate the influence of the vibration properties on the process parameters. Two simulations were performed, one where the die and the punch were defined as rigid bodies and the other where the punch was modelled as an elastic body. Results showed that the process velocity influences both the amplitude and the mean forming force. The latter decreases because of the reduction of the friction force due to changes in the direction and magnitude of the frictional stress over the vibration period. Moreover, the results showed a lower deflection of the elastic punch, as an indirect consequence of the reduced forming force.