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Preliminary results from fatigue tests on in situ sea ice beams
cold regions science and technology ELSEVIER
Cold Regions Science and Technology24 (1996) 167-176
Preliminary results from fatigue tests on in situ sea ice beams T.G. Haskell
a,
W.H. Robinson
a,
P.J. Langhorne b
a New Zealand Institute for Industrial Research and Development, P.O. Box 31310, Lower Hutt, New Zealand b Physics Department, Uni~,ersity of Otago, P.O. Box 56, Dunedin, New Zealand
Received 26 October 1994; accepted 20 July 1995
Abstract Measurements of the fatigue characteristics of sea ice will give an indication of its possible failure mechanisms under repeated loading such as occur with wave action and the operations of vehicles and aircraft. In this paper we present the results of a series of fatigue experiments carried out in the McMurdo Sound, Antarctica during the summer of 1992. The results presented here are in the form of a standard fatigue curve (with zero mean stress), that is "stress amplitude" versus "number of cycles to failure", commonly known as an S - N curve. The "endurance limit", that is the stress below which the sea-ice can withstand an unlimited number of cycles, is for sea ice in situ, approximately half the failure stress.
I. I n t r o d u c t i o n The annual formation and dissipation of the Antarctic sea ice sheet, which is equal in area to the rest of the permanent Antarctic ice sheet, provides a damping effect which helps to stabilize the world climate. This project on the " L o w cycle fatigue of sea ice" is part of our ten year program: " A multiscale, multiprocess study of sea ice, its break-up, and its effect on the climate of the Southern O c e a n " . A knowledge of the fatigue behavior of sea ice is of importance when assessing the various predictions for the break-up of the sea ice each Austral summer since a significant contribution may be due to fatigue. The experiments on the fatigue of sea ice reported here represent the culmination of three attempts. In the 1 9 8 9 - 9 0 Austral summer the tests were a failure because of the refreezing of saw cuts around a 2.5 m
long handheld chain saw, while the 1991-2 season was aborted when the brand new trench digger's engine failed. Thus, these results for the O c t o b e r November 1992 period of the 1992-93 season, represent the climax of three summer seasons in the Antarctic. While a considerable amount of work has been done on the fatigue of both fresh water ice and sea ice (Haynes et al., 1993; Nixon and Smith, 1986; Nixon and Weber, 1991; Mellor and Cole, 1981; Sinha, 1991) we believe that this is the first attempt at studying fatigue in sea ice in situ. The tests were conducted in situ as the physical characteristics of sea ice change markedly if it is withdrawn from the sea. The fatigue tests were carried out on cantilever beams (Frederking and Timco, 1983; Svec and Frederking, 1981; Svec et al., 1985) cut into the sea ice sheet and cycled at zero mean stress with various amplitudes of stress. The
0165-232X/96/$15.00 © 1996 Elsevier Science B.V. All rights reserved SSDI 0165 -232X(95)00015- 1
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TG. Haskell et al. / Cold Regions Science and Technology 24 (1996) 167-176
dimensions o f the beams were nominally 10 m long, 1 m wide and 2 m deep. While the beams were being cycled to failure, f o r c e - d i s p l a c e m e n t hysteresis loops were recorded, together with the acoustic emission from the area o f the hinge line where the failure was most likely to occur. The results presented here are in the form o f a standard fatigue curve, that is "stress a m p l i t u d e " versus " n u m b e r of cycles to failure", c o m m o n l y known as an S - N curve (Van Vlack, 1985). W e believe this is the first time an S - N curve for the fatigue of sea ice in situ has been presented. The " e n d u r a n c e l i m i t " for sea ice in situ was found to be ~ 0.5 times the failure stress, a value similar to many other materials.
2. Experiment Beam dimensions are primarily determined by the thickness of the sea ice, which in the areas of aircraft and vehicle operations in M c M u r d o Sound range from 1.5 to 2.5 m. The beam dimensions recommended by Schwarz et al. (1981) are beam width greater than 10 times the crystal size and beam length greater than 7 to 10 times its thickness. The first condition causes us no difficulty, with the beams being 1 m wide. The second is more difficult to meet as the time required to cut a longer beam must be weighed up against the physical properties of the ice beam changing due to the influence of the cut. The ultimate failure strength of the ice and the structural requirements of the test rig, together with the stability against twisting o f the beam, determine the width of the test specimen. In this series o f experiments a beam width of l m has been found to be satisfactory. A length of 10 m i.e. a 5 to 1 ratio was used as this provided a satisfactory compromise between the 10 to 1 ratio suggested by Schwartz, and time taken to cut the beam. Consequently once allowance has been made for the space required on the beam for the hydraulic test equipment, the beam dimensions become approximately 2 m d e e p X 1 m w i d e X 12 m long (Fig. 1). The cutting time for beams such as this is approximately four hours in ice where the surface temperature is near to - 12°C. The cutting technique should be well controlled as
it must be done quickly and accurately with as little flooding of the surface of the beam as possible, especially in the hinge area o f the cantilever where the failure of the beam is expected to occur. The cutting of the beam is done with a small tractor mounted chain digger, with a depth of cut of approximately 2.2 m. This machine is relatively light and is rubber tyred preventing damage to the surface of the beam and hence the introduction of stress concentrations from which fracture may start. The cutting is done in a series of stages. Initially the two side cuts of the beam are completed down to a depth some 200 mm less than the depth of the ice, preventing the ingress of warm sea water into the slot before testing. The hydraulic test rig is placed in position over the beam and the fastening screws (Haskell and Robinson, 1994) attached firmly in the ice at the appropriate positions. The test rig is then removed and side cuts completed to full depth. Where the cuts come up to the fixed end of the beam, a hole is drilled at the end of each cut to produce a circular end to the cut. This produces a rounded end which is free of sharp stress concentrations as recommended by Svec et al. (1985) (right hand side of Fig. 2). The hydraulic rig is then repositioned and locked to prevent the beam moving prematurely, and the free end cut is then made across the beam. The beam is cycled using a sinusoidal force or displacement with the amplitude set at the start of the test. This amplitude is chosen so that it is some fraction of the force or displacement which is required to break the beam in a quarter cycle. The cycling period can be set from 128 to 0.25 seconds and the force amplitude can be set from 0 to 200 kN
pplied Displacementmeasured Hinge line Fig. 1. Plan view of beam showing typical dimensions.
T.G. Haskell et al. / CoM Regions Science and Technology 24 (1996) 167-176
169
Fig. 2. Stress relieved end of cut and typical beam failure crack.
( ~ 20 tonne). The shape of the output driving force or displacement can be sinusoidal or triangular. The system which drives the beam measures both force and displacement o f the beam at the free end and displacement across the hinge. Various feedback regimes can be used to close the control loop. In the series of experiments carried out this season force feedback was used exclusively. The power for the hydraulic system comes from the digger which can supply the high pressure oil at the required flow rates. A compromise must be made to determine a suitable period at which to drive the ice beam. This must be considered as the rate of crack formation and development is dependent on strain rate (Sinha, 1982, Sinha, 1988). W a v e s propagate into the sea ice from the open sea at periods ranging from about six to sixteen seconds. On the other hand the waves produced by moving vehicles and aircraft occur at periods from one half o f a second to six seconds. As the water in the slots around the ice beam tends to freeze quickly, especially when the ice is cold, it is necessary to complete the tests as quickly as possible. Finally, a period of eight seconds was decided on as being in about the centre of the range of periods occurring in nature. In future years we may,
depending on the result of more detailed analysis of these results, extend the investigation to a wider range of periods.
3. Results The stress of major interest here is the bending stress occurring across the hinge of the beam and can be calculated from the applied force at the hydraulic actuator and the dimensions of the beam using simple beam theory via or = 6 F l / w h 2
where tr = bending stress across the hinge end of the beam, F = force applied at the end o f the beam, l = distance between the force application point and the hinge o f the beam, w = width of the beam and h = depth of the beam. The beam dimensions are such that stress due to shear is ~ 3% o f that due to bending and can be ignored in the first approximation. Displacement across the hinge end of the beam is measured directly by a linear variable displacement transducer which is fixed to the ice across a line where the break is expected to occur at the fixed end of the
170
T.G. Haskell et a l . / C o l d Regions Science and Technology 24 (1996) 167-176
beam (Figs. 2 and 3). While the beam is undergoing testing, high frequency acoustic emissions are generated by the deformation processes within the beam. These acoustic emissions are detected by piezoelectric sensors and will, once more fully understood, provide a suitable diagnostic tool for use in the determination of the safety of ice near vehicles and aircraft (Langhorne et al., 1990; Squire et al., 1985, Squire et al., 1988). The layout of the sensors relative to the beam can be seen in Fig. 1. The collection of the data from the beam was by way of a small computer with appropriate data logging equipment attached. Usually displacement both across the expected break and near the force actuator are recorded, together with the applied force. During acoustic emission experiments very high speed data from the transducers is recorded on a high speed data
logger and down loaded to a computer for storage when necessary. The sampling rates for the mechanical measurements were of the order of 10 Hz and for the acoustic emission measurements of the order of 40 kHz. As some fatigue experiments may take up to several hours, attempts must be made to keep the water-filled cut around the ice beam from refreezing. This is done by scooping the ice slush from the cut as it forms, enabling beams to remain isolated from the surrounding ice sheet for about four hours. Air temperature for the period of the experiment reported here (24 October 1992 through to l0 November 1992) stayed relatively constant at about - 12°C at the test site. There was about 100 mm of snow cover over the whole site, this was removed just prior to a beam being cut. In an attempt to remove some of the systematic errors associated with the small variations of temperature and consequently brine volume over the test period, the fatigue experiments were carried out in a random order i.e. the maximum stress amplitudes were selected randomly. During the period of the fatigue tests a number of ice cores were cut and analyzed and a buried thermistor temperature measuring array was monitored on a daily basis (Cox and Weeks, 1988). Average brine volume did not change significantly over the period of the tests.
4. E x p e r i m e n t a l r e s u l t s a n d d i s c u s s i o n
Fig. 3. Position of test and measuring equipment around beam.
Fig. 4 shows typical outputs from the force and displacement transducers on the beam during a 30 cycle-to-failure test. Fig. 5 shows the associated hysteresis curves for force and displacement for typical cycles in the 30 cycle-to-failure test. Failure appears to occur very quickly with little warning, the amplitudes of neither the force nor the displacement showing any significant change until a sudden catastrophic failure occurred. Complicating the understanding and analysis of the experimental results is the problem of the initiation and growth of cracks (Sinha, 1991). Since during our fatigue experiments it is not possible to observe the formation and growth of cracks, or analyze the hysteresis loops in the form of elastic plus plastic components (Rodriguea and Rao, 1993),
171
T.G. Haskell et al. / Cold Regions Science and Technology 24 (1996) 167-176
we are limited to the simple standard stress versus number of cycles to failure, c o m m o n l y known as an S - N curve. Temperature, and consequently brine volume, will have a significant effect on the fatigue characteristics of sea ice.
On the S - N curve obtained for sea ice in situ (Fig. 6), the point labelled A was obtained from a beam which did not break but eventually refroze into the surrounding sea ice. Consequently all we know from this point is that the sea ice will stand more
Force at free end of the beam
(a) 25 I - -
i i
20 15 10 5 o
0 -5 -10 -15 -20 150
200
250
300
350
400
450
400
450
Time (sec) (b)
xl0"3
Displacement at free end of the beam r
8
6
4
2
0
-2 -4
-6
150
200
250
300
350
Time (sec)
Fig. 4. Force and displacement curves.
T.G. Haskell et al. / Cold Regions Science and Technology 24 (1996) 167--176
172
than 2500 cycles at this stress amplitude. The point labelled B is calculated from data obtained in another experiment on wave propagation through sea ice, assuming from this data that the period is of the
order of six seconds and the stress amplitude is about 50 kPa and that the sea ice has been present for about six months. It can be seen that the S - N curve when plotted on a stress amplitude against log of
Force displacement curve from an early cycle
(a) 2O 15 lO 5
~
o -5 -101 -15 -20 -3
1
i
i
I
i
-2
-1
0
1
2
Displacement (m)
(b)
x l 0 .3
Force displacement curve from a middle cycle 20 15 10 5 0
o f~
-5 -10 -15 ~ -20 -3
i
L
i
i
i
-2
-1
0
1
2
Displacement (m) Fig. 5. Typical hysteresis curves up to failure.
__
3 x 10 -3
T.G. Haskell et al. / Cold Regions Science and Technology 24 (1996) 167-176
(c)
173
Force displacement curve from a cycle near failure 25
r
20 15 10 5 o
0
U.
-5 -10 -15 -20 -3
i
-2
-1
1
2
3
Displacement (m)
xl0 -3
Fig. 5 (continued).
S-N Curve for First Year Sea Ice 450
i
i
=
<---Yield limit
400 \
\
350 X
\ 5~
300 It. v ¢D
250 Endurance limit--->
¢L
E
X
200
-°-~>
A, Unbroken
(/)
.e
150
100 50 X
---~
B, Unbroken I
10 .2
100
I
=
I
10 a 10 4 Cycles to Failure Fig. 6. S - N curve for fatigue of sea ice.
I
106
=
108
174
TG. Haskell et al. /Cold
Re,yions Science
and Technology
Table I Stress amolitude
cycles to failure, produces a curve typical of many materials as diverse as single and polycrystalline metals, and even wood (Kyanka, 1980). The S-N curve results indicate that the sea ice has an endurance limit of the order of 250 kPa, and a failure stress of the order of 425 kPa. The value for the ratio of the endurance limit to the failure stress is similar to the 0.3 to 0.5 found for many other materials (for example certain type of steels and plastics). The actual values of the stress amplitude across the hinge of the beam calculated from simple beam theory and the associated number of cycles to failure appear in Table 1. Changes in the form of the hysteresis loop (Fig. 5) have been observed, and detailed analysis of these
Cycles
to
failure
Comments
failure strength
0.25
430 400
3
325
30
300
200
275
>200
210
below endurance limit
>3XlOfJ
- 40
below endurance limit
observations is under way. The shape of the hysteresis loops (Anderson, 19911, together with acoustic emission results, point to micro crackjng being one
-15
-20
-5
-10
temperature / 0C
I
0.1
Fig. 7. Typical physical properties
vs. number of cvcles to failure Maximum stress at hinge (kPa)
2
15
5 10 salinity / ppt
24 (I 996) 167- I76
of sea ice over the experimental
0.15 brine volume
0.2
I
0.25
period. Legend:
Date
Core
Symbol
Line
24/10/92 25/10/92 31/10/92 09/l l/92 II/II/92
3 4 6 7 8
0 + * 0 X
solid dash dot dash dash dotted solid
0
T.G. Haskell et al. / Cold Regions Science and Technology 24 (199¢~) 167-176
o f the m e c h a n i s m s which lead to failure o f the ice. In addition the w h o l e process is e x p e c t e d to be c o m p l i cated by a m e c h a n i s m o f s e l f repair. W e b e l i e v e that this " h e a l i n g " process in ice at these t e m p e r a t u r e s is likely to be free sea water p e r m e a t i n g the ice and f r e e z i n g in the m i c r o cracks. This r e f r e e z i n g process m a y m a k e the ice as strong as it was initially. If this is so, fatigue of sea ice in situ is likely to be rate d e p e n d e n t as well as b e i n g d e p e n d e n t on brine volu m e and p r e v i o u s history. In the 1994 and 1995 seasons we intend to extend these results to c o v e r both variations in brine v o l u m e , stress a m p l i t u d e and rate o f excitation o f the beam. A s m e n t i o n e d p r e v i o u s l y the brine v o l u m e rem a i n e d relatively constant o v e r the period w h e n most o f the fatigue m e a s u r e m e n t s w e r e made. l-'lots o f salinity, temperature and brine v o l u m e appear in Fig. 7. B e a r in m i n d that m o s t o f the e x p e r i m e n t a l w o r k was done in the period 24 O c t o b e r 1992 to the 31 O c t o b e r 1992.
5. Future work It is intended, if e n o u g h e x p e r i m e n t a l i n f o r m a t i o n can be obtained, to relate the fatigue properties o f first year sea ice to the f o l l o w i n g p a r a m e t e r s i.e. the n u m b e r o f c y c l e s - t o - f a i l u r e to the strain amplitude, brine v o l u m e and strain rate. T h e S - N c u r v e presented here is just a cut through the surface linking those parameters.
6. Conclusions 1. It is possible, with s o m e difficulty, to conduct l o w - c y c l e fatigue e x p e r i m e n t s on sea ice in situ in c o l d regions such as the M c M u r d o Sound, Antarctica. 2. P r e l i m i n a r y results for the stress versus n u m b e r o f cycles to failure, that is an S - N c u r v e (Fig. 6), indicate that the sea ice b e h a v e s in a similar w a y to other materials, with an e n d u r a n c e stress level, o f 250 kPa, a p p r o x i m a t e l y 5 0 % o f its failure stress.
175
Acknowledgements This research was supported by the F o u n d a t i o n for R e s e a r c h S c i e n c e and T e c h n o l o g y , the N e w Z e a l a n d Institute for Industrial R e s e a r c h and D e v e l o p m e n t and the U n i v e r s i t y o f Otago. T h e authors also wish to a c k n o w l e d g e the National S c i e n c e F o u n d a t i o n for logistical support in Antarctica.
References Anderson, T.L., 1991. Fracture Mechanics. CRC Press, ISBN 0-8493-4277-5. Cox, G.F.N. and Weeks, W.F., 1988. Profile properties of undeformed first-year sea ice. CRREL Report 88-13. Frederking, R.M.W. and Timco, G.W., 1983. On measuring flexural properties of ice using cantilever beams. Ann. Glaciol., 4: 58-65. Haskell, T.G. and Robinson, W.H., 1994. Techniques for fastening hydraulic test systems to sea ice. Cold Reg. Sci. Technol., 23: 105-107. Haynes, D.F., Kerr, A.D. and Martinson, CR., 1993. Effect of fatigue on the bearing capacity of floating ice sheets. Cold Reg. Sci. Technol., 21: 257-263. Kyanka, G.H., 1980. Fatigue properties of wood and wood composites. Int. J. Fract., 16: 609-616, Langhorne, P.J., Robinson, W.H. and Squire, V.A., 1990. Acoustic emission generated by moving loads on sea ice. Cold Reg. Sci. Technol., 18: 337-342. Mellor, M. and Cole, D., 1981. Cyclic loading and fatigue in ice. Cold Reg. Sci. Technol., 4: 41-53. Nixon, W.A. and Smith, R.A., 1986. The fatigue behavior of freshwater ice. J. Phys. Coll. CI, Suppl. aun 3, 48: 329-335. Nixon, W.A. and Weber, L.J., 1991. Fatigue-crack growth in fresh-water ice: preliminary results. Ann. Glaciol., 15: 236241. Rodriguea, P. and Rao, K.B.S., 1993. Nucleation and growth of cracks and cavities under creep-fatigue interactions. Prog. Mater. Sci., 37(5): 403-480. Schwarz, J., Frederking, R., Gavrillo, V., Petrov, 1.G., Hirayarna, K.I., Mellor, M., Tryde, P. and Vaudry, K.D., 1981. Standardized testing methods for measuring mechanical properties of ice. Cold Reg. Sci. Technol., 4: 245-253. Sinha, N.K., 1982. Acoustic emission and microcracking in ice. In: Proceedings of SESA, Honolulu, Vol. II, pp. 767-772. Sinha, N.K., 1988. Crack-enhanced creep in polycrystalline material: strain-rate sensitive strength and deformation of ice. J. Mater. Sci., 23(12): 4415-4428. Sinha, N.K., 1991. Cracking kinetics and failure on repeated loadings of ice. In: ISFF '91 Proceedings, Madras, pp. 137150.
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T.G. Haskell et al. / Cold Regions Science and Technology 24 (1996) 167-176
Svec, O.J. and Frederking, R.M.W., 1981. Cantilever beam tests in an ice cover: influence of plate effects at the root. Cold Reg. Sci. Technol., 4: 93-101. Svec, O.J., Thompson, J.C. and Frederking, R.M.W., 1985. Stress concentrations in the root of an ice cover cantilever: model tests and theory. Cold Reg. Sci. Technol., 11 : 63-73. Squire, V.A., Robinson, W.H., Haskell, T.G. and Moore, S.C.,
1985. Dynamic response of lake and sea ice to moving loads. Cold Reg. Sci. Technol., 11: 123-129. Squire, V.A., Robinson, W.H., Langhome, P.J. and Haskell, T.G., 1988. Vehicles and aircraft on floating ice. Nature (London), 33: 159-161. Van Vlack, LH., 1985. Elements of Materials Science and Engineering. 5th ed. Addison-Wesley.
Cold Regions Science and Technology24 (1996) 167-176
Preliminary results from fatigue tests on in situ sea ice beams T.G. Haskell
a,
W.H. Robinson
a,
P.J. Langhorne b
a New Zealand Institute for Industrial Research and Development, P.O. Box 31310, Lower Hutt, New Zealand b Physics Department, Uni~,ersity of Otago, P.O. Box 56, Dunedin, New Zealand
Received 26 October 1994; accepted 20 July 1995
Abstract Measurements of the fatigue characteristics of sea ice will give an indication of its possible failure mechanisms under repeated loading such as occur with wave action and the operations of vehicles and aircraft. In this paper we present the results of a series of fatigue experiments carried out in the McMurdo Sound, Antarctica during the summer of 1992. The results presented here are in the form of a standard fatigue curve (with zero mean stress), that is "stress amplitude" versus "number of cycles to failure", commonly known as an S - N curve. The "endurance limit", that is the stress below which the sea-ice can withstand an unlimited number of cycles, is for sea ice in situ, approximately half the failure stress.
I. I n t r o d u c t i o n The annual formation and dissipation of the Antarctic sea ice sheet, which is equal in area to the rest of the permanent Antarctic ice sheet, provides a damping effect which helps to stabilize the world climate. This project on the " L o w cycle fatigue of sea ice" is part of our ten year program: " A multiscale, multiprocess study of sea ice, its break-up, and its effect on the climate of the Southern O c e a n " . A knowledge of the fatigue behavior of sea ice is of importance when assessing the various predictions for the break-up of the sea ice each Austral summer since a significant contribution may be due to fatigue. The experiments on the fatigue of sea ice reported here represent the culmination of three attempts. In the 1 9 8 9 - 9 0 Austral summer the tests were a failure because of the refreezing of saw cuts around a 2.5 m
long handheld chain saw, while the 1991-2 season was aborted when the brand new trench digger's engine failed. Thus, these results for the O c t o b e r November 1992 period of the 1992-93 season, represent the climax of three summer seasons in the Antarctic. While a considerable amount of work has been done on the fatigue of both fresh water ice and sea ice (Haynes et al., 1993; Nixon and Smith, 1986; Nixon and Weber, 1991; Mellor and Cole, 1981; Sinha, 1991) we believe that this is the first attempt at studying fatigue in sea ice in situ. The tests were conducted in situ as the physical characteristics of sea ice change markedly if it is withdrawn from the sea. The fatigue tests were carried out on cantilever beams (Frederking and Timco, 1983; Svec and Frederking, 1981; Svec et al., 1985) cut into the sea ice sheet and cycled at zero mean stress with various amplitudes of stress. The
0165-232X/96/$15.00 © 1996 Elsevier Science B.V. All rights reserved SSDI 0165 -232X(95)00015- 1
168
TG. Haskell et al. / Cold Regions Science and Technology 24 (1996) 167-176
dimensions o f the beams were nominally 10 m long, 1 m wide and 2 m deep. While the beams were being cycled to failure, f o r c e - d i s p l a c e m e n t hysteresis loops were recorded, together with the acoustic emission from the area o f the hinge line where the failure was most likely to occur. The results presented here are in the form o f a standard fatigue curve, that is "stress a m p l i t u d e " versus " n u m b e r of cycles to failure", c o m m o n l y known as an S - N curve (Van Vlack, 1985). W e believe this is the first time an S - N curve for the fatigue of sea ice in situ has been presented. The " e n d u r a n c e l i m i t " for sea ice in situ was found to be ~ 0.5 times the failure stress, a value similar to many other materials.
2. Experiment Beam dimensions are primarily determined by the thickness of the sea ice, which in the areas of aircraft and vehicle operations in M c M u r d o Sound range from 1.5 to 2.5 m. The beam dimensions recommended by Schwarz et al. (1981) are beam width greater than 10 times the crystal size and beam length greater than 7 to 10 times its thickness. The first condition causes us no difficulty, with the beams being 1 m wide. The second is more difficult to meet as the time required to cut a longer beam must be weighed up against the physical properties of the ice beam changing due to the influence of the cut. The ultimate failure strength of the ice and the structural requirements of the test rig, together with the stability against twisting o f the beam, determine the width of the test specimen. In this series o f experiments a beam width of l m has been found to be satisfactory. A length of 10 m i.e. a 5 to 1 ratio was used as this provided a satisfactory compromise between the 10 to 1 ratio suggested by Schwartz, and time taken to cut the beam. Consequently once allowance has been made for the space required on the beam for the hydraulic test equipment, the beam dimensions become approximately 2 m d e e p X 1 m w i d e X 12 m long (Fig. 1). The cutting time for beams such as this is approximately four hours in ice where the surface temperature is near to - 12°C. The cutting technique should be well controlled as
it must be done quickly and accurately with as little flooding of the surface of the beam as possible, especially in the hinge area o f the cantilever where the failure of the beam is expected to occur. The cutting of the beam is done with a small tractor mounted chain digger, with a depth of cut of approximately 2.2 m. This machine is relatively light and is rubber tyred preventing damage to the surface of the beam and hence the introduction of stress concentrations from which fracture may start. The cutting is done in a series of stages. Initially the two side cuts of the beam are completed down to a depth some 200 mm less than the depth of the ice, preventing the ingress of warm sea water into the slot before testing. The hydraulic test rig is placed in position over the beam and the fastening screws (Haskell and Robinson, 1994) attached firmly in the ice at the appropriate positions. The test rig is then removed and side cuts completed to full depth. Where the cuts come up to the fixed end of the beam, a hole is drilled at the end of each cut to produce a circular end to the cut. This produces a rounded end which is free of sharp stress concentrations as recommended by Svec et al. (1985) (right hand side of Fig. 2). The hydraulic rig is then repositioned and locked to prevent the beam moving prematurely, and the free end cut is then made across the beam. The beam is cycled using a sinusoidal force or displacement with the amplitude set at the start of the test. This amplitude is chosen so that it is some fraction of the force or displacement which is required to break the beam in a quarter cycle. The cycling period can be set from 128 to 0.25 seconds and the force amplitude can be set from 0 to 200 kN
pplied Displacementmeasured Hinge line Fig. 1. Plan view of beam showing typical dimensions.
T.G. Haskell et al. / CoM Regions Science and Technology 24 (1996) 167-176
169
Fig. 2. Stress relieved end of cut and typical beam failure crack.
( ~ 20 tonne). The shape of the output driving force or displacement can be sinusoidal or triangular. The system which drives the beam measures both force and displacement o f the beam at the free end and displacement across the hinge. Various feedback regimes can be used to close the control loop. In the series of experiments carried out this season force feedback was used exclusively. The power for the hydraulic system comes from the digger which can supply the high pressure oil at the required flow rates. A compromise must be made to determine a suitable period at which to drive the ice beam. This must be considered as the rate of crack formation and development is dependent on strain rate (Sinha, 1982, Sinha, 1988). W a v e s propagate into the sea ice from the open sea at periods ranging from about six to sixteen seconds. On the other hand the waves produced by moving vehicles and aircraft occur at periods from one half o f a second to six seconds. As the water in the slots around the ice beam tends to freeze quickly, especially when the ice is cold, it is necessary to complete the tests as quickly as possible. Finally, a period of eight seconds was decided on as being in about the centre of the range of periods occurring in nature. In future years we may,
depending on the result of more detailed analysis of these results, extend the investigation to a wider range of periods.
3. Results The stress of major interest here is the bending stress occurring across the hinge of the beam and can be calculated from the applied force at the hydraulic actuator and the dimensions of the beam using simple beam theory via or = 6 F l / w h 2
where tr = bending stress across the hinge end of the beam, F = force applied at the end o f the beam, l = distance between the force application point and the hinge o f the beam, w = width of the beam and h = depth of the beam. The beam dimensions are such that stress due to shear is ~ 3% o f that due to bending and can be ignored in the first approximation. Displacement across the hinge end of the beam is measured directly by a linear variable displacement transducer which is fixed to the ice across a line where the break is expected to occur at the fixed end of the
170
T.G. Haskell et a l . / C o l d Regions Science and Technology 24 (1996) 167-176
beam (Figs. 2 and 3). While the beam is undergoing testing, high frequency acoustic emissions are generated by the deformation processes within the beam. These acoustic emissions are detected by piezoelectric sensors and will, once more fully understood, provide a suitable diagnostic tool for use in the determination of the safety of ice near vehicles and aircraft (Langhorne et al., 1990; Squire et al., 1985, Squire et al., 1988). The layout of the sensors relative to the beam can be seen in Fig. 1. The collection of the data from the beam was by way of a small computer with appropriate data logging equipment attached. Usually displacement both across the expected break and near the force actuator are recorded, together with the applied force. During acoustic emission experiments very high speed data from the transducers is recorded on a high speed data
logger and down loaded to a computer for storage when necessary. The sampling rates for the mechanical measurements were of the order of 10 Hz and for the acoustic emission measurements of the order of 40 kHz. As some fatigue experiments may take up to several hours, attempts must be made to keep the water-filled cut around the ice beam from refreezing. This is done by scooping the ice slush from the cut as it forms, enabling beams to remain isolated from the surrounding ice sheet for about four hours. Air temperature for the period of the experiment reported here (24 October 1992 through to l0 November 1992) stayed relatively constant at about - 12°C at the test site. There was about 100 mm of snow cover over the whole site, this was removed just prior to a beam being cut. In an attempt to remove some of the systematic errors associated with the small variations of temperature and consequently brine volume over the test period, the fatigue experiments were carried out in a random order i.e. the maximum stress amplitudes were selected randomly. During the period of the fatigue tests a number of ice cores were cut and analyzed and a buried thermistor temperature measuring array was monitored on a daily basis (Cox and Weeks, 1988). Average brine volume did not change significantly over the period of the tests.
4. E x p e r i m e n t a l r e s u l t s a n d d i s c u s s i o n
Fig. 3. Position of test and measuring equipment around beam.
Fig. 4 shows typical outputs from the force and displacement transducers on the beam during a 30 cycle-to-failure test. Fig. 5 shows the associated hysteresis curves for force and displacement for typical cycles in the 30 cycle-to-failure test. Failure appears to occur very quickly with little warning, the amplitudes of neither the force nor the displacement showing any significant change until a sudden catastrophic failure occurred. Complicating the understanding and analysis of the experimental results is the problem of the initiation and growth of cracks (Sinha, 1991). Since during our fatigue experiments it is not possible to observe the formation and growth of cracks, or analyze the hysteresis loops in the form of elastic plus plastic components (Rodriguea and Rao, 1993),
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T.G. Haskell et al. / Cold Regions Science and Technology 24 (1996) 167-176
we are limited to the simple standard stress versus number of cycles to failure, c o m m o n l y known as an S - N curve. Temperature, and consequently brine volume, will have a significant effect on the fatigue characteristics of sea ice.
On the S - N curve obtained for sea ice in situ (Fig. 6), the point labelled A was obtained from a beam which did not break but eventually refroze into the surrounding sea ice. Consequently all we know from this point is that the sea ice will stand more
Force at free end of the beam
(a) 25 I - -
i i
20 15 10 5 o
0 -5 -10 -15 -20 150
200
250
300
350
400
450
400
450
Time (sec) (b)
xl0"3
Displacement at free end of the beam r
8
6
4
2
0
-2 -4
-6
150
200
250
300
350
Time (sec)
Fig. 4. Force and displacement curves.
T.G. Haskell et al. / Cold Regions Science and Technology 24 (1996) 167--176
172
than 2500 cycles at this stress amplitude. The point labelled B is calculated from data obtained in another experiment on wave propagation through sea ice, assuming from this data that the period is of the
order of six seconds and the stress amplitude is about 50 kPa and that the sea ice has been present for about six months. It can be seen that the S - N curve when plotted on a stress amplitude against log of
Force displacement curve from an early cycle
(a) 2O 15 lO 5
~
o -5 -101 -15 -20 -3
1
i
i
I
i
-2
-1
0
1
2
Displacement (m)
(b)
x l 0 .3
Force displacement curve from a middle cycle 20 15 10 5 0
o f~
-5 -10 -15 ~ -20 -3
i
L
i
i
i
-2
-1
0
1
2
Displacement (m) Fig. 5. Typical hysteresis curves up to failure.
__
3 x 10 -3
T.G. Haskell et al. / Cold Regions Science and Technology 24 (1996) 167-176
(c)
173
Force displacement curve from a cycle near failure 25
r
20 15 10 5 o
0
U.
-5 -10 -15 -20 -3
i
-2
-1
1
2
3
Displacement (m)
xl0 -3
Fig. 5 (continued).
S-N Curve for First Year Sea Ice 450
i
i
=
<---Yield limit
400 \
\
350 X
\ 5~
300 It. v ¢D
250 Endurance limit--->
¢L
E
X
200
-°-~>
A, Unbroken
(/)
.e
150
100 50 X
---~
B, Unbroken I
10 .2
100
I
=
I
10 a 10 4 Cycles to Failure Fig. 6. S - N curve for fatigue of sea ice.
I
106
=
108
174
TG. Haskell et al. /Cold
Re,yions Science
and Technology
Table I Stress amolitude
cycles to failure, produces a curve typical of many materials as diverse as single and polycrystalline metals, and even wood (Kyanka, 1980). The S-N curve results indicate that the sea ice has an endurance limit of the order of 250 kPa, and a failure stress of the order of 425 kPa. The value for the ratio of the endurance limit to the failure stress is similar to the 0.3 to 0.5 found for many other materials (for example certain type of steels and plastics). The actual values of the stress amplitude across the hinge of the beam calculated from simple beam theory and the associated number of cycles to failure appear in Table 1. Changes in the form of the hysteresis loop (Fig. 5) have been observed, and detailed analysis of these
Cycles
to
failure
Comments
failure strength
0.25
430 400
3
325
30
300
200
275
>200
210
below endurance limit
>3XlOfJ
- 40
below endurance limit
observations is under way. The shape of the hysteresis loops (Anderson, 19911, together with acoustic emission results, point to micro crackjng being one
-15
-20
-5
-10
temperature / 0C
I
0.1
Fig. 7. Typical physical properties
vs. number of cvcles to failure Maximum stress at hinge (kPa)
2
15
5 10 salinity / ppt
24 (I 996) 167- I76
of sea ice over the experimental
0.15 brine volume
0.2
I
0.25
period. Legend:
Date
Core
Symbol
Line
24/10/92 25/10/92 31/10/92 09/l l/92 II/II/92
3 4 6 7 8
0 + * 0 X
solid dash dot dash dash dotted solid
0
T.G. Haskell et al. / Cold Regions Science and Technology 24 (199¢~) 167-176
o f the m e c h a n i s m s which lead to failure o f the ice. In addition the w h o l e process is e x p e c t e d to be c o m p l i cated by a m e c h a n i s m o f s e l f repair. W e b e l i e v e that this " h e a l i n g " process in ice at these t e m p e r a t u r e s is likely to be free sea water p e r m e a t i n g the ice and f r e e z i n g in the m i c r o cracks. This r e f r e e z i n g process m a y m a k e the ice as strong as it was initially. If this is so, fatigue of sea ice in situ is likely to be rate d e p e n d e n t as well as b e i n g d e p e n d e n t on brine volu m e and p r e v i o u s history. In the 1994 and 1995 seasons we intend to extend these results to c o v e r both variations in brine v o l u m e , stress a m p l i t u d e and rate o f excitation o f the beam. A s m e n t i o n e d p r e v i o u s l y the brine v o l u m e rem a i n e d relatively constant o v e r the period w h e n most o f the fatigue m e a s u r e m e n t s w e r e made. l-'lots o f salinity, temperature and brine v o l u m e appear in Fig. 7. B e a r in m i n d that m o s t o f the e x p e r i m e n t a l w o r k was done in the period 24 O c t o b e r 1992 to the 31 O c t o b e r 1992.
5. Future work It is intended, if e n o u g h e x p e r i m e n t a l i n f o r m a t i o n can be obtained, to relate the fatigue properties o f first year sea ice to the f o l l o w i n g p a r a m e t e r s i.e. the n u m b e r o f c y c l e s - t o - f a i l u r e to the strain amplitude, brine v o l u m e and strain rate. T h e S - N c u r v e presented here is just a cut through the surface linking those parameters.
6. Conclusions 1. It is possible, with s o m e difficulty, to conduct l o w - c y c l e fatigue e x p e r i m e n t s on sea ice in situ in c o l d regions such as the M c M u r d o Sound, Antarctica. 2. P r e l i m i n a r y results for the stress versus n u m b e r o f cycles to failure, that is an S - N c u r v e (Fig. 6), indicate that the sea ice b e h a v e s in a similar w a y to other materials, with an e n d u r a n c e stress level, o f 250 kPa, a p p r o x i m a t e l y 5 0 % o f its failure stress.
175
Acknowledgements This research was supported by the F o u n d a t i o n for R e s e a r c h S c i e n c e and T e c h n o l o g y , the N e w Z e a l a n d Institute for Industrial R e s e a r c h and D e v e l o p m e n t and the U n i v e r s i t y o f Otago. T h e authors also wish to a c k n o w l e d g e the National S c i e n c e F o u n d a t i o n for logistical support in Antarctica.
References Anderson, T.L., 1991. Fracture Mechanics. CRC Press, ISBN 0-8493-4277-5. Cox, G.F.N. and Weeks, W.F., 1988. Profile properties of undeformed first-year sea ice. CRREL Report 88-13. Frederking, R.M.W. and Timco, G.W., 1983. On measuring flexural properties of ice using cantilever beams. Ann. Glaciol., 4: 58-65. Haskell, T.G. and Robinson, W.H., 1994. Techniques for fastening hydraulic test systems to sea ice. Cold Reg. Sci. Technol., 23: 105-107. Haynes, D.F., Kerr, A.D. and Martinson, CR., 1993. Effect of fatigue on the bearing capacity of floating ice sheets. Cold Reg. Sci. Technol., 21: 257-263. Kyanka, G.H., 1980. Fatigue properties of wood and wood composites. Int. J. Fract., 16: 609-616, Langhorne, P.J., Robinson, W.H. and Squire, V.A., 1990. Acoustic emission generated by moving loads on sea ice. Cold Reg. Sci. Technol., 18: 337-342. Mellor, M. and Cole, D., 1981. Cyclic loading and fatigue in ice. Cold Reg. Sci. Technol., 4: 41-53. Nixon, W.A. and Smith, R.A., 1986. The fatigue behavior of freshwater ice. J. Phys. Coll. CI, Suppl. aun 3, 48: 329-335. Nixon, W.A. and Weber, L.J., 1991. Fatigue-crack growth in fresh-water ice: preliminary results. Ann. Glaciol., 15: 236241. Rodriguea, P. and Rao, K.B.S., 1993. Nucleation and growth of cracks and cavities under creep-fatigue interactions. Prog. Mater. Sci., 37(5): 403-480. Schwarz, J., Frederking, R., Gavrillo, V., Petrov, 1.G., Hirayarna, K.I., Mellor, M., Tryde, P. and Vaudry, K.D., 1981. Standardized testing methods for measuring mechanical properties of ice. Cold Reg. Sci. Technol., 4: 245-253. Sinha, N.K., 1982. Acoustic emission and microcracking in ice. In: Proceedings of SESA, Honolulu, Vol. II, pp. 767-772. Sinha, N.K., 1988. Crack-enhanced creep in polycrystalline material: strain-rate sensitive strength and deformation of ice. J. Mater. Sci., 23(12): 4415-4428. Sinha, N.K., 1991. Cracking kinetics and failure on repeated loadings of ice. In: ISFF '91 Proceedings, Madras, pp. 137150.
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T.G. Haskell et al. / Cold Regions Science and Technology 24 (1996) 167-176
Svec, O.J. and Frederking, R.M.W., 1981. Cantilever beam tests in an ice cover: influence of plate effects at the root. Cold Reg. Sci. Technol., 4: 93-101. Svec, O.J., Thompson, J.C. and Frederking, R.M.W., 1985. Stress concentrations in the root of an ice cover cantilever: model tests and theory. Cold Reg. Sci. Technol., 11 : 63-73. Squire, V.A., Robinson, W.H., Haskell, T.G. and Moore, S.C.,
1985. Dynamic response of lake and sea ice to moving loads. Cold Reg. Sci. Technol., 11: 123-129. Squire, V.A., Robinson, W.H., Langhome, P.J. and Haskell, T.G., 1988. Vehicles and aircraft on floating ice. Nature (London), 33: 159-161. Van Vlack, LH., 1985. Elements of Materials Science and Engineering. 5th ed. Addison-Wesley.