SURFACE TEXTURING OF COMPOSITE MATERIALS BY INDUCED DAMAGE: SURFACE MORPHOLOGY AND FRICTION

Reza Rizvi, Mechanical, Industrial and Manufacturing Engineering, University of Toledo, Toledo, OH

Sharon Li, Ali Anwer, Hani Naguib, Mechanical and Industrial Engineering, University of Toronto, Toronto, ON, Canada

Tilak Dutta, Geoff Fernie, Toronto Rehabilitation Institute, Toronto, ON, Canada

Abstract

Ice is a unique natural substance, whose solid state behavior is deceiving due to the pervasive presence of a liquid-like surface layer, especially at temperatures close to its melting point (>-10°C). As a result, ice is a very slippery, self-lubricating substance on which most materials, thought to give high traction (e.g. elastomers), cannot achieve high coefficients of friction (COF ~ 0.1). Here, we describe the high friction behavior (COF ~ 0.5) of a new class of textured elastomer fiber composites made using a facile fabrication method of cutting and rearranging molded composites. These fibrous TPU composites have uniformly distributed surface protrusions that are capable of penetrating and interlocking with an ice substrate underneath resulting in static COF that are 4-7X higher the TPU elastomer by itself. Increasing the fiber content improves the surface structure characteristics, namely protrusion density, and hence improves the friction coefficient. Furthermore, increasing the contact pressure increases the depth of protrusion penetration and hence improves the friction force. These structure-property relationships were verifiable through a mechanics model, with the appropriate normalization, that describes the characteristic forces on a single fiber. Strong potential applications of such textured elastomer composites exist for winter safety applications such as footwear and tires.

Introduction Rubbers and other soft elastomers are the

materials of choice for grip/non-slip applications on a variety of surfaces. Their high compliance and viscoelastic behavior allows them to make close contact with a remarkable variety of substrates by filling in surface asperities[1-3]. Furthermore, even in the presence of a lubricant, rubbers undergo significant surface and bulk deformation hysteresis during sliding friction requiring additional work (friction force) to slide[4]. The unified theory of rubber friction, put forward by Kummers[5] suggests the combined contribution of three main mechanisms - adhesion, deformation and wear – that explain the high traction rubber and other soft elastomers enjoy on a variety of dry and contaminated substrates.

Compared to substrates made from typical solids, ice and snow are physically unique materials that pose a significant challenge for maintaining traction. In its solid form (<0°C, 1 atm), the polar nature of the H2O (water)

molecule results in significant structural disorder at the ice surface, that manifests itself as a liquid-like layer in a wide range of temperature and humidity conditions[6]. Therefore despite being much stiffer than rubbers (10GPa vs. 0.01GPa) there is always a lubricating liquid-like layer between the ice substrate and rubber surfaces, preventing any adhesion type friction from occurring. Owing to greater structural disorder, the lubricating liquid-like layer is thicker at elevated temperatures near the melting point of ice[6, 7]. This explains why achieving high traction on ice at elevated temperatures (>-10°C) is so challenging. Achieving high traction at these conditions would be tremendously beneficial for winter tire and footwear industry and would positively impact societies affected by cold climates.

Recent studies into the friction and wear of composite materials based on polymers and elastomers have identified new strategies that may improve their tribological properties [8, 9]. Most of the studies on tribology of composites focus on reducing friction and heat generation and improving lubrication and wear resistance of surfaces. This emphasis is justifiable considering the tremendous economic consequences of friction and wear and the rapid advancements in the development and widespread proliferation of dry lubricants and bearings. Far fewer studies have investigated the use of composites to improve the coefficient of friction between two substrates. Recent examples include the use of vertically aligned nanofibers embedded in PDMS[10] to achieve a high sliding coefficient of friction on glass and vertically grown carbon nanotubes[11] which can provide high frictional anisotropy when sliding. Recently, we have fabricated elastomeric fiber composites such that there is anisotropy in the orientation of the fibrous phase and the fibrous phase is exposed on the surface creating a surface texture that is conducive to achieving high traction on ice and wet ice surfaces[12].

Here, we characterize the surface structure of textured elastomer fiber composites and its effect on the high coefficient of friction on ice observed at various loading pressures and compositions. We also present an analytical model to describe the observed friction results and their universal dependence on pressure and composition.

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Materials A thermoplastic polyurethane (TPU) elastomer,

Desmopan 385E (Bayer Material Science, Germany) was used as the compliant matrix material. The TPU had a density of 1.2g/cc and a melt temperature of 165°C. Short Glass fibers, Chopvantage 3075 (PPG Fiber Glass, Cheswick PA), with a density of 2.51g/cc were used as the reinforcing phase in the TPU. The glass fibers had an average diameter of 13µm and length of 3.2mm.

Methods Composites containing various volume content of

glass fiber (1, 2 and 4vol.%) in TPU were produced using melt mixer and compression molding. The melt mixing was done in continuous mode using a DSM Xplore 15 (DSM, Netherlands) lab-scale mixer at a temperature of 200°C, at a speed of 10rpm. The mixed material was pelletized and re-mixed at the same conditions, in order to ensure homogenous mixing of the two phases. Compression molding of the in-plane aligned composites was carried out on a 12Ton Carver Hot Press (Carver Corp., Wabash IN) at a temperature of 200°C, pressure of 1.3MPa, melt time of 5min and a press time of 5min.

In order to remove the polymeric skin layer and expose the embedded glass fibers, the molded materials (0.5 mm thickness) were shear-sliced using a sharpened stainless steel scalpel with aid of a template with 3mm spacing. The slices were then rearranged and stacked so that the sliced surface with the exposed glass fibers was orthogonal to its initial orientation. The stacked slices were then placed in a clamp and reheated at 160°C for 10min in order to re-fuse them. The final samples were solid, compliant and measured 30mm by 15mm by 3mm.

Figure 1. a) TPU elastomer samples with (right) and

without (left) glass fiber textured surface. b) SEM micrograph highlighting the surface texturing of the

elastomer composites. c) Schematic of the functionality of the textured composites for use as high friction substrate

on ice. d) Linear surface scan profiles of textured composites at various glass fiber content.

The coefficient of friction of the compliant fiber composites were measured using a customized SATRA

slip resistance testing machine STM 603 (SATRA, UK) based on ASTM F2913-2011[15]. The machine is capable of applying a vertical force normal to the two contacting surfaces and then dragging the surfaces against each other at a pre-set strain rate, while monitoring the horizontal force required to drag the surfaces. The coefficient of friction is defined as the ratio between the horizontal and the normal force and is monitored continuously. For the purpose of this study, one of the surface was the fiber composite mounted on a custom rig and the other surface was 5mm thick wet ice maintained between -4 and -1°C that was smoothed and wetted with a damp cloth. The applied normal force was varied (150, 300, 450 and 600N), the time to set was 2s and the strain rate (velocity) of testing was 300mm/s. The first peak value observed was defined as the static coefficient of friction.

The root mean square average surface roughness of the samples was measured using a Mitutoyo SJ-210 linear surface roughness probe (Mitutoyo, Japan). The scan distance was 4mm while the scan speed was 0.5mm/s. A Gaussian filter was applied to determine the mean-line with a cut-off wavelength of 0.8mm. Surfaces were evaluated using the arithmetic mean of the absolute values relative to the filtered mean line. The morphology of the surfaces were viewed using a JEOL JSM6600 scanning electron microscope (Jeol Corp., Japan) operated at 20kV, with the surfaces made conductive using a thin sputter coated layer of platinum.

Results

The textured elastomer fiber composites (Figure 1) consist of a soft thermoplastic polyurethane (TPU) elastomeric matrix reinforced with varying amounts (1, 2 and 4 vol%) of microscopic glass fibers (GF) arranged such that the fibers are exposed and project out of the surface. This unique surface texturing is not present in regular molded composite articles, which always have a thin skin layer of smooth matrix covering the matrix and fiber phase below. The surface texturing of the elastomeric composites in the present study was achieved using a simple method of cutting and rearranging already molded composite articles (See Experimental Section). By cutting a compliant matrix, reinforced with stiff fibers, the fiber pullout phenomena is observed, resulting in a textured surface (Figure 1b). Fiber pullout is a commonly observed damage mechanism in the fracture mechanics of composite materials. It can improve the fracture toughness of ceramic matrix composites[13, 14] by dissipating energy into delaminating the fiber-matrix interface and pulling (sliding) the fibers out.

In the present application the fiber pullout phenomena is used to create a textured surface of a composite material that can be used as high friction substrate for slip resistance applications on ice (Figure 1c). The textured surfaces consisting of protruding glass fibers have a surface roughness (7.14±0.52µm at 4 vol% GF) that is significantly higher than similarly cut surfaces

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without glass fibers (0.75±0.08µm), shown in Figure 1d. The addition of glass fibers from 1 to 2 to 4 vol% has little effect on the surface roughness (indicative of the protrusion length), but it does increase the frequency of the protrusion features, as evident in the surface profile scans. This observation is further supported in the SEM micrographs of the textured surfaces containing varying glass fiber content (Figure 2). Using an image analysis software (ImageJ, National Institutes of Health) additional microstructural information such as the fiber protrusion lengths and angle distributions can be obtained. Based on these micrographs (Figure 2a), average fiber densities, n, of 2232 cm-2, 3740 cm-2 and 6218 cm-2 were measured for 1, 2 and 4 vol% GF in TPU. Average protrusion lengths, L, of 17.5±10.0µm, 20.2±7.3µm and 21.4±8.9µm, and average protrusion angles of 79.8±7.8°, 74.0±13.7° and 76.4±12.0° were obtained for 1, 2 and 4 vol% GF composites, respectively.

Figure 2. Scanning electron micrographs showing the

surface microstructure of textured elastomer fiber composites containing a) 1, b) 2 and c) 4 vol% GF.

The friction performance of the textured composites was measured on ice in a customized test setup based on ASTM F2913-2011[15], which consists of a slip resistance testing machine (STM 603, SATRA, UK) that outputs the coefficient of friction as the ratio between the friction (FF) and the normal (FN) forces. Figure 3 depicts the results of the friction testing of the textured elastomeric composites on wet ice with a temperature between -1 and -4 °C. The friction profiles of textured

composites (low normal force - Figure 3a; high normal force– Figure 3b) begin with a rising friction force up to a maximum peak followed by a reduction in friction force with secondary peaks observable. The maximum peak observed is by definition the friction force used in computing the static effective coefficient of friction (COF - µe).

Figure 3. Friction force generated by sliding textured

TPU-GF composite surfaces on ice at normal force of a) 150 and b) 600N. c) Dependence of friction force (peak

value) on normal force at various GF content. d) Effective coefficient of friction and its dependence on normal force

at various GF content.

It can be seen from the results that both the primary and secondary peak values increase as a result of increasing glass fiber content and protrusion density. At a normal force of 600N (0.77MPa), the maximum friction force achieved was 168±4.3N, when the glass fiber content was 4 vol%. In addition to increasing with fiber content, the maximum friction force improves with increasing normal force (Figure 3c), with the largest slope of 0.21 (R2 = 0.989) seen for 4 vol% GF. In contrast, the dependence of friction force on normal force is weak for elastomers, with pure TPU (0 vol% GF) having a small slope of 0.02 (R2 = 0.991). The friction force can be used to plot an effective coefficient of friction (COF) according to Amonton’s Law, µe= FF/FN, which can be plotted at various compositions and normal force (Figure 3d). The COF decreases non-linearly with increasing normal force, indicating a greater dependence on the increasing normal force (numerator) rather than the increase in frictional force (denominator). Therefore, the maximum COF of 0.486±0.032 was achieved for textured composites containing 4 vol% glass fibers at the lowest normal force of 150N. This is in comparison to pure TPU, which only achieves a maximum COF of 0.110±0.004 at the same applied load – representing a 4.4X increase. At higher pressures (normal force of 600N), the friction performance of the 4 vol% textured composites increases

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to a 7X improvement attributable to the greater penetration of protruding fibers into the ice substrate.

Key to understanding the unique tribological properties of these textured composite surfaces is to model the mechanics that a single fiber protrusion would undergo. Using a few assumptions and derivations, detailed below, the universality of the tribological performance of these composites can easily be demonstrated. This universality exists regardless of the force applied or the concentration of the fibers. The fibers are assumed to be inverted conical frustums with an angle, θ, from the base of 45°, and a narrow diameter, d0 , of 10µm and a wide diameter, ϕd0, where ϕ ≈ 7. These approximations are based on microstructural observations of Figure 2 and give a reasonable total protrusion length of 30µm. Prior to analysis, the friction force is corrected to account for deformation hysteresis, FDH, (manifested as the non-zero y-intercept in Figure 3c) in order to satisfy Amonton’s Law. This hysteresis force is commonly observed in soft materials, where the time-dependent viscoelastic deformation of polymers and elastomers contributes to the total friction force [5, 16, 17].

The normal force, Fn, and friction force, Ff, on a single protrusion can be obtained through a normalization of the total normal force, FN and the corrected total friction force, FF experienced by the textured composite surface. All fibers (total N=nAsample) are assumed evenly distributed across the composite surface and shear the ice surface equally amongst themselves to generate a friction force per fiber - i.e. Ff = FF/N. The normal force per fiber depends on the evenly applied pressure (FN/Asample) distributed across the wide section of the frustum (Aw-

fiber=πϕ2d02/4). Hence, the normal force per fiber, Fn, is

obtained by normalizing the total normal force, FN, by the area-fraction of a single fiber – i.e. Fn = FN(Aw-fiber/Asample). A plot of the normalized forces is shown in Figure 4a where the generated friction force per fiber is plotted on the abscissa and the applied normal force per fiber is plotted on the ordinate. A quick examination of Figure 4a reveals that normalizing the friction force by the surface fiber density and the normal force by the fiber area fraction coalesces the data points from different fiber contents. This apparently universal relationship between two independently measured forces is explained in the ensuing discussion through a simple consideration of the mechanics involved in indenting and sliding textured elastomer fiber composites over an ice surface. The essence of our model is that the friction force, Ff, arises from shearing the glass fibers through the ice, after they have been indented a certain length, l, into the ice due to an applied normal force, Fn. Assuming the ice completely surrounds the indented fibers, then the failure stress determining the strength of the shearing ice-glass contact can be obtained through solving the conforming cylindrical contact problem.

The stress analysis of conforming cylindrical contact was thoroughly investigated by Persson[18] and

Noble and Hussein[19]. In recent years, Ciavarella and Decuzzi[20, 21] have developed a closed form solution which can account for a wide variety of contacting conditions. According to their solution, the maximum pressure, p0, at the contact interface, due to a line load, Ff/l, is given by:

( )( )22

2

2

0

11ln

12

2 bbbb

bb

Fdlp

f +++

++

=pp

(1)

where ( )2tan e=b is the tangent of half the semi-angle of contact, ε. Failure of the contact would occur when a critical maximum pressure is achieved. For Hertzian stresses[20, 21] this pressure is generally related to the maximum tensile strength by a factor of π, i.e. tp ps=0 . For the case of an exact fit (zero clearance) between the ice and the glass fiber, the semi-angle of contact depends only on materials parameters[20] through the following implicit equation:

( ) ( )1221ln 42

--=++a

bb (2)

where α is Dundur’s first material parameter for plane strain defined by:

( ) ( )( ) ( )221

212

221

212

1111

uuuu

a-+----

=EEEE

(3)

where E1 and υ1, and E2 and υ2 are the Elastic modulus and Poisson’s ratio for glass fiber and ice, respectively. Using the materials parameter for glass and ice specified in Table 1, values of α = -0.735 and b = 0.767 are obtained, which correspond to a semi-angle of contact, ε = 74.9°. Based on this, a dimensionless contact pressure (R.H.S. of Equation 1) of 0.807 is obtained. Noting that the diameter of the frustum, d, at any point is related to the length, l, from the narrow diameter, d0, and the tangent of the base angle, θ, from the wide diameter, ϕd0, through the

relation, 0tan2dld +=

q, Equation 1 can be rewritten

as a quadratic equation in terms of l:

ftt Fldl 807.02tan

02 =+ps

qps

(4)

Equation 4 can be solved in terms of l, which is the indentation depth required to cause a failure of ice due to a contact pressure, p0, when a force Ff is applied:

÷÷ø

öççè

æ-+= 1

tan91.121

4tan

20

0f

t

Fd

dlqps

q (5)

The required indentation depth in ice would occur when a sufficient normal force has been applied to puncture and indent the ice. According to the force balance of Figure 4b:

fconebfibern AAF ts += (6)

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The normal force would be the sum of the forces due to a normal bearing stress, σb, acting on the blunt fiber area, Afiber, and an interfacial friction shear stress, τs, acting on the tapered area of the conical frustum, Acone. Similar relations have been used to study the indentation resistance of various metals[22, 23], ceramics[24] and plastics[25, 26]. The tapered area of conical frustum is simply given by the integral of the area of revolution of the radius between the limits of 0 and a desired length, l:

÷÷ø

öççè

æ++== ò ldldAdA

l

cone 0

22

0 tancot1

22

qqpp (7)

Substituting the length expression (Equation 5) into the above area function (Equation 7), and simplifying gives an implicit expression relating the friction force, Ff, on a fiber to the tapered area of an indented conical frustum:

÷÷ø

öççè

æ-++

+= 1

tan91.121

tan46.6

81tan

20

20

220

ft

ft

cone Fd

Fd

dAqpsqps

qp

(8) The other part of the force balance (Equation 6)

is the normal bearing stress at the interface between the fiber at the narrow face of the frustum and the ice. The bearing stress is given by cavity expansion models for deep penetration of different materials[22, 24-26]. Bishop’s[22] solution for spherical cavity expansion, applicable for blunt face indentation, in an ideal elasto-plastic material, with no strain hardening, provides the bearing stress as:

÷÷ø

öççè

æ+

+=t

tb

Esu

ss

)1(ln1

32

2

2 (9)

where σt is the tensile strength of ice and E1 and υ2 are the Elastic modulus and Poisson’s ratio of ice, as before. Using the materials parameters specified in Table 1 gives a bearing stress of 4.8MPa, which is about 7X the tensile strength of ice (0.7 MPa) - agreeing well with published data in literature[27]. A final implicit expression relating the friction force on the fiber, Ff, to the applied normal force, Fn, is obtained by combining Equations 6, 8 and 9 together:

fft

ft

bn Fd

Fd

ddF tqpsqps

qpsp×÷÷ø

öççè

æ-++

++×= 1

tan91.121

tan46.6

81tan

4 20

20

220

20

(10) The conical frustum indentation model described in

Equation 10 is plotted along with the normalized friction and normal forces per fiber in Figure 4a. A bearing stress of 4.8MPa and an estimated interfacial friction shear stress of 0.51 MPa provide a good approximation to the experimentally observed values with a sum of errors squared (R2) of 0.931. The relation between normal and friction force per fiber is not linearly proportional as might be expected for straight cylinder indenting a surface. Even with certain simple assumptions, it is rather non-linear owing to the complex geometry of the fiber protrusions. The complex geometry (Figure 2) is also the reason why there is greater deviation between the theory (Equation 10) and the experimental data at low forces in

Figure 4a. A complex but more accurate estimate of the indentation area could be made by assuming a non-linear surface profile of revolution in Equation 7 or by assuming a hybrid geometry consisting of a cylinder transitioning to a inverted conical frustum. A better estimate of the geometry and its contact area would represent the observed fiber protrusions (Figure 2) more accurately and would increase the accuracy of the relationship between normal and friction forces. However, as the objective for these materials is to maximize the friction force, a better representation of the geometry and accurate modeling for low forces is not a priority.

Figure 4. a) Plot of normalized (per fiber) friction force and normal force at various GF amounts. b) Schematic

showing the various forces (described by Equation 10) on a glass fiber protrusion, modeled as an inverted conical

frustum.

Conclusions

In summary, we have described here the high friction behavior of textured elastomer fiber composites made using a facile fabrication method. These fibrous TPU composites have uniformly distributed surface protrusions that are capable of penetrating and interlocking with an ice substrate underneath resulting in static coefficients of friction that are 4-7X higher the TPU elastomer by itself. Increasing the fiber content improves the surface structure characteristics, namely protrusion density, and hence improves the friction coefficient. Furthermore, increasing the normal force increases the depth of protrusion penetration and hence improves the friction coefficient. These structure-property relationships were verifiable through a universal model, with the appropriate normalization, that describes the characteristic forces on a single fiber. Strong potential applications of such textured elastomer composites exist for winter safety applications such as footwear and tires.

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(3) Ludema, K.; Tabor, D. The friction and visco-elastic properties of polymeric solids. Wear 1966, 9, 329-348. (4) Greenwood, J.; Minshall, H.; Tabor, D. Hysteresis losses in rolling and sliding friction. Proceedings of the Royal Society of London A: Mathematical, Physical and Engineering Sciences. 1961, 259, 480-507. (5) Kummer, H. W. Unified theory of rubber and tire friction, Pennsylvania State University – University Park, College of Engineering, 1966. (6) Rosenberg, R. Why is ice slippery? Physics Today 2005, 58, 50. (7) Dash, J.; Fu, H.; Wettlaufer, J. The premelting of ice and its environmental consequences. Reports on Progress in Physics 1995, 58, 115. (8) Zhang, S. State-of-the-art of polymer tribology. Tribol. Int. 1998, 31, 49-60. (9) Friedrich, K.; Lu, Z.; Hager, A. Recent advances in polymer composites' tribology. Wear 1995, 190, 139-144. (10) Aksak, B.; Sitti, M.; Cassell, A.; Li, J.; Meyyappan, M.; Callen, P. Friction of partially embedded vertically aligned carbon nanofibers inside elastomers. Appl. Phys. Lett. 2007, 91, 061906-061906. (11) Dickrell, P.; Sinnott, S.; Hahn, D.; Raravikar, N.; Schadler, L.; Ajayan, P.; Sawyer, W. Frictional anisotropy of oriented carbon nanotube surfaces. Tribology letters 2005, 18, 59-62. (12) Rizvi, R.; Naguib, H.; Fernie, G.; Dutta, T. High friction on ice provided by elastomeric fiber composites with textured surfaces. Appl. Phys. Lett. 2015, 106, 111601. (13) Kelly, A. Interface effects and the work of fracture of a fibrous composite. Proceedings of the Royal Society of London A: Mathematical, Physical and Engineering Sciences. 1970, 319, 95-116. (14) Thouless, M. D.; Evans, A. G. Effects of pull-out on the mechanical properties of ceramic-matrix composites. Acta Metallurgica 1988, 36, 517-522. (15) ASTM F2913-11, Standard Test Method for Measuring the Coefficient of Friction for Evaluation of Slip Performance of Footwear and Test Surfaces/Flooring Using a Whole Shoe Tester, ASTM International, West Conshohocken, PA, 2011, www.astm.org (16) Smith, R. H. Analyzing friction in the design of rubber products and their paired surfaces; CRC Press: 2010. (17) Adam, C. S.; Piotrowski, M. Use of the unified theory of rubber friction for slip-resistance analysis in the testing of footwear outsoles and outsole compounds. Footwear Science 2012, 4, 23-35. (18) Persson, A. On the stress distribution of cylindrical elastic bodies in contact; Chalmers University of Technology: 1964. (19) Noble, B.; Hussain, M. Exact solution of certain dual series for indentation and inclusion problems. Int. J. Eng. Sci. 1969, 7, 1149-1161. (20) Ciavarella, M.; Decuzzi, P. The state of stress induced by the plane frictionless cylindrical contact. I.

The case of elastic similarity. Int. J. Solids Structures 2001, 38, 4507-4523. (21) Ciavarella, M.; Decuzzi, P. The state of stress induced by the plane frictionless cylindrical contact. II. The general case (elastic dissimilarity). Int. J. Solids Structures 2001, 38, 4525-4533. (22) Bishop, R.; Hill, R.; Mott, N. The theory of indentation and hardness tests. Proceedings of the Physical Society 1945, 57, 147. (23) Riccardi, B.; Montanari, R. Indentation of metals by a flat-ended cylindrical punch. Materials Science and Engineering: A 2004, 381, 281-291. (24) Satapathy, S.; Bless, S. Calculation of penetration resistance of brittle materials using spherical cavity expansion analysis. Mech. Mater. 1996, 23, 323-330. (25) Wright, S.; Huang, Y.; Fleck, N. Deep penetration of polycarbonate by a cylindrical punch. Mech. Mater. 1992, 13, 277-284. (26) Lu, Y.; Shinozaki, D. Deep penetration micro-indentation testing of high density polyethylene. Materials Science and Engineering: A 1998, 249, 134-144. (27) Sego, D. C.; Morgenstern, N. R. Punch indentation of polycrystalline ice. Canadian Geotechnical Journal 1985, 22, 226-233. (28) Petrovic, J. Review mechanical properties of ice and snow. J. Mater. Sci. 2003, 38, 1-6.

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