Recent Advances in Mechanical Engineering Applications

Size: px

Start display at page:

Download "Recent Advances in Mechanical Engineering Applications"

Tabitha Evans
5 years ago
Views:

1 The Effect of Hoop Stress on the Fatigue Behavior of Woven-roving GFRE Closed end Thick Tube Subjected to Combined Bending Moments and Internal hydrostatic Pressure M.N. ABOUELWAFA, HASSAN EL-GAMAL, YASSER S. M. AND WAEL A. AL-TABEY Department of Mechanical Engineering, Faculty of Engineering, Alexandria University, Alexandria (21544), Egypt Abstract:- The effect of hoop stresses on the fatigue behavior of Glass Fiber-Reinforced Epoxy (GFRE) is studied via testing thick-walled, woven-roving specimens with two fiber orientations, [0 o,90 o ] 3s and [±45 o ] 3s, at different pressure ratios ( ), Pr = 0, 0.25, 0.5, 0.75 (i.e. pressures amounting to 0%, 25%, 50% and 75% of the burst pressure). The [0,90 ] 3s specimens were found to have higher bending strength than the another fiber orientation [±45 ] 3s specimens, at all pressure ratios; as being subjected to a minimum value of shear local stress component σ 6 which equal to zero. The effect of pressure ratios on the amplitude bending stress is discussed, It is evident that as increase of the pressure would have an adverse effect on the bending stress rates of the specimens specimens for all fiber orientations, this is due to the pressure increasing the circumferential stresses within a specimens wall. Under all pressure ratios; the hoop stress component had a detrimental effect on the amplitude component for all fiber orientations, [0 o,90 o ] 3s and [±45 o ] 3s, specimens, tending to decrease the amplitude component for the same life. Key-Words: - Hoop Stress; Bending Fatigue; internal hydrostatic pressure; Reinforced Epoxy; composite thick tube; multilayer; fiber orientation; burst pressure. 1 Introduction Composite materials behavior subjected to fatigue load is very complex due to non homogeneous and anisotropic properties, and it has been studied for a long time; however, composite materials design is still based on very long fatigue tests and high safety s are used. The fatigue behavior of composite tubes was studied by Owen et al. [1], who conducted a series of fatigue tests of thin walled glass/polyester tubes under a combination of axial loading and internal pressure. Krempl et al. [2, 3] compared the effect of uniaxial and biaxial loading on fatigue in composite tubes under completely reversed loading. Frost [4, 5] investigated the short and long term performance of GFRE pipes under static and cyclic internal pressurization. He concluded that matrix crack propagation in these types of loading, controls failure through a combination of transverse matrix cracking and ply delamination at the fiber-matrix interface. The ply stresses controlling failure were therefore, transverse and shear stress. Carroll [6, 7] conducted extensive experiments to investigate the effects of load rate and ratio on the fracture behavior of ±55 and multiangle filament wound pipes under biaxial loading. It was observed that the failure mode is very much dependent on the stress ratio and the rate of loading. 2 experimental work 2.1 Testing machine The used testing machine was designed by Abouelwafa M. N. et al [15] and used by other researcher in similar works [8-14], then modifying this designe in new testing machine by Yasser S. M. [16], the important modification to the testing machine is adding hydraulic circuit to study the effect of internal hydrostatic pressure. The general layout of testing machine and hydraulic circuit is shown in Fig.1 and Fig.2, respectevely. The testing machine is a strain controlled, rotating at constant speed of 1250 rpm (.833Hz), and capable of performing three different fatigue loading systems and hydrostatic pressure load. The load systems are independent, and have the facility to apply different stresses. The specimen is subjected to a uniform load, along its whole length, through a gripping system consisting of two halves that enclose the specimen in between. The applied moment was measured via a load cell, fixed on the grippers, consisting of four active strain gauges, forming a full bridge. The signal is amplified and ISBN:

displayed on an oscilloscope and the whole system was calibrated.

change in internal pressure by Pressure transducer, until the specimen fails.

Accordingly, the specimens are fixed to the test system by means of the gripping end closure unit for this test, which is presented in Fig.3.

2 displayed on an oscilloscope and the whole system was calibrated. The objective of hydraulic circuit is to obtain constant pressure inside the specimen and can be controlled by increasing or decreasing by controlling the flow control valve, the system records the change in internal pressure by Pressure transducer, until the specimen fails. The pressure transducer was calibrated and checked it on zero bars and the specimen was considered to have failed, when the pressure transducer reading falls down from its highest value. test. Accordingly, the specimens are fixed to the test system by means of the gripping end closure unit for this test, which is presented in Fig.3. The thickness of the tube ends were built up by additional layer of rubber tube to avoid gripping problems. 2.3 Thick-walled tubes made from three layers of wovenroving E-glass/Epoxy with two fiber orientations, [0 o,90 o ] 3s and [±45 o ] 3s, were used with a fiber volume fraction (V f ) ranging from 55 % to 65 %. This range was used in previous works [8-14] and has proved its suitability to ensure good adhesion between fibers and matrix, good strength and acceptable mechanical properties. Table (1) shows the properties of the used materials. Fig.4 shows the nominal dimensions of the used specimens, which were measured after complete curing. Figure 1.The general layout of testing machine Figure 3.Schematic of Specimen closure system Figure2.The general layout of hydraulic circuit 2.2 Test Fixtures For the application of internal pressure efficiently, the specimen should be fixed properly to the test apparatus. The fixation should be strong enough to avoid leakage of test fluid, fracture or slip of the specimen at the matching region. The closure system should be guaranteed that uniform stresses are obtained through the test section cover the constraint on the test specimen in axial direction for closed end Figure 4.Nominal dimensions [mm] ± 0.1 mm Table 1.Properties of used materials Property Woven-roving E-glass Epoxy Resin fibers Density 2551 kg/m 3 10 kg/m 3 Modulus of E = 76 GPa E = 3.6 GPa elasticity Poisson s ratio ν = 0.37 ν = 0.35 Tensile strength 3.45 GPa 0.25 GPa ISBN:

3 2.4 Stress state are subjected to combined bending fatigue moments and internal Pressure with different pressure values. Being closed end cylindrical in shape, their global stress (σσ xx ), σσ yy and ττ xxxx may be found from the following equation: σσ xx = MMyy II + σσ ll, σσ yy = σσ HH and ττ xxxx = 0 Where: M : applied bending moment (MM = MM mm + MM aa sin(ωωωω)). M m and M a : mean and amplitude bending moments, respectively. I: second moment of area for tube; II = (ππ 64) dd 4 oo dd 4 ii ). σσ ll : Longitudinal stress (MPa), (σσ ll = PP ii rr 2 ii rr 2 2 oo rr ii )for thick tube. σσ HH : Hoop stress (MPa), σσ HH = (PP ii rr 2 ii rr 2 2 oo rr ii )(1 + rr 2 oo rr 2 ) for thick tube. P i : Internal pressure. d o and d i : Outer and inner diameters of the specimen, respectively and rr = dd ii / 2. The [0 o,90 o ] 3s specimens had a pure local stress state, σσ 1 = σσ xx, σσ 2 = σσ yy and σσ 6 = 0, while the [±45 ] 3s specimens had local stress state, σσ 1 = σσ 2 = (1 2) σσ xx + σσ yy and σσ 6 = (1 2) σσ xx σσ yy. 3 test results It is important to note that, in order to avoid any misleading data, only the specimens that had their failure features within the accepted gauge section, the middle third of the whole length were considered; while those that have their failure due to any gripping problems were excluded. 3.1 Static tests Static Bending tests Static bending tests were performed on the tubular specimens of both orientations, [0 o,90 o ] 3s and [±45 ] 3s, in order to find out their ultimate global bending strengths (S u ), which was found to be as follows: (S u ) of the [0 o,90 o ] 3s specimens = 182 MPa (S u ) of the [±45 ] 3s specimens = 159 MPa Static pressure tests Twenty four internal pressure tests are applied on thick-walled woven-roving Glass fiber reinforced epoxy (GFRE) closed tubes. It is important to note that the tests are recorded to be successful if bursting is achieved, resulting in a sudden decrease in internal pressure The burst pressure was recorded and maximum hoop stress was calculated from σσ yy, where rr = dd ii /2, the data for static pressure tests are: (P max, σ Hmax ) of the [0 o,90 o ] 3s specimens = (55 bars, 30.6 MPa) (P max, σ Hmax ) of the [±45 ] 3s specimens = ( bars, 35.8 MPa) 3.2 Fatigue tests All specimens were tested under ambient conditions and constant frequency of.833 Hz. The data points were used to plot the corresponding S-N curves on a semi-log scale, being fitted using the power law: mmmmmmmmmmmmmm ssssssssssss = aann bb, representing the bending fatigue strength (S f ). Failure was considered to occur when the load reading decreased by about % of its original value. In other words, % reduction in the strength of the specimen will represent failure. Tests were performed on both fiber orientations, [0 o,90 o ] 3s and [±45 ] 3s, at four different pressure ratios Pr = 0, 0.25, 0.5, 0.75 (i.e. pressures amounting to 0%, 25%, 50% and 75% of the burst pressure). Fig.5 and Fig.6 show the corresponding S-N curves at all pressure ratios for both fiber orientations. The two constants (a) and (b) were found to have the values given in Table (2) and Table (3). Table 2.Fatigue Constants (a) and (b) for [0 o,90 o ] 3s Pressure ratio [0,90 ] 3s (Pr ) aa (MPa) bb Correlation Table 3.Fatigue Constants (a) and (b) for [±45 ] 3s Pressure ratio [±45 ] 3s (Pr ) aa (MPa) bb Correlation ISBN:

4 σ max (MPa) σ max (MPa) Figure 5.S-N Curve of [0 o,90 o ] 3s = 0.0 = 0.25 = 0.5 = 0.75 = 0.0 = 0.25 = 0.5 = Cycles to Failure (N) Figure 6.S-N Curve of [±45 ] 3s 4 Analysis and discussion 4.1 Analysis of the S-N curves Using the power formula σσ mmmmmm = aann bb under combined internal pressure and completely reversed bending have proved its suitability by given acceptable values for the correlation, Table (2) and Table (3) Analyzing the values of the two constants (a) and (b), resulted in the following conclusions: 1) For both fiber orientations, [0,90 ] 3s and [±45 ] 3s, the S-N curves for different pressure ratios ( = 0, 0.25, 0.5, 0.75) are almost parallel to each other. 2) For both fiber orientations, [0,90 ] 3s and [±45 ] 3s, the S-N curves for pressure ratio ( = 0) has the highest magnitude, the S-N curves for pressure ratio ( = 0.75) has the lowest magnitude, while the other curves for the remaining stress ratios laid in between, with an descending order. 3) Analyzing the values of two fatigue constants (a) and (b) of the data obtained in Table (2) and Table (3) for all pressure ratios ( ), considering the variation of the fiber orientations, Table (2) and Table (3), and Fig.5 and Fig.6 resulted in the following conclusions: i. The deviation in the values of the power (b) at different pressure ratios ( ) is negligible and it may be considered constant, the average value of (b) was calculated and considered to be used at any pressure ratio ( ), as the corresponding slandered deviation was found to have acceptable values, as shown in Table (4). ii. The values of the fatigue constant (a) were found to depend on the pressure ratio ( ) for all fiber orientations. Table 4.Average values of (b) for tested specimens Fiber orientation Average value of (b) Slandered Deviation (%) [0,90 ] 3s [±45 ] 3s Effect of Pressure ratio ( ) The values of fatigue constant (a) of the maximum stress equations are obtained as functions of the pressure ratio ( ), for both fiber orientations, [0,90 ] 3s and [±45 ] 3s, and given in Tables (4), and are clear that: 1) The value of fatigue constant (a) was found to depend on the pressure ratio ( ), for both fiber orientations, as the following relations indicated in Table (5). 2) Increasing the value of pressure ratio ( ) causes a decrease in the corresponding value of fatigue constant (a), i.e. the degradation fatigue strength decreases with the increase of ( ). 3) This leads us to an important conclusion of the effect of pressure ratio ( ); that the value of (a) is constant and function of the static bending strength of the tested material. Finding the value of (a) as a ratio of (S u ) we found that: i. The pressures ratio (Pr) considered corresponded to the ratio of fatigue constant (a) ratios (SS rr = aa SS uu ) for both fiber orientation, as the following relations indicated in Table (6). ii. The pressures amounting to 0%, 25%, 50% and 75% of the burst pressure were investigated. It is evident that as the pressure increased, the bending moment rate of the specimens decreased. Therefore, an increase of pressure would have an adverse effect on the fatigue moment strength rate of the specimen. This is due to the pressure increasing the circumferential stresses within a specimen wall, which in turn would allow the specimen to reach the onset of buckling at lower ISBN:

5 moments, thus reducing the fatigue moment strength rate. Moreover, it can be seen that at lower pressures, higher fatigue moment strength is reached at lower strains. Table 5.Fatigue Constants (a) as a function of pressure ratio ( ) Fiber orientation a (MPa) Correlation [0,90 ] 3s aa = 322 eeeeee( Pr ) [±45 ] 3s aa = eeeeee( 1.56 Pr ) Amplitude Normal Stress (A) (MPa) N=1E+3 N=1E+4 N=5E+4 N=1E+5 N=5E+5 N=1E+6 33 Table 6.Fatigue Constants (a) as a function of pressure ratio ( ) Fiber orientation Amplitude normal stress ratios Correlation [0,90 ] 3s S r =-1.588* [±45 ] 3s S r =-1.398* Hoop-amplitude diagrams The hoop-amplitude diagrams were plotted at different lives for both fiber orientations, [0,90 ] 3s and [±45 ] 3s, as shown in the Fig.7 and Fig.8. The needs for groups of specimens, one at each pressure ratio, having exactly the same life, make it impossible to use the actual experimental data in plotting the hoop-amplitude relations. On the other hand, we used the fitted S-N equations to find out the required points; using these fitted equations is supported by having high correlation s (Table (7) and Table (8)). Plotting the hoop-amplitude components of the [0,90 ] 3s and [±45 ] 3s specimens representing the different pressure ratios and using the static pressure point σσ HHmmmmmm, 0 gave straight line relations, as shown in Figures, with high correlation s. For case study of combined internal pressure and completely reversed bending, the run tube move toward the linear interaction rule (1) [17] can be used to estimate the equation for hoop stresses to be the governing equation for the hoop- amplitude relation. PP + MM = 1.0 (1) PP mmmmmm (MM=0) MM mmmmmm (PP=0) Therefore, the equation (1), for the same specimen σσ specifications, we can be written as: HH + σσ HH mmmmmm (SS uu =0) σσ mmmmmm = 1.0 SS uu σσ HH mmmmmm =0 is the suitable for representing θθ the effect of the hoop stress for all fiber orientations (θθ), [0,90 ] 3s and [±45 ] 3s, under combined pressure and completely reversed bending. Amplitude Normal Stress (A) (MPa) Figure 7.Hoop-amplitude relation for [0 o,90 o ] 3s Hoop Stress (H) (MPa) N=1E+3 N=1E+4 N=5E+4 N=1E+5 N=5E+5 N=1E+6 Figure 8.Hoop-amplitude relation for [±45 ] 3s Table 7.The Hoop-amplitude relation for [0,90 ] 3s specimens Life (N) [0,90 ] 3s Hoop-amplitude relation Correlation 1E+3 A=-3.019*H E+4 A=-2.908*H E+4 A=-2.755*H E+5 A=-2.131*H E+5 A=-1.921*H E+6 A=-1.464*H Table 8.The Hoop-amplitude relation for [±45 ] 3s specimens Life (N) [±45 ] 3s Hoop-amplitude relation Correlation 1E+3 A=-2.004*H E+4 A=-1.799*H E+4 A=-1.625*H E+5 A=-1.457*H E+5 A=-1.352*H E+6 A=-1.048*H Conclusions The concluded points emerged in this work can be summarized as follows: 38 ISBN:

6 1) Using the power formula: σσ mmmmmm = aann bb has proved its suitability for [0,90 ] 3s and [±45 ] 3s specimens subjected to combined internal pressure and completely reversed bending fatigue loading with different pressure values. The two constants (a) and (b) were found to follow the following behavior: i. The value of power (b) was found to have a constant value for each fiber orientation and all pressure ratios with a slight deviation. In other words, the value of (b) depends only on the static bending strength of the material and not the pressure ratio ( ) (Table (3)). ii. The value of the power (a), which represents the failure rate, was found to depend on both the static bending strength of the material and the pressure ratio ( ). The [0,90 ] 3s specimens had higher failure rates that was attributed to the brittle fiber failure due to the tension stress component. iii. An increase of specimen working pressure would have an adverse effect on the fatigue moment strength rate of the specimen. 2) Finally, The hoop stress component was found to have a detrimental effect of fatigue behavior, for both fiber orientations, [0 o,90 o ] 3s and [±45 o ] 3s at all pressure ratios. The straight-line relation was found to be dependent on the range of the corresponding fatigue life, the straight line equation (1) replaced by the corresponding hoop and bending stresses was found to govern the fatigue behavior of the woven-roving GFRE under combined internal pressure and completely reversed bending moment, as follows: σσ HH + σσ mmmmmm = 1.0 σσ HH mmmmmm (SS uu =0) SS uu σσ HH mmmmmm =0 θθ 6 References [1] Owen, M.J. and J.R. Griffiths, Evaluation of biaxial stress failure surfaces for a glass reinforced polyester resin under static and fatigue loading. Journal of Materials Science, : p [2] Krempl, E., et al., Uniaxial and biaxial fatigue properties of thin walled composite tubes. Journal of the American Helicopter Society, (3): p [3] Krempl, E. and N. Tyan Min. Graphite/epoxy [±45 ] tubes-their static axial and shear and fatigue behaviour under completely reversed load controlled loading. in Journal of Composite Materials [4] Frost, S.R. and A. Cervenka, Glass fibrereinforced epoxy matrix filament-wound pipes for use in the oil industry. Composites Manufacturing, (2): p [5] Frost, S.R., Predicting the long term fatigue behaviour of filament wound glass/epoxy matrix pipes. Proceeding of the 10th international Conference of Composite Materials (ICCM 10), : p [6] Carroll, M., et al., Rate-dependent behaviour of ±55 filament-wound glass-fibre/epoxy tubes under biaxial loading. Composites Science and Technology, (4): p [7] Ellyin, F., et al., The behavior of multidirectional filament wound fibreglass/epoxy tubulars under biaxial loading. Composites Part A: Applied Science and Manufacturing, (9-10): p [8] El-Midany A. A., Fatigue of Woven-Roving Glass Fiber Reinforced Polyester Under Combined Bending and Torsion, PhD. Thesis, Alexandria University, Egypt, [9] Mohamed N. A., The Effect of Mean Stress on the Fatigue Behaviour of Woven-Roving GFRP Subjected to Torsional Moments, MSc. Thesis, Alexandria University, Egypt, 02. [10] Mohamed M. Y., The Inclusion Effect on the Fatigue Behaviour of Woven-Roving GRP Composite Materials, MSc. Thesis, Alexandria University, Egypt, 01. [11] Mustafa M. E., Fatigue Behaviour of Woven- Roving GFRP Under Combined Bending and Torsion Moments with Different Fluctuating Stresses, MSc. Thesis, Alexandria University, Egypt, 06. [12] Sharara A. I., Effect of Stress Ratio on Fatigue Characteristics of Woven-Roving Glass Reinforced Polyester, MSc. Thesis, Alexandria University, Egypt, [13] Mustafa M. E., Fatigue Behaviour of Woven- Roving Glass Reinforced Polyester Under Combined Out-of-Phase Bending and Torsion Moments with Different Fluctuating Stresses, PhD. Thesis, Alexandria University, Egypt, 11. [14] Yasser S. M., A Study the Effect of Fiber Orientation and Negative or Positive Stress Ratios on Fatigue Characteristics of Woven- Roving Glass Reinforced Polyester Under ISBN:

7 Combined Bending and Torsional Moments, PhD. Thesis, Alexandria University, Egypt, 11. [15] Abouelwafa M. N., Hamdy A. H. and Showaib E. A., A New Testing Machine for Fatigue Under Combined Bending and Torsion Acting Out-of-Phase, Alexandria Engineering Journal, Vol.28, No.4, Pp , [16] Yasser S. M. and Graduation project groups, Composite Materials, Fatigue Testing and Molding Machines, Graduation Project, Mechanical Engineering Department, Alexandria University, Alexandria, Egypt. [17] Man-Sik M., Yun-Jae K. and Peter J. B., Limit load interaction of cracked branch junctions under combined pressure and bending, J. of Engineering Fracture Mechanics Vol. 86, P.p. 1 12, 12. ISBN:

7RU, UK. Arab Emirates

7RU, UK. Arab Emirates 425 Effects of Winding Angles in Biaxial Ultimate Elastic Wall Stress (UEWS) Tests of Glass Gibre Reinforced Epoxy (GRE) Composite Pipes M.S. Abdul Majid 1, M. Afendi 1, R. Daud 1, A.G. Gibson 2, M. Hekman