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W tym Artykule

  • Podsumowanie
  • Streszczenie
  • Wprowadzenie
  • Protokół
  • Wyniki
  • Dyskusje
  • Ujawnienia
  • Podziękowania
  • Materiały
  • Odniesienia
  • Przedruki i uprawnienia

Podsumowanie

The goal of the study was to develop protocols to prepare consistent specimens for accurate mechanical testing of high-strength aramid or ultra-high-molar-mass polyethylene-based flexible unidirectional composite laminate materials and to describe protocols for performing artificial ageing on these materials.

Streszczenie

Many body armor designs incorporate unidirectional (UD) laminates. UD laminates are constructed of thin (<0.05 mm) layers of high-performance yarns, where the yarns in each layer are oriented parallel to each other and held in place using binder resins and thin polymer films. The armor is constructed by stacking the unidirectional layers in different orientations. To date, only very preliminary work has been performed to characterize the ageing of the binder resins used in unidirectional laminates and the effects on their performance. For example, during the development of the conditioning protocol used in the National Institute of Justice Standard-0101.06, UD laminates showed visual signs of delamination and reductions in V50, which is the velocity at which half of the projectiles are expected to perforate the armor, after ageing. A better understanding of the material property changes in UD laminates is necessary to comprehend the long-term performance of armors constructed from these materials. There are no current standards recommended for mechanically interrogating unidirectional (UD) laminate materials. This study explores methods and best practices for accurately testing the mechanical properties of these materials and proposes a new test methodology for these materials. Best practices for ageing these materials are also described.

Wprowadzenie

The National Institute of Standards and Technology (NIST) helps law enforcement and criminal justice agencies ensure that the equipment they purchase and the technologies that they use are safe, dependable, and highly effective, through a research program addressing the long-term stability of high-strength fibers used in body armor. Prior work1,2has focused on the field failure of a body armor made from the material poly(p-phenylene-2,6-benzobisoxazole), or PBO, which led to a major revision to the National Institute of Justice’s (NIJ’s) body armor standard3. Since the release of this revised standard, work has continued at NIST to examine mechanisms of ageing in other commonly used fibers such as ultra-high-molar-mass polyethylene (UHMMPE)4 and poly(p-phenylene terephthalamide), or PPTA, commonly known as aramid. However, all of this work has focused on the ageing of yarns and single fibers, which is most relevant for woven fabrics. However, many body armor designs incorporate UD laminates. UD laminates are constructed of thin fiber layers (<0.05 mm) where the fibers in each layer are parallel to each other5,6,7 and the armor is constructed by stacking the thin sheets in alternating orientations, as depicted in Supplemental Figure 1a. This design relies heavily on a binder resin to hold the fibers in each layer generally parallel, as seen in Supplemental Figure 1b, and maintain the nominally 0°/90° orientation of the stacked fabrics. Like woven fabrics, UD laminates are typically constructed out of two major fiber variations: aramid or UHMMPE. UD laminates provide several advantages to body armor designers: they allow for a lower-weight armor system compared to those using woven fabrics (due to strength loss during weaving), eliminate the need for woven construction, and utilize smaller diameter fibers to provide a similar performance to woven fabrics but at a lower weight. PPTA has previously been shown to be resistant to degradation caused by temperature and humidity1,2, but the binder may play a significant role in the performance of the UD laminate. Thus, the overall effects of the use environment on PPTA-based armor are unknown8.

To date, only very preliminary work has been performed to characterize the aging of the binder resins used in these UD laminates and the effects of binder aging on the ballistic performance of the UD laminate. For example, during the development of the conditioning protocol used in NIJ Standard-0101.06, UD laminates showed visual signs of delamination and reductions in V50 after ageing1,2,8. These results demonstrate the need for a thorough understanding of the material properties with ageing, in order to evaluate the material’s long-term structural performance. This, in turn, necessitates the development of standardized methods to interrogate the failure properties of these materials. The primary goals of this work are to explore methods and best practices for accurately testing the mechanical properties of UD laminate materials and to propose a new test methodology for these materials. Best practices for ageing UD laminate materials are also described in this work.

The literature contains several examples of testing the mechanical properties of UD laminates after hot-pressing multiple layers into a hard sample9,10,11. For rigid composite laminates, ASTM D303912 can be used; however, in this study, the material is approximately 0.1 mm thick and not rigid. Some UD laminate materials are used as precursors to make rigid ballistic protective articles such as helmets or ballistic-resistant plates. However, the thin, flexible UD laminate can also be used to make body armor9,13.

The objective of this work is to develop methods for exploring the performance of the materials in soft body armor, so methods involving hot pressing were not explored because they are not representative of the way the material is used in soft body armor. ASTM International has several test-method standards relating to testing strips of fabric, including ASTM D5034-0914 Standard Test Method for Breaking Strength and Elongation of Textile Fabrics (Grab Test), ASTM D5035-1115 Standard Test Method for Breaking Force and Elongation of Textile Fabrics (Strip Method), ASTM D6775-1316 Standard Test Method for Breaking Strength and Elongation of Textile Webbing, Tape and Braided Material, and ASTM D395017 Standard Specification for Strapping, Nonmetallic (and Joining Methods). These standards have several key differences in terms of the testing grips used and the specimen size, as mentioned below.

Methods described in ASTM D5034-0914 and ASTM D5035-1115 are very similar and focus on testing standard fabrics rather than high-strength composites. For the tests in these two standards, the jaw faces of the grips are smooth and flat, although modifications are allowed for specimens with a failure stress greater than 100 N/cm to minimize the role of stick-slip-based failure. Suggested modifications to prevent slipping are to pad the jaws, coat the fabric under the jaws, and modify the jaw face. In the case of this study, the specimen failure stress is approximately 1,000 N/cm, and thus, this style of grips results in excessive sample slippage. ASTM D6775-1316 and ASTM D395017 are intended for much stronger materials, and both rely on capstan grips. Thus, this study focused on the use of capstan grips.

Further, the specimen size varies considerably among these four ASTM standards. The webbing and strapping standards, ASTM D6775-1316 and ASTM D395017, specify to test the full width of the material. ASTM D677516 specifies a maximum width of 90 mm. In contrast, the fabric standards14,15 expect the specimen to be cut widthwise and specify either a 25 mm or 50 mm width. The overall length of the specimen varies between 40 cm and 305 cm, and the gauge length varies between 75 mm and 250 mm across these ASTM standards. Since the ASTM standards vary considerably regarding specimen size, three different widths and three different lengths were considered for this study.

The terminology referring to specimen preparation in the protocol is as follows: bolt > precursor material > material > specimen, where the term bolt refers to a roll of UD laminate, precursor material refers to an unwound amount of UD fabric still attached to the bolt, material refers to a separated piece of UD laminate, and specimen refers to an individual piece to be tested.

Protokół

1. Cutting procedure for warp-direction specimens that are cut perpendicular to the axis of the roll

  1. Identify a bolt of unidirectional material to be tested.
    NOTE: There is no warp (used to describe the direction perpendicular to the axis of the roll) and weft (used to describe the direction parallel to the axis of the roll) in the traditional textile sense, as the material used here is not woven, but these terms are borrowed for clarity.
  2. Manually unroll the bolt to expose the precursor material (i.e., the identified material unwound from the bolt but still connected to the bolt).
    NOTE: The width of this bolt will become the material’s total length (refer to Supplemental Figure 1b), so for a 300 mm gauge length (corresponding to a 600 mm total specimen length), using the procedure and testing grips specified below, the piece of material cut from the bolt should be 600 mm wide. The length of this piece of material will be that of the width of the bolt on which the material is rolled (approximately 1,600 mm, in this case). This is depicted in Supplemental Figure 1b.
  3. Visually verify that the principal fiber direction is parallel to the width of the bolt, as shown in Supplemental Figure 1b. The fiber direction of the top layer of the material (i.e., that which a viewer sees when looking down onto the specimen) is termed the principal fiber direction.
  4. Cut a small tab in the precursor material with a scalpel, approximately 3 mm wide, with the tab’s length aligned nominally parallel with the principal fiber direction of the precursor material, as shown in Supplemental Figure 1c.
  5. Manually grasp the tab and pull it up to tear the tab away and expose the fibers on the layer underneath, running perpendicular to the tab. Keep pulling on the tab until the two layers have been separated across the whole length of the precursor material (Supplemental Figure 1d).
    NOTE: This step will produce a region where only cross fibers are visible, as shown in Supplemental Figure 1d.
  6. Remove any loose fibers neighboring the exposed cross fibers remaining from the edge of the tab.
    NOTE: In the current UD laminate system, it was observed that the fibers are not perfectly parallel (as shown in Figure 1) and that they may cross over neighboring fibers. Thus, fibers neighboring those being separated will frequently become separated in this process. The neighboring fibers that become loose may be as much as 1–2 mm away from the expected path of the tab used for separation.
  7. Using a medical scalpel, cut along the exposed cross fibers, thus separating the piece of precursor material from the bolt.
    1. Determine the distance cut that dulls the blade, causing a less clean cut (i.e. after 400 cm of cutting this material, a scalpel could become dull and scratched, as shown in Supplemental Figure 2 and Supplemental Figure 3). Replace the blade before it becomes dull, or if it is damaged. Examine several cutting instruments when testing a different type of material to determine the best one.
      CAUTION: Care must be taken with all sharp blades or cutting tools to avoid injury. Cut-resistant gloves may be worn in this step to reduce the risk of injury.
  8. Turn over the material, so that now, the principal fiber direction is in the warp direction.
    NOTE: Since the principal fiber direction refers to the layer that is being viewed (the top layer), turning the material over will change the principal fiber direction from weft to warp (see Supplemental Figure 1b).
  9. Mark the grip lines on the material aligned in the weft direction.
    NOTE: These lines run from manufactured edge to manufactured edge, parallel to the cut edges and 115 mm from these cut edges. These will be further explained in step 4.4.1, but the grip lines are lines used when loading specimens (which are cut later) into the tensile testing grips.
  10. Determine the principal fiber direction for the specimen to be cut from the material, using step 1.3.
    NOTE: Be aware that fiber orientation may not be exactly perpendicular to the manufactured edge; in that case, follow the exact fiber line. Avoid the area near the manufactured edge because it may not accurately reflect bulk material properties.
  11. Orient the material on a suitable self-healing gridded cutting mat that is large enough to fit the width of the material (between the cut edges) and a length (weft direction) of at least 300 mm, as referenced in step 1.16.
    1. Carefully align the fiber direction with the gridlines on the cutting mat. Use the cut edge of the material as a guide in lining up the material; however, aligning the fiber direction of the specimen is most important.
    2. Tape the material to the cutting mat.
      NOTE: Tape should never be placed anywhere near the center of the specimen; instead, it should be used at what will be the ends of the specimens to be cut from the material. The ends will be in the grips when a specimen is tested; therefore, any damage caused to the material by the tape is minimized. Taping only the corners of the material that are far from the cut will ensure that the material will not move and that, when cutting a specimen, the blade will not also be cutting tape. Low-tack adhesive tape (e.g., painter’s tape) works well because it adheres well enough to keep the fabric in place without damaging the material when it is removed.
  12. Cut the specimens from the material using the blade and a straight edge. The strips formed are the specimens. Do not let the material move in this process; otherwise, determine the fiber direction anew and reorient the material accordingly.
    1. Place the straight edge at the desired location corresponding to the appropriate specimen width (i.e., 30 mm). Note that the medical scalpel is thin enough that no offset in the placement of the straight edge is necessary to account for the cutting location. Align the straight edge to the grid on the cutting mat or any other user-established reference line on the cutting mat.
    2. Clamp the straight edge in place by clamping on either end of the straight edge. Check the positioning of the straight edge after clamping, as it may have moved during the clamping process.
  13. Cut the specimen away from the material along the straight edge, using the medical scalpel. Ensure a single, clean, smooth cut, with a constant velocity and pressure.
    NOTE: Some pressure can be applied by the blade against the straight edge to keep the blade cutting precisely at the edge of the straight edge.
    CAUTION: Care must be taken to avoid injury, so it is advisable to wear cut-resistant gloves when handling the medical scalpel. Furthermore, since the smoothest cut can be obtained while cutting toward the body, wearing a cut-resistant apron or lab coat is advised.
  14. Examine the cut edge of the strip under the microscope. Change the blade if the cut edge has significantly more protruding fibers or other defects when compared to a cut made with a new, sharp blade.
  15. Unclamp the straight edge, taking care that the material does not move in the process. If the material did move, redetermine the fiber direction and reorient the material appropriately.
  16. Repeat steps 1.12–1.15 until the maximum number of specimens that can be cut from 300 mm of material has been obtained.
    NOTE: For specimens with a width of 30 mm, 300 mm of material is equivalent to 10 specimens, while for specimens with a width of 70 mm, this is equivalent to 4 specimens. This 300 mm limit has been determined to work well for the unidirectional laminate studied here but may vary for other laminates.
  17. Repeat steps 1.10–1.11 as needed (i.e., redetermine the principal fiber direction and reorient the material before continuing to cut more specimens).
    NOTE: The protocol can be paused here. If specimens are not to be used immediately, store them in a dark, ambient location.

2. Cutting procedure for weft-direction specimens that are cut along the axis of the roll

NOTE: There is no warp and weft in the traditional textile sense, as the material used here is not woven, but these terms are borrowed for clarity.

  1. Determine the width and length of the material desired according to the number and size of the specimens to be cut.
    NOTE: For this unidirectional laminate and for specimens with a gauge length of approximately 300 mm, two specimens placed end to end can be cut along the width of the bolt. Thus, a set of 40 specimens may be cut out in two columns of 20 specimens each, as shown in Supplemental Figure 4, prior to severing the material from the roll. If the width of the specimens is 30 mm, then the material should be cut at 20x the specimen’s width (as there are 20 specimens per column) with some extra space (i.e., 610 mm).
    1. Determine the fiber direction along the weft for the width of interest, following the instructions from steps 1.4–1.6.
    2. Cut the exposed cross fibers (i.e., across the warp fibers) using a blade, thus separating the precursor material from the bolt.
      CAUTION: Care must be taken with all sharp blades or cutting tools, to avoid injury. Cut-resistant gloves may be worn in this step to reduce the risk of injury.
  2. Prepare to cut off lengths that match the desired specimen length (i.e., cut in the warp direction at the specimen length of interest). To obtain a 300 mm gauge length (corresponding to a 600 mm total specimen length), using the procedure and testing grips specified below, keep in mind that the material should now be 600 mm x 610 mm.
  3. Follow steps 1.9–1.17 to cut out the desired specimens.
    NOTE: The protocol can be paused here. If the specimens are not to be used immediately, store them in a dark, ambient location.

3. Analysis of cutting methods by scanning electron microscopy

  1. Prepare the samples for an analysis by scanning electron microscopy (SEM) by cutting squares of approximately 5 mm in length and width, preserving at least two edges of the square from the cutting technique of interest. These preserved edges should be identified and are the edges that will be evaluated under the microscope.
  2. Mount the samples on the SEM sample holder by adhering them with tweezers onto suitable double-sided carbon tape.
  3. Coat the samples with a thin (5 nm) layer of conductive material, such as gold palladium (Au/Pd), to mitigate surface-charging effects under the scanning electron microscope.
  4. Load the samples into a scanning electron microscope and image them at about 2 kV of accelerating voltage and with a 50–100 pA electron current. Apply charge neutralization settings to counter charging effects where necessary.

4. Tensile testing of UD laminate specimens

  1. Measure the grips to determine the difference between the crosshead initial location value and the distance between where the specimen contacts the top and bottom grips under minimal tension. Read the crosshead location from the testing software. Calculate an effective gauge length from this by measuring the effective gauge length at this crosshead location. Add the offset (amount of displacement) to the crosshead location to determine the effective gauge length (the measured effective gauge length minus the crosshead location).
  2. Number the specimens prepared according to sections 1 and 2 with a soft-tipped permanent marker so the order in which they were prepared is clear. Mark other information as well, such as the date of preparation and orientation.
    NOTE: The specimens used herein have dimensions of 30 mm x 400 mm—but sample dimensions may vary for other materials—and were obtained by following either section 1 or section 2. If the specimens are not to be used immediately, store them in a dark, ambient location.
  3. If the strain will be measured using a video extensometer, manually mark the gauge points with a permanent marker, using a template for consistency, as shown in Supplemental Figure 5a, to give points for the video extensometer to track and, thus, measure strain. If the strain will be calculated from the crosshead displacement, skip this step.
  4. Load the specimen into the center of the capstan grips.
    1. Insert the end of the specimen through the gap in the capstan and position the end of the specimen at the grip line drawn in step 1.9, as shown in Supplemental Figure 5b. Take care to center the specimen on the capstan grips by aligning the center of the specimen within approximately 1 mm of the center of the capstan grips.
    2. Turn the capstan to the desired position, making sure to keep the specimen centered. Use a tensioning device—for example, a magnet placed on the specimen if the grips are magnetic—to gently hold the specimen in place, and lock the capstan in place with the locking pins.
    3. Repeat steps 4.4.1 and 4.4.2 for the other end of the specimen.
  5. Apply a preload of 2 N, or some other suitably small load.
  6. Record the crosshead displacement/actual gauge length.
  7. Program the instrument to perform the tensile test, at a constant rate of extension of 10 mm/min, using the video extensometer or crosshead displacement to record the strain, and press start to begin the test.
  8. Monitor the display and stop the test when the sample has broken, as evidenced by a loss of 90% in the observed load on the display. Record the maximum stress, which is the same as the failure stress due to the nature of the material, and the corresponding failure strain. Repeat steps 4.3–4.8 for the remaining specimens.
  9. Save the broken specimens for further analysis.
  10. Check for stress at failure as a function of specimen number and original specimen placement in the material, as well as other indications of problematic data, for instance, data points that deviate extremely from the Weibull18 distribution, and investigate possible causes, such as samples damaged during preparation or handling, before continuing.

5. Preparation of specimens for ageing experiments

  1. Beginning an ageing experiment
    1. Calculate the total amount of material needed for the study per environmental condition and based on a specimen extraction plan of every month for 12 months.
      NOTE: For this study, 40 specimens per extraction and a total of 12 extractions were used for planning purposes.
    2. Cut the total amount of material needed for each condition. Cut each strip wide enough to accommodate the required number of specimens plus at least 10 mm.
      NOTE: An extra 5 mm of material will be trimmed from each side of the specimen before performing tensile testing. The extra material is used because the edges of the samples may be damaged due to handling during the ageing protocol.
    3. Place the cut ageing strips in trays to be placed in the environmental chamber as shown in Supplemental Figure 5c. The trays used in this study could each hold approximately 120 strips.
    4. Select exposure conditions for the environmental study based on the expected use and storage environment of the material2.
      NOTE: In this study, nominally 70 °C at 76% relative humidity (RH) was used.
    5. Program an environmental chamber for dry, room temperature conditions (e.g., about 25 °C at 25% RH). Allow the chamber to stabilize at these conditions and, then, place the sample tray on a rack in the chamber, away from the walls and any locations in the chamber that appear to attract condensation.
    6. Program the environmental chamber to the desired temperature as determined in step 5.1.4, leaving the humidity about 25% RH.
    7. Once the chamber has stabilized at the target temperature from step 5.1.4, program the chamber to increase the humidity to the desired level as determined in step 5.1.4.
    8. Check the chambers daily to ensure that water supply and filtration are adequate, and note when out-of-tolerance conditions are observed. Recording deviations and interruptions in a log on the front of each chamber or in a nearby notebook is a good practice.
    9. Repeat steps 5.1.5–5.1.8 for all other specimens of interest.
  2. Extracting aged material strips for analysis
    1. When ready to extract the aged material strips from an environmental chamber for analysis, first program the chamber to decrease the relative humidity to approximately 25% RH.
    2. After the environmental chamber has stabilized at the low-humidity condition, program the temperature to drop to, approximately, room temperature or 25 °C. This step prevents condensation when the chamber door is opened.
    3. Once the environmental chamber has stabilized at the conditions of step 5.1.5, open the chamber, remove the tray containing the aged material strips of interest, take out the desired strips, and place them in a labeled container.
    4. Return the tray to the environmental chamber.
    5. Following the procedure given in steps 5.1.6 and 5.1.7, return the chamber to the conditions of interest, if continuing the ageing study. If not, then it may remain at the nominally ambient state.
    6. Record the extraction on the chamber log, if one is being used.
    7. Cut the aged specimens from the aged material strips, following steps 1.7–1.17.
    8. Test the specimens as described in section 4.

Wyniki

Many iterations of cutting and testing were performed to investigate several different variables. Some variables that were examined include the cutting technique and cutting instrument, the testing rate, the specimen dimension, and the grips. One critical finding was the importance of aligning the specimens with the fiber direction. Data analysis procedures (consistency analysis, Weibull techniques, outlier determination, etc.) are discussed below, as are considerations for ageing.

Dyskusje

Proper determination of the fiber direction is critical. The advantage of the method described in steps 1.4–1.6 of the protocol is that there is complete control over how many fibers are used to start the separation process. However, this does not mean that there is a complete control over the final separated region’s width, as the fibers are not fully parallel and can cross over each other. In the process of separating one batch of fibers, frequently, fibers neighboring those being separated will also be sep...

Ujawnienia

The full description of the procedures used in this paper requires the identification of certain commercial products and their suppliers. The inclusion of such information should in no way be construed as indicating that such products or suppliers are endorsed by NIST or are recommended by NIST or that they are necessarily the best materials, instruments, software or suppliers for the purposes described.

Podziękowania

The authors would like to acknowledge Stuart Leigh Phoenix for his helpful discussions, Mike Riley for his assistance with the mechanical test setup, and Honeywell for donating some of the materials. Funding for Amy Engelbrecht-Wiggans was provided under grant 70NANB17H337. Funding for Ajay Krishnamurthy was provided under grant 70NANB15H272. Funding for Amanda L. Forster was provided from the Department of Defense through interagency agreement R17-643-0013.

Materiały

NameCompanyCatalog NumberComments
Capstan GripsUniversal grip company20kN wrap gripsCapstan grips used in testing
Ceramic knifeSlice10558
Ceramic precision bladeSlice00116
ClampIrwinquick grip mini bar clamp
Confocal Microscope
Cutting MatRotatrim A0 metric self healing cutting mat
Denton Desktop sputter coater sputter coater
FEI Helios 660 Dual Beam FIB/SEMFEI HeliosScanning electron microscope
Motorized rotary cutterChickadee
Rotary CutterFiskars49255A84
Stereo MicroscopeNationalDC4-456H
Straight edgeMcMaster Carr1935A74
Surgical Scalpel BladeSklar Instruments
Surgical Scalpel HandleSwann Morton
Universal Test MachineInstron4482Universal test machine
Utility knifeStanley99E

Odniesienia

  1. Forster, A. L., et al. Hydrolytic stability of polybenzobisoxazole and polyterephthalamide body armor. Polymer Degradation and Stability. 96 (2), 247-254 (2011).
  2. Forster, A. L., et al. Development of Soft Armor Conditioning Protocols for {NIJ--0101.06}: Analytical Results. NISTIR 7627. , (2009).
  3. . . NIJ Standard 0101.06- Ballistic Resistance of Personal Body Armor. , (2008).
  4. Forster, A. L., Chin, J., Peng, J. -. S., Kang, K. -. L., Rice, K., Al-Sheikhly, M. Long term stability of UHMWPE fibers. Conference Proceedings of the Society for Experimental Mechanics Series. 7, (2016).
  5. Pilato, L. A. . Ballistic Resistant Laminate. , (1993).
  6. Park, A. D. . Ballistic Laminate Structure in Sheet Form. , (1999).
  7. Jacobs, M. J. N., Beugels, J. H. M., Blaauw, M. . Process for the manufacture of a ballistic-resistant moulded article. , (2006).
  8. . . ASTM E3110-18 Standard Test Method for Collection of Ballistic Limit Data for Ballistic-resistant Torso Body Armor and Shoot Packs. , (2018).
  9. Russell, B. P., Karthikeyan, K., Deshpande, V. S., Fleck, N. A. The high strain rate response of Ultra High Molecular-weight Polyethylene: From fibre to laminate. International Journal of Impact Engineering. 60, 1-9 (2013).
  10. Czechowski, L., Jankowski, J., Kubiak, T. Experimental tests of a property of composite material assigned for ballistic products. Fibres and Textiles in Eastern Europe. 92 (3), 61-66 (2012).
  11. Levi-Sasson, A., et al. Experimental determination of linear and nonlinear mechanical properties of laminated soft composite material system. Composites Part B: Engineering. 57, 96-104 (2014).
  12. . . ASTM D3039/D3039M-17 Standard Test Method for Tensile Properties of Polymer Matrix Composite Materials. , (2017).
  13. Hazzard, M. K., Hallett, S., Curtis, P. T., Iannucci, L., Trask, R. S. Effect of fibre orientation on the low velocity impact response of thin Dyneema®composite laminates. International Journal of Impact Engineering. 100, 35-45 (2017).
  14. ASTM D5034-09. Standard Test Method for Breaking Strength and Elongation of Textile Fabrics. Annual Book of ASTM Standards. , 1-8 (2017).
  15. ASTM D5035-11. Standard Test Method for Breaking Force and Elongation of Textile Fabrics (Strip Method). Annual Book of ASTM Standards. , 1-8 (2015).
  16. ASTM D6775-13 . Standard Test Method for Breaking Strength and Elongation of Textile Webbing, Tape and Braided Material. Tape and Braided Material.” Annual Book of ASTM Standards. (Reapproved). , 1-8 (2017).
  17. ASTM D3950. Standard Specification for Strapping, Nonmetallic (and Joining Methods). Annual Book of ASTM Standards. , 1-7 (2017).
  18. Weibull, W. A Statistical Distribution Function of Wide applicability. Journal of applied mechanics. 18 (4), 293-297 (1951).
  19. Coleman, B. D. Statistics and time dependence of mechanical breakdown in fibers. Journal of Applied Physics. 29 (6), 968-983 (1958).
  20. Coleman, B. D. Time dependence of mechanical breakdown phenomena. Journal of Applied Physics. 27 (8), 862-866 (1956).
  21. Coleman, B. D. Time Dependence of Mechanical Breakdown in Bundles of Fibers. III. The Power Law Breakdown Rule. Journal of Rheology. 2 (1), 195 (1958).
  22. Coleman, B. D. Application of the theory of absolute reaction rates to the creep failure of polymeric filaments. Journal of Polymer Sciences. 20, 447-455 (1956).
  23. Coleman, B. D. A stochastic process model for mechanical breakdown. Transaction of the Society of Rheology. 1 (1957), 153-168 (1957).
  24. Phoenix, S. L., Beyerlein, I. J. Statistical Strength Theory for Fibrous Composite Materials. Comprehensive Composite Materials. , 559-639 (2000).
  25. Newman, W. I., Phoenix, S. L. Time-dependent fiber bundles with local load sharing. Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics. 63 (2), 20 (2001).
  26. Phoenix, S. L., Newman, W. I. Time-dependent fiber bundles with local load sharing. II. General Weibull fibers. Physical Review E - Statistical, Nonlinear, and Soft Matter Physics. 80 (6), 1-14 (2009).

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