# Strength analysis of adhesive joints of riser pipes in deep sea environment loadings

- Yu Zhang
^{1}Email author, - Tai Yan Qin
^{2}, - Nao Aki Noda
^{3}and - Meng Lan Duan
^{1}

**1**:9

https://doi.org/10.1186/2196-4351-1-9

© Zhang et al.; licensee Springer. 2013

**Received: **2 September 2013

**Accepted: **30 October 2013

**Published: **30 December 2013

## Abstract

Nowadays, adhesive joints are widely used in riser pipes, which are subjected to many kinds of loadings in deep sea, such as external pressure, internal pressure, tension, torsion, bending, and also a combination of these loadings. Adhesive joints of riser pipes are the most dangerous parts in term of strength, as singular stress fields exist at the end of the interface between the adhesive and the adherends, so it is very important to evaluate the strength of adhesive bonded joints for riser pipes in deep sea environment loadings. In this research, the strength of adhesive joints of riser pipes is studied under external pressure, internal pressure, tension, torsion, bending loadings, and it is found that singular stress fields exist around the end of the interface. The riser pipe under external pressure, internal pressure and tension loading is more prone to break than under bending and torque loading.

## Keywords

## Background

Due to low manufacturing costs, low stress concentration and ease of maintenance, adhesive joints are most frequently used in numerous industrial sectors such as automobile, shipbuilding, aeronautical, etc., replacing or supplementing traditional joining technologies, such as welding or riveting. Adhesive bonded joints are also widely used in riser pipes because of their light weight, high strength, and high corrosion resistance[1]. With the wide use of adhesive joints, many research works have been done to evaluate their strength including experimental and analytical methods [2–8].

The mismatch of different materials properties may cause stress singularity at the end of the interface between different materials, which leads to failure of the bonding part in structures, so it is very important to analyze the stress singularity field for evaluating the strength of adhesively bonded joints. Many researchers did some valuable work to analyze the stress singularity field at the end of interface between the adhesive and the adherends, such as Koguchi et al. [9], Kilic et al. [10], Van Tooren et al. [11], and Goglio and Rossetto [12]_{,} Tilscher [13]. Zhang [14] proposed one easy method to evaluate the effect of adhesive thickness and length on the strength of adhesive joints. Moreover, Zou and Taheri [15] analyzed stress distributions of adhesive bonded sandwich pipe joints subjected to torsional loadings. Da Silva et al. made a detailed and comprehensive comparion between studies about adhesively bonded joints [16, 17].

### Methods

#### Theoretical analysis

*σ*

_{ ij }(

*ij*=

*rr*,

*θθ*,

*rθ*) goes to infinity at the edge of the joint and has a singularity of

*σ*

_{ ij }∝ 1/

*r*

^{1 − λ}when

*a*(

*a*-2

*β*) > 0.

*K*

_{σ}is the parameter used to evaluate the intensity of singular stresses, where ${K}_{\sigma}=\underset{r\to 0}{lim}\left({r}^{1-\lambda}\times {\sigma}_{\theta}\right)$. Besides, when

*θ*=

*π*/2, the singularity of the stress

*λ*at the joint interface can be expressed by the following equation [18–20].

Here *r, θ* are the polar coordinates around the interface edge, *a*, *β* are Dunders’ parameters which are expressed by Possion’s ratio *v* and shear modulus *G*.

### Numerical model

In this paper, the scaling model with the following dimensions was used: adhesive thickness h_{0} = 6 mm, cover thickness h_{1} =10 mm, total length 2 L = 200 mm and coupling length 2c = 25 mm. The outer diameter of the adherend was 140 mm and the inner diameter was 110 mm. The adherend steel elastic properties were E = 70,000 MPa, *v* = 0.33. The adhesive material elastic properties were E = 3500 MPa, *v* = 0.30, which means that the existence of singular stress fields condition *a*(*a*-2*β*) > 0 is satisfied at the edge of interface between adhesive and adherend.

The commercial software ABAQUS was used to perform the analysis. The finite element method model was constructed using 3-D solid elements (Figure 3). Two mesh densities were used to conduct the analysis. A coarse mesh with the mesh density of 32 rows of elements circumferentially 2 rows (radially) · 30 rows (axially) was used to model the pipe region, while the mesh density was doubled to model the joint region. Moreover, the mesh of the joint region was graded along the axial direction of the pipe, finer toward the free edges of the joint.

## Results and discussion

### External pressure loading case

*P*

_{ op }

*= ρgH*=14.7 MPa was applied the adhesive joint. The boundary conditions for this case were : ur = 0, at x = 0; ux = 0, x = 0; and us = 0, x = 0. According to the theroretical analysis, a singular stress field exists around the end of the interface between the adhesive and the adherends. Here, one example of the stress distribution at the interface of the joint subjected to the external pressure is shown in Figure 4. It is found that stresses at the end of interface tend to infinity, which indicates that a singular stress field exists around the end of the interface.

### Internal pressure loading case

Generally, the internal pressure of a riser pipe is higher than the external pressure to prevent buckling of the pipe, and in this research, an internal pressure *P*_{
ip
} = 15.0 MPa was chosen. The boundary conditions for this case were: *u*_{
r
} = 0, at *x* = 0; *u*_{
x
} = 0, *x* = 0; and *u*_{
s
} = 0, *x* = 0.

### Tension loading case

*T*= 20.0 MPa was considered in this paper, and the boundary conditions are the same as those used for out pressure and inner pressure, which are ur = 0, at x = 0; ux = 0, x = 0; and us = 0, x = 0. Figure 6 shows the stress distribution at the interface between the adhesive and the adherends. Stress values at the end of the interface are related to the elment sizes, but it can be found that stresses at the end of the interface tend to infinity with the element sizes in this paper, which indicates that a singular stress field exists at the end of the interface.

### Bending loading case

*P*= 200 N prependicular to the pipe axis, and the left end of the riser pipe was fixed as:

*u*

_{ r }= 0

_{, θr = 0,}at

_{x = 0;ux = 0, θ x = 0,}at

_{x= 0;}and

*u*

_{ s }= 0,

*θ*

_{ s }= 0 at

*x*= 0 Figure 7 shows the stress distribution at the interface. It indicates that stress distribution is unsymmetric, and stresses decrease from on end of the interface, which is because moments along the pipe are not symmetric. However, the stress distribution indicates that both ends of the interface have singular stress fields.

### Torque loading case

*P = 200 N*which was tangent to the circumference of the riser pipe section, so the torque is equal to 200 × 140 = 28000 M mm. Figure 8 shows the stress distribution at the interface, and it indicates that the stress also trends to infinity.

### Comparison of stress intensity fields between the cases of external pressure, internal pressure, tension, bending and torque loading

Stress values at the end of the interface are related to the element sizes, and models under different loading cases have the same mesh sizes in this paper. From the comparison, it can be said that different loading cases have different gradients of stress lines. The gradient of stress lines indicates the index of the singular stresses singularity at the end of the interface. If the loading values increase, the stress values at the end of the interface will also increase, without changing the gradient of the stress lines. So the gradients of stress lines are only related to the loading conditions if the mesh sizes do not change.

## Conclusions

In this paper, a 3D adhesive joint model was constructed using FEM, and the singular stress field around the end of the interface between the adhesive and the adherend was analyzed for cases of external pressure, internal pressure, tension, bending and torque loadings. Singular stress fields exist for all the loading cases, and the stress singularity is larger for cases of external pressure, internal pressure and tension loading compared to the cases of bending and torque loading, which means that the riser pipe under external pressure, internal pressure and tension loading is more prone to break than under bending and torque loading in deep sea environment.

## Declarations

### Acknowledgements

The authors appreciate the reviewer’s constructive comments and detailed feedback for improving the manuscript. This research was supported by Science Foundation of China University of Petroleum, Beijing (No. 2462013YJRC44), and the National Basic Research Program of China (973 Program) Grant No. 2011CB013702.

## Authors’ Affiliations

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## Copyright

This article is published under license to BioMed Central Ltd. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.