Simulation Study of Shear Stress Distribution in Bolted Connection Structures of Sandwich Composite Plate

Abstract

For the shear problem of the bolt connection structure of Sandwich Composite Plate, shear test is carried out on two kinds of Bolt Connection Structure of Sandwich Composite Plate, namely, Pre-embedded countersunk bolt and Assembled countersunk bolt, and the shear strength and stress distribution of the two kinds of bolt connection structure are investigated by using ABAQUS, and the finite element simulation results coincided with the test phenomenon well. Using this model, the stress distribution under shear damage of the Bolt Connection Structure of Sandwich Composite Plate is analysed, and the influence of bolt preload is also analysed, and the results showed that: the stress of the Sandwich Composite Plate is mainly concentrated in the Skin on the bottom side, and gradually decreased to the top surface; the influence of bolt preload could be disregarded in the analysis of the shear strength and stress peak of the Sandwich Composite Plate.

1 Introduction

Sandwich Composite Plate is composed of high-strength Composite Plate Skins and lightweight Core Materials, which are widely used in the manufacture of ships and marine structures by virtue of their light weight, high stiffness, high strength, and superior acoustic stealth properties [1]. In the ship structure, the steel structure as the main structure, Sandwich Composite Plate is often used as a component fixed to the main structure by bolts [2], Sandwich Composite Plate, due to the characteristics of its constituent structure, the strength of the various components of the larger differences, the damage mode is more complex and serious compared to the Metal Materials and Composite Materials. At the same time for the demand of bolt connection structure, the Sandwich Composite Plate for the open hole or cross-section mutation processing, inevitably cause the phenomenon of stress concentration, so the mechanical properties of the Sandwich Composite Plate and steel skeleton bolt joints research is very important.

In recent years, a large number of scholars have carried out meticulous experimental and numerical studies on the bolted connection structure of composite laminates, Chishti, Chen, and Liu [3,4,5] studied the countersunk bolt connection structure of composite laminates, using experimental, numerical simulation, and theoretical analysis to study different bolt countersunk sizes, analysis the force state of the countersunk bolts, and reveal the damage mechanism of composite plywood connection structure, Sen and Ascione [6, 7] conducted experimental studies on the effects of bolt hole size and the distance from the hole to the edge of composite plywood on the bolted structure of sandwich composite plywood, Xu [8] carried out experimental studies on the bolted structure of composite plywood of L-type and Π-type, An [9] carried out fatigue tests on a number of 3-nailed carbon fibre reinforced Plastic and titanium alloy countersunk bolt connection structures with bushings, and established a fatigue numerical analysis model to compare with the connection model without bushings, which showed that the bolt connection structure with bushings had higher fatigue life.

And less research on Sandwich Composite Plate [10, 11], this paper for the actual situation of Sandwich Composite Deck Structure, Pre-embedded countersunk bolts and Assembled countersunk bolts two kinds of connection structure for finite element simulation, using commercial finite element software ABAQUS and the different bolt preload under the shear strength and stress distribution of the analysis and comparison, to provide a research foundation for exploring the design and application in bolted connection structures of Sandwich Composite Plate.

2 Structural Shear Test in Bolted Connection Structures of Sandwich Composite Plate

2.1 Test Specimen

Reference to the typical parts of the hull deck and rigid skeleton connection, the structural shear specimen of sandwich composite and steel skeleton connection assembled with pre-buried countersunk head bolts and assembled countersunk bolts is designed, which consists of two parts: the Sandwich Composite Plate and the steel skeleton plate, and is connected by a special bushing and high strength bolt. Pre-embedded countersunk head bolts are buried to the inner side of the skin, and Assembled countersunk head bolts run through the Sandwich Composite Plate, and the bolts are tightened with a torque of 20 N m during installation. The specific dimensions of the connection structure are as follows: the Sandwich Composite Plate is a 300 mm × 150 mm × 66 mm rectangle; the sandwich Plate Skin layup material is glass fibre, with a thickness of about 3 mm; the Core Material is 60 mm of polyethylene foam; the special bushing is T-shaped, with an outer diameter transitioning from 45 to 30 mm and an inner diameter transitioning from 25 to 22 mm. The center of the bolt hole is located 45 mm from the short edge of the Sandwich Composite Plate, and bolt diameter is 20 mm.

2.2 Test Equipment and Process

The hull deck boundary is generally supported by strong components (e.g. steel skeleton, hull wall, etc.), when the hull deck is loaded, the bolts at the connecting structure are in the shear condition, and through the design of reasonable tooling, the loading conditions in the laboratory are as much as possible in line with the actual working conditions. Changchun Qianbang test equipment QBS-350A electro-hydraulic servo fatigue testing machine is used to carry out the shear strength test, the test steps are as follows: (1) numbering of the specimen before the test; (2) determining the position of the tooling, bolting the tooling to the test platform; (3) fixing the specimen on the tooling, loosening all the fixing bolts, and using the test machine to preload the specimen, so that the test machine loading collet is vertically corresponds to the loading position, packing the test specimen, and then the test specimen is preloaded. (4) fix all the constraints, debug the test system, and complete all the preparatory work; (5) The shear strength test adopts displacement control, and the test piece is loaded at a displacement rate of 0.1 mm/s until the end of damage.

2.3 Experimental Phenomena

Through the shear test of the Sandwich Composite Plate and steel skeleton connection structure, it is found that the bolts located in the lower Skin appeared to be bent and deformed, as well as the lower side of the skin bolt holes appeared to be extruded damage, while the upper side of the Skin and the Core Material did not appear to be damaged, as shown in Fig. 1.

Fig. 1

Shear test phenomena in the bolt connection structures of Sandwich Composite Plate

3 Finite Element Model

3.1 Geometric and Material Model

The finite element software ABAQUS is used to carry out finite element simulation analysis on the bolt connection structure of Sandwich Composite Plate. According to the actual size of the test specimen, the bolt, bushing, composite Skin, Core Material and rigid connecting plate are modeled according to the actual size of the test specimen, with the intersection point of the bolt centerline and the lower surface of the sandwich composite material plate as the origin, the bolt centerline as the y-axis, and the axis of symmetry of the short side of the sandwich composite material as the x-axis. Detailed dimensions of the finite element simulation model are given in Sect. 2.1, and the structural characteristics of the connection are shown in Fig. 2.

Fig. 2

Geometric model in the bolt connection structures of Sandwich Composite Plate

The Skin of Sandwich Composite Plate is made of glass fibre reinforced material, and the Core Material is made of polyethylene foam. The lamination sequence of Skin is [0/90/0/90] s. Based on the structural characteristics of Sandwich Composite Plate, the lamination direction is not established when modelling the composite material Skin. The Skin is modeled as an anisotropic laminate. The relevant material parameters of composite material Skin are shown in Table 1, and the relevant material parameters of polyethylene Core Material are shown in Table 2, See Table 3 for material parameters of connecting bolts.

Table 1 Material parameters of composite material skin

Table 2 Material parameters of polyethylene core material

Table 3 Material parameters of connecting bolts

3.2 Interaction and Loading

The model is set up with two kinds of interactions of “Tie” constraints and contact pairs. According to the principle of “main surface principle”, the main surfaces are selected according to the order of bolts, connecting Plate, bushing, Skins and Core Materials. In order to study the effect of bolt connection structure on the shear strength of the Sandwich Composite Plate, contact pairs are set on the contact surfaces of the bolt and the bushing, the bushing and the Core Material, the bushing and the Skin, the bolt and the Skin, and the Skin and the connecting plate; and “Tie” constraints are set on the contact surfaces of the Skin and the Core Material, and the bolt and the connecting surface. The contact constraints are tangential behaviour with a friction coefficient of 0.1 and normal behaviour for hard contact. The gap between the bolt and the bushing is realised by means of the Interference Fit function in the contact settings.

The fixed constraint is applied to the right end of the sandwich composite material, and a displacement of 5 mm is applied to the left side of the connection plate. The bolt tightening torque is applied by the Bolt load command in ABAQUS [12], and its preload magnitude is calculated by the formula equation as (1).

$$F = \frac{T}{1.2\mu d}$$

(1)

When $T = 20\,{\text{N}}\,{\text{m}},d = 26.08\,{\text{mm}}\,\,{\text{and}}\,\,\mu = 0.2,$ then $F = 3.195\,{\text{kN}}$.

The Static, Risk analysis step is used to perform the shear strength analysis, and the Static, general analysis step is added to add the bolt preload to the model prior to the shear strength analysis.

3.3 Mesh Division Convergence Analysis

Eight-node hexahedral linear reduced integral solid elements (C3D8R) are used to divide the model, and according to the research focus, the model is divided into three parts, the first part is the bolt and the bushing; the second part is the focus area of the Sandwich Composite Plate, which is a square area with a side length of 90 mm centered on the bolt axis; and the third part is the non-focus area of the Sandwich Composite Plate, which is all the other areas except the focus area. In order to reduce the computation time, smaller element sizes are set in the first and second parts, while larger element sizes are set in the third part. Comparison of the number of elements and calculated shear strength of the models with different element sizes is shown in Table 4, from which it can be seen that the shear strength of the connecting structure is greatly affected by the element sizes of the bolts in the first part, and the stress distribution of the Sandwich Composite Plate is greatly affected by the element sizes of the first part and the second part, so in order to save the computation time and to ensure the accuracy of the calculation, model 3 (the first part of the element sizes of 2 mm, the second part of the element sizes of 3 mm, the third part of the element sizes of 5 mm) is selected as the model of the bolted connection structure of the Sandwich Composite Plate.

Table 4 Comparison table of different models^a

4 Finite Element Analysis in Bolted Connection Structures of Sandwich Composite Plate

4.1 Shear Stress Distribution Analysis

Shear analysis is conducted on the bolted connection structures of two types of Sandwich Composite Plate. The Mises stress cloud maps of each component at the maximum shear force are taken as shown in Figs. 3, 4 and 5. The deformation of the bolts in Fig. 3 is basically consistent with the deformation of the bolts in the experimental phenomenon in Fig. 1. The Mises stress above 1000 MPa appeared in the Skin on bottom side of Fig. 5, which is consistent with the phenomenon of compression failure in the Skin on bottom side of the experimental phenomenon. It can be verified that the numerical simulation technology used is true and effective.

Fig. 3

Stress distribution and deformation of bolts in the bolt connection structures of Sandwich Composite Plate

Fig. 4

Stress distribution of core material in the bolt connection structures of Sandwich Composite Plate

Figure 6 shows the stress variation curve along the length of Sandwich Composite Plate, where the horizontal coordinate is the x-axis coordinate of the finite element model, and the vertical coordinate is the Mises stress. It can be seen from Fig. 6 that the stress distribution trend of Sandwich Composite Plate of the pre-embedded countersunk bolt connection structure and the assembled countersunk bolt connection structure is basically the same, which manifests itself in that the stress on the bottom surface is much larger than that on the top surface, and the Skin on bottom side and the lower surface of Core Material reach peak value on the side of the bolt hole wall close to the loading end. And the Skin on top side and upper surface of Core material reach the peak at the side of the bolt hole wall near the fixed end. From Fig. 6b, it can be found that the peak stress of Core Material of assembled countersunk head bolt connection structure is larger than that of pre-embedded countersunk head bolt connection structure.

Figure 7 shows the stress variation curve along the width of Sandwich Composite Plate, where the horizontal coordinate is the z-axis coordinate of the finite element model, and the vertical coordinate is the Mises stress. It can be found from Fig. 7 that the stress distribution trend of Sandwich Composite Plate of the pre-embedded countersunk head bolted connection structure and the assembled countersunk head bolted connection structure is basically the same, which manifests itself in the fact that the stress on bottom surface is much greater than that on top surface, and the stress reaches the peak in the wall of the bolted holes, and the pre-embedded countersunk head bolted connection structure exhibits a greater peak of the stress on the Skin on the bottom side and the lower surface of the Core Material, whereas the assembled countersunk head bolted connection structure exhibits a greater peak of the stress on the Skin on the upper side and the upper surface of the Core Material.

Figure 8 shows the stress variation curve along the thickness of Sandwich Composite Plate, where the horizontal coordinate is the y-axis coordinate of the finite element model and the vertical coordinate is the Mises stress of the bolt hole wall. From Fig. 8, it can be observed that the stress on the bolt hole wall inside the Core Material gradually decreases from bottom to top, while the stress of the Skin on bottom side is much greater than that of the Core Material, and the stress of the Skin on top side is slightly greater than that of the Core Material.

Fig. 5

Stress distribution of skin in the bolt connection structures of Sandwich Composite Plate

Fig. 6

Stress variation curve along the length of Sandwich Composite Plate

Fig. 7

Stress variation curve along the width of Sandwich Composite Plate

Fig. 8

Stress variation curve along the thickness of Sandwich Composite Plate

4.2 Analysis of the Influence of Bolt Preload

Figure 9 shows the variation curve of shear strength of the bolt connection structures of Sandwich Composite Plate with bolt preload, where the horizontal coordinate is the bolt preload, and the vertical coordinate is the shear strength of the connection structure, from the figure it can be seen that the shear strength of the two kinds of bolt connection structure is similar, and is less affected by the bolt preload, and under the action of different bolt preloads, the shear strength is all between 133–135 kN. Figure 10 shows the variation curve of maximum stress of sandwich composite plate connection structure with bolt preload, where the horizontal coordinate is the bolt preload, and the vertical coordinate is the maximum stress of core and skin when the connection structure reaches the shear strength. Figure 10 shows the variation curve of maximum stress of connection structure with bolt preload, where the horizontal coordinate is the bolt preload, and the vertical coordinate is the maximum stress of Core Material and Skin when the connection structure reaches the shear strength, and it can be found in the Fig. 10 that the maximum stress of the bolt connection structure of the Sandwich Composite Plate is less affected by the bolt preload, and the maximum stress of the pre-buried countersunk head bolted connection structure is larger than that of the assembled countersunk head bolt connection structure, in which the maximum stress of skin is about 13.88% greater than that of the assembled countersunk head bolt connection structure, and the maximum stress of the Core Material is about 9.20% larger.

Fig. 9

Variation curve of shear strength of the bolt connection structure of Sandwich Composite Plate with bolt preload

Fig. 10

Variation curve of maximum stress of the bolt connection structure of Sandwich Composite Plate with bolt preload

5 Conclusions

The shear failure phenomenon of the bolt connection structure of Sandwich Composite Plate is studied through test, and then the finite element simulation model is established to study the pre-embedded countersunk bolt connection structure and assembled countersunk bolt connection structure. The bolt deformation of finite element simulation and the stress concentration phenomenon of the Skin of Sandwich Composite Plate coincide well, based on which the stress distribution of the bolt connection structure of Sandwich Composite Plate and the influence of the bolt preload on the shear strength and maximum stress of the connection structure are analyzed, and the following conclusions are obtained:

• (1) The structural shear failure modes of the bolt connection structure of Sandwich Composite Plate is bolt shear damage and extrusion damage at the Skin openings on the bottom side.

• (2) The shear stress distribution of the two bolted connection structures is basically consistent, which manifests itself in that the stress on the bottom surface is much larger than that on the top surface, and the Skin being much greater than the Core Material. In contrast, the stress peak of the embedded countersunk bolt connection structure is more unfavorable, with the peak stress of the Skin being about 13.88% higher and the peak stress of the Core Material being about 9.20% higher.

• (3) When analysis the shear strength and stress peak value of Sandwich Composite Plate bolt connection structure, the influence of bolt preload can be ignored.

Appendices

Appendices

$F$:

Bolt preload

$T$:

Bolt tightening torque

$\mu$:

Frictional coefficient

$d$:

Major diameter of bolt external thread.