Profiled polymer pipes as re-usable energy absorption elements

*Corresponding author.

International Journal of Mechanical Sciences 41 (1999) 1385}1400

Pro"led polymer pipes as re-usable energy absorption elements

H. El-Sobky!,*, A. A. Singace"!Mechanical Engineering Department, UMIST, P. O. Box 88, Manchester M60 1QD, UK

"Mechanical Engineering Department, University of Bahrain, P. O. Box 32038, Manama-Bahrain

Received 28 July 1997; received in revised form 21 July 1998

Abstract

The deformation of double-skin pro"led polyethylene pipes under axial and lateral load is studied. Theload}displacement relationship and speci"c energy of such pipes were measured under single and repeatedloading. The e!ect of repeating load was observed and discussed. The results show that the visco-elasticnature of the material as well as the periodic axisymmetric pro"le of the outer skin make this type of pipesa good candidate for re-usable energy absorption devices. ( 1999 Elsevier Science Ltd. All rights reserved.

1. Background

There exists a wealth of literature on the energy absorption characteristics of hollow and "lledtubular devices of various shapes and materials. The e!ects of material properties, "lling medium,geometry and loading speeds have been extensively studied [1}11]. Most of these elements rely onplastic deformation to dissipate energy and are used in the design of systems which are intended fora single performance of their function as energy absorption devices. Examples include crashbarriers, collapsible steering columns as well as some structural elements and car body panels. Withthe exception of systems which include hydraulic elements, e.g. vehicle suspension system, little isreported on re-useable devices exhibiting full or partial recovery after initial deformation.

In a recent publication by Carney et al. [12], the energy absorption performance of polymerpipes was investigated by full-scale lateral tests and computational modelling. However, nothingwas reported on the characteristics of these pipes under hysteresis and repeated lateral or axialloading.

In a previous study [13], the authors investigated the behaviour of pre-formed metallic tubesunder axial loading. These were tubes with pre-formed axisymmetric corrugations, the purpose ofwhich was to force the formation of rings of plastic hinges at the corrugation and force the

0020-7403/99/$ - see front matter ( 1999 Elsevier Science Ltd. All rights reserved.PII: S 0 0 2 0 - 7 4 0 3 ( 9 8 ) 0 0 0 8 7 - 3

Fig. 1. (a) Geometry and axial loading position for the pro"led pipe. (b) Geometric collapse progress of a typicalconvolution of a double skin pipe subjected to axial crushing load. (c) Proposed material model for the double skin pipe.

deformation to occur in concertina mode at pre-determined intervals along the tube generator.This increases the overall energy absorption e$ciency of a tubular element. One of the earlypractical tests on pro"led tubes was reported by White et al. [14]. The favourable characteristics,found in corrugated tube used as crash attenuator, was quoted by Carney [15] some years later.The subject of this study is a thermoplastic double-skin pipe, the outer skin has axisymmetricconvolutions with a square wave-like cross-section and is perfectly bonded to the inner skin(Fig. 1). The material in this case is medium density polyethylene (MDPE).

The behaviour of the double-skin pipes is similar to that of the corrugated tubes [13]. Thedeformation locations are pre-determined and will occur within the square convolutions of theouter skin, where wall thickness and the second moment of area are minimum.

The shape of a typical ring abcd (Fig. 1b), implies that the structure will collapse along the lengthad and will occur where the section has minimum second moment of area, provided that ad doesnot exceed the minimum fold length [16]. In the case of metals, the material is elastic}plastic withor without work hardening. The elastic deformation is very small compared with the plasticdeformation and is disregarded in most cases. In any case, the elastic and plastic deformations takeplace successively, whereas in visco-elastic material, the two behaviours are exhibited simulta-neously.

A Voigt model, or the generalized Voigt model with a spring attached to it in series, can be usedto illustrate this kind of behaviour. It is this feature of simultaneous contribution of a viscousdissipation of energy and an elastic storage of energy of comparable order of magnitude, whichmakes thermoplastics a candidate material for re-usable energy absorption devices. Furthermore,the recovery of thermoplastic is partially instantaneous (element E in Fig. 1c) and partially

1386 H. El-Sobky, A.A. Singace / International Journal of Mechanical Sciences 41 (1999) 1385}1400

Fig. 1. (Continued)

a function of time (element k in Fig. 1c). Further analysis of the generalized behaviour of suchmechanical models can be found in Ref. [17].

As the deformation continues, Fig. 1b, point a moves towards point d, and eventually a plastichinge will form at point m, somewhere between a and d while the outer skin abcd acts as a spring, ina fashion similar to the expansion bellows, with possible visco-elastic deformation in the regions ofpoints b and c. Plastic hinges are expected to occur at points a, b, c and d as the fold at m progresses.

Upon removal of the load, the residual elastic deformations in the regions ab, bc and cd will causean instantaneous partial recovery. In addition, long-term recovery will occur in the regions ofplastic hinges due to the visco-elastic nature of the material.

The Voigt model is used arbitrarily to illustrate the general concept of visco-elastic energydissipation recovery and subsequent re-usability. In fact, any other appropriate visco-elastic model

H. El-Sobky, A.A. Singace / International Journal of Mechanical Sciences 41 (1999) 1385}1400 1387

can be used following the same procedure described below. However, it is di$cult in general todetermine real material properties which would correspond to those used in visco-elastic models.More realistic constitutive equations, the constants of which can be determined experimentally, canbe used to carry out the calculations to predict the behaviour of real materials.

With reference to Fig. 1c, the material is represented by the viscous element with coe$cient k andthe elastic constant E connected in parallel. This is known as the Voigt model, which is capable ofdescribing the material behaviour under constant stress rate, constant strain rate, relaxation andrecovery. It can be shown that the stress and strain and their derivative are related by Eq. (1).

p"Ee#keR , (1)

where p is the stress, e is the strain, E is the modulus of the spring, k is the viscosity coe$cient of thedashpot component and e is the strain rate.

By applying a constant strain rate, eR , the strain at any time is given by

e"eR t

and

de"eR dt.

Eq. (1) can be written as

p"EeR t#keR . (2)

The total energy absorbed per unit volume by the system at time t and total strain e is given by

;"Pt

0peR dt. (3)

Substituting from Eq. (2) into Eq. (3) and integrating, we obtain

;"

Et2eR 22

#keR 2t, (4a)

i.e.

;"

Ee22

#keeR . (4b)

The "rst term determines the elastic energy stored in the spring and the second term determinesviscous energy dissipation in the viscous element. Eq. (4) also re#ects the sensitivity of the materialto the rate of loading.

At load removal, i.e. the external load is zero and after manipulation, Eq. (1), the recovery of thespring towards its original position driven by the stored energy can be shown to be

e"e0e~t2@q, (5)

where e0

is the maximum strain after loading, t2

is anytime after load removal and q is therelaxation time which is property of the material de"ned as k/E.

The experimental study, reported here, is con"ned to the investigation of the energy absorptionperformance of medium density polyethylene (MDPE) pro"led pipes, originally intended for use as


Table 1The dimensions and mass of the PE double-skin pipes

Label/mass (g)

Type ofloading

Insidediameter(2R) (mm)

Pipelength(mm)

R13

(mm)!R

#1(mm)"

R#2

(mm)#Z"R

13 *100/R kJ/kg J/mm

pipe1 228.5 g Lateral 153 136.5 3.01 0.25 0.43 0.984 0.233 0.55pipe2 435 g$ Axial 153 310 3.01 0.25 0.43 0.984 1.6% 2.22

2.1&

pipe3 454.6 g Axial 153 313 3.01 0.25 0.43 0.984 1.463 2.56pipe4 482.3 g Lateral 200 204 5.21 0.3 0.75 1.303 0.38 0.705pipe5 985.1 g Axial 200 41 5.21 0.3 0.75 1.303 0.81 1.831pipe6 1018 g Lateral 278 223 5.03 0.37 0.87 0.905 * *

pipe7 1715 g Axial 278 378 5.03 0.37 0.87 0.905 1.47 6.685

! R13"Radius of gyration of the pro"led cross-section.

" R#1"Radius of gyration of the straight cross-section closing the pro"le, see Fig. 1 for details.

# R#2"Radius of gyration of the straight c. s. between two subsequent boxes.

$ Pipe2 with foam has a mass of 682.4 g.% Empty pipe.& Foam-"lled pipe.

underground pipes. The long-term recovery and the behaviour of such pipes under intermittentloading are investigated.

2. Experimental program

Di!erent sizes of double skin pro"led PE pipes were subjected to axial and lateral quasi-staticloading at 5 mm/min using a universal-testing machine. The dimensions of the pipe specimens usedin the tests as well as the type of loading are tabulated in Table 1. In this experimental program, "vetypes of quasi-static tests were carried out as follows:

(a) Single axial compression. With reference to Table 1, three sizes of pipes, specimens 3, 5 and7 and of length to diameter ratio (¸/D) of approximately 2, 2 and 1.4, respectively, were axiallycrushed and the performance of which is summarized in Table 2. The load}displacement curves aregiven in Fig. 2.

(b) Axial compression of foam-,lled pipe. The in#uence of "lling the pipe core with Polyurethanefoam with density of 40 kg/m3 (specimen 2) on the overall performance was measured. The axialdeformation recovery is shown in Table 2 and the load}displacement diagram is shown in Fig. 3.

(c) Successive axial compressions. Repeated axial loading tests were performed, on specimen 3,over a period of "ve consecutive days. In each test, the pipe was fully crushed, unloaded and left torecover at room temperature for 24 h after which the crushing was repeated. Table 3 gives the e!ectof the repeated loading on the overall length recovery and the load-displacement characteristics areshown in Fig. 4.


Table 2The performance of di!erent sizes of pipes under axial loading

Specimen Overallcompressedlength

Instantlengthrecovered

Final lengthrecovered(%)

(%) (%)

pipe2 52 72.1 98.2pipe2* 51.6 71.0 95.4pipe3 54.1 73.5 95.5pipe5 48.2 80.2 97.6pipe7 46.3 86.0 98.7

!Foam-"lled (density 40 kg/m3).

Fig. 2. Load}displacement characteristics of axially loaded pipe of di!erent sizes.

(d) Single lateral compression. Three pipe sizes, specimen 1, 4 and 6, of ¸/D ratios of 0.9, 1.0 and0.8, respectively Table 4, were laterally crushed using the procedure shown schematically in Fig. 5.The average diametrical recovery for each pipe is given in Table 5.

(e) Successive lateral compressions. The repeated lateral loading was carried out on specimens1 and 4, see Table 1, over a period of four consecutive days. The pipes diametricalrecovery performance is shown in Table 6 and their load-de#ection characteristics are shown inFigs. 6}8.


Fig. 3. E!ect of foam "lling on the energy absorption capacity of the pro"led pipe under axial load.

Table 3The performance of pipe3 under repeated axial loading

Testdate

Lengthbeforetesting (mm)

Overallcompressedlength (%)

Immediaterecoveredheight (%)

ratio of recoverycompressedheight

Day1 313 45 70 1.55Day2 304 54.6 79.9 1.47Day3 298 52 78.5 1.50Day4 298 52.6 80.5 1.53Day5 298 52.3 80.5 1.53

3. Results and observations

A special extrusion process produces the pro"led pipes under consideration. The cross-section ofthe pipes is shown in Fig. 1. The hollow box shape pro"le is intended to enhance the lateral rigidityof the pipe when buried underground. These can be regarded as external ring sti!eners causing thelocalization of the collapse region as described above. The axially crushed pipes were observed tocollapse in the concertina mode. The axisymmetric folds occurred on the inner skin (Fig. 9), withinthe square section of the outer skin as anticipated in the introduction, Fig. 1b.


Fig. 4. E!ect of axial load repetition on the performance of pro"led pipes.

Table 4The Lateral loading of di!erent sizes of pipes

Specimen Instant diametricalrecovery (%)

"nal diametricalrecovery (%)

pipe1 68 90.9pipe4 67 92pipe6 67.6 93.7

Fig. 5. Schematic diagram of the pro"led pipe under lateral compression.


Table 5The e!ect of repeated lateral loading on the performanceof pipe1

Crushingsequence

Instant diametricalrecovery (%)


1st day 68 90.72nd day 59.15 843rd day 62.4 83.74th day 68.3 84.6

Table 6The performance of pipe4 under lateral compression cycle

Crushingsequence

Instant diametricalrecovery (%)


1st day 67 92.552nd day 69.75 883rd day 70 87.14th day 64.5 89.3

Fig. 6. Load}de#ection curves of laterally loaded pipes of di!erent sizes.

The load}displacement curves for the axial compression of specimens 3, 5 and 7 are shown inFig. 2. In the case of the smallest and the biggest pipes (3 and 7), the curves are characterized bya small number #uctuation of the load after the "rst peak. In fact, the two curves could be describedas smooth with little variation about the mean collapse load. The middle size pipe, 5, displayed


Fig. 7. Load}de#ection behaviour of pro"led pipe subjected to repeated lateral loading (specimen 1).

Fig. 8. E!ect of repeated lateral loading on the load-de#ection characteristics of pro"led pipe (specimen 4).

some variations about the mean collapse load. The energy per unit length for specimen 7 is morethan twice that for specimen 3 and over three times that for specimen 5. The speci"c energy forspecimens 7 and 3 is 80% more than that for specimen 5. Photographs for specimens 5 and 7 asthey progressively collapse under axial load are shown in Figs. 10 and 11. As can be clearly seen


Fig. 9. Geometrical model for the collapse of pro"led pipe under axial load.

from Fig. 10, the collapse started at the lower end of the pipe and progressed upwards, Fig. 10.Fig. 10h shows the pipe being compressed to about 50% of the original length; Fig. 10i shows theinstant recovery to about 75% of the original pipe length. All the pipes recovered almost fully aftera very long time compared to the duration of the test.

Fig. 3 shows some distinctive feature of the pro"led pipes when subjected to repeated axialloading. The #uctuations produced by the "rst loading of specimen 3 diminished completely in thesubsequent compression tests. The load}displacement curves for the subsequent tests were almostsmooth following a uniform trend, and resembled behaviour similar to that of lateral compression


Fig. 10. Progressive collapse of pro"led pipe (specimen 5) under axial load. (a) Initial position. (b) Collapse of the "rstpro"led box at the bottom of the pipe. (c) Three pro"led boxes have already collapsed. (d}g) progression of collapse. (h)Full collapse of pipe before unloading. (i) Pipe recovering after unloading.


Fig. 11. Progressive collapse of pro"led pipes (specimen 7) under axial load. (a) initial position. (b) Collapse of the "rstpro"led box at the middle of the pipe. (c}g) progression of collapse. (h) Full collapse of pipe before unloading. (i) Piperecovering after unloading.


Fig. 12. Progressive collapse of pro"led pipe (specimen 4) under lateral load. (a) Initial position at the instance of loading.(b) The pipe starting to deform. (c) Diametrical deformation is obvious. (d}e) Clear hinge line is developing across thebottom inside surface of the pipe. (f ) Full collapse of pipe before unloading. (g}h) Pipe recovering after unloading.

of metal rings. In analogy to metals, this may be attributed to the fact that the total work done inthe crushing of the pipe is mainly due to the initiation of plastic hinge along the inner generator ofthe pipe, rotation at the hinges and stretching between them. However, it is perhaps worthwhilenoting, that the collapse of such tubes cannot be attributed as due to the formation of plastichinges, as in metals, but rather to the visco-elastic nature of PE materials. The collapse in thesubsequent compression tests could be due to rotations about the visco-plastic regions developedas a result of the structural collapse in the "rst round of crushing. The mean crushing load, theenergy per unit length and the speci"c energy for "rst day were more than 21

2times higher than the

subsequent days. The immediate recovery in the pipe length is maintained at 80% of the originallength and the "nal recovery is 95%. The recovery property in the PE pipes can be explained interms of long-term visco-elastic recovery they have, described in general by Eq. (5).

This behaviour is analogous to shakedown in metals. This feature makes pipes made of thismaterial worthy of exploration for multiple use of energy absorption devices.

Specimen 2, "lled with polyurethane foam "ller (density"40 kg/m3), was also axially crushedand as expected, the polyurethane enhanced the load-displacement characteristics of the pipe. Thespeci"c energy for the foam "lled pipe was increased by 33% and the energy per unit length is twicethat of the empty one. In both cases, empty and "lled, the pipes exhibited a "nal recovery of 95% ofthe original length after a very long period of time relative to the duration of the test.

A typical Lateral compression of the pro"led pipe is illustrated in Fig. 5. The load}displacementbehaviour of two sizes of pipes, specimens 1 and 4, is given in Fig. 6. The change in the size of thepipes improved the energy per unit length by over 23%, but had little e!ect on the speci"c energy


value. As the ring collapse was completed, see Fig. 12f, a totally di!erent geometry came intooperation marked by a sudden increase in the load with insigni"cant change in the deformationstatus. The sequence of collapse of specimen 4 is shown in Fig. 12.

This behaviour of the PE pipes subjected to repeated axial loading was exhibited again whenthe pipes were subjected to repeated lateral loading of specimens 1 and 4. Figs. 7 and 8 show theload}displacement characteristics of those specimens when subjected to repeat lateral loading. Thespeci"c energy for the "rst round of lateral crushing was reduced by 40% while the energy per unitlength is reduced by 20%.

4. Concluding remarks

The experiments showed that after the "rst loading, the deformation of the pipe recoverssu$ciently to be used again. The characteristic peaks in the loads}displacement diagrams disap-pear and the curves become relatively smooth. The mean axial load is reduced after severalcrushings to about 40% of that of the "rst use and appears to be independent of the number of loadrepetitions. The recovery is mainly attributed to the visco-elastic phenomenon and the structuralelasticity of the double-skin pipes. The residual energy absorption makes this class of materials,with the appropriate geometry, a good candidate for several uses as energy absorber, though ata reduced capacity of about 40% before it has to be replaced. This "gure of 40% may be improvedby further investigation using other materials and geometries. The total number of uses before thepipes develop cracks, tears, crazes and "nally fails, should be investigated.

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Profiled polymer pipes as re-usable energy absorption elements