The effects of off-axis transverse deflection loading on the failure strain of various high-performance fibers

Abstract

Single filaments are subjected to a transverse deflection loading environment in efforts to gain insight into the failure strain of soft-body armor systems experiencing transverse impact. The fiber types utilized for all such experiments are Kevlar® KM2, Spectra® 130d, Dyneema® SK62, Dyneema® SK76, and Zylon® 555. In order to understand the effect of indenter shape, three different indenter geometries are utilized, namely a 0.30 caliber rounded head, a 0.30 caliber fragment simulation projectile (FSP), and high-carbon steel razor blades. The angle at failure is also varied in order to evaluate the presence of a stress concentration developed around such indenters through angles that would be produced during the transverse impact of single fibers/yarns. Loading with the rounded indenter yields failure strain values similar to pure longitudinal tensile experiments. Fibers loaded via a razor blade show a drastic reduction in failure strain, although the demonstrated failure strains are reasonably similar for all tested angles. Most interestingly, fibers loaded with the FSP show a reduction in failure strain with increasing loading angles, with low angle and high angle failure strains being similar to failure strains of fibers loaded with the rounded indenter and razor blade, respectively. In efforts to gain further insight into the method of fiber failure due to different loading configurations, post-mortem fracture surfaces are imaged for Kevlar® KM2 and Dyneema® SK76.

Keywords

high-performance fibers filament transverse impact cutting indenter failure strain

High-performance fibers are often included in advanced structural systems due to their profound tensile strength-to-density ratio. Due to ease, the vast majority of mechanical testing on such filaments and yarns is in the form of longitudinal tensile testing, yielding a linear-elastic stress–strain response for many fiber types.^1–5 This is due to the extremely high level of orientation present for polymeric fibers, resulting in crystallinity values of 75–95%.^2,3 Coupled with their low density (∼1000–2000 kg/m³), they are most routinely employed in products requiring high strength and high stiffness, namely soft or hard composite structures, including hulls of military and sporting watercraft, mooring lines, anti-spall linings in armored vehicles, turbine fragment containment barriers, and of most interest to the current study, body armor. With regards to the latter application, understanding the behavior of the constituent high-performance fibers in both ballistic impact and cutting environments is of extreme importance.

Currently, the most effective means of determining the halting capability of a woven fabric is by actual impact and cutting experiments, which are of course an extremely cost-prohibitive and time-consuming step in the product evaluation process, as large amounts of material are needed to weave a ballistic panel. That said, in recent years much effort has been placed on developing reliable numerical models in efforts to predict how a certain vest may perform, with the capability of altering parameters such as fiber type, weave structure, and the number of plies. Although full system modeling is of great use and is an extremely powerful technique, very few works have adequately achieved predictions of fabric performance. To the authors' knowledge, the most mature constitutive modeling efforts are currently seen from Southwest Research Institute (SwRI), which are capable of adequately predicting ballistic limit velocities for full fabric systems.^6,7

Although these computational methods are quite insightful, additional works have shown that non-dimensional analysis can be of use to understand the ballistic impact of soft-armor systems. Cunniff⁸ developed a non-dimensional parameter that contains the most relevant physical properties involved during transverse impact, namely longitudinal wave speed, $\sqrt{\frac{E}{ρ}}$ , and specific longitudinal yarn toughness, $\frac{σ ɛ}{2 ρ}$ . The Cunniff parameter is thus described by the following:

U = \frac{σ ɛ}{2 ρ} \sqrt{\frac{E}{ρ}}

(1)

where σ, ɛ, ρ, and E represent the fiber tensile strength, failure strain, density, and longitudinal modulus, respectively. The essence of the parameter U represents the energy density required to rupture the fiber material (

\frac{σ ɛ}{2 ρ}

) and the velocity at which energy can be moved away from the impact site,

\sqrt{\frac{E}{ρ}}

. In practice,

U 1 / 3

is used to normalize the fabric ballistic limit (V50) data from different armor systems and, if effective, can collapse the response from different material systems down onto one master curve when plotted against

\frac{A d A p}{m p}

, where A_d, A_p, and m_p represent system areal density, projectile presented area, and projectile mass, respectively. Phoenix and Porwal⁹ furthered the power of this solution by assuming that the impacted fabric can be modeled as a membrane. Using work originally developed by Rakhumatulin and Dem’yanov,¹⁰ they were thereby able to ascertain a closed form solution identical to that from Cunniff while also uncovering additional physical insights into the phenomenon, such as a solution describing the necessary distance needed to halt the projectile. It is important to remember the two key physical parameters found in Equation (1), namely the specific yarn toughness and fiber longitudinal wave speed; a significant amount of impact energy is dissipated via transportation of strain energy away from the impact site at the inherent wave speed in the material. Therefore, increased yarn specific toughness allows for more energy absorption per unit of material, while increased wave speed moves such energy away from the impact site at a higher rate. Thus, a reduction in either of these values will inherently reduce the effectiveness of a soft-armor system.

The relevance of both longitudinal wave speed and toughness within the U parameter is corroborated by external modeling efforts of Roylance and Wang,¹¹ who have shown that the majority of energy during an impact event is dissipated via longitudinal strain energy, longitudinal kinetic energy due to yarn movement from the longitudinal wave, and out-of-plane kinetic energy initiated via passage of the transverse wave front. With this understanding it then becomes of interest to examine if the longitudinal toughness is an unchanged value, especially when the fiber region around the projectile face is loaded in a complex environment that may force the filament to undergo either multi-axial loading conditions, an increase in tensile and compressive strains due to bending around the indenter head, or frictional effects between the fiber surface and projectile. Furthermore, each of the aforementioned works assumes an unaltered failure criterion regardless of loading condition. Such a failure mode is the typical assumption made throughout literature, developing from the classical nylon work that was performed by Smith et al.^12,13 Although a reasonable approximation at the time of the Smith et al. studies, more recent work has shown the effect of multi-axial loading on single fibers, fabrics, and yarns. In fact, it has even been stated that a multi-axial stress state must exist in the fibers directly beneath the footprint of the projectile during transverse impact,^14–19 although to the authors’ knowledge such assertions have not altered the failure criterion used in modeling efforts.

In high-velocity transverse impact of fabric or composite systems, the vast majority of fiber/yarn failure occurs directly beneath the projectile.^14,17,20,21 Thus, the ineptitude of various fabric performance parameters or failure criterion may reside in the absence of a relevant failure criterion for the single filament. It has been shown that an imposed torsional shear strain alters the resulting longitudinal tensile strength of various high-performance fibers.^22–25 Furthermore, Abbott et al.²² found that filaments removed from Kevlar® 29 and 49 yarns undergoing 30 twists per inch yielded longitudinal failure strength values 25% and 32% below strength values from filaments extracted from untwisted yarns, respectively. It was also determined that Kevlar® 29 and 49 single filaments subjected to 20 N/mm transverse compression exhibited a 22–25% reduction in residual tensile strength.²² In contrast, previous work on Kevlar KM2® and A265 filaments has shown minimal longitudinal tensile stress–strain degradation to fibers subjected to transverse compression.^26–29 More closely related to loading seen in body armor materials, it has been shown that transverse deflection of single yarns can degrade the resulting longitudinal failure strain when loaded in a transverse direction with a sharp indenter.^18,19,21 It has also been reported that either increasing the blade sharpness or yarn pretension decreases the resulting failure strain of the yarn when loaded in a transverse deflection environment.³⁰ When loading single fibers with a transverse cutting mechanism, Mayo and Wetzel³¹ demonstrated that the highly anisotropic nature of organic fibers governs failure, and it is alluded that a shear failure criterion may be more realistic to predict failure rather than solely tension as, on average, the aramid and UHMWPE (ultra-high molecular weight polyethylene) fibers tested ruptured at stress values ranging from 22% to 48% of their longitudinal tensile failure strength. On the fabric level, it has also been shown that a sharp blade more easily pushes through a woven ply as compared to a blunt blade, with the majority of the fibers failing at the indenter contact site.²¹

Although the previous list of works demonstrates the presence of a multi-axial stress state of the constituent fibers during a cutting environment, of chief concern to the present work is the possibility of a multi-axial stress condition experienced by a fiber around a projectile during transverse impact. With regards to the transverse impact of single yarns, it has been consistently shown that the velocity required to promote near-immediate rupture upon projectile–yarn contact is much lower than that predicted when using the longitudinal rupture strain as the relevant failure criterion.^22,32–35 In a previous study, the present authors found that transverse deflection of a single Kevlar KM2 fiber with a fragment simulation projectile (FSP) caused a stark reduction in the resulting single filament failure strain when loaded at geometries similar to that produced during single fiber/yarn transverse impact.³⁶ Such a quasi-static environment was utilized in order to negate the effects of wave mechanics, which has been attributed to be the culprit of the reduced instantaneous failure velocity of a yarn subjected to transverse impact.³⁵

The aforementioned pure tension assumption continues to be presented throughout the literature, from single fiber transverse impact analysis, to the vast majority of constitutive models of full fabric. To the authors’ knowledge, no published literature exists that investigates the possibility of a multi-axial stress-state or curvature effects within the geometry present during the transverse impact, although the possibility of its importance has been mentioned on various occasions.^14–19 SwRI does utilize an orthotropic material model in their transverse impact simulations,^7,37 but the implemented failure model is a von Mises surface that is applicable to an isotropic material, which is not representative of high-performance fibers.^26,27,38

Thus, it is proposed that the fidelity of fabric modeling tools may be increased if they contain the proper multi-axial (out-of-plane) stress considerations. In light of this necessity, the aim of the ensuing work is to develop a parametric set of experimental results showing the effect of projectile nose geometry and fiber breaking angle during transverse deflection loading. The former condition is probed in order to determine if projectile geometry has any effect on local stress concentrations exhibited by various fiber types. The latter condition is analyzed in order to determine if the geometry condition that is developed by the transverse wave front in a soft-armor impact event plays any role in reducing the ultimate energy-absorbing capability of the fabric. Finally, filament rupture surfaces generated from the varying test angles and indenters are imaged from each fiber class, namely Dyneema® SK76 and Kevlar® KM2, which are archetype representatives for UHMWPEs and aramids, respectively.

Experimental procedure

Several different organic fiber types are loaded in a transverse deflection environment containing a similar geometry to that produced during transverse impact in order to determine if the effect of a multi-axial loading condition or a curvature effect around the indenter head is relevant. As aforementioned, previous work by the present authors demonstrated the deleterious effect of loading single Kevlar® KM2 fibers with a FSP indenter at various deflection angles.³⁶ Thus, in order to continue this work to additional fiber types, several different single filaments are tested, namely Kevlar® KM2, Spectra® 130d, Dyneema® SK62, Dyneema® SK76, and Zylon® AS-555. Longitudinal tensile properties of each fiber type are presented in Table 1, with most results purposefully coming from manufacturer data sheets if readily available.

Table 1.

Fiber properties collected from producer data sheets and previous testing

Fiber	Kevlar® KM2²⁶	Dyneema® SK76³⁷	Dyneema® SK62⁴⁰	Zylon® AS-555⁴¹	Spectra® 130D⁴²
Density (kg/m³)	1440	980	970	1540	970
Young’s modulus (GPa)	84.62 ± 4.18	132	65–100	180	113
Ultimate yield strength (GPa)	3.88 ± 0.40	3.8	2.4-3.3	5.8	3.25
Failure strain, reported (%)	4.52 ± 0.37	3.5	3–4	3.5	3.2
Failure strain, current data (%)	3.03 ± 0.32	3.54 ± 0.32	3.51 ± 0.57	3.00 ± 0.41	3.56 ± 0.30
Fiber diameter (µm)	12	16.1	19.8 ± 1.6	11.4 ± 0.7	24.4 ± 4.5
Yarn linear density (denier)	600	1350	2400	500	130

Note: Kevlar® KM2 and Dyneema® SK76 properties are measured from single filament tests, while Dyneema® SK62, Zylon® AS-555, and Spectra®130D properties are presumably measured by the manufacturer via yarn testing. Diameter measurements are taken from as-received samples for Dyneema® SK62, Zylon® 555, and Spectra® 130D.

As the experimental geometry currently utilized is similar to that found in Hudspeth et al.,³⁶ only a short description of the experimental setup is provided. Filaments are first carefully removed from fiber bundles via isolating a single fiber from the yarn and then sliding it out lengthwise along the direction of the tow. Said single filaments are then placed into the loading device illustrated in Figure 1, which is capable of producing various deflection angles with a nominal fiber gauge length of 0.55 m. In this setup, in order to alter the fiber failure angle $θ fail$ , the starting angle $θ start$ of the fiber is accordingly changed. Altering $θ start$ is performed by either changing the starting height of the indenter or by moving the gripping mechanism of the fiber inward or outward. The gripping method utilized is via bollards that are traditionally used in longitudinal yarn testing. In efforts to negate slippage of the fiber between the gripping platens, carbon tape (Ted Pella 16073-1) is mounted on the platen assembly. Flags are affixed to the ends of the fiber near the bollards and subsequent tracking reveals no apparent slippage of the fiber between the grips. Furthermore, the load signal generated from the attached load cell reveals no sudden force drops, which if present, would be indicative of fiber slip. Although it may be postulated that slipping could occur without such apparent load drops, the lack of discernible movement of the aforementioned flags along with the measured strain being comparable to traditional fiber failure strains leads the authors to believe that such slipping, if present, is negligible.

Figure 1.

(a) Image and (b) representative schematic of the experimental setup used to load single fibers via transverse deflection. Note $θ start$ is strategically varied so as to produce specific $θ fail$ . Also of note in (a) is the use of a yarn instead of a single fiber in order to provide adequate visualization.

In efforts to determine if there is an effect of curvature radius around the indenter corner, three different indenter heads are implemented: the 0.30-caliber FSP, a razor blade, and a rounded indenter, with each of these being presented in Figure 2. Furthermore, the radius of curvature from each indenter head is measured and can be found in Figure 3. For the FSP and razor blade indenters, measurement is performed by sectioning the indenter, polishing the cross-section to a mirror finish, and then imaging the corner geometry via optical microscopy. The radius of curvature of the round indenter does need to be directly measured via microscopy, as it is of appropriate size to be determined via calipers. The radii of curvature for the round, FSP, and razor blade indenters are 3.8 mm, ∼20 µm, and ∼2.3 µm, respectively. Furthermore, the design of the FSP follows dimensions given by MIL-DTL-46593B, but with an increase in chamfer angle to 55^o that allows for high fiber angles to be achieved (MIL-DTL-46593B). The razor blade is typical high-carbon steel (Personna 94-0152) and is changed for each experiment.

Figure 2.

Three different indenters used for transverse deflection loading. From left to right they are a 0.30-caliber fragment simulation projectile, a 0.30-caliber rounded head, and a razor blade. It is important to note that the razor blade was changed for all tests in efforts to minimize blade dulling.

Figure 3.

Radius of curvature of both the (a) fragment simulation projectile and (b) the razor blade is measured via polishing the indenter cross-section.

Indenter displacement is determined via measurement of a signal output from a servo-hydraulic load frame (MTS 810), while the vertical load produced onto the indenter is sensed with a force transducer (Interface 1500ASK-25). Both signals are simultaneously tracked on a Tektronix DPO4032 oscilloscope at a sampling frequency of 250 Hz, and a representative set of results can be seen in Figure 4(a). The resulting displacement data is then used to determine the failure strain of the fiber via post-process analysis using a computer-aided design software and known geometry conditions of the experimental setup. Furthermore, the starting and failure angles of the fiber are determined, and due to the low failure strain exhibited by these fiber types, both of these angles only differed by a few degrees. The starting angle, $θ start$ , is recorded just as a load is measured from the force transducer, thus at a zero force pretension of the fiber, while the failure angle, $θ fail$ , is recorded when the load measured by the transducer suddenly drops to zero. An example of the range between $θ start$ and $θ fail$ is given in Figure 4(b) for Dyneema® SK62. In efforts to ensure negligible pretension in the fiber at the start of the experiment, the slack-start procedure has been implemented, similar to that found in typical yarn tension tests (ASTM, D7269). The cross-head velocity used for all experiments is 1.2 mm/s, resulting in a nominal strain rate of 0.005/s. Finally, it is important to note that the angle $θ start$ is varied to ensure that geometric conditions similar to that found in transverse impact are enforced. In total, with variations in fiber type (five fiber types), indenter geometry (three indenters), and failure angle (five angles), roughly 700 experiments are performed, as each loading case is repeated 10 times.

Figure 4.

(a) Representative indenter vertical displacement and vertical force exhibited onto the indenter as a function of time during testing. The experiment shown consists of a Dyneema® SK62 fiber loaded to a $θ fail$ value of 51^o, using the fragment simulation projectile (FSP) indenter. (b) Range in angle during transverse loading, from starting angle ( $θ start$ ) to failure angle ( $θ fail$ ), plotted against failure angle ( $θ fail$ ). Data shown is from FSP loading of Dyneema® SK62 fibers.

Single fibers with a gauge length of 557 mm are also pulled in longitudinal tension so as to measure a baseline failure strain without the induced stress concentration produced by the indenter. Single fibers are pulled in tension using the bollard grips in a similar fashion to that used in yarn tension tests (ASTM, D7269). Use of the bollard grips is employed so as to ensure a similar boundary condition to that used in the transverse loading environment. Thus, similar to the transverse loading experiments, carbon tape is affixed to the compressive platens so as to negate any grip slip. The slack-start procedure is used in this testing sequence in efforts to minimize any fiber pretension. Displacement and load signals are gathered similar to the transverse loading experiments.

Finally, the fracture surfaces from both the Kevlar® KM2 and Dyneema® SK76 fibers are imaged via a scanning electron microscope (SEM; FEI Nova and Hitachi S-4800) in efforts to gain insight into the failure mechanisms presented from both the aramid and UHMWPE fiber classes, respectively. The working distance and accelerating voltage for all samples ranges between ∼5–9 mm and 1–10 kV, respectively. All imaged samples are coated with a thin layer of Au in a SPI 6.2 sputter coater in efforts to negate the presence of charging.

Results and discussion

Transverse loading – the effect of angle and indenter geometry on failure strain

Kevlar® KM2, Spectra® 130d, Dyneema® SK62, Dyneema® SK76, and Zylon® 555 are loaded in a transverse deflection environment, as previously described and as shown in Figure 1, using three different indenter types, namely FSP, razor blade, and rounded indenters. A report of fiber longitudinal failure strain resulting from the transverse loading experiments using all three indenters at varying failure angles, $θ fail$ , can be found in Figure 5. The traditional theory wherein failure strain is assumed to be minimally affected by loading angle is also overlaid on the plot as a dash-dot line, with values being identical to those shown in Table 1. This failure strain value is determined by filament longitudinal tension tests with a gauge length similar to that used for the transverse loading scheme. Use of axial failure strain rather than axial failure stress has been chosen so as to follow the traditional input failure criterion described by the classical Smith equations, which are shown below in Equations (2)–(6).¹²

Figure 5.

Experimental results of fiber longitudinal failure strain as a function of failure angle for three different indenter types for (a) Kevlar® KM2, (b) Spectra® 130d, (c) Dyneema® SK62, (d) Dyneema® SK76, and (e) Zylon® 555. Round, fragment simulation projectile (FSP), and razor blade indenters are implemented, represented by solid gray, solid black, and gray dotted lines, respectively.

For all fiber types studied, the trend in failure strain with increasing failure angle is consistent with the three different indenter geometries. The round indenter shows negligible degradation to the failure strain as compared to the fiber longitudinal tensile failure strain, which is listed in Table 1, due to the minimal stress concentration presented on the fiber–indenter contact site. The razor blade indenter shows a direct reduction in failure strain as compared to the fiber longitudinal tensile failure strain. Furthermore, for fibers loaded with the razor blade indenter, there appears to be a negligible effect of failure angle on the resulting failure strain, although there is a slight correlation for the Kevlar® KM2 fiber. This sharp drop in failure strain can be attributed to an extreme stress concentration present at the indenter fiber interface, which may have reached a critical value, as there is minimal correlation with the failure angle for all fiber types. It is important to mention that the radius of curvature of the blade is extremely fine, measuring roughly 2 µm, which can be seen in Figure 3(b).

Most intriguing to this study, the FSP exhibits a definite reduction in failure strain with increasing levels of $θ fail$ , demonstrating that there is a clear stress concentration developed around such a geometry, which is directly affected by the test angle. In addition, the failure strain as a function of $θ fail$ of the filaments loaded by the FSP indenter appears to be bracketed above and below by the resulting round indenter and razor blade indenter results, respectively. On the appropriate plots, cut data is overlaid from Mayo and Wetzel³¹ and Shockey et al.,²¹ who analyzed the effect of a razor blade cutting through fiber and yarn, respectively. All data from Mayo and Wetzel that are marked in Figure 5 are derived from strength values,³¹ wherein failure strength data is converted to failure strain assuming the fiber exhibits a linear-elastic loading response. Thus, failure strain is determined as $ɛ = \frac{σ}{E}$ , wherein the E utilized is that given in Table 1. Data from Shockey is taken directly from Shockey et al.²¹ As can be seen from the plots in Figure 5, the Mayo and Wetzel results line up quite well for Dyneema® SK-76, while for both Kevlar® and Zylon® the current data set lies above that found in Mayo and Wetzel, possibly due to a difference in fiber type (the current data set uses Kevlar® KM2 rather than Kevlar® 129 and the type of Zylon® used is not listed in the Mayo and Wetzel article) or a difference in blade sharpness both at the onset of testing and subsequent loading. The blades used in the current data set have a curvature radius of ∼2.3 µm, while the blade shown by Mayo and Wetzel was measured at 1.5 µm. Furthermore, it has been reported that Zylon® yarn was able to deform a hardened steel utility blade,³⁰ so it is possible that the blade used in the current setup may be softer than that utilized by Mayo and Wetzel, thereby being more easily blunted. It is also important to note that for an unknown reason, loading Zylon® filaments with razor blades is extremely difficult to perform as filaments fail during the sample loading process, thus only experiments at an angle of 10^o are shown.

Shin et al.³⁰ assessed the effect of cutting through yarns composed of Zylon®, Spectra®, and Kevlar® and determined that Zylon® exhibited a much higher energy to break than both Kevlar® and Spectra®, which differs from Mayo and Wetzel, who found that Zylon®, Kevlar®, and Dyneema® filaments all possessed a reasonably similar degradation in failure strength.³¹ Mayo and Wetzel attribute the differences in the two studies to three factors:³¹ (a) Zylon® has a higher elastic energy to break, thereby inherently increasing the level of absorbed strain energy for Zylon® fibers; (b) in yarn testing, the Zylon® force curve drops off slowly after peak loading while Kevlar yarns fail rather quickly post peak load, thereby increasing the level of energy dissipation for Zylon®, with such a delayed post-peak drop-off possibly arising due to the blade tilt; and (c) inter-fiber friction could keep the Zylon® yarn from flattening out during cutting, thereby keeping fibers away from the sharp cut surface. In light of such discrepancy, the effect of blade tilting needs further analysis in efforts to better analyze cutting events that may occur to a soft-armor system during use, such as slashing caused by a knife blade.

It is of importance to note that the angle created during an actual transverse impact event is due to the impacting velocity and material properties of the fiber, not exclusively the indenter head.¹² A schematic of the transverse impact event can be seen in Figure 6, and is described by Equations (2)–(6).

Figure 6.

Schematic of transverse impact of a fragment simulation projectile (FSP) into a high-performance yarn/fiber.

Upon contact of the projectile with the yarn, a longitudinal stress wave is developed and moves at the material sound speed, described by c in Equation (2):

c = \sqrt{\frac{E}{ρ}}

(2)

where E and ρ are the longitudinal elastic modulus and the fiber density, respectively. Material behind the wake of the longitudinal wave is set in motion towards the impact sight, moving with a particle velocity described by W in Equation (3):

W = c ɛ

(3)

where ɛ represents the longitudinal strain developed in the filament. At the time of impact a transverse wavefront is also emanated from the impact site moving at a velocity U being described by Equation (4):

U = c (\frac{ɛ}{1 + ɛ}) 1 / 2

(4)

Material in the wake of the transverse wavefront is set in motion in the direction of the impacting projectile, moving with a particle velocity V described in Equation (5), which is identical to the projectile impact velocity:

V = [(1 + ɛ) 2 U 2 - ((1 + ɛ) U - W) 2] 1 / 2

(5)

If Equations (2)–(5) are solved simultaneously, a velocity causing immediate failure (instantaneous rupture velocity) can be determined if one knows the fiber breaking strain. Finally, the angle developed during impact is described by θ in Equation (6):

θ = \tan - 1 (\frac{V}{U (1 + ɛ) - W})

(6)

It is postulated that such angles that have undergone during transverse impact would produce sharp kinks or local stress concentrations even with a rounded indenter at the leading edge of the transverse wavefront. This is evidenced by the instantaneous local failure of UHMWPE yarns when impacted by high-velocity 5.5-mm steel spheres, wherein it was found that the transverse impact event produced fibers bearing localized failure surfaces that had been sheared through their cross-sectional thickness,³² which is similar to the razor blade and high $θ fail$ results from the FSP indenter shown in the previous section. Such a kink angle is not developed for rounded indenters during the current quasi-static testing setup, as the fiber will always leave the rounded indenter head tangent to the large radius indenter surface curvature. Thus, the rounded indenter experiments performed here more appropriately mimic pure longitudinal tensile testing, and the resulting similarity in failure strain demonstrates the lack of stress concentration developed at both the indenter head and the bollard grip contact site. Thus, it is postulated that the stress concentration developed during a transverse impact event can be reasonably approximated using the current results listed for the FSP indenter.³⁶

In order to visualize the difference in failure strain degradation with increasing failure angles between the five fiber types, FSP data from Figure 5 are re-plotted in Figure 7. From this set of data, it can be surmised that all fiber types tested show a demonstrative effect due to the angle of failure. It is also important to note that error bars have been omitted from the presented curves so as to make the figure more clear, but said error bars are presented in Figure 5, and the reader is directed to said figures if error bars are of interest.

Figure 7.

Shown in this plot is the comparison between the failure strain as a function of angle using a fragment simulation projectile indenter for Kevlar® KM2, Spectra® 130d, Dyneema® SK62, Dyneema® SK76, and Zylon® 555 (data identical to that found in Figure 5). Data for 0^o has been taken from longitudinal tension tests and is identical to the failure strain listed in Table 1.

As can be seen, while all fiber types exhibit a demonstrative coupling to the failure angle, the UHMWPE and Zylon® fibers have a higher failure strain for the entire range of failure angles tested when compared to Kevlar® KM2. The Kevlar® KM2 fiber also presents the highest degree of degradation due to the change in angle when loaded by the FSP. It is also important to note the unexpected low value of failure strain exhibited by Kevlar® and Zylon® when pulled in pure tension (0^o tension tests). The zero-degree tests were conducted a second time in an effort to ensure that the data is not due to testing error conditions. Furthermore, the fibers fail in the gauge section for all listed pure tension tests. When using the FSP indenter, it is found that failure always occurs at either edge of the indenter, rendering the length of the fiber affected by the stress concentration quite localized, as failure is not seen to occur randomly throughout the gauge length, but at the indenter corner. Most importantly, it is imperative to reiterate that the FSP loading geometry drastically affects the resulting longitudinal failure strain of all fibers tested, especially at higher loading angles.

The reason for such a reduction in failure strain could be due to a number of scenarios, such as an increased shear loading between fibrils, a detrimental compressive stress felt under the filament neutral axis that ultimately causes kink bands, an additional tensile stress at the top surface of the fiber due to bending, or even abrasive friction along the length of the fiber. Regardless, the presence of such degradation is clear, which shows the effect of loading a fiber in a multi-axial environment. It is imperative to state that such failure in this quasi-static regime is clearly a function of the indenter shape, while such geometry is of no consequence during transverse impact. Carr³² has shown that both aramid (Kevlar® 129 and KM2) and UHMWPE (Dyneema® SK66) fibers exhibit a greatly reduced instantaneous rupture velocity when impacted by 5.5-mm steel spheres, being quite similar to results of Chocron et al.,⁶ who used a FSP during transverse impact experiments. Such an absence of geometrical effects yields the current authors to postulate that failure could also be caused at the kink created by the transverse wavefront, although no immediate effort has been made to verify such a suggestion. Regardless, clearly there is an effect of both loading angle and indenter geometry during quasi-static transverse deflection and further analysis is most definitely required to determine if such an effect is also present during actual transverse impact experiments. Additional reasoning of such a failure process is provided by Hudspeth et al.³⁶

Transverse loading – the effect of angle and indenter geometry on filament failure surfaces

In efforts to gain insight into the effect of the changing loading geometry, fracture surfaces from a representative aramid (Kevlar® KM2) and UHMWPE (Dyneema® SK76) are imaged via a high-resolution SEM (FEI Nova and Hitachi S-4800). Rupture surfaces from all three indenters are analyzed for 10^o, 20^o, 30^o, 40^o, and 50^o, with representative fracture morphologies being presented in Figures 8 and 9 for Kevlar® KM2 and Dyneema® SK76, respectively.

Figure 8.

Scanning electron micrographs taken of the various rupture surfaces presented by the KM2 fiber when loaded by the three different indenters and failing at the described failure angles. The failure surfaces match very well with the failure strain data presented in Figure 5(a).

Figure 9.

Scanning electron micrographs of the rupture surfaces developed by the Dyneema SK76 fiber when loaded with the three different indenters at the various failure angles. Similar to the KM2 failure surfaces, the SK76 results follow extremely well with the failure strain results presented in Figure 5(d).

For the Kevlar KM2 fiber, the failure surfaces match very well with the failure strain data presented in Figure 5(a). The rounded indenter, which promoted a reasonably constant failure strain, produces similar fracture pattern for all tested angles, being defined by fibrillation, which is the typical failure surface found in aramids when pulled in pure axial tension.³⁹ Similarly, the razor blade indenter, which also caused a relatively constant failure strain value for all of the tested angles, produced very similar fracture patterns at all $θ fail$ , being defined by a localized failure, seeming as though the blade shears through the fiber thickness, along with a slight degree of axial splitting due to the extremely poor transverse bonding between fibrils. Such local failure due to transverse cutting has been previously documented by several authors,^21,30,31 although the current failure surfaces do not exhibit the locally splayed out pattern that is sometimes presented during low angle transverse cutting. It is also important to note that at lower $θ fail$ geometries, it looks as though the majority of the fiber is cut through the cross-section thickness, with the final remaining portion looking like a ribbon that fails either by being stripped off along the surface until a critical defect is reached or more simply via tensile fibrillation failure. Reasoning for such a failure process may be due to local yielding/dulling of the razor blade, which could push fibrils to the point of separating from the main fiber body until ultimate failure. Most interestingly, the FSP indenter, which as previously mentioned caused a reduced failure strain with increasing $θ fail$ , likewise promotes a changed fracture pattern with increasing $θ fail$ . At low $θ fail$ values, the fracture morphologies exhibit definite fibrillation, similar to that produced from the rounded indenter. At high $θ fail$ values, the post-mortem rupture surfaces possess a much more local failure, looking quite similar to the samples loaded by the razor blade indenter. Furthermore, it is important to note that even with the measured radius of curvature of the FSP being roughly twice the diameter of the Kevlar KM2 fiber, there must exist a definite local stress concentration around the contact boundary, as the fiber clearly transitions from a long-range fibrillated failure surface to a much more local rupture that looks like it is sheared through the filament thickness.

Similar to the Kevlar KM2 failure surfaces, the Dyneema® SK76 results follow quite well with the failure strain results presented in Figure 5(d), albeit the Dyneema® fracture surfaces do not present as stark of a transition from fibrillation to local shearing, although the variation is still present. As can be seen, loading by the rounded indenter, which causes a reasonably unchanged fiber failure strain, produces a fibrillated microstructure with a reasonable level of axial splitting similar to that seen in pure longitudinal tension tests.³⁹ It is important to note that at higher $θ fail$ , the fracture patterns produced by the rounded indenter do seem to possess fibrils that have deformed into slightly bulbous shapes, which may possibly be due to snap-back of the fiber post failure. The razor blade indenter, which also produces a relatively unchanged failure strain, promotes a similar rupture morphology for all tested failure angles, being defined by a local through-thickness shearing failure. Similar to the Kevlar® failure, at low $θ fail$ the razor blade seems to cut through the majority of the fiber via local shearing. The final failure looks to promote a longer range artifact being caused by either the aforementioned ribboning or because of fibrillation. Regardless, this final failure effect is believed to be caused by blade dulling. Again, as with the Kevlar® KM2 micrographs, the effect of the FSP on the Dyneema® SK76 failure surfaces shows an evolution from fibrillation/axial splitting at low failure angles, being similar to failure surfaces caused by the rounded indenter, to short-range cutting/shearing, being quite similar to the razor blade micrographs. Clearly, the effect of the FSP corner instigates a local stress concentration into the fiber as it is pulled in tension, demonstrated by the rupture morphology evolution from longer range fibrillation to short-range shearing at increasing values of $θ fail$ . It is also important to note that such short-range failure in UHMWPE fibers has also been recorded by filaments loaded via transverse impact up to velocities causing instantaneous fiber rupture.³² Interestingly, the projectile used was a steel sphere. From the current rounded indenter micrographs, it is concluded that such a shearing failure mode is not caused by a rounded indenter. Rather, this mode of shear failure is caused by a local sharp angle produced by a small radius of the curvature corner, demonstrating that such shearing effects may not be caused by the projectile geometry, but rather by the geometry produced from the transverse wave propagation during transverse impact.

Conclusions

Single high-performance fibers are loaded in a transverse deflection environment in efforts to gain insight into the effect of large deflection angles on the resulting filament longitudinal strain at failure. Further analysis on the effect of indenter geometry is explored by using a 0.30-caliber rounded head, a 0.30-caliber FSP, and razor blades. The fiber types explored in this study are Kevlar® KM2, Spectra® 130d, Dyneema® SK62, Dyneema® SK76, and Zylon® 555. For all fiber types experimentally studied, when using the rounded indenter, there is a negligible reduction in longitudinal fiber strain with increasing angle, with the strain value being quite similar to the respective longitudinal tensile failure strain resulting from tension experiments implementing a similar gauge length of 0.56 m. Fibers loaded by the razor blade show a demonstrative decrease in strain to failure as compared to the rounded indenter, but there is little to no effect of loading angle on the resulting failure strain. Most interestingly, the fibers loaded by the FSP show a large effect from the loading angle on the resulting longitudinal fiber strain at failure. While the low angle experiments yield results quite close to that from the rounded indenter, with increasing loading angle, there is a stark drop in the strain to failure. At the largest angles tested, the failure strain is quite close to the results from the razor blade indenter. In addition to tracking the strain to failure for the different loading conditions, post-mortem fracture surfaces from Kevlar® KM2 and Dyneema® SK76 are imaged in order to gain further insight into the fracture mode exhibited for the various experiments. Rupture morphology evolution follows extremely well with the strain-to-failure results. The rounded indenter promotes rupture surfaces exhibiting long-range fibrillation similar to that found in pure longitudinal tension tests, while the razor blade is found to enforce short-range failure caused by through-thickness shearing. As with the strain-to-failure results, the FSP indenter promotes a variation in failure mode with increasing deflection angles; fibrillated fracture surfaces are found at low deflection angles, while local shearing is demonstrated at high deflection angles. From both the strain-to-failure results and rupture morphology trends, it is clear that there exists a demonstrative effect of loading conditions on the failure strain and failure mechanism of high-performance fibers. Clearly the assumption of pure longitudinal tension properties being the sole indicator of ballistic performance of high-performance fibers must be reconsidered. To the authors’ knowledge, such an assumption is used in the all-analytical and constitutive models for fiber, yarn, and fabric, especially for soft-body armor systems.

Footnotes

Declaration of Conflicting Interests

The authors declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The authors disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: This work was supported through a cooperative agreement between US Army Program Executive Office – Soldiers and Purdue University. The experiments on Spectra® fibers were supported by JHU/ARL MEDE program through a subcontract from University of Delaware.

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