Bonded joints are very common in many pipeline systems, in which the bond behavior of the joint interface is of crucial importance. This paper presents two analytical solutions for the debonding process of a pipe joint under torsion, assuming that the bond interface follows either an exponential softening bond-slip law or a simplified bilinear model. The solutions are general, applicable to composites and metallic and indeed other pipes. Based on the analytical solutions, the influences of the bond length and stiffness on the torque-displacement curve and ultimate load are investigated. The solutions can be used to explain the stress transfer mechanism, the interface crack propagation, and the ductility of the joint.

Pipes are very important structures in many industries such as energy, aerospace, and construction [

For metallic piping system, the joints can be divided into three types: flange coupling, welding, and adhesive bonding. The first two traditional connections have the same shortage, such as high stress concentration. However, the adhesively bonded pipe joint can effectively lower the stress concentration [

Adhesively bonded pipe joints provide uniform load transfer over the bonded area. Nevertheless, stress distribution in the bondline adhesive is nonuniform. Among all the possible loading configurations, such as tension, torsion, and bending, torsion is one of the fundamental types. Due to the difficulties in the analysis of interfacial behavior, few theoretical studies of mode III (torsion) interfacial fracture problems are available in the previous references.

Based on the mechanics of composite materials and the maximum strain failure criterion, an analytical and experimental study was conducted to investigate the elastic and failure behavior of composite laminated pipe under torsion [

Finite element results are good supplements to analytical research. A finite element analysis was used to calculate the residual thermal stresses generated by cooling down from the adhesive cure temperature and a nonlinear analysis incorporating the nonlinear adhesive behavior was performed [

In all previous solutions, linear elastic properties are assumed for the entire pipe joints. The linear elastic behavior may be appropriate for the pipes themselves. While for the adhesive layer which is usually the weakest link in the bonded joints and often suffers from microcracking and local damage, nonlinear modeling may be necessary. When the crack tip experiences inelastic damage, the concepts based purely on the theory of elasticity are not valid. Therefore, different bond-slip models with softening region were proposed in the previous references, such as rigid-softening, bilinear, trapezoidal, and exponential models [

However, there are very few studies focusing on the analytical solution of full debonding process of pipe joints in the literatures. To the best of the authors’ knowledge, linear elastic properties are assumed for the entire pipe joints and very few researchers have taken interfacial softening and debonding into consideration. In the present study, there are two analytical solutions for the failure process of adhesively bonded interface, assuming that the bond interface follows either an exponential softening bond-slip law or a simplified bilinear model. The expressions for the interface slip and shear stress are derived for the different failure stages. The present research improves and clarifies the understanding of the interfacial debonding problem of bonded pipe joints under torsion. By modifying different shear modulus, the present results may be further extended to composite pipe joints, composite-metal pipe joints, or metallic pipe joints.

Figure

An adhesively bonded pipe joint.

Cross section

Side view

Right half of the pipe joint

The following assumptions are made for the simplicity:

The adherents are homogeneous and linear elastic.

The adhesive is only under pure shear.

The pipe joint is under pure torsion which is resisted by the main pipe and coupler pipe; that is, the adhesive layer is assumed to only transmit shear stresses between Pipes 1 and 2, not contributing to any direct resistance to the torque.

Local bending effects in the pipe joint under the torsional load are neglected.

According to the classical torsion theory, the internal torsion

As the torque resultant in the soft and thin adhesive layer is ignored following assumption number 3 above, the equilibrium between external and internal torsion load in the pipe joint requires

Let the relative rotation between Pipes 1 and 2 at

Equilibrium of local interfacial shear stresses.

As introduced before, researchers have proposed various bond-slip models. Experimental results indicate that the bilinear model which features a linear ascending branch followed by a linear descending branch provides a close approximation [

For the exponential bond-slip law (Figure

Bond-slip models.

At small loads, there is no interfacial softening or debonding along the interface, so the entire length of the interface is in an elastic stress state. Substituting the first expression in (

As the load increases, the interfacial slip reaches

In bonded joints, there is usually an effective bond length

As the load increases, the peak of the shear stress moves towards the middle of the joint (

The solution for the elastic stage is the same as that in Section

As the load increases, softening commences at

If

This stage is governed by (

As the load increases, the shear stress peak moves towards

The results of an adhesively bonded metal-composite pipe joint are presented here. The typical inner diameter and thickness are assumed to be 300 and 10 mm for the metallic main pipe, respectively. And the inner diameter and thickness of the composite coupler are assumed to be 320.4 and 5 mm, respectively. For metallic main pipe, the mechanical properties are chosen as

According to the material properties and geometry parameters given above, the critical bond length for bilinear model can be calculated as

The load-displacement curve for exponential model is shown in Figure

Load-displacement curves: exponential model.

When the bond length is shorter than

Load-displacement curves: bilinear model.

The shear stress distribution for exponential model is shown in Figure

Shear stress distribution: exponential model.

The shear stress distribution of

Shear stress distribution: bilinear model.

Figure

Effect of bond length on load-displacement.

Bilinear model

Exponential model

Figure

Comparison of the load-displacement curves predicted from using the two bond-slip models.

Figure

Effect of torsion stiffness on the load-displacement curve.

Bilinear model

Exponential model

Figure

Effect of the torsion stiffness ratio on the effective bond length.

Through the numerical computation, the ultimate load of exponential and bilinear models for different bond lengths could be obtained. Figure

Effect of the bond length on the ultimate load.

On the basis of fully understanding the mechanical behavior of the joint interface, this paper gives a further understanding of the key factors of interfacial debonding. By modifying different shear moduli, the present results may be further extended to composite pipe joints, composite-metal pipe joints, or metallic pipe joints. Based on the derivations in the current study, some important conclusions are summarized as follows:

Through the nonlinear fracture mechanics, the analytical expressions of the interfacial shear stress and the load-displacement relationship at loaded end of pipe joints under torsion loads could be gotten. Thus the shear stress propagation and the debonding progress of the whole interface for different bond lengths could be predicted.

The influences of different bond length on the load-displacement curve and the ultimate load are studied through the analytical solutions. The stress transfer mechanism, the interface crack propagation, and the ductility behavior of the joints could be explained.

The authors declare that they have no competing interests.

The authors gratefully acknowledge the financial support provided by the Science and Technology Scheme of Guangzhou City (201510010013), Science and Technology Scheme of Guangdong Province (2012A030200003), and the Natural Science Foundation of China (National Key Project no. 11032005).