1 Abstract
High density polyethylene has been widely used in marine and gas transportation, storm sewers, culverts and city drainage system. Compared with other conventional pipes, it has its own advantages, such as, chemical and corrosion resistance, toughness, flexibility, easy splicing and consequent easy handling and installation. In this paper, and in order to predict the remaining lifetime of a pipe having a defect and subjected to internal pressure, it is necessary to estimate KI stress intensity factor during the propagation of the crack. The finite element method is used to assess the values of the stress intensity factor of an axially oriented semi-elliptical crack located at the inner surface of an HDPE pipe. The crack configuration is described by the relative wall thickness (t/R), the relative crack depth (a/t) and the crack aspect ratio (a/c). The lifetimes presented are discussed according to the size of the crack and the stress intensity factor in each case.
Keys words: HDPE Pipe, Crack, Rupture, Finite Element Method FEM, Stress Intensity Factor, Lifetime.
1. Introduction
High density polyethylene (HDPE) is a thermoplastic material commonly used for piping structures. There are two modes of failure of a pipeline system: (i) is the rapid crack propagation (RCP) that could affect a significant length of the pipeline, and (ii) is the fragile failure of the system due to slow growth of cracks (SCG) initiated by a pre-existing defect in the pipe causing fragile fracture locally. These two failure modes depend on the age of the structure, service environment and operating conditions [1]. In pressurized plastic pipe applications, a majority of fractures are attributed to slow crack growth (SCG).It is a brittle fracture which is characterized by stable growth with few macroscopic plastic deformations [2].The main technical issues surrounding the use of HDPE pipe including premature failure due to SCG were identified as follows: (i) Effect of high temperature, (ii) Effect of permissible defect size (10% the thickness of the wall), (iii) safety factor in the design, (iii) the analytical models for the long-term lifetime prediction [3].In service, the service life typically required in water and natural gas distribution systems covers up to 50 years and more. It is clear that pressure pipe applications require polymers with a very long service life.
However, the problem lies in the development of adequate tests that are able to simulate the mechanism taking place and estimate the lifetime in a relatively short time [4].In the various models and tests, the high temperature is used as an acceleration factor in short-term tests based on the Time Temperature Superposition Principle (TTSP) principle. The models currently available for the prediction of service life of PE pipes can be divided into three
Estimated life time in an HDPE pipe with a semi-elliptical defect under internal pressure.
L. Alimi1,2, K. Chaoui2, M. Hassani1, A. Azzi1
1Centre de Recherche en Technologies Industrielles (CRTI) BP 64, Route de Dely Brahim, Chéraga 16014 Alger – Algérie, L.alimi@crti.dz
2Mechanics of Materials and Plant Maintenance Research Laboratory (LR3MI), Mechanical Eng. Dept., BadjiMokhtar University, PO Box 12, Annaba 23000, Algeria,latifaalimi@yahoo.fr
2 groups: (1) The Rate Process Method or RPM, (2) The Bi-Directional Shift Approach, and (3) Methods of the Fracture Mechanics. In the latter category, there are several approaches: "The Pent Service Life Correlation" and "Integration of Time to Flaw Initiation and Growth to Failure" [5].The fracture mechanics is a good example to approach the life of HDPE pipes. Its main objective is to study the severity of defects at the macroscopic scale requiring the determination of stress fields and deformations in the vicinity of the crack. Several studies have been developed to understand and explain the phenomenon of breaking structures with defects. The problem remains difficult because in linear fracture mechanics theory, the stress and deformation levels tend towards infinity by approaching the crack tip [6].
This paper discusses some prediction models of life based on the fracture mechanics. These approaches involve the critical stress intensity factor (KIC) or KI followed by a description of a critical applied stress. The stress intensity factor is calculated according to the size of the crack in three different cases. Mathematical models describing the propagation of the fissure are then used to estimate the residual life of a polyethylene pipe subjected to internal pressure.
2. Finite element modeling
The crack structure shown in Figure 1 is designated here by some non-dimensional parameters, specifically, the relative wall thickness (t/R), the relative crack depth (a/t), the crack aspect ratio (a/c). The code ANSYS with interface Workbench is employed here to simulate the cracked pipe. The proposed code permits the operator to get automatically the variations of stress intensity factor along the crack front for a given set of non-dimensional parameters. It precedes with the materials properties and the geometric parameters of pipe and the applied loads, here the pressure of the transported liquid, and then generates a finite element model of the pressurized pipe with a 3D semi-elliptical crack. In our simulation, the tetrahedral elements are used to discretize the mesh of the entire structure with a refined mesh used exclusively in the singularity zone, i.e. of around the crack. The symmetry conditions in the longitudinal direction were exploited to decrease the computational time. Primary, a half of the pipe was modeled then analyzed. As stated earlier, the crack front should be confined by singular elements, therefore a minor size called tunnel including the singular elements were designed round the crack front. (Fig. 2)
Figure 1 Scheme inner surface of the pipe with a semi-elliptical crack dimensions (a, 2c).
3 Figure 2 Finite element model of the tube with crack.
3. Stress intensity factor calculation
The stress intensity factor (SIF) is one of the main parameters in fracture mechanics. Brittle fracture in cracked engineering parts is generally inspected by SIF. The stress intensity factor is also essential for analyzing ductile fracture which is a more common mode of failure in pipelines. Once the crack is identified in a structure, SIF can be calculated by numerous experimental or theoretical approaches such as finite element analysis. When SIF is known, the possibility of brittle or ductile fracture can be assessed with a suitable fracture criterion [7].The numerical calculation by EF, based on modeling of the cylindrical structure. Here only half of the pipe is used. In the elastic domain, the stress intensity factor in mode I KI in a system of local coordinates fixed to the front of a crack is given by Equation 1 with r the radius of the crack and σ the stress applied:
𝐾𝐼 = lim
𝑟 0 2𝜋𝑟 . 𝜎 (1) 4. Results and discussions
A comparison of the stress intensity factor KI as a function of the normalized length of the crack (a/t) is illustrated in Figure 3.We used the simulation to show the influence of the size of the crack within the pipe studied on the stress intensity factor. Three fault values were chosen, the first two based on the work of A. Frank, assuming that the size of the crack or the permissible defect present in a tube is in the range 100 and 400μm [8]. For the third defect, we took a ratio (a/t = 10%) as cited in the work of [6]. We note that the stress intensity factor
4 0
0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9 1
0 2 4 6 8 10
Stress intensity factor KI, (MPa.m0,5)
a/t(-) ainit=0,1mm
ainit=0,4mm ainit=1,14mm
increases with increasing crack size, and becomes critical when the crack propagates more in the pipe wall.
Figure 3 Comparison of stress intensity factor in a pipe with a
internal semi-elliptical crack under pressure excerpted from the numerical simulation EF.
After calculating the stress intensity factor in mode I given by the simulation, it remains to calculate the residual life of the pipe using the formula proposed by [9].This suggests that the time a crack needs to grow and spread in a structure can be calculated by transforming Equation 2 in Equation 3.The total time for the rupture of the pipe consists of the sum of the time of the crack initiation tinit and the crack growth time tSCG (Equation 4) [10].
𝑑𝑎
𝑑𝑡 = 𝐴𝐾𝐼𝑚(2)
𝑡𝑆𝐶𝐺 = 1 𝐴
1 𝐾𝐼𝑚
𝑎𝑓
𝑎𝑖𝑛𝑖𝑡
𝑑𝑎(3)
𝑡𝑓 = 𝑡𝑡𝑜𝑡~𝑡𝑖𝑛𝑖𝑡 + 𝑡𝑆𝐶𝐺(4)
After integration of the Equation 2, we obtain the general shape of calculating the service life to rupture of a pressure HDPE pipe as shown in equation 5, according to [11]:
m init m minit tot
f a
Y m t A
t
t
2 /2
2
2 (5)
A and m are parameters of the material as explained in [12].For the prediction of pipe life, we assume that the crack initiation time tinit is neglected and that slow crack growth occurs
5 immediately after the pipe is loaded or pressurized. This assumption is taken with caution because the studies on time initiation of crack HDPE are not yet established. The results obtained are shown in Table 1, which gives the time of rupture of a pipe exposed to a stress equal to 2.192MPa and working at an operating temperature of 23°C.For a defect of 0.1mm, we found that the fracture time tf which is the time required for propagation of the crack (tSCG) is very large (about 363 years or 3.18x106 hours), and that the crack can take a lot more time to propagate in the wall of the pipe by comparing it with the other defects studied (ainit: 0.4mm and 1.14mm).Under the present conditions presented (σ, T°C), the estimated lifetimes in the three cases treated are in good agreement with the recommendations dictated by the MRS classification and which have a minimum lifetime of 50 years(MRS : Minimum Required Strength).
Table 1Failure time in an HDPE pipe 80, σ: 2.192MPa (4bar), T: 23°C Crach size (mm) Failure time (years)
ainit=0.1 tf=363 (>106hours) ainit=0.4 tf=176 (>106hours) ainit=1.14 tf=89(>105hours)
5. Conclusion
The fracture mechanics is a good example to approach the life of HDPE pipes. Its main objective is to study the gravity of the defects on the macroscopic scale requiring the determination of the stress and deformation fields in the vicinity of the crack. This study made it possible to evaluate the residual lifetime of an internal pressure pipe on the basis of the relation da/dt=AKIm.
A finite element model of a pipe with an initial defect was suggested in order to calculate the stress intensity factor. A comparison of the stress intensity factor KI as a function of the normalized length of the crack (a/t) was established. We note that the stress intensity factor increases with increasing crack size, and becomes critical when the crack propagates more in the pipe wall.
For predicting the lifetime of the pipe, assuming that the crack initiation time tinit is neglected and that the SCG occurs immediately after the pipe is loaded or pressurized. Under the present conditions presented (σ, T°C), the estimated lifetimes in the three cases treated are in good agreement with the recommendations dictated by the MRS classification and which have a minimum lifetime of 50 years (MRS : Minimum Required Strength).
References
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