Methodology to Investigate the Transformation Plasticity for Numerical Modelling of Hot Forging Processes

Hot forging is a complex process involving the mutual influence of numerous thermo-mechanical-metallurgical material phenomena. In particular, the strains of transformation-induced plasticity (TRIP) have a significant influence on the distortions and residual stresses of the components. The TRIP strains refer to the anisotropic strains depending on the orientation and significance of the stress conditions during cooling superimposed to the phase transformation. With the use of numerical models, the impact of this effect can be investigated in order to ensure the production of high quality components. However, an experimental determination of the characteristic values of TRIP is challenging, which is why only few corresponding data are available in the literature. Therefore, this paper presents an experimental and numerical methodology as well as the results of studies on the interaction between stresses and phase transformations in the materials AISI 4140 and AISI 52100. The investigations of the TRIP strains are carried out using hollow specimens, which are thermo-mechanically treated in the physical forming simulator Gleeble 3800-GTC. The specimens are austenitised, quenched to test temperature and held there while diffusion controlled phase transformation takes place. The extent of TRIP as a result of different superimposed tensile or compressive loads is determined by means of dilatometry. In addition, the extent of TRIP for diffusionless martensitic phase transformations was investigated by continuous cooling tests under tensile and compressive loads. It was found that the transformation plasticity varies depending on the material, the phase type, the temperature and the tensile or compressive stresses. Subsequently, simulations of the physical experiments using the FE software Simufact.Forming verified the determined phase specific values of TRIP.


Introduction
Forging processes have proven valuable in industrial mechanical engineering for the production of complex and heavily loaded components [1]. The high forming temperatures of up to 1250 °C reduce the yield stress, which enables improved material flow, decreased forming forces and thus the production of geometrically challenging parts. At the same time, the forging process generates a fine microstructure in the material, which results in advantageous strength and service life properties [2]. However, designing a hot forming process is challenging as numerous influencing parameters interact with each other, which makes a purely analytical consideration impossible [3]. As shown in Fig. 1a, there are close relationships between mechanical, thermal and metallurgical material phenomena, defining the final properties of the component according to the chemical composition of the material. For this reason, hot forming processes are often designed using the finite element (FE) method. Due to the numerous influencing parameters in the thermo-mechanical-metallurgical process, this represents a challenge. In order to compute these processes, the additive strain decomposition method was used for instance by Denis et al. [4] for calculation of stresses during quenching of a cylindrical specimen from a low alloy steel or by Behrens et al. [5] in order to simulation press hardening of a manganese-boron steel. Thereby, the five parameters of elastic, plastic, thermal, transformation related and transformation plasticity strains are considered separately and summed up to the total strain increment as shown in Fig. 1b. Fig. 1: Interrelated thermo-mechanical-metallurgical material phenomena during thermomechanical processing of steel (a) and basic principles of the additive strain decomposition method (b) according to [6].
The transformation related strains denote the volumetric strains experienced by a polymorphic material as a result of the phase transformations. Thereby, austenite with a face-centered cubic lattice transforms to the microstructural constituents ferrite, pearlite, bainite or martensite with a bodycentered cubic lattice or body-centered tetragonal lattice. In a stress-free state, these strains are of isotropic nature. However, if the phase transformation is superimposed by a stress, anisotropic transformation strains occur. For instance, in the case of uniaxial tensile stress, the strain is increased in the direction of the predominant stress, while smaller strains result in the other directions in accordance with the volume constancy. This effect is described by the transformation plasticity strains.
From the perspective of material characterisation, the acquisition of characteristic values of elastic, plastic and thermal strain behaviour is already well researched and numerous literature data are available concerning these aspects [7]. To model the elastic strains, Young's moduli are usually determined in tensile tests [8]. The plastic deformation behaviour can be described based on flow curves from uniaxial upsetting tests [9]. Likewise, the coefficients of thermal expansion to simulate thermal expansion can be determined in dilatometric studies, e. g. according to [10].
In contrast, there are far fewer norms and standards for the characterisation of material phenomena resulting from metallurgical effects and the acquisition of such material data requires special equipment. Therefore, material data can hardly be found in the literature in this regard. At present, guidelines only exist for determining the transformation times in the form of continuous cooling transformation (cct) or time temperature transformation (ttt) diagrams, such as the ASTM A1033 [11]. From an engineering point of view, these cct and ttt diagrams provide a reasonable guide for the design of heat treatment programs. However, these can only be used to draw conclusions about the transformation times and the amount of the transformed phase fraction. The previously mentioned transformation related and transformation plasticity strains cannot be calculated based on this data. Particularly these data are crucial to optimise forging processes regarding the development of distortion and residual stresses [12]. For the calculation of transformation related strains, the approach shown in equation (1) is often reported in the literature [13].

Achievements and Trends in Material Forming
In this context, (∆Vtr/V0)A→ph denotes the volumetric strain that occurs when the austenite is completely transformed into phase ph, dξ is the incremental proportion of the transformed phase ph and δij represents the Kronecker delta, which is used to account for the strains in the main directions of strain. The growth of the phase can be determined from ttt diagrams, as described in [14]. The phase-specific volume expansion, on the other hand, cannot be determined from ttt diagrams. Simsir [13] calculates this constant via the density-ratio of the parent and the emerging phase for simulation of residual stress development in different carbon steels due to a heat treatment. Olle [15] utilised the ratios of the lattice constants at each phase from literature data [16] to calculate (∆Vtr/V0)A→ph for press hardening simulation of a manganese-boron steel. Friction welding of a carbon steel and a low alloy steel was simulated by Chugreev [17] using data for (∆Vtr/V0)A→ph from the thermo-dynamic material simulation software JMatPro [18,19]. As these three examples of application show, for the process simulation, theoretical values were used with regard to (∆Vtr)A→ph. In the field of experimental material characterisation, the diffusion-controlled phase transformations of an AISI 52100 were investigated by Dalgic et al. [20] with regard to its volume expansions. The volume change of partially hollow specimens after austenitisation at 850 °C was investigated at different isothermal test temperatures by means of two dilatometers in a Gleeble system. In addition, the (∆Vtr/V0)A→ph for a low-alloy and a carburised steel were also investigated by Ahrens [21] on hollow specimens after austenitisation at 860 °C using two dilatometers in a universal testing machine. Few volume change data can be found in the literature for other forging steels and the corresponding austenitisation temperature of more than 900 °C relevant for hot forming.
To account for the anisotropy of the transformation strains under a superimposed stress, equation (2) can be used, where Kph tp is the phase-specific coefficient of the transformation plasticity. In addition to Kph tp , the stress deviator Sij and a function of the current fraction of the emerging phase describing the evolution of transformation plasticity are included in the calculation. As shown in equation (3) Kph tp is a proportionality factor between transformation plasticity strain and the superimposed stress [22]. For the function of transformation evolution f(ξ), there are several approaches from authors like Abrassart [23], Sjöström [24] and Fischer et al. [25] which are used depending on the material type. However, the approach by Leblond [26] in equation (4) is most commonly used.
There are different approaches in the literature for determining Kph tp . The aforementioned authors calculate Kph tp from the yield strength of the austenitic phase as well as the constant (∆Vtr/V0)A→ph and further material dependent coefficients [27]. This type of approach is used, for example, from Behrens et al. [14] to simulate a press hardening process of a manganese-boron steel. A similar process is simulated by Olle [15] using literature data for the manganese-boron steel from [28] for the bainitic and martensitic phase transformation. Thereby, a differentiation is made between the stress types tension (Kph tp = 8.68 * 10 -5 MPa -1 ) and compression (Kph tp = 9.33 * 10 -5 MPa -1 ). For the simulation of friction welding processes, phase-specific and temperature-dependent coefficients Kph tp for a carbon steel and a low alloy steel are calculated by Chugreev [17] using JMatPro. This shows that process simulations are mostly relying on highly simplified models based on theoretical material data or on generalised experimental data. However, some experimental work show that the transformation temperature, the type of transformation and the applied stress state (tension/compression) significantly influence transformation plasticity. For example, Ahrens [21] investigated the transformation plasticity of a low-alloy steel and a carburised low-alloy steel after austenitisation at 860 °C. Thereby, constants from Kph tp = 4 to 9 * 10 -5 MPa -1 were found, depending on the phasetype and temperature as well as on the type of stress. Furthermore, it was found that a superimposed stress increases the phase transformation rate. Besserdich et al. [29] studied the martensitic phase transformation of AISI 4140 after austenitisation at 860 °C, where Kph tp = 4.2 * 10 -5 MPa -1 was determined. Behrens et al. [30] also investigated the martensitic phase transformation of the alloy AISI 4140 and found similar results as Besserdich. Besides, it has been discovered that the austenitisation temperature (950 °C compared with 1200 °C) has an influence on the extent of transformation plasticity and thus on Kph tp . Furthermore, Dalgic et al. [20] studied transformation plasticity with superimposed tensile loads during diffusion controlled phase transformation of AISI 52100 after austenitisation at 850 °C for temperatures in the range of 300 °C to 700 °C. They determined constants of about Kph tp = 6 to 15 * 10 -5 , varying the transformation temperature and the type of transformation.
From this literature review, it can be deduced that, on the one hand, the consideration of phase transformations in hot forming process simulations is crucial for the calculation of distortion and residual stresses as it is taken into account in many applications. On the other hand, theoretical or generalised material parameters are often used for the phase transformation simulations, which leads to imprecise results. This is due to the fact that up to now only few experimental data are available for the corresponding conditions, such as austenitisation temperatures typical for hot forming, phasespecific and temperature-dependent data as well as data for superimposed tensile and compressive stresses. In turn, this can be explained by the complex and so far non-standardised determination procedures that require special technical equipment. As some fundamental research work has shown, there is a significant relation between Kph tp and the aforementioned conditions. Therefore, the aim of this work is to present a method for determining the constant Kph tp depending on these conditions in the Gleeble system. In addition, this work is intended to create a database for the two typical forging steels investigated, AISI 4140 and AISI 52100, for use in hot forming simulations.

Methodology for the Investigation of Transformation-Induced Plasticity
Investigated Materials. For the investigations in this work, two different typical hot-forging steel alloys were used. The first one was alloy AISI 52100, also referred to as 1.3505 according to the international standard ISO 683-17 [31], which is typically used for the production of roller bearing rings. The second one was alloy AISI 4140, also referred to as 1.7225 according to the international standard ISO 683-1 [32], which is used as heat-treatable steel for highly-loaded components, for example in the automotive sector. The chemical compositions provided by the supplier are listed in Table 1. Experimental set-up at the Gleeble 3800-GTC. The principle test setup used at the Gleeble 3800-GTC is presented in Fig. 2a. The Gleeble is prepared with the so-called low-force testing apparatus, which allows high-precision force measurement via a load cell of up to 20 kN. Fig. 2b shows an installed specimen with the attached lengthwise extensometer, while the geometry of the used hollow specimen is shown in Fig. 2c. To realise high cooling rates from the austenitisation temperature to the test temperature, this thin-walled specimen can be cooled with nitrogen from the inside via the bore. During the tests, the strain of the specimens was measured by two extensometers, a lengthwise and a crosswise extensometer, respectively, as shown in Fig. 2d. The specimen is clamped in the custom-made grips by means of M12 threads. Clamping via threads allows both tensile and compressive loads to be applied to the specimen. One side has a left-hand thread, the other a right-hand thread. This ensures that the specimen does not move as a result of thermal expansion during heating. The lengthwise extensometer is a full-bridged strain gauged design transducer of the type HZT071 from DSI Inc. with a resolution of ±2 µm. The push rods are pressed onto the specimen via ceramic fiber cords. The crosswise extensometer is a linear variable differential transducer based

550
Achievements and Trends in Material Forming dilatometer type 39018 from DSI Inc. with a resolution of ±0.4 µm. The specimen is placed between the angled push rods, which are preloaded with a low spring force. Both of the gauges can be used permanently at specimen temperatures in the range of 10 °C and 1200 °C.  Fig. 4b are applied as boundary conditions in order to simulate the transformation relatedand transformation plasticity effects. The principle design is shown in Fig. 3a. Within in the model only the relevant centre section of the specimen with the measuring length of 18 mm was considered and modelled using rotational symmetry by 332 quad-elements of MSC.Marc-Type 10. In order to model the tensile or compressive forces, the auxiliary modelling tools A and B are used, which feature no heat transfer to the specimen. The auxiliary modelling tools are bonded to the specimen, whereby the movements of the specimen in x-and y-direction are permitted without friction. The tensile or compressive forces are generated in Simufact.Forming via generic spring A and B, on which table driven force profiles can be applied. Since the applied superimposed forces in this study do not cause plastic deformations at any test temperature, but are in the elastic range, it is sufficient to use only elastic material parameters in the simulations. Therefore, the elastic Young's moduli were calculated by JMatPro based on the chemical composition of the alloys (Table 1) and are listed in Table 2. For both materials the Poisson's ratio ν = 0.3 was used. The coefficients of thermal expansion for the austenitic phase were determined from the experimental results described in the next section according to equation (5). To calculate the coefficient of thermal expansion from austenite, the quotient of the strain difference and temperature difference obtained during cooling from 1000 °C to the martensite start temperature in the diffusionless phase transformation experiments was determined. For AISI 4140 αA = 2.43906 * 10 -5 K -1 and for AISI 52100 αA = 2.63616 * 10 -5 K -1 were identified. To calculate the coefficient of thermal expansion of martensite, after completed cooling to room temperature, the specimens were reheated to martensitestart temperature and the quotient from the strain difference and temperature difference between martensite start temperature and room temperature was determined. For AISI 52100 αM = 1.18155 * 10 -5 K -1 and for AISI 4140 αM = 1.29589 * 10 -5 K -1 were identified. To model the phase transformation onset and duration, ttt diagrams were taken from a previous work of the authors concerning the investigated materials [33].

Fig. 3: Schematic design of the simulation model for the characterisation tests (a) and demonstration of the approximately uniform uniaxial stress state and the stress distribution in the z-direction from an exemplary test with AISI 52100 at 600 °C and a superimposed load of 1.1 kN (b).
Procedure for determining the metallurgical material data. For investigation of metallurgical material data, the specimens are heated with a heating rate of 10 K/s to the austenitisation temperature of 1000 °C and held there for 300 s. Subsequently, to investigate the diffusion-controlled phase transformations, the specimens are quenched at a cooling rate of 60 K/s in average to the respective test temperature Ttr and held at this temperature until the phase transformation is complete. In the case of investigating diffusionless phase transformations, the specimens were cooled down to room temperature at a constant rate of ̇c r = 10 K/s. Immediately before the start of the phase transformation, the force to be investigated was applied to the specimen within 3 s in each case. As the experimental plan in Fig. 4b shows, axial stresses σL = 0, ±12.5, ±25 or ±50 MPa were applied depending on the test temperature. According to the dimensions of the specimen in Fig. 2c, this corresponds to forces of about 0, 0.27, 0.55 or 1.1 kN.

Fig. 4: Procedure of the test with regard to temperature and superimposed force (a) as well as experimental plan for the materials AISI 4140 and 52100 (b).
Before the investigation of the transformation plasticity can be conducted, the transformation related volumetric strains (∆Vtr/V0)A→ph in the stress-free state must be determined. As explained in the introduction, the transformation plastic strains solely describe the anisotropic deviations occurring under certain stresses from the purely isotropic transformation related strains. For the simulation of the transformation plasticity strains, the transformation related strains must therefore be calculated first. From the measurement data of the length change Δl(t) as well as the diameter change Δd(t), the

Achievements and Trends in Material Forming
strains in length direction εl(t) as well as in crosswise direction εd(t) can be computed using equation (6). Subsequently, the volume change ΔV/V0(t) as a function of time can be calculated, considering small displacements [21]. The experiments were evaluated with the constants l0, d0 and V0 set to the values present at the time t0 at the beginning of phase transformation for initial length, diameter as well as volume. Accordingly, the volumetric strains (∆Vtr/V0)A→ph equals the volume change at the time t1 at finishing of phase transformation. The times for the beginning and end of the respective phase transformations were determined graphically by applying tangents to the εl-t-courses [34]. In addition, the volume expansion can be used to calculate the proportion of the emerging phase ξph(t) as a function of time according to equation (7). In this way, it can be subsequently investigated to what extent the transformation rate is influenced by the superimposed force.
Following the stress-free experiments, the tests were simulated for further calibration of the values (∆Vtr/V0)A→ph and the ttt diagrams used. Subsequently, the experimental investigations are carried out with superimposed force according to the experimental plan in Fig. 4b. The transformation plasticity strains are calculated at the end of the phase transformation according to equation (8).

Results from the Investigations of Transformation-Induced Plasticity
Material data characterising the transformation related volumetric strains. The data from ttt diagrams describing the transformation times as well as the transformation-related volumetric strains (∆Vtr/V0)A→ph represent the basis of the investigations on transformation plasticity. For the simulation of the experimental tests, the ttt diagrams from a previous work of the authors [33] were used and further calibrated on the basis of the stress-free tests. As the results in Fig. 5 show, the two materials have a differing transformation behaviour. Common to both materials is the transformation of the ferritic/perlitic phase at 700 °C and 600 °C as well as the bainitic transformation at 500 °C and 400 °C. It can be concluded, that a pure transformation of the respective phase takes place at these testing temperatures, which is why they were chosen in Fig. 4b for investigating the phase-specific and temperature-dependent transformation plasticity characteristics. According to equations (6) and (7), the volumetric strains (∆Vtr/V0)A→ph for the two materials at different temperatures and the different phases were calculated using the stress-free test results. The results are presented in context with the data from the JMatPro calculation software in Fig. 6 for evaluation purposes. It should be noted that two different temperatures were considered for the ferritic/perlitic and the bainitic phase transformation. However, since the martensitic phase transformation cannot   Material data characterising the anisotropic strains due to transformation plasticity. After the data for the ttt diagrams and the volumetric strains (∆Vtr/V0)A→ph were adjusted by numerical simulations, the experimental tests with superimposed loads were carried out according to the experimental plan in Fig. 4b. The experimental results are exemplarily shown in Fig. 7a and b for AISI 52100 and isothermal transformation at 600 °C, whereby εtp,l and εtp,d were calculated by means of equations (6). Using the transformation plasticity lengthwise strains εtp,l, the Kph tp was determined via equation (3) and further calibrated by a comparison with the simulation results. As a result, the investigated materials showed a clear transformation plasticity effect at all temperatures and for all phase types. For the isothermal pearlitic transformation at 600 °C of AISI 52100, for example, a transformation plasticity lengthwise strain of εtp,l = 0.6 % was determined at a tensile stress of σL = 50 MPa. In contrast, at the compressive stress of σL = -50 MPa, a negative lengthwise strain εtp,l = -0.39 % was determined, cf. Fig. 7a. Besides, the simulations are in good agreement with the experimental courses of the εtp,l. Corresponding to the volume constancy, diameter reductions were found for the transformation plasticity crosswise strains under tensile loading, while diameter increases were found under compressive loading, cf. Fig. 7b. As with the lengthwise strains, the final crosswise strains could also be modelled well, using the presented numerical model. However, especially regarding the crosswise strains under superimposed load, an altered transformation cinematic was found. As already observed by Ahrens [21], both tensile and compressive loads lead to an accelerated phase transformation. This effect results in different time courses between experiment and simulation as shown by the arrows in Fig. 7b. While in the experiment the strain increases significantly faster, in the simulation the strain increments take place with the same speed as in the stress-free state. However, in case of lengthwise strain, this effect is only slightly noticeable. This effect can be confirmed by visualising the evolution of the pearlitic phase fraction in Fig. 7c calculated via equation (7). It is clearly visible that especially the compressive stresses contribute to the accelerated phase transformation compared to the stress-free state. In order to deal with this effect numerically, it would be necessary to consider the effect of an accelerated phase transformation under superimposed loads in the ttt diagram. For this purpose, data such as transformation start and end times or martensite start and martensite finish temperatures would have to be considered in dependence on the stress.
All in all, the material data (∆Vtr/V0)A→ph and Kph tp could be calibrated successfully, so that the presented model was able to reproduce the experiments well. Calibrating the data to the numerical models in this way allows the material data to be implemented and used directly in other, more complex simulation models of hot forging in a next step. Further results of the investigations on the transformation plasticity are summarised in Fig. 8 and in Table 3. It was found that both materials AISI 52100 as well as 4140 and each phase type has its own transformation plastic characteristics. In addition, the temperature influences the transformation plasticity behaviour. In particular, the ferritic/pearlitic phase transformation has a stronger transformation plasticity effect in contrast to the bainitic or martensitic transformation of the two materials. Overall, an increase of the transformation plasticity effects with rising temperature can be observed. Furthermore, under compressive stresses different Kph tp were observed than under tensile stresses, which is why a distinction is made in Table 3 between tensile and compressive stresses. The transformation plasticity tends to be more pronounced under tensile stresses than under compressive stresses, which was already noted in [13,35].

Conclusion
In this paper, a methodology for researching the transformation plasticity effect was presented. The experimental tests were carried out on a Gleeble 3800-GTC using two extensometers to measure lengthwise and crosswise strains. In addition, the tests were numerically modelled using Simufact. Forming 16 to verify the data obtained and to further calibrate the data.
For a comprehensive investigation of the transformation plasticity strains and to simulate the transformation plasticity effect numerically, ttt data and characteristic data of the volumetric strains were determined in stress-free experiments and further calibrated in simulations. Subsequently, a database of experimentally determined and numerically calibrated transformation plasticity parameters was established. These data were provided for the materials AISI 52100 and 4140 phaseand temperature-specific as well as for compressive and tensile stresses.
The material data determined using the described method are directly suitable to use in further, even more complex simulation models. In a next step, the material data will be used to predict the distortions and residual stresses in a forging process of a complex demonstrator component inspired by a connecting rod. The overall aim is to enable the realistic virtual analysis of the important parameters of forging technology like distortions or residual stresses already in the course of process design by taking into account all occurring material effects and their interactions. This is intended to improve the process design in favour of the component properties.