Shear strength of homopolymer and copolymer aramid fibers

Journal Pre-proof Shear strength of homopolymer and copolymer aramid fibers K. Şahin, J.K. Clawson, J. Singletary, I. Chasiotis PII:

S0032-3861(19)31040-7

DOI:

https://doi.org/10.1016/j.polymer.2019.122034

Reference:

JPOL 122034

To appear in:

Polymer

Received Date: 11 August 2019 Revised Date:

22 November 2019

Accepted Date: 26 November 2019

Please cite this article as: Şahin K, Clawson JK, Singletary J, Chasiotis I, Shear strength of homopolymer and copolymer aramid fibers, Polymer (2019), doi: https://doi.org/10.1016/ j.polymer.2019.122034. This is a PDF file of an article that has undergone enhancements after acceptance, such as the addition of a cover page and metadata, and formatting for readability, but it is not yet the definitive version of record. This version will undergo additional copyediting, typesetting and review before it is published in its final form, but we are providing this version to give early visibility of the article. Please note that, during the production process, errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain. © 2019 Published by Elsevier Ltd.

K. Şahin: Conceptualization, Methodology, Investigation, Software, Formal Analysis, Writing-Original Draft, Writing-Review and Editing, Visualization, J. K. Clawson: Investigation, J. Singletary: Writing – Review and Editing, I. Chasiotis: Conceptualization , Writing-Review and Editing, Visualization, Supervision, Project administration, Funding acquisition, Resources

Novel Specimen Design

Aramid Fiber Shear Strength 200

Shear Stess (MPa)

Shear Surface

150 100 50

K119 119 AuTx

0

10 μm

0

0.5

1

1.5

2

Cross-head Displacement (μm)

F

100 μm

MEMS Device for Single Fiber Shear Testing

Shear Failure Surface

Shear Strength of Homopolymer and Copolymer Aramid Fibers K. Şahina, J. K. Clawsona, J. Singletaryb, I. Chasiotisa a

Aerospace Engineering, University of Illinois at Urbana-Champaign, Urbana, IL, USA DuPont Protection Solutions, E.I. du Pont de Nemours and Company, Richmond, VA, USA

b

Abstract Novel shear experiments with homopolymer and copolymer high performance aramid fibers were conducted via a custom designed MEMS device to examine the correlation between shear and tensile strength. A finite element analysis was utilized to design the shear test fiber specimen geometry to eliminate the stress singularity at the notch tip and ensure uniform shear stress in the majority of the shear zone. The test results conducted on single fiber specimens from homopolymer and copolymer aramid fibers pointed to the significantly higher shear strength of the copolymer fibers: the average shear strength of the homopolymer and the copolymer fibers was 85±7.6 MPa and 169±17 MPa, respectively. In comparison, the tensile strength of the homopolymer fibers was 3.97±0.3 GPa, and of the copolymer fibers 5.1±1.2 GPa, namely a 100% increase in shear strength resulted in 25% higher tensile strength. This drastic difference in fiber shear strength is due to stronger intermolecular interactions stemming from improved crystallite ordering in copolymer aramid fibers with 2-4° misorientation angles, as opposed to an average 16.7° misorientation angle in the homopolymer fibers.

Keywords: Fiber strength, van der Waals bonding, Kevlar fibers

1

1.

Introduction Aramid or aromatic polyamide fibers are distinguished by their high specific strength,

modulus, high temperature stability, and cut resistance [1-4]. These extreme mechanical properties have attracted major scientific interest towards understanding their microstructure visà-vis failure initiation, mainly focusing on their outstanding tensile properties [5-18]. Under tensile loading, the shear stresses developing due to crystallite misorientation result in improved orientation via rotation and sliding of crystallites, which is a rate dependent process of breaking and reforming of secondary bonds [7,9,10-20]. A recent study has shown that commercial grade Kevlar® fibers (119, 29, KM2, and 49), although may have initial moduli in the broad range of 65-120 GPa, the unloading moduli of all four types of fibers at 90% of their tensile strength converge to 160-170 GPa and the crystallite orientation distribution also converges from an initial range of 16.7-9.7 to the narrow range of 6°-6.5° [20]. Therefore, there appears to be a critical orientation at the point of failure. Microstructural studies pointed to a critical shear stress that is responsible for the onset of tensile failure, while early studies have also shown a close correlation between the shear strength and the tensile fiber strength [11,22]. Compared to the vast literature on the tensile behavior of aramid fibers, only a few studies have focused directly on the shear strength [21-23] by measuring the τθz component of shear stress via twisting individual aramid filaments. However, the τθz component of shear stress due to torsion attains its maximum value on the fiber outer surface, thus probing a very small volume of the fiber at the fiber skin-core interface that has been shown to be a weak interface [20]. On the other hand, the τrz component of stress (on the plane defined by the longitudinal and transverse fiber directions) is responsible for interfibrillar load transfer and crystallite reorientation under tensile load, and controls the local shear deformation that results in sliding of crystallites, defect nucleation, and finally tensile fiber failure. Understanding the role of shear stress on the tensile fiber strength could guide computational and synthesis studies on liquid crystal and other fibrous nanomaterials with strong secondary bond interactions between nanoscale building blocks. Motivated by this important knowledge gap, this study focuses on the shear and tensile strengths of individual fibers from two different classes of aramid fibers: DuPont’s Kevlar® 119 filaments and AuTx (Russar family) filaments. The latter type of aramid fibers has twice the initial elastic modulus and ~30% higher tensile strength than Kevlar® 119. Microstructurally speaking, Kevlar® 119 is a homopolymer aramid with initial crystallite 2

orientation distribution of 16.7° [20], while AuTx is a copolymer aramid fiber with crystallite orientation distribution of 2-4° [24]. While the tensile properties of the aforementioned aramid fibers are fairly straightforward to obtain, there are no proven methods for fiber testing in pure shear. Such tests require careful consideration of the stress distribution in order to maintain uniform shear stresses while minimizing the tensile and compressive stresses in the region of interest. Specimen geometries, such as the Iosipescu [25,26] and Miyauchi [27-29] have been developed and further refined in the past, but are applicable to two-dimensional, plate-like specimens. Standardized specimen geometries following the ASTM standard B831 [30] and shear compression specimens [31,32] generate a shear zone under far field tension or compression. Other studies have focused on the analysis of the stress distribution in the slotted shear specimen to ensure shear dominant deformation and shear strain uniformity by inserting rounded [33-38] or eccentric notches [39,40]. Thinning down the shear zone in the out-of-plane direction has been shown to minimize the inherent problem of shear plane rotation due to the asymmetry in slotted shear specimens [41-45] while specialized holders can also restrict rotation [46]. However, the aforementioned shear specimen geometries are not directly applicable to fiber specimens. An approach, recently reported to split aramid filaments by generating a shear dominant region in a fiber via Focused Ion Beam (FIB) cuts [47], provides the first step towards the goal of pure shear tests with single filaments. The reported 90° asymmetric slotted shear specimens were effective in revealing the inner fibrillar structure of aramid fibers and enabling the study of the split surfaces via AFM [48]. However, issues arising from the use of two normal cuts, such as rotation and normal stresses around the shear zone, require further work before this concept is applied to microfiber shear testing. This study developed a new slotted fiber specimen geometry to obtain the shear strength of high performance aramid fibers, specifically homopolymer and co-polymer aramid fibers. A Finite Element Model (FEM) was utilized to determine the specimen geometry and dimensions that eliminate the stress singularities and, thus, achieve a nearly uniform shear stress zone in the middle of a fiber. The experimental results are discussed in the context of fiber tensile strength and the microstructure of the shear failure surfaces of the two classes of fibers.

3

2. 2.1.

Materials and Methods Microstructure of Aramid Fibers Two aramid fibers with different microstructure and tensile properties were utilized as

specimens in this study. The first was Kevlar® 119, which is a homopolymer fiber of poly(pphenylene terephthalamide) (PPTA) [2,49,50]. Kevlar® 119 fibers are dry-jet wet spun from anisotropic solution of PPTA dissolved in ≥99.8% sulphuric acid (H2SO4) [51,52] at a specific concentration with as many nematic liquid crystallites as possible [51,53]. The spinning solution passes through an orifice into an air gap followed by a coagulation bath of water where fibers rapidly solidify while losing the solvent resulting in the skin-core structure [54-56]. The fibers are highly crystalline due to the liquid crystal nature of the spinning dope, as evidenced by the sharp diffraction peaks in X-Ray studies [57-60]. The second type of fiber was AuTx™, a copolymer aramid fiber based on Rusar (Russian aramid fiber) technology produced by Kamenskvolokno in collaboration with Alchemie Group [61,62]. The chemical composition of the particular macromolecule can be optimized for strength, stiffness, or thermal resistance [63,64]. AuTx is a heterocyclic para-aramid synthesized with copolycondensation of diaminobenzimidazole with p-phenylene diamine [65]. In general, the spinning process is similar to that for Kevlar® 119, however, the gel emerging from the spinneret passes through an air gap into a coagulation bath of water and alcohol. The addition of diaminobenzimidazole decreases the crystallinity of the fiber [65-67]. On the other hand, as-spun fibers with less crystallinity result in higher macromolecular mobility, which in addition to better orientation, facilitates stronger intermolecular interactions and promotes ordering of the structure after post-process heat treatment [65], hence resulting in misorientation angles as low as 2-4° [24]. Such high temperature drawing can take place before the fibers are wound onto rollers followed by additional annealing of the bobbins at 250°C [63]. In Kevlar® fibers, the PPTA macromolecules form sheets with hydrogen (H-) bonds in the transverse direction, while the sheets are held together by van der Waals forces [58,59] giving rise to a 3D long range order with some amorphous phase [68,69]. Such detailed data are not available for AuTx fibers, but in the case of the Rusar fiber, the effect of H-bonds is strengthened with heat treatment [24] while X-ray data for the Armos fibers, which are chemically similar to AuTx, showed a high order in the axial direction and no order in the transverse direction [68,70], thus producing a 2D long range order. Hence, it was proposed that the macromolecules in Armos form sheets with strong 4

H-bonds, which have crystalline orientation in the transverse direction. For Armos fibers, increasing temperature results in sharper XRD scan peaks, also suggesting structural rearrangements in the transverse planes and formation of H-bonds between macromolecules [70].

2.2.

Specimen Design for Single Fiber Shear Testing The shear strength of aramid fibers was measured through a modified slotted shear

specimen inspired by the ASTM B831 standard. A FE model of the specimen geometry is shown in Figure 1(a), where the slots are terminated with eccentric half-circles to eliminate the stress singularity at the edges of the tip of the notches and achieve near uniform shear stress and sheardominated deformation along and around a zone in the middle of the fiber. The FEM mesh consisted of 8-node linear brick elements away from the shear zone, and 10-node quadratic tetrahedron elements with increasing mesh density around the shear zone, Figure 1(b). FE simulations were performed using Abaqus/Standard allowing for large deformations to ensure that possible rotations in the shear zone are properly captured. To decrease the computational cost half of the fiber is modeled by applying a symmetry boundary condition for plane 1-3. One end face of the fiber is clamped and a uniform traction is applied to the other end face in the 3direction. The shear stress developing in the shear zone increased proportionally with this applied until the maximum applied force of 10 mN, therefore the effect of rotations at the shear zone is insignificant. The elastic constants for the transversely isotropic model for Kevlar® 119 fibers are summarized in Table 1, where E1 and E2 are the transverse elastic moduli, E3 is the elastic modulus along the fiber axis, G13 and G23 are the shear moduli for the transverse-longitudinal plane, ν12 is the Poisson’s ratio for the transverse-transverse plane, and ν31 is the Poisson’s ratio for the longitudinal-transverse plane. These properties follow the work by Singletary et al. [71] for non-heat-treated PPTA fibers and also agree with values reported by Kawabata [72-74]. The elastic modulus values along the fiber axis, E3, was measured in this work. The main difference between the Kevlar® 119 fibers and previously characterized PPTA fibers is the orientation distribution of crystallites along the fiber axis [20], which mainly affects the elastic modulus, E3, due to the highly anisotropic nature of the monoclinic crystals making up the fibers. Based on this background it is reasonable to assume comparable transverse elastic properties for all Kevlar 5

grades, which is also verified by literature studies [74]. For AuTx fibers, the elastic constants measured by Lim et al. [75] for the A265 fiber, which is an AuTx fiber, were used except for E3 that was measured in this work, Table 1.

Clamped end face 1-3 symmetry plane

Uniform σ33 applied on end face

(a)

(b)

Figure 1. (a) FE model of slotted shear specimen, and (b) detail of the mesh in the shear zone.

Table 1. Elastic constants of transversely isotropic Kevlar® 119 fibers adopted mainly from Kawabata [72] and of AuTx fibers from Lim et al. [75]. The E3 values were obtained in this work. E1, E2 (GPa) Homopolymer (119) Copolymer (AuTx)

G13, G23

E3 (GPa)

(GPa)

ν12

ν31

2.45

66

2.2

0.43

0.63

1.83

138

12.03

0.4

0.402

6

2.3.

Experimental Methodology Single fibers were isolated from bundles and 10 mm gauge length fibers were tested in

tension, as described in [20]. The shear tests were carried out with 100 µm long fiber specimens with the aid of a Microelectromechanical Systems (MEMS) type device, Figure 2(a), which was fabricated via the PolyMUMPS process of MEMSCAP (NC, USA). During testing, one end of a fiber is placed in a channel pointed out in Figure 2(b) such that it sits closer to the neutral axis of the MEMS device, hence reducing the out-of-plane bending moment under a tensile force [76]. The device also consists of a pull pedal where a probe is attached to extend the fiber with the aid of an external piezoelectric actuator. By virtue of Digital Image Correlation (DIC) applied to high magnification optical microscopy images, the displacement, u, of the numbered pads in Figure 2(b) can be calculated with ~20 nm resolution [77]. This method and MEMS device enable the simultaneous measurement of the force applied to the fiber as the product of load cell stiffness × (uII – uIII), and the fiber elongation as (uI-uII), where uI, uII and uIII are the rigid body displacements of the three numbered parts in Figure 2(b) [78]. Figure 2(c) shows a notched Kevlar® 119 fiber attached to a MEMS device, with the details of the notched test specimen shown in Figure 2(d). The milling current to form the edge notches was 2 nA at 16 kV voltage.

7

Fiber Grips

Channel for Fiber Placement and Gripping

Pull Pedal

Force Sensor

I

II

III

Fixed Fiber Grip

(a)

(b)

(c)

(d)

Figure 2. (a) MEMS tension testing device with a folded beam type loadcell. The arrow on the pedal points to the direction of actuation with the aid of an external piezoelectric actuator. (b) Close-up of the device loadcell and fiber grip: One fiber end is placed inside the channel and attached with an adhesive while the other end is attached to the fixed grip. The rigid body motion of the three numbered pads (Roman numerals) provides simultaneous measurement of the applied force and the fiber stretch ratio or engineering strain. (c) A Kevlar® 119 fiber fixed onto a MEMS device with edge notches created via a FIB. (d) Close-up view of the fiber surface after machining the section that will be subjected to pure shear.

8

3. 3.1.

Results and Discussion Stress Distribution in Shear Zone Placement of eccentric half-circles at the edge of each notch tip eliminated the stress

singularity to achieve nearly uniform shear stress along and around a zone in the middle of individual fibers, as shown in Figure 3(a) for a Kevlar® 119 fiber which is loaded by a 1 mN axial force applied to the end face designated in Figure 1(a). The detailed contour plot of the fiber section, indicated in the schematic in Figure 3(b), is given in Figure 3(c). The latter shows the good uniformity of τ13 in the 3 µm shear zone, and the 0.1 µm radius stress relief notches at the tips of the two opposite slots, which, for this specific loading condition, resulted in a maximum shear stress of 33 MPa in the shear zone. In order to demonstrate the uniformity of shear stress, the normalized shear stress, τnorm, is defined as the ratio of the local shear stress, as computed via FEA, τFEA, to the average shear stress: =

(1)

where F is the applied tensile force on the fiber and A is the area of the shear plane. As deduced from Figure 3(d), τnorm is uniform in the majority of the surface in the central region of the fiber while the highest shear stress is observed in the center area. Thus, the specimen geometry could be optimized for a relatively uniform shear stress profile in the shear zone. Moreover, by shaping the stress profile to result in a non-singular stress state at the notch tip, the shear stress is vanishingly small in the potentially amorphized regions due to Ga+ ion milling, thus averting premature failure due to FIB-induced damage. The highest shear stress is along the center line (x=0, y=0), e.g. Figure 3(c). Figures 4(a,b) show the normalized shear stress along the center line, in the fiber direction designated in Figure 3(b), vs. the shear zone length. The normalized coordinates 1 and -1 correspond to the position of the notch tips. A shear zone length of 3 µm is shown to provide a nearly uniform shear stress profile for at least half of the shear zone length for both Kevlar® 119 and AuTx fibers. Then, the shear strength,τmax, is computed by =

(2)

9

where Fmax is the macroscopically applied force at failure.

is the maximum value of τnorm,

which, for example for the shear zone length of 3 µm in Figure 4(a), is equal to 1.16. This stress distribution, e.g. Figure 3(d) guarantees that shear failure will occur when the peak stress along the central line reaches the shear strength of the material. The value of the normal stress in the transverse direction, σ11, which could result in crack opening in the transverse direction, may affect the calculated shear strength. To assess the role of

σ11 and σ33 in the measured tensile force value that initiates failure, their values in the shear zone are plotted in Figures 5(a) and 5(b), respectively, for a 119 fiber with 3 µm shear zone length. The significance of the maximum value of σ11 (6 MPa), Figure 5(a), can be assessed through a comparison with the fiber strength in the transverse direction in which cohesive forces arise from van der Waals interactions: a value of 100 MPa is a reasonable cohesive tensile strength for a van der Waals solid with a transverse modulus of E=2 GPa (following the rule of thumb that the van der Waals strength scales as ~E/10), which means that σ11 does not play a role in failure initiation in the shear zone. Similarly, the maximum tensile σ33 (30 MPa) in Figure 5(b) is more than two orders of magnitude smaller than the ~4 GPa tensile strength of 119 fibers, while the maximum compressive σ33 (45 MPa) is smaller than the reported compressive strength of aramid fibers of 300-700 MPa [21,79]. Therefore, the normal components of stress in the shear zone are not expected to cause tensile fibril failure or microbuckling, and the dominant mode of failure in this specimen is shear failure. Finally, according to the FE model all other components of shear stress, namely τ12 and τ23, are significantly smaller than τ13, and σ22 is much smaller than σ11. Thus, this asymmetric shear specimen geometry exhibits shear stress profiles that ensure accurate maximum shear strength measurements in micrometer scale fibers. Yet, during specimen preparation via FIB milling the notch geometry may not be as precisely defined. Although the 45° notch angle does not deviate by an appreciable amount, the intended 3 µm shear zone length could be within the 2.5-3.5 µm range. This range in shear zone length results in τnorm in the range 1.13-1.18 for a Kevlar® 119 fiber, Figure 4(a), while still maintaining a plateau in the middle of the shear zone, whose length can be measured quite precisely before testing via SEM. Similarly, the sensitivity of τnorm on the variation of the circular notch radius through the fiber thickness was evaluated via FEA for a 3-µm zone length and different semicircle radii. Figure 4(c) shows that the maximum τnorm along the center line varies in the 10

range 1.16-1.2 for a 119 fiber suggesting a minimal effect. While a 0.05 µm radius is very small to achieve via FIB ion-milling, 0.1-0.2 µm radii could be machined consistently, which was used in the calculations shown in Figures 5(a,b). Similar conclusions are derived for the optimal circular notch radius in an AuTx fiber, as shown in Figure 4(d).

Shear zone length

3

2

3 1

(a)

(b) τ13

6

30

4

τnorm

6

33

1.2 1.1

4

1.0

2-a xis (µ m)

2-a xis (µ m)

27 2 24 0

22 19

-2

2 0.9 0

0.8 0.7

-2

17 -4 -6 -1.5

0.6 -4

15 13 -1.0

-0.5

0.0

0.5

1.0

-6 -1.5

1.5

0.6 0.5 -1.0

-0.5

0.0

0.5

3-axis (µm)

3-a xis (µm)

(c)

(d)

1.0

1.5

Figure 3. (a) Shear stress distribution demonstrating relative uniformity along and around the specimen shear zone. (b) Schematic of fiber specimen showing the curved out shear zone length, and the orientation of the shear stress distribution in the shear zone surface given in the contour plot of (c) τ13, and (d) the normalized shear stress, τnorm.

11

1.4

1.2

1.2

Normalized Shear Stress

Normalized Shear Stress

1.4

1 Shear zone length (µm)

0.8 0.6

2 3 4 5 6

0.4 0.2

Shear zone length (µm)

0.8 0.6

2 3 4 5 6

0.4 0.2

0

0 -1

-0.5

0

0.5

1

-1

-0.5

0

0.5

Normalized shear zone length

Normalized shear zone length

(a)

(b)

1.4

1.6

1.2

1.4

1

Normalized Shear Stress

Normalized Shear Stress

1

Semicircle radius (µm)

0.8

0.05

0.6

0.10 0.4

0.15

0.2

0.20

0

1

1.2 Semicircle radius (µm)

1 0.8

0.05

0.6

0.10

0.4

0.15

0.2

0.20

0

-1

-0.5

0

0.5

1

-1

-0.5

0

0.5

Normalized shear zone length

Normalized shear zone length

(c)

(d)

1

Figure 4. Shear stress profiles along the center line, (x=0, y=0) in Figure 3(b), with different shear zone lengths for a (a) Kevlar® 119, and (b) AuTx fiber. Shear stress profiles along the center line (x=0, y=0) in Figure 3(b) for a (c) Kevlar® 119, and (d) AuTx fiber with 3-µm shear zone length and different semicircle radii.

12

σ33 (MP a )

σ11 (MPa ) 6

6

6 3

4

30 21

4

11

2-a xis (µ m)

2-a xis (µ m)

1 2 -2 0

-5 -8

-2

2 2 0

-8 -17

-2

-11 -4

-26 -4

-13

-6 -1.5

-16 -1.0

-0.5

0.0

0.5

1.0

-6 -1.5

1.5

3-a xis (µm)

-36 -45 -1.0

-0.5

0.0

0.5

1.0

1.5

3-a xis (µm)

(a)

(b)

Figure 5. Normal stress (a) σ11 (transverse direction) and (b) σ33 (axial direction) in the shear zone for a Kevlar® 119 fiber with 3 µm shear zone length.

Additional uncertainties may stem from the eccentricity of the FIB cuts. The two edge notches may be off-axis by a distance, δ, Figure 6(a), that could be as much as 0.5 µm. This issue could arise due to non-circular fiber cross-section and tilt in the sample during FIB milling. As shown in Figure 6(a) for a fiber with 3 µm shear zone length, 0.1 µm semicircle radius and various out-of-axis values, the off-axis distance did not affect the value of τnorm. For edge notches with non-zero off-axis distance, the shear surface area could be calculated quite precisely by using SEM images. Finally, SEM observations indicated that FIB-generated edge notches could be eccentric (overlapping) by as much as e = 0.25 µm. The eccentricity of the two notches was considered in the FEM analysis as shown in the schematic in Figure 6(b). For a fiber with 3-µm shear zone length and 0.1 µm circular notch radius, the fiber eccentricity is the most important factor, as a typical eccentricity of 0.25 µm could result in ~10% error in the calculated shear strength compared to an ideal specimen geometry. However, the eccentricity could be accounted for from SEM measurements before testing and by using the corresponding τnorm value from the plots derived via the FEM analysis as in Figure 6(b). Similar plots were also calculated for AuTx fibers and were used in the shear strength calculations with experimental inputs from SEM images.

13

δ

Normalized shear stress

1.4

Off-axis distance (δ), (µm)

1.2 1

0.0

0.8

0.5 1.0

0.6

1.5

0.4 0.2 0 -1

-0.5

0

0.5

1

Normalized shear zone length

(a) 1.4

e e

Normalized shear stress

Eccentricity

1.2

(e) (µm)

1

0.00

0.8

0.25 0.5

0.6

0.75

0.4 0.2 0 -1

-0.5

0

0.5

1

Normalized shear zone length

(b) Figure 6. (a) Schematic of a fiber in which the shear surface is off-axis, and corresponding plot of normalized shear stress in the shear zone. The actual shear surface area was used in shear stress normalization in the plot. (b) Schematic of a fiber with eccentric (overlapping) edge notches and plot of normalized shear stress. All results shown in the plots were derived for a Kevlar® 119 fiber.

14

3.2.

Fiber Shear and Tensile Strength Figure 7(a) shows typical stress strain curves for Kevlar® 119 and AuTx fibers. The

Young’s moduli were measured to be equal to 65.6±0.8 GPa [20] and 138 GPa, and the tensile strength 3.97±0.3 GPa and 5.1±1.2 GPa for Kevlar® 119 and AuTx fibers, respectively. Figure 7(b) shows a plot of the maximum shear stress vs. cross-head displacement of the ends of the Kevlar® 119 and AuTx test fibers which, at the peak tensile force, failed along the uniform stress portion of the shear zone marked in the schematic in Figure 3(b). The non-linearity in the curves is due to the deformation of the compliant epoxy used to attach the fiber to the MEMS device. The average shear strength values of 85±7.6 MPa and 169±17 MPa were calculated from three Kevlar® 119 and three AuTx fibers, respectively, by carefully measuring the shear zone length, circular notch radius, off-axis distance and eccentricity of the FIB milled specimens before testing and using the τnorm calculated via a FEM analysis that employed the specific geometric parameters. In prior research on the shear strength of aramid filaments the shear strength was calculated from the torsional strain at the periphery of a fiber [21-23] where also the skin-core interface resides. The shear strength, τθz, values of various experimental and commercial aramid filaments were reported to be in the range of 25-180 MPa. This large variation in values measured may also be, in part, due to variabilities in the rather weak skin-core interface. In the present work we report on the τrz shear strength that controls the maximum load transfer due interfibrillar shear interactions during uniaxial tension, with minimal influence of the weak skincore interface that has been shown to be a limiting factor of the tensile strength of aramid fibers [20]. Based on the present experimental results, the 25% difference in tensile strength between a homopolymer and copolymer aramid fiber corresponds to a 100% increase in shear strength, namely fibers with stronger van der Waals interactions have higher tensile strength. The stronger van der Waals interactions stem from the better crystallite alignment in AuTx fibers. For small fibril misorientation angles, θ, the fiber strength, σf, can be related to the fiber shear strength, τ, via [11] =

!"

#$ +

15

&

'() "# $

)"

# $*

(3)

where σ0 = 24 GPa is the crystal strength [12,80,81] of PPTA fibers also taken as the theoretical strength of the composite fiber. Equation (3) is applicable to small crystallite angle misorientations which is the case for the AuTx fibers. Stipulating a similar theoretical strength and a misorientation angle of 2° in Equation (3) we find τAuTx = 175 MPa, which is close to the measured value of 169±17 MPa. Equation (3) is not applicable to Kevlar® 119 because of the large effective misorientation angle of 16.7° [20].

6

200

Shear Stess (MPa)

Stress (GPa)

5 4 3 2 K119 119

1

Strain

0.04

50

K119 119

0

0 0.02

100

AuTx

AuTx 0

150

0 0.5 1 1.5 2 Cross-head Displacement (µm)

0.06

(a)

(b)

Figure 7. (a) Stress-strain curves for Kevlar® 119 and AuTx fibers subjected to uniaxial tension. (b) Shear stress vs. cross-head displacement of a Kevlar® 119 fiber with true shear strength of 81 MPa, and an AuTx fiber with true shear strength of 170 MPa.

Importantly, the shear tests also revealed the internal structure of Kevlar® 119 and AuTx fibers. Upon shear failure, the Kevlar® 119 fibers demonstrated a fine (layered) fibrillar structure and damage (in the form of interlaminar failure and severed fibrils) occurring in the 2-3 parallel planes that were sheared with respect to each other, as pointed out by the arrows in Figures 8(a,b). This provides evidence for the parallel sheet structure of Kevlar® fibers due to H-bonds. Upon shear failure there is significant splitting between fibrils as indicated by the arrow in the upper corner of Figure 8(b), contrary to no fibril splitting on the shear failure surface of AuTx fibers, Figures 8(c,d), due to the much higher shear strength of the latter fibers. Moreover, as pointed out by the arrows in Figure 8(b), the shear failure surfaces of Kevlar® 119 fibers were 16

(a)

(b)

(c)

(d)

Figure 8. (a) SEM image of a Kevlar® 119 fiber after shear failure. The arrows point to the layered fibrillar structure and debonding of the skin due to skin-core differentiation. (b) Fine fibrillar structure with parallel sheets of fibrils indicating shear failure, also showing separated shear failure planes, and pleated surface (arrows). (c) Uniform internal fine fibrillar structure on the shear failure surface of a AuTx fiber. (d) High fibrillar alignment along the shear failure plane and lack of the pleated structure and fibril misorientation seen in (b) for a Kevlar® 119 fiber. The skin fragment that is pointed out provides evidence for skin-core differentiation in AuTx fibers too.

wavy due to fibril misorientation (16.7°), also reflecting the pleated structure of Kevlar® fibers. Analogous observations were obtained from AuTx shear failure surfaces, Figures 8(c,d), with shear failure occurring on a single plane of fibrils as compared to the separation of fibril planes

17

in Kevlar® 119 fibers. The higher shear strength and degree of fibril alignment (2-4°) of AuTx fibers, prohibited the peeling of fibril layers. Finally, as pointed out in Figure 8(d), AuTx fibers were also subject to skin-core differentiation with some skin separation occurring at failure. SEM images of the inner surface of skin fragments showed no fibrillar structure for the skin as opposed to the fibrillar core that is clearly seen in the shear failure surfaces.

4.

Conclusions The first of their kind uniform shear experiments with high performance aramid fibers

were performed via a custom designed MEMS device to examine the correlation between shear and tensile strength. A FE analysis was utilized to design the shear test specimen geometry and dimensions with a uniform shear stress profile along a 3-µm longitudinal shear zone in 9-12 µm diameter fibers. The specimen geometry eliminated the stress singularity at the notch tip and ensured that the uniform shear stress in the majority of the shear zone was also the highest shear stress in the test specimen. Tests conducted on fiber specimens from homopolymer (Kevlar® 119) and copolymer (AuTx) aramid fibers pointed to the significantly higher shear strength of the copolymer fibers: the average shear strength of the homopolymer fibers was 85±7.6 MPa vs. 169±17 MPa for the copolymer fibers. In comparison, the tensile strength of the homopolymer fibers was 3.97±0.3 GPa and of the copolymer fibers 5.1±1.2 GPa. Therefore, a 100% increase in shear strength results in 25% higher tensile strength. The drastic increase in fiber shear strength is due to stronger intermolecular interactions stemming from improved crystallite ordering in copolymer aramid fibers with 2-4° misorientation angles, as opposed to an average 16.7° misorientation angle in the homopolymer fibers.

Acknowledgements This research was supported by the office of PEO Soldier Protection under contract number W91CRB-16-C-0011. The authors thank Suzanne Horner and Dr. James Zheng from PEO Soldier Protection, and Professor Assimina Pelegri from Rutgers State University for their support and productive discussions.

18

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23

Highlights: •

Measured for the first time the shear strength of individual aramid fibers using uniform shear stress fields.

•

New method for measurement of shear strength of single microscale polymer fibers.

•

Shear strength of homopolymer and copolymer aramid fibers correlated with their tensile strength.

•

Found that a 100% increase in shear strength results to a 25% increase in fiber tensile strength.

•

Shear failure surfaces were characterized by wavy crystallites in low shear strength homopolymer aramid fibers, and highly oriented crystallites in high shear strength copolymer aramid fibers.

Declaration of interests ☒ The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. ☐The authors declare the following financial interests/personal relationships which may be considered as potential competing interests: