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 h s work

aluminum alloy cylindrical shells are selected for study which has similar stress-

strain 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

I Silicon 1 0.452. 1

Alloying

Element

I 1ron ) 0.42 1 I

Percentage of

Composition

/ copper 1 0.012, I / Manganese 1 0.01 6 I 1 Magnesium / 0.567 I

6.1 MANUFACTUFUNG OF THIN CYLINDlUCAL SHELLS

I

To produce thin cylindrical shells fiom a extruded tube, the following steps

listed below are followed:

Chromium

(i) First, the extruded tube is cut into pieces of 1 53 mm length.

(ii) Length correction to the dimension of 150 i 0.1- on these

cylindrical specimens is done by facing operations.

0.036

(iii) 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.

(iv) 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

(v) 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 t h n 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.

f i e 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. m e 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 i x nrm b 0 5 8 5 2x in radians

Fig. 6.7 Contd ...

(0 pig. 6.7 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 1 0 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 h o b 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 d m i n 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 . 1 4 5 m 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 0.1 15mm 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

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

Edge displacement measurement in

mm (at limit load condition)

0.413

0.423

0.395

0.40 1

0.409

0.417

Test Cylindrical shell with type of imperfections

Test cylindrical shells without dent but containing only distributed geometrical imperfections

Test cylindrical shells with both distributed geometrical imperfections and a circumferential dent

Test cylindrical shells with distributed geometrical

imperfections and a longitudinal dent

Sample No.

A1

A2

B1

B2

C1

C2

Experimental buckling

strength in

0 6.2

6.2

5.8

5.9

6.1

6.2

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

shell A2

From the imperfection measuren

Fig. 6.7(c) it was found that maximu1

(radially outward direction) and negative

to be 0.246mm and 1.742 mm (taken as 1

imaginary perfect cylindrical shell of

llindrical shell A1 and (b) test cylindric

rent of test cylindrical shell B1, shown

n amplitude of imperfection on positj

side (radially inward direction) was fou

depth of dent) respectively, with respect

radius 47.8rnrn. Similarly, for B2 ti

in

.ve

nd

to

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, 6.1 1 (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 1 9 . 5 m 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 i n 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.