Characterization of the tensile behaviour of a co-woven-knitted composite in the continuous and discrete frequency domain

Abstract

Laplace-transform and Z-transform theories have been applied to analyze the tensile stress–strain curves of a co-woven-knitted (CWK) composite under quasi-static (0.001/s) and high strain rates (up to 2586/s) tension. The transform results were extended to characterize the tension failure and dynamic responses of the CWK composite in the frequency domain. Specifically, the Laplace-transform theory was employed to analyze the stress–strain curves of the CWK composite along 0°, 45° and 90° directions when the composite is assumed to be a continuous system, while the Z-transform theory was used for the discrete system for the composite. From the transformed results, it was found that the stress–strain curves of the CWK composite specimen under different strain rates tension have similar stability behaviours for the Laplace- and Z-transform. For the continuous system, few pole plots are distributed on the left side of the imaginary axis, which means the system is unstable. Nevertheless, the pole-plot distribution is stable before the post-critical deformation of the CWK composite. For the discrete system, most of the poles are located inside the unit circle before post-critical deformation, indicating the system is stable. From the stiffness–time history and fracture morphology, the stability of the pole-plot distribution corresponds to the stiffness stability and fracture uniformity. From continuous and discrete system analyses, it is found that the stress–time and strain-time histories of the CWK composite can be regarded as a digital signal system. Digital signal processing (DSP) methods can be extended to the investigation of the mechanical behaviour of composites.

Keywords:

• co-woven-knitted (CWK) composite
• tensile impact behaviours
• Laplace transform
• Z-transform
• continuous system
• discrete system

Acknowledgements

The authors acknowledge the financial supports from the National Science Foundation of China (Grant Numbers 10802022, 10872049 and 11072058) and the Key-grant Project of Chinese Ministry of Education (No. 309014). The financial supports from Foundation for the Author of National Excellent Doctoral Dissertation of PR China (FANEDD, No. 201056) and Shanghai Rising-Star Program (11QH1400100) are also gratefully acknowledged. We also acknowledge the two anonymous referees and editors for useful and constructive suggestions, which have resulted in a significant improvement in the manuscript.