Analysis of Phenomenon of Plasticity Loss of Steel Core Made by Selective Laser Melting Method in Zone of Pressure Mould Conformal Cooling Channel

This paper presents the results of testing the mechanical properties of maraging steel 1.2709 that were obtained by the SLM method under uniaxial and triaxial states of stress. The triaxial state of stress was realised by making circumferential notches in the samples with different radii of rounding. The specimens were subjected to two types of heat treatment, which consisted of ageing at 490 °C and 540 °C for 8 h. The results of the tests that were conducted on the samples were considered as references and compared with the results of the strength tests that were conducted directly on the SLM-made core model. Differences were found between the results of these tests. Based on the experimental results, the relationship between the equivalent strain of the specimen in the bottom of notch εeq and triaxiality factor η was determined. Function εeq = f(η) was proposed as a criterion for the decrease in the plasticity of the material in the area of the pressure mould cooling channel. Using the FEM method, equivalent strain field εeq and triaxiality factor η were determined in the conformal channel cooled core model. Based on the proposed criterion of plasticity loss and the results of numerical calculations, it was shown that the values of equivalent strain εeq and triaxiality factor η in the core that was aged at 490 °C did not meet this criterion. On the other hand, the values of strain εeq and triaxiality factor η did not exceed the safety limit when ageing was carried out at 540 °C. The plasticity loss method presented in this paper assumes that the value of the triaxiality factor in the vicinity of the channel is influenced by the shape, cross-sectional dimensions and trajectory of the channel axis. Using the methodology proposed in this paper, it is possible to determine the value of allowable deformations in the cooling channel zone and to determine whether the heat treatment applied to the SLM steel does not cause an excessive reduction in the plastic properties.


Introduction
Significant advances in the development of 3D printing methods-including SLM (selective laser melting) technology [1]-create the possibility of its application for fabricating tooling parts of pressure casting moulds. The use of the SLM method for fabricating pressure mould parts significantly expands the range of available design solutions for the designed mould cooling system as compared to machining methods. By matching the trajectory of the channels to the shape of the surface of the mould cavity or core, the rate of the heat removal from the solidifying metal is increased, resulting in a more homogeneous temperature field in the casting [2]; also, shrinkage porosity can be largely eliminated, and a fine-grained structure of the casting can be achieved [3][4][5]. This results in a casting with greater mechanical strength and tightness. The use of conformal channels also reduces the cycle time of the pressure machine. Compared to the classical way of designing cooling channels, conformal channels are located closer to the metal¬-mould contact surface and have smaller diameters. The design distances between the surfaces of adjacent channels The surfaces of the mould or core that are in contact with the metal are always machined, whereas the surfaces of the cooling channels in the SLM mould core are not machined. Their surface has the texture and roughness produced by the SLM process. In contrast to the external surfaces of a mould cavity or core, the initiation of a crack on a channel surface does not immediately eliminate the mould from use. Crack development is highly dependent on the values of the components of the stress-strain tensor, as well as on the triaxiality factor. Therefore, this article proposes a plasticity loss criterion based on the analysis of the stress-strain state. This criterion can be used to predict the possibility of cracks forming on the surface of mould cooling channels. Due to the much higher operating temperature range of a pressure mould compared to an injection mould, the use of conformal cooling poses greater research and design problems. Consequently, the use of the right steel grade, SLM process parameters, and heat treatment parameters is a very important issue. The most commonly used material for SLM mould parts is maraging steel powder with the symbol of 1.2709. The SLM process results in a steel with a martensitic structure whose hardness is too low as related to that which is required for pressure mould parts. Therefore, heat treatment is recommended for the printed parts, which results in the strengthening of the alloy through the separation of the intermetallic phases [19][20][21]. The recommended ageing process for 1.2709 SLM steel is carried out at 490 • C [22] or 540 • C [23], obtaining hardnesses of 50-57 and 52 HRC, respectively. An increase in the ageing temperature results in austenite reversion, decreases in toughness and hardness, and a concomitant increase in the ductile properties of the steel [24]. The choice of heat treatment parameters for a pressure mould part should ensure that a material with the required hardness, a high yield strength, and sufficient ductility is obtained. As mentioned above, a characteristic feature of the conformal channel is the frequent change in its trajectory, resulting in numerous surface kinks in the forms of curves with small, rounded radii. As a result, a notch-influenced phenomenon occurs in numerous places in the area in which a triaxial stress state is present. The triaxial stress state limits the development of plastic deformation as the stress level increases. This phenomenon means that a material that exhibits plastic characteristics in a static tensile test can change its properties and become brittle. In the presence of material defects in the forms of inclusions, voids, or unmelted powder grains, the triaxial stress state stimulates the formation of microcracks in their surroundings, which increase in size due to plastic deformation until the voids coalesce and eventual plastic fracturing occurs. This paper presents the results of an experimental study to determine the effect of changes in triaxiality factor η on the value of equivalent strain ε eq for maraging steel that was obtained by the SLM method and subjected to two types of heat treatment. Experimental results and FEM calculations were used to determine the plasticity loss of SLM steel on the surface of the conformal cooling channel based on the proposed criterion.

Materials and Methods
The test specimens and mould core model were made by the SLM method from maraging steel powder with the trade symbol of "CL50WS" and obtained by gas atomisation (recommended by Concept Laser General Electric Additive Company). The chemical composition of the powder corresponds to martensitic, hot work steel 1.2709. The chemical composition of the powder (determined on the basis of spectroscopic tests) is listed in Table 1. The chemical composition of the powder was determined by spectral analysis using a Spectro Midex energy-dispersive X-ray fluorescence spectrometer (ED-XRF) from SPECTRO Analytical Instruments GmbH, Kleve, Germany. The samples for the testing and the core were made using an M2 Concept Laser Cusing device. The material was printed with the parameters that are listed in Table 2. The sample and core axes were located perpendicular to the surface of the M2 printer work platform. The island-scanning pattern was used. In this scanning strategy, part of the surface of each slice was divided into small square islands. The islands were scanned in a random manner, while the scanning direction was altered at right angles with respect to the neighbouring islands. The relative density of the fabricated specimens was measured according to Archimedes' principle. The relative density of the fabricated specimens reached 99.91%. Smooth specimens were not machined. The surface of the notches has been machined to ensure dimensional accuracy. The material was heat treated by ageing at temperatures of 490 • C (HT490) and 540 • C (HT540) for 8 h. The heating and cooling of the specimens was carried out at a rate of 100 K/h. Heat treatment was carried out in a "Mini Tube KJ 1200" (Zhengzhou Kejia Furnace Co., Ltd., Zhengzhou, China) oven. The diameter of the furnace chamber was 40 mm, and its length was 200 mm. The control and steering of the temperature changes was carried out by a microprocessor. Uniaxial tensile tests were carried out on specimens with a diameter of 5 mm using an MTS 810 testing machine according to ISO 6892-1. An MTS extensometer with a 20-mm base was used to measure the elongation. The specimens that were intended to be subjected to investigations in a multiaxial stress state had circumferential notches with different radii of ρ = 0.5, 1.5, 2.5, 3.5, 4.5, and 6.5 mm (as shown in Figure 1). The diameter of all of the specimens was D = 10 mm, and the minimal diameter at the notch was 2r = 5 mm. The strain rate for the smooth specimens was 0.001 s −1 in the elastic range and the predicted strain rate was 0.002 s −1 when the yield point was exceeded. For notched specimens, the test stress rate was 2.5 MPa/s. The number of smooth specimens was 5 for each heat treatment (10 specimens in total), whereas ring notched specimens were 4 for each notch radius (48 in total).  Measurement of the diameter of the specimen at the bottom of circumferential notch 2r and the radius of notch ρ before and after the tensile test (2r0 and ρ0 respectively) were carried out using an optical microscope image and a clamping fixture that was specially made for this purpose. The metallographic tests of the microsections and fractures were performed using a Nikon SMZ 745T stereoscopic optical microscope (Konan, Japan), a Nikon Eclipse metallographic microscope with a DsFi1 camera that enabled digital image analysis, and a Hitachi S-3400N scanning electron microscope (Tokyo, Japan) with a Thermo Noran energy dispersive X-ray spectroscope (Waltham, MA, USA). Strength tests of the core that was made by the SLM method were carried out according to the following procedure using DIN SPEC 4864: "Test method for the determination of flow curves and Measurement of the diameter of the specimen at the bottom of circumferential notch 2r and the radius of notch ρ before and after the tensile test (2r 0 and ρ 0 respectively) were carried out using an optical microscope image and a clamping fixture that was specially made for this purpose. The metallographic tests of the microsections and fractures were performed using a Nikon SMZ 745T stereoscopic optical microscope (Konan, Japan), a Nikon Eclipse metallographic microscope with a DsFi1 camera that enabled digital image analysis, and a Hitachi S-3400N scanning electron microscope (Tokyo, Japan) with a Thermo Noran energy dispersive X-ray spectroscope (Waltham, MA, USA). Strength tests of the core that was made by the SLM method were carried out according to the following procedure using DIN SPEC 4864: "Test method for the determination of flow curves and benchmark characteristic values for tensile testing by means of minor destructive indentation, 3D measurement, and finite-element material models" [25]. The numerical calculations that were used to determine the strain field and triaxiality factor η in the mould core were performed with the program Abaqus v. 2019.

Thermal and Strain-Stress Model of Phenomenon
The High Pressure Die Casting (HPDC) process repeats cyclically. In the numerical model, the duration of one HPDC cycle was assumed to be 35 s. The thermal model assumed the division of each work cycle into four stages: alloy crystallisation and casting cooling-22 s; casting extraction-2 s; spraying the surface of the mould with water suspension-3 s; and preparing the mould for reclosure-8 s. The cycle time assumptions given are based on the operating parameters of the FRECH 510 horizontal cold-chamber HPDC machine. The core with the conformal cooling channel referred to in the article is mounted in the mould and works in the cycle described.
The geometrical model consisted of a core, casting, and mould cavity; all are shown in Figure 2. A thermal surface contact model was used to describe the boundary conditions of the heat transfer between the mould and the casting. In the model, the temperaturedependent properties of the AlSi9Cu3 alloy were assumed. The calculations assumed an initial alloy temperature of Tinit_1 = 680 • C and an initial core temperature of Tinit_2 = 50 • C. The strain-stress model took the geometry of the casting and the conformal core into account. Its attachment was determined by taking away degrees of freedom on the mould's contact surfaces. The strains and stresses and the triaxiality factor η in the core were calculated based on the temperature fields. As a result of numerical calculations, the following were calculated: the values of equivalent deformation εeq as determined by Equation (1) [26], and triaxiality factor η (whose definitions and discussion are presented in Section 3.1).
where ε1, ε2, ε3 are the principal strains, and ν is Poisson's ratio. A detailed description of the temperature model and the material characteristics that were adopted in the numerical calculations are presented in [27].

Criterion for Plasticity Loss
The material resistance is usually estimated during the uniaxial tensile test (even though the material is usually subjected to multiaxial stress states in many parts of the The strain-stress model took the geometry of the casting and the conformal core into account. Its attachment was determined by taking away degrees of freedom on the mould's contact surfaces. The strains and stresses and the triaxiality factor η in the core were calculated based on the temperature fields. As a result of numerical calculations, the following were calculated: the values of equivalent deformation ε eq as determined by Equation (1) [26], and triaxiality factor η (whose definitions and discussion are presented in Section 3.1).
where ε 1 , ε 2 , ε 3 are the principal strains, and ν is Poisson's ratio. A detailed description of the temperature model and the material characteristics that were adopted in the numerical calculations are presented in [27].

Criterion for Plasticity Loss
The material resistance is usually estimated during the uniaxial tensile test (even though the material is usually subjected to multiaxial stress states in many parts of the structure). In a multi-axis stress state, the properties of the material and the manner of its decohesion change with the value of triaxiality factor η. The triaxiality factor is defined as the ratio of mean stress σ m to the Mises criterion σ v [28,29].
where σ 1 , σ 2 , and σ 3 denote the principal stresses. Triaxiality factor η can often be used to predict the type of fracture within a region that is defined by this stress state. High-stress triaxiality promotes brittle cleavage fractures as well as dimple formation within an otherwise ductile fracture. Low-stress triaxiality corresponds with shear slip and, therefore, greater ductility. An experimental observation of a triaxiality factor that is greater than 2/3 rather indicates that the biaxiality condition of the plane stress test was lost and a three-dimensional stress state started to exist in the sample [30]. Experimental studies to determine the effect of triaxiality factor η on changes in the plastic properties of the material can be carried out on circumferentially notched specimens. The stress distribution in the region of a notch that is made in the bar can be determined by using the Bridgman equation [31,32]. This equation gives the relationship between triaxiality factor η at the point of intersection of the specimen axis with the plane that passes through the bottom of the circumferential notch: The values of the η coefficients for the circumferential notch samples with different radii ρ were calculated based on Equation (5). The radius of ring notch ρ was determined for each sample based on the image that was obtained by the optical microscope; they were measured in the same way. The equivalent strain ε eq along the minimum cross section is given by the following [33]: The η values that occurred in the pressure mould core model during the operating cycle were determined from the numerically calculated components of the stress tensor using Equations (2)-(4). Based on the experimental results, the graphs of function ε eq /ε eq_s = f(η) were constructed (ε eq_s -the equivalent strain of the smooth sample at rupture). Function f(η) was proposed as a criterion for the plasticity loss of the material in the area of the pressure mould cooling channels.

Strain and Triaxiality Factor in Mould Core Model
As a result of the FEM calculations, the changes in the equivalent strain ε eq and triaxiality factor η that occurred in the core during the stabilised cycle of the pressure mould were determined. In Figure 3, the left column shows the field of equivalent strain ε eq in three sections of the core after 2.1 s from the moment of injecting the metal into the mould (when their values were the highest), while its right column shows the field of the triaxiality factor η values in the same sections of the core and at the same moment of time. Both the strain and the triaxiality factor had the highest values in the vicinity of the cooling channels. Most often, the value of equivalent strain ε eq in the vicinity of the channels is between 0.0012 and 0.0015 (mm/mm); however, the maximum value of the strain increased to about 0.0020 (mm/mm) in the area where there was a large curvature of the channel surface (the area where the direction of the trajectory of the cooling channel axis changed). A typical course of changes in the ε eq strain values during the pressure mould cycle in the area of the change in the trajectory of the channel axis (notch effect) is shown by the "MAX" curve in Figure 4, while the "MIN" curve is shown in the surroundings of the linear channel. Figure 4 shows the initial rapid increase in the strain immediately following the injection of the metal into the mould. The effect of the rapid increase in temperature and the associated increase in the strain values was enhanced by the relatively short distance of the cooling channel from the core-metal contact surface (which was about 4 mm).

Tensile Tests
Strength tests were carried out on smooth specimens in uniaxial stress and triaxi stress states using circumferentially notched specimens. As the results of the uniaxi tensile test, the ultimate tensile stress (UTS), yield stress (σp0.2), modulus of elasticity (E and elongation (A) were obtained. The results of the tensile test for two variants of he treatment ("HT490" and "HT540") are listed in Table 3 as the results that were obtaine on the four specimens. According to the study, a higher ageing temperature causes a decrease in the strengt of SLM steel as well as a simultaneous increase in its ductile properties. The tests that we conducted on circumferentially notched specimens in a triaxial state of stress showed very large effect of triaxiality factor η on the strength and ductility of the steel. As increased, the value of the destructive force of specimen Fd increased ( Figure 5), while th value of the equivalent strain at the bottom of notch εeq decreased ( Figure 6).

Tensile Tests
Strength tests were carried out on smooth specimens in uniaxial stress and triaxial stress states using circumferentially notched specimens. As the results of the uniaxial tensile test, the ultimate tensile stress (UTS), yield stress (σ p0.2 ), modulus of elasticity (E), and elongation (A) were obtained. The results of the tensile test for two variants of heat treatment ("HT490" and "HT540") are listed in Table 3 as the results that were obtained on the four specimens. According to the study, a higher ageing temperature causes a decrease in the strength of SLM steel as well as a simultaneous increase in its ductile properties. The tests that were conducted on circumferentially notched specimens in a triaxial state of stress showed a very large effect of triaxiality factor η on the strength and ductility of the steel. As η increased, the value of the destructive force of specimen F d increased ( Figure 5), while the value of the equivalent strain at the bottom of notch ε eq decreased ( Figure 6).

Fractographic Studies
The main aim of the fractographic examination was to make a qualitative assessment of the fracture morphology in relation to the stress triaxiality factor. The examinations were made on all of the specimens and tested under different spatial stress states. Several photos were taken at different magnifications of the microregions in the centre of each sample. In the central part of the specimen, the hydrostatic stresses were the highest; in this area, triaxiality factor η had the highest value when the specimen ruptured. These examinations indicated that the stress state influenced the fracture surface morphology.

Fractographic Studies
The main aim of the fractographic examination was to make a qualitative assessment of the fracture morphology in relation to the stress triaxiality factor. The examinations were made on all of the specimens and tested under different spatial stress states. Several photos were taken at different magnifications of the microregions in the centre of each sample. In the central part of the specimen, the hydrostatic stresses were the highest; in this area, triaxiality factor η had the highest value when the specimen ruptured. These examinations indicated that the stress state influenced the fracture surface morphology. Figure 7 shows typical fracture images of specimens that were made from 1.2709 steel powder by SLM and aged at 490 °C. The images show the fractures of six specimens with different triaxiality factors.

Fractographic Studies
The main aim of the fractographic examination was to make a qualitative assessment of the fracture morphology in relation to the stress triaxiality factor. The examinations were made on all of the specimens and tested under different spatial stress states. Several photos were taken at different magnifications of the microregions in the centre of each sample. In the central part of the specimen, the hydrostatic stresses were the highest; in this area, triaxiality factor η had the highest value when the specimen ruptured. These examinations indicated that the stress state influenced the fracture surface morphology. Figure 7 shows typical fracture images of specimens that were made from 1.2709 steel powder by SLM and aged at 490 °C. The images show the fractures of six specimens with different triaxiality factors. Circumferentially notched specimens with notch radii of ρ = 0.5 and 1 mm (Figure 8a,b) had a distinguishably higher proportion of brittle fractures than the others (Figure 8c-f). The observations of the fractures correlated with the results of the strength tests, which showed decreases in the proportions of the ductile properties of the SLM steels with increases in η and as a result of the heat treatment at the lower temperature.

Results of Study of Chemical Composition of Conformal Core
The printed 1:2 scale model of the core was cut into two parts. Chemical composition tests were carried out at 20 measurement points on the surface that resulted from the cutting of the core (Figure 9). Cutting the core revealed the outlines of a conformal cooling

Results of Study of Chemical Composition of Conformal Core
The printed 1:2 scale model of the core was cut into two parts. Chemical composition tests were carried out at 20 measurement points on the surface that resulted from the cutting of the core (Figure 9). Cutting the core revealed the outlines of a conformal cooling channel (parts of which can be seen in Figure 9). Table 4 shows the results of the chemical composition tests on the surface of the core section and, additionally, gives the maximum (Max) and minimum (Min) values of the results that were obtained as well as the mean values for the 20 measurements and the standard deviations (σ). The elemental percentages were within the ranges of the values that were expected for this steel grade with the exception of Mo (4.37%) and Ti (0.77%); these average percentages were below the lower limits of the required ranges of the values of Mo (4.50-5.20%) and Ti (0.80-1.20%). The relatively large local fluctuations in the percentage of Ti could have been caused by the formation of large oxide precipitates of this element of about 20 µm, which significantly reduced the mechanical properties of the SLM steels [34].
values for the 20 measurements and the standard deviations (σ). The elemental percentages were within the ranges of the values that were expected for this steel grade with the exception of Mo (4.37%) and Ti (0.77%); these average percentages were below the lower limits of the required ranges of the values of Mo (4.50-5.20%) and Ti (0.80-1.20%). The relatively large local fluctuations in the percentage of Ti could have been caused by the formation of large oxide precipitates of this element of about 20 µm, which significantly reduced the mechanical properties of the SLM steels [34].

Test Results for Mechanical Properties of Mould Core
The testing of the mechanical properties of the pressure mould core was carried out according to DIN SPEC 4864:2019-11 on the same cross-sectional area as for the chemical composition tests. The measurement locations were marked as shown in Figure 10. The method consisted of making a dimple in the test material through an indenter, which was moved orthogonally to the sample surface and penetrated the sample in a force-controlled manner until the test force value was reached. After a specified amount of time, the indenter was removed from the sample. An optical measuring device then determined the resulting three-dimensional deformation of the sample. A finite element programme created a simulation model that provided a realistic representation of the hardness test (constitutive material behaviour, mechanical boundary conditions, friction). The programme's algorithm changed and adjusted the material properties until the shape and dimensions of the virtual dimple (with sufficient accuracy) corresponded to the image of the actual dimple that was obtained by the optical measuring device. The optimisation algorithm changes the coefficients describing the stress-strain curve and simulates, using the FEM method, a virtual indentation imprint in the test material. The coordinates of the points on the surface of the virtual indentation are compared with the actual coordinates of the points in the optical image. If the spatial mapping is optimised, the difference between the virtual and actual coordinates of the indentation surface cannot be greater than 5%, if the mapping is axisymmetric 3%. The mechanical properties of the materials that were tested were taken from the simulation with the best match between the FE solution and the actual shape and dimensions of the dimple. The results of the tests that were carried out are presented in the forms of graphs as functions of the plastic stress strain (Figure 11). These graphs are similar to those that were obtained in the classical tensile test of the metals; the difference lies in the absence of the elastic strain part of the graph, which was not determined due to the nature of the method. Table 5 summarises the results of the yield strength (R p0.2 and R p1.0 ), ultimate tensile stress (UTS), and plastic strain (ε pl ) as determined from the graphs that are presented in Figure 11.

Test Results for Mechanical Properties of Mould Core
The testing of the mechanical properties of the pressure mould core was carried ou according to DIN SPEC 4864:2019-11 on the same cross-sectional area as for the chemica composition tests. The measurement locations were marked as shown in Figure 10. Th method consisted of making a dimple in the test material through an indenter, which wa moved orthogonally to the sample surface and penetrated the sample in a force-controlle manner until the test force value was reached. After a specified amount of time, th indenter was removed from the sample. An optical measuring device then determined th resulting three-dimensional deformation of the sample. A finite element programm created a simulation model that provided a realistic representation of the hardness tes (constitutive material behaviour, mechanical boundary conditions, friction). Th programme's algorithm changed and adjusted the material properties until the shape an dimensions of the virtual dimple (with sufficient accuracy) corresponded to the image o the actual dimple that was obtained by the optical measuring device. The optimisatio algorithm changes the coefficients describing the stress-strain curve and simulates, usin the FEM method, a virtual indentation imprint in the test material. The coordinates of th points on the surface of the virtual indentation are compared with the actual coordinate of the points in the optical image. If the spatial mapping is optimised, the differenc between the virtual and actual coordinates of the indentation surface cannot be greate than 5%, if the mapping is axisymmetric 3%. The mechanical properties of the material that were tested were taken from the simulation with the best match between the F solution and the actual shape and dimensions of the dimple. The results of the tests tha were carried out are presented in the forms of graphs as functions of the plastic stres strain (Figure 11). These graphs are similar to those that were obtained in the classica tensile test of the metals; the difference lies in the absence of the elastic strain part of th graph, which was not determined due to the nature of the method. Table 5 summarise the results of the yield strength (Rp0.2 and Rp1.0,), ultimate tensile stress (UTS), and plasti strain (εpl) as determined from the graphs that are presented in Figure 11. plastic strain (εpl) marked on cross-sectional surface of pressure mould core. Table 5 shows the results of the strength tests that were carried out on the surface of the mould core section in accordance with DIN SPEC 4864:2019-11. Table 5 also shows the maximum (MAX) and minimum (MIN) values of the results that were obtained as well as the mean values and standard deviations (σ) and the differences between the maximum and minimum values (Δ = Max-Min). Figure 11. Plots of stress-strain function defined at Points 1 through 13 (labelled in Figure 10); test was performed in accordance with DIN SPEC 4864:2019-11 standard.  Figure 11. Plots of stress-strain function defined at Points 1 through 13 (labelled in Figure 10); test was performed in accordance with DIN SPEC 4864:2019-11 standard.  Table 5 shows the results of the strength tests that were carried out on the surface of the mould core section in accordance with DIN SPEC 4864:2019-11. Table 5 also shows the maximum (MAX) and minimum (MIN) values of the results that were obtained as well as the mean values and standard deviations (σ) and the differences between the maximum and minimum values (∆ = Max-Min).
Microhardness measurements were also taken on the cross-sectional surface of the core; it was discovered that there were significant differences between the values at different points. The results of these measurements confirmed the variations of the mechanical properties within the mould core that was made by the SLM method. Figure 12 shows the average values from several microhardness measurements that were carried out in the areas that were marked with an ellipse on the cross-sectional surface of the core. Microhardness measurements were also taken on the cross-sectional surface of the core; it was discovered that there were significant differences between the values at different points. The results of these measurements confirmed the variations of the mechanical properties within the mould core that was made by the SLM method. Figure  12 shows the average values from several microhardness measurements that were carried out in the areas that were marked with an ellipse on the cross-sectional surface of the core.

Analysis of Results
The experimental studies and numerical simulations that are presented in this paper were carried out to determine the plasticity loss criterion for steel 1.2709 that was obtained by SLM and then subjected to different heat treatment variants. Based on the formulated criterion, it was possible to determine the allowable value of equivalent strain εeq in the insert or core of the pressure mould as a function of the degree of triaxiality factor η. The criterion can be used in the vicinity of cooling channels, as the value of the mechanical strain there has a direct influence on the strength of the material. The criterion loses validity in those areas of the mould part where the influence of thermal deformation cannot be neglected. The use of the plasticity loss criterion to determine the allowable values of mechanical strains as a function of changes in the triaxiality factor in a core is justified due to the frequently occurring changes in the direction of the axis and the conformal cross section of the cooling channel. Changes in the trajectory of the channel axis cause a notch effect and, thus, a local increase in the triaxiality factor. The result is a reduction in the ductile properties of SLM steels in favour of an increase in strength. Steel whose fracture in the uniaxial stress state has plastic characteristics in the triaxial stress state may have a brittle fracture. This criterion was defined in the form of the function f(η) = εeq/εeq_s that was determined from the results that were obtained from the tensile testing of the circumferentially notched specimens that were aged at 490 °C ( Figure 13) and 540 °C (Figure 14). For the smooth unnotched specimens, the triaxiality factor η in the specimen axis that was calculated using Equation (5) was 0.33, and the value of function

Analysis of Results
The experimental studies and numerical simulations that are presented in this paper were carried out to determine the plasticity loss criterion for steel 1.2709 that was obtained by SLM and then subjected to different heat treatment variants. Based on the formulated criterion, it was possible to determine the allowable value of equivalent strain ε eq in the insert or core of the pressure mould as a function of the degree of triaxiality factor η. The criterion can be used in the vicinity of cooling channels, as the value of the mechanical strain there has a direct influence on the strength of the material. The criterion loses validity in those areas of the mould part where the influence of thermal deformation cannot be neglected. The use of the plasticity loss criterion to determine the allowable values of mechanical strains as a function of changes in the triaxiality factor in a core is justified due to the frequently occurring changes in the direction of the axis and the conformal cross section of the cooling channel. Changes in the trajectory of the channel axis cause a notch effect and, thus, a local increase in the triaxiality factor. The result is a reduction in the ductile properties of SLM steels in favour of an increase in strength. Steel whose fracture in the uniaxial stress state has plastic characteristics in the triaxial stress state may have a brittle fracture. This criterion was defined in the form of the function f(η) = ε eq /ε eq_s that was determined from the results that were obtained from the tensile testing of the circumferentially notched specimens that were aged at 490 • C ( Figure 13) and 540 • C ( Figure 14). For the smooth unnotched specimens, the triaxiality factor η in the specimen axis that was calculated using Equation (5) was 0.33, and the value of function f(η) = 1. Figure 13 shows Points A and B with coordinates (ε eq /ε eq_s , η). Equivalent strain values ε eq and η in the mould core during one cycle of the pressure machine were determined using the FEM method. The coordinates of Point A were determined by the maximum values of ε eq and η that occurred in the vicinity of the rectilinear sections of the cooling channel, while the coordinates of Point B were determined by the maximum values of ε eq and η that were in the vicinity of the curved sections. The ε eq_s strain was the strain of the smooth specimens that were aged at 490 • C. The experimental tests and numerical calculations showed that the HT490 heat treatment caused such a large loss of plasticity in the 1.2709 SLM steel that the ε eq strain and η values that were determined in the core exceeded permissible values ( Figure 13). aterials 2023, 16, x FOR PEER REVIEW 17 of 23 f(η) = 1. Figure 13 shows Points A and B with coordinates (εeq/εeq_s, η). Equivalent strain values εeq and η in the mould core during one cycle of the pressure machine were determined using the FEM method. The coordinates of Point A were determined by the maximum values of εeq and η that occurred in the vicinity of the rectilinear sections of the cooling channel, while the coordinates of Point B were determined by the maximum values of εeq and η that were in the vicinity of the curved sections. The εeq_s strain was the strain of the smooth specimens that were aged at 490 °C. The experimental tests and numerical calculations showed that the HT490 heat treatment caused such a large loss of plasticity in the 1.2709 SLM steel that the εeq strain and η values that were determined in the core exceeded permissible values ( Figure 13).  The failure mode was studied using a scanning microscope on the fracture surfaces of the samples. The specimens were observed and photographed at a central area of the fractured cross section (thus, on the spot that corresponded to the maximal stress concentration). The plasticity loss that was caused by the heat treatment that was shown in the tensile tests was confirmed by the fractographies. The ductile failure of the SLM steel took place through the initiation, increase, and coalescence of the voids that were generated on the inclusion. The voids that were generated around the inclusion during the loading had their reflections as dimples on the fracture surface; this type of fracture can be seen in Figure 7e,f and Figure 8a-f. The brittle failure nucleation locations were the same as the ductile fracture, but the fracture mode was different. The brittle fracture was characterised by a very small proportion of plastic deformation and was mainly developed by cleavage decohesion; this type of fracture is characteristic of heat treatment at 490 • C (Figure 7). In the same way as for Points A and B, the coordinates of Points C and D in Figure 14 were determined. The positions of Points C and D with respect to function f(η) = ε eq /ε eq_s indicates that the heat treatment of HT540 caused such a sufficiently small decrease in the ductility of the 1.2709 SLM steel that the values of the strain and triaxial factor in the vicinity of the cooling channels did not exceed permissible values. The numerical calculations showed that the values of η in the zone of the rectilinear channels (η = 0.65) differed significantly from those in the areas where the curvature of the channel axis changed (η = 1.78). These values changed only slightly during the pressure mould cycle despite the significant changes in the stress and strain (Figure 4). This, of course, applies to the stabilised mould cycle, which occurred several cycles after the first metal injection.  Tests of some of the mechanical properties of the 1.2709 SLM steel were carried out directly on the cross-sectional surface of the printed core in order to compare the results with the reference values that were determined in the tensile and microhardness tests. The SLM process parameters were the same during the printing of the core model and the samples. It was found that the values of yield strength R p0.2 , ultimate tensile strength UTS, and the plastic strain of the SLM steel differed depending on the position of the measurement point on the cross-sectional surface of the core. Figure 15 shows the yield strength values of R p0.2 measured at the 13 points as related to their mean value (represented by the dashed line) and to the value of R p0.2 as determined in the static tensile test (solid line). The difference between the largest and smallest values of R p0.2 that were measured on the cross-sectional area of the core was as high as 213 MPa, and the standard deviation from the mean value for the population of the 13 measurement points was σ = 49.2 MPa. Much smaller was the difference between the average value of R p0.2 that was determined at the same measurement points and the yield strength R p0.2 that was determined in the tensile test-this was 20 MPa. A similar graph was made for the measured UTS values (Figure 16). The difference between the largest and smallest UTS value was 81 MPa, and the standard deviation was σ = 25 MPa. The difference between the average UTS value that was determined for the 13 measurement points and the UTS strength that was determined in the tensile test was 35 MPa in this case. When performing a strength test according to DIN SPEC 4864:2019-11, only the plastic strain of the material's ε pl is determined (the elastic part of strain ε s is omitted). For this reason, Figure 17 shows the plastic strain value that was determined from the static tensile test plots of the SLM steel after omitting the elastic strain. The difference between the largest and smallest ε pl values was 4.1%, and the standard deviation was σ = 1.1%. The difference between the mean value ε pl that was determined at the measurement points and the plastic deformation of the steel that was determined in the tensile test was 0.52%. These results can be used to carry out an analysis to determine the appropriate safety factor for parts that are printed from 1.2709 steel powder via SLM. deformation of the steel that was determined in the tensile test was 0.52%. These results can be used to carry out an analysis to determine the appropriate safety factor for parts that are printed from 1.2709 steel powder via SLM.    deformation of the steel that was determined in the tensile test was 0.52%. These results can be used to carry out an analysis to determine the appropriate safety factor for parts that are printed from 1.2709 steel powder via SLM.    As a supplement to the information on the differences between the reference mechanical properties of the SLM steels and those that were measured on the crosssectional surface of the core, microhardness measurements were carried out on the crosssectional surface of the core. Figure 18 shows the results of the measurements in the 16 areas of the core that were related to a reference value of 636 HV and an average value of the measurements of 621 HV at the 16 points. The standard deviation of the population of the core hardness measurements was 57.8 HV. The reference value was determined by taking a hardness measurement of HV30.

Conclusions
By using conformal cooling channels, it is possible to optimise heat exchange and transfer in the pressure mould. Mould parts cooled using conformal channels are made As a supplement to the information on the differences between the reference mechanical properties of the SLM steels and those that were measured on the cross-sectional surface of the core, microhardness measurements were carried out on the cross-sectional surface of the core. Figure 18 shows the results of the measurements in the 16 areas of the core that were related to a reference value of 636 HV and an average value of the measurements of 621 HV at the 16 points. The standard deviation of the population of the core hardness measurements was 57.8 HV. The reference value was determined by taking a hardness measurement of HV30. As a supplement to the information on the differences between the reference mechanical properties of the SLM steels and those that were measured on the crosssectional surface of the core, microhardness measurements were carried out on the crosssectional surface of the core. Figure 18 shows the results of the measurements in the 16 areas of the core that were related to a reference value of 636 HV and an average value of the measurements of 621 HV at the 16 points. The standard deviation of the population of the core hardness measurements was 57.8 HV. The reference value was determined by taking a hardness measurement of HV30.

Conclusions
By using conformal cooling channels, it is possible to optimise heat exchange and transfer in the pressure mould. Mould parts cooled using conformal channels are made

Conclusions
By using conformal cooling channels, it is possible to optimise heat exchange and transfer in the pressure mould. Mould parts cooled using conformal channels are made using the SLM method. Different from the traditional method of design, a conformal cooling channel system is characterised by a much smaller cross-sectional diameter of the channels, a much smaller distance between adjacent channels, and their smaller distance from the surface of the mould cavity (as well as numerous changes in the direction of the channel axes). All of the above-mentioned features of conformal channels cause a change and local increase in the components of the stress tensor, which can be determined by using triaxiality factor η. A local increase in the value of this factor causes the loss of plasticity in a material. For this reason, the paper proposes a so-called criterion for the loss of plasticity in steel, which can be used to assess a safe level for local strain and the value of triaxiality factor η in the zone of a mould's cooling channels. Restricting the application of this criterion to the cooling channel zone only is related to the minimum value of the thermal deformation in this part of the mould or core. Based on the results of tensile tests on circumferentially notched specimens with different radii of rounding ρ and FEM calculations, a function f(η) was established that determines the allowable values of ε eq and η. The measurements of the yield strength, plastic strain, and hardness that were carried out directly on the cross-sectional surface of the core showed differences as compared to the mechanical properties that were determined on the samples. This fact suggests the continuation and undertaking of new research and analysis that are aimed at determining safety factors for parts that are made via the SLM method. The plasticity loss method presented assumes that the value of the triaxiality factor in the vicinity of the channel is influenced by the shape, cross-sectional dimensions, and trajectory of the channel axis. Using the methodology proposed in this paper, it is possible to determine the value of allowable deformations in the cooling channel zone and to determine whether the heat treatment applied to the SLM steel does not cause an excessive reduction in the plastic properties. The scope of the applicability of the proposed criterion may not only be limited to the case of the core with a conformal channel that was analysed in this paper; it may also be applied where the so-called notch effect occurs and no thermal deformation is present.