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Research ArticleExamining Dent Formation Caused by Hailstone Impact
Mehmet E. Uz 1,2
1Lecturer, Department of Civil Engineering, Faculty of Engineering, Adnan Menderes University, Aydin 09100, Turkey2Honorary Research Fellow, School of Civil, Mining and Environmental Engineering, University of Wollongong, Wollongong,NSW 2500, Australia
Correspondence should be addressed to Mehmet E. Uz; [email protected]
Received 14 November 2018; Revised 22 March 2019; Accepted 17 April 2019; Published 16 May 2019
Academic Editor: Nicola Nistico
Copyright © 2019 Mehmet E. Uz. )is is an open access article distributed under the Creative Commons Attribution License,which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Hailstorms pose significant risk for exposed building cladding materials. Steel sheeting is the most important cladding materialused.)e understanding of steel sheets behavior under hail impact loading is not sufficient for the manufacturing of hail-resistantsheets. With the purpose-built equipment, artificial hailstones of different sizes were launched to impact at steel sheets of differentthicknesses and yield stresses as targets. A theoretical approach for the problem of predicting the dent size due to hailstone impactwas developed and compared to the test results. )e expressions developed in the theory can predict the dent depth before theimpact, assuming the ratio between the dent depth and dent diameter is constant.)e expression is not able to predict the depth ofdents smaller than 0.75mm and cannot predict whether the denting will occur or not. All hailstone sizes lead to visible dent onsteel sheet of thicknesses 0.35mm, 0.42mm, and 0.55mm. Visible denting was also obtained for the 0.75mm steel samples with45mm and 55mm hailstones; however, no denting occurred using 40mm hailstones. It was found that the dent depth wasinversely proportional with thickness and yield stress, while the dent diameter was found to be proportional to yield stress. As theyield stress of the steel sheet increased, the dent depth decreased for G300 and G550 steel. )e dent diameter however increased asthe yield stress increased. When the artificial hailstone shatters on impact, significant energy is lost and less energy is available tocause plastic deformation of the impacted material.
1. Introduction
Damage associated with hailstorms can be on par withearthquake damage. One-third of total economic lossescaused by natural disasters in Australia between 1967 and2003 were as a result of hailstorms [1–3]. On 14 April 1999, ahailstorm in Sydney became the most costly natural disasterin Australian insurance history, causing a total loss of overAUD2.2 billion, with approximately AUD1.7 billion damageinsured. Hailstorms are thought to be more frequent andhave greater potential to cause economic damage and in-juries in the future as climate change takes its toll [4].Australian climate models predict hail days to increase by 1-2 days by 2030 and 4–6 days by 2070 [5]. Due to the low riskto life, there are no specifications in the building codes ofAustralia for building cladding materials to resist hailstorms.A simple increase of the thickness of the steel roofingmaterials to increase the hail impact resistance was
investigated in a report from Bengtsson et al. [6]. In thisreport, the 162000 houses were assumed to be at risk of haildamage. )e change of the thickness of steel roofing panelsfrom 0.40mm to 0.55mm was calculated to save 200 roofsevery year. )e change would result in the prevention ofAUD55 million and would cost AUD145 million in total.)is represents a loss of AUD90 million, indicating that thisadaptation to existing housing stock is not economical. )eeffects of increasing yield stress and optimization of steelsheet profile may see a reduction in implementation cost fordent-resistant roofing without the need to increasethickness.
A hailstone is an ice ball with a diameter greater than5mm [7–10]. Over 75% of hailstones are spherical, and theyare generally found to have densities within the range of700 kg/m3 to 910 kg/m3. Hailstones have a lower densitythan the pure ice because of the air bubbles trapped within[11–14]. Terminal velocity of spherically shaped hailstones
HindawiShock and VibrationVolume 2019, Article ID 6175206, 16 pageshttps://doi.org/10.1155/2019/6175206
was investigated by Laurie [15]. Terminal velocities fordifferent diameter hailstones are shown in Table 1.)e use ofspherical ice molds monolithically cast with distilled water isspecified by the test standards ASTM E822 and FM4473.)is method wasmodified to fill the silicone ice molds in twostages to prevent cracking upon expansion during freezing[14]. )e use of layered ice balls was also investigated bycomparing the monolithically cast ice balls and horizontallylayered ice balls. However, the force imparted on the targetmaterial was unaffected by the hailstone casting method [8].)is indicates that the use of horizontal layered ice balls didnot influence the simulation capability of monolithically castice balls. )e measurement techniques for dent penetrationand diameter were improved by Long et al. [25] and Loz-owski and Strong [16]. In their studies, exact solutions weregiven to calculate the dent depth and diameter veryaccurately.
Research on hail impacts on steel is primarily focused onbuilding materials, automotive panels, and aircraft panels.Measurement of hail impact resistance of steel plates usuallyrelies on static or quasi-static loading conditions. Findingthe minimum energy required to initiate a dent is the ob-jective of these investigations. American Society for Testingand Materials developed the ASTM D3746. In the test, thehail impact resistance of the specimen is evaluated bydropping 2.27 kg steel projectile with a 25mm radiushemispherical head from a height of 1350mm onto thespecimens. Another test standard is ANSI/FM 4473, whichevaluates impact resistance of the cladding material subjectto impact by the spherical ice balls of 31.8mm, 38.1mm,44.5mm, and 50.8mm. Velocities of the propelled pro-jectiles cause the kinetic energy to exceed a specified targetkinetic energy by less than 10%.)e use of kinetic energy as aparameter for assessing hailstone impacts has not beenadequately investigated and assumes a proportional re-lationship between the hailstone mass and velocity squared.)e uncontrollability of the loss of energy and energytransferred to the specimen is also difficult. Researchers haveprovided several ways to simulate hail impact to assessimpact resistance. )is study aims to develop a method tomeasure hail impact resistance and to examine the effects ofhailstone impact. A testing method was developed by Uzet al. [9, 17] for the bachelor thesis of Maguire in theUniversity of Wollongong in Australia and is now going tobe used in this study [18].
2. Dent Resistance of Steel Sheets
Impact resistance, particularly dent resistance, of the steelsheet is its ability to resist denting under impact loading.Efforts have beenmade to test the impact resistance staticallydue to relative simplicity to conduct tests and the re-producibility of the tests. Dynamic testing, however, sim-ulates the real conditions much better. )e energy toproduce a 0.1mm dent in car door panels and stretcheddome panels increased with increasing load rate [19].)erefore, as the inertial effects of the impact increase, anincrease in dent resistance can be observed. )is test wascarried out from a quasi-static to dynamic loading of up to
26.8m/min. )rough dynamic testing using a pneumaticgun and steel indenter, Burley et al. [19] found that dynamicdenting was related to panel thickness, yield stress, modulusof elasticity, density, and panel shape. A decrease in panelstiffness of bake hardened steel was found to result in anincrease in dynamic dent resistance [20]. )e results are notreflected in the same paper between the results of dynamicloading and static loading, where the dent resistance wasfound to increase with increasing panel stiffness. Holmbergand )ilderkvist [21] have found that the increase in yieldstress due to work hardening from the application of 2–5%strain on mild steel panels increased the dent resistance 20%despite the associated thickness reduction. Two empiricalformulas to estimate the denting force and denting energyrequired to produce a visible dent was presented by Shi et al.[22]. )e denting force, Fd, was given as follows:
Fd � KS1σ0.718Y t
0.5, (1)
where KS1 is a constant found to be 17.78 for the units MPaand mm. )e energy required to produce a visible dent, W0,was given as follows:
W0 � KS2σ0.915Y t
0.322, (2)
where KS2is a constant found to be 0.005 for the units MPa
andmm.)e experimentation was carried out by dropping aweight. )e indenter was a steel tipped dart.
3. Theoretical Aspects
)e study aims to assess the hailstone impact resistance ofthe steel sheets by developing an equation to give the dentdepth and diameter. Results obtained from the theoreticalequation will be compared to the results obtained fromexperiments. )e experiment arrangement used to conducttests allows the artificial hailstones of various sizes to bepropelled at desired velocities striking steel sheets of variousyield strengths and thicknesses. Bircan et al. [18] mentionedthat the key factor in the hail resistance assessment ofbuilding materials is the velocity measurement equipment.In the study of Bircan et al. [18], the laser sensors were notenough to measure the velocity of hailstones. Hence, in thisstudy, the flight and impact of the projectile is recorded witha high-speed camera. )e camera also helps to capture thesimulation of artificial hailstone on impact whether it isshattered or intact. )e final dent depth and diameter arerecorded. To analyze the data, some assumptions andgeneralizations are made.
Table 1: Terminal velocity for hailstones of various diameters givenby Laurie [15].
Diameter (mm) Terminal velocity(m/s)
Approximate impactenergy (J)
25 22.3 <1.432 25.0 5.438 27.4 10.945 29.6 19.0
2 Shock and Vibration
3.1.DynamicHail ImpactTestEquipment. )e test scheme ofthe study relies on pneumatic propulsion of artificial hail-stones. )e test scheme can be used for propelling otherobjects onto other specimens as well. )e purpose-built testscheme mainly consists of the hail launcher, protective unit,and recording devices. )e experiment was conductedparallel to the ground, as given in Figure 1. Mounting thepneumatic gun vertically was not found to result in sig-nificant benefits [23]. On the contrary, mounting thepneumatic gun in a vertical manner would make the testscheme more complicated and increase the safety hazards.)e horizontal test scheme was used successfully by severalresearchers [7, 8, 14, 24–26]. For the support system(boundary condition), the steel sheeting is screwed to timberbattens spaced at 600mm from each other and the projectileis aimed perpendicularly at the middle between the twobattens. According to Kim et al. [27], the boundary con-dition does not strongly change the dynamic dent resistanceeven if it affects the stiffness. Juntikka and Olsson [28] statedthat the force generated during the dynamic impact is in-dependent of the boundary conditions as the impact is lo-calized. )e artificial hailstones used in the study aremonolithically cast spherical pure ice balls of various di-ameters. Ice balls are chosen as artificial hailstones as pureice can be close to the densities of the natural hailstones, andthey display the surface melting behavior observed in naturalhailstones. For all cases, the freezer temperature is remainedat −12°C. Based on the rate of melting recording during thisstudy, no loss of mass occurred between the initial recordingand the recording at two minutes for nominal diameter 40,45, and 55mm hailstones. )erefore, hailstones were storedat ambient temperature for no more than two minutesbefore testing to reduce melting and maintain accuracy ofresults. Hail launcher consists of air compressor, regulator,barrel, gas valve, hail holder, and pneumatic gun mount.
Compressor was used to provide the necessary pneu-matic pressure in order to propel the projectile. Regulatorallows for measuring the correct pressure for the desiredvelocity. Receiver holds the pressure until firing the gun,having a safety valve to relieve the compressed air based onthe AS 1210 standard for pressure vessels. Barrel had ahollow smooth bore steel cylinder wide enough to fireprojectiles of different sizes. A ruler was attached at the endof the barrel to allow velocity measurement. Gas valve acts asa trigger to fire the projectile. Holder was placed before theice ball to act as a sabot, preventing the ice ball to bedamaged while exiting the barrel. )e gun is fixed on themount, which allows the gun to be moved easily withoutdisassembling. Protective unit is a box-shaped structure thatallows for propelling the ice balls in a safe manner while alsoacting as a mounting frame for the steel samples. It providesa physical barrier for ricocheting projectiles and fragments.)e walls of the protective unit are manufactured fromplywood laminated with acoustic insulation, providing somedegree of noise reduction from the barrel of the gun andimpact onto specimens. One side of the unit acts as a door toallow access inside, and the other side has a glass windowthat allows the impact and travel of projectiles to be observedand recorded.)e unit has two rows of six access holes to fire
at different places of the steel sheet without detaching andreattaching the steel sheet to the mounting frame. Recordingdevices are a high-speed camera and the lighting necessary touse the camera effectively. Impacts are recorded at 1000frames per second.
3.2. Steel Samples. Steel samples used in the study wereselected to provide a variety of target panels, but the choiceswere limited due to availability locally. Two steel grades areselected: G300 and G550 (manufactured to AS 1397–2011).Data given by manufacturer for the yield strengths of300MPa and 550MPa, respectively, were assumed to becorrect. )e thickness of the steel samples varied between0.35mm and 1.0mm. )e steel samples used in the test arelisted in Table 2. In the absence of tensile testing on all steelsamples, it was necessary to use the nominal yield strength ofthe steel material for analysis although elongations atfracture over 15mm, 25mm, and 50mm gauge lengths anduniform elongation outside the fracture ε15, ε25, ε50, and εuoof the steel materials were later on obtained for somesamples given in Table 3. )e measured yield strengths forboth materials are now available and significantly higherthan the nominal yield strength during the revision processof this paper. Six 12.5mm wide tension coupon tests wereconducted to provide the yield stress of each type of sheetsteels. Half of the specimens were tested in the rolling di-rection of the steel sheet (denoted with prefix “L” in Table 4)and the other half in the direction perpendicular to therolling direction (denoted with prefix “T” in Table 4). )estroke rate was taken as 1mm/minute. Six tests were con-ducted on each steel sheet, with artificial hailstones of40mm, 45mm, and 55mm in diameter. All testing would becarried out with perpendicular impacts. Tests were labeled asfollows: (steel thickness (mm))/(steel nominal yield stress(MPa))/(hailstone nominal diameter (mm)) (test number).For example, a test using the 0.35mm thick G550 steelsample with a 55mm hailstone at 0° pitch (degrees fromperpendicular) would be labeled: 0.35/550/55 (1). Anothertest using the same parameters would be labeled 0.35/550/55(2). A total of 36 tests would be conducted.
3.3. Assumptions Applied. To develop a theory giving thedent depth and diameter of a hailstone of a known size, somegeneralizations and assumptions are made to simplify theprocess. )ese are as follows:
(1) A constant proportion of kinetic energy in thehailstone is converted into work that is denting thesteel sheet
(2) Dents in the steel sheet are in the shape of a sphericalcap
(3) No strain occurs in the outside of the dented area(4) Uniform strain occurs throughout the dented area(5) Stress-strain behavior of the steel is elastic-perfectly
plastic(6) )ickness of the steel is uniform throughout the
dented area
Shock and Vibration 3
)efirst assumption is necessary to determine the energyavailable to deform the steel sheet. Hailstone kinetic energythat is not transferred to the steel sheet is lost through othermechanisms such as noise and heat. )is would be veryminimal in this study. Kinetic energy may be retained in thefractures of the hailstone if the hailstone is broken duringimpact. Kinetic energy will also be retained as the hailstonerebounds from steel sheet. Further energy losses will occurthrough the elastic deformation from the impact point to theboundaries of the steel sheet. To account for the energy loss,an energy loss coefficient, Ce, is applied to the hailstonekinetic energy. Two parameters were defined to describe thedent shape: average dent diameter, Dd, and dent depth, Dz.)e dent shape was assumed to be spherical cap, as shown by
the dent cross section in Figure 2, for the analysis. )e dentdepth, Dz, and dent average radius, rd, are shown in Figure 2.Dent radius is the half of the average dent diameter. It can beassumed that the dent shape is a spherical cap as the sphereradius, r′, is greater than dent depth, Dz. All assumptions aremade to make the study easier while interfering with realconditions as little as possible. Hailstones were made in aroughly spherical shape. However, several samples containednotable irregularities. )e one having the formation offractures during freezing was not used in the test. After usingfinger smoothing to remove any air bubbles trapper near themold hole, mass and diameter of hailstones were recorded.)e surface area of the dent, assuming it is a spherical cap, inthree dimensions is given by the following equation:
Table 3: Average material properties of G550 and G300 steel sheets with the thickness of 0.55mm and 1.00mm, respectively.
Grade Measured thickness, t (mm) σy (MPa) σu (MPa) σu/σy ε15 (%) ε25 (%) ε50 (%) εuo (%)
G300 1.01 397 448 1.13 43.6 36.7 27.5 22.9G550 0.55 731 753 1.03 9.22 5.80 2.97 1.85
Table 4: Measured yield stresses of G550 and G300 steel sheets.
Grade σy −L1 (MPa) σy − L2 (MPa) σy −L3 (MPa) σy −T1 (MPa) σy −T2 (MPa) σy −T3 (MPa) Average (MPa)
G300_0.35mm 278 310 301 314 281 320 301G300_0.55mm 328 268 314 362 337 285 316G550_0.35mm 568 652 588 623 654 623 618G550_0.42mm 652 647 619 654 706 620 650G550_0.75mm 692 693 714 745 735 727 717G550_1.00mm 589 544 650 631 655 689 626
Ruler
Protective unit
Barrel
Steel sample
High-speedcamera
DC light
(a)
DC fireunit
Pressure valve
Hail launcher
Air compressor
(b)
Figure 1: Experimental set up.
Table 2: Steel samples used in this study.
Steel grades )ickness (mm) Number of sheetsG300 0.35 1G300 0.55 3G550 0.35 4G550 0.42 4G550 0.75 4G550 1.0 4
4 Shock and Vibration
Ad � π r2d +D2z( ) � π
D2d4+D2
z( ). (3)
Change in area over the initial area gives the �nal strainof the material where denting has occurred. Initial area isgiven by the diameter of the initially �at section, which is
A0 �πD2
d4. (4)
�erefore, material strain is
εd �π D2
d/4( ) +D2z( )− πD2
d( )/4( )πD2
d( )/4( )� 2Dz( )/Dd( )2. (5)
Steel stress-strain behavior is used to determine the workdone per unit volume of material to achieve the �nal strain,εd, after denting. Assuming that the material is elastic-perfectly plastic, Figure 3 shows the stress-strain behaviorduring denting. σy is the material yield stress, E is thematerial modulus of elasticity, and εE is the elastic strain.�ework done during denting per unit volume of material isshown by the shaded area in Figure 3 and is given by thefollowing equation:
Wd
Aot� εd + εE( )σy −
12εEσy � εd +
12εE( )σy. (6)
Elastic strain, εE, is given by
εE �σyE. (7)
If equations (4), (5), and (7) were substituted intoequation (6), the expression for the work required to create adent in a �at steel sheet is given as follows:
Wd �2Dz
Dd( )
2
+σy2E
πD2dσyt4
. (8)
Hailstone kinetic energy provides the work required tocreate a dent, of diameter Dd and depth Dz. �e proportionof kinetic energy, Ek, that is converted into dent deformationis assumed to be a constant factor Ce. �erefore,
Wd � CeEk. (9)
Hailstone kinetic energy is given by the followingexpression:
Ek �12mv2. (10)
Substituting and rearranging equations (8) and (10) intoequation (9) would give the following relationship. �etheory has three expressions. First one gives the dent depth
with the dent diameter as an input variable. Second one givesthe dent diameter with dent depth as an input variable.�irdone gives the dent depth with the ratio of dent diameter todent depth as an input variable:
Dz �
������������Cemv
2
2πσyt−D2
dσy8E
√√
, (11)
Dd �
���������������8Eσy
Cemv2
2πσyt−D2
z( )
√
. (12)
Equations (11) and (12) have a limited versatility as theyhave two unknown variables,Dz andDd, respectively, whichare either the dent depth or diameter that must be known inorder to determine the other. Equation (11) can be rewrittenas
Dz �
������������������������Cemv
2
2πσyt 1 + σy/8E( ) Dd/Dz( )2( )
√√. (13)
A solution for the dent depth is allowed if the ratio ofdent diameter over dent depth is assumed to be constant.�e dent depth can be predicted for a given steel sampleunder the impact of a given hailstone at terminal velocity.
4. Results and Discussion
After comparing the results from the tests and the theory,several conclusions have been drawn in Table 5. Severalresults were not taken into consideration, and some con-ditions were not tested. A di�erence between naturallyformed hailstones and arti�cial hailstone made of mono-lithically cast pure ice was observed.
Flat steel sheetFlat steel sheetr′
rd rd
Dd
Dz Dz
Figure 2: Cross section of dent depth and diameter.
E
σ
σy
εd ε
εE
Figure 3: Behavior of stress-strain during denting.
Shock and Vibration 5
Tabl
e5:
Experimentalresults
obtained
from
thisstud
y.
Test
IDPressure
(psi)
V(m
/s)
m(g)
Kinetic
energy
(J)
)ickn
ess
(mm)
Dz(m
m)
Dd
(mm)
Test
IDPressure
(psi)
V(m
/s)
m(g)
Kinetic
energy
(J)
Steel
thickn
ess
(mm)
Dz(m
m)
Dd
(mm)
300/55
(1)
2077
0.55
1.23
28.5
550/55
(2)
12.5
2571.7
22.41
10
0300/55
(2)
1572.8
0.55
0.47
16550/55
(3)
2029
65.4
27.5
10
0
300/55
(3)
1076.6
0.55
0.83
16.5
550/55
(4)
2540
79.8
63.84
10
0
550/55
(1)
1026
70.2
23.73
0.35
1.3
19.5
550/45
(1)
01
550/55
(2)
12.5
2879.2
31.05
0.35
1.06
17.5
550/45
(2)
01
550/55
(3)
12.5
2966.8
28.09
0.35
1.09
17.5
550/40
(1)
01
550/45
(1)
12.5
3538.1
23.34
0.35
0.92
14.5
550/40
(2)
01
550/45
(2)
12.5
3344.3
24.12
0.35
0.9
15.5
300/55
(4)
12.5
2880.6
31.6
0.55
0.82
21
550/40
(1)
12.5
3526.6
16.29
0.35
0.17
16.5
300/55
(5)
12.5
2875
29.4
0.55
3.06
25.5
550/40
(2)
1033
24.8
13.5
0.35
0.22
14.5
300/45
(1)
12.5
3043.5
19.58
0.55
0.39
17.5
550/55
(1)
12.5
2577.8
24.31
0.42
1.12
22300/45
(2)
12.5
3541.7
25.54
0.55
0.87
18.5
550/55
(2)
12.5
2464.5
18.58
0.42
1.16
21.5
300/45
(3)
12.5
3539.1
23.95
0.55
1.21
17.5
550/45
(1)
12.5
3938.6
29.36
0.42
0.26
17.5
300/40
(1)
1030
24.6
11.07
0.55
0.17
13.5
550/45
(2)
12.5
3538.6
23.64
0.42
0.37
17.5
300/40
(2)
1030
22.1
9.95
0.55
0.34
12.5
550/40
(1)
1035
24.9
15.25
0.42
0.1
15300/55
(1)
12.5
2064.2
12.84
0.35
1.42
17550/40
(2)
1032
2512.8
0.42
0.04
13.5
300/55
(2)
12.5
2476.1
21.92
0.35
1.63
20
550/55
(1)
12.5
2471.3
20.53
0.75
0.37
15300/45
(1)
12.5
942.5
1.72
0.35
0.07
7550/55
(2)
12.5
2772
26.24
0.75
0.35
17.5
300/45
(2)
12.5
3232.7
16.74
0.35
0.86
9.5
550/45
(1)
12.5
3444.9
25.95
0.75
0.31
13.5
300/40
(1)
1032
23.9
12.24
0.35
0.81
11550/45
(2)
12.5
3647
30.46
0.75
0.11
12.5
300/40
(2)
1030
27.7
12.47
0.35
0.29
14
550/40
(1)
1031
21.4
10.28
0.75
00
300/55
(x)
12.5
2877.4
30.34
0.35
1.18
23550/40
(2)
1032
22.7
11.62
0.75
00
300/55
(x2)
12.5
64.8
0.35
0.83
18.5
550/55
(1)
12.5
2372.7
19.23
10
0—
——
——
——
—
6 Shock and Vibration
4.1. Comparison ofNaturally FormedHailstones andArtificialHailstones. It is not uncommon to see hailstone bouncingoff the surfaces during a hailstorm. Because hail freezes fromthe inside out, a strong and complex shell structure isformed. )e term hail is used when ice particles are largerthan 5mm in diameter, with smaller particles being clas-sified as ice pellets [10]. Such behavior was observed in thetest with relatively small and often large hailstones. Artificialhailstones freeze from the surface to the inside instead of theinside to the surface as seen in natural hailstones. A hailstonewas removed from the freezer before it was completelyfrozen to confirm this. )e interrupted hailstone was frozenaround the surface while entire core of the hailstone was stillin a liquid state.
Artificial hailstones are not as resistant to fracturing astheir natural counterparts. )e reason is thought to be theformation of fractures during freezing. )ese fractures mayhave been caused by the expansion of the core duringfreezing causing a tensile stress to be applied to the frozen. Inaddition to having a fractured surface, the artificial hail-stones, shown in Figure 4, have a white opaque area offsetfrom the center of the hailstones and caused entrapped airwhich cannot escape the mold or the outer shell duringfreezing. Natural hailstones also contain entrapped air, butthe distribution is more evenly distributed than artificialones. )e trapped air in the artificial hailstones was confinedto a local area, creating a weak point. Due to the weak pointon the surface, the artificial hailstones were observed tofracture on impact with the steel sheets. Fracturing of theprojectiles caused a loss of energy that could have beentransferred to the steel sheet that would have caused a greaterdent size. With the use of a high-speed camera, fracturing ofhailstones could be observed at 1000 frames/s. In Figure 5,the hailstone can be seen breaking apart. )e outer partbreaks into pieces up to a tenth of its original size. )e innerpart shatters into even smaller pieces. Upon shattering, thefragments dispersed in a radial pattern perpendicular to thehailstones initial motion. )is behavior is shown in Figure 5and was observed in the tests but one when the hailstone(Test 0.55/300/55 (5)) bounced off the steel plate intact andas relatively large dent was observed in.
4.2. Dent Depth. True yield stress of the steel sheets shouldbe greater than the nominal value provided. Error was re-duced to some degree with the use of the energy loss co-efficient, which scaled to the experimental results. Despitethe presence of a few errors, a high degree of accuracy is notneeded for the practical application of results as the yieldstress of steel sheets used for building cladding can vary andonly nominal values are used for calculations. )e averagevalue between the yield stresses measured in the rollingdirection and in the perpendicular direction of each steelsheet given in Table 4 is now used in the related calculations.Dent depths of all the 550MPa steel sheets are shown inFigure 6. For the thicknesses 0.35mm, 0.42mm, and0.75mm, the dent depth decreases with decreasing hailstonediameter as expected. Additionally, the depths were to beinversely to the sheet thickness. 0.75/45 (2) (kinetic energy is
30.6 joule, while the hailstone mass was 47.0 g) has 0.11mmdent depth, while 0.42/45 (2) (kinetic energy is 29.36 joule,while the mass was 38.6 g) has 0.26mm dent depth as anumber of other tests with similar variations in test variablesstill showed consistent dent depths.)e specimen 0.75/45 (1)has 20.53 joule of kinetic energy on impact with the mass of44.9 g, while 0.42/45 (1) specimen has 23.64 joule with38.6 g·mass. Hence, the repeated tests of the related steelsamples with the same nominal size hailstone had the samedent depth recorded as 0.37mm. A good degree of exitvelocity control was not achievable through control of the airreceiver pressure using the hollow steel barrel for thespecimen named 0.42/45 (1) having the velocity more thanits terminal velocity. No visible denting occurred on 1.00thick steel sheet with tests performed with four 55mmhailstones. Given that the largest diameter hailstone was notable to produce a dent, no further tests with lower diameterhailstone were conducted. Similar trends were observed with300MPa, as shown in Figure 7, steel sheet with the exceptionof two outliers. Dent depths of the 300MPa steel sheets werefound to be less consistent when compared to the dentsobserved in 550MPa steel sheets. Two tests 0.55/300/45 (3)and 0.55/300/45 (1), despite being tested with hailstones ofsame nominal size and steel sheet thickness, dent depthswere 1.21mm and 0.39mm, respectively. )e hailstonemasses were 39.1 g and 43.5 g, while the velocities were 35m/s and 30m/s, respectively. Large differences with dent depthshere were unexpected as a number of other tests with similarvariations in the test variables still showed consistent dentdepths. For example, tests 0.35/300/55 (1) and 0.35/300/55(2) produced 1.42mm and 1.63mm dent depth, respectively.)e hailstone masses were 64.2 g and 76.1 g, and the ve-locities were 20m/s and 24m/s, respectively.
Test 0.55/300/55 (5) produced the larger dent depth of allthe tests conducted. In the test, the hailstone remained intactinstead of shattering upon impact as was the case with otherhailstones in the study. A dent depth of 3.06mm wasrecorded. )e same steel sample was tested with another55mm hailstone which shattered on impact like the majorityof hailstones. )e dent depth was 0.82mm. Comparison ofthe dent depths of the 550MPa and the 300MPa steel sheetsof 0.35mm thickness shows that dent depth is reduced as theyield stress increases for both the 55mm and 40mm hail-stones. )is can be seen in Figure 8. However, it was foundthat the two tests performed with 45mm hailstone producedlower dent depths in 300MPa steel sheet than 550MPa steelsheet. Dent depth of 0.07mm was obtained in the test 0.35/300/45 (1).)is result is inconsistent with other results and ispossibly unreliable.
4.3. Dent Diameter. Measurement of the dent diameter wasdone by taking the average value of two perpendicularmeasurements: horizontally and vertically across the steelsheets. )e measurement was taken from the farthest twopoints between which permanent deformation has occurred,as shown in Figure 2.)emeasurement, however, involved adegree of subjectivity as the point where the permanentdeformation began was not always clear. In such cases, the
Shock and Vibration 7
values were taken to nearest millimeter accuracy. To reducethe impact of subjectivity on the recorded measurement, thecalipers used were opened much wider than the dent di-ameter and reduced down to the diameter for each mea-surement. )is prevented any visual guesses from beingbased on previous measurements. Additionally, dent di-ameter is not as great of a concern as the dent depth, whenthe cosmetic appearance is considered. Some assumptionswere applied to simplify the data analysis due to the many
variables involved. )e effects of hailstone size, steelthickness, and steel yield stress were investigated. All othervariables were assumed to be constant. Hailstone velocitywas also assumed to be constant. Velocity of 30m/s wastargeted as it was found to be the terminal velocities of thehailstones of tested sizes, and the velocity was achievablewith the test scheme. However, velocity varied among tests.)is was considered for individual tests where the velocitywas significantly different from the target velocity of 30m/s.
Diameter: 45 mm
Diameter: 40 mm
(a)
Air bubble
(b)
Figure 4: Artificial hailstone surface cracking.
(a) (b)
(c) (d)
Figure 5: Hailstone on impact: (a) intact; (b) minor; (c) major break; (d) shattering.
8 Shock and Vibration
General trends were identi�ed assuming a constant velocitythough. Experimental velocities were used in the calcula-tions to discard this assumption from the comparison oftheory and experimental results.
�e average dent diameter for the 550MPa steel sheetswas proportional to the hailstone size for thicknesses of0.42mm and 0.75mm, as shown in Figure 6. However, for the0.35mm thick sheet, the trend is not as obvious. On the0.35mm thick steel plate, the average dent diameters for the40mm hailstones were 16.5mm and 14.5mm; for 45mmhailstones, 14.5mm and 15.5mm; and for 55mm hailstones,19.5mm and 17.5mm. Dents caused by the 40mm hailstoneswere observed to be larger than dents caused by the 45mmhailstones. For the 300MPa steel sheets of 0.35mm inthickness shown in Figure 7, dents observed in two tests withthe 40mm hailstones were also observed to be larger thandents caused by the 45mm hailstones. For the 0.55mm thick
steel sheets, the dent diameter was inversely proportional tothe hailstone size. Hailstone used in the test 0.55/300/55 (5)did not shatter on impact. Although the hailstone did notshatter on impact with the steel sheet, resulting in a relativelylarge dent depth of 3.06mm, the dent diameter was notsigni�cantly a�ected. �e dent diameter was 25.5mm, largerthan the 21mm diameter obtained from test 0.55/300/55 (4).A comparison between 300MPa and 550MPa steel sheets of0.35mm thickness, shown in Figure 8, reveals that, on av-erage, dent diameters of the 550MPa sheets were larger thanthe ones of the 300MPa sheets.
4.4. Comparison of Experimental Results with �eoreticalValues. �e increase of thickness resulted in a decrease indent depth and diameter. An empirical equation correlationbetween the thickness and dent size was not developed due
0.35
/55
(1)
0.35
/55
(2)
0.35
/55
(3)
0.35
/45
(1)
0.35
/45
(2)
0.35
/40
(1)
0.35
/40
(2)
0.42
/55
(1)
0.42
/55
(2)
0.42
/45
(1)
0.42
/45
(2)
0.42
/40
(1)
0.42
/40
(2)
0.75
/55
(1)
0.75
/55
(2)
0.75
/45
(1)
0.75
/45
(2)
0.75
/40
(1)
0.75
/40
(2)
1/55
(1)
1/55
(2)
1/55
(3)
1/55
(4)
Test ID: sheet thickness (mm)/hail nominal diameter (mm)
Observed dent diameterObserved dent depth
0.0
5.0
10.0
15.0
20.0
25.0
Den
t ave
rage
dia
met
er, D
d (m
m)
0.000.200.400.600.801.001.201.401.601.802.00
Den
t dep
th, D
z (m
m)
Figure 6: Dent depth and diameter for G550 steel samples.
Test ID: sheet thickness (mm)/hail nominal diameter (mm)
0.55
/55
(4)
0.55
/55
(5)
0.55
/45
(1)
0.55
/45
(3)
0.55
/40
(1)
0.55
/40
(2)
0.35
/55
(1)
0.35
/55
(2)
0.35
/45
(1)
0.35
/45
(2)
0.35
/40
(1)
0.35
/40
(2)
Observed dent diameterObserved dent depth
0.00
0.50
1.00
1.50
2.00
2.50
3.00
3.50
4.00
Den
t dep
th, D
z (m
m)
0.0
5.0
10.0
15.0
20.0
25.0
30.0
Den
t ave
rage
dia
met
er, D
d (m
m)
Figure 7: Dent depth and diameter for G300 steel samples.
Shock and Vibration 9
to the constraints of the study such as the limited sampleamount, unknown hailstone behavior conditions, and thelack of tensile testing. It was found that visible denting hasoccurred for the steel sheets of 0.35mm, 0.42mm, and0.55mm of thickness. Visible denting was obtained on the0.75mm steel sheets with the 45mm and 55mm hailstones;however, no denting was visible for the 40mm hailstones.No denting was observed on the 1mm steel sheets, irre-spective of the use of 55mm hailstone with 30m/s terminalvelocity. Using the measured mass, velocity, and dent di-ameter for each test as shown in Table 5, the theoreticalvalues of dent depth were determined. Nominal yieldstrength of the steel sheets was used for analysis as tensiletesting was not available in the �rst revised manuscript. Inthis paper, the measured yield stresses given in Table 4 arenow used for the theoretical and predicted calculations. �evalues reduced by 2% for the G300 steel sheets, while thevalues for the G550 sheets dropped to almost 12% which
made the estimation results better with the experimentalresults once the measured yield stresses were used in thetheoretical and predicted calculations. Steel elastic moduluswas taken as 200GPa, and the coe�cient of energy lost,Ce, istaken to be 0.03 with the e�ect of high-speed camera al-though Bircan et al. [18] found that the value of Ce was 0.20based on the energy loss due to errors in the measurement ofthe velocity with laser sensors. �e value of Ce indicates thatonly 3% of the total hailstone kinetic energy is used fordenting, assuming the theoretical expression is accurate.�enominal thicknesses for each sheet are veri�ed to be samethickness as the nominal value provided. Results for thetheoretical dent depths with their corresponding experimentresults can be seen in Figures 9 and 10.
In Figure 9, dent depths for all 550MPa steel sheets canbe seen. For the 0.35mm thickness, experiment results andtheoretical values show good correlation for the 55mm and45mm hailstones. Dent depths of the 0.35mm thick steel
Test ID: steel yield stress (MPa)/hail nominal diameter (mm)
550/
55 (1
)
550/
55 (2
)
550/
55 (3
)
550/
45 (1
)
550/
45 (2
)
550/
40 (1
)
550/
40 (2
)
300/
55 (1
)
300/
55 (2
)
300/
45 (1
)
300/
45 (2
)
300/
40 (1
)
300/
40 (2
)
Observed dent diameterObserved dent depth
0.0
5.0
10.0
15.0
20.0
25.0
Den
t ave
rage
dia
met
er, D
d (m
m)
0.000.200.400.600.801.001.201.401.601.802.00
Den
t dep
th, D
z (m
m)
Figure 8: Dent depth and diameter for 0.35mm steel samples having G550 and G300 grades.
Test ID: sheet thickness (mm)/hail nominal diameter (mm)
0.35
/55
(1)
0.35
/55
(2)
0.35
/55
(3)
0.35
/45
(1)
0.35
/45
(2)
0.35
/40
(1)
0.35
/40
(2)
0.42
/55
(1)
0.42
/55
(2)
0.42
/45
(1)
0.42
/45
(2)
0.42
/40
(1)
0.42
/40
(2)
0.75
/55
(1)
0.75
/55
(2)
0.75
/45
(1)
0.75
/45
(2)
0.75
/40
(1)
0.75
/40
(2)
1/55
(1)
1/55
(2)
1/55
(3)
1/55
(4)0.00
0.20
0.40
0.60
0.80
1.00
1.20
1.40
Den
t dep
th, D
z (m
m)
Observed dent depthTheoretical dent depth
Figure 9: �eoretical dent depth for G550 grade steel samples.
10 Shock and Vibration
with the 40mm hailstone were overestimated by the theorygiving an experimental dent depth of 0.20mm. �e theoryalso overestimated the dent depths of 0.42mm, 0.75mm, and1mm steel sheets. For these tests, the denting either was eithervery small or nonexistent. In Figure 10, dent depths of the300MPa steel sheets are shown. �eoretical values appear tofollow the trend of the experiment results. However, just likethe 550MPa steel sheets, the theory tends to overestimate lowdent depths including tests 0.55/300/40 (1), 0.55/300/40 (2),0.35/300/45 (1), and 0.55/300/40 (2). �e dent depth of test0.55/300/55 (5), where the arti�cial hailstone did not shatteron impact, was underestimated. A larger energy loss co-e�cient should be considered for this case. When the testresults gave dent depth below 0.75mm, an accurate esti-mation could not be achieved with the expression in equation(11). Otherwise, the expression tends to follow the trend andgive a good estimation of the dent depth.
�e results are shown in Figures 11 and 12. Unlike thedent depth, theoretical values of the dent diameter do notcorrelate well with experimental results. In most cases, thetheoretical dent diameter is over twice as large as theircorresponding experimental values. Furthermore, for thetests 0.35/550/55 (1), 0.42/550/55 (1), and 0.42/550/55 (2),invalid results were obtained as a negative value appearedwithin the square root of the equation. Again, the theory failsto deliver accurate results for the cases where no dent wasobserved. In Figure 11, it can be seen that the theoryoverestimated the dent diameters for the 300MPa steelsheets in similar manner with the 550MPa steel sheets. For300MPa steel sheets, theoretical values were over three timeslarger than experimental results. It can also be seen that thetheoretical results of tests 0.55/300/55 (5), 0.55/300/45 (3),0.35/300/55 (1), and 0.35/300/55 (2) were invalid, as given inFigure 12.
Test ID: sheet thickness (mm)/hail nominal diameter (mm)
0.55
/55
(4)
0.55
/55
(5)
0.55
/45
(1)
0.55
/45
(3)
0.55
/40
(1)
0.55
/40
(2)
0.35
/55
(1)
0.35
/55
(2)
0.35
/45
(1)
0.35
/45
(2)
0.35
/40
(1)
0.35
/40
(2)0.00
0.50
1.00
1.50
2.00
2.50
3.00
3.50
Den
t dep
th, D
z (m
m)
Observed dent depthTheoretical dent depth
Figure 10: �eoretical dent depth for G300 grade steel samples.
Test ID: sheet thickness (mm)/hail nominal diameter (mm)
0.35
/55
(1)
0.35
/55
(2)
0.35
/55
(3)
0.35
/45
(1)
0.35
/45
(2)
0.35
/40
(1)
0.35
/40
(2)
0.42
/55
(1)
0.42
/55
(2)
0.42
/45
(1)
0.42
/45
(2)
0.42
/40
(1)
0.42
/40
(2)
0.75
/55
(1)
0.75
/55
(2)
0.75
/45
(1)
0.75
/45
(2)
0.75
/40
(1)
0.75
/40
(2)
1/55
(1)
1/55
(2)
1/55
(3)
1/55
(4)0.0
10.0
20.0
30.0
40.0
50.0
60.0
Den
t ave
rage
dia
met
er, D
d (m
m)
Observed dent diameterTheoretical dent diameter
Figure 11: �eoretical dent diameters for G550 grade steel samples.
Shock and Vibration 11
4.5. Comparison of Experimental Results with PredictedValues. A limitation of equations (11) and (12) is that eitherdent depth or dent diameter must be known to determinethe other. For this reason, the theory is not useful forpredicting the dent depth or the diameter before the impact.�is limitation was addressed with the development ofequation (13). By applying a further assumption that Dd/Dzis a constant value, the dent depth can be predicted for agiven steel sheet under impact of a given hailstone at itsterminal velocity. �e average value of Dd/Dz was taken as52 from the data collected. �e predicted, theoretical, andobserved dent depths are compared in Figures 13 and 14. InFigure 13, the predicted dent depths for the 550MPa steelsheets are very similar to theoretical values given in all tests.
�e predicted values are accurate for the 0.35mm thick steelsheet for the 45mm and 55mm hailstones. Similar totheoretical dent depth values, predicted dent depth valueswere not accurate for depths less than 0.75mm. Inaccuracyis particularly visible for tests with 0.75mm and 1.00mmthick steel sheets. In Figure 14, the predicted dent depths forthe 300MPa steel sheets appear to be consistent with the-oretical values, similar to the 550MPa steel sheets. For all300MPa sheets, the all predicted dent depths were eitherequal to or slightly lower than theoretical values.
4.6. Determination of the Dd/Dz Parameter. �e value ofDd/Dz was assumed to constant, and an average of 52 was
Test ID: sheet thickness (mm)/hail nominal diameter (mm)
0.55
/55
(4)
0.55
/55
(5)
0.55
/45
(1)
0.55
/45
(3)
0.55
/40
(1)
0.55
/40
(2)
0.35
/55
(1)
0.35
/55
(2)
0.35
/45
(1)
0.35
/45
(2)
0.35
/40
(1)
0.35
/40
(2)0.0
10.0
20.0
30.0
40.0
50.0
60.0
70.0
80.0
Den
t ave
rage
dia
met
er, D
d (m
m)
Observed dent diameterTheoretical dent diameter
Figure 12: �eoretical dent diameters for G300 grade steel samples.
Test ID: sheet thickness (mm)/hail nominal diameter (mm)
Observed dent depthTheoretical dent depthPredicted dent depth
0.35
/55
(1)
0.35
/55
(2)
0.35
/55
(3)
0.35
/45
(1)
0.35
/45
(2)
0.35
/40
(1)
0.35
/40
(2)
0.42
/55
(1)
0.42
/55
(2)
0.42
/45
(1)
0.42
/45
(2)
0.42
/40
(1)
0.75
/55
(1)
0.42
/40
(2)
0.75
/55
(2)
0.75
/45
(1)
0.75
/45
(2)
0.75
/40
(1)
0.75
/40
(2)
1/55
(1)
1/55
(2)
1/55
(3)
1/55
(4)0.00
0.20
0.40
0.60
0.80
1.00
1.20
1.40
Den
t dep
th, D
z (m
m)
Figure 13: Predicted dent depth for G550 steel samples.
12 Shock and Vibration
used. Experimental results of dent depth, Dd, and dentdiameter,Dz, were used to create Table 6. Despite thatDd/Dzwas assumed to be constant and 52, the value can be between8 and 338. While the assumption of a constant value is nottrue, its results are satisfactory when compared to theoreticalvalues. In Figures 15 and 16, equation 13 has low sensitivityregarding the Dd/Dz factor. In Figure 15, the predicted dentdepths are for theDd/Dz value of 8.�e predicted dent depthwas increased by 5% in most cases. �e predicted dentdepths are given in Figure 16 for theDd/Dz value of 100.�epredicted dent depth has reduced by 20% in most cases. Dueto the low sensitivity of equation 13 to the Dd/Dz value overa large range, it is believed to be acceptable to take its value as8. �is is strongly supported by the strong consistencyachieved with theoretically determined dent depths. Al-though the ratio of dent diameter to dent depth is required asan input, the result was found to be not very sensitive to thisinput value. Plot ofDd againstDz is given in Figure 17. It canbe seen that the slope is close to �at with the increasing valueof Dz.
5. Conclusions
�e experiment conducted in the study examined hailstonesof varying diameters and impact velocity striking steel sheetsof varying yield stresses and thickness. All arti�cial hail-stones but one shattered upon impact. �e hailstone thatremained intact caused a dent with a depth twice as higher asthe second largest dent depth observed. �is is due to ahigher proportion of kinetic energy being transferred to thesteel sheet, instead of transferring energy to the dispersingfractures. It should be noted that natural hailstones com-monly bounce o� surfaces and remain intact. Withoutfracturing, the coe�cient of energy loss can be assumed to behigher than 0.03 used in analysis. �ere were some
Test ID: sheet thickness (mm)/hail nominal diameter (mm)
0.55
/55
(4)
0.55
/55
(5)
0.55
/45
(1)
0.55
/45
(3)
0.55
/40
(1)
0.55
/40
(2)
0.35
/55
(1)
0.35
/55
(2)
0.35
/45
(1)
0.35
/45
(2)
0.35
/40
(1)
0.35
/40
(2)
Observed dent depthTheoretical dent depthPredicted dent depth
0.00
0.50
1.00
1.50
2.00
2.50
3.00
3.50
Den
t dep
th, D
z (m
m)
Figure 14: Predicted dent depth for G300 steel samples.
Table 6: Dd/Dz for all tests.
Test Dd/Dz
0.35/550/55 (1) 150.35/550/55 (2) 170.35/550/55 (3) 160.35/550/45 (1) 160.35/550/45 (2) 170.35/550/40 (1) 970.35/550/40 (2) 660.42/550/55 (1) 200.42/550/55 (2) 190.42/550/45 (1) 670.42/550/45 (2) 470.42/550/40 (1) 1500.42/550/40 (2) 3380.75/550/55 (1) 410.75/550/55 (2) 500.75/550/45 (1) 440.75/550/45 (2) 1140.75/550/40 (1) —0.75/550/40 (2) —1.00/550/55 (1) —1.00/550/55 (2) —1.00/550/55 (3) —1.00/550/55 (4) —0.55/300/55 (4) 260.55/300/55 (5) 80.55/300/45 (1) 450.55/300/45 (3) 140.55/300/40 (1) 790.55/300/40 (2) 370.35/300/55 (1) 120.35/300/55 (2) 120.35/300/45 (1) 990.35/300/45 (2) 110.35/300/40 (1) 140.35/300/40 (2) 48
Shock and Vibration 13
unexpected trends. For example, increasing yield stressresulted in an increased dent diameter. It was found that40mm hailstones caused larger dent diameters than 45mmhailstones with the same impact velocity. As the yield stressof the steel sheet increased, the dent depth decreased forG300 and G550 steel. �e dent diameter however increasedas the yield stress increased. With the �rst expression, thetheory failed to model dent depths below 0.75mm or theabsence of denting. �is was caused by assumptions made todevelop the expressions. �e second expression over-estimates the dent diameter by a signi�cant factor. �e
theoretical values were over three times as large for 550MPasteel sheets and over twice as large for 300MPa steel sheets.�is expression is unsuitable for application. �e thirdexpression, for a given unknown dent diameter, has pre-dicted the dent depth values that align well with theoreticalvalues obtained from �rst expression. Using the measuredyield stresses for each steel sheet results, a decrease is seenslightly in the theoretical calculations as the measured yieldstresses are higher than the nominal ones, especially in theG550 steel sheet with the thickness of 0.75mm. Although theratio of dent diameter to dent depth is required as an input,
Test ID: sheet thickness (mm)/hail nominal diameter (mm)
0.35
/55
(1)
0.35
/55
(2)
0.35
/55
(3)
0.35
/45
(1)
0.35
/45
(2)
0.35
/40
(1)
0.35
/40
(2)
0.42
/55
(1)
0.42
/55
(2)
0.42
/45
(1)
0.42
/45
(2)
0.42
/40
(1)
0.42
/40
(2)
0.75
/55
(1)
0.75
/55
(2)
0.75
/45
(1)
0.75
/45
(2)
0.75
/40
(1)
0.75
/40
(2)
1/55
(1)
1/55
(2)
1/55
(3)
1/55
(4)
Observed dent depthTheoretical dent depthPredicted dent depth
0.00
0.20
0.40
0.60
0.80
1.00
1.20
1.40
Den
t dep
th, D
z (m
m)
Figure 15: Predicted dent depth with Dd/Dz of 8 for G550 steel sheets.
Test ID: sheet thickness (mm)/hail nominal diameter (mm)
0.35
/55
(1)
0.35
/55
(2)
0.35
/55
(3)
0.35
/45
(1)
0.35
/45
(2)
0.35
/40
(1)
0.35
/40
(2)
0.42
/55
(1)
0.42
/55
(2)
0.42
/45
(1)
0.42
/45
(2)
0.42
/40
(1)
0.42
/40
(2)
0.75
/55
(1)
0.75
/55
(2)
0.75
/45
(1)
0.75
/45
(2)
0.75
/40
(1)
0.75
/40
(2)
1/55
(1)
1/55
(2)
1/55
(3)
1/55
(4)
Observed dent depthTheoretical dent depthPredicted dent depth
0.00
0.20
0.40
0.60
0.80
1.00
1.20
1.40
Den
t dep
th, D
z (m
m)
Figure 16: Predicted dent depth with Dd/Dz of 100 for G550 steel sheets.
14 Shock and Vibration
the result was found to be not very sensitive to this inputvalue. Using a lowest value of 8 inCe gave results that alignedwell with theoretical results. But this expression also failed tomodel dents of 0.75mm in depth or the absence of a dent.�e indentation results of the pure clear ice balls obtainedfrom this manuscript will be validated against those of ar-ti�cial hailstones that happened to remain intact after impactat similar velocities in future studies.
Data Availability
�e Excel data used to support the �ndings of this study areavailable from the corresponding author upon request.
Conflicts of Interest
�e author declares that there are no con�icts of interest.
Acknowledgments
�e author would like to thank Vice-Chancellor and DeanProf. Halil Kirnak at Aydin Adnan Menderes University forproviding a laboratory environment for this work and mybachelor students Ms. Dilara Kop and Mr. Mehmet Goren,my previous master student (un�nished) Mr. IbrahimOzturk at Adnan Menderes University, and my previousstudents Mr. Talha Bircan and Mr. Eren Erdem at IzmirInstitute of Technology for helping me for the set-up.
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R2 = 0.3894
0.00 1.00 1.50 2.00 2.50 3.00 3.500.50Dz (mm)
0
5
10
15
20
25
30
Dd (
mm
)
Figure 17: Correlation of Dd against Dz.
Shock and Vibration 15
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16 Shock and Vibration
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