Time-dependent response of thermoplastic matrix composite material under the cyclic loadings

Abstract

Under the service conditions, steel pipelines coated with the thermal protection system are subjected to cyclic loadings of axial tension and hydrostatic pressure. The finite element method generally used to simulate the behavior of composite structures under these loadings allows us to estimate the stresses generated in the system and to conclude on several origins of damage. However, for the framework of displacement or deformation analyses in such multilayer systems, these calculations do not allow a better prediction of their behavior. The methods used do not take sufficiently into account the characteristics of the different coating materials to predict their response in service conditions under cyclic loading. In this paper, we consider the viscosity of the thermoplastic materials used for the five layers coating system. Finite element calculations allow us to observe the areas of highest stress concentration at the interface with the steel pipe. Simulations allowed us to observe that the applied loads lead to increases in residual deformation in the thermoplastic matrix composite material. Cyclic tensile loading causes cracks in the matrix of the syntactic foam material. The study carried out here makes it possible to justify the origin of the failure mechanism in the composite material at the time of the installation of the pipelines which could limit the duration of their use in an offshore environment. The tensile failure of the syntactic foam considered as the polypropylene matrix composite material on which cyclic loads have been applied, is due to the stress level at a given temperature.

Keywords

Composite material cyclic loading multilayer offshore pipeline creep-recovery

Introduction

The use of offshore pipelines requires a certain level of performance in the face of mechanical loads that may arise from installation processes and during the fluid transport phase at sea surface level.¹ High mechanical loads and strong thermal gradients can cause a situation of asphalt formation and paraffin deposit which may limit for this purpose the flow rate of the fluid along the steel pipe. In order to maintain the oil production, thermal insulation systems have been proposed. However the type of system consisting of five layers has been widely used by the companies.¹ This system consists of adhesive Epoxy, adhesive polypropylene, solid polypropylene and syntactic foam with a polypropylene matrix (GSPP).^1–3 This system is recognized as bringing together the different advantages that a single material could not have had.² During the manufacturing of thermally insulated pipelines, the steel pipe coating process is carried out by the heating, and then water-cooling of the whole structure.^2,3 At the end of this manufacturing, residual stresses are developed in the thickness of materials polymers.³ Commissioning is a process during which the pipelines held in any position must support the various loads applied.^4,5 under service conditions, pipelines must be subjected to hydrostatic pressure type loads.^3,6–9 The experimental analysis carried out in Rizzi et al.¹⁰ made it possible to underline the plastic behavior of the syntactic epoxy matrix foam under various loads. A nonlinear Drucker-Prager model was then proposed for the numerical simulation of the mechanical behavior of the material.¹⁰ Attention is paid to the stress states developed in the pipes in installations. The use of long life pipes requires the inclusion of a time-dependent overall response for the multilayer thermal insulation system. The objective of our work is therefore to improve the tools for optimizing mechanical performance during the design and sizing of passive pipeline protection systems used in deep water. This study consists in numerically evaluating the time-dependent mechanical behavior of the materials constituting the multilayered pipe system under the influence of the various loads applied to the assembly. Within the framework of this modeling, the loading conditions were represented by the application of a tension and external pressure at the external borders. The characteristics of the constituent materials derived from the experimental analysis are obtained in the literature.^1,3,11–14

Materials and geometry of the structure

The coating system used to provide the thermal insulation function of the steel pipeline in the offshore environment can be either three-layer or five-layer.¹⁵ We are interested in the five-layer system which also has the advantage of good resistance to hydrostatic pressure by inserting a thickness of syntactic foam material.^2,3 Figure 1 shows the geometry and constituent materials of the five-layer surfacing system. According to the geometry of this structure, the five-layer system is based on the first three materials of the three-layer system that has been in use for several years. Tables 1 and 2 show the thicknesses and the elastic properties of the materials used in both types of systems. $ρ$ is the density, E is the Young’s modulus, $ν$ is the Poisson’s coefficient and α is the coefficient of thermal expansion. The current problem is that it is still not possible to predict the response of such a system in real conditions under cyclic loads of tension force and hydrostatic pressure. Work carried out in the literature^1,3,15 seems to show that the use of the finite element method makes it possible to be closer to the reality of the installation and immersion processes of steel pipelines coated with thermal insulation protection.^3,11 However, the best approach would be to develop appropriate models for each type of material for calculations by numerical code. The contribution of our work then lies in improving the prediction of the response of the syntactic foam type composite material which is the main thermal insulation material in the five-layer coating system. Numerical calculations are performed on both types of systems to ensure the adhesion and protection of the bonded assembly of steel and composite materials in offshore environments.

Figure 1.

The five and three layers systems of thermal insulation.

Table 1.

Materials thickness.²

Materials	Thickness (mm)
Steel	18.26
First Bonded Epoxy	0.25
Adhesive polypropylene (APP)	0.25
Solid polypropylene (SPP)	2.5
PP syntactic foam (GSPP)	55
Polypropylene topcoat	3

Table 2.

Polymers and steel pipe properties at the temperature of 20°C.²

Materials	$ρ$	E (GPa)	$ν$	α (°C⁻¹)
Steel	7.85	218	0.33	$1 \times 10^{- 5}$
Epoxy	1.2	3	0.4	$3 \times 10^{- 5}$
Polypropylene	0.9	1.3	0.4	$1.6 \times 10^{- 5}$

During the numerical calculations two types of loads are used in the static and time domain. Tensile loading conditions consist in applying a force to the outer boundaries of the structure using a triangular mesh and the displacements are blocked in the direction perpendicular to the loading direction. The pressure loading conditions remain the same but the loads are applied to all the external boundaries of the structure. Figure 2(a) to (d) shows the different constituents of pipe and loading conditions used in the finite element code of the Comsol Multiphysics Software.

Figure 2.

(a) 3D geometry of the five layers systems under cyclic tensile and pressure loadings; (b) 2D axisymmetric geometry of the three layers system under pressure loadings; (c) 2D axisymmetric geometry of the assembly of the polypropylene materials and glass syntactic polypropylene foam under tension force, (d) Pressure loadings conditions applied to the three layers system

Methods

Overview

The glass syntactic polypropylene foam is a thermoplastic composite material used in the lining of Offshore pipeline to provide adequate performance under severe environmental conditions. The characterization of the behavior of this material is therefore carried out to optimize the tensile and pressure strength of thermal insulation system in installation and immersion conditions. Creep loading tests are therefore well suited to study the behavior of this material. The temperature and the stress must be analyzed simultaneously in the permanent deformation of the material.

Constitutive equations of the models

The overall resistance of a thermal insulation system will be analyzed in this manuscript by studying the individual behavior of the constituent materials. The metal steel tube is the tube in which the fluid circulates. This tube is protected by a system of five layers of materials mainly made of polypropylene material (5LPP).^2,3,12 The time-dependent behavior patterns selected for each polymer material are shown below. We assume that each material has a response that takes the following general form:

ε^{t} = ε^{e} + ε^{v e} + ε^{v p} + ε^{p},

$ε^{e}$ , $ε^{v e}$ , $ε^{v p}$ and $ε^{p}$ are the elastic, viscoelastic, viscoplastic and plastic strains respectively.

The steel material has an elastic behavior ( $ε^{v e} = 0$ , $ε^{v p} = 0$ and $ε^{p} = 0$ ) because we assume that the uniaxial tensile load applied does not exceed the elastic limit of the material and that the considered temperature does not considerably change its mechanical properties.^1,2 Its elastic behavior is then sufficiently described with Hook’s law.

The first layer of the coating system is epoxy and acts as an adhesive between the metal tube and the thermal insulation materials. This layer is only a few millimeters thick enough to fulfill its role.^12,15 The viscous strain of this material will not also be considered here owing to the fact that its mechanical response consists mainly of the instantaneous strain under the level of applied creep stress.¹⁵

Then, three layers of polypropylene materials are deposited on the steel tube.² The first layer acts as an adhesive to improve the adhesion of materials with the steel tube. The second layer acts as a solid polymer to protect the primary insulation material Glass Syntactic polypropylene from impact loading. The third layer protects all of the constituent materials against external corrosion.^1,3,12 The viscoelastic character of the polymer material will be simulated with the generalized Maxwell model.^3,15

The model connects the different deviatoric parts of the strain and the stress.¹¹ The deviatoric stress $σ^{D}$ is expressed by the hereditary integral of the history of the deformation Eqn.(2):

σ^{D} = \int_{0}^{t} G (t - t^{'}) \frac{\partial ε^{D}}{\partial t^{'}} d t^{'},

$ε^{D}$ is the deviatoric strain. $G (t)$ is the relaxation shear modulus distributed in a number of branches M and function of time. The details of this model are presented in Phan et al.¹¹ This model will allow us to simulate the viscous deformation of polypropylene materials. Using two branches made of spring and dashpots.

The layer of composite material, which acts as the main thermal insulation material, has a greater thickness.^2,3,12 Its resistance is at the center of studies of the overall system due to the particular properties of the material, namely the reduction in the weight of the structure, the maintenance of the temperature of the hot fluid, the guarantee of the longevity of the system and its buoyancy at the sea.² Recently a spectral model has been presented for polymeric and composite materials.^16,17 The model is used for the simulation of the syntactic foam material response.³ This spectral model gives the viscous elementary strain $ξ_{i j}$ distributed according to several branches associated with a relaxation time $τ_{i}$ and weighted by a weight specific $μ_{i}$ .^3,16,18 The following equation (3) gives the elementary strain rate:

{\dot{ξ}}_{i} = - \frac{1}{τ_{i}} (ξ_{i} - μ_{i} S_{R} : σ) .

$σ$ is the Cauchy’s stress. The viscoelastic strain rate ${\dot{ε}}^{v e}$ is obtained by the total sum of the elementary strain of each branch Eqn. (4):

{\dot{ε}}^{v e} = \sum_{i = 1}^{n_{b}} {\dot{ξ}}_{i} .

We can operate this model using the details presented by Treasurer et al.¹⁹ By solving the differential equation (3), we will introduce the total linear viscoelastic deformation $ε^{v e}$ in the expression (1). The viscoelastic flexibility matrix S_R depend on three parameters n_o, n_c and A. The times $τ_{i}$ and weight $μ_{i}$ respect the same representations as rheological models.²⁰ The distribution of the weight $μ_{i}$ thus respects the Prony series just like the Maxwell’s model presented above. The stresses do not generate any plastic deformation. The spectrum is chosen as triangular and the $τ_{i}$ and $μ_{i}$ parameters are found by the equations below¹⁹:

n_{i} = i \times Δ + n_{c} - n_{o},

$Δ = \frac{2 n_{0}}{n_{b} + 1}$ is the interval used between relaxation times.

τ_{i} {= 10}^{n_{i}},

for $n_{i} \in [(n_{c} - n_{o}), n_{c}]$

μ_{i} = a (n_{i} - (n_{c} - n_{o})),

for $n_{i} \in [n_{c}, (n_{c} + n_{o})]$

μ_{i} = - a (n_{i} - (n_{c} + n_{o})),

The normalization of the weighting coefficients is given by:

\sum_{i}^{n b} μ_{i} = 1

$a = \frac{2}{n_{0} (n_{b} - 1)}$ is the slope of the relaxation time spectrum. The parameters n_c and n_o are the standard deviations and the mean of the relaxation times.

The experimental analyses of the creep behavior of composite materials were carried out in the literature.^16,18 They made it possible to identify the irreversible nature of the latter. The model proposed to take into account the irreversible mechanisms in the deformation of polymer and composite materials is that of Zapas and Crissmann.²¹ This model will permit to link the response of the Glass syntactic polypropylene material to the three variables time, temperature and stress by Eqn. (9):

ε^{v p} = C {(σ^{N} t)}^{n},

where C, N and n are the material parameters to be determined.

Results and discussions

In this part, we perform analysis of the constituent materials response of the thermal insulation coating system. The objective is to determine their behavior in service when the axial tension and the external pressure are applied.^22–24

Two organic coatings under tensile loads

The installation and immersion phases of the pipes can be carried out by the J-shaped installation method.²⁵ This method has the advantage of reducing the effects of certain installation constraints.^3,22,24,25 During the installation process, axial tension loads can occur in the thicknesses of the different materials constituting these structures.^4,25 We consider a five-layer system of Glass Syntactic Polypropylene (see Figure 1)^2,3,12 and a three layers system of polypropylene (see Figure 1)^26,27 under the effects of loadings in axial tensile load. The experiments details of quasi-static tensile tests are presented by Vestrum et al.^13,14 The response of the pipeline samples was obtained using a deformation hydraulic piston. An Instron general purpose machine with the ability to increase the force was used to perform all tests. The force was measured by a load cell and the displacement was recorded by two sets.^13,14

The geometric characteristics of the two types of thermal insulation system considered here have been presented in Aris-Brossou et al.,¹² Joliff et al.¹⁵ and Bouchonneau et al.^1,2 During the axial tension experiments performed on two pipe sections, the thermal insulation system showed an elastic behavior even under the two forces of 300 kN and 600 kN. The axial tension experiments performed on the materials use machines whose forces does not usually exceed 300 kN. In order to note the consequences of such a critical force on the structure we have applied it in the numerical study. The geometry of the system is chosen in 3D dimension (see Figure 2(a)) to be able to study the mechanical strength under the application of the force of 300 kN.⁴ Axial tension forces are considered only in the longitudinal direction F_x to represent the actual application of the tension force in the thicknesses of the materials. Figure 3(a) shows the mechanical response obtained during the application of this force on the structure of the syntactic foam pipe. The displacement is given according to the thickness of the steel and syntactic foam materials on the mapping. We can observe that the exerted force results in a maximum displacement level of 0.7 mm. Figure 3(b) also shows the map for induced displacements in the polypropylene structure. The maximum level of displacement induced by the axial tensile force is 0.23 mm. The results show that both materials have specific resistances when subjected to the axial tensile force. The displacement levels obtained show that the two materials contribute to the overall resistance of the pipe during the application of the axial tension loading.²⁵ This observation makes it possible to identify the response of the thermal insulation system during the quasi-static tests carried out under axial tension by Vestrum et al.^13,14 The mechanical resistance of the pipe structure under the axial tensile load is no longer limited only to that of the metal steel tube but also includes the resistance of the different layers of the coating system.^4,22 The deformation process of these coating materials can be changed due to their nonlinear character.

Figure 3.

Displacements distribution in the five and three layers system of thermal insulation.

Three layers coating under external pressure

We study the effect of external pressure applied to the polypropylene thermal insulation structure. We choose three pressure levels (7, 15 and 30 MPa) representing any depth of immersion.^1,28,29 The distributions of stresses and displacements will be obtained in the thickness of the thermal insulation system in Polypropylene PP material. The experimental details of the hydrostatic compression tests are presented by Bouchonneau et al.^1,2 A high-pressure vessel was used for the prototype testing. The pressure and water temperature were regulated and monitored inside the pressure tank. Figure 2(b) presents the 2D axisymmetric geometry and the constituent materials of the pipe structure type. The mesh used for the computation by finite elements is of triangular type.¹ The loading conditions are represented at the external borders of the structure for all the levels of external pressure (see Figure 2(d)).

Stress distribution

The quantification of the stresses is carried out in the pipe structure in order to evaluate the resistance of the materials in their elastic domain during the application of the external pressure.³⁰ The Von Mises criterion is used to identify the failure mechanisms of these materials.

Figure 4 shows the maximum stress distributions of Von Mises in the polypropylene (PP) coating system. The maximum Von Mises stresses are obtained for different levels of external pressure applied to the pipe structure. We can observe that for the pressure of 7 MPa, the maximum level of the Von Mises stress is 46,243 MPa, then for the pressure of 15 MPa, the maximum level is 99,914 MPa and finally for the pressure of 30 MPa this maximum is 197.05 MPa. Observations on the various Von Mises maximum stresses show that these are slightly above the breaking stress of the polypropylene material at low pressure (7 MPa) and are rather very high compared to the limit stress of this material for higher pressures (15 and 30 MPa). The response of the polypropylene material under the external pressure loading may involve a domain of plasticity just as in the case already observed on the polyethylene material¹⁵ and the steel material.²⁸ We can say that the presence of plastic deformations of the material can be more or less marked according to the level of external pressure.^1,3,6,8 Within the framework of a study of the viscoelastic and plastic properties of the primary epoxy and polyethylene materials, the influence of the coating thickness was observed during the manufacturing process of the passive protection system.¹⁵ This justifies in the context of this study the dependence of the response of the polypropylene material on the level of external pressure. The viscous properties of the polypropylene material are furthermore temperature sensitive.¹²

Figure 4.

Von Mises stress (MPa) distribution in the polypropylene system for the pressure of 7, 15 and 30 MPa.

Total displacement distribution

We can also observe the displacements in the three-layer polypropylene system. Figure 5 shows the maps of the deformities during the application of the different pressure levels on the polypropylene thermal protection system. We can then note for the pressure of 7 MPa a maximum displacement of 0.054 mm, then for the pressure of 15 MPa the maximum displacement is 0.1158 mm and finally for the pressure of 30 MPa this maximum displacement is 0.2521 mm. The calculations show that the viscous response of the material consists largely of a viscoelastic strain.²⁹ The results allow to note that the time-dependent response of the material can be sufficiently described under a low pressure level by a linear viscoelastic behavior model.^3,12

Figure 5.

Distributions of the total displacement (mm) in the polypropylene system for the pressure of 7, 15 and 30 MPa.

Comparison under hydrostatic pressure

We now compare the resistance of syntactic foam coating systems to those of polypropylene. A study had been carried out by Grosjean et al.⁶ on the influence of the hydrostatic pressure applied to the pipe structure coated with syntactic foam. The experiment details of the confined Compression test is found in Grosjean et al.⁶ A confined compression set-up allowed the application of a non-isotropic solicitation with a strain rate of $5 \times 10^{- 3}$ mm/min at room temperature. The results showed that the Von Mises stresses were not negligible when pressure loads are exerted in the thickness of the composite material. The stress tensor being a symmetrical tensor and therefore diagonalizable, we can thus obtain the main stresses in the two types of thermal insulation structures.

Figure 6 shows the different distributions of the main stresses in the thickness of the Glass Syntactic Polypropylene material. The results show higher inward Von Mises stresses. The Von Mises criterion is moreover based on the presence of deviatoric stresses. This will justify the damage of the Glass syntactic polypropylene material which seems to increase with the presence of these deviatoric stresses directed toward the assembly with the steel material.¹ The results of the numerical calculations carried out in this work show deviatoric stresses in the thickness of the syntactic foam admitting a non-isotropic pressure loading.^1,6 While these stress levels are lower in the thicknesses of polymer materials (see Figure 7). This difference in distribution is also due to the particular properties of the composite with respect to those of the polymers.^1,2,13,14 In literature, Grber et al.⁹ studied the buckling performance of thick composite cylinders loaded in compression. The results showed that the buckling failure would occurs before the strength failure under the hydrostatic pressure. The calculations carried out within the framework of this study (see Figures 6 and 7) show that the behavior of polymer structures can be modeled with the finite element calculation code and can also be extended to cyclic loading to include the fatigue of the constituent materials.²⁹ From the numerical modeling, we can see that damage could occur in the thickness of the syntactic foam under hydrostatic pressure as predicted by the literature.^6,9

Figure 6.

Stress repartitions in the GSPP thickness (GPa).

Figure 7.

Stress repartitions in the polypropylene thickness.

Time-dependent mechanical responses

Viscoelasticity of the polypropylene material

The analysis of the response of the polymer and the composite materials is carried out here under the uniaxial tensile stress. We consider the creep phenomena which will translate the application of a load in the thickness of materials during a rather significant period.³

Experimental studies of the assembly behavior were carried out by Cognard et al.³¹ The analysis therefore made it possible to improve the results with the Arcan-modified assembly.^32,33 Recently, a model was developed for an epoxy adhesive layer by the same experimental technique.¹⁷ This model is based on the Gaussian form spectral approach.¹⁷ Our objective is to develop a database for the analysis of the long-term behavior of a multilayer system using numerical analysis. This approach seems advantageous to us because the authors implemented the model in the finite element calculation code of the Comsol software. A few years ago, the use of the polypropylene material for the pipeline coating was recognized as a good candidate for a three-layer assembly due to its toughness in the marine environment.^26,27 This type of material still lends itself well to use as a coating in the multilayer system.¹² Under creep-type loading, the viscoelastic behavior of a polypropylene material can be modeled using two branches of the generalized Maxwell model presented in section (3.2).³ The installation phase always imposes axial stresses in the thicknesses of the pipeline structural materials. Until now, the numerical calculations of the stresses and strains generated by this type of loading have only concerned the steel tube.^4,5 Significant shifts in the thicknesses of the materials studied have been observed in the previous sections. Furthermore, a study in the quasi-static field carried out by Vestrum et al.^13,14 made it possible to note the contribution of the polymer coating in the overall resistance of the multilayer structure. A numerical simulation of this installation phase for very short-term creep phenomena under the different types of loading is necessary to predict the level of stress developed. This would in fact make it possible to predict damage and obtain the optimal performance of multilayer structures.³ Thus, to carry out the numerical calculations for such phenomena, we considered the characteristics of the materials of polypropylene and of polypropylene matrix syntactic foam already provided by Phan et al.³

The numerical simulation of the response of the assembly is carried out in time regime and for an elastic model chosen for the Glass Syntactic Polypopylene by considering the temperature level of 20°C and a force of 300 kN applied to the external borders. We can represent in 2D axisymmetric (see Figure 2(c)), the geometry of the assembly of the Glass Syntactic Polypropylene material from the inside to the outside with the solid polypropylene.^2,12,13 The viscoelastic parameter of the polypropylene materials are given in Table 3. It is thus possible to observe in Figure 8 the stress distributions of Von Mises and those of the total displacement in the thicknesses of the materials of the thermal insulation system for the applied force. The numerical calculations were carried out in the time-dependent framework and we can observe on the mapping the zones for levels of the maximum Von Mises stress in Figure 8(a) and of the maximum displacement in Figure 8(b). These areas of high stress concentration are found at the interfaces of polypropylene PP and Glass syntactic polypropylene materials. Once more the numerical calculations make it possible to observe the zones of high stresses in the interface part.³⁰ Interface areas are critical areas for the type of assembly under the axial tensile load applied in the thicknesses of the materials during the installation process. The modeling of a bonded assembly of polypropylene and syntactic foam was carried out in the study by Phan et al.³ to analyze the process of making a field-joint which is the zone made up of two sections of pipe. The results obtained during this study made it possible to observe the fracture envelope of this assembly of the two materials. The levels of displacements obtained by our numerical calculations are comparable to the levels of displacements admitted during the experimental characterization carried out by Phan et al.³

Table 3.

Viscoelastic parameters of the polypropylene material at different temperature.¹¹

Parameters	Values
E(GPa)	$- 0.0018 \times T^{3} + 0.363 \times T^{2}$
	$- 39.921 \times T + 1645.24$
$λ_{1}$	$6917 - 52.209 \times T$
$λ_{2}$	$124 - 0.374 \times T$
$μ_{1}$	$0.388 - 0.002 \times T$
$μ_{2}$	$0.393 - 0.002 \times T$
$μ_{0}$	$1 - μ_{1} - μ_{2}$

Figure 8.

(a) Von Mises stress repartition (MPa) and (b) distribution of the total displacement (mm).

Viscoelastic-viscoplastic behaviors of the GSPP

The mechanical behavior of polypropylene matrix syntactic foam has been studied in numerous works.^1,3,10 The linear viscoelasticity hypothesis of syntactic foam has been best presented in the work of Phan et al.^3,11 Indeed, the material describes a complex behavior including the constituents (matrix and hollow glass microspheres). We use the approaches of this viscoelasticity to resume the reversible part of the viscous deformation of the syntactic foam material. Table 4 provides us with the viscoelastic properties obtained during the characterization tests in uniaxial creep tension at different temperatures (T denotes temperature). In Figure 9, we can observe the results of the correlation of the simulation with the experiment of Phan et al.³ The response of the material in creep under uniaxial tension include other time-dependent phenomena related to the nature of the matrix. In order to validate the numerical modeling, time-dependent tests have been conducted on a block of syntactic foam. Usually, A 100 KN capacity load cell with a temperature control system depending on the loadings conditions allows to perform the Creep-recovery tests.¹⁸ The mechanical behavior of this material in creep consists of elastic, viscoelastic deformations.³ Hook’s law and the spectral models make it possible to predict the volumetric deformation of the material under the loading in hydrostatic compression.³ Within the framework of a cyclic loading, the model of Zapas-Crissmann will make it possible to describe the irreversibility of the strain in creep of the material under uniaxial tension. First, we consider that when the material is subjected to creep at a stress of 0.5 MPa, its total strain is then mostly reversible. We assume that the stress levels do not generate any damage to the material. Temperature dramatically alters the properties of the syntactic foam material.³ In order to take this effect into account, the temperature levels chosen are 25° and 80° for the situations of pipeline storage and transport of the fluid in the marine environment. Figure 9 shows the material response obtained at 25°C. During the cyclic loading, a stress of 0.5 MPa is applied on the polypropylene syntactic foam.³

Table 4.

Viscoelastic parameters of the GSPP material at different temperature.³

E(GPa)	−0.0118 × T + 1.4197
$ν$	0.32
$A_{v i s c}$	1.1504 × $10^{- 7}$ × T⁴ + 4.0976
n_c	0.0244 × T + 2.6643
n ₀	0.0360 × T + 1.7979
n_b	5
$ρ$	0.64

Figure 9.

Correlation between numerical simulation and experiment³ at 25°C.

The evolution of the applied load in the band of values generally admissible in the real context had not been addressed. The numerical calculations using the viscoelastic parameters of the material for another load allowed to conclude on the observation that the temperature could modify the mechanical behavior of the composite materials for each load as predicted by Hamel et al.³⁴

Figure 10(a) and (b) presents the evolutions of the reversible creep strains for the two temperatures considered. We thus show an influence of temperature on the creep strain of the composite material. This influence is noted by observing the significant difference between the two strains of the material at stresses of 0.5 MPa and 1 MPa. The results show an increase in the reversible strain which occurs with temperature for the same level of creep stress. The response of the material is sufficiently described here with the spectral model proposed by Phan et al.³

Figure 10.

Axial strain with temperature and time: (a) for $σ = 0.5 M P a$ , (b) for $σ = 1 M P a$ .

We are now interested in the contribution of the irreversible deformation of the material during the loading and unloading cycles. We consider the stress levels low. Through the experimental analysis and by noting the level of contribution of the residual part in the recovery phase, we can observe a part dependent on the stress and the time for the temperature of 25°C (see Figure 11).³ Figure 11(a) presents the evolution of the residual part with time through the Zapas-Crissmann model then its contribution to the axial creep strain.²¹ The stress level chosen here is 0.5MPa. The number of load cycles used in the creep-recovery tests is five. The applied load induces cracks in the matrix of the composite material without causing microspheres failure. This allows to neglect the effect of the latter in the residual deformation. Thus all the residual deformation during tensile creep becomes mainly viscoplastic deformation due to the irreversibility of the matrix. We observe that despite this evolution over time, the contribution of this residual part compared to the instantaneous part is negligible.²⁹ We show for this level of applied stress that the viscous part can be assimilated to the linear viscoelasticity of the matrix.³ Three longitudinal stress levels of 1.5, 2.5 and 3.5 MPa are chosen for the numerical simulation using the Table 4. We use Table 5 for a comparison with the additional residual strain. These longitudinal stress levels were chosen to determine the effect of residual strains in the viscous strain of the material. We can analyze and better define the residual part of the axial deformations (see Figure 11(b)). The contribution of the breakage of glass microspheres has been mentioned in the case of hydrostatic pressure loadings of 30 MPa in Phan et al.¹ This hydrostatic pressure level is however located below the collapse or crush pressure level of the material obtained experimentally at nearly 60 MPa.³

Figure 11.

(a) Residual strain evolution with time at 25°C. (b) Effect of residual strain on mechanical response by varying stress level at 25°C.

Table 5.

Viscoplastic parameters for the GSPP material.

Temperature (°C)	25
C	$2.3168 \times 10^{- 5}$
N	7
n	0.21

We then show the changes over time of the axial strain as a function of different longitudinal stresses applied in uniaxial traction in Figure 11(b). We can observe the differences in axial strain between the reversible and irreversible process which become much more significant with increasing stress. Under conditions of use in an offshore environment, the thermal insulation systems of the pipes will have an overall behavior depending on the weather, temperature and loading level. During their deformation mechanism, the response of the materials will involve their viscoelastic and viscoplastic character and mainly when the load is not initially damaging. Similar conclusions were retained in the studies carried out in the literature.^16,18,19 The use of the power-law offer a potential tool for predicting the time and stress of long-term creep rupture of the syntactic foam. The conclusion is the same as in Hamel et al.³⁴ So, the failure strain at multiple stress levels is observed and the tensile failure of the Glass Syntactic polypropylene foam is due to the stress level.

Conclusion

In this paper, we analyzed the mechanical behavior of polypropylene and syntactic foam materials for thermal insulation lining of offshore pipelines. We studied the effects of mechanical loadings applied to three-layer and five-layer systems under suspension conditions in offshore environments. Results showed a contribution of polymer and composite coatings in the overall strength of the structure when axial tensile forces are applied. Using Maxwell’s model, the results showed quite significant admissible displacements in material assemblies. A characterization of the syntactic foam showed the viscoelastic and viscoplastic behaviors. The residual part can be neglected at low stresses. This will require to consider the behavior of the material as linear viscoelastic. While for a rather significant contribution of this residual deformation, the temperature variation may allow a significant increase in the deformation of the syntactic foam material. Under this effect of temperature, the damage of a polypropylene matrix composite material occurs before its strength failure during cyclic loadings, highlighting the criticality of polymer-composite materials assemblies used in deep sea where polymers are used as adhesives. In perspective, an analysis of the assembly behavior with syntactic foam and polymeric materials should be performed to allow a more robust modeling of the thermal insulation material response under the conditions of mechanical loading and temperature.

Supplemental Material

Supplemental Material, sj-pdf-1-jtc-10.1177_08927057211051417 - Time-dependent response of thermoplastic matrix composite material under the cyclic loadings

Supplemental Material, sj-pdf-1-jtc-10.1177_08927057211051417 for Time-dependent response of thermoplastic matrix composite material under the cyclic loadings by Ismael Figapka Pagore, Guy Richard Kol and Jean Gambo Betchewe in Journal of Thermoplastic Composite Materials

Footnotes

Funding

The author(s) received no financial support for the research, authorship, and/or publication of this article.

ORCID iD

Ismael Figapka Pagore

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