Mechanical behaviors of auxetic polyurethane foam at quasi-static, intermediate and high strain rates

Highlights

• A long and regular Kolsky compression bars were used to study the stress-strain behaviors of auxetic polyurethane foam at intermediate and high strain rates, respectively.

• The Poisson's ratios of the auxetic polyurethane foam were characterized using a precision LED optical micrometer or an ultra-high-speed camera at all strain rates tested.

• At quasi-static and intermediate strain rates, the stress-strain curves of the material were nonlinear monotonic, while nonlinear stiff-plateau-densification stress-strain behaviors were observed at high strain rates.

• All the specimens were auxetic at all the strain rates tested in this study except that some specimens exhibited small positive Poisson's ratio at small strains under high strain-rate loadings.

• The Poisson's ratio of the material depends on both the strain and strain rate. Generally, it increased from a negative initial value as the material was compressed and the initial value of the Poisson's ratio increased as the strain rate increased.

Abstract

We experimentally determined the uniaxial compressive stress-strain responses of an auxetic polyurethane (PU) foam at quasi-static (0.01/s), intermediate (1/s, 10/s and 745/s) and high (1430/s, 1870/s and 2290/s) strain rates. A hydraulically driven materials testing system (MTS) was used to perform the experiments at the strain rate of 0.1/s, 1/s and 10/s, while higher intermediate (745/s) and high strain-rate compressive loadings were introduced using long and regular Kolsky bars, respectively. The Poisson effect of the auxetic PU foam was also investigated during the experiments using a precision LED optical micrometer system (OMS) (0.01/s–10/s) or an ultra-high speed camera (745/s–2290/s). Our results show that the compressive stress-strain curves of the auxetic PU foam are non-linear and strain-rate sensitive. In all the experiments, the Poisson's ratio, with an initial negative value at small strains, progressively increased toward 0 as the specimen was further compressed. The strain-rate effect on the material's Poisson's ratio is also evident in our study, as the specimens subjected to high strain-rate loadings exhibited smaller negative Poisson's ratios (NPR) in absolute sense at small strains in comparing with those at quasi-static and intermediate strain rates.

Introduction

Auxetic polyurethane (PU) foam is one class of material that possesses an unusual mechanical property: it exhibits a negative Poisson's ratio (NPR) behavior under mechanical loadings. Specifically, the auxetic PU foam contracts in the transverse direction when being compressed axially, while expands transversely when stretched in the axial direction [1], [2], [3], [4], [5]. Although, as early as nineteen century, researchers had already found such auxetic material has certain superiorities, such as preeminent bending resistance, indentation resistance, crashworthiness, outstanding cushion and sound absorption capabilities compared with traditional materials [6], they attracted limited attention because of their rarity in nature and difficulty in massive fabrication. However, since 1987 when Lakes first reported that artificial auxetic PU foam could be simply developed through a tri-axial compression process at elevated temperature [1], the enhanced properties of auxetic PU foam have prompted their promise in many applications, such as those for personal protective equipment [7], [8], [9], [10], [11], [12], aerospace engineering [13], [14], functional construction element [8], [15], [16], [17], [18], damping and wave absorption [7], [19], [20], [21], [22] together with biomedicine [23], [24], [25].

In all those applications, the auxetic PU foam is subjected to loadings over a wide spectrum of rates, from quasi-static to impact and blast. For example, auxetic PU foam is commonly used to build structures for military or civilian personal protective equipment for energy absorption during impact and blast events. Part of those structures and materials located at the center or in the vicinity of the impact site, including auxetic PU foam, are subject to large deformations within a short period of time and their mechanical behaviors under such high strain-rate loading have been of great interest in structural impact applications and the energy-absorbing systems for safety calculations and hazard assessments [26]. Around the high-rate deformation region, materials are deformed under loading at intermediate strain rate. For materials even further away from the impact site, it is likely that they are subjected to minimum inertial effects and hence are deformed at quasi-static rate. Therefore, materials, such as auxetic PU foam, can be deformed over a wide range of strain rates during impact and blast events. Quantitative understanding of the mechanical behaviors of auxetic PU foam at quasi-static, intermediate and high strain rates is essential for designs of more efficient equipment and structures for impact energy absorption.

Many studies on the mechanical behaviors of auxetic PU foam have shown succinctly that both the strength and Poisson's ratio of the material are strain dependent [8], [9], [27], [28], [29], [30], [31]. However, the reality is that most of these works were performed at low strain rates within the order of 10/s, where it is comparatively straight forward to load the material and to collect data, although the auxetic PU foam is generally used in the scenarios that are associated with much higher strain rates: intermediate and high strain rates. At quasi-static strain rates, the stress-strain behaviors of auxetic PU foam were reported to be non-linear and monotonic [8], [9], [27], [28]. The effect of strain rate (up to ∼35/s) was also characterized and a highly strain-rate sensitivity of the material's mechanical properties was reported in the literature [29], [30], [31]. Comparisons between the mechanical behaviors of auxetic and corresponding conventional PU foam were reported by many researchers [8], [9], [27], [28]. It was suggested that auxetic PU foam had smaller Young's modulus and behaved more resilient after being transformed from the conventional foam [27]. Under cyclic compressive loadings, the energy dissipated by the auxetic PU foam had an increase up to 16 times compared with the conventional ones [28]. Experiments were also conducted to reveal the relation between the mechanical behaviors and manufacturing parameters of auxetic PU foam [8]. The most significant manufacturing factor on the mechanical properties, such as Poisson's ratio, stiffness and dissipation of energy was found to be the overall compression ratio applied during the re-entrant process [8]. With the help of in situ X-ray microtomography, the mechanisms for the auxetic behavior under static tensile loading were revealed to be not only the straightening of bent ribs and rotation of junctions but also rotation of ribs at the junctions and stretching and twisting of ribs [9]. Measurements of Poisson's ratio of auxetic PU foam have been carried out in experiments at strain rate up to 12/s [28], [29]. A negative value of Poisson's ratio was initially observed at lower axial strains and it progressively increased to a positive value as the specimen was further deformed [28], [29]. At higher strain rate of 15/s and 38/s, auxetic PU foam exhibited similar superior properties regarding damping and acoustic when comparing with the original conventional foam [30], [31]. However, few data of the mechanical behaviors and Poisson effect of auxetic PU foam at intermediate and high strain rates that are associated with dynamic and impact events could be found in the literature.

Consequently, we experimentally characterized the stress-strain behaviors and Poisson's ratio-strain responses of the auxetic PU foam over a wide range of strain rates (10⁻²/s– ∼ 2.3 × 10³/s). A hydraulically driven materials testing system (MTS) combined with a precision micrometer was used in this work for experiments at quasi-static and intermediate (1/s, 10/s) strain rates. A long and a regular Kolsky bar apparatus were used to introduce the constant higher intermediate (745/s) and high strain-rate loadings, respectively. A high-speed video camera with a frame rate up to 10⁷ frames per second (fps) and a frame size of 400 pixels in width, 250 pixels in height was used to record the specimen's radial deformation during the experiment on Kolsky bars.