Study of residual stresses in steel components produced via wire-arc directed energy deposition: finite element analyses and experimental approach

doi:10.21203/rs.3.rs-4486978/v1

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Study of residual stresses in steel components produced via wire-arc directed energy deposition: finite element analyses and experimental approach

https://doi.org/10.21203/rs.3.rs-4486978/v1

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Residual stress evaluation in directed energy deposition processes is of great importance, since its underestimation or lack of control can result in mechanical properties degradation of the produced components and even failure in service, particularly when there is an overlap of tensile stresses originating from repeated thermal cycles. The objective of this study was to perform a systematic analysis of the residual stress generation in wire-arc directed energy deposition produced steel samples. For this purpose, a finite element model was first developed and validated in order to understand the stress distribution in the longitudinal and transverse sections. In addition, test specimens with different numbers of deposited layers were produced by a bidirectional continuous strategy using the cold metal transfer deposition modality, and subjected to experimental residual stress measurements employing an optical hole-drilling method. Dimensional, microstructural, and hardness profile analyses were performed as well. The results obtained in this study demonstrate that the residual stress distribution is not uniform in the wire-arc directed energy deposition produced samples because of the different cooling rates and deposited material volume in the different parts of the studied components. Moreover, different numbers of beam layers, and consequently varying thermal cycles have a significant influence on the type, magnitude, and distribution of the residual stresses, as well as on the dimensional stability and microstructure changes.

Residual stress

Additive manufacturing

Wire – arc directed energy deposition

Cold metal transfer

Finite element analyses

The growing interest in wire-arc DED in industrial and academic segments is related to its potential to create components with complex geometries, large-scale production, high deposition rates, material usage efficiency, and reduced production costs. In comparison to traditional subtractive manufacturing methods, DED can reduce the lead time by 40–60% and the finishing time by 15–20%, depending on the component size [1]. For instance, recent advancements in additive manufacturing technologies have enabled approximately 78% raw material savings in the fabrication of aircraft landing system elements when compared to conventional manufacturing methods [2].

The wire-arc DED process involves the direct automated deposition of metal in its molten state, in which successive layers form the designed final product geometry. Consequently, complex thermal cycles occur during this deposition, potentially resulting in the coexistence of different physical states of the deposited material, including the solid, liquid, or solidifying phases. Subsequently, owing to repetitive exposure to the heat generated by the arc, the deposited layers consist of overlapped fusion (FZ) and heat-affected zones (HAZ) and are subjected to cumulative thermomechanical effects. This phenomenon influences the resulting microstructure in a complex manner and leads to the development of residual stresses that can reach up 60–100% of the yield strength [3], depending on the material and its properties, significantly compromising the quality and reliability of the produced mechanical parts [4–7]. In addition, a systematic review of the defects present in DED – produced components demonstrated that residual stress in steel and aluminum samples can be as severe as deformation and cracking [1].

The study of the residual stress in components produced via wire-arc DED presents some challenges, both in theoretical fundamentals that explain the mechanisms behind the generation of these stresses and in experimental/numerical simulation aspects that provide accurate values for design purposes and service life prediction. The theoretical models are relatively recent and not as widespread as, for example, the models for traditional arc welding [8, 9]. Thus, Hönnige et al. [3] proposed a model for residual stress distribution in a sample composed of a mechanically restrained substrate and horizontally deposited layers (beam), as shown in Fig. 1. In this model, the authors explained that under these conditions, constant longitudinal tensile stresses develop in the resultant component beam, whereas constant compressive stresses develop in the substrate throughout its thickness. According to the authors, each deposited layer contributes the same tensile stress during thermal contraction owing to the solidification and cooling phenomena occurring in the beam. After the restriction is removed, the tensile stress in the beam induces bending of the substrate along its longitudinal section (Fig. 1(b)), which in turn causes stress redistribution in the deposited layers and the substrate itself (Fig. 1(c)). The inherent compressive plastic strain in the deposited wall causes the upwards bending of the specimen, which significantly reduces the tensile stresses on the top of the wall and increases the tensile stresses at the bottom of the substrate. To achieve equilibrium after unclamping, the net bending moment across the section must be equal to zero. As a result, both the substrate and beam undergo a transition from tensile residual stresses at the bottom to compressive stresses at the top.

In this context, Colegrove et al. [10] experimentally confirmed, using neutron diffraction method, the development of compressive stresses at the top of deposited beams while investigating the residual stress distribution in steel components. In a related study, Köhler et al. [11] examined the stresses resulting from DED in aluminum alloys using X-ray diffraction techniques. Their results revealed that the stress magnitudes in the last layer of the deposited beam ranged from approximately − 150 MPa, while at the substrate's surface, the obtained values were approximately − 50 MPa (both cases exhibited compressive stresses). The authors of the study also concluded that, in order to maintain equilibrium within the fabricated component, the initial layers of the beam and the substrate base should experience tensile stresses, aligning with the theoretical model proposed in [3]. However, owing to the strong and complex dependency on the component geometry and manufacturing process itself, as well as on the measurement techniques employed, the generation and distribution mechanism of residual stress in DED components remains unclear.

In order to obtain a better understanding of the transition between tensile and compressive stresses within the body of the wire – arc DED – produced aluminum components, Sun et al. [12] developed a numerical model for different deposition cases with the number of layers ranging from 1 to 30. The simulation results demonstrated that with an increase in the beam height, the magnitude and nature of the residual stresses change in both the beam and substrate. For instance, as illustrated in Fig. 2, for a 15-layer sample, tensile stresses develop throughout the beam, including the top of the component (a result that differs from those reported in [3], [10], and [11]). In contrast, for a 30-layer sample, the residual stresses start as compressive in the initial layers, change in nature at a height of approximately 25 mm, and return to compressive values in the last layer (in accordance with the model proposed in [3]). Another observation that can be obtained from this study is that, for the same beam height (e.g., 15 mm or approximately 10 deposited layers), samples with 30, 20, 15, and 10 final layers exhibit residual stresses that differ in magnitude and nature. Thus, the higher the sample beam, the lower the simulated tensile stress values, resulting even in compressive magnitudes for the highest 30-layer deposited beam. The authors explained this by the fact that both the longitudinal and transverse restraint degrees of the top layers were lower than those of the bottom layers; however, a weldment model was considered for this statement and not the DED one. According to the presented results, the residual stress distribution in the substrate was also found to be dependent on the total number of layers in the component, that is, tensile throughout the substrate in the lower – beam samples and tensile – to – compressive in the higher – beam samples.

Although the simulation results presented in [12] are of a paramount importance for understanding the phenomenon of residual stress generation and distribution in DED – produced components, their validation still lacks experimental data. This is particularly pertinent because the measurement of stresses in the referred study was performed only for a 20-layer sample (via the X-ray diffraction method) and exhibited a 120% difference between the predicted and experimentally obtained values for the longitudinal component of the residual stress. Moreover, there is a lack of information in current research reports on the residual stress distribution throughout the thickness of the beam and the length of the substrate, which is relevant because stress accumulation in a specific part of the component may lead to unpredictable failure in service.

Therefore, the objective of this study was to perform a systematic analysis of the residual stress distribution in wire – arc DED – produced steel samples by employing both finite element modeling and an experimental approach. A better understanding of this phenomenon is expected to clarify the generation mechanisms of the residual stress in DED processes and provide suggestions for reducing the resulting high stress values in order to improve the performance of the fabricated components.

This study was divided into several stages: fabrication of the wire – arc DED test samples, finite element model development and its experimental validation, residual stress measurements, dimensional, microstructure, and microhardness analysis. The details are presented below.

2.1. Specimen fabrication

For the purposes of this study, the test samples were fabricated using the gas-shielded wire – arc DED process on its Cold Metal Transfer (CMT) modality, known for its low heat input, good deposition control, and superior quality of the produced pieces [1, 13, 14]. Thus, beams with 10, 25, 50, and 100 overlapping layers were deposited on a 6.35 mm thick AISI 1020 steel substrate (previously clamped) using an ER70S-6 wire with a 1.20 mm diameter as the additive material. The experimental setup and strategy employed for continuous bidirectional deposition are shown in Fig. 3. The respective deposition mode was chosen owing to its favorable geometry, surface finishing, and heat input aspects [15].

The compositions and properties of the deposited material and substrate are listed in Tables 1 and 2, respectively. The previously tested process parameters [15] used for DED are listed in Table 3. After specimen fabrication, the dimensions (length, height, and thickness of the deposited beams) were measured using a caliper with a measurement range from 0 to 150 mm and a 0.02 mm resolution. A series of 20 measurements was taken for each analyzed dimension in order to observe its variation in different parts of the deposited beam.

Table 1

Composition and properties of the deposited material.
Nominal chemical composition of the ER70S-6 wire, wt. (%)		Yield strength (MPa)		Young's modulus (GPa)	Poisson's ratio
C	0.07 0.85 1.50	420	500	207	0.292
Si
Mn

Table 2

Composition and properties of the substrate.
Nominal chemical composition of the AISI 1020, wt. (%)		Yield strength (MPa)		Young's modulus (GPa)	Poisson's ratio
C	0.20 0.22 0.66	350	420	205	0.290
Si
Mn

Table 3

Wire – arc DED process parameters.
Parameter	Unit	Value
Mean current (I_m)	A	62
Mean voltage (U_m)	V	20.6
Travel speed (V_x)	mm/s	24
Build-up speed (V_z)	mm/s	8
Layer pass (P_z)	mm	1.20
Shielding gas		Ar + 18%CO₂
Gas flow	l/min	15
Wire feed speed (V_f)	m/min	2.60
CTWD	mm	12
Interpass temperature	(°C)	̴ 420°

2.2. Residual stress measurements

The residual stress experimental measurements in the DED – produced samples were performed under as – fabricated conditions (without previous cutting) after clamp removal, employing the optical Electronic Speckle Pattern Interferometry (ESPI) hole-drilling method [16]. The tests were carried out using the equipment shown in Fig. 4 (a), which consisted of a camera for image capture, drilling tool, sample fixture device, and laser beam with all its known properties. During the measurement procedure, the beam is divided into two parts: the first one is launched on the sample and reflected to the camera, whereas the second one (referred as the reference beam) passes through a piezoelectric phase-change system and is subsequently directed to the same optical device. When a hole is drilled in the sample and the stress present in the material is relieved by local deformation, the light beam reflected from the surface of the sample changes its characteristics. When compared to the reference beam, the reflected beam exhibits a phase shift, which leads to a new grain pattern (pixels) in the recorded camera images. From the difference in pixel arrangement before and after drilling, that is, before and after stress relief, a speckle pattern is obtained (see Fig. 4 (b)). Subsequently, the spackle patterns are processed as digital interferograms [17] with an equipment algorithm in order to obtain the local surface displacements caused by the machining of the sample and the corresponding residual stress present in the material before drilling.

The ESPI-based hole-drilling method has already been employed in residual stress studies [18–20], demonstrating an acceptable error of 3.5% for aluminum samples and 5% for steel samples. In this study, the equipment was previously calibrated using a standard four-point bending device [21], and good accuracy was also reported (with a mean error of 5.8%), as well as a good precision (with a coefficient of variation of 6%), and measurement sensitivity, even when applied to irregular surfaces typical of DED parts (more details can be found in [22]).

Both for finite element model validation and definitive residual stress evaluation, series of measurements were carried out drilling 0.8 mm diameter hole at a rotational speed of 25000 rpm and 0.05 mm/s feed rate reaching the maximum hole depth of 0.4 mm. These parameters are recommended in the current literature to achieve high – quality hole opening [18, 23]. For each drilling pass increment, which was set as 0.05 mm for this study, the equipment's software provides longitudinal (σ_x) and transverse (σ_y) stress values as a response.

The residual stresses in the wire – arc DED – produced specimens were measured at the surface of the deposited layers at points distributed along the Z-axis, as illustrated in Fig. 5. The drilling direction (Y-axis) was chosen to ensure that the longitudinal (σ_x) and transverse (σ_y) stresses were measured by the equipment aligned with the actual longitudinal and transverse stress components according to recent theoretical models [3, 12]. Drilling was performed in both the substrate and the layers, with approximately 6.5 mm intervals along the height of the beams (considering that a 3 mm distance between the hole openings is recommended in order to avoid the drilling influence on the stress state in the material). Consequently, three measurements (hole openings) were taken in the 10-layer specimen, five measurements in the 25-layer specimen, seven measurements in the 50-layer specimen, and twelve measurements in the 100-layer beam, summarizing in 27 experimental tests.

2.3. Macrography and hardness evaluation

For microstructural and hardness analysis, DED – produced samples were cross-sectioned in the central part perpendicular to the layer direction. Small rectangular specimens were extracted from the substrate, bottom, and top layers of the examined pieces in order to evaluate their microstructure, fusion, and heat-affected zone dimensions, as well as the hardness changes due to DED processing. Thus, these samples were cold-mounted in resin, grounded using abrasive silicon carbide papers with nominal densities of 800, 1000, 1200, and 2000, and then polished with fine diamond paste. Finally, the polished samples were etched in 2% Nital solution (2 ml HNO₃, 98 ml ethanol) for 20s at room temperature until the grain boundaries were revealed.

By employing a stereoscope and optical microscope, it was possible to discern the dimensions of the fusion and heat-affected zones in the substrates, as well as to analyze the microstructures in different parts of the DED – produced samples. Hardness measurements were performed to investigate the variation in this property as a function of the number of deposited layers using a Vickers hardness tester operating at 200 nN and 0.5 mm increment.

2.3. Finite element analyses (FEA)

A thermomechanical finite element simulation for the residual stress analysis in wire – arc DED – produced components was developed and processed using SYSWELD^® software. First, a full three – dimensional solid meshed model of the structure was created, consisting of a substrate and 10 consequently deposited layers, as shown in Fig. 6. Since on the one hand, the quality of FEA is strongly influenced by the meshing features of the part being modelled and on the other, fine meshing incurs high computational cost, a compromising meshing technique that uses variation in mesh density (biased mesh) across different regions was adopted in this study. The regions that were comparatively close to the heat source in the substrate and deposited layers were densely meshed because of the steep temperature gradients. In addition, a substrate with smaller dimensions was designed (with 100 mm length instead of 200 mm of the test sample) in order to optimize the computational time and efficiency.

The total number of nodes was 84.329 and that of the meshes was 67.532. The minimum size of the element at the beam area was approximately 0.5 × 0.5 × 0.5 mm. The respective material properties for the substrate and beam were used from the software database to feed the FEA. The simulated conditions resembled the real conditions: free air cooling (convective and radiative) on all open surfaces, rigid clamping of the base plate, and the same heat input and speeds.

The thermal stresses generated during the material deposition on the clamped baseplate was calculated in two steps. The first step in the uncoupled thermomechanical simulation was transient thermal analysis, which was performed to calculate the time-dependent temperature distribution. Second, the temperature field output from the thermal analysis at each time step was used to calculate the stress field in the subsequent structural analysis of the unclamped sample.

Progressive material deposition with respect to time and the corresponding position was considered during both the thermal and mechanical simulations. The material deposition was executed by an individual element activation algorithm by means of the element birth method. The elements were initially deactivated in the first step and then activated sequentially by following the movement of the arc heat source [24, 25]. During the analysis, any element that was defined as activated was filled with material, whereas elements that were not considered for calculation were considered inactive. For example, during the deposition of the first layer, elements representing the remaining upper layers are assigned as empty (inactive), as per the timeline.

Goldak’s double ellipsoidal heat source [26] was employed to model the heat flux in the thermal analysis in this study, as illustrated in Fig. 7. As the movement of the heat source during material deposition generates an inconsistent energy distribution in the form of heat flux density, as per the model definition for element nodes, its flux is given by the equations below:

$$q \left(x, y, z\right)=\frac{6\sqrt{3 {f}_{f/r} }}{abc\pi \sqrt{\pi }}Q{e}^{\left(-\frac{3{x}^{2}}{{c}_{f/r}^{2}}\right)}{e}^{\left(-\frac{3{y}^{2}}{{a}^{2}}\right) }{e}^{\left(-\frac{3{z}^{2}}{{b}^{2}}\right)}$$

$$Q= \eta IU$$

$${f}_{f}+ {f}_{r}=2$$

where x, y, and z are the reference axes; a, b, and c are the variables that define the dimensions of the ellipsoidal heat source, according to Fig. 7; Q is the heat source power, calculated according to Eq. 2, considering the data from Table 4 and thermal efficiency of 0.65; f defines the energy flow intensity, and subscript “f ” and “r” represent the front and the rear region of the deposited layers melt pool, respectively, from the origin of the axes as depicted in Fig. 7. The values used are listed in Table 3.

After numerical simulation of the 10 layers deposition, the developed model was experimentally validated by the macrographic dimensions of the fusion and heat-affected zones of the respective DED – produced sample and longitudinal residual stress measured in the substrate, 1st, 4th, 8th and 10th layers employing the ESPI-based hole-drilling technique described in the Section 2.2.

Table 4

Goldak’s heat source model parameters.
a (mm)		b (mm)	c_f (mm)	c_r (mm)	f_f	f_r	Q (W)
3		2.5	2	6	0.6	1.4	1300

3.1. Dimensional and microstructural analysis

The specimens fabricated with different numbers of deposited layers and used for the posterior experimental evaluation of dimensional stability, macrography, hardness, and residual stress are shown in Fig. 8. As can be observed, the layers of all the test samples were well-formed. No clear delineations were reported between the layers. Visible discontinuities or cracking on the wall surfaces were absent.

The dimensions of the deposited beams are shown in Fig. 9. The length of the walls (L) did not undergo significant changes owing to the automated travel trajectory of the welding torch. The small variations observed in Fig. 9 (a) are probably the consequence of partial plastic deformation experienced by the samples, especially because larger length alternations were reported for the higher beams (for 50-layer and 100-layer specimens), where the restriction to contraction was lower.

As expected, the height H of the beams (Fig. 9 (b)) varied with the number of layers. However, this variation was not directly proportional to the number of depositions. For example, a 150% increment in the number of deposited layers (from 10 to 25) resulted in only a 120% increase in the wall height. Similarly, a 100% increment from 25 to 50 layers and from 50 to 100 layers resulted in 84% and 93% increases in wall height, respectively. Thus, the lower the beam, the higher the disproportionality.

Considering that the process parameters and volume of the melted wire were maintained for all test samples, this disproportionality was compensated by an increase in the thickness T of the top layers of the beams (Fig. 9 (c)). A similar observation was made by Laghi et al. [27] for stainless steel planar plates and tubular structures, where a 13% larger thickness than the nominal thickness was reported for the wire – arc DED process. This phenomenon can be explained by the progressive preheating effect of the material owing to previous depositions, resulting in decreased viscosity and better spreading over the wall. Further studies should be conducted to determine whether this behavior is progressive, potentially leading to significant dimensional instability or, at a certain point, preheating of the previously deposited layers is saturated, and the height-to-width proportionality no longer changes beyond a certain deposition height.

Figure 10 shows the overall microstructure of the DED – produced steel walls in different regions: coupling of the substrate and the bottom layers, substrate (base metal), bottom layers, and top layers. The substrate was represented by grains uniformly distributed throughout the structure, displaying a ferritic matrix with perlite grains evenly dispersed across the entire region. The bottom layers, characterized by being in contact with the cold substrate before the deposition and the consequent high thermal gradient from one side and post heating coming from the top layers from another, represent the formation of acicular ferrite and bainite needles in all the analyzed samples. In turn, the upper layers that experience the preheating effect from the previously deposited layers from one side and contact with the air environment from another manifest a higher thermal shock and completely different microstructure of the lamellar type. In particular, it is possible to distinguish that the microstructure consists of bainite lath aggregates composed of both ferrite and cementite. As the cooling starts from a temperature approximately 70°C greater than the critical temperature for the used steel, the growth of ferrite laths devoid of carbon is justified. In fact, because the carbon in the ferrite is contained in smaller quantities, it migrates to the upper areas, and the laths are filled with carbon. Similar results for ER70S-6 steel walls were previously reported in [6, 28].

As for the FZ and HAZ of the substrate-beam coupling, their widths were varied for samples with different numbers of deposited layers, as shown in Fig. 11. Thus, the FZ dimensions demonstrated the highest value for the lowest deposited wall (10-layer), decreasing with the number of layers, resulting in the lowest value in the highest wall (100-layer). The HAZ, in contrast, increased in width with an increase in the number of deposited layers. As the heat input was equal for all the samples, the repetitive thermal cycles and consequent reheating could influence the FZ + HAZ region decomposition, decreasing the fusion area and increasing the heat-affected area for each deposited layer.

The hardness results in terms of the beam height are shown in Fig. 12. Mean values exhibited acceptable variations resulting in 188.8 HV, 213.0 HV, 201.3 HV and 197.9 HV for the 10-layer, 25-layer, 50-layer and 100-layerwalls, respectively. However, a considerable hardness discrepancy was observed along the beam height for all the analyzed samples. The standard deviation of the measured values was reasonably high because the indentations were made in different beam microstructures. Therefore, a linear fit was applied to understand better the hardness changes in the DED beams. It can be observed that for all the tested samples, this material characteristic presented lower values at the bottom of the beam and higher values in the upper layers owing to the highest hardness of the bainite microstructure at the top layer. This tendency can be attributed to HAZ softening [29, 30] in the intermediate layers and carbon accumulation at the top of the beam [28]. Similar hardness results have been previously reported for DED – produced samples with ER70S-6 wire [6, 28].

3.2. Finite element analyses (FEA)

As mentioned above, a finite element model was developed in this study for a 10-layer deposition on a rigidly clamped substrate. Before further analysis, this model was validated by the FZ and HAZ dimensions obtained from the macrography of the equivalent fabricated sample as well as by the longitudinal residual stress measured using the EPSI-based hole-drilling technique, as shown in Fig. 5. Thus, according to the images in Fig. 13 and data presented in Table 5, error between the measured and simulated FZ depths is 3.5%, whereas error between the measured and simulated HAZ depths is 0.8%. The difference between the measured and simulated FZ + HAZ areas was estimated to be 1.6%, demonstrating a good correlation between the finite element model and experimental data obtained from the 10 – layer DED – produced sample.

For the residual stress values, a comparison between the simulated and experimentally obtained data is shown in Fig. 14 for the substrate and several beam layers, considering different measurement depths. An acceptable correlation was reported from the illustrated tendencies, with maximum and mean errors of 12% and 7.6%, respectively.

Table 5

Experimental and simulated data obtained from the macrography and finite element modeling.
	FZ depth (µm)	HAZ depth (µm)	FZ + HAZ area (mm²)
Macrography data	689	361	3.87
Simulated data	713	358	3.93
Error (%)	3.5	0.8	1.6

From Fig. 15 (a), where the simulated model is illustrated, it can be observed that the residual stress distribution varies in both the X (length) and Z (height) directions. These variations are mainly related to the degree of restraint present in different parts of the DED – produced component and the heating/melting/cooling occurring during deposition. Thus, the bottom layers of the beam are more restricted than the top layers. This is because the structural stiffness related to the height/width ratio of the beam decreased with the height of the deposited material. Similarly, the side ends of the beam were less mechanically restricted than those in the center part of the beam. It can then be assumed that less restricted parts (top layers and side ends) can suffer partial thermal expansion during reheating and partial shrinkage during cooling. This generates a lower longitudinal residual stress in the piece. In contrast, the more restricted (by the substrate and wall sides) central part cannot expand/contract, even partially, leading to the development of tensile stresses in the lower center part of the deposited beam. Moreover, there is an effect of a lower temperature gradient caused by the preheating effect of the previous layers on the latter ones, explaining why the maximum longitudinal tensile residual stress in the beam was found at the bottom layers but not at the intermediate ones, where the restriction was also considerable.

In addition, compressive stresses were demonstrated by the finite element model at the top of the simulated deposition, which also varied in the Y – coordinate. For stress equilibrium and no bending moment, compressive residual stress is generated in the top layers of the beam. Higher compressive values were observed at the top side ends of the model. These were the points where the last deposition ended, and the last solidification of the material occurred. Similar longitudinal stress results were obtained in a finite element analysis conducted by Abusalma et al. [31] for Inconel 718 deposition on an A36 steel substrate. Moreover, the residual stress distribution observed along the height and length of the sample agreed with the experimental results reported in [3], [10], [12].

The residual stress distribution inside the DED – produced pieces is not uniform according to the finite element model, as shown in Fig. 15 (b). This phenomenon is expected because of the different cooling rates experienced by the surface and inner volume of the product. Nevertheless, unlike in the single-pass welding models [8], [9], where the maximum tensile stress was concentrated at the center of the weld bead, and in the DED case, this concentration occurred at the surface and under the surface area of the lower beam layers. Thus, in addition to the previous demonstration in Fig. 14, it can be observed that at the bottom layers (from 1st to 4th ), the stress values decrease from approximately 250 MPa at a depth of 0.5 mm (surface and under surface region) to 60 MPa at the center of the beam (in the transverse direction). Because the central part of the beam (which is the center of the weld pool during the deposition) is the last to experience solidification, there is sufficient time for stress relaxation until total cooling of the deposited layer. Moreover, this relaxation can occur during refusion and/or reheating when subsequent layers are deposited. This is why the stress gradient in the intermediate layers in the transverse direction was not as high as that in the bottom layers. A decrease in residual stress values with distance from the surface in the transverse direction has been previously observed for DED products in [10] and [19].

In contrast, the residual stress values increased from 60 MPa at the surface to 140 MPa at the center of the beam for the 8th layer height. In this case, the increase in values with distance from the surface can be related to the microstructural changes to the phases with a higher yield stress and hardness (discussed in Section 3.1), as well as to the transition area due to residual stress redistribution from tensile at the bottom to compressive at the top, as discussed previously. However, the tensile stress magnitudes in this area were still not as high as those at the lower surface of the beam (reaching up to 60% of the material yield stress).

As a result of the FEA, the longitudinal residual stress values demonstrated a tensile nature in the lower part of the beam and a compressive nature at its upper layers (both of different gradients in the X-and Z-axis), aligned with the Hönnige et al. [3] model demonstrated in Fig. 1. As for the substrate, compressive and tensile stresses, both of low magnitude, were reported in this study.

3.3. Experimental results of the residual stresses

The results of the mean (in terms of the measured depths) residual stress obtained experimentally from each measurement point according to Fig. 5 for the wire – arc DED – produced samples are shown in Fig. 16 for both the longitudinal (σ_x) and transverse (σ_y) components. From the raw data, a polynomial interpolation function was applied to trace their respective tendencies. It can be observed that the transverse residual stress exhibits lower magnitudes when compared to the longitudinal stress. This is because of the material volume of the samples subjected to expansion and contraction processes during the thermal cycles in each direction. As reported in [10] and [32], the volume of the heated material, together with the cooling rate and metallurgical transformations, are the factors that govern the stress generation in processed samples. Because this volume in the transverse section was much smaller than that in the longitudinal section for the DED beams, the thermal and consequent residual stresses resulted in lower magnitudes in this direction.

The distribution of the longitudinal component (σ_x) in the substrate and in the beams of the samples fabricated with different numbers of layers is illustrated in Fig. 16(a). The magnitude of the substrate stress was dependent on the number of deposited layers. They were compressive for all the studied cases, which aligns with the experimental results reported by Köhler et al. [11] for aluminum samples, the simulated results reported by Sun et al. [12], and the FEA in Fig. 15 for the 10-layer model. There also was an increase in the stress magnitudes in this area: from − 73.4 MPa (25 layers) to -223 MPa (50 layers), followed by a decrease to -71.6 MPa (100 layers). While the referred increase in the longitudinal compressive stresses with the number of layers ranging from 10 to 50 can be explained by the growth of the bending deflection in the samples, the decrease between 50 and 100 layers is justified by the saturation of the thermal impact at a certain height owing to the cooling of the bottom layers in the case of higher beam depositions.

A strong correlation with the number of deposited layers was observed with respect to the distribution of these stresses (σ_x) along the height of the beams. Thus, in the 10-layer beam, σ_x starts as compressive in the substrate and evolves into tensile stresses of greater magnitude in the bottom layers of the beam and, subsequently, into compressive ones in its upper layers. For the 25-layer sample, residual stresses begin as compressive at -73.4 MPa in the substrate, become nearly null at the point of substrate-beam coupling, and evolve into tensile stresses of approximately 22% of the material’s yield strength in the bottom layers. In the intermediate layers of this deposited sample, the stresses changed in nature again, resulting in compressive magnitudes at the top. In the 50-layer test specimen, the substrate stresses were compressive, as well as at substrate-beam coupling, evolving into tensile stresses in the intermediate layers and changing to compressive stresses in the upper layers. Finally, in the test specimen with the highest number of deposited layers, the longitudinal stresses exhibited compressive values in the substrate, at the area of substrate-beam coupling, and in the bottom layers, evolving into tensile stresses in the intermediate layers (reaching 38% of the material’s yield strength) and changed to compressive stresses in the top layers.

Thus, all the samples produced with the DED process for the purpose of this study exhibited compressive residual stresses (σ_x) in the substrate and at the top of the beam. The stresses in the bottom and intermediate layers were demonstrated to be dependent on the final height of the deposition; for the lower samples, the concentration of the tensile magnitudes occurred in the initial layers, and for the higher samples, this concentration occurred in the upper ones. These experimental results align with the simulated data for 20 and 30 layers, as illustrated in Fig. 2. However, in contrast to the conclusions of Sun et al. [12], this study demonstrated that the greater the number of layers, the higher the magnitude of the residual stresses along the height of the beams. Specifically, as the height of the depositions increased, the magnitude of the tensile stresses at the intermediate layers also increased, and the magnitude of the compressive stresses at the top layers decreased. This discrepancy between the numerical model data reported in [12] and the experimental results presented in this study can be justified by the dimensional instability shown in Fig. 9, particularly with respect to the thickness of the top layers. Thus, as a greater amount of the solidifying material accumulated in the upper layers of the beam owing to the preheating effect of the latter layers, higher residual stresses were generated in this area. This observation warrants further investigation, as there is a notable trend of a significant increase in tensile longitudinal residual stresses in the intermediate layers, potentially reaching material yield strength values at a certain point. Additionally, the experimental results indicate that the theoretical model presented by Hönnige et al. [3], as illustrated in Fig. 1, cannot be universally applied to DED components of all sizes.

Finally, it can be observed that regardless of the number of the deposited layers, all the test specimens exhibited compressive longitudinal residual stresses in the top layers, in agreement with [11] and [12]. These compressive stresses were greater for the shorter beams and lower for the higher beams. Following this trend, it can be assumed that with an even greater number of deposited layers (200–300, for instance), tensile stresses may be achieved in the surface layers of the DED – produced components (which would be an undesirable effect from the perspective of dynamic/cyclic service conditions and fatigue resistance). Further studies are required to confirm this hypothesis.

A systematic analysis of the residual stresses in the wire – arc DED – produced pieces was performed using finite element and experimental approaches. The obtained results demonstrate that the stress distribution is not uniform in both the substrate and beam of the DED products due to the different cooling rates experienced by distinct parts of the studied components and the dimensional instability caused by the preheating effect. From the finite element model and ESPI-based hole-drilling tests, it was observed that the concentration of tensile residual stresses (which are of the greatest concern) occurred in the bottom layers of the beams for the lower deposition cases. Nevertheless, the highest tensile values (up to 60% of the yield strength of the material) were observed for the intermediate layers of the 50 – and 100 – layer samples. Moreover, different numbers of deposited beam layers and, consequently, varying thermal impact have a significant influence on the type, magnitude, and distribution of the residual stresses, as well as on the dimensional stability and microstructure changes. This evidence should be considered during the design and parameter selection of the DED processes in order to guarantee the security and service life of fabricated components.

CRediT authorship contribution statement

Olga Liskevych: Writing – original draft, Conceptualization, Methodology, Formal analysis. Maksym Ziberov: Writing – review & editing, Methodology, Investigation, Conceptualization. Rogerio Lima Mota de Oliveira: Writing – review & editing, Methodology, Investigation. Milton Sergio Fernandes de Lima: Writing – review & editing, Visualization, Methodology, Conceptualization, Software.

Declaration of competing interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Data availability

Data will be made available on request.

Acknowledgement

This research did not receive any specific grant from funding agencies in the public, commercial, or not-for-profit sectors.

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Study of residual stresses in steel components produced via wire-arc directed energy deposition: finite element analyses and experimental approach

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Abstract

Figures

1. Introduction

2. Methodology

2.1. Specimen fabrication

2.2. Residual stress measurements

2.3. Macrography and hardness evaluation

2.3. Finite element analyses (FEA)

3. Results and discussion

3.1. Dimensional and microstructural analysis

3.2. Finite element analyses (FEA)

3.3. Experimental results of the residual stresses

4. Conclusions

Declarations

References

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