Underlying Mechanisms for Developing Process Signatures in Manufacturing
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Abstract
The concept of Process Signatures allows the reliable and knowledgebased prediction of material modifications (e.g., changes of hardness, residual stress, microstructure and chemical composition) researchers in the field of surface integrity, and manufacturing technologies have already been seeking for a long time. A Process Signature is based on the correlation between the internal material loads in manufacturing processes (e.g., stress, strain, temperature) and the resulting material modifications. The target of this paper is to get a comprehensive view on the development of single Process Signature Components for processes with different predominant impacts. Particularly, a mechanismbased approach leading to significant descriptives of internal material loads for a specific material modification is proposed. By this, a deeper understanding of the underlying mechanisms leading to changes of the workpiece surface layer properties caused by manufacturing processes is provided. The challenging identification of significant mechanisms and descriptives of internal material loads is highlighted for each process, and supporting measurement methods and modeling approaches are presented. Process Signatures are expected to enable the solution of the socalled inverse problem in manufacturing.
Keywords
Surface integrity Machining Microstructure Process SignaturesList of symbols
 A_{c1}
Transformation start temperature (°C)
 c
Phase fraction (%)
 c_{0}
Initial phase fraction (%)
 d_{b}
Tool diameter in deep rolling (mm)
 d_{z}
Thickness of heataffected zone (µm)
 f
Helmholtz free energy (J)
 E
Electric field strength (V m^{−1})
 e_{me}
Stored mechanical energy (J mm^{−3})
 e_{th}
Experienced thermal energy (J mm^{−3})
 h
Heat transfer coefficient (W m^{−2} K^{−1})
 I_{e}
Pulse current in EDM (A)
 k_{f}
Flow stress (MPa)
 l_{g}
Geometrical contact length (mm)
 t
Time (s)
 t_{c}
Contact time (s)
 t_{e}
Pulse duration in EDM (µs)
 v_{ft}
Feed speed in grinding (mm min^{−1})
 z
Depth below workpiece surface (mm)
 ε
Strain (mm/mm)
 \( \dot{\varepsilon } \)
Strain rate (s^{−1})
 ε_{pl,eq}
Equivalent plastic strain (mm/mm)
 ε_{total,eq}
Total strain magnitude (mm/mm)
 ϑ
Temperature (°C)
 σ
Stress (MPa)
 \( \sigma_{} \)
Residual stress in feed direction (MPa)
 σ_{eq}
von Mises equivalent stress (MPa)
 σ_{I}
Firstprincipal residual stress (MPa)
 σ_{II}
Secondprincipal residual stress (MPa)
 φ_{ch}
Chemical potential (J/mole)
 φ_{el}
Electrode potential (V)
 Δx
Change of x
Mathematical operator
 \( \dot{x} \)
Time derivative of x
 ∇x
Spatial derivative of x
 dx
Total derivative of x
 max(x)
Maximum of x
 mean(x)
Arithmetic mean of x
Abbreviations
 As
Atomistic scale level
 BVP
Boundary value problems
 CIRP
International Academy for Production Engineering
 ECM
Electrochemical machining
 EDM
Electric discharge machining
 FEM
Finite element method
 FVM
Finite volume method
 FFT
Fast Fourier transform
 FP
Ferritic/pearlitic
 L
Internal material load
 LA
Laser ablation
 LCM
Laserchemical machining
 M
Material modification
 MS
Microstructural scale level
 PC
Polycrystalline scale level
 PSC
Process Signature Component
 QT
Quenched and tempered
 RVE
Representative volume element
1 Introduction
The prediction of subsurface properties after machining in terms of surface integrity has been an objective of researchers in the field of manufacturing technology for decades. However, even today desired material modifications, e.g., hardness, residual stress, microstructure and chemical composition, cannot be generated in prescribed tolerances with sufficient reliability. Especially for highly loaded components, the demand for an optimal state of material modifications and resulting optimal functional properties is a major challenge. In this paper, the underlying mechanisms leading to material modifications for specific manufacturing processes are investigated by means of analyzing the internal material loads. This mechanismbased view on surface integrity was introduced in the framework of “Process Signatures” in 2011 by Brinksmeier et al. [1]. Based on the description of the meaning and notation of a Process Signature, the papers’ objective is to introduce individual Process Signature Components for processes with different predominant impacts. In particular, the major target of this work is to propose a mechanismbased approach to identify suitable descriptives of internal material loads for experimentally observed workpiece material modifications. Moreover, examples are given on how internal material loads can be determined by innovative inprocess measurements and process simulations on the polycrystalline and microstructural scale level.
2 Evolutionary View on Surface Integrity
In the 1960s, researchers and practitioners in the field of manufacturing processes were mainly concerned about the geometrical properties of the finished component. The decision whether the component is capable of being used for the intended application or has to be sorted out or reprocessed only depended on the compliance with design tolerances. The cornerstones of manufacturing, published in 1956 by Kienzle [2], testify this geometrydriven view on the manufacturing processes. Modifications of the workpiece material due to the manufacturing process and their effect on the functional performance of the component instead, were not considered, neither by the manufacturer nor by the designer. In the following years, researchers like von Weingraber, Peters, Whitehouse and others identified the microgeometry, and with this the surface topography of the component, to be highly important for a variety of functional properties [3]. By paying more attention to the workpiece surface, more and more manufacturinginduced alterations in the surface area were considered by researchers. Finally in 1971, this development induced Field and Kahles [4] to release an extensive list of alterations and to define the term surface integrity for describing the condition of a surface after being generated. Since then, in addition to the geometrical properties, the state of surface integrity has been investigated by many researchers, concerned about the functional performance of manufactured components. In particular, changes in hardness, material structure and residual stress [5] were of major interest. In the 1980s, the importance of surface integrity was proven and the accumulated data showed that all manufacturing processes have certain effects on the workpiece material. With the increasing demands for highly stressed components, the request for a reliable prediction of the surface integrity emerged. A first approach toward a prediction of material modifications due to a process was presented by Malkin [6] in terms of grinding. His correlation of the specific energy with process parameters allowed the prediction of grinding burn. Brinksmeier [7] determined correlations of the changes of residual surface stress with the specific grinding power. By this, the prediction of residual surface stress, e.g., for different cutting speeds, could easily be calculated for the investigated grinding processes. Further investigations by Heinzel [8] considered the heat exposure time and led to a process window for grind hardening. Today, for selected processes, numerical [9, 10, 11] and analytical [12] models allow to choose suitable process parameters without iterative or experiencebased knowledge. However, there is no commonly valid procedure to determine the required machining parameters for a given desired surface integrity in a knowledgebased way. This lack of knowledge was also confirmed within a collaborative work of CIRP from 2009 to 2011. Most of the participating research institutes were not able to generate a predefined surface residual stress of − 200 MPa by a manufacturing process of their own choice [13]. The authors of this publication are convinced that this lack of knowledge results from the common processoriented view in which the material modifications are directly correlated with the machining parameters. The internal material loads, e.g., stress, strain, temperature and temperature gradient, which actually lead to the observable modifications, are rarely or even not at all under consideration. As a consequence, the acquired correlations are mostly processspecific and cannot be transferred to modified or even other processes. Therefore, the objective of the 2011 coined term “Process Signature” for a new approach introduced in the following, and the 2014 established associated transregional Collaborative Research Center CRC/TRR 136 in Bremen, Aachen and Oklahoma is the systematic knowledgebased selection and configuration of manufacturing processes and their chains with regard to the desired surface integrity. Process Signatures correlate the material modifications with the internal material loads which lead to modifications by activating mechanisms such as yielding and phase transformations. It is expected that the utilization of Process Signatures should enable a comparability of apparently different machining processes, assuming that similar internal material loads will lead to similar material modifications. Consequently, Process Signatures are assumed to facilitate the solution of the socalled inverse problem in manufacturing [14].
3 Process Signatures
3.1 Meaning and Notation
3.2 Developing Process Signature Components
Expected relevance of internal material loads on the polycrystalline scale for manufacturing processes according to their predominant impact on material modifications
3.2.1 Exemplary Process Signature Component for Processes with a Mechanical Main Impact
When analyzing the internal material loads of processes with a mechanical main impact, the available Process Signature Components as presented by Meyer and Kämmler [15], Brinksmeier et al. [14] and Langenhorst et al. [16] focus on strains and strain fields in the subsurface layers. The investigations deal with deep rolling and grind strengthening (grinding with mechanical main impact). For both processes, the geometrical contact conditions and the acting contact forces exert a certain pressure on the workpiece surface. This causes specific stress and strain fields within the surface and subsurface layers which are hard to assess experimentally. Tausendfreund et al. [17] presented a specklebased method to deduce stress and strain fields from local displacements of speckles during manufacturing processes. Furthermore, workpieces with integrated thin film sensors were developed. Meyer et al. [18] performed in situ Xray diffraction experiments to analyze the stress fields in a deep rolling process. Promising results can be observed regarding these experimental approaches. However, analytically and numerically based assessments of the conditions during processes with a mechanical main impact also led to several Process Signature Components.
For processes with a mechanical main impact it can be assumed that the material modification is generated by plastic deformations due to yielding of the workpiece material. Yielding starts if an equivalent stress (e.g., von Mises stress) generated by the process reaches the yield strength. Hertz [19] derived equations to describe the mechanical loads in purely elastic bodies. With his equations combined with the maximum distortion energy theory by von Mises, equivalent stress distributions between interacting bodies can be predicted. This was done by Meyer and Kämmler to get a first impression whether equivalent stresses are suitable quantities to derive Process Signature Components for a deep rolling process. In [15], the authors correlated the analytically predicted maximum equivalent stresses max(σ_{eq}) with the maximum residual stresses measured after the process max(\( \sigma_{} \)). Despite some limitations (purely elastic assessment of the equivalent stresses in an elastoplastic deep rolling process), they obtained a reasonable functional interrelation. This indicated that for processes with a mechanical main impact, strain and stress are, as expected, suitable quantities to represent the internal material loads. In particular, the results suggest that the complex tensorial stress field during the process can be characterized in a simplified way by a scalar value, namely the von Mises equivalent stress σ_{eq}. Furthermore, residual stress seems to be sensitive and a significant material modification. The plastic deformations of the surface and subsurface layers inevitably cause distortions of the crystal lattice which manifest themselves in a change of the residual stress state. Thus, residual stress is ranked as an ideal material modification to focus on when it comes to correlating the internal material loads in processes with a mechanical main impact with changes of the surface and subsurface characteristics.
Langenhorst et al. [16] developed a new way to describe the mechanical loads caused by a single abrasive grain during grind strengthening by numerically modeling the contact with the workpiece as a moving normal and tangential pressure source. For the given contact conditions of a flattened single grain, the authors managed to reveal the interrelation between the maximum total strain magnitude max(ε_{total,eq}) (internal material load) and the maximum residual stress max(\( \sigma_{} \)) (material modification). Also in this case the Process Signature Component for grinding observed by the authors is in good agreement with the ones presented in [14, 15] for deep rolling. This is another strong indication that Process Signatures have the potential to describe the effect of manufacturing processes in a mechanismbased and ideally in a processindependent way.
3.2.2 Exemplary Process Signature Component for Processes with a Continuously Thermal Main Impact
If a martensitic layer is formed, the resulting residual surface stress can be described by max(∇ϑ), too (Fig. 6, red dots). But it has to be taken into account that for smaller values of this parameter the heat transfer coefficient h and the maximum temperature have an influence. With increasing max(∇ϑ) the resulting thickness of the martensitic layer decreases, because the minimal temperature for initiating the austenite formation moves closer to the surface. Therefore, the effects of martensite formation decrease. At a maximum temperature gradient of 250 K/mm a minimal residual surface stress is achieved. For higher values of the gradient the influence of this effect becomes smaller and smaller. Additionally, heat conduction from the surface to the bulk dominates more and more and subsequent selfquenching loses its influence.
3.2.3 Exemplary Process Signature Component for Processes with a Discontinuously Thermal Main Impact
The Process Signature Components of two machining processes with a discontinuously thermal main impact are considered in this section, i.e., electrical discharge machining (EDM) and laser ablation (LA). With both processes material is removed from the workpiece surface due to a local temperature reaching values above the melting or even the evaporation point of 42CrMo4 (AISI 4140). Single sparks (EDM) or laser pulses (LA), with a repetition rate in the order of 100 kHz, are used to remove the workpiece material. In the EDM process usually a dielectric liquid fluid such as oil or deionized water is used, in which the spark propagates from the electrode to the workpiece. The short impact of the high electric current or the energetic laser pulse strongly heats up the surface such that it melts and possibly evaporates.
The determination of a Process Signature requires a suitable descriptive of the internal material load for a specific material modification. The chemical load in form of the dielectric fluid can be responsible for carbon diffusion into the material such that a slightly higher residual austenite concentration can be observed in the workpiece. In both machining processes, however, the thermal load can be considered as the main impact, which has a strong influence on the residual stress, the hardness and ultimately on the fatigue limits. The local high power of the pulses leaves a volume of liquid material, which partly is removed and partly resolidifies. Beneath the resolidified layer a heataffected zone, in which phase transformation occurs, is generated. Since the temperature distribution varies strongly in space and time, a suitable descriptive of the internal material load has to be determined. Direct temperature measurements are typically not feasible due to the remarkable tiny spatial (µm) and temporal (µs) scales. Therefore, the temperature field in the workpiece must be determined by a simulation approach, which needs to assume an energy input of the laser pulse in LA or the spark in EDM. This energy input, however, is not exactly known. Therefore, an approximate energy amount, absorbed by the workpiece, has to be assumed. For the EDM process, investigations have shown that an energy fraction of about 50% going into the workpiece seems to be a good assumption [22].
The present investigations only consider singlepulse effects. Future work will concentrate on the analysis of the cumulative effect of multiple pulses. Additionally, a refined model for the material modification will be developed with the aim to identify the most suitable descriptives of the internal material load for Process Signatures. First approaches were already obtained and published by Klocke et al. [25].
3.2.4 Exemplary Process Signature Component for Processes with a ThermoMechanical Impact
Most of the manufacturing processes involving primarily mechanical impacts can in fact not be addressed as pure mechanical processes only. Looking on structural or even atomistic level of matter, internal mechanical loads will also involve and evoke a thermal response of the material. Under certain conditions the thermal impact may be neglected and processes be treated like ones with a mechanical main impact, but in principle the thermal impact has to be accounted for, and depending on the nature of the process itself, processes with mechanical impact may even be governed by thermal effects. With respect to modeling of Process Signature Components both impacts mechanical and thermal may be treated separately first and then combined by superposition. But moreover both impacts are influencing each other: for instance internal thermal loads can be generated through mechanical impacts and, on the other hand, thermal loads are altering the mechanical properties and consequently the elastoplastic material behavior. Some material modification mechanisms only occur if both mechanical and thermal impacts occur simultaneously, e.g., dynamic recrystallization. Thus, a far more sophisticated approach is needed to identify the relevant descriptives of the internal material loads.
So far for this kind of processes a number of different experimental and modeling efforts have been undertaken to analyze the thermomechanical behavior of steel in cutting processes. Common experimental methods have been applied to measure external material loads inprocess [26], and new techniques have been developed to measure simultaneously the internally acting mechanical and thermal loads as well [27]. These inprocess measurements together with intense postprocess material characterization of microstructure, hardness and residual stress are applied to analytical and numerical process models for further analysis and comprehension of the underlying mechanisms of the material modification.
Within welldefined limits of the stored mechanical energy e_{me} and the experienced maximum thermal energy max(e_{th}) specific areas for residual stress can be obtained. The mechanical energy e_{me} is the plastic work done on a volume element of the workpiece material and is a function of the strain ε and the flow stress k_{f}. The flow stress k_{f} itself is a function of the temperature ϑ, the strain ε and the strain rate \( \dot{\varepsilon } \). Therefore, the mechanical energy is a highly aggregated quantity to describe the mechanical impact of the internal material load taking into account the influence of strain hardening during the process. The results indicate its usefulness in describing the mechanical impact of a thermomechanical process. The maximum thermal energy max(e_{th}) is proportional to the maximum temperature ϑ of the volume element and takes into account the temperaturedependent thermophysical material properties. The Process Signature Component shows that when the thermal energy falls below a certain limit, the mechanical impact starts dominating the resulting material modifications leading to residual compressive stress. With increasing mechanical energy also more heat is generated during the process, ultimately leading to residual tensile stress in the workpiece surface layer [28, 29].
As outlined above the mechanism of dynamic recrystallization can lead to white layers when machining steel. Besides the governing temperature also strain and strain rate are the decisive parameters of this mechanism. But also other mechanisms can lead to a reduction of grain size, e.g., phase transformation; here temperature is crucial as well, but additionally the duration of the temperature impact is determining the resulting material modification. To distinguish these modifications and their underlying mechanisms further investigations, characterization and modeling are necessary to fully understand the influence of thermomechanical impacts of machining processes on the elastoplastic material behavior and the resulting material modification. In addition the analyses presented here addressed primarily the polycrystalline level. In order to fully understand and adequately describe the mechanisms leading to material modifications within the framework of Process Signatures it is necessary to extend the modeling and simulation approaches to the microstructural level as presented in Sect. 4.
3.2.5 Exemplary Process Signature Component for Processes with a Chemical and ThermoChemical Impact
Processes with a predominantly chemical and thermochemical impact—like electrochemical machining (ECM) and laserchemical machining (LCM)—include the internal material loads of local chemical potential φ_{ch}, electric field strength E and temperature ϑ. Besides that, also the local mechanical surface tensions resulting from fluid–structure interactions have to be considered as an important loading for high fluid flow rates. By the main underlying mechanism of local chemical reaction in terms of anodic metal dissolution on the atomistic scale different resulting workpiece surface layer modifications can therefore be identified especially on the microstructural scale [31]. For both abovementioned processes these modifications include changes of the chemical composition and of complete phase fractions (e.g., oxide and passivation layer formation) at the surface as well as the formation of surface topography and also porosity due to pitting corrosion and selective dissolution [32].
The graph represents a first Process Signature Component for processes with chemical and thermochemical impact in a general form and especially independently of the individual process technologies and machine tool settings. It distinguishes between areas with stable and unstable passive layer formation for local loadings of temperature and electrode potential for a given workpiece material and chemical potential φ_{ch} defined by the used electrolyte. In this specific case, it can clearly be seen that for LCM (generally applied at room temperature) an additional electrode potential is necessary to achieve a sufficient surface passivation. For locally increased temperatures caused by the laser beam machining can be performed and controlled keeping the electrode potential constant. For ECM at elevated temperatures also the required minimum electrode potential can be identified.
Future modeling approaches for Process Signature Components of processes with chemical and thermochemical impact will focus on a more comprehensive energybased description based on the Gibbs free energy, cf. [33]. It is assumed that this will allow a persistent modeling approach also enabling inverse approaches to deduce appropriate process parameter settings to achieve the desired surface integrity of workpieces. This will finally allow to reach the targeted part functionalities [36] of chemically and thermochemically treated parts in a defined way.
3.2.6 Interim Conclusion
The exemplary discussions for different classes of manufacturing processes show that the approach of building a logical chain from the observed material modification via the underlying mechanisms to the internal material load is very promising to systematically develop Process Signature Components.
Summary of discussed descriptives of internal material loads as a result of the mechanismbased approach
Impact  Material modification  Mechanism  Descriptive of the internal material load 

Mechanical  • max(Δ\( \sigma_{} \))  • Yielding • Strain hardening • Strain rate hardening  • max(σ_{eq}) • max(ε_{pl,eq}) • max(ε_{total,eq}) 
Continuously thermal  • Δ(\( \sigma_{} \)(z = 0)) • Δ(z (\( \sigma_{} \) = 0))  • Yielding • Strain hardening • Phase transformation  • max(ϑ) • max(∇ϑ) • max(Δϑ)·\( \sqrt {{\text{t}}_{\text{c}} } \) • max(Δϑ)^{2}·\( \sqrt {{\text{t}}_{\text{c}} } \) 
Discontinuously thermal  • Δd_{z} • \( \sigma_{} \) (z = 0)  • Solidification • Phase transformation  • max(∇ϑ) • mean(ϑ) 
Thermomechanical  • max(σ_{I}) • max(σ_{II}) • Average grain size  • Yielding • Strain hardening • Strain rate hardening • Thermal softening • Dynamic recrystallization  • e_{me} • e_{th} • max(e_{th}) • df • ϑ 
(Thermo) chemical  • Passivation layer formation • Δ phase fractions  • Chemical reaction  • φ_{el} • φ_{ch} • ϑ • max(E) 

A simplified quantification of the complex timedependent and spatially varying fields of the stress and strain tensor seems to be feasible. For processes with a mechanical main impact equivalent stresses and/or strains as descriptives for the internal material loads result in plausible Process Signature Components. This observation is highly important since a reduction of complexity is essential to utilize Process Signatures in practical applications which is the ultimate goal of the presented research.

For processes with a thermal main impact the heat exposure time needs to be taken into account. For example the thickness of the heataffected zone depends on the temperature increase and on the duration of the temperature increase. Due to the diffusive nature of heat conduction in solids the square root of the time is the decisive quantity that also should be taken into account (c.f. Figure 7).

Energybased quantities should be taken into account if they are required for an adequate description of the material modification mechanism. For example, in hard turning the onset of dynamic recrystallization, which is in this case the mechanism for the formation of a white layer, depends on three descriptives: simultaneously the mechanical and thermal energy must surpass a critical value and the total derivative of the Helmholtz free energy must be smaller than zero. This example also implies that a comparatively simple graphical representation of Process Signature Components is not always possible.

In some cases the material modification depends on the interaction of internal material loads. For example for the formation of a passivation layer in ECM the minimum required electric field strength depends on the temperature. This dependence should be reflected by the notation of the relevant descriptives, e.g., for the abovementioned case: ϑ, E(ϑ).

With the exception of ECM mechanisms were solely analyzed on the polycrystalline scale for which mostly phenomenological models were utilized. Simulations on the microstructural scale would allow a more realistic description of the mechanisms involved and may therefore lead to more suitable descriptives of the internal material loads (c.f. Sect. 4).

The Process Signature Components presented in this paper are based on a specific workpiece material (42CrMo4) heattreated in two different ways: tempered to a ferritic/pearlitic microstructure and quenched and tempered. If other initial microstructures or other steel grades will be used, it cannot be assumed that the correlations found between internal material loads and modifications will remain unchanged. In this case the relevant material properties have to be integrated into the descriptives of the internal material loads.
In order to develop Process Signatures a detailed knowledge about the internal material loads is required. Due to technological limitations they are not accessible by the available techniques in a broad range of process conditions. Consequently, the internal material loads and their suitable descriptives presented here were mostly determined in numerical simulations. Nevertheless, new measurement techniques for quantifying internal material loads during the manufacturing process are developed aiming at a validation of the simulation results and the underlying models for specific process conditions.
4 Finding Relevant Internal Material Loads by Modeling on Different Scales
The microstructure of most materials of technological importance is characterized by a complex distribution of individual grains and phase constituents which might vary in their size, morphology and orientation. Depending on the processinduced material load, this microstructure evolves (e.g., by martensitic phase transformations [37] or dynamic recrystallization [38]) which influences not only the physical, topological and statistical characteristics of the microstructure but also the workpiece material behavior during the process. Since such process–microstructure–property relations and the resulting Process Signature Components [30, 39] cannot be established based on experimental data only, numerical methods are often employed.
Although the FE^{2} method represents a flexible and wellestablished numerical tool, highfidelity twoscale simulations of complex processes with heterogeneous microstructures are correlated with an excessive computational effort. Therefore, recently, FEFFTbased methods [44, 45, 46] have been developed which represent a powerful and an efficient alternative to the classical FE^{2} method. In this case the BVP at the microstructural scale is solved using fast Fourier transforms (FFT) and fixedpoint methods [47]. Different authors [48] have shown that such FFTbased numerical schemes are computationally more efficient than FEbased approaches. Focusing on polycrystalline materials with elastoviscoplastic constitutive behavior, small [46] and finite strain [49] twoscale models have been developed as well as phasefield modeling of martensitic phase transformations [45]. For the elastoviscoplastic constitutive model, the twoscale FEFFTbased approach has qualitatively been validated based on experimental threepoint bending tests [46].
4.1 Modeling on the Microstructural Scale Level
As alluded above, the balances of linear momentum and energy are solved in an iterative fashion at the microstructural scale yielding the local displacement field and temperature distribution. Based on the kinematic and constitutive assumptions, the strain and stress fields as well as the heat flux are computed. In order to account for microstructural evolution, additional field variables are introduced. These are the socalled phase fields or nonconserved order parameters. The latter describe the spatial distribution and volume fraction of the different phase constituents. The evolution of the phase fields is governed by the Allen–Cahn equation which minimizes the total free energy of the system. Note that the special form of the free energy density defines the phenomenon to be modeled and represents the coupling between the thermomechanical problem and the evolution of the microstructure.
4.2 Transfer between Microstructural and Polycrystalline Scale Level
At the polycrystalline scale the FE method is employed to determine the nodal displacements and temperature. In each integration point the displacement gradient and heat flux are computed and imposed to the RVE. The FFTbased solution of the BVP at the microstructural scale leads to the heterogeneous displacement and temperature field distribution. Homogenization of the latter quantities leads to the effective thermomechanical constitutive response of the microstructure. For the mechanical part, the homogenization procedure is simply given through the volume average of the microstructural stress distribution [49]. Appropriate volumeaveraging concepts for the thermal part have been proposed by [51]. This means that the transfer between both scales only requires the transfer of the displacement gradient and temperature and the computation of the homogenized constitutive RVE response. Internal variables associated with dissipative processes (e.g., plasticity, damage) as well as the order parameters are solely defined at the microstructural scale and have to be stored at each integration point at the polycrystalline scale for each loading step. Thus, twoscale simulations of technologically relevant processes (e.g., deep rolling, metal cutting) represent still a tremendous challenge. The improvement of the micromechanical Fourier spectral solver and development of model order reduction techniques for FFT methods are subject of current research and might increase the efficiency of twoscale fullfield simulations tremendously. Then, numerical and experimental results of complex processes can be compared not only qualitatively but also quantitatively. On this basis, internal material loads and processinduced modifications are accessible on both scales and can be used for a detailed analysis and the establishment of Process Signature Components.
5 Summary and Outlook
This paper summarizes the current state of the art in developing and determining Process Signatures in a mechanismbased way and gives examples of Process Signature Components for different processes. The concept was proven for the investigated cases, varying in the mechanical, thermal and chemical impact on the workpiece material. The major challenge of determining the significant descriptives of the internal material loads for a specific material modification is presented for all cases. Within this approach a deep understanding of the underlying mechanisms can be established. For this objective, the paper shows how modeling on different scales can make substantial contributions. In future work, these approaches will help to consider the impact of the initial material state of the workpiece material and the impact of multistage processing and process chains in the framework of Process Signatures.
Notes
Acknowledgements
The authors wish to thank the German Research Foundation (DFG) for funding this work within the transregional Collaborative Research Center SFB/TRR 136 “Process Signatures”, subprojects M01, M03, M04, M05, F01, F02, F03, F05, F06. Also, the valuable contributions of F. Frerichs (Leibniz Institute for Materials Engineering IWT), S. Eckert (BIAS—Bremer Institut für angewandte Strahltechnik) and S. Harst (Laboratory for Machine Tools and Production Engineering WZL) are gratefully acknowledged.
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