Experimental Evaluation of Hoop Stress–Strain State of 3D-Printed Pipe Ring Tensile Specimens

: Data on the strain and stress status of the pipe in the circumferential direction are required for various pipe manufacturing procedures (e.g., in the oil business, the process of manufacturing seamless pipes with a conical shaft). The aim of this study is to develop a procedure to determine the strain and stress behavior of Pipe Ring Tensile Specimens (PRTSs) in the hoop direction, as there are a lack of ofﬁcial standardized methods for testing PRTS. This paper discusses the application of the Digital Image Correlation method for testing plastic PRTSs. PRTSs are tested using a specially designed steel tool with two D blocks. A 3D-printed PRTS is placed over two D-shaped mandrels, which are ﬁxed on a tensile tool and tensile testing machine. The strain evolution in the gage length of the specimens is captured using the three-dimensional Digital Image Correlation (3D DIC) method. To check the geometry of the cross-section of the PRTS after fracture, all the specimens are 3D scanned. For the study, six groups of PRTS are analyzed, consisting of three ﬁlling percentages (60, 90, and 100%) and two geometry types (Single and Double PRTS). The results show that the type and percentage of ﬁlling, as well as the method of printing, affect the material behavior. However, the approach with the DIC system, 3D printer, and scanner shows that they are effective instruments for mapping complete strain ﬁelds in PRTS, and thus are effective in characterizing the mechanical properties of pipes.


Introduction
Different pipe production processes need data regarding the stress state of the pipe in the circumferential direction. The first example of such a process is the process of forming seamless pipes using a conical shaft in the oil industry. This is a process whereby a conical shaft is inserted into the formed glowing sample, which, by passing through the sample, radially expands the pipe to the desired diameter. The second is the production of polymer pipes, which causes a significant difference in the mechanical behavior between traditional tensile test specimens from basic materials and the final product of plastic pipes [1]. Due to the long distance and complex terrain of pipeline transportation, high toughness, fatigue resistance, corrosion resistance, and fracture resistance are necessary properties of pipeline materials [2].
Standard procedures for measuring material tensile properties are performed according to ASTM A370 [3], ASTM E8 [4], and ASTM D638-14 [5]. Most often, the specimens are cut from a plate or a pipe. In the case of pipes, there is an additional preparation process, i.e., flattening the specimen to be placed on the tensile testing machine. Studies [6,7] in which the effects of the flattening process have been analyzed prove that it significantly affects the material properties. Flattening causes pre-strains and residual stresses in the

Materials and Methods
In this study, a 3D printer (German RepRap GmbH, Feldkirchen, Germany) was used to produce the PRTS, as additive manufacturing is currently one of the promising methods for the fabrication of products of complex shapes [28]. The reason for using a 3D printer was the fast manufacturing of all PRTSs. The specimens were printed from polylactic acid (PLA) plastic material on a RepRap x400 3D printer (German RepRap GmbH, Feldkirchen, Germany) to develop a procedure for testing PRTS. PLA is an available biobased polymer [29] that is commonly used for Fused Deposition Modeling. It has good dimensional accuracy and is suitable for rapid specimen fabrication.
The dimensions of the PRTS were taken for the pipe DN32 (Ø42.4 mm × 2.8 mm), and the dimensions and appearance of the standard specimen were taken from the ASTM A370 standard [3]. Two types of test specimens were made for the procedure development: 1.
Single PRTS with standard specimen configuration on one side (Figure 1a-d); 2.
Double PRTS with standard specimen configuration on two sides with a mutual angle at 180 • (Figure 1e-h).
2. Double PRTS with standard specimen configuration on two sides with a mutual angle at 180o (Figure 1e-h).
In total, 30 PRTS were prepared, five per each of six PRTS groups in three different filling percentages (60, 90, and 100%) and with two geometry types (Single and Double PRTS). All the specimens were printed with a honeycomb structure. For the DIC method, all PRTS were painted with white paint as a base color for spraying a stochastic pattern of black dots prior to the experiment. The hoop tensile strength of a composite pipe specimen was measured experimentally using the test method with D blocks [30]. A PRTS testing tool with D blocks was created for the testing and development of the PRTS testing procedure. The PRTS testing tool was made of X20CrMoV12-1 steel, as shown in Figure 2 Figure 2. The D blocks simulated the internal pressure in the PRTS, which is the most common load on the pipeline. The PRTS testing tool used a fork to transfer the load from the tensile testing machine ( Figure 2, position 1) to the D blocks and PRTS.
PRTS were tensile tested in a Shimadzu Autograph AGS-X Series tensile testing machine (Shimadzu, Kyoto, Japan) with maximum test loads of 100 kN. The tensile testing machine was set for testing according to [3] with a test speed of 1 mm/min for all PRTS. During the experiment, stroke displacements and force values were monitored using the Trapezium software. Tensile test in order to determine the apparent hoop tensile strength [31].
Strain fields are measured during the specimen using stereo Digital Image Correlation (DIC) system [32]. The Aramis 2M system (GOM, Braunschweig, Germany) was used In total, 30 PRTS were prepared, five per each of six PRTS groups in three different filling percentages (60, 90, and 100%) and with two geometry types (Single and Double PRTS). All the specimens were printed with a honeycomb structure. For the DIC method, all PRTS were painted with white paint as a base color for spraying a stochastic pattern of black dots prior to the experiment.
The hoop tensile strength of a composite pipe specimen was measured experimentally using the test method with D blocks [30]. A PRTS testing tool with D blocks was created for the testing and development of the PRTS testing procedure. The PRTS testing tool was made of X20CrMoV12-1 steel, as shown in Figure 2  PRTS were tensile tested in a Shimadzu Autograph AGS-X Series tensile testing machine (Shimadzu, Kyoto, Japan) with maximum test loads of 100 kN. The tensile testing machine was set for testing according to [3] with a test speed of 1 mm/min for all PRTS. During the experiment, stroke displacements and force values were monitored using the Trapezium software. Tensile test in order to determine the apparent hoop tensile strength [31].
Strain fields are measured during the specimen using stereo Digital Image Correlation (DIC) system [32]. The Aramis 2M system (GOM, Braunschweig, Germany) was used to conduct strain field experiments. The Aramis 2M is based on the three-dimensional Digital Image Correlation (3D DIC) method. Calibration was conducted as part of the preexperimental preparations. Several studies [21][22][23][24][25][26][27] discuss the detailed mode of operation, calibration, preparation of the measuring object, and measuring technique. The Aramis setup parameters for this study were as follows: • Two CCD cameras with a resolution of 1600 × 1200 pixels; to conduct strain field experiments. The Aramis 2M is based on the three-dimensional Digital Image Correlation (3D DIC) method. Calibration was conducted as part of the preexperimental preparations. Several studies [21][22][23][24][25][26][27] discuss the detailed mode of operation, calibration, preparation of the measuring object, and measuring technique. The Aramis setup parameters for this study were as follows: • Two CCD cameras with a resolution of 1600 × 1200 pixels; • Two 50 mm camera lenses; • Measuring volume of 105 mm × 75 mm × 55 mm; • Measuring distance (distance between camera support and center of measuring volume) of 800 mm; • Facet (subset) size of 25 × 20 pixels; • Calibration point variability of 0.031 pixels (for correct calibration, the manufacturer states that calibration deviation may be between 0.01 and 0.04 pixels); • LED lamp for specimen lighting. The test procedure consisted of the following steps: • Specimen preparation. All PRTSs were painted with white paint as a base color and a stochastic pattern of black dots, as the measuring surface must have a high contrast pattern to clearly allocate the pixels in images.

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DIC system calibration, including adjusting and calibrating the cameras. To check the geometry of the cross-section of the PRTS after the tensile test, a 3D scanner Atos Core 200 (GOM, Braunschweig, Germany) was used. The Atos Core 200 setup parameters were as follows: The test procedure consisted of the following steps: • Specimen preparation. All PRTSs were painted with white paint as a base color and a stochastic pattern of black dots, as the measuring surface must have a high contrast pattern to clearly allocate the pixels in images.

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DIC system calibration, including adjusting and calibrating the cameras. • Tool and specimen positioning, including placing the testing tool on the tensile testing machine, assembling the D blocks inside the PRTS, and mounting the assembly on the testing tool.

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Tensile testing machine setup, including defining the test parameters on the tensile testing machine. • DIC measurement-after successful calibration, a DIC measurement was carried out. The tensile test procedure was conducted according to the definition outlined in Standard [3]. The testing installation scheme is illustrated in Figure 2. Digital images were recorded manually immediately every 1 s during the loading. The first recorded image (before the loading) was the nominal image for data processing. • DIC data processing-afterwards, computation was performed using the Aramis software.
• Three-dimensional scanner calibration, including adjusting and calibrating the cameras. • Three-dimensional scanner measurement. After successful calibration, a measurement was carried out. • Three-dimensional data processing. Afterwards, computation was performed using the Atos software (GOM, Braunschweig, Germany).

Results and Discussion
The fracture of all single PRTSs occurred on the side on which the camera was recording. In the case of Double PRTS, the fracture place occurred on both sides. The diagram in Figure 3 shows the average value of break force for all PRTSs with standard deviation. Both Single and Double PRTS showed negligible differences between 90 and 100% infills. However, there was a significant difference for both PRTS types with 60% infill compared to with 90 and 100% infill. The recommendation for future experimental studies is to use the 90% infill specimens, as their break force is similar to the 100% infill case and their time for printing, as well as material consumption, is reduced.
The tensile test procedure was conducted according to the definition outlined i Standard [3]. The testing installation scheme is illustrated in Figure 2. Digital image were recorded manually immediately every 1 s during the loading. The first recorde image (before the loading) was the nominal image for data processing.
• DIC data processing-afterwards, computation was performed using the Aram software. • Three-dimensional scanner calibration, including adjusting and calibrating the cam eras. • Three-dimensional scanner measurement. After successful calibration, a measure ment was carried out. • Three-dimensional data processing. Afterwards, computation was performed usin the Atos software (GOM, Braunschweig, Germany).

Results and Discussion
The fracture of all single PRTSs occurred on the side on which the camera was re cording. In the case of Double PRTS, the fracture place occurred on both sides. The dia gram in Figure 3 shows the average value of break force for all PRTSs with standard de viation. Both Single and Double PRTS showed negligible differences between 90 and 100% infills. However, there was a significant difference for both PRTS types with 60% infi compared to with 90 and 100% infill. The recommendation for future experimental studie is to use the 90% infill specimens, as their break force is similar to the 100% infill case an their time for printing, as well as material consumption, is reduced.  The PRTS cross-sectional dimensions after fracture were analyzed using the Atos Core 200 (GOM, Braunschweig, Germany). As illustrated in Figure 4, the dimensions were analyzed on both sides of the PRTS. Each side was measured in two orthogonal directions-one direction in specimen width (lines A1-A2 and A3-A4) and one direction in specimen thickness (lines B1-B2 and B3-B4). Lines A1-A2 and B1-B2 were positioned on the specimen side where the area of interest was analyzed. All measuring lines were placed at specimen edges. Figure 4 shows a Single PRTS, with 90% infill, showing the measurement points and analyzed distances.
The PRTS cross-sectional dimensions after fracture were analyzed using the A Core 200 (GOM, Braunschweig, Germany). As illustrated in Figure 4, the dimensions w analyzed on both sides of the PRTS. Each side was measured in two orthogonal di tions-one direction in specimen width (lines A1-A2 and A3-A4) and one direction specimen thickness (lines B1-B2 and B3-B4). Lines A1-A2 and B1-B2 were positioned the specimen side where the area of interest was analyzed. All measuring lines w placed at specimen edges. Figure 4 shows a Single PRTS, with 90% infill, showing measurement points and analyzed distances.  Table 1 shows the percentage changes in cross-sectional dimensions for all type PRTS. The results of the change in cross-sectional dimensions indicated a negligible ference between PRTS with 90% and 100% filling. The differences were more noticea for PRTS with 60% infill compared to 90 and 100% PRTS infill.

Single PRTS 60%
Double PRTS 60% For all PRTS types and filling percentages, the engineering stress was calculated ing the force data from the tensile testing machine for all stages and nominal cross-sect areas. The strain was obtained using the Aramis 2M system. The engineering stress-str diagrams are presented in Figure 5a,b. Figure 5a shows a stress-strain diagram for no nal specimen cross-section dimensions without the percentage infill impacts. To consi the effect of filling on the stress value, Figure 5b shows a stress-strain diagram with c rected cross-section areas and correction factors of 0.6, 0.9, and 1.0 for PRTSs with 6 90%, and 100% infill, respectively. All stress values are in MPa and strain is given in p  Table 1 shows the percentage changes in cross-sectional dimensions for all types of PRTS. The results of the change in cross-sectional dimensions indicated a negligible difference between PRTS with 90% and 100% filling. The differences were more noticeable for PRTS with 60% infill compared to 90 and 100% PRTS infill.

Single PRTS 60%
Double PRTS 60% For all PRTS types and filling percentages, the engineering stress was calculated using the force data from the tensile testing machine for all stages and nominal cross-section areas. The strain was obtained using the Aramis 2M system. The engineering stress-strain diagrams are presented in Figure 5a,b. Figure 5a shows a stress-strain diagram for nominal specimen cross-section dimensions without the percentage infill impacts. To consider the effect of filling on the stress value, Figure 5b shows a stress-strain diagram with corrected cross-section areas and correction factors of 0.6, 0.9, and 1.0 for PRTSs with 60%, 90%, and 100% infill, respectively. All stress values are in MPa and strain is given in percentages. It can be seen from the diagram in Figure 5a,b that the fracture occurred after reaching the maximum stress value, which indicated that it was a distinctly brittle fracture. The stress values for Single PRTS for all filling percentages were lower than the stress values of Double PRTS, as the loaded cross-sectional area for Double PRTS was smaller than that of Single PRTS. The stress-strain curve differences and similarities were more noticeable when presented with correction factors.
Metals 2022, 12, x FOR PEER REVIEW 7 of 12 reaching the maximum stress value, which indicated that it was a distinctly brittle fracture. The stress values for Single PRTS for all filling percentages were lower than the stress values of Double PRTS, as the loaded cross-sectional area for Double PRTS was smaller than that of Single PRTS. The stress-strain curve differences and similarities were more noticeable when presented with correction factors.
The results of the von Mises strain are presented in this study for the DIC measurement. The strain field (Figures 6a and 7a) was analyzed with two sections (Sections 0 and 1) and four points (stage points 0-3). Section 0 was placed horizontally (black line) and was located in the junction of the D blocks. Section 1 was orthogonal to Section 0, placed vertically on the area of interest (yellow line). Stage points were placed at the ends of all sections. Stage points 0 and 1 were placed on Section 0 and stage points 2 and 3 were placed on Section 1. Figures 6a and 7a show a visualization of the von Mises strain field just before the fracture for Single and Double PRTS with 90% infill as a function of section length, respectively. The experimental results presented in Figures 6b and 7b show that the highest strain values were registered at the area of interest in the D block junction. The highest von Mises values were 11.2% (Single PRTS 90% infill) and 9.4% (Double PRTS 90% infill), which are shown as the peak (yellow line) in Figures 6b and 7b. The diagrams in Figures 6c and 7c show the von Mises strain as a function of time for four stage points. The stage point diagram (Figure 6c) has a similar trend, which is constant from the beginning to the thirtieth stage, but the strain values exponentially increase from the thirtieth stage to the fracture with a maximum von Mises strain of 2,4% (Single PRTS 90% infill). The stage point diagram (Figure 7c) shows a similar trend for stage points 0-1 and 2-3, which are approximately linear from the beginning to the fracture, with a maximum von Mises strain of 2% (stage points 2-3), and constant from the beginning to the sixtieth stage, but the strain values exponentially increase from the sixtieth stage to the fracture with a maximum von Mises strain of 5.76% (stage points 0-1). The results of the von Mises strain are presented in this study for the DIC measurement. The strain field (Figures 6a and 7a) was analyzed with two sections (Sections 0 and 1) and four points (stage points 0-3). Section 0 was placed horizontally (black line) and was located in the junction of the D blocks. Section 1 was orthogonal to Section 0, placed vertically on the area of interest (yellow line). Stage points were placed at the ends of all sections. Stage points 0 and 1 were placed on Section 0 and stage points 2 and 3 were placed on Section 1. Figures 6a and 7a show a visualization of the von Mises strain field just before the fracture for Single and Double PRTS with 90% infill as a function of section length, respectively. The experimental results presented in Figures 6b and 7b show that the highest strain values were registered at the area of interest in the D block junction. The highest von Mises values were 11.2% (Single PRTS 90% infill) and 9.4% (Double PRTS 90% infill), which are shown as the peak (yellow line) in Figures 6b and 7b. The diagrams in Figures 6c and 7c show the von Mises strain as a function of time for four stage points. The stage point diagram (Figure 6c) has a similar trend, which is constant from the beginning to the thirtieth stage, but the strain values exponentially increase from the thirtieth stage to the fracture with a maximum von Mises strain of 2,4% (Single PRTS 90% infill). The stage point diagram (Figure 7c) shows a similar trend for stage points 0-1 and 2-3, which are approximately linear from the beginning to the fracture, with a maximum von Mises strain of 2% (stage points 2-3), and constant from the beginning to the sixtieth stage, but the strain values exponentially increase from the sixtieth stage to the fracture with a maximum von Mises strain of 5.76% (stage points 0-1).      The diagrams in Figure 8a,b show average strain-stage dependence with standard deviation values for PRTS with 90% and 100% infill. The values for Single and Double PRTS with 60% infill are not graphically represented due to high result variations, as shown in previous paragraphs. The diagram in Figure 8a shows an average strain-stage dependence with standard deviation values at stage points 0-3 for Single PRTS with 90% and 100% infill. The graph in Figure 8a shows a similar trend of von Mises strain and standard deviation values for Single PRTS with 90% and 100% infill, which have an approximately linear trend. The diagram in Figure 8b shows average strain-stage dependence with standard deviation values at stage points 0-3 for Double PRTS with 90% and 100% infill. The graph in Figure 8b shows similar a trend of von Mises strain and standard deviation values for Double PRTS with 90% and 100% infill, which have an approximately linear trend. The difference in standard deviation value for Single PRTS with 90% and 100% infill (Figure 8a,b) is observed before fracture (from the seventy-fifth stage to the end), where the Single and Double PRTS with 90% infill have slightly higher values (average 38.96%) than Single and Double PRTS with 100% infill.
shown in previous paragraphs. The diagram in Figure 8a shows an average strain-stage dependence with standard deviation values at stage points 0-3 for Single PRTS with 90% and 100% infill. The graph in Figure 8a shows a similar trend of von Mises strain and standard deviation values for Single PRTS with 90% and 100% infill, which have an approximately linear trend. The diagram in Figure 8b shows average strain-stage dependence with standard deviation values at stage points 0-3 for Double PRTS with 90% and 100% infill. The graph in Figure 8b shows similar a trend of von Mises strain and standard deviation values for Double PRTS with 90% and 100% infill, which have an approximately linear trend. The difference in standard deviation value for Single PRTS with 90% and 100% infill (Figure 8a,b) is observed before fracture (from the seventy-fifth stage to the end), where the Single and Double PRTS with 90% infill have slightly higher values (average 38.96%) than Single and Double PRTS with 100% infill.
Diagram 8a shows that the deformation value for Single PRTS with 90% infill is higher than that for Single PRTS with 100% infill on average by 0.34% for each stage, but that Single PRTS with 100% infill has a more linear strain-stage dependence than Single PRTS with 90% infill. Diagram 8b shows that the deformation value for Single PRTS with 90% infill is higher than that for Single PRTS with 100% infill on average by 0.17% for each stage, but that Single PRTS with 100% infill has a more linear strain-stage dependence than Single PRTS with 90% infill. The limitations of this study are the PRTS material used, the infill percentage of PRTS material, the location of the fracture, and equipment limitations. The behavior of PLA plastic does not reflect the characteristics of conventional pipe materials because of the pronounced occurrence of brittle fracture, but it is sufficient to develop the procedure that will later be applied to the steel PRTS. The results of stress-strain and cross-sectional dimensions indicate a negligible difference between PRTS with a 90% and 100% filling. The differences are more noticeable for PRTS with 60% infill compared to that with 90 and 100% PRTS infill. The application of DIC cameras in Double PRTS is questionable because the location of the fracture is not predetermined. The application of the DIC method is recommended for Single PRTS. The 3D DIC method has some limitations. Correct 3D cal- Diagram 8a shows that the deformation value for Single PRTS with 90% infill is higher than that for Single PRTS with 100% infill on average by 0.34% for each stage, but that Single PRTS with 100% infill has a more linear strain-stage dependence than Single PRTS with 90% infill. Diagram 8b shows that the deformation value for Single PRTS with 90% infill is higher than that for Single PRTS with 100% infill on average by 0.17% for each stage, but that Single PRTS with 100% infill has a more linear strain-stage dependence than Single PRTS with 90% infill.
The limitations of this study are the PRTS material used, the infill percentage of PRTS material, the location of the fracture, and equipment limitations. The behavior of PLA plastic does not reflect the characteristics of conventional pipe materials because of the pronounced occurrence of brittle fracture, but it is sufficient to develop the procedure that will later be applied to the steel PRTS. The results of stress-strain and cross-sectional dimensions indicate a negligible difference between PRTS with a 90% and 100% filling. The differences are more noticeable for PRTS with 60% infill compared to that with 90 and 100% PRTS infill. The application of DIC cameras in Double PRTS is questionable because the location of the fracture is not predetermined. The application of the DIC method is recommended for Single PRTS. The 3D DIC method has some limitations. Correct 3D calculation and strain computation for sample edges are not achievable since the 3D computation of the measuring points is based on pixels that need to be observed from the right and left cameras with the individual facet pattern. As a result, the high strain values (red color) seen on the strain field edges reflect system problems that are ignored.

Conclusions
The lack of standard methods for testing PRTS necessitates further development. From the presented experimental results, the following conclusions can be drawn:

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The DIC approach and the Aramis 3D optical system are effective instruments for mapping complete strain fields in PRTS, and thus are effective in characterizing pipe mechanical properties.

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The proposed methodology is shown to be applicable to Single PRTS.

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The results of the change in cross-sectional dimensions indicate a negligible difference between PRTS with a 90% and 100% filling. The differences are more noticeable for PRTS with 60% infill compared to that with 90 and 100% PRTS infill.

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Single PRTS 90% and 100% infill showed similar results, from which it can be concluded that for further research in the field of plastic PRTS, the recommendation is to work with Single PRTS 90% because the consumption of printing material is smaller and the printing time is shorter.