1 Introduction

Functionally graded additive manufacturing (FGAM) is a special branch of additive manufacturing (AM) and describes the production of components with varying material compositions or microstructures in order to achieve specific locally varying component properties (Ref 1). By locally adapting the composition, FGAM enables the production of components with increased performance and improved functionality and offers potential for optimization and material savings (Ref 2,3,4). Review articles from recent years provide a comprehensive insight into this field (Ref 5,6,7,8,9). Various processes have already been successfully used for the production of functionally graded additive components. According to Reichardt et al (Ref 9), DED processes offer the most advantages to produce such components. These include powder-based free-form processes such as DED-Laser and DED-Arc. In contrast to single wire-based processes such as Wire Arc Additive Manufacturing (WAAM), where the use of a wire with a constant material composition, when used result in abrupt transitions between different deposition layers (Ref 10,11,12,13), the use of powder offers the advantage that a greater variety of materials can be used, allowing mixtures to be dosed and adapted in situ.

A key area for future research in FGAM is the modeling of FGAM structures, as emphasized by Saleh et al (Ref 5). The understanding and prediction of mechanical properties are important parts of the characterization of FGAM components. Existing models face challenges due to the complex thermal cycles and material transitions during production. Rapid solidification, high cooling rates, and large thermal gradients can lead to microstructures that are not in equilibrium, causing property variations between layers and within individual layers. In addition, material properties such as melting temperature and thermal conductivity have a large influence on the process parameters, which complicates the development of predictive models for the technology. Common approaches include the idealization of the exponential law for fracture mechanics and the power law for stress analysis, which are described in the literature (Ref 14). An alternative method is to divide material variations into small elements or “maxels,” where the properties should be automatically assigned based on functions. The finite element method (FEM) can then be used to analyze the structural responses (Ref 15). Furthermore, additional phases that form at material interfaces must be identified, as precipitates and lack of fusions can lead to failure of the entire component. Simple predictions of phase properties may be insufficient in such cases. Advanced modeling strategies that integrate phase transformation effects and interface characteristics are essential to improve property predictions in FGAM and enable optimized material distributions and improved structural performance (Ref 16).

The concept of this study is to evaluate the usability of the Schaeffler diagram as an additional tool contributing to a more comprehensive prediction model. One goal is to reduce and better structure the experimental effort for the evaluation of new material combinations. In principle, the Schaeffler diagram is a widely used tool for predicting the phase composition of weld metal based on its chemical composition. Originally developed for iron-based alloys, it provides information on weldability and microstructure by relating chromium and nickel equivalents to the resulting phases such as martensite, ferrite, and austenite. Although the diagram is primarily applied to stainless steels, it can theoretically be extended to material mixtures containing nickel-based alloys by using the chromium and nickel equivalent calculations. However, its applicability to additively manufactured graded structures remains uncertain, as the diagram does not account for non-equilibrium solidification, thermal cycling, or element segregation effects that strongly influence microstructural evolution in processes such as DED (Ref 17, 18).

Giseung Shin et al. investigated the phase prediction using the Schaeffler diagram for a material combination of SS 316L and a low-carbon steel in the DED-Laser process. For this purpose, a sample graded in the Z-direction with coarse transitions was used. The phase determination based on the Schaeffler diagram generally agreed with the experimentally observed microstructure, although some deviations were observed. These inconsistencies were primarily attributed to the high cooling rates and strain-induced phase transformations in DED, which are not accounted for in diagrams based on equilibrium equations. This highlights the need for more refined, process-oriented modeling approaches that account for non-equilibrium solidification and mechanical effects (Ref 19).

Inwoong Noh et al. also investigated a material pairing using this approach with the DED-Laser process. The transition from the austenitic-ferritic region to fully austenitic was investigated at certain points and led to similar results. The study confirmed that although the Schaeffler diagram provides a useful theoretical basis, deviations due to process-specific thermal effects underline the need for further refinement of the prediction modeling. These thermal effects, such as varying cooling rates, element segregation, and secondary phase formation, significantly influence the actual microstructure and are not fully accounted for by conventional equilibrium-based diagrams (Ref 20).

In order to investigate further areas in the Schaeffler diagram, the transition from the martensitic to the austenitic area was described in this article. The material pairing 42CrMo4 and Alloy 625 was selected for this purpose. In addition, the sample is graded in deposition direction and not layer by layer in order to achieve a higher resolution for the analysis and thus implement a different evaluation approach.

2 Materials and Methods—Experimental and Analytical Approach

In this study, the Schaeffler diagram was used to predict microstructural transitions in graded additive structures produced by a powder-based DED-Arc process. To evaluate the diagram’s suitability for predicting the resulting microstructures and identifying volatile property ranges at material transitions, a material pairing of a martensitic and an austenitic alloy was selected. The steel 42CrMo4, known for its high strength and wear resistance, was paired with the nickel-based alloy Inconel 625, recognized for its corrosion resistance and high-temperature stability. The nominal chemical compositions of the materials are shown in Table 1. Both materials were used in powder form, with spherical particle sizes ranging from 50 to 150 µm.

Table 1 Nominal chemical composition of used materials
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2.1 Calculation and Prediction using the Schaeffler Diagram

In order to classify the materials in the Schaeffler diagram, the chromium and nickel equivalents were calculated using standard formulas (formula 1, 2) so that the positions of the individual materials could be plotted in the diagram (Fig. 1). The material transition between material A (42CrMo4) and material B (Alloy 625) was visualized by connecting these points.

$$ {\text{Chromium equivalent}} \left( {{\text{Cr}}_{{{\text{eq}}}} } \right) = \% {\text{Cr}} + \% {\text{Mo}} + 1.5 \cdot \% {\text{Si}} + 0.5 \cdot \% {\text{Nb}} + 2 \cdot \% {\text{Ti}} $$
(1)
$$ {\text{Nickel equivalent}} \left( {{\text{Ni}}_{{{\text{eq}}}} } \right) = \% {\text{Ni}} + 30 \cdot \% {\text{C}} + 0.5 \cdot \% {\text{Mn}} $$
(2)
Fig. 1
figure 1

Calculated classification of the material transition in the Schaeffler diagram using the nickel equivalent (formula 3), labeling of the three main areas passed through.

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For the materials used in this study (see Table 1), the calculated equivalent values are as follows:

42CrMo4

Alloy 625

\({\text{Cr}}_{{{\text{eq}}{\text{.A}}}} \, = \,1.65\)

\({\text{Cr}}_{{{\text{eq}}{\text{.B}}}} \, = \,32.25\)

\({\text{Ni}}_{{{\text{eq}}{\text{.A}}}} \, = \,11.8\)

\({\text{Ni}}_{{{\text{eq}}{\text{.B}}}} \,{ = }\,{58}{\text{.525}}\)

The resulting course of the material transition covers three different microstructural areas: martensitic, martensitic + austenitic, and austenitic (M, M + A, A). Considering the nickel equivalent, the transitions from M to M + A and from M + A to A occur at values of 15.5 and 19.75 (cf. Fig. 1). The theoretical chemical compositions at which the range boundaries lie were then calculated. To determine the specific proportions of each material in the mixture at these transition points, the equation for the nickel equivalent can be rearranged and solved. fA and fB represent the fractions of material A (42CrMo4) and material B (Alloy 625), required to achieve the desired Nickel Equivalent (Nieq,target), which are marked red in the diagram.

$$ \begin{gathered} {\text{Ni}}_{{{\text{eq}}{\text{.target}}}} = f_{A} \times {\text{Ni}}_{{{\text{eq}}{\text{.A}}}} + f_{B} \times {\text{Ni}}_{{{\text{eq}}{\text{.B}}}} \hfill \\ {\text{Ni}}_{{{\text{eq}}{\text{.target}}}} = f_{A} \times {\text{Ni}}_{{{\text{eq}}{\text{.A}}}} + (1 - f_{A} ) \times {\text{Ni}}_{{{\text{eq}}{\text{.B}}}} \hfill \\ f_{A} = \frac{{{\text{Ni}}_{{{\text{eq}}{\text{.target}}}} - {\text{Ni}}_{{{\text{eq}}{\text{.B}}}} }}{{{\text{Ni}}_{{{\text{eq}}{\text{.A}}}} - {\text{Ni}}_{{{\text{eq}}{\text{.B}}}} }} \hfill \\ \end{gathered} $$
(3)

The theoretical transitions of the microstructural phases, therefore, occur at the following calculated material compositions:

(I) M → M + A

(II) M + A → A

\(f_{A} = \frac{15.5 - 58.525}{{11.8 - 58.525}}\)

\(f_{A} = \frac{20 - 58.525}{{11.8 - 58.525}}\)

\(f_{A} = 0.9208\)

\(f_{A} = 0.8245\)

\(f_{B} = 0.0792\)

[92.1%/7.9%]

\(f_{B} = 0.1755\)

[82.5%/17.5%]

Using the chromium equivalent to calculate these composition proportions gives the same result. Given these predicted transition zones, it is assumed that the properties of additive structures, such as hardness values, also vary depending on the microstructural composition. Volatile property changes are expected at the described compositional transitions. To verify this hypothesis, additive structures were produced with a material transition that covers these transition areas.

2.2 Experimental Setup

Regarding the system technology (Fig. 2), a powder-based tandem DED-Arc process with two plasma torches of the 230MV type was used, each with a power source (PS250) and a wheel powder conveyor from Plasmastar. The communication between the power sources was conducted via a “primary-secondary” control.

Fig. 2
figure 2

Experimental setup powder-based tandem DED–Arc with designations, arrangement of plasma torches.

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As shown in Fig. 3, the torches were arranged in a tandem configuration, creating a common melt pool due to the close alignment of their focal points. Figure 3 provides a process snapshot captured using laser illumination and a narrow-band filter centered at 820 nm ± 3 nm, alongside a cross-sectional view of the weld seam for a clearer understanding of the tandem process and the results it can produce. Previous studies have highlighted the advantages of this tandem arrangement (Ref 21, 22); in addition to an increased deposition rate, it offers more possibilities for powder supply and targeted local injection, as up to four channels are available for the supply of independent powder materials. The parameters used to generate the additive structures in this study vary depending on the application situation, material mix, and component size, so that only the rough working ranges for some parameters are listed in Table 2 for orientation. For effective layer bonding, an increased linear energy input is required in the initial deposition layers. As the build height increases, the heat dissipation mechanism transitions from three-dimensional to two-dimensional conduction. Consequently, the linear energy must be progressively reduced to maintain dimensional accuracy and prevent melt pool overflow along the edges of the deposited wall.

Fig. 3
figure 3

(a) Weld seam, (b) process snapshot, each torch (I = 160 A, \( \dot{V} \)PG = 2 l/min, vS = 20 cm/min, \( \dot{m} \)p = 30 g/min, ht = 14 mm).

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Table 2 Parameter ranges
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Energy input control was achieved through coordinated adjustments of arc current and deposition speed. While material properties significantly influence parameter selection, no in situ parameter adaptation was performed. Adjustments were only made between individual layers. However, this aspect lies beyond the scope of the present investigation.

2.3 Sample Plan Description

Based on the selected material pairing and the theoretically predicted microstructural transitions derived from the Schaeffler diagram, a sample plan was designed for property evaluation. The samples were produced as additive wall structures with a progressive material gradient in deposition direction in order to evaluate the hardness profile in the material transition zone (Fig. 4). A steel substrate plate made of S355 J2 (1.0577) was used as the construction platform but was not included in the evaluation. The material transition was designed from [100/0]-[70/30] (42CrMo4 in % / Alloy 625 in %) to cover the three microstructural regions predicted by the Schaeffler diagram (see Fig. 1). The additive walls consist of 15 layers, deposited at an interlayer temperature of 200 °C. To ensure consistent material distribution across all layers, each layer was applied with the same start and endpoint, without alternating deposition patterns. The material composition was adjusted in real time by controlling the rotational speed of two power-regulated wheel powder conveyors from Plasmastar. The powders were mixed in a shared hose package before being split and fed into the torches, where they melted into a common pool and were being deposited.

Fig. 4
figure 4

Classification of material transition within the sample, location of predicted boundaries from the Schaeffler diagram, and positioning of hardness and EDX measurement lines.

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For better process control and analysis, the material transition was divided into two additive walls, each part measuring 150 mm in length and 25-30 mm in height, where the first transition segment covered [100/0]-[85/15] and the second [85/15]-[70/30]. These walls were cut lengthwise into thirds for analysis. Hardness measurements were conducted along two horizontal lines to evaluate the mechanical properties of the material transition zone. Additionally, EDX line scans were performed along the same horizontal lines to correlate hardness values with material composition. To enable a detailed investigation of the material transition, the data acquisition was carried out with 20 hardness measurements per centimeter and 50 EDX measuring points per millimeter. To analyze the microstructure, cross sections of the samples were prepared, ground up to a 3200-grit finish, and polished using diamond suspension with 1-µm particles. Selected samples were etched using Adler’s reagent which consists of a mixture of hydrochloric acid, iron (III) chloride, and copper ammonium chloride and distilled water to enhance microstructural visibility.

3 Results and Discussion

3.1 Hardness and Element Distribution

This section presents the fabricated samples and the evaluated results. Figure 5(a) displays one of the two additive walls with the material transition [100/0]-[85/15] as described in sect. 2.3. The sample has a total length of 150 mm, starting with an initial build height of 30 mm at the left end, which gradually decreases to 20 mm at the right end of the individual layers. This height difference results from the toolpath strategy used for constructing the deposition wall. The individual layers were always deposited in the same direction rather than alternating, ensuring a consistent material transition in deposition direction. In addition, the material composition changes gradually, resulting in a significantly higher nickel content at the end point. The different material properties result in a wider layer geometry with a lower deposition height. When accumulated over multiple layers, this effect contributes to the overall height difference between the start and end points. The width changes from 10 to 12 mm along the weld seam. Externally, the sample exhibits a continuous and defect-free bond. For further analysis, both wall segments were divided into three subsections and separated longitudinally.

Fig. 5
figure 5

(a) Lateral view of the wall structure graded in the direction of application, (b) example of a longitudinal section of a partial segment ([94/6] → [87/13]), with associated measuring line position.

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Figure 5(b) illustrates the internal surface of one of the six subsections, where identical measurements were taken at predefined regions. These measurements include a series of hardness tests conducted in both the upper (hardness top) and lower areas (hardness bottom) of the specimen, as well as an elemental line scan analysis (EDX) along the lower hardness measurement line. The figure presents a macroimage of the longitudinal section, showing a material transition from [94/6]-[87/13]. The specimen was etched using Adler’s reagent, revealing no macroscopic defects and a continuous bond to the base material. However, the etching process highlighted differences between the upper and lower regions of the sample, with a progressively weaker etching response as the nickel content increased. These microstructural variations are further analyzed in detail in the subsequent section on metallographic analysis.

Figure 6 illustrates the trends of the key elements iron and nickel alongside the corresponding hardness values in a dual-axis diagram. The gradual material transition was achieved without significant composition jumps. In the upper region of the sample, hardness values decreased from 585 HV1 at a composition of [94/6] to approximately 510 HV1 at [87/13]. In contrast, the lower hardness profile showed an increase from around 470 HV1 to 510 HV1. At a mixing ratio of [94/6], the hardness values in the upper sample area were significantly higher than those in the lower area, with a difference of 100 HV1. As the proportion of Alloy 625 increased, this difference in hardness began to decrease and balanced out at a composition of 9% Alloy 625. The upper area with deviating hardness values extends over 11 mm, corresponding to 6 application layers. This is presumably due to a hardening effect resulting from the rapid cooling of the top buildup layers. During the additive application of further layers, the layers underneath are repeatedly heated to temperatures above 450 °C, which aligns with the known tempering temperature range for this material (Ref 23, 24). In contrast, the upper layers remained in a light quenched state and would transition into a tempered state as additional layers were deposited. The alignment of hardness values beyond a certain material composition can be explained using the Schaeffler diagram. As the Alloy 625 content increases, the theoretical boundary of purely martensitic region is left behind at approximately [92/8], with an increasing fraction of austenite present. This reduces the hardenability through rapid cooling. Beyond this point, hardness values remained consistent along the Z-direction across all segments.

Fig. 6
figure 6

Progression of the hardness values from the upper and lower areas of the sample along the material transition from [94/6] to [87/13].

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All subsequent sections were analyzed using the same methodology, and the compiled data were evaluated for the entire sample. The overall hardness distribution along the lower hardness measurement line (hardness bot) for the complete material transition from [100/0] to [70/30] is illustrated in Fig. 7. To improve visualization, element distributions were represented as trend lines, as no significant fluctuations were observed beyond this region. While element compositions followed a nearly linear transition, hardness values exhibited a more irregular progression. Theoretical phase transitions derived from the Schaeffler diagram occur at a composition of [92.1/7.9] for the shift from martensitic (M) to martensitic-austenitic (M + A) and at [82.5/17.5] for the transition from martensitic-austenitic (M + A) to fully austenitic (A). Three distinct hardness levels with nearly constant values were identified:

  • 370 HV1 in area a) [100/0]-[96/4]

  • 510 HV1 in area b) [91.5/8.5]-[84.5/15.5]

  • 215 HV1 in area c) [81/19]-[70/30]

Fig. 7
figure 7

Course of hardness values from the lower sample area (hardness bottom) and element composition (EDX) along the material transition from [100/0] to [70/30].

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with two transition zones between these areas (Fig. 7). The transition between area a) and b) occurs gradually, with a hardness increase of 130 HV1 over a composition range of 3%, corresponding to the theoretic shift from a martensitic to an austenitic-martensitic microstructure. Within area b), the highest recorded hardness of 540 HV1 was observed at 10% Alloy 625. The second microstructural transition also comes close to the theoretically determined values at [82/18] and occurs much more abruptly with a significant drop in hardness of 250 HV1 within a composition change of only 1.5%. Beyond 19% Alloy 625, hardness stabilizes at 215 HV1, remaining constant from this point onward.

The hardness values in area a) correspond to those of 42CrMo4 in the quenched and tempered condition, while the hardness values in area c) correspond to those of Alloy 625 in comparable additive structures (Ref 23,24,25). In area b), the hardness exceeded that of the individual base materials. This increase is due to the development of the microstructure and probably the formation of precipitates. A more detailed analysis of these structures is provided in the following section.

3.2 Evaluation of the Microstructure and Precipitates

To evaluate and compare the microstructure, optical microscope images of the longitudinal sections from relevant areas a), b), and c) of the mixtures were taken and analyzed using a scanning electron microscope. The images (Fig. 8) show sample areas from the same application height 10 mm above the substrate material with a magnification of 2000x. The corresponding elemental analyses of a comparable surface from the same area are shown below the sample images, showing the evolution of the precipitates and their structure.

Fig. 8
figure 8

SEM images of different material compositions with the corresponding layer images of the element analysis [42CrMo4 / Alloy 625] in %, as welded, etched Adler, 2kx.

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The microstructure of pure 42CrMo4 (Fig. 8a) exhibits similarities to normalized condition, structured with ferrite and fine-grained pearlite, which also compare to samples from semi-finished goods (Ref 26,27,28,29). The elemental analysis shows an even distribution of the elements without major irregularities.

With the raising admixture of Alloy 625 (Fig 8b, e), the microstructure becomes finer compared to pure 42CrMo4, although it still resembles the structure. Additionally, arranged dendritic structures are now present. These areas are likely columnar interdendritic residual solidification zones. These interdendritic areas increase in size as the proportion of Alloy 625 increases (Ref 30), which is due to the rising amounts of precipitation-promoting elements such as Cr, Mo, and Nb (Ref 31). The elemental analysis showed that niobium and molybdenum accumulate particularly in these areas. As described in the literature, the line structure forms along the build-up direction, thus following the direction of the plasma arc (Ref 25, 32). The measured hardness values in this region also increased significantly, reaching over 500 HV1. This is due to the greater presence of hard precipitate areas as well as their arrangement. The geometry used for the hardness impression (pyramidal) at HV1 covers approximately 3 dendritic arms, so the average hardness of the region was measured here. The hardness of the matrix alone is likely lower, while that of the precipitates is higher, but this could not be further analyzed with the system used.

In the following image, region c) (Fig 8c, f), the microstructure between the precipitation areas now more closely resembles that of pure Alloy 625, which would be austenitic (Ref 33). These changes also correspond to the information from the Schaeffler diagram, and the transitions are clearly visible. The shape of the precipitate changes to a more cellular form, and they are now found at the grain boundaries. The hardness values here dropped significantly to 215 HV1. It can be assumed that the precipitate areas still have a higher hardness, but they are pressed into the softer austenitic matrix, and the measured hardness value is an average value of the supported matrix. The exact composition of the precipitate areas and the matrix will be provided in the following detailed spectrum measurements.

To characterize the resulting microstructural components with increasing addition of Alloy 625, exemplary EDX point measurements were taken on the [80/20] composition (see Table 3). The four spectra examined cover the following areas: S1 base matrix, S2 precipitate area at the edge, S3 precipitate area in the center, and S4 other round precipitate forms. The characteristic elements for each spectrum are highlighted in bold in Table 3.

Table 3: Chemical composition of the measurement spectra, sample composition [80/20]
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The analysis of the base matrix shows that the composition ratio of 80/20 is present, with the iron content at 79.8%. Niobium and molybdenum are found at lower concentrations than theoretically expected for this mixture, because they accumulate more in the precipitation areas and the element content in the other sample regions drops.

The chemical composition of spectrum 2 predominantly showed the increased presence of niobium, molybdenum, and slightly increased chromium, while the iron content was below the expected average. This confirms the precipitation of niobium and molybdenum in the interdendritic space, as described in the literature, and thus the formation of primary carbides MC (M = Nb, Mo) (Ref 31, 34). The high carbon content resulting from the use of the 42CrMo4 mixing partner also contributes to this development, which could be determined in a comparative measurement of the carbon content between the matrix and the precipitation areas. A high carbon-to-niobium ratio is crucial for the formation of such a microstructure (Ref 35). The less pronounced precipitation of chromium is also consistent with the literature, as it is only observed in the form of M23C6 carbides at longer aging times and elevated temperatures (Ref 31).

In spectrum 3, rod-shaped or linear precipitates were visible within the interdendritic regions. These contain the highest proportion of niobium and have a comparable form to the Laves phase described in the literature (Ref 36,37,38,39). Under high loads or internal component stresses, this phenomenon promotes crack initiation in these regions (Table 3), which has also been described in similar studies on pure arc-welded Alloy 625 due to the reduced ductility of the carbide-rich areas (Ref 25, 35). Carroll et al. report that in the additive manufacturing of FGMs from 304 stainless steel and Alloy 625, this occurs with similar admixture proportions as seen here (Ref 32).

Spectrum S4 represents a round precipitate with increased amounts of manganese. These are only found sporadically within the sample.

4 Summary and Conclusions

This study explored the use of the Schaeffler diagram as a predictive tool for evaluating microstructural transitions and resulting mechanical properties in FGAM using the powder-based DED-Arc process. A material system consisting of 42CrMo4 and Alloy 625 was selected to investigate the relationship between calculated phase predictions and experimentally observed characteristics. Based on chromium and nickel equivalents, the Schaeffler diagram indicated three primary microstructural regions across the composition gradient: martensitic, mixed martensitic-austenitic, and fully austenitic. A wall structure with material transition was produced, which transitions from 100% 42CrMo4 to a 70/30% mixture with Alloy 625, covering the predicted phase transitions. Elemental analysis confirmed a continuous material gradient along the deposition direction. Hardness measurements revealed three distinct regions with nearly stable values (approx. 370 HV1, 510 HV1, 215 HV1), with clear transitions aligning well with predicted phase boundaries. A maximum hardness of 580 HV1 was observed at 90/10 (42CrMo4/Alloy 625), likely due to niobium- and molybdenum-rich precipitates. The study also found a certain variation in hardness in the martensitic range, which is caused by thermal cycling and stabilizes during the transition to the austenitic range. The results confirm that the Schaeffler diagram provides a valuable guide for identifying critical transition zones and understanding phase behavior in FGAM. It can support the targeted design of material transitions and reduce experimental effort by narrowing down the relevant compositional regions for analysis.

As an outlook, integrating the Schaeffler-based approach with advanced simulation tools such as JMatPro could enable more accurate predictions of phase formation and accordingly mechanical properties across transition zones, further supporting efficient material development in FGAM applications.