There have been a substantial number of field and medium-scale laboratory ice impact experiments since the 1980s. Examples include the Polar Sea trials ('84), the series of indentation experiments performed at Hobson's Choice ice island ('89 & '90), as well as numerous laboratory studies (Daley, 1992; Daley, 1994; Gagnon, 2004a; Gagnon, 2004b; Sayed and Frederking, 1992). The purpose of the experiments was primarily to determine the characteristics of ice loading on ships or offshore structures to support growing arctic offshore resource development. It became clear that measured ice pressures are highly dependent on the resolution of the sensing equipment employed.
The pressure-area curve became one common method of presenting ice load data. Frederking (1999) suggested separating pressure-area curves into two forms: ‘Process’ and ‘Spatial’. The process pressure-area curve describes the changing average pressure across the entire contact area and is determined from externally measured loads. In a typical example of a laboratoryscale ice crushing test, an ice sample with a specific geometry is crushed against a surface, and the load is measured using some form of sensor. Typically only the nominal contact area can be determined. From this data, the ‘Nominal’ process pressure-area curve is developed.
In contrast, the spatial pressure-area curve describes the changing pressures
Chemical PIF is a potentially attractive option. The films used in this paper have micron-scale resolution and leave pressure patterns that remain upon completion of an impact event. This makes it possible to investigate the activated contact area and pressure distributions within the contact area at any particular time step of a collision. From the pressure films, pressure distribution plots and spatial pressure-area curves were created. A process of calibrating the films is established. Nominal process pressure-area curves are also created from load cell data.
SPECIFICATION OF PRESSURE INDICATING FILM
Fujifilm Prescale® PIF was adopted in this research. There are seven ranges of pressure film, from ‘Extreme Low’ up to ‘Super High’, categorized by the detectable pressure range. Several pre-tests were performed to identify the pressure ranges encountered during the ice crushing tests in the laboratory. Most of the detected pressures were between 2.5
[Table 1] Detectable pressure range by film type.
Detectable pressure range by film type.
There are two types of PIF that are ‘Mono’ and ‘Two’ sheet type. Structures of each type were illustrated in Fig. 1.
The reaction mechanism is identical in both types of film. If the pressure is applied on the face of the film, microcapsules are broken creating a color forming a chemical reaction. This turns the film a shade of red with the shade corresponding to a specific pressure. Higher pressure causes more capsules to break leading to a darker shade.
VERIFICATION OF STEPPED CRUSHING TEST
In order to create spatial pressure-area curves, the pressure pattern at a specific instant of a collision needs to be recorded. It is not possible to sample the pressure films at a specific instant in time during a continuous collision, so a different method needs to be used. In this study, a ‘stepped’ crushing method was employed. The crushing event was allowed to proceed for a specific duration at which point it was stopped, the film was replaced, and the crushing was allowed to continue. This process repeated for a specific number of steps. In order to verify the validity of this method, a continuous crushing test was compared to a stepped test using the same set of parameters. This would indicate any unrealistic or spurious behavior caused by stopping and restarting the ice crushing. The results are shown in Fig. 2.
No significant divergences between the load histories of the continuous and stepped crushing method are apparent. The stepped crushing method was, therefore, chosen as a reasonable method for use with the pressure films.
PREPARATION OF CONE SHAPE ICE SAMPLE
For these tests, 10
Table 2 shows the test conditions employed. Cold room temperature, grain size, crushing speed (strain rate) and ice cone angle were chosen as controlled variables for the tests. This study is focusing on the applicability of PIF in the laboratory scale test. Details of the analysis of test results regarding the effect of temperature, grain size and crushing speed, are discussed by Ulan-Kvitberg (2012).
For the 30° ice cone, the tests consisted of three crushing steps (9
The pressure films were analyzed post-test using three steps: 1) Pressure film scanning, 2) Determination of pixel value and 3) Conversion of the pixel value to pressure value. A detailed description of each process is given below.
Pressure films were scanned post-test into 1,200
Step 2: Determination of pixel value
Before determining the pixel values of the pressure patterns, the scanned images were cleaned of any smudges, scratches or other obviously spurious data. After the image cleaned, the file was converted into a 16-bit image from which XY coordinates and the corresponding pixel in RGB format were extracted. This was converted into a text file containing X, Y, RGB for the entire pressure film for all non-zero (no pressure pattern) pixels.
Step 3: Pressure value conversion
The obtained pixel numbers were then converted into an actual pressure value (
PRESSURE INDICATING FILM CALIBRATION
Conversion data sheets were provided with each pressure film. However, these sheets were calibrated between 5
Calibration test preparation
To calibrate the films, a controlled pressure was applied on the film using a circular steel ‘stamp’. The films were placed on top of a polypropylene plate to create elastic boundary conditions in order to ensure an uniform contact surface.
Fig. 5 shows examples of the calibration test patterns.
Using the image processing method described, a pixel value was obtained for each test pattern. Despite the attempts to create uniform patterns, there still remained a degree of variation in the pixel patterns throughout the contact area. A similar phenomenon was discussed by Liggins et al. (1992). In this study, the average pixel value for each calibration pattern was taken to be the representative pressure.
Using the applied load and contact area, the pressure was determined. From this, regression equations were created by plotting the average pixel number vs. pressure for each film range. The calibration curves are shown in Fig. 6.
METHODOLOGY OF SPATIAL PRESSURE-AREA CURVE PLOTTING
There is no unique method of plotting spatial pressure-area curves. Daley (2004) plotted spatial pressure-area curves using data from the ‘Polar Sea’ trials by starting at the highest pressure and expanding in a continuous area to include lower and lower pressures.
If there is only one peak pressure zone, this method is very adequate for plotting spatial pressure-area curves. However, if there is more than one peak zone, as was detected in these experiments such as in Fig. 7, the area cannot be expanded continuously and this method cannot be used.
In this study, two different methods for plotting spatial pressure-area curves were employed (Kim et al, 2012). A detailed description of each method is given below.
In the SAM, square sub-areas are expanded from the centroid of the pressure pattern, with the sub-area calculated at each step. The squares are expanded outward until the entire pattern is enclosed, and at each step the average pressure is calculated, allowing the plotting of a spatial pressure-area curve. Fig. 8 graphically demonstrates the SAM.
The SAM cannot be used to determine the actual value of maximum pressure at any specific location within the contact area. However, the method could prove useful in the design stage since the shape of the square area is similar to the general arrangement of a structure constituted by, for example, a plate and a stiffener. In this respect, the SAM could be useful when considering structural behavior due to ice-structure collisions. The SAM may be defined as spatial pressure-area curves plotted from the perspective of structural mechanics.
The CAM is similar to the method suggested by Daley, with slight differences. In pressure distributions with multiple peak locations, the adding of continuous areas is impossible as discussed. In the CAM, the starting point of the spatial pressure-area curve is chosen from the maximum pressure value within the entire pressure distribution. The pressure values are then added sequentially from high to low. At each step, the total area containing a specific pressure is considered, and the location of each pressure value is meaningless. Fig. 9 details the method.
In Fig. 9, the first point of the spatial pressure-area curve will be the entire area containing pressures S1. The second point is the average of the total area S1 added to total area S2 and so on until the entire contact area is considered. This method can be thought of as topographically slicing planes through the pressure ‘peaks’, averaging all pressures within the areas above the chosen plane.
The CAM is useful for determining the magnitude of pressure that may occur during the actual ice-structure collision. The CAM may be defined as spatial pressure-area curves plotted from the perspective of ice mechanics.
The SAM expands outwards from the centroid of the pattern, regardless of the location of the pressure peak. Therefore, the spatial pressure-area curve may show increased as well as decreasing trends as different pressure peaks and valleys are added. By contrast, the CAM necessarily shows a decreasing curve, much as in Daley's method, since the starting point of the curve is the maximum pressure.
PRESSURE PATTERN AND PEAK PRESSURE LOCATION INDEX
A comparison of the plotted spatial pressure-area curve created by the square-averaging and the CAM is useful for unerstanding the patterns of pressure distribution.
As discussed, the SAM always begins at the centroid of the pressure pattern. The CAM begins at the highest pressure. If the peak pressure is located at the centroid of the pressure distribution during a collision, the starting point will be higher for the SAM than if the peak pressure were located away from the centroid. By contrast, the starting point of the CAM will not change depending on the location of the peak pressure. Therefore, expected that the CAM will always begin with a higher initial point on the spatial pressure-area curve than the SAM unless the peak pressure is located at the centroid.
The existence of a peak pressure at the centroid can be determined by comparison of the starting points of the two spatial pressure-area curves created by the two methods. The closer the two starting points are, the closer the pressure peak is to the centroid. The further apart they are, the further the peak is from the centroid.
In addition, a comparison of the slopes of the spatial pressure-area curves from each method provides an indication of the shape of the pressure distribution. If the pressure patterns develops close to a nominal contact area of test ice sample (for example a circle), the spatial pressure-area curve developed from the box averaging method showed a similar slope to the CAM.
By contrast, if the pressure pattern follows a more random shape lower pressures and higher pressures will be more ranomly added to the average pressure as the square areas are expanded outwards and the slope of the spatial pressure-area curve may diverge significantly from the contour-averaging created curve.
In order to compare the spatial pressure-area curves from each method, trend lines of the form ‘P = αAβ’. SAM parameters are indicated with a subscript ‘S’, while CAM parameters are indicated by a subscript ‘C’. Fig. 10 shows the pressure pattern from step 4 of test 3. The overall pressure pattern is close to a nominal circle (nominal area of a cross section of the ice sample) with peak pressures close to the center. It can therefore be expected that α and β values will be similar between both methods.
From Fig. 11, αc and βc were 3.98 and -0.206, respectively. By contrast, αS and βS were 3.70 and -0.176. The results show a ratio of αS/ αc and βS/ βc to be 93% and 85%, respectively. Since the ratios are close to 100%, 1) the pressure pattern formed is close to uniform and 2) the location of the peak pressure is close to the center of the pressure distribution.
Fig. 12 shows the pressure distribution of step 4 of test 7. In this test, the overall pressure pattern is highly irregular with significantly off centered peak pressure. It can be expected that α and β values will differ between the two methods.
From Fig. 13, αc and βc were 1.67 and -0.405, respectively. By contrast, αS and βS were 9.62 and -0.001. The results show a ratio of αS/ αc and βS/ βc to be 576% and 0.25%, respectively. Both ratios are highly diverged from 100%, corresponding to the highly irregular pattern and highly off-centered pressure peak.
Table 3 shows the pressure pattern, α and β values for each test. As expected, information about the overall pattern can be found by comparing the parameters. The pressure patterns were relatively circular for Test 3 and 5 and, correspondingly, the ratios βS/ βc were 85.4% and 80.0%, respectively. In addition, some of the peak pressure were located at the center, so αS/ αc was close to 100%, being 93.0% and 106.4%, respectively.
[Table 3] α and β value at each test (only final step).
α and β value at each test (only final step).
By contrast, the pressure patterns were highly irregular for test 2 and test 4. This leads to a large divergence in slope between the methods with βS/ βc being 33.0% and 34.5%, respectively. In addition, αS/ αc ratios of 180.7% and 231.4% match the fact that the peak pressure was not located at the center, but rather was scattered throughout the distribution. The parameters ‘α’ and ‘β’ may, therefore, be defined as ‘pressure pattern index’ and ‘peak pressure location index’.
CONCEPT OF PROCESS PRESSURE-AREA CURVE AND COMPARISON
As Daley suggested, spatial pressure-area and process pressure-area curves may be connected whereby the terminal points of the spatial pressure-area curves lie on the process pressure-area curve. This is true regardless of the method of creating the spatial pressure-area curves since the terminal point is the average pressure across the entire contact area.
It is commonly believed that process pressure-area curves will always decline with the increasing contact area (Sanderson, 1988; Frederking, 1999). Daley (2004) suggested, in his reanalysis of the ‘Polar Sea’ trial data, that process pressure-area curves can, in fact, show an increasing trend in certain cases. This increasing trend was observed in the laboratory tests conducted in this study, and could be due to increasing confinement of the breaking ice.
In the tests performed in this study, that of the ice sample is a known parameter while the external loads are recorded by an external load cell and data-acquisition system using a universal testing machine. Process pressure-area curves can be created, as discussed either by plotting pressure against nominal contact area or by connecting the terminal points of the spatial pressurearea curves. It is worthwhile comparing these curves. The regression of ‘nominal’ process pressure-area curve is defined as PPAN, while the curves created by the square-averaging and CAMs can be defined as PPAS and PPAC.
Fig. 14 shows each of the three process pressure-area curves. Overall, PPAN followed a generally decreasing trend with increasing area. Trend of PPAS, however, showed an up and down trend (step 1 to 2: increasing, step 2 to 3: decreasing). PPAC showed a generally decreasing trend as similar to PPAN.
In case of PPAC, 90% of pressures were captured between 30-70
However, up and down trend of PPAS in test 2 can be explained by analyzing pressure distribution plot shown in Fig. 15. High pressure was captured in step 1; however, pressure pattern was not allocated at the center of the PIF. To obtain a high average pressure by SAM, pressure pattern should be located uniformly at the center of the square. If not, zero-value pressure pixel will be included during the calculation process of average pressure. This will decrease the overall average pressure at a specific step.
Compared to step 1, pressure pattern in step 2 located close to the center and also there were much higher pressures captured. Therefore, average pressure at the end of the step 2 was higher compared to step 1. As a result, the trend of PPAS curve showed an increasing trend from step 1 to 2. In step 3, the overall pattern was located somewhat uniformly at the center; however, the shape of the pattern was not perfectly circular. In this case, many zero-value pressure pixels tend to include during an average pressure calculation. As a result, the trend of the curve again declined in step 3.
PPAN in test 4 showed a continuous increasing trend as represented in Fig. 16. However, the trends of PPAS and PPAC both showed a different behavior compared to PPAN, which is us and down.
In the case of PPAC, close to 70% of pressure value was obtained between 20-50
However, between step 2 and 4, curve dropped dramatically. This could be explained by checking pressure distribution range and percentage as similar to test 2. Over 80% and 88% of pressure were captured in 10-40
Trend of PPAS shown in Fig. 16 can be explained as explained in test 2. The pressure distribution pattern was offset to the right from the center in step 1. In this case, zero-value pixel includes excessive and will decrease the overall average pressure. Trend of curve increased between step 1 and 2 as shown in Fig. 16. The pattern was not perfectly located close to the center; however, getting close to the center compared to step 1. Also, a high pressure values were captured. PPAS starts decreasing from step 2 to 4. Pattern located close to the center; however, many zero -value pixel was appeared and percentage of high pressure decreased as step proceeded.
The result of the comparison showed that the distribution of pressure pattern is the most significant factor in case of PPAS curve trends. In addition, pressure value was also important, but the inclusion of zero-value pressure was the main factor in SAM. In contrast, the percentage of each pressure range was the most significant factor to determine overall pressure average as well as trend of PPAC curve in case of CAM.
RESOLUTION SENSITIVITY EVALUATION
The effect of changing resolution in this study is an important point to consider. There is a trade-off between increasing resoluion of the film scans and increasing computational requirements (memory and time). There is likely an optimal resolution past which computational drains increase with diminishing returns. For comparison, the activated area, total force and pressure distribution plots are compared for five different unit pixel sizes: 5.0
Fig. 18 represents the activated Area, or total pressure pattern area, at each crushing step at all five different resolutions. The total activated area did not differ significantly with varying resolution, except for step 3 of test 1 and step 4 of test 4. A more in-depth comparison of the data is presented in Table 4 to Table 7 for each step.
[Table 4] Results of activated area: Step 1.
Results of activated area: Step 1.
[Table 5] Results of activated area: Step 2.
Results of activated area: Step 2.
[Table 6] Results of activated area: Step 3.
Results of activated area: Step 3.
[Table 7] Results of activated area: Step 4.
Results of activated area: Step 4.
At crushing step 1, test 3 and 4 both satisfied the ±5% analysis criteria. By contrast, all of the results of Test 6 were out of range. The data in Table 4 indicate that the acceptable range tends to decrease as the pixel size increases. Approximately 37.5% of the obtained results fall outside of the ±5% error range. However, only 9% fall outside of the ±10% error range.
Comparison of the results for step 2 is shown in Table 5. 21.9% of the activated areas fall outside of the ±5% error range, while only 3% fall outside of the ±10% error range. Except for Test 4, the majority of the results fall within the acceptable range of ±5% regardless of the resolution. With the increasing activated area, the sensitivity to resolution appears to decrease.
As shown in Table 6 for step 3 25% of the data fall outside of the ±5% error range, while none of the data falls outside of the ±10% error range. Test 1 and 7 show three results outside of the ±5% error range while the rest shows acceptable error across most if not all resolutions.
In Step 4, shown in Table 7, the percentage of results that fell outside of the ±5% range fell to 18.8%, while none of the data fell outside of the ±10% error range. This further indicates that the sensitivity to resolution decreases with the increasing activated area.
Overall, the percentage of ‘out of range’ results decreased for the ±5% range, from 37.5% to 21.9% to 25.0 % to 18.8%. The sensitivity to pixel size (resolution) clearly decreases as the activated area increases. If the acceptable range is expanded to ±10% the effect of changing pixel size quickly diminishes to zero by the midpoint of the ice crushing test.
Fig. 19 shows a comparison of the total load at each step, for each test, at the varying resolutions. In contrast to the comparison of the activated area, the calculated total load shows an increased sensitivity to resolution. Again, comparative tables for each step offer a more detailed look at the data and are shown in Tables 8 to 11.
[Table 8] Results of total force: Step 1.
Results of total force: Step 1.
[Table 9] Results of total force: Step 2.
Results of total force: Step 2.
[Table 10] Results of total force: Step 3.
Results of total force: Step 3.
[Table 11] Results of total force: Step 4.
Results of total force: Step 4.
As shown in Table 8, all of the results for test 1, 2, 4, 7 and 8 falls outside of the ±5% acceptable error range. Expanding to ±10% error range still leaves test 4 and 8 outside of the acceptable criteria. Only test 3 fell within the acceptable criteria of ±5% for all resolutions. Approximately 78.1% of the results fall outside of the ±5% error range, while 43.8% fall outside of the ±10% range. Clearly calculating the total load from the pressure films is much more highly sensitive to resolution than activated area.
The calculations of the total load for each resolution at step 2 are shown in Table 9. Similar to step 1, a large percentage (71.9%) of the results falls outside of the ±5% error range. 40.6% fall outside of the ±10% error range. Tests 1, 4, 5, 6 and 7 all fall outside of the ±5% range, regardless of the resolution, while test 1 and 7 all fall outside of the ±10% range. A very slight improvement in resolution sensitivity with expanding contact area is shown from Step 1. Comparatively, significant improveent in resolution sensitivity of the activated area was seen between step 1 and step 2.
Table 10 shows the results of the total load for each resolution at step 3. 75.0% of the results fall outside of the ±5% range, while 25.0% fall outside of the ±10% range. This indicates an improvement from step 1 and step 2, although again the improvement is not nearly as great as for the activated area. By step 3, the amount of activated area results outside of the ±10% error range had reduced to zero.
No significant improvements of resolution sensitivity for calculated the total load were made at step 4. 75.0 % of the results fall outside of the ±5% error range, while 37.5% fall outside of the ±10% error range (an increase in sensitivity from step 3). Clearly calculating the total load from the pressure films is, in contrast to the activated area, highly sensitive to the chosen scan resolution.
Pressure distribution comparison
Fig. 20 shows the pressure distributions of test 1 from steps 1 to 3. Fig. 20(a) shows the original low-range pressure film scans for each step. Fig. 20(b) to (f) shows the pressure distribution for changing pixel size for each step. As expected, reducing pixel size increases fineness of the image and clarity of details. 5.0
Figs. 21 and 22 show the low-range pressure patterns for tests 2 and 3. The results are similar to test 1. 5.0
CONCLUSIONS AND RECOMMENDATIONS
High resolution PIF was adapted to obtain detailed pressure distributions during ice-structure crushing experiments. Use of the pressure film eliminated the need for highly specialized instrumentation. Pressure films were calibrated to the cold test environment and regression equations for conversion of pixel number to pressure value were obtained. Pressure distribution maps were created from the scanned pressure film.
A stepped ice crushing test method was validated and employed to obtain pressure patterns at various time steps. Spatial pressure-area curves were created using two distinct methods defined as the ‘Square-averaging’ and ‘Contour-averaging’ methods. Comparison of the two methods allowed for an understanding of characteristics such as the overall shape of the pressure pattern and the location of peak pressures. Process pressure-area curves were plotted. The trends of the spatial pressurearea curves were compared to the nominal process pressure-area curves. The results indicate that there is still room for different interpretations of the test results depending on the perspective taken by the researcher.
Sensitivity of the pressure film data to scan resolution was analyzed by comparing pixel size numbers. Activated area, total force and pressure distribution plots were calculated/created and compared to a range of pixel sizes. Activated area did not appear to be greatly affected by resolution beyond the initial stages of ice crushing. Total force, by contrast, was found to be highly sensitive to resolution. An optimum balance must be determined by the researcher between resolution and computational time. Decreasing pixel size improved the level of detail in the pressure distribution plots; however, 1.0 mm gave an adequate level of detail. Further improvement showed a slight increment of the level of detail but likely at a high cost to computational time.
Improvements to the experimental design can be made by increasing the number of test steps. This would allow for the creation of more precise spatial pressure-area curves and pressure distributions. Increasing the number of steps will give a more accurate calculation of applied load and activated area. If circumstances permit, a repeat of the above experiment with increased test steps will prove beneficial.
A usage of the PIF can be expended to larger scale ice crushing test or practically apply on the surface of model ships in the ice tank. However, there is more detailed preparation will be required, for example, a method to obtain a perfect watertightness (chemical side of the PIF will be damaged if interrupted by water) and replacement of the film during the test. Further application of PIF will be considered for the future work.