Three-dimensional textile structural composites under high strain rate compression: Z-transform and discrete frequency-domain analysis

Abstract

Z-transform theory was applied to several three-dimensional (3D) textile structural composites, including an angle-interlock woven composite, a multilayer multi-axial warp knitted composite and a 4-step braided composite, to characterize their system dynamic behaviour in the frequency domain. More specifically, the analysis focused on the relationship between the compressive load and the system response under static (strain rate 0.001 s À1 ) and impulsive (strain rate up to 2700 s À1 ) strain along both the in-plane and out-of-plane directions, respectively. The high strain rate compressions were tested using a split Hopkinson pressure bar apparatus, and the input and output (the stress-strain curve) of the test specimen was obtained by recording the signals using a computer for further analysis. Z-transform was then used to analyze the dynamic response and stability of the composites of different preform structures and at various loading conditions. This is the first such attempt to study the compression behaviour of 3D textile structural composites at various strain rates in the frequency domain in order to reveal their mechanical behaviour and features of the materials from a new perspective.

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

“…It is extremely difficult to describe the responses of the two systems under different strain rates via a single equation. According to method of Sun et al [11], for a given strain rate, the system can be simplified as a secondorder equation as follows:…”

“…Tensile tests under high strain rates are also known as tensile impact tests. Schematic illustrations and the principle of the SHTB apparatus are discussed in [9][10][11][12]. With the SHTB apparatus, a momentum trapping device, a 14.5-mm inner diameter gas gun, a maraging steel incident bar of 14.5 mm in diameter and 1140 mm in length, and a 14.5-mm diameter/ 640-mm length transmission bar were employed.…”

“…Z-transform plays an important role in discrete time signals analysis for a linear time-invariant (LTI) system, just like the Laplace transform for the continuous time signals [11,20,21].…”

“…They found that the energy absorption power of the 3-D braided composite was mostly concentrated in the high frequency region at high strain rates and the power was distributed in a very narrow frequency region at quasi-static conditions. Sun et al [11] compared the frequency responses of 3-D woven, knitted and braided composites with the Z-transform theory. Sun et al [13] also studied the compressive behaviour of a 3-D angle-interlock woven composite under high strain rates with FFT and wavelet packet analysis.…”

“…The heterogeneous microstructures of the composites and the difference in stress wave speed in fibres and matrices further complicate any attempt at analysis. All of these render it difficult, if not impossible, to establish a continuum constitutive equation for the dynamic response of composite materials [11]. Gu et al [12] used fast Fourier transform (FFT) to discuss the energy absorption features of a four-step 3-D braided rectangular composite under various strain rates compression.…”