# Study on Quasi-Static Uniaxial Compression Properties and Constitutive Equation of Spherical Cell Porous Aluminum-Polyurethane Composites

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## Abstract

**:**

## 1. Introduction

_{2}O

_{3}composite foams, using the space-holder method, and investigated the mechanical properties and energy absorption behavior of open cell Al foams, containing different volume fractions of Al

_{2}O

_{3}. Du et al. [9] examined the effect of nanoparticles on the micro-structure, compressive performance and energy absorption of Al foams. Furthermore, Sun et al. [10,11] prepared nanocopper coated aluminum foam and studied the mechanical properties of Al/Cu hybrid foam via experimental investigation and numerical modeling. Li et al. [12] reported the mechanical properties of open-cell aluminum foam wrapped with zinc film and highlighted the influence of coating time on the mechanical characteristics. The above-mentioned enhancement methods can be attributed to the addition of alloying elements and hard particles to strengthen the cell wall of aluminum foams. This idea has been utilized, and illustrated by Duarte and Ferreira [13] in detail, in many cases. However, recently, another alternative to increase the mechanical properties of porous aluminum was proposed by the introduction of polymers, owing to its simplify and effectivity. In fact, the concept of combining the advantages of porous aluminums and polymers is receiving renewed attention. Cheng and Han [14] developed a type of aluminum foam-silicate rubber composite and examined the effect of filler on the compressive behavior and energy absorption. Kitazono et al. [15] strengthened closed-cell aluminum foam using polyester resin and highlighted the impact of surface treatment methods on the compressive strength and energy absorption. Vesenjak et al. [16,17] prepared porous materials-silicone rubber composites and investigated the -influences of the base materials, specimen size and strain rate on the compressive performances and energy absorption capacity of composites. Kishimoto et al. [18] analyzed the mechanical properties of closed-cell aluminum foam-polyurethane and closed-cell aluminum foam-epoxy composites by measuring deformation distributions, adopting the digital image correlation method. Based on their studies, Yuan et al. [19] produced closed-cell aluminum foam epoxy resin composites and discussed the effect of the composite form, the relative density and the content of epoxy resin on the mechanical characteristics and energy absorption. Moreover, they presented a mathematical model to describe the plateau stress and energy absorption capacity. Furthermore, Liu et al. [20] validated the effectiveness of polyurethane (PU) for increasing the damping of open-cell aluminum foam by cyclic compression tests. Nevertheless, the aforementioned studies concerning porous aluminum-polymer composites are limited to non-spherical cell porous aluminum. PU is one of the most commonly utilized polymers in the energy absorption systems; moreover, its superior damping capacity and easy filling property have been proved [20]. Consequently, PU is adopted as the filling polymer here to improve the mechanical properties of the SCPA.

## 2. Experimental Procedure

#### 2.1. Specimen Preparations

^{3}, the tensile strength is approximately 4 MPa, and the elongation at the break is 655%. The SCPA should be wrapped in PU so as to reduce the volume shrinkage of PU. The SCPA-PU composites were prepared employing the procedure shown in Figure 1. A uniform pressure of around 0.5 MPa was applied to press the PU elastomer into the SCPA. Finally, the specimens of the SCPA-PU composites were produced after they were heated at 100 °C for ten hours. The open-cell spherical cell could be filled with PU due to the excellent fluidity and longer curing time of PU. Three kinds of specimens, which are named SCPA, PU and SCPA-PU composites, are illustrated in Figure 1c.

#### 2.2. Compressive Test

## 3. Results and Discussion

#### 3.1. Compressive Stress-Strain Behavior

#### 3.2. Energy Absorption Characteristics

#### 3.3. Uniaxial Compression Constitutive Equation of SCPA-PU Composites

#### 3.3.1. Existing Phenomenological Models

#### Rusch Model

#### Liu and Subhash Model

#### Avalle Model

#### 3.3.2. Evaluation of Model Performance

## 4. Conclusions

- The compressive stress-strain curves of spherical cell porous aluminum-polyurethane composites (SCPA-PU composites) consist of three stages: Linear elastic part, plateau region and densification segment. Furthermore, PU is beneficial to the increase of the plateau stress and elongation of the densification strain.
- The energy absorption capacity of SCPA-PU composites is superior to that of the SCPA. The densification strain energy of the SCPA-PU composites, with the relative density values of 0.263, 0.298, 0.326, and 0.374, is 28.59%, 33.65%, 31.59%, and 51.55% higher than those of the SCPA, with the same relative density value, respectively. Besides, the weak dependence of the densification strain of the SCPA-PU composites on the relative density is seen, while the plateau stress and the densification strain energy increase as the relative density increases. Furthermore, the ideal energy absorption efficiency (I)-strain curves of SCPA-PU composites and SCPA consist of three parts: Fast ascending branch, plateau stage, and descending region. The plateau I value of SCPA-PU composites is close to that of SCPA, while it has a wider plateau strain range. It is also found that the plateau I value of SCPA-PU composites is insensitive to the relative density of the SCPA.
- Based on the calculated root mean square error results of SCPA-PU composites with different relative density values, the best phenomenological model to characterize the constitutive equation of SCPA-PU composites is the Avalle model. This conclusion provides a foundation for the following research regarding the constitutive model of SCPA-PU composites considering strain rate and temperate factors.

## Author Contributions

## Acknowledgments

## Conflicts of Interest

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**Figure 1.**Fabrication procedure of the spherical cell porous aluminum-polyurethane composites (SCPA-PU composites): (

**a**) The specimen of the spherical cell porous aluminum (SCPA); (

**b**) fabrication method of the SCPA-PU composites; and (

**c**) image of specimens from left to right: SCPA, polyurethane (PU), and SCPA-PU composites.

**Figure 6.**Comparison of SCPA and SCPA-PU composites specimens, with different relative density values for (

**a**) the densification strain; (

**b**) plateau stress; and (

**c**) densification strain energy.

**Figure 7.**$I-\epsilon $ curves of the SCPA and the SCPA-PU composites with different relative density values.

**Figure 8.**(

**a**) Comparison between the curve predicted by the Rusch model and the experimental curve (${\rho}^{\ast}/{\rho}^{s}$ = 0.326); and (

**b**) model prediction error.

**Figure 9.**(

**a**) Comparison between the curve predicted by the Liu and Subhash model and the experimental curve (${\rho}^{\ast}/{\rho}^{s}$ = 0.326); and (

**b**) model prediction error.

**Figure 10.**(

**a**) Comparison between the curve predicted by the Avalle model and the experimental curve (${\rho}^{\ast}/{\rho}^{s}$ = 0.326); and (

**b**) model prediction error.

**Figure 11.**Comparison of the root mean square error of each model for (

**a**) 0.263; (

**b**) 0.298; (

**c**) 0.326; and (

**d**) 0.374 relative density values.

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**MDPI and ACS Style**

Bao, H.; Li, A.
Study on Quasi-Static Uniaxial Compression Properties and Constitutive Equation of Spherical Cell Porous Aluminum-Polyurethane Composites. *Materials* **2018**, *11*, 1261.
https://doi.org/10.3390/ma11071261

**AMA Style**

Bao H, Li A.
Study on Quasi-Static Uniaxial Compression Properties and Constitutive Equation of Spherical Cell Porous Aluminum-Polyurethane Composites. *Materials*. 2018; 11(7):1261.
https://doi.org/10.3390/ma11071261

**Chicago/Turabian Style**

Bao, Haiying, and Aiqun Li.
2018. "Study on Quasi-Static Uniaxial Compression Properties and Constitutive Equation of Spherical Cell Porous Aluminum-Polyurethane Composites" *Materials* 11, no. 7: 1261.
https://doi.org/10.3390/ma11071261