Image Analysis of Kevlar 49 Fabric at High Strain Rate

Transcription

1 Proceedings of the XIth International Congress and Exposition June -5, 8 Orlando, Florida USA 8 Society for Experimental Mechanics Inc. Image Analysis of Kevlar 49 Fabric at High Strain Rate Deju Zhu (), Barzin Mobasher* (), Subramaniam Dharmarajan (3) Graduate Research Assistant, Department of Civil and Environmental Engineering, Arizona State University, Tempe, AZ, 8587, Deju.Zhu@asu.edu Professor, Ph.D., P.E., Department of Civil and Environmental Engineering, Arizona State University, Tempe, AZ, 8587, corresponding author, Barzin@asu.edu 3 Professor, Ph.D., Department of Civil and Environmental Engineering, Arizona State University, Tempe, AZ, 8587, S.Rajan@asu.edu ABSTRACT The investigation of mechanical properties of materials at high strain rates has become increasingly important in recent years. To establish the dynamic behavior of materials the acquisition of full-scale deformation field plays a key role. Traditional strain measuring techniques rely on the use of extensometers and strain gauges. But there are certain limitations of traditional measuring techniques, such as frequency response, rate of loading, and range of strain in which situation non-contacting measuring technique is highly preferred. This paper presents a straightforward measuring technique using image analysis to obtain the deformation of Kevlar 49 fabric over a range of strain rate from to 7 s -. Based on image analysis results the stress-strain curves of Kevlar 49 fabric at different strain rate were constructed and compared with those based on actuator (LVDT) measurement. Good agreement was achieved between image analysis and LVDT measurement. Keywords: Image analysis, high strain rate, Kevlar 49 fabric. Introduction Materials loaded at high strain rates can exhibit mechanical characteristics that are different from those obtained under quasi-static loading. The mechanical properties at high strain rates are of interest for various applications, including structural, military, impact, blast, earthquake and wind gust loading. Aramid and other high strength fibers and fabrics have been studied extensively due to their application in a wide range of products such as bullet-proof vests, cut-resistant gloves, tires and sports equipment. These applications have created a demand for numerical modeling of the fabrics and more in depth information about the behavior of fibrous materials and yarns. Manufacturers of yams usually provide quasi-static tensile strength for the single fibre form of the material. However, this information cannot be scaled up directly for a yarn consisting of many fibres. Also, the strain rate at which this information is obtained is not in the same order of magnitude as the strain rates observed in ballistic applications []. A number of experimental techniques exist to investigate high strain rate material properties: split Hopkinson bar devices, falling weight devices, flywheel facilities, hydraulic machine, etc. [, 3, 4, 5]. During recent years much progress has been made in the field of force measurement. Traditional strain measuring techniques rely on the use of extensometers [6] and strain gages [7]. But there are certain limitations of traditional measuring techniques, such as high testing temperature, rate of loading, and range of strain in which situation noncontacting strain measuring technique is highly preferred. Due to the uneven woven surface and dramatic shape change of Kevlar fabric during test and particular illumination required for high speed test, it is extremely difficult to use laser extensometer which is suitable for specimen with even and reflectable surface, and image correlation technique based on the correlation of gray intensity of images which needs stable illumination and reflection of specimen surface.

2 This paper presents one practical and straight-forward method for image analysis for fabric at high strain rate testing by marking lines on the specimen surface. The image processing toolbox of MATLAB was used to analyze the fabric images captured by a Phantom 7. high speed digital camera at sampling rate of fps (frame per second) during tests. A series of tests of Kevlar 49 fabric were conducted at a wide strain rate range from to 7 s -. The image analysis result was compared with actuator (LVDT) measurement to further verify the validity of image analysis. And the stress-strain curves were constructed based on image analysis and actuator measurement.. Methodology. Specimen Preparation The test specimen is Kevlar 49 fabric. In order to achieve high strain rate, the shortest possible test specimens should be used. One must also consider the size of the grip sets and the operation convenience to determine the possible minimum size of test specimen. Figure and show the real specimens,.8 inch wide, with gauge length of inch and inch respectively. Figure - Constructed test specimens: inch gauge Length, inch gauge Length As the size of original Kevlar 49 fabric is too large to be used directly in the high strain rate test, the fabric has to be cut by using an electrical cutter. Much attention was paid to make sure that there are exactly eight yarns in the section of gauge length. Thin aluminum sheets were glued by using epoxy on both ends of the specimen to reduce the stress concentration affect near the front end of gripping wedges.. Test Setup and Image Acquisition The test specimen was assembled with a steel grip set ensuring that the grip wedges are properly aligned. The grips were tightened from the end screw part using a torque wrench to ensure proper tightening. After placing the test specimen in testing frame, a Phantom v.7 high speed camera was aligned to ensure that good quality video could be obtained. The Phantom high speed camera has GB onboard memory and can record tests at sample rate up to 5, fps with resolution of 56 x 5 pixels. At present the camera is set at, fps (time interval, µs) with exposure of 95 µs and resolution of 56 5 pixels. Proper illumination is extreme important to obtain high quality images. Four high intensity lamps were used for the illumination. The test setup is shown in Figure. Figure - Test setup: schematic, actual

3 .3 Analysis of the Captured Images Five lines were marked on each specimen with inch gauge length along the fill yarn direction with interval of.375 inch, defining four sections as shown in Figure 3. For specimen with inch gauge length two sections with interval of.5 inch are defined by three marked lines as shown in Figure 3. The deformation and strain can be calculated based on the images of specimen at different time steps. Due to the limit of resolution of image only two time steps are chosen which are the time when the specimen starts to deform and the time when it fails. When the specimen has totally failed, the lines are no long available for image analysis. A MATAB program was developed for image analysis which could calculate the strain at each section separated by the marked lines and the total strain of the whole specimen by comparing the first image and last image. Six points were chosen along each marked line in the fill yarn direction to obtain the full-field strain distribution and also calculate the average to reduce measurement error. Assuming total deformation of specimen is linearly proportional to the sum of sections with the ratio of :.5 and :.5 for inch and inch gauge length specimen respectively. The maximum strain is calculated by the total deformation divided by gauge length. Fill yarn Section Section Section 3 Section Section Warp yarn Section 4 Figure 3- Division of sections: inch gauge length specimen, inch gauge length specimen Since six points were chosen along each boundary line of sections, there are six strain rate values for each test based on image analysis. The average of these six strain rate values gives the strain rate for each test. To further investigate the strain rate consistency during test, the strain rate was also calculated based on actuator velocity. The actuator velocity based on LVDT measurement is the slope of displacement versus time curve before the specimen is loaded corresponding to zero time, as shown in Figure 4, which is 66 inch/sec. So the strain rate is 66 s - for inch gage length specimen, named as calculated strain rate. Figure 4 shows the strainstress curve of one typical test. The behavior of the fabric is nonlinear, and the stiffness values are not constant. The fabric has three distinct regions during loading: an initial region of low stiffness resulting from the low stress required to straighten the yarns (or crimp region), a region of high stiffness where strain increases results in large stress increases (or elastic region), and a region of negative stiffness where the stress decreases rapidly with an increase in strain (or post-peak region).

4 Displacement, inch LVDT/Stroke Linear Fitting Equation Y = -66 * X Time, sec True Stress, ksi 3 Elastic Region Crimp Region Post-peak Region...3 True Strain, in/in Figure 4- Typical curves of one test: actuator displacement versus time, true stress versus true strain 3. Results and Discussion 3. Comparison of strain rate between image analysis and LVDT measurement Nominal strain rate is defined as the maximum strain of tested specimen measured by actuator (LVDT) divided by the test duration of each test. Figure 5 and show the correlation between calculated strain rate and averaged strain rate of image analysis and the correlation between nominal strain rate and averaged strain rate of image analysis, respectively. The horizontal error bars represent standard deviation of image analysis. When the strain rate is below 4 s -, calculated strain rate, nominal strain rate and averaged strain rate from image analysis are almost identical. When the strain rate is higher than 4 s -, the calculated strain rate is higher than strain rate from image analysis. The strain rate from image analysis matches nominal strain rate well even there is a relative large standard variation for image analysis. There are two possible reasons: one is that the image at the moment before the final failure is used for image analysis, so a relatively lower strain value is obtained from image analysis compared to LVDT measurement; the other is that the strain rate is calculated from the actuator velocity before the specimen is loaded which is usually higher than the actual actuator velocity during the specimen being loaded because the reaction force of specimen will slow down the actuator. 6 Calculated Strain Rate, s Strain Rate of Image Analysis, s - Nominal Strain Rate, s Strain Rate of Image Analysis, s - Figure 5- Correlation of strain rate between different measurements: calculated strain rate versus averaged strain rate of image analysis, nominal strain rate versus averaged strain rate of image analysis

5 3.3 Full field strain distribution of specimen As the inch and inch gage length specimens are divided into four and two sections by marked lines, respectively, and six locations on each marked line are used for image analysis, there are total twenty-four and twelve strain values available to construct the full-field distribution of strain for inch and inch gage length specimen respectively. Figure 6 and show the full field strain distribution of inch gage length specimen at calculated strain rate of 3 s - and that of inch gage length specimen at calculated strain rate of 66 s -, respectively. One can see the strain distribution is not uniform during loading. Full Field Strain Distribution Full Field Strain Distribution.5. Strain Strain Warp Yarn Direction Fill Yarn Direction.5 Warp Yarn Direction Fill Yarn Direction 6 Figure 6- Full field strain distribution: inch gage length specimen, calculated strain rate = 3 s -, inch gage length specimen, calculated strain rate = 66 s Comparison of stress-strain curves based on image analysis and LVDT measurement The stress-strain curves at different strain rate were constructed based on the image analysis and LVDT measurement. Figure 7 and show two typical sets of stress-strain curves which correspond to the calculated strain rate of and 7 s -, respectively. Overall the stress-strain curves based on image analysis agree well with those based on LVDT measurement because same stress data is used for each set and the stress-strain curve depends on the accuracy of strain measurement. 4 3 Strain Rate = s- LVDT Measurement Image Analysis 4 3 Strain Rate = 7 s- LVDT Measurement Image Analysis True Stress, ksi True Stress, ksi...3 True Strain, in/in True Strain, in/in Figure 7- Comparison of stress-strain curves obtained by LVDT and image analysis: calculated strain rate = s -, calculated strain rate = 7 s -.

6 4. Conclusions An image analysis method was used to obtain the strain rates, strain values and full field strain distribution of Kevlar 49 fabric over a range of strain rate from to 7 s -. The strain rates based on image analysis and actuator (LVDT) measurement were compared with each other. Furthermore the stress-strain curves of Kevlar 49 fabric at different strain rate were constructed based on strain values of image analysis and actuator (LVDT) measurement. The following conclusions can be made: () Image analysis for fabric material at high strain rate testing is feasible with proper test setup and by using image processing toolbox functions of MATLAB. () When the strain rate is below 4 s -, calculated strain rate, nominal strain rate and the average of strain rate from image analysis are almost identical. When the strain rate is higher than 4 s -, the calculated strain rate is higher than the others. The strain rate based on image analysis matches nominal strain rate well in the strain rate range of to 7 s -. (3) Good agreement was obtained for the stress-strain curves constructed based on both measurements at the strain rate range. Acknowledgements This work was supported by the Federal Aviation Administration s Airworthiness Assurance Center of Excellence and with additional support from the Aircraft Catastrophic Failure Prevention Program. Reference [] Farsi Dooraki, B., Nemes, J. A. and Bolduc, M., Study of Parameters Affecting the Strength of Yarns, J. Phys. IV France 34, 83-88, 6. [] Meyers M.A., Dynamic Behavior of Materials, John Wiley& Sons, New York, 994. [3] Nicholas, Tensile Testing of Material at High Rates of Strain, Experimental Mechanics, May, p.77-85, 98. [4] Kenneth G. H., Influence of strain rate on Mechanical Properties of 66.T6 Aluminum under uniaxial and biaxial states of stress, Experimental Mechanics, April p. 4-, 966. [5] Zabotkin K., O Toole B. and Trabia M., Identification of the dynamic properties of materials under moderate strain rates 6 th ASCE Engineering Mechanics Conference, July, 3. [6] Extensometers and Clip Gage Catalog, MTS System Corporation, Minneapolis, MN, 993. [7] Strain Gage Technology, Measurements Group, Raleigh, NC, 993.