Biaxial Testing Machine: Development and Evaluation

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Article Biaxial Testing Machine: Development and Evaluation

António B. Pereira 1,* ,Fábio A.O. Fernandes 1,* , Alfredo B. de Morais 2 and João Maio 1

1 TEMA-Centre for Mechanical Technology and Automation, Department of Mechanical Engineering, University of Aveiro, Campus de Santiago, 3810-193 Aveiro, Portugal; [email protected] 2 RISCO Research Unit, Department of Mechanical Engineering, University of Aveiro, Campus Santiago, 3810-193 Aveiro, Portugal; [email protected] * Correspondence: [email protected] (A.B.P.); [email protected] (F.A.O.F.)

Received: 28 June 2020; Accepted: 16 July 2020; Published: 21 July 2020

Abstract: Biaxial mechanical testing gained increased importance for characterization of materials that present anisotropic behavior and/or diﬀerent responses when subjected to tensile and compression loadings. In this work, a new biaxial testing machine was developed. The various systems and components were designed, manufactured, assembled, and assessed. Uniaxial tensile tests were performed to validate the device, showing results consistent with those obtained on a universal testing machine. Finally, biaxial tensile tests were also performed on polypropylene cruciform specimens. The results revealed high precision levels, thus showing the potential of this new machine.

Keywords: testing machine; biaxial tests; video-extensometer; cruciform specimen; polypropylene

1. Introduction In a highly competitive industry, it is essential to always be one step ahead of competition. Therefore, there is an enormous need to develop profitable products. The deep knowledge about a material is necessary to optimize its use, leading to the tightening of safety margins and to waste minimization [1]. Materials, depending on their application, can be subjected to different loadings, such as tensile, compression, and shear. These may arise individually or combined. The most common way to characterize a material is through uniaxial tests [2]. When the material is isotropic, only a few uniaxial tests are necessary to fully characterize it within the scope of material behavior models, such as the von Mises yield criterion for metals. When the mechanical behavior of the material is quite complex, uniaxial tests are not enough to properly characterize it. For instance, polymers behave differently under tensile and compression loadings [3]. Thus, multiaxial tests make it possible to obtain a wider knowledge of the mechanical behavior of a material [1]. However, these present the disadvantage of being more complex to perform and analyze. Thus, biaxial tests present a balance between the significance and complexity of the results. Recently, the mechanical behavior of materials under biaxial stress has acquired great importance, both practical and theoretical [4]. This is valid for both static and dynamic loading cases, the latter being particularly interesting for high frequency multiaxial fatigue testing [5] and also for strain rate dependent materials. There are different types of biaxial tests, which can be divided into two categories: tests with a single loading system and tests using two or more independent loading systems [6]. In the first category, the biaxial stress ratio depends on the specimen geometry and/or the loading fixture configuration, whereas in the second category, it depends on the magnitudes of the applied loads [7]. Examples of the first category are bending tests on cantilever beams, anticlastic bending tests of flat plates, bulge tests, and tests using special fixtures [7]. Bulge tests are performed at very high pressures, resulting in

Machines 2020, 8, 40; doi:10.3390/machines8030040 www.mdpi.com/journal/machines Machines 2020, 8, 40 2 of 15 necking and fracture, being used to determine the formability limits. However, the high pressure leads to uncontrollable neck and crack propagation, because of the force-controlled nature of the experiment [1]. Regarding independent loading systems, examples are a round bar under torsion combined with bending, thin-wall tubes subjected to a combination of tension/compression and torsion or internal/external pressure, and cruciform specimens under in-plane biaxial loading [7]. The thin-wall tube is the most popular one, allowing any constant load ratio [7–11]. However, it also has some disadvantages, such as the existence of non-negligible radial stress gradients depending on the tube thickness and the applied load, the fact that thin-wall tubes are more complex to manufacture for some materials, the elastic instability when subjected to circumferential, axial compression, or torsion loads, and the anisotropic properties of tubes and plate materials being often different, among others [7,12,13]. Biaxial tests are desirable for inducing plane stress. To carry out a valid plane biaxial test for a cruciform specimen, it is necessary to guarantee a uniform stress/strain state at the specimen center, which has to be fixed in space during testing, and failure has to occur in the test zone and not in the uniaxially loaded arms [14,15]. To fulfill such requirements, the influence of some parameters needs to be properly handled, such as the thickness of the biaxially loaded test zone in relation to the thickness of the uniaxially loaded arms, the radius of the corner fillet at the intersection of the arms, and the presence and dimension of slits across the arms [1,7,14,16]. Additionally, to guarantee the null displacement of the central point, it is necessary to have four movable arms, with both endpoints in the same axis moving at the same speed in opposite directions. In 1967, Shiratori and Ikegami [17] developed an automated biaxial testing machine with two hydraulic actuators and loading capacity of 50 kN. Makinde et al. [18] developed a machine with two servo-hydraulic actuators per axis, capable of delivering the same load in both axes. Two electro-hydraulic closed-loop channels that independently controlled the two axes made it possible to fix the central point of the specimen. The load in each direction was measured using four load cells. Later, Boehler et al. [19] developed a screw-driven biaxial testing machine based on the one designed in Makinde et al. [18]. The machine was equipped with TMD-governors that enable constant speeds to be maintained on DC-motors, together with a closed-loop control system using optical incremental encoders. It also has four AC-motors that work independently from each other and allow fast positioning. Overall, it consists of four double-acting screw-driven pistons, two in each direction, rigidly supported on an octagonal vertical frame. In each direction, the maximum load is about 100 kN in tension and compression. It has an unobstructed working area of 900 900 mm2 that enables tests × on specimens with a size up to 500 500 mm2. Therefore, the vertical installation of the octagonal × frame which surrounds the specimen ensures excellent accessibility from both sides to the working area, which facilitates the mounting and observations throughout a test. The described mechanical concept and servo-control system allow cruciform specimens to be subjected to large strain biaxial tensile and compressive tests without kinematic incompatibilities. However, the dead weight of the gripping system causes a prestress in the cross-sectional area of the specimen. Kuwabara et al. [20] presented a machine similar to the one developed by Makinde et al. [18]. It uses opposing hydraulic cylinders connected to common hydraulic lines and is thus subjected to the same hydraulic pressure. The hydraulic pressure of each pair of cylinders is servo-controlled independently, and a load cell is included in each loading direction. The displacement of opposing hydraulic cylinders are equalized using a pantograph-type link mechanism, maintaining the center of the cruciform specimen always at the center of the testing apparatus. This linking mechanism was effective in reducing the production cost. In this work, the development of a new biaxial testing machine is presented, intended for polymer testing at quasi-static rates. The main characteristics desired were robustness, reduced size (compact), ease of use, precision, and, at the same time, low cost. The steps of development and its several mechanical, electrical, and control systems are described here. Machines 2020, 8, 40 3 of 15 Machines 2020, 8, x 3 of 16

2.2. Materials Materials and and Methods Methods ThisThis section section describes describes the the mechanical, mechanical, electr electrical,ical, and and control control systems systems developed developed for for the the new new biaxialbiaxial testing testing machine. machine. They They allowed allowed the the capacity capacity of of 10 10 kN kN to to be be delivered delivered reliably reliably and and robustly. robustly. Overall,Overall, this equipmentequipment consists consists of of the the machine machine structure, structure, electrical electrical panel, panel, data acquisition,data acquisition, and control and controlsystems systems (Figure 1(Figure). 1).

Machines 2020, 8, x 3 of 16

2. Materials and Methods This section describes the mechanical, electrical, and control systems developed for the new biaxial testing machine. They allowed the capacity of 10 kN to be delivered reliably and robustly. Overall, this equipment consists of the machine structure, electrical panel, data acquisition, and control systems (Figure 1).

(a) (b)

FigureFigure 1. 1. BiaxialBiaxial testing testing machine: machine: (a) (1) (a )machine (1) machine structure; structure; (2) electrical (2) electrical panel; (3) panel; acquisition (3) acquisition system; andsystem; (4) computer and (4) computer for control; for control;(b) Uniaxial (b) Uniaxialtensile testing tensile (horizontal testing (horizontal axis) showing axis) showing the video- the extensometervideo-extensometer system. system. (a) (b)

Figure 1. Biaxial testing machine: (a) (1) machine structure; (2) electrical panel; (3) acquisition system; 2.1.2.1. Mechanical Mechanicaland Design Design (4) computer for control; (b) Uniaxial tensile testing (horizontal axis) showing the video- extensometer system. 2.1.1. Main Structure 2.1.1. Main2.1. Structure Mechanical Design Figure2 presents the main structure of the biaxial testing machine. It has a support base, inspired Figure2.1.1. 2 presents Main Structure the main structure of the biaxial testing machine. It has a support base, inspired in the biaxial machine from Boehler et al. [19]. This arrangement makes it possible to easily position the in the biaxial machineFigure 2 presents from the Boehler main structure et al. of the[19]. biaxia Thisl testing arrangement machine. It has makes a support it base, possible inspired to easily position specimen and the video-extensometer apparatus. The supporting base also makes it easier to transport. the specimenin the and biaxial the machine video-extensometer from Boehler et al. [19]. apparatus. This arrangement The makes supporting it possible to baseeasily positionalso makes it easier to The structurethe specimen was built and the by video-extensometer welding, which apparatus. resulted The insupporting minor base deformations. also makes it easier These to were considered transport. The structure was built by welding, which resulted in minor deformations. These were during thetransport. project, The and structure thus, was corrected built by welding, by adjusting which resulted the ﬁnal in minor alignment. deformations. These were consideredconsidered during duringthe project, the project, and and thus, thus, co correctedrrected by adjusting by adjusting the final alignment. the final alignment.

FigureFigure 2. Main 2. Mainstructure. structure. 2.1.2. Alignment 2.1.2. Alignment

The alignment between lateral plates is fundamental, not just for the assembly, but also to guarantee proper working conditions, including the alignment of the axes. The lateral supports were welded, Figure 2. Main structure.

2.1.2. Alignment

Machines 2020, 8, x 4 of 16

MachinesThe 2020alignment, 8, 40 between lateral plates is fundamental, not just for the assembly, but also4 to of 15 guarantee proper working conditions, including the alignment of the axes. The lateral supports were welded, having the screwed plates with guides between each other (Figure 3). Therefore, it was necessaryhaving theto find screwed a way plates to align with and guides block between it in space, each which other (Figureinfluenced3). Therefore, the geometry it was of necessarythe lateral to plates.ﬁnd a way to align and block it in space, which inﬂuenced the geometry of the lateral plates.

] FigureFigure 3. 3.EquipmentEquipment overview overview for for compressive compressive testing: testing: (1–4) (1–4) lateral lateral plates; plates; (5,6) (5,6) axis; axis; (7)(7) sample sample for for compressivecompressive test; test; (8) (8) lateral lateral support. support.

ConsideringConsidering that that the the gripping gripping system system would would be be in inthe the center center of ofthe the crosshead, crosshead, the the guides guides would would blockblock the the specimen specimen center. center. Instead, Instead, the the methodolog methodologyy adopted adopted to toavoid avoid this this was was to toarrange arrange the the side side platesplates and and the the crossheads diagonallydiagonally (Figure (Figure4). 4). While While providing providing a greater a greater ﬁeld offield view of for view the specimen,for the specimen,it also reduces it also thereduces deviation the deviation caused by caused perpendicular by perpendicular forces from forces crossheads from crossheads on the other on the axis. other Machines 2020, 8, x 5 of 16 axis.

(a) (b)

Figure 4. IntermediateFigure 4. Intermediate solution solution for the for alignmentthe alignment ofof the the plates: plates: (a) Frontal (a) Frontal view—detail view—detail of the visibility of the visibility and accessibility to the specimen area; (b) Lateral view—lateral plate. and accessibility to the specimen area; (b) Lateral view—lateral plate. Once the specimen was sufficiently visible, it was necessary to align the lateral plates between Once thethem. specimen However, was the plates suﬃ representedciently visible, in Figure it 3 wascannot necessary be properly toaligne alignd since the they lateral only have plates between them. However,two points the platesof contact represented with the structure. in Figure When modifying3 cannot the be geometry properly of the aligned plates, four since contact they only have points could be obtained that allowed the adjustment in any direction. The adjustment is quite simple, using a screw to force the plate to approach the structure and two others that force it in the opposite direction, blocking it in any desired position (Figure 5a). The positions of the guides make it possible to have a field of view of the specimen of 300 × 300 mm2. The plate has a wider zone to provide space for the bearing, as well as a series of threaded holes for subsequent motor placement (Figure 5b).

(a) (b)

Figure 5. Final lateral plate: (a) Position adjusting system (no scale); (b) Isometric view.

2.1.3. Guidance System A 30 mm diameter chrome-plated bar CK45 was used for the guides, having the necessary stiffness to avoid significant bending and, at the same time, low roughness. Bearings are commonly used to guarantee low friction in linear guidance systems. Two NBS KB3068 linear bearings per crosshead were employed to ensure accurately guided movements. The radial loads resulting from the crosshead weights and the manufacturer’s datasheet point to a long lifespan. However, the

Machines 2020, 8, x 5 of 16

(a) (b)

Figure 4. Intermediate solution for the alignment of the plates: (a) Frontal view—detail of the visibility and accessibility to the specimen area; (b) Lateral view—lateral plate.

Machines 2020, 8, 40 5 of 15 Once the specimen was sufficiently visible, it was necessary to align the lateral plates between them. However, the plates represented in Figure 3 cannot be properly aligned since they only have twotwo points points of ofcontact contact with with the the structure. structure. When When modifying modifying the the geometry geometry of ofthe the plates, plates, four four contact contact pointspoints could could be be obtained obtained that that allowed allowed the the adjustment adjustment in inany any direction. direction. The The adjustment adjustment is quite is quite simple, simple, usingusing a screw a screw to toforce force the the plate plate to toapproach approach the the stru structurecture and and two two others others that that force force it itin inthe the opposite opposite direction,direction, blocking blocking it itin inany any desired desired position position (Figur (Figuree 5a).5a). The The positions positions of of th thee guides guides make make it itpossible possible toto have have a field a ﬁeld of of view view of of the the specimen specimen of of 300 300 × 300300 mm mm2. The2. The plate plate has has a wider a wider zone zone to toprovide provide space space × forfor the the bearing, bearing, as as well well as as a series a series of of threaded threaded holes holes for for subsequent subsequent motor motor placement placement (Figure (Figure 5b).5b).

(a) (b)

FigureFigure 5. 5.FinalFinal lateral lateral plate: plate: (a) (Positiona) Position adjusting adjusting system system (no (no scale); scale); (b) ( bIsometric) Isometric view. view.

2.1.3.2.1.3. Guidance Guidance System System A A30 30 mm mm diameter diameter chrome-platedchrome-plated barbar CK45 CK45 was was used used for thefor guides,the guides, having having the necessary the necessary stiffness stiffnessto avoid to significantavoid significant bending bending and, at and, the sameat the time, same low time, roughness. low roughness. Bearings Bearings are commonly are commonly used to usedguarantee to guarantee low friction low friction in linear in guidancelinear guidance systems. systems. Two NBS Two KB3068 NBS KB3068 linear bearings linear bearings per crosshead per crossheadwere employed were employed to ensure to accurately ensure accurately guided movements. guided movements. The radial loadsThe radial resulting loads from resulting the crosshead from theweights crosshead and theweights manufacturer’s and the manufacturer’s datasheet point todatasheet a long lifespan. point to However, a long lifespan. the rupture However, of a cruciform the specimen can cause imbalances that may generate much higher radial loads in the bearings. Thus, the apparent oversizing provides strengthened confidence regarding the movement of the crossheads, avoiding the occurrence of gaps and other issues caused by repeated use of the machine.

2.1.4. Transmission System A precise system must be developed to carry out quasi-static testing (e.g., 1 mm/min) with loads up to 10 kN. A ball screw linear actuator with nut system was employed to transform the rotation imposed by the motors in linear motion. The choice of using a ball screw instead of a lead screw is justified by the superior transmission efficiency (90% versus 30%). Since this is an efficient system, the weight of the crossheads is enough to cause rotation, which was a decisive factor in the selection of the electrical motors (Section 2.2). The wearing is also much lower with the ball screw. The NBS VFU3205 ball screw was employed, with an outer diameter of 32 mm and a lead of 5 mm. It has an expected service life of 106 rotations for a uniform axial load of 14.5 kN. On the other end of the spindle, a bearing responsible for axially fixing it without restricting its rotation was employed. It also supports axial loads during the testing. It is an angular contact double row ball bearing, reference 3205B.2RSR.TVH from FAG. It supports dynamic axial loads up to 15 kN and static ones up to 19 kN (neglecting radial loads). A KM 5 lock nut was used to fix it. Rigid coupling was used for the connection with the motor, through a keyway–key connection as depicted in Figure6. Machines 2020, 8, x 6 of 16 rupture of a cruciform specimen can cause imbalances that may generate much higher radial loads in the bearings. Thus, the apparent oversizing provides strengthened confidence regarding the movement of the crossheads, avoiding the occurrence of gaps and other issues caused by repeated use of the machine.

2.1.4. Transmission System A precise system must be developed to carry out quasi-static testing (e.g., 1 mm/min) with loads up to 10 kN. A ball screw linear actuator with nut system was employed to transform the rotation imposed by the motors in linear motion. The choice of using a ball screw instead of a lead screw is justified by the superior transmission efficiency (90% versus 30%). Since this is an efficient system, the weight of the crossheads is enough to cause rotation, which was a decisive factor in the selection of the electrical motors (Section 2.2). The wearing is also much lower with the ball screw. The NBS VFU3205 ball screw was employed, with an outer diameter of 32 mm and a lead of 5 mm. It has an expected service life of 106 rotations for a uniform axial load of 14.5 kN. On the other end of the spindle, a bearing responsible for axially fixing it without restricting its rotation was employed. It also supports axial loads during the testing. It is an angular contact double row ball bearing, reference 3205B.2RSR.TVH from FAG. It supports dynamic axial loads up to 15 kN and static ones Machinesup to 192020 kN, 8 ,(neglecting 40 radial loads). A KM 5 lock nut was used to fix it. Rigid coupling was6 of 15 used for the connection with the motor, through a keyway–key connection as depicted in Figure 6.

FigureFigure 6. Drawing 6. Drawing of the of transmission the transmission system: system: (1) motor; (1) motor; (2) rigid (2) coupling; rigid coupling; (3) cover (3)cover plate;plate; (4) lateral (4) lateral plate;plate; (5) spindle; (5) spindle; (6) bearing; (6) bearing; (7) nut; (7) (8) nut; keys. (8) keys.

2.1.5.2.1.5. Crossheads Crossheads The crossheadsThe crossheads are movable are movable parts of parts the structur of the structures,es, being supported being supported by the guidance by the guidance system and system fixedand to the fixed nuts to of the the nuts ball of screws. the ball These screws. move These along move the alongtwo axes the twoof the axes machine. of the machine.Its geometry Its geometrywas stronglywas stronglyinfluenced influenced by the transmission, by the transmission, gripping, gripping, and guidance and guidance systems. systems. Once Oncethe spindle the spindle is is immobile,immobile, it is itin is the in theway way of the of the gripping gripping system system when when the the crosshead crosshead is is forced forced back. To solvesolve this this issue, issue,the the crossheads crossheads have have two two bars: bars: anan anterioranterior oneone where the nut is is fixed, fixed, and and a a posterior posterior one one with with the the grippinggripping and and acquisition acquisition systems. systems. The distanceThe distance between between these these two bars two barsis extremel is extremelyy important important since sinceit is the it is course the course available, available, influencedinfluenced by the by the accessories accessories of of each each crosshead—e.g.,crosshead—e.g., havinghaving or or not not a load a load cell—resulting cell—resulting in crossheads in crossheadswith di ffwitherent different distances distances between between plates. This plat ises. configuration This is configuration has the advantage has the ofadvantage allowing greaterof allowingdistances greater between distances bearings. between These bearings. plates neededThese plates to be perfectlyneeded to aligned, be perfectly and the aligned, whole setand had the to be wholerobust. set had A hollowto be robust. bar was A used,hollow placing bar was the used, bearings placing inside the it, bearings and its exterior inside it, aligned and its and exterior kept fixed alignedrelative and kept to the fixed plates. relative Additionally, to the plates. two reinforcementAdditionally, platestwo reinforcement were added toplates minimize were theadded maximum to minimizeMachinesdeflection 2020the ,maximum 8 of, x the set. defl Figureection7 depicts of the theset. crossheadFigure 7 depicts and its the constituents. crosshead and its constituents. 7 of 16

FigureFigure 7. Crosshead 7. Crosshead drawing: drawing: (1) anterior (1) anterior plate; (2) plate; nut; (2)(3) nut;reinforcement (3) reinforcement plate; (4) plate;hollow (4) bar; hollow (5) ball bar; bearing;(5) ball (6) bearing; posterior (6) plate. posterior plate.

Figure 8 shows the adjustment stops included in the design. Once these collide with the crosshead, the ball screw nut system becomes inoperable. In the opposite direction, when it collides with the posterior plate, the motor does not have enough torque, leaving the rotor blocked.

(a) (b)

Figure 8. Adjustment stops for crossheads: (a) with load cell; (b) without load cell.

2.1.6. Gripping System Two pairs of 5 kN wedge grips from Shimadzu were employed. To make the positioning of cruciform specimens easier, an unusual configuration was adopted. By rotating the grips, the openings are on opposite sides, but the specimen can be placed by rotation of the straps (Figure 9).

Machines 2020, 8, x 7 of 16

Figure 7. Crosshead drawing: (1) anterior plate; (2) nut; (3) reinforcement plate; (4) hollow bar; (5) ball Machinesbearing;2020, (6)8, 40 posterior plate. 7 of 15

Figure 8 shows the adjustment stops included in the design. Once these collide with the Figure8 shows the adjustment stops included in the design. Once these collide with the crosshead, crosshead, the ball screw nut system becomes inoperable. In the opposite direction, when it collides the ball screw nut system becomes inoperable. In the opposite direction, when it collides with the with the posterior plate, the motor does not have enough torque, leaving the rotor blocked. posterior plate, the motor does not have enough torque, leaving the rotor blocked.

(a) (b)

FigureFigure 8. 8. AdjustmentAdjustment stops stops for for crossheads: crossheads: (a ()a )with with load load cell; cell; (b (b) )without without load load cell. cell.

2.1.6.2.1.6. Gripping Gripping System System TwoTwo pairs pairs of of 5 5 kN kN wedge wedge grips grips from from Shimadzu Shimadzu were were employed. employed. To To make make the the positioning positioning of of cruciformcruciform specimens easier,easier, an an unusual unusual conﬁguration configuration was was adopted. adopted. By rotating By rotating the grips, the the grips, openings the openingsareMachines on opposite are2020 on, 8, xopposite sides, but sides, the specimen but the specimen can be placed can be by placed rotation by ofrotation the straps of the (Figure straps9). (Figure 9).8 of 16

(a) (b) (c)

FigureFigure 9. 9.Illustration Illustration of of the the placement placemen oft of a cruciforma cruciform specimen: specimen: (a ()a typical) typical conﬁguration; configuration; (b ()b adopted) adopted conﬁguration;configuration; (c )(c cruciform) cruciform specimen specimen ready ready for for testing testing (no (no scale). scale).

2.1.7.2.1.7. Load Load Cell Cell Horizontal Horizontal Support Support TheThe load load cells cells used used (Section (Section 2.2 2.2)) are are exclusively exclusively for for compression compression and and tensile tensile loads. loads. Due Due to to the the verticalvertical arrangement arrangement of of the the machine, machine, the the horizontal horizontal axis axis load load cell cell is is subjected subjected to to a a momentum momentum caused caused byby the the weight weight of of the the grip. grip. Thus, Thus, the the cell cell could could be be loaded loaded in in a a direction direction to to which which it it was was not not designed designed forfor and and this this could could negatively negatively inﬂuence influence the the results. results. Therefore, Therefore, an an additional additional structure structure was was created created (Figure(Figure 10 10),), which which gives gives side side support support to to the the load load cell cell but but still still allowing allowing movement movement in in the the horizontal horizontal direction.direction. In In this this support, support, a a PAP PAP 3025-P10 3025-P10 plain plain bearing bearing was was used used since since the the loads loads are are low low and and the the movementsmovements are are reduced, reduced, resulting resulting in in minimal minimal wear. wear.

Figure 10. Illustration of the grip support.

2.1.8. Compression Test System To make it possible to carry out tensile–compression and compression–compression biaxial tests, a particular system was designed. First, it is necessary to remove the grips, coupling parts, and the support of the load cell in the specific axis. In the crosshead, where the load cell is placed, a new support structure was designed, again due to the weight of some parts, but also to avoid compressive deformations during testing. Figure 11 illustrates the compression test arrangement, where the force is transmitted to the load cell thanks to a rod.

Machines 2020, 8, x 8 of 16

(a) (b) (c)

Figure 9. Illustration of the placement of a cruciform specimen: (a) typical configuration; (b) adopted configuration; (c) cruciform specimen ready for testing (no scale).

2.1.7. Load Cell Horizontal Support The load cells used (Section 2.2) are exclusively for compression and tensile loads. Due to the vertical arrangement of the machine, the horizontal axis load cell is subjected to a momentum caused by the weight of the grip. Thus, the cell could be loaded in a direction to which it was not designed for and this could negatively influence the results. Therefore, an additional structure was created (Figure 10), which gives side support to the load cell but still allowing movement in the horizontal direction.Machines 2020 In ,this8, 40 support, a PAP 3025-P10 plain bearing was used since the loads are low and 8the of 15 movements are reduced, resulting in minimal wear.

FigureFigure 10. 10. IllustrationIllustration of of the the grip grip support. support.

2.1.8.2.1.8. Compression Compression Test Test System System ToTo make make it itpossible possible to to carry carry out out tensile–compre tensile–compressionssion and and compression–compression compression–compression biaxial biaxial tests, tests, a aparticular particular system system was was designed. designed. First, First, it itis isnecessary necessary to to remove remove the the grips, grips, coupling coupling parts, parts, and and the the supportsupport of of the the load load cell cell in in the the specific speciﬁc axis. axis. In In the the crosshead, crosshead, where where the the load load cell cell is isplaced, placed, a anew new supportsupport structure structure was was designed, designed, again again due due to to the the weig weightht of of some some parts, parts, but but also also to to avoid avoid compressive compressive deformationsdeformations during during testing. testing. Figure Figure 11 11 illustrate illustratess the the compression compression test test arrangement, where thethe forceforce is Machinesistransmitted transmitted 2020, 8, x to to the the load load cell cell thanks thanks to to a a rod. rod. 9 of 16

FigureFigure 11. 11.CompressionCompression configuration: conﬁguration: (1) posterior (1) posterior plate; plate; (2) load (2) load cell; cell; (3) outer (3) outer tube; tube; (4) rod; (4) rod; (5) plain (5) plain bearing;bearing; (6) (6)cover cover plate. plate.

In theIn the other other crosshead, crosshead, only only a rod a rod is necessary is necessary to make to make it sturdy, it sturdy, avoiding avoiding bending bending or oranother another formform of deformation. of deformation. Both Both rods rods are arethreaded threaded on onthe the ends ends to couple to couple testing testing components, components, which which varies varies accordingaccording to the to the specimen specimen and and its itsdimensions. dimensions. Both Both configurations conﬁgurations are are presented presented in Figure in Figure 12. 12 .

(a) (b)

Figure 12. Compression system: (a) with a load cell; (b) without load cell (no scale).

2.2. Electrical Design, Control, and Data Acquisition The electrical project of the machine here developed consists of a series of connected components essential for properly carrying out the experiments, such as moving the crossheads and data acquisition from the load cells. Figure 13 presents the schematics of the main electrical connections.

Figure 13. Schematics of the main electrical connections.

Machines 2020,, 8,, xx 9 of 16

Figure 11. Compression configuration: (1) posterior plate; (2) load cell; (3) outer tube; (4) rod; (5) plain bearing; (6) cover plate.

In the other crosshead, only a rod is necessary to make it sturdy, avoiding bending or another Machinesform of2020 deformation., 8, 40 Both rods are threaded on the ends to couple testing components, which varies9 of 15 according to the specimen and its dimensions. Both configurations are presented in Figure 12.

(a) (b)

FigureFigure 12.12. Compression system: ( a) with a load cell; (b) without load cellcell (no(no scale).scale).

2.2.2.2. Electrical Design, Cont Control,rol, and Data Acquisition TheThe electrical project ofof the machine here developed consists of a series of connected components essentialessential forfor properly properly carrying carrying out out the experiments,the experime suchnts, assuch moving as moving the crossheads the crossheads and data acquisition and data fromacquisition the load from cells. the Figure load cells. 13 presents Figure 13 the presents schematics the ofschematics the main of electrical the main connections. electrical connections.

FigureFigure 13.13. Schematics of the main electrical connections.

Almost all the electrical components are in a portable electrical panel (with proper shielding and labeling), connected to the motors through a 24-pin connector. Stepper motors were used due to the necessity of precise control of the testing speed and higher torque at low speeds. The 34HS38-4004D-SG20 stepper motor was used. It is a high torque motor, including a spur type planetary gearbox with a gear ratio of 20:1, which satisfies the necessity of precise control, especially at low speeds with higher torque. High-performance MA860H microstepping drivers were used to power and control the stepper motor. This driver amplifies the signal from the microcontroller, which controls the motor speed. With four of these drivers, it is possible to control each motor individually. In the end, the testing speed is defined by the capacity of the microcontroller, the motor gearbox gear ratio, and the spindle lead, which resulted in 400 impulses/rot. On the other hand, the current for the motors was based on the maximum force expected for testing. The machine was designed for 10 kN, but to guarantee a safety margin, a higher load was expected for the crossheads. The value was obtained considering the motor torque of 4.5 N.m at 4 A, the gearbox efficiency of 70%, and the equation given by the ball screw manufacturer

Mm = Pmax L/(6820 η), (1) × × Machines 2020, 8, 40 10 of 15

where Mm is the motor torque, Pmax is the maximum axial load, L is the spindle lead, and η is the efficiency of the transmission. The power supply of the various circuits is done through three power sources, two SP-500-48 power supplies for the drivers and the one S-201-12 power supply for the microcontroller and the remaining control circuit. Also, an auxiliary power circuit was employed to reduce the ATmega328 microcontroller power need. Screw shielding was used to improve the connections to the Arduino Uno Rev3. Two S-type tensile/compression 10 kN load cells were used, one in each axis. The power supply of the load cells and the data acquisition are performed thanks to the National Instruments simultaneous bridge module NI-9237, together with the NI cDAQ-9178 CompactDAQ USB chassis. For signal processing, the module uses a combination of analog and digital filters, obtaining a correct representation of the in-band signals, while rejecting the out-of-band signals. The three main filters used are: passband, stopband, and alias-free bandwidth. The first filter only lets a range of frequencies pass, attenuating the remaining frequencies. The remaining two avoid and eliminate the phenomenon described by aliasing: when a signal is sampled at a frequency lower than twice the highest frequency of the signal, sampling can confuse a signal of a higher frequency into a lower frequency signal, leading to distortions between the real and sampling [21]. With all the motors and drivers working, the maximum noise influence is around 2 N. ± The control project focused mainly on the Arduino for both manual automatic controls. LabVIEW was used for both data acquisition and automatic control, incorporating all in the same program. A sampling rate of 2.5 kHz was defined for data acquisition. The load cells are calibrated considering the weight of the parts that might influence the measurements. In the end, it is possible to control each one of the four motors independently, to define the type of load (tensile/compression) and the speed of the test, all in automatic or manual mode.

2.3. Experimental Testing The load cells were calibrated using a universal testing machine, the Shimadzu 50 kN-AG. The calibration was performed already using the hardware and software of the biaxial testing machine. It was performed both types of loading. A regression analysis was performed obtaining R2 values of almost 1. The linear regression equations for the x-axis (horizontal) and y-axis (vertical) were, respectively, F = 4.86875 U + 0.10492 and F = 4.88140 U 0.12813, where F is the load (kN) and U is the − normalized voltage (mV/V). The automatic zero load calibration, useful to eliminate the influence of the weight of the grip, showed that the constants in the regression lines should be ignored and only the slope should be considered for calibration. One of the limitations found was the impossibility of placing a calibration table for each cell in the software. Since the slopes of the regression lines are almost independent of the load cells, an average between the two slopes giving F = 4.875075 U was used to create the final calibration table. This approximation leads to an error of 0.13% between the actual value of each cell and the read value. Considering that the load cell will not be subjected to more than 5 kN, the error for such a load corresponds approximately to a 6.5 N difference between the real and the read values, and considering the 0.25 N error of the calibration in the universal testing machine, this an acceptable approach. In this work, the sample deformations were obtained with a video extensometer, the Messphysik ME-46NG. The dot tracking and displacement measurement was carried out with the DotMeas software, with micrometrical precision and acquisition frequencies of 3 Hz. Experimental tests were performed to validate the present machine systems here developed by comparison with results of uni-axial tests conducted in a Shimadzu 50 kN-AG universal testing machine. It was decided to use polypropylene (PP), chosen for its low cost, good machinability, and low rigidity, which makes it easier to measure the deformations in a relatively small central area, where the specimen is supposed to fail. Machines 2020, 8, x 11 of 16

One of the limitations found was the impossibility of placing a calibration table for each cell in the software. Since the slopes of the regression lines are almost independent of the load cells, an average between the two slopes giving F = 4.875075 U was used to create the final calibration table. This approximation leads to an error of 0.13% between the actual value of each cell and the read value. Considering that the load cell will not be subjected to more than 5 kN, the error for such a load corresponds approximately to a 6.5 N difference between the real and the read values, and considering the 0.25 N error of the calibration in the universal testing machine, this an acceptable approach. In this work, the sample deformations were obtained with a video extensometer, the Messphysik ME-46NG. The dot tracking and displacement measurement was carried out with the DotMeas software, with micrometrical precision and acquisition frequencies of 3 Hz. Experimental tests were performed to validate the present machine systems here developed by Machines 2020, 8, 40 11 of 15 comparison with results of uni-axial tests conducted in a Shimadzu 50 kN-AG universal testing machine. It was decided to use polypropylene (PP), chosen for its low cost, good machinability, and low rigidity, which makes it easier to measure the deformations in a relatively small central area, Thewhere specimens the specimen were is obtainedsupposed to from fail. a 5 mm PP sheet thick plate, using a bandsaw and the CNC Machining CenterThe specimens Mikron were VCE500 obtained (HAAS from a VF-0).5 mm PP The sheet specimens thick plate, forusing uniaxial a bandsaw tensile and the testing CNC (Figure 14a) followedMachining the guidelines Center Mikron of the VCE500 ISO 527-2 (HAAS standard VF-0). The [ 22specimens]. The for cruciform uniaxial tensile specimens testing (Figure (Figure 14a) 14 b) resulted from a ﬁnitefollowed element the guidelines based of study the ISO described 527-2 standard in [23 [22].]. TheseThe cruciform specimens specimens have (Figure reduced 14b) resulted thickness near the from a finite element based study described in [23]. These specimens have reduced thickness near the central areacentral in area order in order to promote to promote failure failure inin this region. region.

(a) (b)

FigureFigure 14. 14.Specimens Specimens for tensile tensile loading: loading: (a) uniaxial; (a) uniaxial; (b) biaxial. (b ) biaxial. To start the experimental campaign, first, it is necessary to ensure the correct position of the To startgrips, theguaranteeing experimental the specimen’s campaign, centering. ﬁrst, In it addition, is necessary it is necessary to ensure to mark the correctthe test pieces position with of the grips, guaranteeingthe dots the to be specimen’s tracked by the centering. video-extensometer. In addition, To center it isnecessary the grips, a block to mark withthe a drawn test cross pieces was with the dots to be trackedused. By by placing the video-extensometer. the block supported on To the center lower thegrip,grips, it is possible a block to withmove athe drawn crossheads cross was used. individually, until all the grips align their center with the lines, thus ensuring that all grips are at the By placingMachines the 2020 block, 8, x supported on the lower grip, it is possible to move the crossheads12 individually, of 16 until all the grips align their center with the lines, thus ensuring that all grips are at the same distance and properlysame distance aligned and (Figure properly 15 aligned). After (Figure alignment, 15). After the alignment, crossheads the crossheads must always must move always together move until together until the beginning of the test, maintaining the alignment and thus the symmetrical testing the beginning of the test, maintaining the alignment and thus the symmetrical testing conditions. conditions.

Figure 15. Gripping system alignment. Figure 15. Gripping system alignment. 2.3.1. Uniaxial Tests For video-extensometer analysis, 40 μm points were marked in the samples, one in the center and two equally distanced from it by 10 mm. The real distance was measured in an optical microscope—Mitutoyo TM, at a resolution of 0.001 mm—to calibrate it in the DotMeas software. Pre- loads were carefully avoided, and thus no deformation was caused to the samples during their placement in the grips. The uniaxial tensile tests were carried at a speed of 10 mm/min and the criterion used to stop testing was necking observation. Four tests were carried out, two per each axis.

2.3.2. Biaxial Tests Similar to the specimens for uniaxial tensile testing, points were also marked to measure deformations. Two additional points for the second loading direction when performing biaxial tensile tests. The same procedure and conditions were employed for marking, measuring, calibration, and pre-load elimination. Lines were also marked on the test piece arms for alignment, ensuring that the specimen was centered. The biaxial tensile tests were carried out at a speed of 10 mm/min, equal on both axes, and the criterion used to stop testing was necking observation.

3. Results

3.1. Uniaxial Tests The measured load-displacement data were used to compute the stress-strain behavior from the uniaxial tests as

σ = P/A0, (2)

ε = (L – L0)/L0, (3) In the first stage, the uniaxial tests allowed to confirm the equivalence between the x-axis and y- axis systems (Figure 16). The differences between the various curves that can be explained by the natural dispersion of material properties. Figure 17 compares the results with those obtained from

Machines 2020, 8, 40 12 of 15

2.3.1. Uniaxial Tests For video-extensometer analysis, 40 µm points were marked in the samples, one in the center and two equally distanced from it by 10 mm. The real distance was measured in an optical microscope—Mitutoyo TM, at a resolution of 0.001 mm—to calibrate it in the DotMeas software. Pre-loads were carefully avoided, and thus no deformation was caused to the samples during their placement in the grips. The uniaxial tensile tests were carried at a speed of 10 mm/min and the criterion used to stop testing was necking observation. Four tests were carried out, two per each axis.

3. Results

3.1. Uniaxial Tests The measured load-displacement data were used to compute the stress-strain behavior from the uniaxial tests as σ = P/A0, (2) ε = (L L )/L , (3) − 0 0 In the first stage, the uniaxial tests allowed to confirm the equivalence between the x-axis and yMachines-axis systems 2020, 8, x (Figure 16). The differences between the various curves that can be explained by13 of the 16 natural dispersion of material properties. Figure 17 compares the results with those obtained from teststests inin aa universaluniversal testingtesting machine.machine. There is good agreement between the results of both machines, thusthus validatingvalidating thethe loadingloading andand measurementmeasurement systemssystems ofof thethe biaxialbiaxial machine.machine.

FigureFigure 16.16. Stress–strain curves obtained from uniaxial tensile tests performedperformed in thethe biaxialbiaxial testingtesting machinemachine onon MEBMEB (horizontal(horizontal axis—blueaxis—blue curves;curves; verticalvertical axis—redaxis—red curves).curves).

Figure 17. Stress–strain curves obtained from uniaxial tensile tests performed in the biaxial testing machine on MEB ((horizontal axis—blue curves; vertical axis—red curves) compared with the ones performed in a universal testing machine (in black).

Figure 18 shows a specimen after testing, which presents a uniform distribution in the gauge zone (lighter area), but also a necking region formed at the end of the test.

Figure 18. Uniaxial tensile test sample after testing.

Machines 2020, 8, x 13 of 16 tests in a universal testing machine. There is good agreement between the results of both machines, thus validating the loading and measurement systems of the biaxial machine.

Machines 2020, 8, x 13 of 16

tests in a universal testing machine. There is good agreement between the results of both machines, thus validating the loading and measurement systems of the biaxial machine.

Figure 16. Stress–strain curves obtained from uniaxial tensile tests performed in the biaxial testing machine on MEB (horizontal axis—blue curves; vertical axis—red curves).

Machines 2020, 8, 40Figure 16. Stress–strain curves obtained from uniaxial tensile tests performed in the biaxial testing 13 of 15 machine on MEB (horizontal axis—blue curves; vertical axis—red curves).

Figure 17.Figure Stress–strain 17. Stress–strain curves curves obtained obtained from from uniaxial uniaxial tensile tensile tests tests performed performed in the biaxial in the testing biaxial testing machine on MEB ((horizontal axis—blue curves; vertical axis—red curves) compared with the ones machine on MEB ((horizontal axis—blue curves; verticalvertical axis—red curves) compared with the ones performed in a universal testing machine (in black). performed in a universal testing machine (in(in black).black). Figure 18 shows a specimen after testing, which presents a uniform distribution in the gauge Figurezone 1818 shows(lightershows area), a a specimen specimen but also a after neckingafter testing, testing, region which formed whic presents ath thepresents end aof uniform the a uniformtest. distribution distribution in the in gauge the gauge zone (lighterzone (lighter area), area), but also but a also necking a necking region region formed formed at the at end the of end the of test. the test.

Figure 18. Uniaxial tensile test sample after testing.

Machines 2020, 8, x 14 of 16 3.2. Biaxial Tests 3.2. Biaxial Tests The results of the biaxial tensile tests showed good repeatability (Figure 19), and there was a great similarity betweenThe results the load–displacement of the biaxial tensile tests curves showed of thegood two repeatability axes. (Figure 19), and there was a great similarity between the load–displacement curves of the two axes.

Figure 19. FigureLoad–displacement 19. Load–displacement response response measured measured inin the biaxial biaxial tensile tensile tests tests(solid (solidcurves—horizontal curves—horizontal axis; dashed curves—vertical axis). axis; dashed curves—vertical axis). However, after the tests it was seen that failure did not start in the measurement zone, in the However,center, after but actually the tests in itthe was areas seen around that it, failure where didthere not were start stress in concentrations the measurement (Figure zone, 20). This in the center, but actuallyshows in thethat areasthe chosen around specimen it,where geometry there is not were well-suited stress for concentrations determining the stress–strain (Figure 20 curves). This shows that the chosenup to failure. specimen Nevertheless, geometry as expected is not from well-suited the biaxial forload determining combination, imposed the stress–strain failure took place curves up to at a 45° orientation relative to the loading axes.

(a) (b)

Figure 20. Cruciform sample after the biaxial tensile testing: (a) before failure; (b) at failure (no scale).

4. Conclusions The present work presents the development of a new biaxial testing machine, describing in detail its design, assembly, control system, and data acquisition. The solution here presented is quite interesting for testing polymers, being robust, precise, and low cost. Moreover, the preparation and execution of the tests are quite simple. The load cell data acquisition system and the video extensometer were successfully combined, providing the necessary data to characterize the materials. Good repeatability and consistency between the horizontal and vertical axes were observed, as

Machines 2020, 8, x 14 of 16

3.2. Biaxial Tests The results of the biaxial tensile tests showed good repeatability (Figure 19), and there was a great similarity between the load–displacement curves of the two axes.

Figure 19. Load–displacement response measured in the biaxial tensile tests (solid curves—horizontal Machines 2020, 8, 40axis; dashed curves—vertical axis). 14 of 15

However, after the tests it was seen that failure did not start in the measurement zone, in the center, but actually in the areas around it, where there were stress concentrations (Figure 20). This failure. Nevertheless,shows that the as chosen expected specimen from geometry the biaxial is not we loadll-suited combination, for determining imposedthe stress–strain failure curves took place at a up to failure. Nevertheless, as expected from the biaxial load combination, imposed failure took place 45◦ orientation relative to the loading axes. at a 45° orientation relative to the loading axes.

(a) (b)

Figure 20. Cruciform sample after the biaxial tensile testing: (a) before failure; (b) at failure (no scale). Figure 20. Cruciform sample after the biaxial tensile testing: (a) before failure; (b) at failure (no scale). 4. Conclusions 4. Conclusions The present work presents the development of a new biaxial testing machine, describing in detail The presentits design, work assembly, presents control the system, development and data acqu ofisition. a new Thebiaxial solution testinghere presented machine, is quite describing in interesting for testing polymers, being robust, precise, and low cost. Moreover, the preparation and detail its design, assembly, control system, and data acquisition. The solution here presented is execution of the tests are quite simple. The load cell data acquisition system and the video quite interestingextensometer for testing were successfully polymers, combined, being providing robust, precise,the necessary and data low to characterize cost. Moreover, the materials. the preparation and executionGood of repeatability the tests and are consistency quite simple. between The the horizontal load cell and data vertical acquisition axes were observed, system as and the video extensometer were successfully combined, providing the necessary data to characterize the materials. Good repeatability and consistency between the horizontal and vertical axes were observed, as shown by comparison with uniaxial tensile tests performed on a universal testing machine. The results of biaxial tensile tests reinforced conﬁdence in the developed machine. Although the main goals were achieved, future improvements can be made to this biaxial testing machine. For instance, at the mechanical level, the development of a ﬁxed support system for easy placement of the video-extensometer apparatus. At the software level, the automatic combination of data from the load cells and the video-extensometer, as well as the use of digital image correlation. The use of electrical limit switches would also increase safety by preventing damage to the components and by simply being a simpler solution than the installed mechanical limit switches.

Author Contributions: Conceptualization, A.B.P., F.A.O.F., A.B.d.M., and J.M.; Data curation, A.B.P.; Formal analysis, A.B.P., F.A.O.F., and A.B.d.M.; Funding acquisition, A.B.P.; Investigation, A.B.P., F.A.O.F., A.B.d.M., and J.M.; Methodology, A.B.P., F.A.O.F., A.B.d.M., and J.M.; Project administration, A.B.P. and A.B.d.M.; Resources, A.B.P.; Software, J.M.; Supervision, A.B.P. and A.B.d.M.; Validation, A.B.P., F.A.O.F., A.B.d.M., and J.M.; Visualization, A.B.P. and J.M.; Writing—original draft, A.B.P., F.A.O.F., A.B.d.M., and J.M.; Writing—review and editing, A.B.P., F.A.O.F., and A.B.d.M. All authors have read and agreed to the published version of the manuscript. Funding: This work was supported by the projects UIDB/00481/2020 and UIDP/00481/2020-FCT- Fundação para a Ciencia e a Tecnologia; and CENTRO-01-0145-FEDER-022083—Centro Portugal Regional Operational Programme (Centro2020), under the PORTUGAL 2020 Partnership Agreement, through the European Regional Development Fund. Acknowledgments: The researchers, under grant (CEECIND/01192/2017), would like to acknowledge the Fundação para a Ciência e a Tecnologia (FCT). Conﬂicts of Interest: The authors declare no conﬂict of interest.

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