Development of Process Signatures for Manufacturing Processes with Thermal Loads without and with hardening

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Procedia CIRP 00 (2018) 000–000 Procedia CIRP 00 (2018) 000–000

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Procedia CIRP 00 (2017) 000–000 Procedia CIRP 71 (2018) 418–423 www.elsevier.com/locate/procedia

4th 4th CIRP CIRP Conference Conference on on Surface Surface Integrity Integrity (CSI (CSI 2018) 2018)

Development Process Signatures 28th CIRP Design Conference,for MayManufacturing 2018, Nantes, FranceProcesses Development of of Process Signatures for Manufacturing Processes with with Thermal Loads and hardening Thermal Loads without without and with with A new methodology to analyze the functional andhardening physical architecture of * *, Th. Lübben F. existing products for an assembly oriented product family identification F. Frerichs Frerichs , Th. Lübben Leibniz Institute for Materials Engineering IWT, Badgasteiner Str. 3, 28359 Bremen, Germany Leibniz Institute for Materials Engineering IWT, Badgasteiner Str. 3, 28359 Bremen, Germany

Paul Stief *, Jean-Yves Dantan, Alain Etienne, Ali Siadat * Corresponding author. Tel.: ++49 (0)421 218-51338; fax: ++49 (0)421 218-51333. E-mail address: [email protected] * Corresponding author. Tel.: ++49 (0)421 218-51338; fax: ++49 (0)421 218-51333. E-mail address: [email protected]

École Nationale Supérieure d’Arts et Métiers, Arts et Métiers ParisTech, LCFC EA 4495, 4 Rue Augustin Fresnel, Metz 57078, France

*Abstract Corresponding author. Tel.: +33 3 87 37 54 30; E-mail address: [email protected]

Abstract

The presented investigation focuses on the correlation between concrete physical quantities and resulting modifications. The idea The presented investigation focuses on the correlation between concrete physical quantities and resulting modifications. The idea is that not the different manufacturing processes itself produce the modifications but the generated physical and chemical loads. is that not the different manufacturing processes itself produce the modifications but the generated physical and chemical loads. Abstract The correlation between the generated loads and the modifications is called Process Signature. Every process has its own Process The correlation between the generated loads and the modifications is called Process Signature. Every process has its own Process signature, which are than directly comparable to Process signatures of different Processes. If the loads of different Process which environment, are than directly comparable to product Processvariety signatures of different isProcesses. If the loads of different Insignature, today’s business the trend towards and customization Due to this theProcess needfor of signatures are equal, the modifications should more be equal, too. This contribution presentsunbroken. the development ofdevelopment, Process Signatures signatures are equal, the modifications should betoequal, too. This contribution presents the development of and Process Signatures for agile and reconfigurable production systems emerged cope with various products and product families. To design optimize grinding and induction-heating with and without hardening. Based on Finite Element simulations and experimental production work the grinding and with product and without hardening. Based methods on FiniteareElement work the systems well induction-heating as to chooseoftheboth optimal matches, product analysis needed. simulations Indeed, most and of theexperimental known correlates methods aim to externalasthermal loading processes were characterized by the resulting temperature development, which with external thermal loading of both processes were characterized by the resulting temperature development, which correlates with analyze a product or one product family on the physical level. Different product families, however, may differ largely in terms of the number and the change of the residual stress state. To provide a comparable simulation approach, moving heat source theory in combination the change of the residual stress state.anToefficient providecomparison a comparable simulation approach,product moving heat combinations source theoryforinthe combination nature of components. This fact and choice of appropriate family production with energetic quantities wereimpedes applied. The investigations show that surface grinding and induction-heating are interchangeable with energetic quantities were applied. The investigations show that surface grinding and induction-heating are interchangeable system. A newparameter methodology is proposed to analyze view of their and physical architecture. The aim is tothermal cluster for certain regimes regarding the existing changesproducts of the inresidual stressfunctional state. Mainly temperature gradients and for certain parameter regimes regarding changes the residual stress state. Mainly and temperature and thermal these products new assembly oriented productthe families for theofoptimization of existing assembly creationgradients ofand future reconfigurable diffusion areinresponsible for the considered modifications. The comparison of heatinglines withoutthehardening processes with diffusionsystems. are responsible for the considered The comparison ofanalyzed. heatingFunctional without hardening andareprocesses with assembly Based Datum Flow Chain,into themodifications. physical structure of the products and hardening delivers an on additional insight the thermal processes and canis help to understand subassemblies and distinguish identified, the different hardening delivers an additional insight into the thermal processes and can help to understand and distinguish the different aworking functional analysis is performed. mechanisms within theMoreover, processes.a hybrid functional and physical architecture graph (HyFPAG) is the output which depicts the working between mechanisms within the processes. similarity product families by providing design support to both, production system planners and product designers. An illustrative © 2018 The Authors. Published Published by by Elsevier Elsevier B.V. Ltd. This is an open access article under the CC BY-NC-ND license © 2018 The B.V. example of a Authors. nail-clipper is used to explain the proposed methodology. An industrial caseonstudy on two product families Peer-review under responsibility of the scientific committee of the 4th CIRP Conference Surface Integrity (CSI 2018).of steering columns of (https://creativecommons.org/licenses/by-nc-nd/4.0/) Peer-review under responsibility of the scientific committee of the 4th evaluation CIRP Conference on Surface Integrity (CSI 2018). thyssenkrupp Presta France is then carried out to give a first industrial of the proposed approach. Selection and peer-review under responsibility of the scientific committee of the 4th CIRP Conference on Surface Integrity (CSI 2018). ©Keywords: 2017 TheSurface Authors. Published by Elsevier B.V. stress; Process Signatures heating; induction heating; residual Keywords: Surface heating; induction heating; residual stress; Process Signatures Peer-review under responsibility of the scientific committee of the 28th CIRP Design Conference 2018. Keywords: Assembly; Design method; Family identification

1. Introduction 1. Introduction

The importance of manufacturing processes on the The importance of manufacturing processes on the 1.functional Introduction performance of components is generally known functional performance of components is generally known [1,2,3]. This is especially true for finishing processes such as [1,2,3]. is especially true for finishing such of as Due This toor the development in processes thethe domain grinding hardfastturning which affect functional grinding or hard turning which affect the functional communication an ongoing of digitization and performance byandchanging the trend workpiece surface layer performance manufacturing by changing enterprises the workpiece surface layer digitalization, are facing important properties, e.g. residual stresses, microstructure, and hardness. properties, e.g. residual stresses, microstructure, and hardness. challenges in today’s environments: However, even under market laboratory conditions aa continuing controlled However, even under laboratory conditions a controlled tendency towards reduction product is development generation of surface layer of properties not state oftimes the artand in generationproduct of surface layer properties is there not state ofincreasing the art in shortened lifecycles. In addition, is an machining [2]. machining [2]. demand customization, at the same a global It is of assumed that thisbeing knowledge gap istime the in result of a It is assumed that this knowledge gap world. is the This resulttrend, of a competition with competitors all over the process-oriented view that has been prevailing in the scientific process-oriented view that has been prevailing in the scientific which is inducing developmentthe from macro workpiece to micro analyses in which the predominantly resulting analyses results in which predominantly the resulting workpiece markets, in diminished lot sizes due to augmenting material modifications are correlated with the machining materialvarieties modifications are correlated with production) the machining product (high-volume to low-volume [1].is parameters and/or process quantities [4,5,6,7]. The reason parameters and/or process quantities [4,5,6,7]. To cope with this augmenting variety as well as The to bereason able tois identify possible optimization potentials in the existing 2212-8271 © system, 2018 The Authors. Publishedtobyhave Elsevier B.V. production is important a precise knowledge 2212-8271 © 2018 The it Authors. Published by Elsevier B.V.

that internal material loads, i.e. stresses, stress gradients, that internal material loads, i.e. stresses, stress gradients, strains, strain gradients, temperatures, and temperature strains, strain gradients, temperatures, and temperature gradients, which actually lead to the observable modifications gradients, which actually lead to the observable modifications of product range and or characteristics manufactured arethehard to determine even not known at all. and/or As a are hard to determine or even not known at all. As ina assembled in this system. of In the thisfindings context,isthe main challenge consequence the validity very limited. consequence validityisofnow the findings very limited. modelling andtheanalysis onlyis to cope withonsingle A material-oriented view notwhich focused the A material-oriented view which focused on the products, a limited product range or existing product families, mechanisms leading to workpiece material modifications by mechanisms leading to workpiece material products modifications by but also to be able to analyze to compare define manufacturing processes, as and the introduced concept oftoProcess manufacturing processes, as the introduced concept of Process new product[8] families. can be resolve observed that classical existing Signatures intends,It should this lack of knowledge. Signatures [8] intends, shouldinresolve thisoflack of knowledge. product families are regrouped function clients or features. In the frame of Process Signatures, the material modifications In the frame of Process Signatures, the material modifications However, assembly product families are hardly find. are correlated with oriented the internal material loads which to lead to areOn correlated with the internal material loads which lead to the product family level, products differ mainly in two modifications by activating mechanisms such as phase modifications by activating mechanisms such as phase main characteristics: number of components and (ii) the transformations and(i) the plasticity (yielding, transformation transformations and plasticity (yielding, transformation type of components (e.g. mechanical, electrical, electronical). plasticity) [9] . The utilization of Process Signatures enables a plasticity) . The utilization of Process Signatures enables a Classical[9] methodologies mainly single processes products comparability of seeminglyconsidering different manufacturing comparability of seemingly different manufacturing processes or solitary,that already existing families analyze assuming similar internalproduct material loads will leadthe to assuming that similar internallevel material loads level) will lead to product structure on a physical (components which causes difficulties regarding an efficient definition and comparison of different product families. Addressing this

Peer-review under responsibility of the scientific committee of the 4th CIRP Conference on Surface Integrity (CSI 2018). Peer-review under responsibility of the scientific committee of the 4th CIRP Conference on Surface Integrity (CSI 2018). 2212-8271 © 2018 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0/) 2212-8271 © 2017 The Authors. Published by Elsevier B.V. Selection and peer-review under responsibility of the scientific committee of the 4th CIRP Conference on Surface Integrity (CSI 2018). Peer-review under responsibility of the scientific committee of the 28th CIRP Design Conference 2018. 10.1016/j.procir.2018.05.057

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similar material modifications. For the application of Process Signatures in industrial practice it is additionally necessary to correlate the internal material loads with the process quantities. In the present work material modifications as a result of generated physical quantities will be exemplary presented for surface and volume heating respectively (Fig. 1). Both processes produce thermal loads and should therefore have similar Process Signatures. 2. Objectives and Procedure Surface and volume heating generate own characteristic time depend temperature fields, which contain the relevant internal material loads. The thermal and mechanical material properties are temperature dependent. Hence the generated temperature distribution governs the distribution of the material properties. As described in [10] for heating without phase transformations the most important characteristics are the maximum temperature, the maximum temperature gradient, and because of thermal diffusion the contact time t c. In case of austenite formation additionally the temperature and the temperature rate become important for the changes of the microstructure [11]. The temperature gradients are the origin of elastic and, if the yield strength is exceeded, plastic strains. Additionally, in case of phase transformations, density variations occur [12], which can lead to elastic strains too. Phase transformations paired with stresses, even below the yield strength, produce transformation induced plasticity and therefore additional changes of the stress and residual stress state [9]. Thus, the number of mechanisms increases significantly due to the additional occurrence of phase transformations. Therefore it is very interesting whether the number of the internal material loads changes too and if the formulations of the internal material loads for sole heating are transferable to processes with phase transformations. Thermal load

Surface heating (grinding) v ft

vs (dq/dt)s

Volume heating (induction heating)

lg

Thermal impact over surface

v ft (dq/dt)vol

W

Thermal impact over volume

Fig. 1. Basic models of external thermal loads due to grinding and induction heating.

For comparison with the results in [10] in the present work almost the same material modifications were considered. These are the surface residual stresses and the zero crossings of the residual stresses from tensile to pressure. But in comparison to sole heating an additional zero crossing of the residual stress profile from pressure to tensile stress occurs. This has to be included in the new process signatures. Both processes were again modeled as moving surface and moving volume heat sources, respectively. As a variation to [10] the

419

volume heat source was modeled including the Maxwell equations. This leads to a modified heat source (temperature depend) inside the sample and a better agreement between measured and calculated heating curves. 3. Methods 3.1. Heating processes Experimentally the surface heating can be compared with shallow cut grinding even though mechanical material loads in case of real grinding processes occur. But in case of grinding without external cooling the largest fraction of mechanical generated energy transforms in heat. Taylor et al. (1934) [13] estimated this fraction for turning to 90%. For grinding this fraction is even higher. During the contact time between grinding wheel and sample the applied model assumes a constant heat flux . The contact time is given by tc = lg/vft for each point of the treated surface. After Malkin [14] the maximum temperature for such a moving surface heat source occurs at the surface and is proportional to the heat flux and the square root of the contact time tc. Hence, in a double logarithmic plot of heat flux and contact time constant temperatures form straight lines (Fig. 2). The presented temperature values were calculated for the investigated 42CrMo4 with an initial microstructure of ferrite/pearlite. 100

Heat flux (dq/dt)S [W/mm²]

2

incomplete austenitization full austenitization

Θmax

10

1 0.01

heating without phase transformation

1150 C 900 C 750 C 500 C 250 C

0.10 1.00 10.00 Contact time Δt c [s]

Fig. 2. Process window for grinding with and without hardening [15].

The volume heat source of an induction heating process was modeled in [10] by a constant, temperature independent by penetration depth. In reality the heat production electromagnetic induction depends because of temperature dependent electromagnetic properties strongly on temperature and according to the Maxwell equations additionally on the distance to the surface [16,17]. These effects become very strong if the Curie temperature of 768°C for iron is exceeded. In that case, the depth of the volume heat source increases significantly. Fig. 3 shows the heat production beneath an infield inductor with concentrator material which has a width W in feeding direction of 18 mm. The example was calculated with a feed speed in z-direction of 15 mm/s and a maximal inductor current of 650 A. This simulation has taken the Maxwell equations and the temperature dependent electromagnetic material properties within a coupled 2Dtranslation symmetric model into account. The maximum temperature of 978 °C occurs at the surface and the maximal

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depth below the surface (x-direction) of the heat source exceeds 4 mm. To compare surface and volume heating an equivalent surface heat flux in case of induction heating has to be defined:

q  1/ W



d

 q

vol

dxdz

(1)

z   x  0

This averaging is only an approach and possibly not the optimal solution. But it is a good method to estimate the maximal temperature at the surface (cf. section 4.1 Fig. 6). In will be used as equivalent values and the following and will be denoted with If the temperature exceeds 750 °C the microstructure can transform, independently of the heating method, to austenite. The transformed proportion depends on steel grade, initial microstructure, temperature, and heating rate [11]. In case of the used 42CrMo4 the proportion of austenite is almost 100% if the maximum temperature exceeds 900°C and the heating rate is below 2000 K/s [11]. Between 750 and 900°C a mixture of ferrite/pearlite and austenite possibly exists. To avoid such mixtures at the surface only processes above 900°C maximum temperature and heating rates below 2000 K/s were considered. The phase transformation ferrite/pearlite to austenite enables the formation of martensite if a subsequent quenching is carried out. In this study the quenching was simulated with a constant heat transfer coefficient of 2000 W/m²K, which can be considered as a mean value for different quenching media [18]. The transformation austenite to martensite was modeled with a modified Koistinen-Marburger equation [19]. The temperature dependent material parameters of 42CrMo4 (ferrite/pearlite) were taken from [20] and own investigations. z

x

0 4.3 8 12 Distance to inductor center [mm]

-4

0

As described in section 2 the appropriate internal material loads should closely be connected to the changes of temperature and temperature gradient during the considered heating process. In Fig. 4 four examples of temperature distributions with the same contact time t c are shown. For the equals 8.0 . lower temperature the term Under these conditions the temperature increases at the surface to approximately 750 °C. A phase transformation does ) the not occur. In case of the higher value (11.5 W temperature evolution lead to a phase transformation ferrite/pearlite to austenite. In all cases the maximal temperature appears at the surface. 1200

surface 11.5

1000

volume 11.5

4

surface 8.0

800

W/mm² ∙ s 1/2 (tc = 1.8 s)

volume 8.0

600 400

feeding direction

Θmax = 978 C

-12 -8

4.1. Correlation of process quantities and temperature evolution

200

Depth below surface [mm]

Power [W/mm³]

W/mm³ 15 12-15 12 9-12 9 6-9 6 3-6 3 0-3 0

4. Results

Fig. 3. Power density distribution of the volume heat source calculated with a coupled 2D translation symmetric induction simulation.

3.2. Simulation parameters According to the preliminary considerations in section 3.1 the process quantities for processes with phase transformations were chosen in such a way that maximal temperatures at the surface between 900 and 1200 °C were achieved. The simulations for surface heating were performed with contact lengths lg between 4 – 20 mm, feed velocities vft between 4 - 60 mm/s, and heat fluxes of 1 to 85 W/mm². 3D simulations with the finite element code SYSWELD were

0

0

2 4 6 8 Depth below surface [mm]

10

Fig. 4. Temperature distribution at the moment of maximal temperature at the surface for tC = 1.8 s)

0 grad Θ max [K/mm]

eq S

3

carried out for sample length of 50 mm, width of 30 mm, and height of 18 mm. The 2D translation symmetric volume heating simulations take the Maxwell equations and temperature dependent electrical properties into account. All volume simulations were carried out with the same inductor geometry (width W = 18 mm). The feed speed vft varied between 3.6 and 90 mm/s, between 12 and 85 W/mm². the equivalent heat flux

Θ [ C]

420

0

Depth below surface [mm] 2 4 6 8

10

-100

-200 -300 -400 -500

-600

surface 11.5 volume 11.5 W/mm² ∙ s 1/2 surface 8.0 (tc = 1.8 s) volume 8.0

Fig. 5. Exemplary depth profiles of temperature gradient for surface and volume heating.

Fig. 5 presents the maximal temperature gradients of the temperatures shown in Fig. 4. The examples point out the

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main differences between both heating methods. Firstly, the maximal temperature gradient for surface heating occurs at the surface whereas for volume heating it occurs below the surface. Secondly, the magnitude of the gradient is significantly lower in case of volume heating. Because of the temperature dependent depth of the heat production in case of volume (induction) heating the distance of the maximal gradient to the surface increases with maximal temperature. The effect of latent heat is significant in case of surface heating. Until a depth of approximately 0.9 mm the initial microstructure in case of the example in Fig. 5 transformed to austenite. This transformation lowers the gradients in the subsurface area. A time depend analysis shows that the maximal gradient occurs short before the beginning of the phase transformation. This result differs from sole surface heating processes. Without phase transformation the maximal gradient occurs in the moment of the maximal temperature [10]. Fig. 6 shows the dependency of the maximal temperature . Surface heating processes (blue squares and dots) on reveal independently of phase transformation an almost linear dependency. For volume heating a deviation from the linear behavior results, if the Curie temperature is exceeded (Fig. 6 red squares and dots). The comparison of the results for surface and volume heating shows that the definition of the equivalent surface heat flux is an acceptable approach. 1400

volume heating Θmax > 900 C surface heating Θmax > 900 C

1200

Curie temperature (768 C (Fe))

800 600

volume heating Θmax < 800 C surface heating Θmax < 800 C

400 200

0

Fig. 6. Dependency of

5 10 15 dq/dt √tc [W/mm 2 s 1/2] on

grad Θ max [K/mm]

for surface and volume heating

To compare the results with [10] the target quantities are again the residual stresses at the surface and the zero crossings of the residual stress profile. Fig. 8 summarizes schematically the considered target quantities. In case of heating without phase transformations (dashed lines) the stress at the surface is mainly tensile [10]. Therefore, as a main characteristic of the modification, the depth of sign change of residual stress from tensile to pressure was considered. In case of austenitization and a subsequent hardening the residual stress at the surface is typically pressure. The residual stress increases in deeper areas and crosses the zero line. The second change of the depth profile from tensile to pressure in case of hardening is comparable to the zero crossing from tensile to pressure in case of sole heating. Below this position the residual stress profile is mainly governed by bending stress. Fig. 9 presents the dependency of the residual stress at the surface parallel to the feed direction on the maximal temperature gradients. The results confirm the investigations in [10]: The maximal temperature gradient is again an appropriate characteristic measure of the internal material load with respect to the residual stress at the surface. This is independent of the type of heating and of phase transformations. Θmax < 750 C

600

1200

surface heating Θmax > 900 C

900

Θmax < 750 C

600

Θmax < 750 C 0

10 20 Heat flux [W/mm²]

200

RS at surface

-200 -600

-1000

volume heating Θmax > 800 C

300

0

20

4.2. Correlation of internal material loads and material modifications

RS║ [MPa]

0

austenitization

Fig. 7 summarizes all calculated maximal temperature gradients plotted over . For surface heating the maximal temperature gradients increase nearly linear with . But the slopes differ significantly whether the maximal temperatures are lower or higher than 750°C. If diffusion governs the heat transportation the temperature gradient at the surface depends mainly on the quotient of and heat conductivity λ [14]. For austenite the heat conductivity is lower than for ferrite/pearlite with temperatures lower than 750°C [20]. In case of volume heating to higher temperatures diffusion is not anymore the main transportation mechanism. The increase of the gradients is lower than in case of comparable surface heating processes.

30

Fig. 7. Absolute value of the maximal temperature gradients

Martensite [-]

Θ max [ C]

1000

421

0

RS zero crossing (pressure to tensile)

Θmax > 900 C with austenitization

1 0.5

RS zero crossing (tensile to pressure)

Θmax < 750 C 0.1

1 10 Depth below surface [mm]

Fig. 8. Target quantities for material modifications

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422

3

600 300 0

surface h. induktion h.

Θmax < 750 C

surface h. induktion h.

Θmax > 900 C

Depth of zero crossing [mm]

Θmax < 750 C

-300 -600 -900

-1200

0

1000 2000 3000 (gradΘ)max [K/mm]

4000

Fig. 9. Residual surface stresses parallel to the feed direction over the maximal temperature gradient for surface and volume heating

Without phase transformations the stresses are tensile in each case. If phase transformations occur the results are more complex. In relation to the residual stresses an optimal temperature gradient exists. For higher and lower gradients the stresses increase in direction to tensile stresses. If the gradient approaches zero the process is comparable with through hardening with typically tensile stresses at the surface [18]. Differing from the results in [10] in case of heating with phase transformation a second zero crossing is of interest (cf. Fig. 8). Fig. 10 presents the depth of zero crossings from tensile to pressure. For surface heating the depth is a function of represents the maximal temperature increase. This result is independent of austenite formation. In case of volume heating the depth increases stronger with temperature. Exceeding the Curie temperature enlarges the .changes significantly. depth and the dependency on

Depth of zero crossing [mm]

8

volume heating Θmax > 900 C surface heating Θmax > 900 C

6

surface heating

2

1

0

0

10 20 (ΔΘmax ) 2 √tc [10 5 K2 s 1/2 ]

30

Fig. 12 plots simulated residual stresses at the surface over simulated depth of 50% martensite and compares these data with experimental values for grinding and induction heating. The induction heating experiments in [17] were achieved with cylinders using hardened and tempered 42CrMo4. In [21] the authors report of experiments with cuboids using the same steel grade. The agreement between experimental and simulated data is very good. The results of grind hardened samples were achieved with cuboids made of 42CrMo4 with an initial ferrite/pearlite structure. The data in Fig. 12 are complemented schematically by a dashed line which approaches results of very short heat treatments, for example by electrical discharge machining (EDM) [22]. For EDM processes only a very thin layer beneath the surface is transformed. 400

EDM [22]

0

50% martensite [mm]

0

-400 -800

0

2

4

6

8

0.5

RS

martensite

[21] induction [17] induction own grind hardening

-1200

4

Fig. 12. Dependency of the residual stress at the surface on the depth of 50% martensite proportion. Comparison of simulated (red and blue marks) and measured data (black marks).

volume heating Θmax < 800 C surface heating Θmax < 800 C

2

0

volume heating

Fig. 11. Depth of zero crossing over for surface and volume heating at different maximal temperatures (valid if austenitization occurs).

Residual stress σ║ [MPa]

Residual stress σ║[MPa]

900

5

0

500 1000 ΔΘmax √tc [K s 1/2 ]

1500

Fig. 10. Depth of zero crossing over for surface and volume heating at different maximal temperatures (valid if (gradΘ)max>100 K/mm)

Fig. 11 shows the results for the zero crossing from pressure to tensile stress, which appears only if an is an austenitization and hardening occurs. appropriate internal material load for the depth of this zero crossing. The depth in Fig. 11 correlates very well with the depth of 50% martensite content. A plot of both values delivers a bisector.

5. Conclusions and Outlook Process Signatures developed for heating without austenitization [10] has been enhanced for processes with phase transformations. In case of hardening several additional mechanisms such as density changes [12], transformation induced plasticity [9], and strains due to the subsequent quenching have an effect on the stress evolution at the end of the process. As well as in [10] without any transformations, the maximal temperature gradient is for processes with austenitization and hardening again an appropriate characteristic material load for the residual stresses at the surface.

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Independently whether phase transformations occur or not yielding works during both heating process. The zero crossing tensile to pressure is describable with the same internal material load as for heating without phase transformation. This supports the hypotheses, that yielding as a result of temperature gradients dominates the effect. In [10] the term was considered as a description of the internal material load for the zero crossing tensile to pressure. The formulation combines thermal diffusion and the temperature rate. This description was necessary to include the behavior for very low temperature gradients without or with only slight yielding processes respectively. If the maximal temperature gradient exceeds approximately 100 K/mm [10] sufficient yielding occurs. For larger has temperature gradients only the diffusion part to be taken into account. In [10] volume heating was modeled with a constant depth profile of the heat density. This is no longer valid if induction heating at higher temperatures is involved. The depth of the maximal gradient increases significantly, especially if the Curie temperature is exceeded (cf. Fig. 5). The depth of the zero crossing increases in that case, too. If no phase transformation occurs only one zero crossing from tensile to pressure stress has to be considered in the residual stress profile (Fig. 8). In case of austenitization and hardening the martensite dominated microstructure in the surface near layer has a lower density than the initial microstructure [12]. This leads to pressure stresses at the surface. In consequence an additional zero crossing from pressure to tensile stress appears. The depth of the zero crossing pressure to tensile are for . But as both heating methods describable by well as for the zero crossing tensile to pressure both heating methods lead to different curves. The similarity of the temperature evolutions of both processes is not given any more. Nevertheless, the descriptive variable is the same and hence the Process Signatures of both processes are comparable even though the results do not overlap completely. The simulations confirm the well known observation [17] that the zero crossing depth pressure to tensile correlate with the position of the 50% martensite proportion. In Fig. 12 the position of the 50% martensite proportions is compared with the residual stress at the surface. Both values are easily measurable and therefore available in literature. The agreement between simulated and experimental data of [17] and [21] is very good and therefore an indicator for the quality of the simulations. Furthermore extrapolations to very short (cf. Fig. 12, EDM [22]) and very long processes (cf. Fig. 9 through hardening [18]) give reasonable results. The presented analyses of the correlations between internal material loads with process quantities and material modifications provide a possibility to engineer the workpiece surface layer properties in a knowledge-based way. If a specific residual stress at the surface and a specific zero crossing is sought, the necessary internal material loads and with the availability of process models - the necessary process parameters are determinable.

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