CHAPTER 6 EXPERTMENTAL STUDY OF COMBINED EFFECT OF BOTH DISTRIBUTED GEOMETRICAL IMPERFECTIONS AND DENT ON BUCKLING STRENGTH OF THIN CYLINDRICAL SHELLS The main aim of this part of the research work is to experimentally determine the combined effect of both distributed geometrical imperfections and localised geometrical imperfections namely dent on buckling strength of thin cylindrical shells subjected to uniform axial compression. In the earlier works, thin cylindrical shells were manufactured by different manufacturing processes such as electro forming (example: Arbocz and B abcock 1969), rolling and welding (example: Han et a1 2006, Athiannan, and Palaninathan 2004), machining process (example: Boote et a1 1997), spin casting (example: Schneider 1996) etc., and also in most of the earlier works, r/t ratios of thn cylindrical shell taken for research work were greater than 100. In some earlier works, for example by Han et al (2006), Boote et a1 (1997), the r/t ratios of the thin cylindrical shell taken for their studies were less than 60. Initially it is planned to manufacture thin cylindrical shells kom stainless steel material and it is found that for inside diameter of around POrnrn, only cast stainless steel tubes are available commercially which may consist blow holes and other casting defects which may affect the aim of our study and hence in hs work aluminum alloy cylindrical shells are selected for study which has similar stressstrain pattern of material property as that of stainless steel. The other reasons for selecting Aluminum alloy seamless tubes are (1) To avoid inclusion of imperfection due to weldment. (2) A1 alloy seamless tubes are available commercially.
In this part of the work, to study the combined effects said above, aluminium of Grade 51000-A (IS: 737 (1986)) h n cylindrical shells of size internal diameter (ID) 94.6 mm, length 15k1.m and thickness lmm are produced by tuning operation f?om the extruded pipe of size ID 94.6rnrn, length 3m and wall thickness 3m. To avoid the variation in chemical composition and material properties all the cylindrical shell test specimens were manufactured from the same extruded tube. The composition of A1 alloy and its IS Grade are determined by Spectro- chemical analysis. Test report of the same is tabulated in Table 6.1. Table 6.1 Composition of A1 alloy by Spectro Chemical Analysis Alloying Element Percentage of Composition I Silicon 1 0.452. 1 I 1ron ) 0.421 I / copper 1 0.012, I / Manganese 1 0.016 I 1 Magnesium / 0.567 I Chromium I 0.036 6.1 MANUFACTUFUNG OF THIN CYLINDlUCAL SHELLS To produce thin cylindrical shells fiom a extruded tube, the following steps listed below are followed: (i) First, the extruded tube is cut into pieces of 153 mm length. (ii) Length correction to the dimension of 150 i 0.1- on these cylindrical specimens is done by facing operations.
(iii) (iv) (v) Grinding operation was done on both the edges of the cylindrical shells to maintain the perpendicularity with respect to the axis of the cylindrical shell and parallelism between top and bottom edges within a tolerance limit of k0.01mm. These pieces are held in between centers on the Lathe Machine using two flanges which have true centers with live and dead centers and also these flanges have sliding fit with the ID of the cylindrical specimens Then, turning operation is performed on the outer surface of the cylindrical specimens to reduce the wall thickness to1 mm. Thus the thm cylindrical shells required for this work are prepared. The final dimensions of the thn cylindrical shell specimens are Length (L) =I50 k 0.01 mm Inner diameter (ID) = 94.6mm (same as extruded pipe ID- the manufacturer assured ID variation is + 0.05mm) Wall thickness (t)=l * 0.01 mm According to Ref (Cook et a1 1995), if a shell is to qualifjr as thin shell, its r/t ratio should be greater than 20. Hence in th~s work, the cylindrical tube was turned to reduce wall thickness from 3rnrn to Irnm, so that the rit ratio obtained as 47.3 is greater than 20. Reducing the wall thickness of the cylindrical shell further, caused manufacturing difficulties such as, thickness variation of shell due to wobbling of specimen while performing skin turning operation of specimen, clinging specimen to the specimen holder and undesirable noise from the specimen while performing skin turning operation due to elastic deformation of the specimen, even for the small cutting force applied. Because of the above said reasons and also due to limited facilities available to manufacture thin cylindrical shells without undesirable imperfections other than geometrical imperfections, the wall thckness is limited to 1k0.0 1 mm in all the test cylindrical shells manufactured. The hckness variation was verified by cutting the cylindrical shell into strips without plastic deformations and measuring the thicknesses at different locations using digital vernier caliper.
6.2 FORMATION OF DENTS ON TEST CYLINDRICAL SHELL SPECIMENS Totally, 18 test cylindrical shells were manufactured and tested, but out of these only six test cylindrical shells for which imperfection measurements taken are presented here. (c) All ckirnensions are in mm Fig. 6.1 Dimensional details of the (a) indenter and (b) die groove for circumferential dent (c) the die groove for longitudinal dent (Details not to scale)
A circumferential dent was formed on two (out of six) test thin cylindrical specimens (named as B 1 and B2) at half the height of the specimens using a semi cylindrical mild steel indenter and a mild steel die groove as shown in Fig. 6.1@). similarly, a longitudinal dent was formed on other two test specimens (named as C1 and ~ 2 such ) that the dent center lies at half the height of the test specimen using a similar semi cylindrical indenter and a mild steel die groove as shown in Fig.6.1 (c). The remaining two test cylindrical specimens (named as A1 and A2) were used without dent formation to determine the effect of distributed geometrical imperfections alone. The Fig. 6.1 shows the dimensional details of the indenter and the die groove used to form the dents on test cylindrical shells. 6.3 MEASUREMENT RIG TO MEASURE, GEOMETRICAL IMPERFECTIONS It was planned to get geometrical imperfections data from test cylindrical shells for every 10 mm distance approximately along the longitudinal direction and every 5' along the circumferential direction. But in case of dented cylindrical shell near the dent location longitudinal distance between two rings of measurements is taken as approximately 2rnm. htially it was planned to get imperfections data using Coordinate Measuring Machine (CMM-manual type) because of its measurement accuracy. Later, it is realized that measurement of imperfections mainly depends upon the operator's skill and operator's fatigue to measure thousands of such imperfections data. To overcome these difficulties, an imperfection measurement rig was developed. This rig is designed such that once a test* cylindrical shell and the measuring instrument are loaded on this rig, both of them are not be disturbed until complete measurement is carried out, and also pressure applied on the measuring probe for measurement should be maintained constant to avoid error due to contact Pressure variation. The Fig. 6.2(a) shows the cross section and end view and Fig. 6.2(b) shows 3 D model of geometric imperfection measurement rig.
This rig includes three major parts as listed below: (a) Main frame with centers @) Specimen holder, and (c) Dialholder u Fig. 6.2 (a) FulI sectional front view and side view of Imperfection measurement rig to measure geometrical imperfections @) 3D view of the Imperfection measurement rig
6.3.1 Main frame with centers The photo graphic view of the main Erame with centers is shown in Fig 6.3. fie main frame consists of a bed with a guide ways supported on four rigid columns. On one end of the bed a fixed live centre with indexing mechanism is rigidly fixed and on the other end of the bed a movable live centre is mounted. This movable live centre can be moved back and forth on the guide ways by ball screw mechanism and it can be clamped at any location on the bed. The indexing plate consists of 72 holes, so as to index the test cylindrical shell for every 5' about the axis of between centers. A pin - hole mechanism in conjunction with indexing mechanism is used to locate the test cylindrical shell for every 5' in circumferential direction. A dowel pin attached to the fixed live centre is used to transmit positive motion between indexing plate and test specimen. Fig. 6.3 Photo graphic view of main frame with centers 6.3.2 Specimen holder The photo graphic view of the specimen holder is shown in Fig 6.4. This is used to mount the test cylindrical shell between the centers. This has a mandrel with a fixed flange at one end. me fixed flange has a step projection for 20mm on its
face which is used to locate the test cylindrical shell and this step projection has sliding fit with the ID of the test cylindrical shell. Another guide flange nearer to other end of mandrel is also used to locate the test cylindrical shell. The guide flange also has flat milled surface as shown in Fig. 6.4. to avoid interference with dent on the cylindrical shell. The OD of this guide flange also has clearance fit with the ID of the test specimen. The specimen holder also has a removable clamp flange which has a step projection for 5 mm to locate this removable clamp flange by test specimen. AAer locating the test cylindrical shell and clamp flange, both are held together on the mandrel by clamp screws. Fig. 6.4 Photographic view of specimen holder 6.3.3 Dial holder It is planned to measure the imperfections on the cylindrical shell by using a Mitutoyo Digital micron dial indicator. The did holder is designed such a way that it hold the dial indicator and at the same time ensures constant pressure on the dial indicator probe. Fig.6.5 shows the photographic view of dial holder. It has two major parts namely saddle and holding stand. The saddle can be moved back and forth longitudinally on the bed with the help of the guide way of the bed on the main frame. The saddle also has transverse slide ways to move the dial indicator stand
in the transverse direction. Both. saddle and transverse slide are clamped together on fie bed, so as to restrain the motion of dial holder on both the directions. The longitudinal location of saddle is measured with the help of vernier caliper. On one end of the transverse slide commercially available dial indicator stand is retrofitted which can provide 3 rotational degree of freedoms for the dial indicator. Fig. 6.5 Photographic view of assembly of dial holder Fig. 6.6 Photographic view of measurement rig loaded with thin cylindrical shell
., Fig 6.6 shows photographic view of the finished measurement rig loaded with a test cylindrical shell. Finally, the imperfection measurement rig is checked for its accuracy. Two important aspects of measurements are checked. After the final assembly the run out on the live centre are found to be within 1 micron and taper between centers is found to be 4 microns for a length of 180 m on the test mandrel. 6.4 GEOMETRICAL IMPERFECTION MEASUREMENTS ON THIN CYLINDRICAL SHELLS Using this specially fabricated imperfection measurement rig, imperfection measurement was carried out on six test cylindrical shells. Out of these two test cylindrical shells have a circumferential dent, other two test cylindrical shells have a longitudinal dent and the rest two test cylindrical shells have no dents. Table 6.2 shows sample of imperfection measurement data taken from specimen Al, which had only distributed geometrical imperfection present on the cylindrical shell. Fig 6.7 (a), (b), (c), (d), (e) and (f) are the plots of measured geometrical imperfection data taken from samples Al,A2, B1, B2, C1 and C2 respectively.
Pig. 6*7 Contd.
uxial distonce ix nrm b 0 5 8 5 2x in radians Fig. 6.7 Contd...
pig. 6.7 (0 Plots of measured geometrical imperfections taken from different test cylindrical shells
6.5 EXPERIMENTAL PROCEDURE ADOPTED TO PREDICT BUCJSLING STRENGTH OF THIN CYLINDRICAL SHELLS In this work, 100 kn UTM (FIE Indian make UTN 40 model) was used to predict the buckling strength of cylindrical shells and thls machine has a resolution of 0.1 kn in the loading range of 0 to 40kN. Before performing compression test on utm, the following chechnghnitial settings had been carried out. 6.5.1 Initial setting (i) On the machine Checking for face out and parallelism of platens of UTM. In this work, initially both top and bottom platens are checked for face out using micron dial indicator and it is found that there are no face outs on the working surface of the platens. The parallelism limit of 10 microns between the platens is ensured. (ii) On specimens Before applying load on the test cylindrical shell, the parallelism between top edge of test specimen and top platen was checked using feeler gauge and it was found to be within the tolerance limit of 30 microns. To ensure extremely slow loading on the cylindrical shell, first, the upward. movement of the lower ram was controlled at rate of approximately 0.5Mm/rnin. And further, to ensure same loading rate, while testing all the other specimens, loading hob of the machine was provided with a stopper at that particular position. A micron dial indicator with its magnetic base is mounted on the machined surface of the bottom ram and the measuring probe of the dial indicator touches the machined surface of the upper fixed ram as shown in Fig. 6.8. On loading, as the lower ram moves upward the dial indicator shows the reduction in gap between the two platens which is nothing but edge displacement applied on the test cylindrical shell on loading.
6.6 EXPERIMENTAL PROCEDURE ADOPTED 1. First, the test cylindrical shell was kept centrally and vertically on the bottom platens. 2. The upper platen was moved downward direction nearer to the top edge of the test cylindrical shell rapidly. 3. Then, the lower platen was moved upward direction at a required (low) loading rate of approximately 0.5 dmin by turning the loading knob of the UTM up to the preset stopper position, 4. As soon as the upper edge of the test cylindrical shell touches top platen, at which increase in micron dial indicator reading stops for a while and that micron dial indicator reading (R1) was noted. 5. The uniforrn displacement load from the bottom platen was allowed to apply on the specimen, until the cylindrical shell collapses. 6. As soon as the load applied reaches the limit load condition (at which arm of the live dial indicator of the UTM tends to return back on further loading) both the limit load value on the dial indicator of the UTM and micron dial indicator vafue (R.2) was noted at the same time. R1 -R2 is taken as edge displacement reading. The experimental values of both limit load and edge displacement of all the tested cylindrical shells taken for study are tabulated in Table 6.3. Fig 6.8 shows photograph of the test cylindrical shell compressed axially on the UTM machine between platens to determine the buckling strength experimentally.
Fig. 6.8 Photograph of the test cylindrical shell B2 compressed axially on the UTM machine 6.7 RESULTS AND DISCUSSION 6.7.1 Test cylindrical shells without dent Both the test cylindrical shells A1 and A2 taken for study (which contained only distributed geometrical imperfections) failed at the maximum load of 6.2 kn by forming partial ring of bulge deformations at both top and bottom edges of the cylindrical shells. The bucme patterns of the test cylindrical shells A1 and A2 are shown in Fig.6.9 (a) and Fig. 6.9(b) respectively. It was found that maximum amplitude of imperfections on test cylindrical shells on positive side (radially outward direction) and negative side (radially inward direction) were 0.145m and 0.195mm respectively with respect to imaginary perfect cylindrical shell of radius 47.8mm and development of imperfections of the same is sown in Fig. 6.7(a). Similarly, maximum amplitude of imperfections on positive and negative directions of the test cylindrical shell A2 was found to be 0.104mm and 0.115mm respectively and development of imperfections of the same is shown in Fig. 6.7(b). Even though the test cylindrical shells A1 and A2 had different imperfections pattern and different amplitudes of imperfections, experimentally showed the buckling strength
of 6.2kN, which means that thn cylindrical shells are not very sensitive / less sensitive (i.e., may be less than 0.1~N ) for initial distributed geometrical imperfections. Tlxs insensitiveness or less sensitiveness to initial geometrical imperfections may be due to the fact that the test cylindncal shell taken for study is relatively thick thin shell with ritz47.3. Atluannan and Palaninathan (2004) in their work pointed out that as the r/t ratio decreases the distributed geometrical imperfection effect on buckling strength also decreases. Th~s is once again proved here experimentally. Table 6.3 Experimental Buckling strength of test cylindrical shells Test Cylindrical shell with type of imperfections Test cylindrical shells without dent but containing only distributed geometrical imperfections Sample No. A1 A2 Experimental buckling strength in 0 6.2 6.2 Edge displacement measurement in mm (at limit load condition) 0.413 0.423 Test cylindrical shells with both distributed geometrical imperfections and a circumferential dent B1 B2 5.8 5.9 0.395 0.40 1 Test cylindrical shells with distributed geometrical imperfections and a longitudinal dent C1 C2 6.1 6.2 0.409 0.417 6.7.2 Test cylindrical shells with a circumferential dent The test cylindrical shells B1 and B2 having a longitudinal dent failed at the critical buckling load of 5.8kN and 5.9 kn respectively. In both the cases, on reaching the Iimit load condition the first plastic failure of the cylindrical shells was noticed on the dent geometry of cylindrical shell. The buckle pattern of the test
cylindrical shells B 1 and B2 are shown in Fig.6.10 (a) and Fig. 6.10(b) respectively. Before performing the buckling test on the test cylindrical shells B 1 and B2, the size of the dent is measured by marking the extent of dent depression. These marks covering the dent depression were then measured on the measurement rig using slide movement of dial holder and the angular moment of the specimens. The size of dent depression on the cylindrical shell B1 was length 32.5mm x width 17.5m1-n x depth 1.742mm. Similarly the size of dent depression on test cylindrical shell B2 was found to be length 23.5mrn x width 16mm x depth 2.05mm. Fig. 6.9 Buckle patterns of (a) test cy llindrical shell A1 and (b) test cylindric shell A2 From the imperfection measuren rent of test cylindrical shell B1, shown in Fig. 6.7(c) it was found that maximu1 n amplitude of imperfection on positj.ve (radially outward direction) and negative side (radially inward direction) was fou nd to be 0.246mm and 1.742 mm (taken as 1 depth of dent) respectively, with respect to imaginary perfect cylindrical shell of radius 47.8rnrn. Similarly, for B2 ti est
cylindrical shell, the positive and negative maximum amplitudes of imperfections were found to be 0.1 65mm and 1.443rnrn (taken as depth of dent) respectively. From the above measurement it is clear that the difference in buckling strengths between B1 and B2 test cylindrical shells may be due to combined effects of increase in length and depth of dent on the test cylindrical shell B1 (compared with dent dimensions on test cylindrical shell B2). Since, it is already proved that in the chapter IV, section 4.2, the effect of circumferential dent width variation on buckling strength is negligible. Also, distributed geometrical imperfection effect is not significant for test cylindrical shells taken for study. In both the cases, on reaching the limit load condition, permanent plastic failure is noticed only at the dent geometry of the test cylindrical shell as shown in Fig. 6.10. As the load applied on the test cylindrical shells is increased beyond the limit load condition, the dent geometry deformed further in radially inward direction and also expanded along the longitudinal axis of dent. And on hrther loading, a partial ring of plastic bulge zone excluding dent effective region (means that the extent of circumferential width over which dent effectiveness can be realized) was formed at the top edge of the cylindrical shell. This part of experimental work further shows that the effect of a circumferential dent on buckling strength and the failure patterns on limit load condition obtained by numerical analyses in the chapter IV, section 4.2, for stainless steel cylindrical shells. i.e., cylindrical shells with a circumferential dent will have lowest buckling strength compared to other angles of inclination of dent and plastic failure is first noticed only at dent geometry.
Fig. 6.10 Buckle patterns of (a) test cylindrical shell B1 and (b) test cylindrical shell B2 c) Test cylindrical shells with a longitudinal dent The test cylindrical shells C1 and C2 having a longitudinal dent failed at the critical buckling load of 6.lkN and 6.2 kn respectively. In both the cases, on reaching the limit load condition the failure of the cylindrical shells were noticed with the formation of partial ring of plastic bulge at the top edge of the cylindrical shell. The buckle patterns of the test cylindrical shells C1 and C2 are shown in Fig.6.11 (a) and Fig, 6.11 (b) respectively. Here also, before performing the buckling test on the test cylindrical shells C1 and C2, the size of the dents were measured by marking the extent of dent depression. These marks covering the dent depression were then measured on the measurement rig using slide movement of dial holder and the angular moment of the specimens. The size of dent depression on the cylindrical shell C1 was length 3lmm x width 19.5m x depth 2.536m.m. Similarly the size of dent depression on test cylindrical shell C2 was found to be length 31.5mm x width 17.5m.m x depth 2.05mm. From the imperfection measurement of test cylindrical shell C1, it was found that maximum amplitude of imperfection on positive (radially outward
direction) and negative side (radially inward direction) was found to be 0.288mm and 2.536 mm (taken as depth of dent) respectively with respect to imaginary perfect cylindrical shell of radius 47.8mm. Similarly for C2 test cylindrical shell, the positive and negative maximum amplitudes of imperfections were found to be 0.132mm and 2.485rnm (taken as depth of dent) respectively. From the above measurement it is clear that the difference in buckling strength between C1 and C2 test cylindrical shells may be due to combined effects of increase in width and depth of dent on the test cylindrical shell C1 compared with dent dimension on test cylindrical shell C2. This part of experimental work further evidences that the effect of a longitudinal dent on buckling strength and the failure patterns obtained from numerical analyses in the chapter IV, section 4.2,for stainless steel cylindrical shells. i.e., Cylindrical shells with a longitudinal dent will have the highest buckling strength compared to other angles of inclination and the cylindrical shells fails by forming ring of plastic zone excluding dent effective region just on reaching the limit load condition. (a) (b) Fig. 6.11 The photographic view of buckled test cylindrical shells C1 and C2 with a longitudinal dent
Since, there was no significant variation in length of dent and also it is already proved that in the chapter IV, section 4.2, effect of longitudinal dent length variation on buckling strength is negligible. Also, distributed geometrical imperfection effect is not significant for test cylindrical shells taken for study. In the chapter IV, section 4.2, it was concluded that the buckling strength of cylindrical shells with a longitudinal dent are having almost equal strength as that of the cylindrical shell without dent but with small amplitude of distributed geometrical imperfection only. The reasons for this effect can be assigned as the extent of dent effective region is less compared to circumferential dent and therefore reduction of load support region excluding dent effective region is less and further, the longitudinal dent is oriented along the load direction, which slightly increases the stiffness of the cylindrical shell in the dent region compared to other region of cylindrical shells. The net effect of reduction of load carrying capacity due to the dent effective region and increase in load carrying capacity due to dent stiffness cause the cylindrical shell, with a longitudinal dent to have buckling strength closer to buckling strength of cylindrical shell without dent and at the same time higher buckling strength than cylindrical shells with circumferential dent. The maximum and minimum, variation between longitudinal and circumferential dents is between 3.4% and 6.9% with respect to the lowest bucming strength of 5.8k.N. It was noticed that the load on the cylindrical shells reaches the limit load condition; a partial ring of plastic bulge was noticed at top edge of the cylindrical shells. And on further loading beyond limit load condition the longitudinal dent also plastically deformed forming circwnfaential lobes at half the height of the cylindrical shells i.e. along the transverse axis of the dent and fails like circumferential dent.