Features of the Stress–Strain State of 3D Metal Objects Produced by Additive Microplasma Deposition of the Powder of a Fe–Cr–Ni–B–Si System

Abstract

The objective of this study was the additive microplasma powder deposition of 3D metal products. The regularities of the influence of technological parameters of additive microplasma deposition of spatial objects using the powder filler material of a Fe–Cr–Ni–B–Si system on the formation of the microstructure and stress–strain state of 3D product material were studied in this work. Product walls with a layered metal structure with a deposited layer height of about 650 µm and 3.0–3.5 mm thickness were formed as a result of additive microplasma deposition of the HYF–103 powder of a Fe–Cr–Ni–B–Si system. The deposited metal ensured a high ultimate strength (above 600 MPa). The finite element method was used to derive the solution of the thermomechanical problem of additive deposition of 3D prototypes («cylinder», «triangular prism», «square prism», «reverse cone», «straight cone») with HYF–103 powder. The equivalent stresses of the highest magnitude (565 MPa) were predicted in the model sample of the “reverse cone” type, and the lowest stresses (552 MPa) were present in the sample of the “straight cone” type. For all the models, the maximal values of radial movements corresponded to the range of 0.22–0.28 mm. The respective technological mode of deposition was selected to minimize the stress–strain state of the produced 3D objects.

1. Introduction

In modern industry, manufacturers are increasingly interested in additive manufacturing. The combination of accuracy and productivity of additive manufacturing is becoming more and more relevant in the production of military equipment parts in field conditions [1], in particular, for the maintenance and repair of armored vehicles at isolated technical maintenance facilities of the tactical level in the conditions of hostilities or for the manufacture of damaged components of other equipment, including small arms [2].

The application of additive technologies allows for saving materials in the fabrication of 3D structures [3]. The ratio of the consumed material weight to the finished part weight for this technology is most often equal to 1:1. When manufacturing a similar part from sheet blanks, this parameter is 4:9 [4]. The mechanical properties of the produced parts are similar [5]. In some capacities, the parts made by additive manufacturing technologies are superior to their analogs produced by traditional methods.

Additive welding technologies allow the production of both regular metal and bimetal complex–shaped parts with inner stiffeners. For instance, it was proposed to manufacture, via the WAAM (Wire–Arc Additive Manufacturing) method, bimetal steel–bronze 3D parts, which are rather difficult to produce using the traditional technologies of casting, powder metallurgy, etc. [6]. Another example of a promising application of additive technologies of arc deposition is producing 3D structures from titanium alloys, in particular, complex–shaped panels with stiffeners from Ti–6Al–4V alloy [4,7]. One more promising direction of WAAM technology application is the fabrication of large–sized extended 3D structures of a complex shape, for instance, an aircraft wing from a high–strength aluminum alloy [8].

Another promising approach to manufacturing 3D metal products is the application of plasma–arc welding (PAW) technologies. For instance, in ref. [9], additive manufacturing of 3D parts via the PAW deposition of steel shot was proposed. For the cost–effective and energy–efficient additive deposition of small–sized metal products with the general purpose of repairing and/or reconditioning defective dies, molds, and other parts, it is proposed to apply the microplasma deposition process (μ–PTA—microplasma–transferred arc) [10]. Herein, it was suggested to use steel wire of 300 μm in diameter from the AISI P20 tool as the filler material, which was deposited at the rate of 42 g/h. Such a process is characterized by the absence of cracks or pores, despite the high hardness of the filler material. The μ–PTA process is a less expensive competitor of the known SLM (Selective Laser Melting) process. It was established that this process allows for the production of straight walls with a width of 2.45 mm, an effective width of 2.11 mm, and a deposition efficiency of 87% [11]. The MPPD (microplasma powder deposition) process was developed to create freeform metal parts via SFF (solid freeform fabrication) technology, as well as parts with functionally graded components [12]. With such an approach to the additive deposition of metal parts, the arc length is controlled by monitoring the arc voltage [13].

The application of plasma–arc additive technology for growing 3D parts was proposed by the Honeywell Aerospace Company—the IFF (ion fusion formation) process [14]. The good prospects for the application of additive powder microplasma deposition technology were confirmed by practical results derived at Southern Methodist University (Texas, USA). This method was used to grow 3D products of a cylindrical or other spatial shape [15]. One of the promising features of powder microplasma deposition is the possibility of manufacturing products from hard alloys, in particular those with a high Young’s modulus. In ref. [16], a variant of deposition of cobalt–based alloys was developed. From an industrial perspective, however, more attractive is the deposition of iron–based hard alloys, for instance, those close to the FeNiCoCrAl1.3Mo0.5 alloy described in ref. [17]. However, a combination of the laser and microplasma processes was required for the deposition of this alloy, which markedly lowered the adaptability–to–manufacture and increased the cost. The relevance of this work lies in the development of an additive microplasma process involving the deposition of powder filler materials from higher–strength alloyed steel to manufacture 3D objects.

Ref. [18] performed a comparison of additive deposition technologies, demonstrating that it is rational to apply the SLM technology to achieve the highest 3D product shape accuracy and to minimize its surface roughness. If maximal productivity is required, WAAM and PAW technologies at more than 100–150 A currents are suitable. Thus, microplasma powder additive deposition represents a certain compromise between shaping accuracy (SLM technology) and productivity (WAAM and PAW). This makes this technology quite attractive for industrial use [19].

However, for the development of the processes of microplasma additive powder deposition, it is necessary to take into account the significant thermal impact of the microplasma energy source on the produced 3D object. Here, in addition to the possibility of predicting the formation of the required structures of 3D object metal, it is necessary to be able to predict the susceptibility to residual deformations of its walls and to assess the level of residual stresses in the deposited metal. The absence of such a prediction procedure hinders the application of 3D printing of finished products by the method of additive microplasma powder deposition. This work aimed at the development of the respective procedure and studying the effectiveness of its application in the case of 3D printing with the powder of higher–strength alloyed steel.

The objective of this work lies in the investigation of the regularities of the influence of the technological parameters of additive microplasma deposition of spatial objects, using powder filler materials from higher–strength alloyed steel, on the formation of the microstructure and stress–strain state (SSS) of the material of 3D products and the creation, based on these approaches, to the automatic 3D printing of spatial metal products with a predicted structure and stressed state.

The following tasks were solved to reach the defined objective:

• Investigations of the regularities of the influence of the technological procedures of layer–by–layer deposition on the peculiarities of the formation of the structure and properties of 3D metal objects were performed;
• The prediction of the stress–strain state of the produced 3D metal objects was carried out;
• The development of basic technological procedures of additive microplasma deposition, aimed at minimizing the stress–strain state of the produced 3D objects, was carried out.

2. Materials and Methods

For the manufacturing of the 3D metal objects, layer–by–layer deposition of the powder of a Fe–Cr–Ni–B–Si system on the metal substrates from AISI 304 steel with dimensions of approximately 100 × 100 × 10 mm was performed. The chemical composition of the substrate material and powder is given in

Table 1. Chemical composition of the applied materials.

Material	Element Content, wt. %
	Fe	B	C	Si	Mn	Ni	Cr	Cu	P	S	Other
Substrate metal
AISI 304 steel	Base	–	<0.8	<0.8	<0.2	9–11	17–19	<0.3	<0.035	<0.02	Ti < 0.5
Filler (deposition) materials
HYF–103 powder (40–60 µm size)	Base	1.15	–	0.75	0.6	7.85	15.55	–	<0.02	<0.01	–

. A batch feeder of the original design was used for the filler powder feeding to the plasmatron.

In order to conduct deposition, preliminary preparation of the filler powder was performed as follows: heating at the temperature of 150…200 °C to remove moisture and calibration by sifting in a set of special sieves. The particle size distribution of the powder was checked via optical microscopy, and its chemical composition was verified via scanning electron microscopy.

Investigations of the particle size distribution of HYF–103 powder showed its inhomogeneity. This powder consists both of coarse and fine particles of predominantly spherical shape (Figure 1). Their size varies from 15.39 µm to 67.85 µm. The mean size is 39.88 µm. The size of some particles is 109.45 µm. Investigations of oxidized powder showed the stability of its chemical composition (

Table 2. Chemical composition of the particles of HYF–103 powder according to the data gathered via scanning electron microscopy.

Spectrum	Element Content, wt. %
	B	O	Si	Cr	Mn	Fe	Ni
1	5.57	2.79	1.51	17.33	0.28	65.21	7
2	6.19	2.68	1.41	17.34	0.37	64.8	7.08
3	6	2.98	1.47	17.48	0.23	65.06	6.61
4	6.69	2.65	1.42	17.81	0.45	64.88	6.11
5	3.6	1.83	1.46	17	0.38	67.2	8.53
6	4.43	2.94	1.17	15.6	0.2	66.79	8.86
7	2.65	3.97	2.04	15.68	0.3	67.07	8.29
8	5.97	–	1.16	17.05	0.15	66.75	8.92
9	3.33	1.43	1.25	17.41	0.24	71.81	4.29
10	2	1.98	1.55	17.09	0.33	68.07	8.85

).

For the selection of the powder material for deposition, the following aspects were taken into account. In keeping with ref. [20], the deposition of the powder material of the Fe–Mn–C–B–Si–Ni–Cr system promotes the segregation processes, which is revealed by investigations performed by the methods of X-ray photoelectron spectroscopy and X-ray diffraction analysis. So, during friction as a result of tribological testing, the segregation of C, B, and Si atoms was observed. The presence of the following compounds was recorded in the subsurface layers: oxides (B₂O₃, SiO₂, Cr₂O₃); carbides (Fe₃C, Cr₇C₃), and borides (FeB, Fe₂B). This is indicative of intensification of the processes of phase formation as a result of deformation effects. The formation of such structures improves the wear resistance of the coating material. The intensification of phase formation processes will enhance the structural strengthening of the deposited metal. Such a process may also influence the level of local internal stresses in the surface layer structure due to the redistribution of crystalline lattice defects. Here, nanophase particles are formed [21]. The uniform distribution of dispersed particles of strengthening phases in the deposited metal matrix will promote the gradientless distribution of the dislocation density. It will prevent the formation of local internal stress raisers: cracking centers [22]. The appearance of large phase formations, however, may promote the development of dislocation clusters with their higher density. Such a structural state may lead to the formation of zones of deformation localization and an abrupt increase in the level of local internal stresses in these structural zones [23]. This, in turn, will lead to cracking in the deposited layer material.

In ref. [24], it is shown that alloys of a Fe–Cr–C system with a different B₄C content were successfully deposited on the surface of stainless steel, for instance, AISI 316, via plasma–arc welding. The coating microstructure was predominantly a γ–Fe,Ni eutectic matrix, and hexagonal carbides (Cr, Fe)₇(C,B)₃ and (Cr, Fe)₂₃(C,B)₆ were not uniformly distributed in the eutectic matrix. The average microhardness of the deposited coating was equal to 820 HV, which was almost five times higher than that of the substrate from AISI 316 stainless steel (180 HV). The maximal value of the coating microhardness was close to 1280 HV. Such structural features of the deposited coatings can considerably influence the stress–strain state of the produced layers.

It is anticipated that the absence of carbon in the composition of the selected HYF–103 powder (Table 1) will promote the improvement of service properties of printed products from austenitic materials due to the reduction of the formation of secondary phases of the carbide type [25]. The presence of boron in the powder composition will promote an increase in the equivalent concentration of nickel and will ensure the formation of a fine–grained austenitic structure. It is known that grain refinement is one of the most efficient methods to improve the material strength properties without increasing their brittleness. The effectiveness of boron influence, as an austenitizer, is quite high; for instance, boron is approximately a 10–fold stronger austenitizer than nickel [25].

Thus, the application of HYF–103 powder of a Fe–Cr–Ni–B–Si system for 3D printing via the additive deposition method is promising in terms of producing sufficiently hard and wear–resistant metal products with a high corrosion resistance and good tribological properties. However, during the layer–by–layer deposition of this material, zones of deformation locatization with an increased level of residual stresses can form, which may lead both to cracking in the deposited layer material and to the development of defects of the printed geometry as a whole. This makes it necessary to assess and minimize the residual stress–strain state of basic spatial primitives printed by the selected method using HYF–103 powder.

To reach the defined objective and solve the proposed tasks, the following investigation procedure was adopted:

• selection of the technological diagram of the process of additive powder microplasma deposition, filler materials, and tentative mode parameters;
• selection of spatial geometrical prototypes of the main basic shapes of the deposited 3D products and finite element modeling of their stress–strain state;
• correction of the selected tentative parameters of the technological mode of microplasma deposition, taking into account the possibilities for minimizing the residual stressed state of a 3D product, produced by additive deposition;
• development of an experimental stand for technological studies with a plasmatron of an original design, which ensures a stable laminar mode of compressed plasma generation;
• conducting experiments on the deposition of spatial geometric primitives via the microplasma method;
• metallographic studies of the deposited samples, determination of the presence of the characteristic defects and ways to eliminate them, and making the necessary corrections at selection of the deposition modes;
• analysis of the results of powder microplasma deposition, and determination of the technological potential of the process.

To carry out experiments on 3D printing, we chose the microplasma powder surfacing scheme shown in Figure 2.

Equipment described in detail in ref. [26] was used for powder microplasma deposition. It included a power source, which ensured nonconsumable electrode deposition at straight polarity current in the range of 5–100 A and at the voltage of 10–30 V. Plasma arc ignition was performed by a plasma module with a pilot arc current in the range of 5–50 A and at plasma gas flow rates from 0.1 to 10 L/min. The deposition was conducted with a proprietary plasmatron, to which powder was fed by an original batcher–feeder in the range of powder flow rates of 2.0–7.0 g/s [27]. For experiment performance, the plasmatron was fastened to a 3D plotter carriage, which moved it relative to a stationary table with a substrate from AISI 304 steel of 100 × 100 × 10 mm dimensions. The test 3D object was successively built up on this substrate.

The structures of the metal of welds and heat–affected zone (HAZ) were studied via light microscopy (Neophot–32 microscope, Carl Zeiss, Jena, Germany). Mechanical testing was performed in a versatile servo–hydraulic testing complex MTS 318.25 (MTS Systems Corporation, Eden Prairie, MN, USA) with a maximal force of 250 kN. Tests were carried out in accordance with DSTU ISO 6892–1:2019 Metallic materials. Tensile test. Part 1: Test method at room temperature [28].

3. Results and Discussion

3.1. Technological Studies of the Formation of Spatial Primitives Using Additive Deposition Processes

Technological studies of the process of additive powder microplasma deposition of 3D objects were performed using the technological diagram, according to which the filler wire was fed into a constricted arc through the respective nozzle by the transporting gas flow [26].

Optimized technological modes of powder microplasma additive deposition, at which a “thin wall” and other spatial primitives were formed, are given in

Table 3. The parameters of microplasma deposition during additive growing of a 3D product of the “thin wall” type.

Composition and Flow Rate of Plasma–Forming/Shielding Gas, L/min	Current, A	Voltage, V	Speed of Torch Movement Relative to Deposition Surface, m/min	Filler Powder	Powder Flow Rate, g/min	Minimal Thickness of the Deposited Wall, mm
Ar/Ar. 0.8–1.5/5–12	25	30	0.5–0.6	HYF–103	2.0–7.0	3.0–3.5

. The formation of a sound metallurgical bond between the layers and the substrate and between each other, as well as the formation of an equilibrium grain structure of the deposited layers, were used as the optimization criteria.

To conduct metallographic analysis, templates were cut out of the deposited samples and microsections were prepared. Samples of the type of wall (plate) were produced by 3D deposition in order to determine the ultimate strength, tensile strength, and relative elongation of the deposited metal at uniaxial tension. Respective testing was conducted on samples cut out of the plate produced by additive deposition using a diagram and sketch, as shown in Figure 3.

Deposited metal strength was assessed by the results of testing three samples under the conditions of uniaxial tension. Testing was conducted in an all–purpose rupture testing servohydraulic MTS 318.25 system using standard samples (

Table 4. The results of static tensile testing of the samples of additive wall deposition with HYF–103 powder of the Fe–Cr–Ni–B–Si system.

	Sample №1	Sample №2	Sample №3	Averaged Value
Tensile strength, MPa	606	627	618	617

).

To obtain the highest values of the powder consumption coefficient (PCC) during deposition, a distance of 3–5 mm from the plasmatron edge to the deposition surface was experimentally selected. A reduction in this distance lowers PCC due to incomplete melting of the powder, and an increase due to powder losses through plasma jet expansion. Also, should an increase in this distance occur, gas shielding of the microplasma jet will be impaired, leading to the appearance of defects in the deposited layers.

A stable running of the microplasma arc was observed at a plasma gas flow rate of 0.2–0.4 L/min. At lower flow rates, the arc disappeared, and at higher rates, liquid pool spattering was observed. For the shielding gas flow, the flow rate range of 5–6 L/min was selected. At lower flow rates, oxidation of the weld pool molten metal was observed, and at higher rates, turbulences could occur, which created atmospheric air suction and deposited surface irregularities in the form of depressions.

Investigations on the printing of a primitive “thin wall” type were conducted to determine the potential of the processes of additive powder microplasma deposition. In addition to a spatial primitive of the type of “thin wall” (or «parallelepiped»), a range of other objects were manufactured, in particular a ring, square, triangle, straight and reverse cones, etc.

During the performance of technological studies on powder microplasma deposition, the features of the change in the deposited product stress–strain state were studied, among other characteristics. Investigations were conducted during the deposition of the above–listed spatial primitives. The following phenomena were detected:

(1)

The plate on which the product was deposited was significantly deformed along the vertical axis. To avoid such an effect, it was decided to use deposition fixtures, which would contain and preserve the plane geometry of the plate;

(2)

A product of a cylindrical shape was prone to radial displacement; after 20 deposited layers, the product diameter was reduced by almost 1 mm. To prevent such deformation, a conclusion was made about the need to compensate for the deformation by means of a gradual increase in the diameter during part deposition.

Based on investigations of the features of spatial primitive formation, the characteristic disadvantages of metal object formation via additive deposition were determined. In particular, when forming corners, the deposition rate was non–uniform, leading to a greater amount of metal in this zone and overheating of the material of the formed object. The elimination of this disadvantage requires the application of the respective control program and monitoring system. Moreover, disturbances in the plasma–forming and shielding gas flows arose in the corners and at the wall crossings. To solve this problem, it is necessary to study the features of microplasmatron gas dynamics and to develop an appropriate design optimized by the criterion of laminar gas flows.

3.2. Metallographic Investigations of the Results of Manufacturing Metal Spatial Primitives via the Additive Deposition Method

The main methods of metallographic analysis, first of all, optical and electron microscopy and microhardness measurements, were applied for the analysis of the structural features of multilayer deposition. In particular, the dimensions of grains (dendrites), which were used to determine the grain shape factor ᴔ, as a ratio of its length to its width ᴔ = l/h, were measured.

Investigations of the macro- and microstructure of the deposited layers were performed on a primitive “thin wall” type. During the additive deposition of such a wall, complete melting of the powder occurred. The metal structure was characterized by a pronounced laminarity, and the thickness of the layer deposited in one pass was 650 µm. The deposition was performed in several passes with successive deposition of metal layers—one in each pass. The structure of the fusion zones between the layers was homogeneous.

Transverse macrosections were prepared from the produced wall, to study the tendency toward the formation of such defects, such as cracks and inner pores (Figure 4). The structures of the produced samples were of a continuous regular nature. No susceptibility to the formation of inner porosity or cracks was found.

It was established by electron microscopy methods that the sample’s metal structure was dendritic and contained both relatively coarse and fine grains. Coarse and fine dendrites form colonies, disoriented relative to each other (Figure 5).

The formation of crystals during the successive deposition of metal layers was different in the sample’s upper and lower parts, and it was determined under nonequilibrium crystallization conditions. In the lower part of the deposited metal, the heat was transferred into the base substrate, whereas, in the sample’s upper part, it was predominantly due to heat radiation and removal into the lower deposited layers. This resulted in the slow cooling of metal in the sample’s upper part, and, hence, it led to significant grain growth.

In the longitudinal direction, the dendrites form extended crystal branches, oriented predominantly in the direction of heat removal and united into colonies. Analysis of the microstructure of a sample cut out in the lower part showed that the crystal growth took place in one direction (Figure 5a). The dendrites consisted of grain blocks of a similar crystalline orientation, the boundaries of which were revealed by etching. Comparison of the structure of metal of specimens cut out in the longitudinal direction in the sample upper and lower parts pointed to a different nature of crystallization during the part upward formation (Figure 5).

Microanalysis of individual regions of the structure showed that the deposited metal composition was close to that of the deposited powder. Therefore, and also due to the presence of boron in the composition of the initial powder, the resulting structure, with a high probability, should be austenitic [25]. The dimensions of the resulting structure were as follows: h × l = (40–100) × (400–600) µm in the deposited metal lower part (Figure 5a, ×200), h × l = (40–100) × (200–400) µm in the middle layer (Figure 5b, ×200), and h × l = (20–80) × (140–360) µm in the deposited metal upper layer (Figure 5c, ×200). At the transition from the deposited metal lower section into the middle layer, the crystallite width was the same, but the length became smaller after a decrease in grain shape factor ᴔ from ᴔ = 6–10 (deposit bottom) to ᴔ = 4–5 (middle). In the upper layer of the deposited metal, the crystallite size decreased by 1.1–1.4 times relative to the middle part at ᴔ = 4.5–7.

The inner structure of the crystallites has a cellular substructure of the following dimensions: d_c = 20–30 µm in the deposited metal lower part (Figure 5a, ×1000), d_c = 15–25 µm in the middle layer (Figure 5b, ×1000) and d_c = 10–20 µm in the deposited metal upper layer (Figure 5c, ×1000). In the deposited metal upper part, the metal substructure was refined compared with the lower and middle layers, on average, by 1.7 and 1.25 times, respectively.

A slight coarsening of the grain and subgrain structure in the deposited metal lower and middle parts is associated with slowing down of the heat removal process and lowering of the metal cooling rate. In the deposited metal upper part, a finer structure formed, ensuring both the strength and toughness of the deposited material.

Conducted investigations of mechanical properties (

Table 5. Properties of HYF–103 deposited metal produced by layer-by-layer additive building-up.

Sample Number	Fo, mm2	Lo, mm	Le, mm	σT, MPa	ΣY, MPa	δ, %
1	7.15	20.02	20.49	606	474	3.164856
2	7.16	19.78	20.78	627	510	5.055612
3	7.15	22.14	22.94	618	462	3.613369

F_o is the sample cross-sectional area, L_o and L_e are the initial and final lengths of the sample, σ_T is tensile strength, Σ_Y is yield strength, and δ is the relative elongation.

) led to the conclusion that metal deposited by the additive method ensures high strength, reaching more than 600 MPa.

3.3. Prediction of the Stress–Strain State of the Produced Metal 3D-Objects

The finite element method was used for predictive modeling of the stress–strain state of spatial primitives of 3D products [29]. In the general form, for the determination of the stress–strain state using this method, mathematical modeling of the problem of the 3D stress–strain state can be presented in vector form, which includes the equations of motion and equilibrium, the geometrical equation for the small strain tensor, and the physical equation in the form of a generalized Hooke’s law:

$$\left\{\begin{array}{c}\mathsf{\nabla }·\sigma +f=0\\ \epsilon =\frac{1}{2}\times (\mathsf{\nabla }u+u\mathsf{\nabla })\\ \sigma =C:\epsilon \end{array}\right.$$

(1)

where $\mathsf{\nabla }=\frac{\partial }{\partial x_i}$, (i = 1,2,3) is the Hamiltonian operator, m⁻¹; x₁, x₂, and x₃ are the Cartesian coordinates, m; $\mathsf{\nabla }·\sigma$ is the operator of scalar product of a vector and a tensor; σ is the symmetric stress tensor of the second rank, Pa; f is the vector of volumetric forces, Pa; ε is the symmetric tensor of the second rank of Cauchy elastic deformations; u = (u₁, u₂, u₃) is the movement vector, m; $\mathsf{\nabla }u,u\mathsf{\nabla }$, $C_{ijkl}=\mu \times \left({\delta }_{ik}\times {\delta }_{jl}+{\delta }_{il}\times {\delta }_{jk}\right)+\lambda {\times \delta }_{ij}\times {\delta }_{kl}$ are the components of the fourth–rank tensor of elastic properties of an isotropic material, Pa; C: is the double scalar product operator; $\mu =\frac{E}{2\times (1+\upsilon )}$ and $\lambda =\frac{E\times \upsilon }{(1+\upsilon )\times (1-2\times \upsilon )}$ are the Lamé coefficients, Pa; E is the modulus of elasticity during stretching, Pa; $\upsilon$ is the Poisson’s ratio; and ${\delta }_{ij}=\left\{\begin{array}{c}1 \mathrm{at} i=j\\ 0 \mathrm{at} i\ne j\end{array}\right.$ is Krokener’s symbol.

In the case of a thermoelastic problem for an isotropic medium, the generalized Hooke’s law takes a slightly different form:

$${\sigma }_{ij}=C_{ijkl}\times ({\epsilon }_{ij}^e-{\epsilon }_{ij}^T)$$

(2)

where ${\epsilon }_{ij}^e$ are the components of the tensor of small elastic Cauchy deformations; ${\epsilon }_{ij}^T=\beta \times (T-T_0)\times {\delta }_{ij}$ are the components of the tensor of thermal deformations; $\beta$ is the coefficient of linear temperature expansion of the material, K⁻¹; $T i{ T}_0$ are the initial and current body temperature, respectively, K; and ${\delta }_{ij}$ is the Krokener symbol.

For the unambiguity of the system of differential Equation (1), it is only necessary to write down the boundary conditions. As the problem is stationary, the initial conditions are not used. An exception is the temperature when allowing for the temperature load in the definition of problem (2), which can be assigned as $(T-T_0)$ difference in the determination of the thermal deformation tensor ${\epsilon }_{ij}^T=\beta \times (T-T_0)\times {\delta }_{ij}$.

The boundary conditions for the system of Equation (1) are as follows:

-

movements or pinching (in at least one point on the body’s surface):

$${\left.u\right|}_{S_u}=0$$

(3)

where $S_u$ is the surface (or surface point), on which movement is assigned;

-

symmetry

$${\left.n\times u\right|}_{S_{su}}=0$$

(4)

where n = n_i is the vector of the normal to the surface; $S_{su}$ is the surface of symmetry of the body;

-

from the action of an external force

$${\left.\sigma \times n\right|}_{S_p}=p$$

(5)

where p = p_i is the vector of external force, acting on surface $S_p$;

-

from the action of an external pressure

$${\left.(\sigma \times n)\times n\right|}_{S_p}=p$$

(6)

where p is the external pressure assigned on the surface $S_p$, Pa [30].

The stress–strain state in the deposited products depends on the thermal deformation processes proceeding during deposition. Analysis of the thermal processes of arc deposition was performed using a volumetric heat source according to J. Goldak with a normal (Gaussian) distribution of the specific thermal power along all the coordinate axes within the body, having the form of a volumetric semi–ellipsoid (Figure 6) [31].

A feature of the model is the independent assignment of the distribution of specific thermal power q_v in the front (index f) and tail (index r) parts of the ellipsoid:

$$q_{vf}=f_f\frac{6\times \sqrt{3\times q}}{a_f\times b\times c\times {\pi }^{\raisebox{1ex}{$3$}\!\left/ \!\raisebox{-1ex}{$2$}\right.}}\exp \left\{-3\left[{\left(\frac{x+v\times \left(t-\tau \right)}{a_f}\right)}^2+{\left(\frac{y}{b}\right)}^2+{\left(\frac{z}{c}\right)}^2\right]\right\}$$

(7)

$$q_{vr}=f_r\frac{6\times \sqrt{3\times q}}{a_r\times b\times c\times {\pi }^{\raisebox{1ex}{$3$}\!\left/ \!\raisebox{-1ex}{$2$}\right.}}\exp \left\{-3\times \left[{\left(\frac{x+v\times \left(t-\tau \right)}{a_r}\right)}^2+{\left(\frac{y}{b}\right)}^2+{\left(\frac{z}{c}\right)}^2\right]\right\}$$

(8)

$$q=\eta \times \mathrm{I}\times \mathrm{U}$$

(9)

where q is the effective thermal power of the heat source; η is the surfacing arc efficiency; I is the deposition current; U is the deposition voltage; $\tau$ is the dwell time calculated from the start of the source action; t is the current time; v is the speed of the source movement (deposition rate); x, y, and z are the ellipsoid semi–axes in the direction of coordinate axes OX, OY, and OZ; f_f and f_r are the coefficients determining the ratio of heat applied to the frontal and the tail part of the ellipsoid; and a_f, a_r, b, and c are the respective radii of normal distribution.

Coefficients f_f and f_r are related as follows:

$$f_f=\frac{2\times a_f}{a_f+a_r} ; f_r=\frac{2\times a_r}{a_f+a_r} ; f_f+f_r=2$$

(10)

In our case, it was assumed that f_f = 0.4; and f_r = 1.6. During the calibration of the J. Goldak model, the linear dimensions of the real weld pool were taken into account to select the respective dimensions of a_f = 3 mm, a_r = 5 mm, b = 1.7 mm, and c = 0.8 mm parameters of the ellipsoid (Figure 6), as required for calculation in Equations (7) and (8). Calculations performed via the method of finite element modeling were performed, taking into account the model of the source of a 3D stress–strain state (1–2) with boundary conditions (3–6) and the thermal powder distribution (7–9) for the selected coefficients (10) [32].

Computations performed via the finite element method used an irregular grid of prismatic 3D elements, the size of which was 0.3 × 0.3 × 0.25, 0.6 × 0.6 × 0.5, and 1.25 × 1.25 × 1.0 mm. Outside the highly heated region, the size of finite elements was increased to 2.5 × 2.5 × 1.0 and 5.0 × 5.0 × 1.0 mm to shorten the computation time. To ensure convergence of the finite element model grid, the transition between zones modeled by elements with different base sizes was provided by finite elements with rectangular–trapezoidal bases of appropriate sizes. The boundary conditions of the third kind, determining the heat exchange between the body’s surface and the environment, were assigned by 2D elements in the form of a heat transfer surface, modeling convection, and radiant heat exchange during deposition. Temperature changes in the thermal–physical properties of the deposited HYF–103 alloy of the Fe–Cr–Ni–B–Si system were taken into account both during heating and at cooling (Figure 7).

To study the formation of the residual stress–strain state in the deposited spatial primitives, five models of different shapes (

Table 6. The geometrical parameters of the deposited 3D primitives.

Name	Ring (Cylinder)	Triangle	Square	Reverse Cone	Straight Cone
Model sample
Characteristic size	Ø	Side length	Side length	Øbot/Øtop	Øbot/Øtop
Value, mm	40	50	50	60/64	60/56
Model
Deposited sample

) were created, according to which deposition of the respective samples was performed (Figure 8). To make the calculated results comparable with experimental values, the creation of finite element (FE) models was based on physical analogs previously obtained via 3D printing.

For the selected spatial primitives, the equivalent stresses (Figure 8) were determined; these stresses allow tracing the features of the stress–strain state (Figure 8) characteristic for all the modeled samples.

As one can see from Figure 8, the maximal values of equivalent stresses of ~520 MPa formed in the points of contact of the first bead with the substrate, which is due to the high rigidity of the substrate, thereby preventing the free shrinkage of the metal of the first roller.

The lowest values of ~9 MPa were found in the location of an abrupt change in the bead trajectory, which is due to the sample shape (presence of corners) and stress redistribution during cooling. On the whole, the level of stresses in the residual state in the prototypes after the deposition of three beads corresponded to 400–440 MPa.

The level of stresses in the substrate varied in the range of ~120–350 MPa. Residual stresses in the cross–sections of HYF–103–deposited beads were nonuniformly distributed along the printed prototype height: the highest stresses of the order of 500 MPa formed on the surface of the first bead, and the lowest stresses of 390 MPa on the surface of the third bead.

As one can see from Figure 9, the extent of movements in 3D prototypes deposited with the HYF–103 powder was not more than 0.28 mm, which ensures an appropriate level of precision of the geometrical dimensions in the printed parts and minimizes the need for further machining.

On the whole, analysis of the results of modeling the movements in 3D prototypes deposited with HYF–103 powder showed that the substrate did not undergo deformations or movements during the process of bead deposition, which is indicated by calculation data in Figure 9.

Equivalent plastic deformations, maximal and minimal values of equivalent stresses, and movements for all the models are given in

Table 7. Comparative table of the parameters of residual SSS in 3D prototypes deposited with the HYF–103 powder.

Model Sample
Residual equivalent stresses, MPa
Bead №	Max	Min	Max	Min	Max	Min	Max	Min	Max	Min
1	520	400	500	170	510	50	500	400	500	400
2	490	190	480	50	500	50	400	280	500	280
3	400	390	390	40	400	30	400	390	400	390
Model	562	26	558	9	558	1	565	3	552	2
Residual equivalent plastic deformations, ×10−2, %
Model	17.4	0	15.6	0	16.4	0	17.4	0	14.6	0
Movements, mm
Total	0.23		0.25		0.28		0.25		0.22

.

Analysis of the axial movements for the modeled samples showed that their components had the same order of significance (0.10–0.25 mm) and were in the following ranges:

• Cylindrical prototype (X;Y;Z): −0.22–0.22; −0.17–0.21; −0.17–0.13;
• Prototype of the hollow triangular prism (X;Y;Z): −0.24–0.20; −0.25–0.2; −0.14–0.12;
• Prototype of the hollow square prism (X;Y;Z): −0.24–0.25; −0.23–0.23; −0.14–0.10;
• Prototype of the reverse cone (X;Y;Z): −0.25–0.25; −0.23–0.25; −0.12–0.12;
• Prototype of the straight cone (X;Y;Z): −0.12–0.13; −0.11–0.13; −0.20–0.13.

For the experimental verification of modeling of the stress–strain state of a 3D metal product, additive microplasma deposition of a prototype sample of a hollow cylinder of about Ø40 × 32.5 size with a 3.5 mm wall thickness was performed using the HYF–103 powder. For this purpose, the distributions of temperature (Figure 10a) and residual deformations (Figure 10b) in the product at its layer–by–layer deposition were calculated via the finite element method and using the above–mentioned models. Reduction of the residual deformation influence on deviations of the shape of the cylinder printed via additive deposition from the digital prototype was achieved as a result of the prediction of the stress–strain state using the finite element method and making respective corrections in the algorithm used to manufacture the printed part.

To check the effect of radial displacement of the object wall during its additive deposition, a measurement of the geometrical parameters was performed after the deposition of each layer. A certain effect of radial displacement (Figure 10b) was observed, which was later on eliminated using several modeling iterations and experimental verification of the deposition mode parameters. A comparison of the dynamics of the modeled and real displacement is presented in the graphs in Figure 11. Investigations showed that the deposited products had no more than 20% deviation from the modeled value, which is indicative of sufficient modeling efficiency.

3.4. Development of the Basic Techniques of Additive Manufacturing

The development of additive manufacturing techniques was conducted in the case of manufacturing a “hollow cylinder” spatial primitive. Such a cylinder from the HYF–103 powder of the Fe–Cr–Ni–B–Si system should have the dimensions of Ø40 × 32.5 mm with a wall thickness of 3.5 mm and should be deposited in 20 passes. The dimensions of the substrate from the AISI 304 stainless steel for primitive deposition were equal to 200 × 100 × 10 mm.

After several iterations of calculations of the mode with minimal residual strains and stresses, the following mode parameters were derived: values of the main (microplasma) arc current I_MA = 25 A, voltage U = 30 V, and deposition rate V = 550 mm/min. Here, the following geometrical parameters of the pool were obtained: depth—0.7–1.0 mm; width—3.5 m; and length—8 mm.

In order to more precisely determine the flow rates of filler powder Q_f and working gases (plasma–forming Q_PL, shielding Q_SH, and transporting Q_TR), several technological experiments were conducted, the results of which are given in

Table 8. The parameters of the modes of additive microplasma deposition of a “cylinder” spatial primitive with HYF–103 powder at the rate of 550 mm/min with the application of argon as a plasma–forming (Ø1.0 mm nozzle) and transporting (Ø4.0 mm nozzle) gas.

Mode №	Technological Mode Parameters								Energy Input E. J/m	Result/Residual Movements after 5 Passes, mm
	IPA. A	QPA. L/min	IMA. A	QPA. L/min	QSH. L/min	U. V	QF. g/min	QTG. g/min
1.	25	2.5	30	0.3	25	27	6.5	3	71	After the 10th pass, there was a considerable difference in the height of bead formation/0.20–0.23
2.	25	2.5	30	0.3	25	33	9	3	86	After the 20th pass, there was a considerable difference in the height of bead formation/0.25–0.28
3.	25	2.5	30	0.3	25	33	9	3	86	After the 20th pass, there was a considerable difference in the height of bead formation/0.25–0.28
4.	20	4	25	0.2	25	42	6	4	92	Good bead formation/0.24–0.27
5.	30 ignition, 20 working h.	4	35 ignition, 25 working h.	0.2	25	40	6	4	87	Good bead formation/0.20–0.23

Note: PA—pilot arc; MA—main arca; F—filler; TG—transport gas.

. For each mode, input energy E (J/mm) was determined, allowing for the efficiency factor of the microplasma deposition process (of the order of 0.8 according to ref. [33]).

The performed technological investigations allowed the establishment of the optimal mode at which the pre–determined product is formed (a cylinder in this case)—mode №5, Table 8. It was established that, to achieve a positive result, it is necessary to minimize the power consumption and somewhat increase the energy input. Here, in order to begin the deposition process, 35 A current was used at the start, and after achieving a stable process (within 2–3 s), the main arc current was reduced to 25 A.

In addition to the case of the cylinder, deposition modes were also selected for a range of basic spatial prototypes and arbitrary objects (Figure 12). This allowed for the creation of a database of optimal parameters of the modes of additive microplasma powder deposition, which can be applied for process automation by developing a control program and an automatic monitoring system. A reduction in deviations from the specified dimensions within up to 1 mm was the optimization criterion.

Technological investigations were performed using a microplasmatron with transporting nozzle channel diameters d_T of 2.5 mm, 3.5 mm, and 4.5 mm, respectively. At these dimensions, its stable operation is ensured at the main arc current of 20–40 A. The width of the deposited metal pool (or the deposited bead) varied with an increase in deposition current from 25 to 35 A at a constant speed of microplasma arc movement in the range from 2.5 mm up to ~5.0 mm (

Table 9. The deposited metal’s specific weight M_d and bead width B during additive microplasma deposition depending on the diameter of the plasmatron transporting nozzle channel, d_T.

DT. mm	I. A	B. mm	MD. g/min	PUC
4.5	25	2.5	4.7	0.72
	30	4.0	4.5	0.69
	35	5.0	4.6	0.70
3.5	25	2.5	5.3	0.82
	30	3.5	5.2	0.80
	35	4.5	5.4	0.83
2.5	25	2.5	5.6	0.86
	30	3.0	5.7	0.88
	35	3.5	5.8	0.89

).

The HYF–103 filler powder with a particle size of 40–60 µm used in the experiments was fed at a rate of up to G₀ = 6.5 g/min. The specific weight of the deposited bead M_d was determined experimentally by weighing the grown plate–like samples with an accuracy of 0.02 g before and after 1 min of deposition. The powder utilization coefficient (PUC) was defined as the ratio of M_d to powder feed rate G₀.

The results demonstrate the advantage of the application of transporting nozzles with small diameters (d_T = 2.5 mm) during the additive microplasma deposition of beads via plasmatrons with transporting nozzle channel diameters d_T ≤ 4.5 mm from the viewpoint of optimizing the efficiency of filler powder utilization [34]. The walls of the obtained metal 3D objects had a roughness in the range of Rz 60–120 μm.

4. Discussion of the Research Results

4.1. Analysis of the Influence of the Main Parameters of Microplasma Arc and the Two–Phase Flow of “Microplasma–Filler Powder” on the Dimensions of the Deposited Layer

During the manufacturing of spatial products via additive building–up of the layers using successive deposition, the size of the built–up layer (deposited metal bead) is a very important parameter, as it determines the characteristics of the shape and surface, as well as the accuracy of the product. In this regard, it is necessary to solve the problem of determining an optimal ratio of the coefficients of concentration of the specific flows of filler powder and microplasma arc heat, as well as the ratio of the effective diameters of the powder feeding spot and heating spot.

Another important task is reducing the powder losses during the additive building–up of the part. The main cause of powder filler losses is the movement of the dispersed particles over the periphery of the plasma arc column and, moreover, their elastic reflection from the deposited product surface beyond the zone of the formed deposited metal pool [35].

Therefore, in the case of the realization of additive technology of building up thin–walled metal products with a wall thickness of approximately 3.5 mm, it is important to control the dimensions and characteristics, in particular, the concentration of the microplasma arc during the addition of the powder filler. In particular, to optimize the trajectories of filler material movement in the plasma arc, it is recommended to add filler powders to the arc at the velocity of not less than 2 m/s at up to 40–45° angle with the plasmatron axis [36].

To determine the best conditions for focusing the two–phase flows of microplasma, filler powder, which ensures filler material transportation through the high–temperature region of the microplasma arc to the deposition pool at the formation of the deposited layer of approximately 3.5 mm width, lets us analyze the studied technological features of additive microplasma deposition (Table 9).

The weld pool shape becoming close to a circle at typical modes of microplasma powder deposition allows us to assume the correspondence to the normal law of radial distribution of the filler material in the microplasma arc on the level of the surface of the anode (the weld pool). In order to check the assumption, the effective diameter d_ef of the powder feeding spot was determined (

Table 10. The experimental parameters of the effectiveness of powder additive microplasma deposition.

DT. mm	Def. mm	Sef. mm2	r0. mm	B. mm	PUF
4.5	7.0	38.5	2.5	5.0	0.72
3.5	5.5	23.8	2.25	4.5	0.82
2.5	4.0	12.6	1.75	3.5	0.88

), the comparison of which with the concentration of the specific heat flow on the product surface, 2r₀, allows the tentative determination of PUC.

It was found that a reduction in the diameter of the microplasmatron–transporting nozzle channel from 4.5 m to 2.5 mm ensures a change in area S_ef of the effective spot of powder feeding from 38.5 mm to 12.6 mm², i.e., approximately three–fold. An analysis of the experimental data (Table 10) shows that an increase in PUC value in the range from 0.72 to 0.88 corresponds to a reduction in the equivalent radius r₀ of _the powder feeding spot. In order to ensure high efficiency of filler powder utilization, which is mainly set by value d_t, condition B ≥ 2r₀ should be fulfilled [37].

The coefficient of concentration k of the specific heat flow of the microplasma arc without powder feeding was determined via the procedure of ref. [34] using calorimetry in a two–section flow calorimeter. For a microplasma arc in the current range of 20–40 A with an equivalent diameter of the heating spot of 2.5–5.0 mm, the experimental k values are equal to 3.5–5.5 cm⁻², depending on the degree of its constriction by plasma–forming (d_pl = 1.0–2.5 mm) and –transporting (d_t = 2.5–4.5 mm) nozzles of the plasmatron.

A comparison of experimental data on the effective diameter of powder feeding (Table 10) and specific heat flow on the product surface shows that, during additive building–up of the layers with powder feeding into the microplasma jet, the relationship between the respective coefficients is in the range of 1.1–1.6.

During microplasma powder deposition of the wall with a thickness of 2.5 mm, the filler consumption can be reduced not only due to the reduction in d_t in the microplasmatron, but also due to the optimization of the microplasma powder’s flow concentration by a rational selection of the distance from the transporting nozzle edge to the product. An analysis of powder flow concentration was performed in the mode of monitoring its feeding with the flow rate of 2.0–7.0 g/min, which allowed deposition of a layer of 0.5–0.8 mm height in one pass. It was found that such a flow preserved its concentration, assigned by the diameter of the transporting nozzle channel at the distance of up to 3–5 mm from its edge, and then it expanded significantly.

Considering the dependence of the duration of the weld pool metal staying in the molten state on the energy input value [38], the modes of microplasma powder deposition may need optimization of their parameters via the criterion of the weld pool volume (deposited metal weight). At the average deposition current of up to 40 A, the criterion of average input energy 0.8(I·U)/V < 130 J/mm promotes a limitation of the weld pool dimensions, deposited metal weight, and duration of the layer deposition. Such an approach helps analyze the modes of multilayer microplasma powder deposition when building–up elements of a complex profile.

Thus, the following technological recommendations can be defined: application of a transporting nozzle with channel diameter close to 2.5 mm; stabilization of the microplasmatron–to–product distance at the level of 3 mm (3–5 mm) with the accuracy of ±0.5 mm; delivery of filler material to the weld pool through the high–temperature region of the arc; and additive powder microplasma deposition of beads with widths of 2.5 mm. These recommendations can be used for further optimization of structural parameters of industrial microplasmatrons with a high concentration of the dispersed filler feed, the application of which allows achieving minimal possible dimensions of the built–up layers, as well as the maximal precision and roughness of the products in the manufacture of 3D metal products.

4.2. Prediction of the Stress–Strain State of the Deposited Products, Allowing for the Statistical Data on the Change in Their Geometry

Analysis of the modes of microplasma deposition of layers of 2.5 mm width revealed that beginning from a certain value of effective power of the microplasma arc, a little higher than the minimal possible value for the start of a stable process, the weld pool volume can increase by 2–3 times without any significant rise in the arc power due to an increase in the amount of the dispersed filler, which is added. As the total heat input into the product is proportional to the weld pool dimensions and deposition efficiency, optimization of the plasma deposition modes by the criteria of the deposited metal weight and energy input may be required. Evaluation of the amount of heat applied to the product allowed for eliminating microcracking in the deposited metal at multilayer deposition of elements of a complex profile at the stage of technology optimization.

As a result of the analysis of the statistical data, obtained by the method of measurement of the actual deposited products and the performed modeling of the stress–strain state of the deposited parts, it is possible to select deposition parameters such as rate, microplasma arc current, gas flow rates, filler material flow rate, and arc length. By controlling the microplasmatron movement (trajectory and speed) and pre–selected parameters of the deposition process, it is possible to achieve an improvement in the quality of the deposited product formation.

During deposition, it is proposed to maintain a stable arc length using feedback from the system of automatic control of arc voltage (ACAV), which measures the voltage and adjusts the microplasmatron position by height in real–time. Thus, a stable voltage is ensured, which automatically maintains the required arc length. The ACAV system was used as an additional system at the initial stage of investigations, to the extent of the absence of a sufficient volume of statistical data, in cases when it was difficult to predict, with sufficient accuracy, the height of the layers in 3D parts being deposited.

Let us consider an example of microplasma powder deposition of a «hollow cylinder» part. Modeling of the residual stress–strain state of such a deposited part allowed the determination and minimization of stresses normal to axes X and Y, equivalent stresses, and residual deformations along axis Z due to selection of the heat input (Figure 13). For the calculation of the stress–strain state of the finished part, the respective parameters of the technological mode were selected, and they were used to create the part (Figure 14a). Note that at a certain height of the cylinder building–up, certain instabilities in the deposited bead formation began to appear because of the part overheating. In case of a combination of the results of modeling of the residual stress–strain state of the product with additional analysis of the accumulated statistical data, corrections were made in the additive deposition process, which greatly increased the deposited cylinder height without deterioration of the quality (Figure 14b).

Producing an S–shaped wall is an example of the potential of a corrected process of additive powder microplasma deposition (Figure 15). The HYF–103 powder was used for its manufacturing, and №5 mode from Table 8 was selected as the basic one. For programming each subsequent trajectory of movement of the microplasmatron tool during additive deposition, a combination of the results of modeling the residual stress–strain state of the product with additional analysis of the accumulated statistical data was used. Dynamic stabilization of the arc length was performed via the stabilization of arc voltage using the ACAV system.

Thus, it can be considered proven that the application of prediction of the stress–strain state in combination with the acquisition of statistical data on the actual deposited parts and development of software for their analysis and selection of the parameters of additive microplasma deposition of 3D metal products further enhances their manufacturing efficiency.

Furthermore, the proposed approaches to adjustment of the stress–strain state of the products made by additive microplasma deposition will be the basis for designing the respective hardware and software complex. The hardware and software complex for microplasma deposition developed on the base of program analysis and selection of process parameters can significantly expand the capabilities of the regular deposition process and bring this process to a fundamentally new level with the capability of predicted detection of deviations from printing accuracy. It will allow optimizing the parameters of the technological process of manufacturing spatial objects using an analysis of the model–accumulated data by the criterion of minimizing the residual stresses and deformations (movements).

Thus, we proposed the basic principles for the creation of the hardware–software complex for microplasma deposition, which has the capability of analysis of data accumulated through modeling to provide automatic 3D printing of spatial metal products with a predictable structure and stressed state. Future application of such a complex will ensure industrial 3D printing of metal product billets for mass production. For instance, this method enables the manufacturing of complex–shaped parts for aviation, automotive, railway, and sea transport, such as complex pipe adapters, etc. Note that because of the considerable roughness of the produced billet walls (of the order of Rz 60–120 μm), their machining is required, for instance, finish milling.

Despite the need for finish machining, the speed of producing finished parts by the proposed 3D printing method is higher than that of SLM printing, which is associated with a larger volume of the liquid metal pool at similar printing speeds. So, the efficiency of the SLM method of producing the finished part is of the order of 10–100 cm³/h [39], whereas the efficiency of producing the billet by the proposed method is equal to 200–3000 cm³/h which, allowing for finished machining, is approximately 10–20 times higher than the speed of producing a finished part by SLM printing. The efficiency of producing the part billets via the WAAM method using the MIG/MAG process is equal to 500–6000 cm³/h on average [39], which is 2–3 times higher than the speed of producing the billet by the proposed method. It should be taken into account, however, that the proposed method allows producing the minimal thickness of the deposited wall of the order of 3.0–3.5 mm, whereas for the WAAM method, it is not less than 5–6 mm. This determines certain limits of the proposed process applicability, compared to SLM and WAAM processes. The proposed process envisages finish machining, and it is rational to apply it to produce finished metal parts with a wall thickness of the order of 2–4 mm.

5. Conclusions

• It was established that additive microplasma deposition of powder of Fe–Cr–Ni–B–Si system (40–60 µm particle size) results in the formation of a layered metal structure with the deposited layer height of the order of 650 µm and wall thickness of 3.0–3.5 mm. Metal distribution by the sample height is uniform. Additive formation of a sample by powder deposition results in the appearance of colonies of coarse and fine dendrites, the size and orientation of which change along the wall height. The deposited metal has a presumably austenitic structure with (40–100) × (200–600) µm grain size and 15–30 µm substrain size (lower and middle part) with its refinement in the upper part and reduction of grain shape coefficient ᴔ by 1.3 times on average. The subgrain structure of the deposited metal is of a cellular type, and it provides a certain effect of metal strengthening. Deposited metal ensures a high ultimate strength (more than 600 MPa). Susceptibility to porosity or cracking is absent;
• The finite element method was used to derive a solution to the thermomechanical problem of additive deposition with HYF–103 powder of the Fe–Cr–Ni–B–Si system for five selected hollow spatial prototypes («cylinder», «triangular prism», «square prism», «reverse cone», and «straight cone»). It was found that in all the cases in the first bead of the modeled samples, there was a high level of residual equivalent stresses (~500 MPa) due to the substrate rigidity. In each subsequent deposited bead, the residual equivalent stresses decreased by 7–20%, which corresponds to the level of 390 MPa in the third pass. Equivalent stresses of the greatest magnitude (565 MPa) are predicted in the model sample of the «reverse cone» type, and the smallest ones (552 MPa) in the sample of the «straight cone» type. The maximal values of radial movements corresponded to the range of 0.22–0.28 mm for all the models. Experimental studies of residual deformations of the deposited products showed an up to 20% deviation from the modeled values, which is acceptable;
• To minimize the stress–strain state of the manufactured 3D objects, basic techniques of the process of additive microplasma deposition were developed, including the process starting at a higher current (~35 A) with a rapid transition (~1 s) to a stable mode (~25 A); reduction in the filler powder flow rate (to 6 g/min); lowering of the plasma–forming gas flow rate from 0.4 to 0.2 L/min; stabilization of the process energy input at the level of 85–90 J/mm; and minimization of the arc length (to 5 mm). The application of a system of automatic regulation of arc voltage was proposed for the stabilization of the energy input and the arc length.