Scholarly article on topic 'Impact of scaling on fracture strength of adhesively bonded fibre-reinforced polymer piping'

Impact of scaling on fracture strength of adhesively bonded fibre-reinforced polymer piping Academic research paper on "Materials engineering"

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{"Adhesive bonding" / "Pipe joining" / VCCT / "Finite element method"}

Abstract of research paper on Materials engineering, author of scientific article — Avinash Parashar, Pierre Mertiny

Abstract The development of fibre-reinforced polymer (FRP) piping with high corrosion resistance and specific properties is an attractive engineering proposition with high potential. Advantageous properties make FRP piping a potential candidate for replacing metallic piping structure in the oil and gas industry. Despite the advantages associated with FRP, their application is limited due to, in part, unsatisfactory methods for joining composite subcomponents and inadequate knowledge of failure mechanism under different loading conditions. Aim of the present paper is to study the effect of pipe scaling on the strength of adhesively bonded FRP pipes. Using finite element analysis, a study was performed to investigate dimensional effects on adhesive joint strength based on strength-of-materials and fracture mechanics considerations. Results indicate a shift in failure from adhesive to composite material with increasing pipe diameter. The Tsai-Wu and von Mises failure criteria were employed for the strength analysis of composite pipe sections and the adhesive material, respectively. A fracture mechanics approach was used to assess changes from cohesive failure (within adhesive) to interfacial failure (adhesive/FRP interface) with increasing pipe diameters. © 2011 Published by Elsevier Ltd. Selection and peer-review under responsibility of ICM11

Academic research paper on topic "Impact of scaling on fracture strength of adhesively bonded fibre-reinforced polymer piping"

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Procedía Engineering 10 (2011) 455-459

Impact of scaling on fracture strength of adhesively bonded fibre-reinforced polymer piping

Avinash Parashar, Pierre Mertiny*

University of Alberta, 4-9 Mechanical Engineering Building, Edmonton Alberta T6G 2G8, Canada

Abstract

The development of fibre-reinforced polymer (FRP) piping with high corrosion resistance and specific properties is an attractive engineering proposition with high potential. Advantageous properties make FRP piping a potential candidate for replacing metallic piping structure in the oil and gas industry. Despite the advantages associated with FRP, their application is limited due to, in part, unsatisfactory methods for joining composite subcomponents and inadequate knowledge of failure mechanism under different loading conditions. Aim of the present paper is to study the effect of pipe scaling on the strength of adhesively bonded FRP pipes. Using finite element analysis, a study was performed to investigate dimensional effects on adhesive joint strength based on strength-of-materials and fracture mechanics considerations. Results indicate a shift in failure from adhesive to composite material with increasing pipe diameter. The Tsai-Wu and von Mises failure criteria were employed for the strength analysis of composite pipe sections and the adhesive material, respectively. A fracture mechanics approach was used to assess changes from cohesive failure (within adhesive) to interfacial failure (adhesive/FRP interface) with increasing pipe diameters.

© 2011 Published by Elsevier Ltd. Selection and peer-review under responsibility of ICM11

Keywords: Adhesive bonding; Pipe joining; VCCT; Finite element method

1. Introduction

Light weight fibre-reinforced polymer (FRP) structures with high specific stiffness and strength have widely been used in the aerospace, construction and automobile industry [1-3]. Filament winding is commonly used method for manufacturing composite pressure vessels and piping [4]. In recent times, FRP structures have increasingly been considered a potential candidate for replacing heavy metallic components especially in the oil and gas industry. Vital research on joining FRP structures is still ongoing due to inadequate knowledge of failure mechanisms. Adhesive bonding of FRP pipe components is a promising joining technique since it can be accomplished without damaging the underlying fibre architecture [5-7]. Several attempts have been made by researchers to design and manufacture adhesively bonded FRP pipe joints [5, 8]. Due to handling issues associated with larger diameter pipes, research in the field of adhesive bonding of FRP piping has thus far mainly been limited to small diameter pipe.

Details on the physical configuration and manufacturing processes for joining pipe sections with an adhesively bonded coupler sleeve as considered in the present modelling work are provided in [8]. Through finite element (FE)

* Corresponding author. Tel.:+1-780-492-6982; fax: +1-780-492-2200. E-mail address: pmertiny@ualberta.ca.

1877-7058 © 2011 Published by Elsevier Ltd. doi:10.1016/j.proeng.2011.04.077

analyses this paper contributes to a better understanding of damage mechanics in adhesively bonded tubular joints. A strength-of-materials as well as a fracture mechanics approach based on the Virtual Crack Closure Technique (VCCT) were employed in this work to quantify the performance of adhesively bonded tubular joints under axial tensile loading. Diameter scaling was conducted to study cohesive as well as interfacial failure phenomena.

2. Theory

A FE model was developed for the present analyses, which assumes a stacking sequence of [±30n,±60m] and [±60a,±30b] for the FRP pipe sections and overlapping sleeve couplers respectively. Laminates were modelled assuming orthotropic material properties. Methodologies adopted for the strength-of-materials and the fracture mechanics approaches are described in the following sections. Figure 1 shows a schematic of the FE model employed in this investigation. Midplane and axis-symmetry were utilized to realize efficient modelling.

2.1. Strength of material approach

In this study, the well-known von Mises criterion was used to indicate the onset of failure in an isotropic material, such as the polymer adhesive. For predicting failure in anisotropic composite structures, several criteria are available [9]. Commonly employed are the maximum stress, the maximum strain, the Tsai-Hill and the Tsai-Wu theories. In this paper the Tsai-Wu criterion was used to quantify the region of initial failure/damage. The Tsai-Wu theory describes a three-dimensional failure envelope that is defined by the following quadratic expression:

F O + F Oj > 1

where Fi and Fij are, respectively, a second and fourth-order tensor describing the material strength parameters. Theoretically these parameters need to be determined experimentally; but in practice, apposite data is often available in the technical literature. The left-hand-side of Eq. 1 may also be considered a failure index, which, if greater than one, indicates the failure in the material under consideration. Stresses stated in the equation, a1, a2, a3, correspond to the local coordinate system of a unidirectional lamina, where '1' defines the fibre direction, and '2' and '3' the in-plane and out-of-plane directions transverse to the fibres respectively. Global stresses, obtained e.g. from post processing of FE analysis results, can readily be transformed into local stresses using a transformation matrix (see [9] for details).

2.2. Fracture mechanics approach

The VCCT was adopted in this study to investigate the fracture of adhesively bonded tubular joints subjected to tensile loading. Raju [10] formulated a finite element methodology for calculating the strain energy release rate (SERR) with higher order finite elements. Corresponding numerical expressions for calculating the SERR GI for mode I fracture (opening) and GII for mode II fracture (in-plane shear) are explained with the help of Fig. 2 and Eqs. 2 and 3 respectively.

Crack A (adhesive) Crack B (resin layer)

[±30°] layer in FRP pipe

[±60°] layer in FRP pipe

Fig. 1. Schematic of axis-symmetric model oftubular joint

Fig.2 Eight-node solid elements with crack opening

G, = -(2A)-1 (P3y (v, - v1')+(v2 - v2'))

V! - V)+p „ v - (2;

GU = -(2A)-1 (P3xx («1 - P4x («2 - «2')) (^

where P are the nodal forces at the 1th node from the crack tip. 3. Finite Element Model

The FE based approach adopted in this paper used the ANSYS 11 software environment to model the joint geometry and perform the analyses. Two-dimensional 8-node structural solid elements (PLANE82) with axis-symmetric properties were used to model the joint configuration. For the resin-rich layer on the pipe surface (with crack B) four elements were used across its thickness. For the adhesive bondline (with crack A), the element thickness was identical to that of the resin-rich layer. The total number of elements varied for the different models. For the model with 100 mm pipe diameter, for example, this number was in the order of 12,000. Singularities at the bi-material interface of adhesive and FRP coupler were avoided considering the stresses and strains at the third node from the singularity location; this method was described previously by Gleich et al. [11]. Material properties were assumed to be orthotropic for the FRP pipe and coupler, and isotropic for the unreinforced resin and adhesive. Corresponding data are given in Tables 1 and 2. A common elasticity approach (i.e. composite cylinder assemblage model) was employed to calculate the elastic properties of the FRP assuming a fibre volume fraction of 60%.

Four geometrically similar models of different scales were considered in this study. The geometrical specifications are given in Table 3. Pipe wall thickness scaling was based on the notion of imposing a constant hoop stress (rhoop for each pipe size for a specific internal pressurization p, i.e. according to Eq. 4 the ratio of internal pipe diameter D to wall thickness t must remain constant for different scales of the structure. For each model, the taper angle of the coupler was kept constant at 45°; the length of overlapping sleeve coupler was three times the diameter of the pipe; and the thickness of the resin rich layer on the pipe surface was 0.2 mm. As for the adhesive bondline thickness, a linear increase was assumed with increasing pipe diameter as with larger pipe diameters a tight adhesive gap will be more difficult to achieve. Finally, the coupler thickness was adjusted for the different pipe scales according to the rationale explained in Section 4.1.

°hoop = — (4)

Table 1. Youngs moduli (E), shear moduli (G) and Poisson's ratios ( v); subscripts x, y, z indicate the radial, axial and hoop direction of the tubular structure respectively

Elastic FRP FRP Resin- Adhesive

property [±30°] [±60°] rich layer

Exx [GPa] 15.309 15.309 3.2 3.4

Eyy [GPa] 27.318 14.279 3.2 3.4

Ezz [GPa] 14.279 27.318 3.2 3.4

Gxy [GPa] 5.601 5.4263 1.2 1.8

Gxz [GPa] 5.4263 5.601 1.2 1.8

Gyz [GPa] 11.439 11.439 1.2 1.8

vyx 0.1627 0.2913 0.40 0.34

Vzx 0.2913 0.1627 0.40 0.34

vzy 0.3012 0.5762 0.40 0.34

Table 2. Ultimate (failure) strength properties for a unidirectional FRP material; values were computed using methods and data presented in [9] and [12] respectively

Strength FRP

property

Ultimate tensile [MPa] 1140

parallel to fibre direction

Ultimate compressive [MPa] 620

parallel to fibre direction

Ultimate tensile [MPa] 41

transverse to fibre direction

Ultimate compressive [MPa] 128

transverse to fibre direction

Ultimate shear strength [MPa] 89

Table 3. Geometrical specification for models of joined tubular structures of different scale

Table 4. Failure indices for the adhesive joint of Model #2 (inside pipe diameter of 100 mm)

Specification Model #1 Model #2 Model #3 Model #4 Adhesive Pipe [±30°] layer Coupler [±30°] layer

Inside pipe 50 100 200 400 Failure index 1.01 0.96 0.61

Laminas in PiPe [ / ] Laminas in coupler [ / ]

Adhesive thickness [mm]

4 4 0.2

16 10 0.6

32 15 0.8

4. Results and Discussion

4.1. Strength of material approach

Finite element analysis was performed to obtain stresses at failure applying aforementioned failure criteria. Since similar findings were made for the different pipe scales, the discussion of results was limited in this paper on Model #2 (pipe diameter of 100 mm), in which case an axial tensile load of 36.5 kN was imposed as indicated in Fig. 1. Using the von Mises criterion for the adhesive material, and the Twai-Wu criterion for [±30°] layers of the pipe and sleeve coupler, failure indices were calculated as shown in Table 4. These results indicate that failure will occur in the adhesive and the pipe's [±30°] layers rather than in the coupler. In particular, the vicinity of the pipe/adhesive interface was found to be most susceptible to damage initiation in the joint under tensile loading.

As mentioned above, the coupler thickness was adjusted with increasing pipe diameter. Analyses involving the strength-of-materials approach indicated that an increase in coupler thickness negatively affects joint strength. At the same time, the failure indices showed that compared to the pipe and adhesive the coupler is furthest from failing. A similar behaviour was observed in [8] where increasing the coupler thickness was found to overall amplify SERR values. Hence, in the present study the coupler thickness was adjusted only to a level that allowed the coupler to bear the applied tensile loading.

4.2. Fracture mechanics approach

The subsequent modelling stage involved crack A that was assumed to exists in the adhesive layer (see Fig. 1). SERR values (Gi, Gii and GTotal) were computed for Models #1 to #4 imposing a constant axial strain of 5% (which implies increased tensile loading for larger pipe scales). Ratios of Gii/Gl with respect to crack length are plotted in Fig. 3. It can be observed from these data that the GII/GI ratio trends towards unity for increasing pipe diameters. In other words, for the larger pipe diameters a mixed mode fracture behaviour (including a significant opening mode I component) is operative, whereas in smaller diameter pipes, mode II fracture (in-plane shear) plays a more dominant role. Large diameter pipe joints thus approach the fracture behaviour of plane single-lap joints. Adhesives bonds are known to be particularly prone to failure under opening mode fracture, and hence, scaling effects must be considered carefully.

In the final stage of modelling, the total SERR (GTotal = Gi + Gn) for cracks A in the adhesive and crack B in the resin-rich layer were calculated for the various models. Ratios of GTotal(adhesive)/GTotal(resin-rich layer) are shown Fig. 4. These data indicate a clear trend with respect to diameter scaling, i.e. for ratios above unity, which is the case for pipe diameters up to 100 mm, cohesive failure in the adhesive will occur, whereas for ratios less than unity, interfacial failure in the resin-rich layer is the expected type of failure.

CD 2 1

50 100 150 Crack length [mm]

Fig. 3. Ratio of GiJGi with respect to crack length

5. Conclusions

m 1.01

Î 0.99

ra 0.98

CD 0.97

Model #1 (50 mm pipe)

Model #2 (100 mm pipe)

Model #3 (200 mm pipe)

Model #4 (400 mm pipe)

10 20 30 Crack Length (mm)

Fig.4. Ratio of total SERR between fracture in the adhesive bondline and the resin-rich layer with respect to crack length

In this research paper a strength-of-material approach followed by a fracture mechanics technique (VCCT) was employed in conjunction with a FE modelling environment to study the failure mechanics of pipe sections joined by means of adhesively bonded overlap sleeve couplers. The impact of diameter scaling was investigated. The strength-of-material approach indicated that damage initiation is to be expected in the pipe and the adhesive bondline rather than the coupler structure. The study of fracture behaviour involved several diameter models in which fracture propagation was considered in the adhesive bondline and the thin resin-rich layer. The analysis of SERR data indicated that with increasing pipe diameter an increase in opening mode fracture behaviour will occur. The examination of SERR data further revealed that small diameter piping (less than 100 mm) has a propensity for cohesive failure in the adhesive bondline. For larger diameter pipes (greater than 100 mm), however, interfacial failure in the thin resin-rich layer on the outside surface of FRP piping is the likely location of damage propagation. The analyses conducted in this study thus indicate that dimensional scaling and its effects on damage behaviour are important design considerations for the given joint configuration.

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