Construction of 3-D realistic representative volume element failure prediction model of high density rigid polyurethane foam treated under complex thermal-vibration conditions

Highlights

• Mechanical failure model of RPUF is constructed by experiments and simulation.

• Realistic RVE model of RPUF is established by tessellations method.

• Failure constitutive relation of RPUF treated under complex conditions is derived.

• Simulation work is extended through assigning constitutive relation to RVE of RPUF.

Abstract

The mechanical failure behaviors prediction model of rigid polyurethane foam (RPUF) treated under complex thermal-vibration conditions was constructed by experiment of tensile properties and numerical simulation for the further analysis of the failure progress and mechanism of RPUF. On the basis of scanning electron microscope (SEM) observation, a realistic representative volume element (RVE) of RPUF was firstly established by means of Voronoi-spherical tessellations. Tensile properties of RPUF treated under different thermal-vibration conditions were measured subsequently. Results of the tensile properties characterization of RPUF suggested that the thermal and vibration treatment on RPUF reduced its tensile strength and fracture elongation decrease due to the chemical degradation of polyurethane (PU) matrix and physical breaking of the foam structure. The tensile constitutive relationship derived from the tensile experiments was assigned to the realistic RVE, and the thermal-vibration failure prediction model of RPUF was further constructed in the ABAQUS software. The numerical simulation results revealed that the stress concentrations appeared and extended along with the weakness regions of RPUF structure under the external load. The stress-strain curves of thermal-vibration treated RPUF obtained from the prediction model were in well agreement with the experimental results, and the average computation error was less than 3%. It indicated that the prediction model can accurately describe the failure progress of thermal-vibration treated RPUF. This work provides ideas for the design of the foam materials with high thermal-vibration aging resistance by numerical simulation in the future.

Introduction

Rigid polyurethane foam (RPUF) with closed-cell structure is widely used in the fields of engineering application such as mechanical supporting structures and thermal insulation materials due to its light weight, high specific strength, high specific modulus and excellent adiabatic properties [1], [2], [3], [4]. However, as a polymer material, RPUF is highly susceptible to the synergistic effect of various external failure factors such as humidity, heat and alternating load during its service life as protective component [5], [6], [7], [8]. As a result, the mechanical properties of RPUF will degrade in different extent [9], [10], [11], [12]. Therefore, it is very necessary to construct the mechanical failure prediction model in order to predict the failure behavior of RPUF under engineering application conditions, thereby reducing and avoiding the damages of protected components caused by the failure of RPUF.

In the past decades, it has been proved to be an effective method to study the properties of foam materials by modeling [13], [14], [15], [16]. Linul and his/her coworkers [17] investigated the change trend of compressive properties of RPUF with the variation of its density by constructing an macroscopic finite element model of the entire foam. They found that the results of numerical simulation were in well agreement with the experiments. Li et al. [18] studied the effects of load direction and strain rate on the mechanical properties of low density RPUF by modified Hopkinson compression test and finite element modeling. The results indicated that the force equilibrium in the foam specimens examined and validated by finite element modeling were in consistent with the experiments. Kim et al. [19] calibrated the hyperelastic and hyperfoam constitutive models of RPUF by the experiments. At the same time, the finite element analysis confirmed that the two models were moderately useful for the practical simulation of the compressive behavior of RPUF. Lee CS and Lee JM [20] also successfully developed a unified anisotropic elasto-viscoplastic-damage model to describe the material nonlinear behavior and predict the damage/crack growth of polyurethane foam. Generally, most of the modeling works abovementioned mainly used the simplified macroscopic geometric models of foam materials to obtain the overall mechanical responses.

In order to further realize the relation between the internal microstructures of foam materials and their properties, several researchers also focused on the microscope modeling of foam materials [21], [22], [23], [24]. Babaee et al. [25] presented a three dimension (3D) model with face-centered cubic structures called rhombic dodecahedrons to predict the mechanical properties and responses of foam materials. Through the construction of finite element model, they found that the monodisperse cellular structure was orthotropic and almost near-incompressible in all load directions. Duan and his/her coworkers [26] carried out the specific surface area of metal foams by a pentagonal dodecahedron model. They found that the specific surface area of metal foams was correlated with the cell size and the width of cell wall. Besides, in our previous studies, a spherical cellular structure model was constructed to analyze the thermal and vibration failure of tensile properties of RPUF based on the Kerner-Rusch relation and tensile properties measurements [27,28]. The final computation error of this model was less than 5% in average compared with the experimental data. In comparison to the macroscopic modeling, although these modeling works have analyzed the microstructures of foam materials to some extent, some idealized hypothesis (such as the regular arrangement of cells) made the simulation results still exist a few discrepancies from the experimental results. For the further realistic simulation of the microstructures of foam materials, in recent, the random tessellations method has been expanded to improve the accuracy of the simulation method. M. Marvi-Mashhadi et al. [29,30] used the microstructure parameters of anisotropy RPUF to build a representative volume element (RVE) by means of Laguerre tessellations, and the influence of structural anisotropy on the compression mechanical behavior of RPUF was obtained by finite element analysis of these RVE. They found that the anisotropy in elastic modulus and plateau stress increased rapidly with the anisotropy in cell shape. Chen et al. [31] investigated the effects of the variations of cell size and cell wall thickness on the compressive and shear strengths of closed-cell foams by tessellation models. It was found that the compressive and shear strengths decreased as the cell size and cell wall thickness increased. Liu et al. [32] designed and fabricated an open-cell functionally graded porous material which satisfied multifold functional constraints by 3D Voronoi tessellations method. They formulated a mapping model from the elasticity distribution to the density field and provided a new route of tailoring the novel foam materials. Ma and his/her coworkers [33] also used Voronoi method to construct the micro-/nano-polymeric foam models for multi-dimensional analysis of RPUF made from supercritical CO₂ (scCO₂). They suggested that the 3D foam structure for nano-/micro-cellular foams made from scCO₂ foaming could be easily constructed on the basis of 2D cross-section foam morphology. However, these tessellation methods mentioned above were mainly limited to the low density foam materials with thin-walled structure. The constructions of microscope models which are applicable to the high density closed-cell foam materials were rarely reported.

In general, the previous modeling studies mainly paid attention to the construction of mechanical properties model of foam materials. The modeling studies on the analysis of the microstructure of foam materials have also been expanded to some extent. However, the construction of prediction model describing the mechanical failure behavior of RPUF treated under thermal, vibration or radiation conditions has get less attention in both macroscopic and microscopic view. Our previous modeling study has also only preliminarily established the failure model with regular cell arrangement of RPUF treated under single heat or vibration treatment condition. It is of great significance to the investigation of failure degree prediction of RPUF with high density treated under complex treatment conditions in the realistic engineering service cases by tessellations method in microscopic view.

The experimental studies on the mechanical failure and failure mechanism of RPUF have been expanded relatively adequately in previous [34], [35], [36], [37]. Yang et al. [38] investigated the thermal degradation mechanism of RPUF. Results showed that there two main degradation processes were contained. The first step was the cleavage of the urethane linkage with the release of isocyanate, and the second step was the dominant dissociation of macromolecules with the release of volatiles such as CO₂ and etc. Yarahmadi et al. [39] studied the thermal degradation characteristics of RPUF in both air and nitrogen atmospheres. They found that in both two aging atmosphere the flexural strength of RPUF decreased after treatments. In comparison to the nitrogen atmosphere, the air atmosphere exhibited a significant accelerated aging effect due to the thermo-oxidative type of degradation in RPUF. Liu et al. [40] researched the aging mechanism of RPUF treated at different hygrothermal conditions. They suggested that the compressive modulus decreased quickly with the increase of aging time due to the hydrolysis of ester group in the RPUF under the high temperature. Besides, Demirel and Tuna [41] studied the effect of density of RPUF on its cyclic fatigue performance through comparing the indentation force deflection (IFD) of RPUF before and after subjected 8000 cycles fatigue load. The results indicated that the IFD loss of RPUF can be obviously reduced with the increase of the density, representing an improvement on foam firmness.

In summary, the previous experimental studies mainly focused on the effect of thermal treatment on the variation of chemical structure of RPUF, and a few investigations on the effect of alternating load on the performance of RPUF was limited in the field of fatigue properties of RPUF. Especially, the failure behavior of RPUF treated under vibration load has not been further extended. Combined with the current situation of simulation works, it will have important significance on the extracting of the failure constitutive relation of RPUF treated under complex thermal-vibration conditions. Through the investigation of its mechanical properties, the constitutive relation is consistent with the reality engineering application conditions, so that the construction of finally failure prediction model of RPUF can be carried out accordingly.

In this paper, the RVE of RPUF with relatively high density was constructed by means of Voronoi-spherical tessellations method according to the cell diameter distribution and cell wall thickness of RPUF obtained by scanning electron microscope (SEM) observation. The RPUF was treated under high-temperature and vibration, respectively, and the mechanical constitution relation of the failure RPUF was derived and integrated by means of the corresponding tensile properties characterization. The failure prediction model of RPUF treated under complex thermal-vibration conditions was built on the basis of the finite element analysis of RVE according to the constitutive relation.