ARTICLE IN PRESS. Property Modelling. Determination of the long-term hydrostatic strength of multilayer pipes. M. Farshad*

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1 Abstract Property Modelling Determination of the long-term hydrostatic strength of multilayer pipes M. Farshad* EMPA, Swiss Federal Laboratories for Materials Testing and Research, Überlandstrasse 129, CH-8600 Dübendorf, Switzerland Received 25 May 2005; accepted 6 July 2005 In this paper, a new methodology for prediction of the long-term (creep rupture) behavior of multilayer pipes under internal hydrostatic pressure is presented. For this purpose, a procedure using the three dimensional theory of thick-walled multilayer pipes together with a combined quadratic/linear regression analysis is used. The theory of thick walled tubes is used to assess the role of each layer in carrying the internal pressure and also the onset of the creep rupture in the composite pipe. For longterm extrapolation, a combined quadratic and linear regression analysis was used and the contribution of each component to the long-term strength of the composite pipe was quantitatively assessed. Using this procedure, the layer at which the creep rupture under internal pressure first initiates would be identified and the additional capacity of the remaining layer would be quantitatively assessed. This procedure is already incorporated in the pipe software called ADAP dealing with the automated design and analysis of pipelines. An example showing this procedure using ADAP is presented. The proposed methodology overcomes the limitations in the existing testing and extrapolation standards and, thus, can be used as a new extrapolative procedure for prediction of the service life of multilayer plastic pipes and pipe fittings. As particular applications, the procedure can be used for the estimation of the long-term behavior of multilayer pipes with metallic inter-layers and also single layer as well as structured pipes. q 2005 Published by Elsevier Ltd. Keywords: ADAP; Multilayer pipes; Long-term hydrostatic strength; Long-term extrapolation 1. Multilayer pipes Multilayer pipes are structural as well as functional fluid conveying elements, which are composed of two or more layers. The layers may consist of thermoplastic materials, fiber reinforced thermoset or thermoplastic resins, or metallic materials such as aluminum layers. The composite multilayer material combines the advantages of each of the constituent layer for the functional and structural requirements. Typical multilayer pipes consist of an internal polymer liner, a reinforcing and/or diffusion barrier layer, and an external protecting layer as scratch protection or Polymer Testing xx (xxxx) flame retardant. The single layers are normally tightly bonded to each other by a special adhesive layer. Table 1 shows the general function of the layers in various multilayer pipes and pipe fittings. Multilayer pipes and pipe fittings are used in a number of industrial applications including drinking water, heating engineering, compressed air supply, and chemical plant. Depending on application area, each layer plays a role on the function of the composite material. The salient features of composite multilayer pipes are lightness, lack of corrosion in the sense of metals, ease of connection, and low thermal expansion. Layers of multilayer pipes are normally bonded to each other. There are cases, however, where the layers may only be in mechanical contact with friction bonds. Design and construction of multilayer plastic pipes should take into account the behavior of each layer and the whole composite as a system. The functional objectives impose requirements on the design of these structural * Tel.: C ; fax; C address: mehdi.farshad@empa.ch /$ - see front matter q 2005 Published by Elsevier Ltd. doi: /j.polymertesting

2 2 M. Farshad / Polymer Testing xx (xxxx) Table 1 Multilayer pipes and pipe fittings Pipe and pipe fitting Internal layer(s) Middle layer(s) External layer(s) Applications Thermoplastic layers Medium compatibility, Structural layer Scratch layer abrasion resistance Thermoplastic layer (s) with metallic (e.g. Strength chemical resistance Diffusion barrier, oxygen tightness, stiffness. Scratch-resistant layer Pressure pipes (gas and water) aluminum) middle layer low thermal expansion Thermoplastic liner with Temperature resistance Strength Stiffness Warm water transport fiber reinforced outer layer Fiber reinforced layers Strength stiffness Shear core Strength stiffness Pressure pipe, sewerage pipe Existing pipe with internal liner Diffusion barrier, abrasion resistance elements. However, in all cases, the long-term behavior of such systems constitutes one of the major concerns in the design and the service life. In the case of pressure pipes, the long-term hydrostatic strength under prescribed temperature and loading is one of the main requirements, which should be fulfilled. Table 2 gives a summary of the potential failure modes of multilayer pipes. 2. Methods for long-term extrapolation of plastic pipes According to the existing design procedures, the internal hydrostatic pressure creep rupture tests and their extrapolation to 50 years of the pipe service life is considered as one of the main design and evaluation criteria. The present guidelines for the design of plastic pipes use the short term and long-term stresses in the pipe and apply a safety factor to the long-term hoop stress under internal hydrostatic pressure. Obviously, the long-term behavior of plastic pipes and their service life is dependent on several factors including material, loading, temperature, medium, and service conditions. In order to determine the long-term behavior and to estimate the service lifetime of plastic pipes, internal hydrostatic pressure creep rupture tests are performed. The creep rupture tests are normally carried out up to about 10, Table 2 Potential failure modes of multilayer pipes Structural layer (strength, stiffness) Pipe relining 000 h at various temperatures [1]. In such experiments, a typical pipe sample is subjected to a prescribed internal pressure, which is kept constant in time until the creep rupture of the sample occurs. Hence, so-called creep rupture data has the time as one coordinate and the internal pressure as another coordinate. The creep rupture test data are then extrapolated to much longer periods of pipe service life. The available schemes use the membrane theory of thin cylindrical shells to calculate the membrane hoop stresses and linear regression analysis for long-term extrapolation. One of the methods for the regression analysis of the thin walled single layer thermoplastic pipes (polyolefins and PVC) is referred to as the Standard Extrapolation Method (SEM). This method has been described in an international standard [2]. An automated version of this procedure is also available as computer software [3]. The existing methods for the long-term extrapolation of plastic pipes are mainly developed for single layer thin walled pipes either of thermoplastic or fiber reinforced materials [2 4]. These methods cannot be applied to the case of multilayer thick walled plastic pipes made of thermoplastic and fiber reinforced layers. The implicit physical assumptions defining the validity of this methodology are: (1) Pipe is made of a single layer homogeneous thermoplastic material. Pipe and/or pipe fitting Internal pressure High temperature External forces Thermoplastic layers Burst Thermoplastic layer(s) with metallic middle layer Burst of the outer and middle layer Buckling and debonding of the internal liner Buckling and debonding of the internal liner Thermoplastic liner with fiber Burst of the outer layer Buckling and debonding of the Debonding of the liner reinforced outer layer internal liner Fiber reinforced layers Burst Buckling, crushing Existing pipe with internal liner Burst of the outer pipe Buckling and debonding of the liner Buckling and debonding of the liner

3 M. Farshad / Polymer Testing xx (xxxx) (2) Pipe is thin-walled, hence the membrane theory of thin walled tubes is used to calculate the hoop stresses in the pipe wall. (3) The regression analysis is applicable. As far as the long-term behavior of multilayer pipes is concerned, a descriptive guideline is available [4]. This guideline uses the procedure in reference [3] and offers procedure of its own. Hence, in addition to deviation of the multilayer pipe from the validity range of [2] due to its layered anisotropy, the possibility of using metallic layers or other materials other than the thermoplastic sheds some doubt on the validity of the existing extrapolation scheme. Hence, the assumptions and limitations in the long-term extrapolation associated with [2,3] still apply. The additional assumptions and limitations in [4] are: (4) Multilayer pipe is composed of thermoplastic layers. (5) No quantitative procedure is suggested for the longterm extrapolation of the layers based on behavior of the composite element. It should be pointed out that, for multilayer pipes, the average hoop stress calculated with the help of the membrane theory of thin walled tubes would not be meaningful and would not address the above question. Instead, using the theory of the multilayer thick wall tubes the hoop stress in each layer should be calculated. An attempt was made to enhance the domain of validity of the existing standards to deal with the long-term behavior of fiber-reinforced pipes in water [5] and in the acid environments [6]. Hence, a new methodology is needed that takes into account the effect of wall thickness, interface pressure, and the difference in the material type. 3. Description of long-term behavior of multilayer pipes A multilayer pipe under constant internal hydrostatic pressure at a specified temperature would fail at a certain period called the creep rupture time. The collection of points having time to failure as the abscissa and the internal pressure as the ordinate constitutes a point in the creep rupture data space. The main question raised is the identification of the layer at which the rupture would initiate. Fig. 1 shows a qualitative classification of the failure modes for a two-layer thermoplastic pipe under internal hydrostatic pressure at room temperature. The set of star-shaped points symbolize the experimental data obtained from the long-term internal hydrostatic pressure test on the composite multilayer pipe. The solid lines depict the calculated hoop stresses in the composite pipe and the dotted lines show the long-term hydrostatic curves of the individual layers. The double lines relate to the external layer, while the single lines belong to the internal layer. The temporal sequence of failure of composite pipe depicted in the set of Fig. 1 may be classified into four categories: (1) Failure of the internal layer. (2) Failure of the external layer. (3) Simultaneous failure of the external and the internal layer. (4) Failure of the whole system. The dotted lines in Fig. 1 provide reference resistance curves for the material failure of the internal and external layers individually subjected to internal hydrostatic pressure. These reference curves can be substituted by a collection of creep rupture data points obtained from the internal hydrostatic pressure tests on the single layer constituting components. The full lines show the share of each layer of the composite pipe in carrying the internal pressure. They represent the calculated hoop stress in each layer caused by the internal pressure based on the share of the internal pressure for that layer. The trend curves shown in the set of Fig. 1 may be interpreted as follows: the case of a reference curve (or data points) lying above the calculated stress for the composite pipe means that the layer is under-stressed and has not yet reached its limiting strength. Consequently, it would be expected that the failure of the composite system would not be expected to initiate in that layer. Conversely, the case of the reference curve (or data points) lying below the calculated stress for the composite pipe means that the layer is over-stressed and has reached its limiting strength. Consequently, it would be expected that the failure of the composite system would be expected to initiate in that layer. Thus, the case shown in Fig. 1(a) implies that the failure is expected to initiate in the external layer, while the case in Fig. 2(b) implies the initiation of the failure in the internal layer. In Fig. 1(c) both of the reference resistance curves are located below the calculated stress in multilayer pipe due to hydrostatic pressure. Hence, it is concluded that the failure of the composite pipe takes place simultaneously in the external and the internal layer. Fig. 1(d) shows the case in which both of the calculated trend curves of failure of multilayer pipe fall above the curved related to each of the constituting layers. In spite of this, the failure of composite system could have happened, which may be attributed to system defects, i.e. parameters, which are not explainable by individual layers. Whether or not such a case would occur in the experiments cannot be verified by this general qualitative explanation. The qualitative explanation represented by Fig. 1(a) (d) was carried out for the rupture behavior of a two-layer thermoplastic pipe. This explanation can be extended to the case of multilayer pipes composed of more than two layers. It should also remain valid for the cases in which one of the layers is metallic; in which case the reference rupture curve for the layer is time-independent and would remain horizontal

4 4 M. Farshad / Polymer Testing xx (xxxx) Hoop stress [MPa] Hoop stress [MPa] Time to failure (a): Failure of the external layer Time to failure (c): Failure of theexternal and the internal layer The explanation offered here should hold for the rupture of multilayer pipes at room temperature. Under such condition, no thermal aging is expected to occur. Hence, the regression curves should not have a knee. For high temperatures, or for the cases in which a knee is to be expected, the explanations should be valid for the pre-knee zone. The qualitative explanation of failure cases would become more involved if the curves cross each other. For example, a modification of the case shown in Fig. 1(a) would be crossing of the lower two curves. Such case would represent failure initiation at the external layer for higher stress (pressure) levels and failure at the external and the internal layers for the lower stress (pressure) levels. Theoretically, a large number of such variations would be imaginable. However, in a specific case, the basic explanation offered through the simple cases presented in Fig. 1(a) (d) can be quite helpful. Hoop stress [MPa] Hoop stress [MPa] Designations: Calculated rupture curve for internal layer Experimental rupture curve for internal layer alone Calculated rupture curve for external layer Experimental rupture curve for external layer alone Processed experimental data points for composite pipe as a single layer isotropic pipe with mean radius and mean wall thickness of composite pipe Time to failure (b): Failure of the internal layer Time to failure (d): System failure Fig. 1. Schematics of the creep rupture of multilayer pipes under internal pressure. 4. Proposed methodology The methodology proposed in this paper aims at the long-term extrapolation of multilayer plastic pipes made of thermoplastics or fiber reinforced layers and also pipes with metallic layers. The steps to be followed in this procedure are: Fig. 2. Two-layer composite pipe

5 M. Farshad / Polymer Testing xx (xxxx) (1) Performance of long-term internal hydrostatic pressure tests (normally up to about 10,000 h) on the composite pipe samples at the specified temperature. In case the reliable creep rupture data are available, they may be used for extrapolations. (2) Use of the theory of thick walled multilayer tubes to find the interface pressure and the maximum hoop stress in each layer (3) Use of combined linear and quadratic regression analysis to find the best fit to the experimental data. The regression analysis should be performed for each layer using the time to failure of composite pipe as the independent variable and the calculated hoop stresses for each layer as the dependent variables. 5. Theoretical basis for long-term extrapolation To process the experimental data, the following theoretical numerical modeling was used. (1) The theory of thick walled composite tubes was used to find the interface pressure between two consecutive layers due to the internal pressure. Consequently, the effective internal hydrostatic pressure applied to each layer was obtained. (2) The theory of thick walled tubes was used to calculate the stresses in each layer and also the inter-laminar shear stresses. (3) Using the creep rupture data points for the composite pipe, the collection of potential rupture points associated with each layer was determined. (4) Combined linear and quadratic regression analysis, based on the method of least squares, was applied to each set of data points and the regression curve for each layer was obtained. (5) In cases in which the creep rupture curves or data points for individual layer are available, a superposition of such data on the above mentioned diagram may also be made. 6. Calculation of interface pressure and hoop stresses Consider a two-layer pipe made of two bonded layers under internal hydrostatic pressure, p i (Fig. 2). The internal radius of the internal layer is designated by a, the internal radius of the external layer by b, and the external radius of the external layer is designated by c. The material of each layer is assumed to be linearly elastic and isotropic. The elasticity material parameters of the internal and the external layer are designated by E i, n i and E o, n o, respectively. Due the action of the internal pressure p i, interaction of the two layers an interface radial stress p f is produced. Using the classical elasticity theory of multilayer thick-walled cylinders, the interface pressure can be obtained by the following relation 2p i p f Z n h io (1) E i ðr 2 i K1Þ 1 R 2 i C1 E i R 2 i K1 Kn i C 1 R 2 oc1 E o R 2 ok1 Cn o where R i Zb/a, and R o Zc/b, in respective fashion, designate the ratios of the radii of the internal and the external layers, respectively. The hoop stresses in the internal and the external layers can be obtained by the following relations s hi Z p i ðr 2 i K1Þ 1 C b2 r 2 K p fr 2 o R 2 i K1 1 C a2 r 2 (2) and s ho Z p f ðr 2 1 C c2 ok1þ r 2 (3) wherein, r designates the radial coordinate of the points on the pipe wall thickness. These relations shall be used to calculate the hoop stresses in each layer of the multilayer pipe under long-term hydrostatic pressure. Setting rza in relation (2) and rzb in relation (3) would give the maximum hoop stress in the internal and the external layers, respectively. 7. Long-term extrapolation with software ADAP Program ADAP (automated design and analysis of pipes) is a means for structural analysis, design, assessment, residual analysis, and long-term extrapolation of pipelines. The computational procedure of ADAP is based on the analytical and parametric modeling of pipelines (see references [7 10]). The procedure outlined in previous sections has already been implemented in the pipe software ADAP. With program ADAP (Version 2) the long-term extrapolation of single-layer pipes, multilayer pipes, and pipes with structured wall thickness under internal hydrostatic pressure can be carried out. This is done with an innovative hybrid linear and quadratic order regression analysis. For regression analysis, one can specify up to 60 data points. For multilayer pipes, using the thick-walled tubes theory, the interface pressure at each layer is calculated and the hoop stress at each layer corresponding to the interface pressure is determined. The regression analysis based on linear and quadratic models is carried out and the smaller of the two regression values is chosen for the graphs of the regression curves. Using this procedure, instead of a sharp knee for the long-term internal hydrostatic strength

6 6 M. Farshad / Polymer Testing xx (xxxx) diagrams for thermoplastics materials at higher temperatures a relatively smooth change of curvature is obtained. 8. Example of long-term extrapolation with ADAP To demonstrate the proposed procedure, a case study dealing with a three-layer pipe at 40 8C was extrapolated with ADAP. The inner and the outer layers were thermoplastic material of polyolefin basis and the middle layer was a metallic material. Table 3 shows the assumed average geometrical dimensions and the short-term elasticity modules of the constituting layers. For the purpose of a comparative numerical study, a fictitious set of hydrostatic internal pressure data was assumed. 9. Results Tables 4 and 5 summarize the regression analysis performed with the software ADAP. Table 4 shows the regression hoop stresses in the individual layers. Table 5 shows the regression results for the effective internal pressure on individual layers and on the whole composite (multilayer) system. Figs. 3 and 4 show the result of long-term extrapolation of experimental data related to the internal hydrostatic pressure tests with the computer software ADAP. These two figures contain useful information, which deserves an appropriate interpretation: (1) In interpreting the extrapolation output data from ADAP an important point should be mentioned. The regression results are not the resistance curves, rather they show the temporal variation of the stresses and effective pressure. In other words, these curves and the corresponding data points represent the state of stress Table 3 Assumed properties for the three-layer multilayer pipe Property Inner layer Middle Outer layer layer Internal radius (mm) External radius (mm) Thickness (mm) Short-term elasticity , modulus (MPa) Short-term Poisson ratio ( ) Long-term elasticity , modulus (MPa) Long-term Poisson ratio ( ) Table 4 Output from ADAP; stresses in each layer Result of regression analysis Temperature: 40 8C Number of data points: 30 Time (h) Long-term hoop stress (MPa) Inner layer Middle layer Quter layer , , , and the state of internal pressure as functions of time. To assess the strength of a multilayer pipe, these regressive predictions should be compared with the resistance values of individual layer materials as shown in Fig. 1. For instance, in the present example, the middle layer was assumed to be metallic with specified strength, which would remain constant in time. Hence, the resistance curve of this layer would be represented by a horizontal line. This strength value would either lie over or under the stress or pressure curve related to this layer. (2) Fig. 3 shows the result of long-term extrapolation for the hydrostatic strength of individual layers in the multilayer pipe. It shows the hoop stress as a function of time on a double logarithmic scale. The solid lines show the long-term curves of hydrostatic strength. The corresponding calculated experimental data related to each of the two layers are also shown in the Fig. 3. (3) In Fig. 3, the long-term extrapolation curve related to the middle metallic layer does not have any knee, while the curves related to the inner and the outer thermoplastic layers show a knee, i.e. a transition zone at higher temperature. Table 5 Output from ADAP; effective internal pressure on each layer and on the multilayer (composite) pipe Result of regression analysis Temperature: 40 8C Number of data points: 30 Time (h) Hydrostatic pressure (MPa) Inner layer Middle Outer Composite layer layer , , ,

7 M. Farshad / Polymer Testing xx (xxxx) Stress [MPa] 100,00 10,00 1,00 0, ,10 Sate of stress- inner layer Sate of stress-middle layer State of stress: outer layer (4) Fig. 4 shows the long-term internal pressure resistance as a function of time on a double logarithmic scale. This extrapolation of experimental data with ADAP predicts a two-part pressure Time [h] Regression stress- inner layer Regression stress- middleayer Regression stress: outer layer Fig. 3. Results of the long-term extrapolation with ADAP. The vertical axis is the hoop stress in the individual layer and the horizontal axis is the time to failure. Internal pressure [MPa] resistance curve with a transition zone. The transition phenomenon observed in this curve arises from the influence of the inner and the outer thermoplastic layers Experimental internal pressure: multilayer pipe Regression internal pressure: inner layer Regression internal pressure: middlelayer Regression internal pressure: multilayer pipe Regression internal pressure: outer layer Time [h] Fig. 4. Results of the long-term extrapolation with ADAP. The vertical axis is the internal pressure at failure of the composite pipe and the horizontal axis is the time to failure

8 8 M. Farshad / Polymer Testing xx (xxxx) Discussion and conclusions In this contribution, a new method for the long-term extrapolation of the internal hydrostatic pressure test data is proposed. For this purpose, the theory of thick-walled tubes was used and the long-term effect of internal pressure on each layer was investigated. For correlation of experimental data, the software ADAP was used. This software had a combined linear and quadratic regression analysis as the basis. For certain thermoplastic materials at higher temperatures, the existing long-term extrapolation routines based on ISO 9080 [2,3] predict a potential knee in the internal hydrostatic pressure diagrams. In comparison, the software ADAP produces a transition curve and not a sharp knee. For example, according to Fig. 4, a transition curve is obtained for the inner layer of the two-layer pipe at 90 8C. No knee is observed for the outer layer. This result is plausible since for the thermoplastic inner layer the occurrence of a transition zone corresponding to a knee is possible, while for the fiber reinforced external layer no such behavior is to be expected. The question as to the initiation of the failure event can be clearly answered by comparing the data points for the composite pipe with the material data for each layer. One of the useful features of the proposed methodology is that the contribution of each layer to the service life of the composite system can be quantitatively estimated. Through such estimation, the failure stresses and the time to failure of individual layers can be obtained. The comparison of the values of different layers makes it possible to evaluate the contribution of the layers and to optimize the design of composite pipe for a more efficient service life. The proposed methodology overcomes the limitations in the existing testing and extrapolation standards and, thus, can be used as a new extrapolative procedure for prediction of the service life of multilayer plastic pipes and pipe fittings. As particular applications, the procedure can be used for the estimation of the long-term behavior of multilayer pipes with metallic inter-layers and also single layer as well as structured pipes. References [1] M. Farshad, Two new criteria for the service life production of plastics pipes, Polymer Testing 23 (2004) [2] pren ISO 1167: Thermoplastics pipes for the conveyance of fluids Resistance to internal pressure Test method (2003). [3] ISO 9080: Plastic piping and ducting systems Determination of the long-term hydrostatic strength of thermoplastics materials in pipe form by extrapolation (2003). [4] ISO/DIS (2003): Plastics piping systems Multilayer pipes Determination of the long-term hydrostatic strength (2003). [5] A. Necola, M. Farshad, Effect of aqueous environment on the long-term behavior of glass fiber-reinforced plastics pipes, Polymer Testing 23 (2) (2004) [6] M. Farshad, A. Necola, Strain corrosion of glass fiberreinforced plastics pipes, Polymer Testing 123 (5) (2004) [7] M. Farshad, ADAP: neues rechenprogramm für die dimensionierung und statische analyse von Rohrleitungen, gwa Nr. 4 (2002) S. 241 S [8] M. Farshad, ADAP: a new software for automated design and structural analysis of plastic pipelines, Journal of Thermoplastic Composite Materials 16 (2003) [9] M. Farshad, ADAP- A Software for Automated Design and Structural Analysis of Plastics Pipelines (Poster Paper), Plastics Pipes XII, Milano, [10] M. Farshad, Rohrberechnungsprogramm-Neue Version des ADAP, gwa 12 (2004)