Design and experiment of high load-bearing acrylic connection node for the world's largest acrylic spherical vessel

Acrylic is a kind of polymer material and is gradually applied to load-bearing components. The working stress and ultimate bearing capacity of the acrylic structure are the main design indexes. Aiming at the world’s largest acrylic spherical vessel, the structural design, finite element analysis and full-size prototype tensile test of a new acrylic connection node were carried out in this paper. This acrylic node will bear 90 kN tension force for 20 years. According to the viscoelastic characteristics of the material and the working environment, the stress of acrylic should be controlled below 3.5 MPa for long term used. At the time, the ultimate bearing capacity should be greater than 6 times the working load. According to the stress-strain curve of acrylic, its tensile strength is about 75 MPa. There is no obvious plastic deformation after fracture, showing the material characteristics of brittle fracture. According to the failure analysis of previous acrylic node structures and the characteristics of acrylic, the new acrylic node structure is proposed in this paper. Its performance is improved by reducing the cutting amount of acrylic nodes, optimizing the structure of embedded part and avoiding sharp corners. A 1/4 symmetrical acrylic node model is established FEA software, and the nonlinear problems such as material nonlinearity and friction contact are solved by finite element method. The FEA results show that the maximum principal stress of the node is about 2.92 MPa. The relative error between the FEA results and the experimental results is 7.24%, indicating that the FEA results are credible. The ultimate tensile load of the node can reach 1000 kN, which is about 11 times the working load. The failure of the node occurs at a sharp corner of the groove, instead of the maximum stress point. Therefore, stress concentration caused by sharp corners should be avoided in the design of acrylic structure.


Introduction
Polymethyl methacrylate (PMMA), also known as acrylic, is a kind of polymer material and is increasingly used in basic scientific experiments because of its high transparency and low radioactivity [1][2][3][4][5]. One of the most important applications is that acrylic works as a load-bearing component. The ultimate bearing capacity and stress of acrylic component has become the key design indicators. According to the handbook of acrylics [6], the stress of the acrylic is required to be less than 5.5 MPa. For long-time use of acrylic components that cannot be repaired during work, the stress requirements should be stricter. For example, the main structure of the detector of Sudbury Neutrino Observatory (SNO) [7] is an acrylic vessel with a diameter of 12 m and a thickness of 5 cm, which requires the stress of the acrylic to be less than 4.0 MPa [8]. In this study, the acrylic vessel with a diameter of 35.4 m and a thickness of 12 cm in the Jiangmen Underground Neutrino Observation (JUNO) [9,10] is almost three times the diameter of the SNO acrylic vessel. This makes the supporting structures of these two acrylic vessels very different. Figure 1(a) shows the central detector of JUNO. The main structure is an acrylic spherical vessel supported by a stainless steel mesh shell. Figure 1(b) shows the acrylic spherical vessel. There are totally 590 acrylic connection nodes on the outer surface of the acrylic vessel. Figure 1(c) shows the details of the connection structure between the acrylic vessel and the stainless steel mesh shell. The support rod connects the acrylic connection node with the stainless steel mesh shell. The density difference of the liquid inside and outside the acrylic vessel makes the acrylic vessel withstand more than 3,000 t of buoyancy. The buoyancy needs to be transferred to the stainless steel mesh shell through the support rod. Therefore, the connection structure between acrylic and stainless steel has become the most critical structure of the acrylic vessel. According to the finite element analysis (FEA) results of Li [11], the maximum tensile force of the support rod will reach 90 kN.
Acrylic is a viscoelastic material. Under the room temperature, the Zhu-Wang-Tang (ZWT) constitutive model has effectively described the rate dependent nonlinear viscoelastic behavior of PMMA [12]. Under quasistatic tensile test, the material shows brittle fracture characteristics. The constitutive model of the material can be approximately expressed by nonlinear elastic model [13,14]. However, when the material is loaded for a long time, its strain will increase with time even at room temperature. Zhou [15] soaked acrylic in scintillator to get the creep curves of materials under different stresses. The creep behavior of materials is simulated by time-stress superposition principle (TSSP) [16,17], and the creep fracture time of materials under low stress is also deduced. In addition, polymer materials will age. Therefore, the performance of the material will decrease in the process of long-term use. Yin [18] studied the aging of acrylic at different temperatures, and deduced the aging time when the material properties decreased by 50% at 20°C by Arrhenius formula. For the acrylic node designed in this paper, considering the long-term use of material, the acrylic stress will be controlled below 3.5 MPa [19]. In terms of short-term performance, the ultimate bearing capacity of the mode should be 6 times greater than the maximum tensile force of the support rod.
At present, there are few designs of high-strength connection structure between acrylic and metal materials. Wang [20,21] designed a connection node with a stainless steel bearing seat embedded in an appended acrylic panel, shown in figure 2(a). The bearing structure can avoid bending moments of the connection node. The appended panel is bonded to an acrylic spherical panel. The stress of the acrylic parts is about 10 MPa under the force of 140 kN, and the ultimate bearing capacity of the node is about 300 kN. Hao [22] optimized the structure and manufacturing process of this node. Although the stress of the connection node has not decreased, the ultimate bearing capacity has increased to 513 kN. For the node A, embedding a large bearing seat into the appended acrylic panel requires removing a large amount of acrylic material from the appended panel, thus weakening the strength of the connection node. Another conceptual design of the connection node shown in figure 2(b) was designed by Lin [23]. It avoids the weakness of node A, but the higher appended acrylic panel will inevitably create a large bending moment at the neck and the bottom edge of the appended panel.
In order to further improve the ultimate bearing capacity of the connection node and control the stress to be below 3.5 MPa under the working load, a new type of connection node between acrylic and stainless steel is designed in this study. The stress distribution of the newly designed node is obtained by FEA. Through the tensile test of the connection node, the ultimate bearing capacity of the node is known. Finally, the FEA results are verified by experiments.
2. Structure design of connection node and experiment device 2.1. Structure of connection node Figure 3 shows the new structure of the acrylic connection node. The appended acrylic panel has a diameter of 900 mm and a thickness of 140 mm. The bottom of the appended panel has an annular groove. Before bonding the appended panel to the acrylic spherical panel, a stainless steel ring is assembled into the groove. A gasket made of rubber is placed between the stainless steel ring and the acrylic. At the top of the node, there is a bearing component, which is connected with the steel ring through 8 bolts. Through the bearing structure, a support rod is hinged with the acrylic node to avoid bending moment on the node. The size of the spherical panel is designed as 1800 mm × 1800 mm, which is used for FEA modeling and prototype testing.
There are three main differences between the new connection node and the Type A node described in Part 1. Firstly, the cavity of the appended panel adopts a groove structure, and the stainless steel ring is embedded in it. The size of the steel ring structure is small to reduce the weakening effect on the appended panel structure. Secondly, the transition between the appended panel and the spherical panel adopts a large arc surface to make the thickness transition smooth and avoid sudden stiffness change. Finally, the acrylic structure and the stainless steel structure are separated by rubber gaskets to avoid hard contact between the two parts. Figure 4 shows the tensile test equipment for the prototype of the connection node. The connection node is placed in a square frame with four piers fixed at the bottom. The node is connected with an oil pump fixed on a horizontal beam. The maximum load provided by the oil pump is 1000 kN. The space between the connection node and the square frame is filled with rubber and cement.   Figure 5 shows the testing curve of the acrylic. The red curve shown in figure 5(a) is the tensile test of the acrylic. When the material breaks, it will not be plastically deformed. The maximum tensile stress is about 75 MPa. The tensile test result shows that acrylic is a kind of brittle material. The dashed black line is the compression test curve of the acrylic. With the increase of stress, the material exhibits obvious plastic deformation. The maximum compressive stress of acrylic is about 113 MPa, which is higher than the tensile fracture stress. As shown in figure 5(b), there is a linear relationship between the stress and strain at low stress. The mechanical properties of acrylic and stainless steel are shown in table 1.

Finite element model
Both the upper and lower gaskets are made of rubber. Figure 6 shows the relationship between normal strain and normal stress of rubber. In the FEA model, the constitutive relation of rubber is described by the Yeoh model.
Because the structure and the load of the numerical model are symmetrical, a quarter model of the connection node is used in the Abaqus finite element software, as shown in figure 7. There are two symmetric planes in this model. The boundary conditions between gasket and acrylic, bearing head and bearing seat are set as friction boundary. The coefficient of friction between the gasket and acrylic is 0.5. The bottom surfaces of square frame in contact with the pier areas are set as fixed boundaries. A tensile force of 90 kN is applied to the top of the bearing head. All parts of the model are divided by linear hexahedral meshes. Since the connection   node is mainly subjected to the bending stress, an 8-layer mesh is used in the thickness direction of the spherical panel to avoid an hourglass phenomenon caused by the use of reduced integrated elements.

FEA result
This section shows the FEA results of the connection node under 90 kN working load. Figure 8 is the stress contour of the connection node. In the figure 8(a), the maximum Von Mises stress is 3.30 MPa, which occurs around the bolt hole. The Von Mises stress at the edge of the appended panel is 2.13 MPa. Figure 8(b) is the absolute maximum principal stress. The maximum principal stress is 2.92 MPa, which also appears around the bolt holes. The maximum principal stress at the edge of the appended panel is 2.57 MPa. In the annular groove where the lower gasket is in contact with the acrylic part, the maximum compressive stress is 3.66 MPa. The load is transmitted from the steel ring and the lower gasket to the acrylic structure. The maximum compressive stress at the bottom surface of the connection node is about 1.56 MPa. The top surface of the connection node is mainly tensile stress.   When testing the ultimate bearing capacity of the node, it is generally believed that failure will occur at two locations first. One of which is located at the edge of the appended panel. This edge is the position of the bonding line, and also the second largest stress position. The reason for the large stress here is that the node thickness is inconsistent. As shown in figure 9, the stresses of the node in the three directions of the cylindrical coordinate system at the edge of the appended panel are 2.44 MPa, 1.31 MPa, and 0.23 MPa, respectively. The stress in the R direction is the largest, so the node is prone to crack in the direction given in figure 9(a). When Wang [20] and Zhou [24] performed the node A experiments, some nodes broke at the edge of the appended panel with a stepped structure. Therefore, the transition between the appended panel and the spherical panel should be smooth.
Another dangerous place is the corner of the annular groove, because acrylic is a fragile material, and it is sensitive to sharp corners. The stress at the corners is not very great. However, with the decrease of the mesh size, the stress at the sharp corners increases, and the stress shows a tendency of non-convergence. In the figure 9(a), the stresses at the four corners in the R direction are 1.23 MPa, 0.18 MPa, 0.62 MPa, and 0.37 MPa, respectively. The maximum stress appears at the corner 1. The figure 10 shows the deformation of the groove on the symmetrical cross section. Under the action of pulling force, the angle of corner 1 and corner 3 becomes larger.
In prototype experiments, the fillet was machined at the corner 1 and 4, as shown in figure 3. Due to the limitation of manufacturing process, it is difficult to round the corner 2 and corner 3. Therefore, when a tensile force is applied to the connection node, the connection node has a high risk of cracking at the corner 3. Figure 11 shows the displacement of the node. The maximum value of the total displacement is 2.15 mm, which is the same as the displacement in the Z direction.

Experimental results
Several prototypes of connection nodes were tested. This study introduces the experimental process, displays the test results of a node, and analyzes the test results.

Instrumentation
The strain rosettes are used to monitor the stress of the node. Using cyanoacrylate glue (also called 502 glue) to bond the strain rosette to the acrylic surface will damage the acrylic surface, thus affecting the ultimate bearing capacity of the node. However, when the surface stress is compressive stress, this negative effect can be reduced. Therefore, all strain rosettes are adhered to the bottom surface of the node and distributed symmetrically, as shown in figure 12. The 45-degree strain rosette shown in figure 13 contains three strain gauges at a certain angle, which can calculate the principal stress on the surface of the connection node. The principal stress can be expressed as:  Figure 14 is the tensile test curves. The time-force curve shown in figure 14(a) includes three stages, namely, loading, holding and unloading. The loading speed is about 30 kN min −1 . When the force reaches the maximum force of 1000 kN which can be provided by the oil pump, the force will be maintained for about ten minutes. The unloading speed is about 50 kN min −1 . The total testing time is approximately 70 min.   Figure 14(b) shows a displacement-force curve. After unloading the force, the displacement-load curve is not a closed loop. This is mainly due to the plastic deformation of parts and the local fracture of acrylic.

Tensile test results
After the experiment, as shown in the figure 15, cracks were found at the corner 3 of the annular groove. The locations of cracks is the same as described in section 4 above. Corner 3 cannot be rounded and has tensile stress. The video shows that the connection node began to crack during the second stage. Therefore, the ultimate bearing capacity of this node is about 1000 kN. Table 2 is the stress comparison between experimental and FEA results. There are totally 20 strain rosettes on the bottom surface of the connection node, which are divided into 7 areas. The maximum coefficient of variation is 32.37%, which occurred at zone VII. Due to the small amount of test data and small data values, the test results in this area vary greatly. Except for this zone, the maximum coefficient of variation is 6.43%, which indicates that   the measured data is reliable. The maximum absolute relative difference between experimental results and FEA results is 7.24% at zone III, which indicates that the FEA results are consistent with the experimental results.

Conclusions
In this study, a high load-bearing acrylic connection node is designed to support the world's largest acrylic spherical vessel. The structure of this node is different from that of Wang [20]. By reducing the size of stainless steel embedded parts, smoothing the transition between the appended acrylic and the spherical acrylic panel, and separating the acrylic from stainless steel with rubber, the ultimate bearing capacity of the connection node is improved. And the stress of the node under 90 kN working load is controlled below 3.5 MPa. Through finite element analysis and tensile test, we can draw the following conclusions: (1) The tensile strength of acrylic is 75 MPa and the compression strength is 113 MPa. After tensile fracture, there is no obvious plastic deformation. The material shows brittle fracture characteristics. Therefore, in the design of acrylic structure, stress concentration caused by sharp corners should be avoided as much as possible.
(2) According to the FEA results, the maximum principal stress of the connection node under 90 kN force of is 2.92 MPa, which meets the requirement of less than 3.5 MPa.
(3) According to the experimental results, the ultimate bearing capacity of the connection node can reach about 1000 kN, which is more than 11 times the working load.
(4) The maximum relative stress difference between the finite element analysis result and the test result is 7.24%. This shows that the FEA results are in good agreement with the experimental results.
This work hopes to provide a design idea for the supporting structure of large acrylic load-bearing components, which can meet the long-term working conditions by controlling the stress of acrylic, and at the same time has a large bearing capacity.

Acknowledgments
Not applicable.

Data availability statement
All data that support the findings of this study are included within the article (and any supplementary files).