A hyper-viscoelastic constitutive model for polyurea

doi:10.1016/j.matlet.2009.01.055

Materials Letters

Volume 63, Issue 11, 30 April 2009, Pages 877-880

https://doi.org/10.1016/j.matlet.2009.01.055 Get rights and content

Abstract

This letter presents a new constitutive model for polyurea by superposing the hyperelastic and viscoelastic behaviors of polyurea. The Ogden model is used for the hyperelastic part and its parameters are determined from curve fitting of quasi-static test data. A nonlinear viscoelastic model is employed for describing the viscoelastic behavior and its relaxation time is obtained based on the test data of shear relaxation modulus. A special form of Zapas kernel for the damping function is found to be very effective to capture the viscoelastic behavior of polyurea subjected to wide ranges of strain rate. Both the versatility and accuracy of the model are examined via virtual testing.

Introduction

Polyurea is a product from the chemical reaction between an isocyanate and an amine. It has been widely used in the coating industry, because of its extensive benefits over existing epoxy adhesives and rubber linings in terms of impact, abrasion and corrosion resistance. With the development of polyurea spray coatings technology, specifically formulated polyurea can be directly and efficiently sprayed on the surface of structural components to enhance the mechanical strength and durability of civil and military structures.

Previous experimental studies [1] have revealed that polyurea exhibits elastic and nearly incompressible behavior to volumetric deformations and its stress–strain behavior depends on strain rate, temperature and pressure [2], [3]. Different from the rubbery behavior under low strain rates, polyurea displays a distinct leathery behavior [4] at high strain rates. Polyurea can be used in a wide range of temperature (from − 50 °C to 150 °C) and has shown a high heat resistance. However, its shear modulus decreases significantly with increasing temperature. The glass transition temperature T_g for polyurea is roughly − 50 °C [1]. Given the stiffening behavior of polyurea material with both increasing strain and strain rate, it has been used either as a protection coating on a metallic structure or an inserted layer between the outer facesheet and the foam core in a blast-tolerant sandwich structure.

Both material certification and performance evaluation of polyurea coated structural components under hostile environment by tests will be prohibitively expensive and time consuming. Development of a high fidelity constitutive model of polyurea is imperative to perform an optimal design of its coated components subjected to a combined dynamic and thermal loading. Currently, there are only two models have been developed specifically for polyurea although some similar models have been proposed for other hyperelastic or viscoelastic materials [5], [6]. One is an experimentally-based linear viscoelastic constitutive model proposed by Amirkhizi et al. [2]. It incorporates the classical Williams–Landel–Ferry (WLF) time-temperature transformation and pressure sensitivity, in addition to a thermodynamic energy dissipation mechanism. The model can reproduce experimental results for confined polyurea tests but has limited capability in simulating the unconfined test data. The other is a more complex model proposed by Elsayed [7] which consists of an elastoplastic network acting in parallel with several viscoelastic networks. Quasi-incompressible Ogden-type potentials were used and the number of model parameters is a function of the number of active Ogden terms and relaxation mechanisms, thus a procedure based on genetic algorithms was employed to calibrate model parameters based on existing experimental data. Although this model is relatively successful in reproducing experimental data, it seems to be too complicated for engineering practice.

A constitutive model for polyurea should cover a wide range of strain rates from static to high speed impact and capture both hyperelastic and viscoelastic material behavior. A rational approach based on a combination of hyperelasticity theory and viscoelasticity theory is needed in deriving the constitutive model. Also, for its practical applications, the model should be comparatively simple to be implemented in a general purpose finite element code while its parameters can be determined experimentally from the standard tests. To meet the model requirements, this letter presents a new hyper-viscoelastic constitutive model for polyurea.

Section snippets

Hyperelastic model for low strain rates

Given the compliant rubber-like behavior of polyurea from quasi-static tests, a hyperelastic constitutive model is selected to characterize its rubbery stress–strain behavior at low strain rates. The constitutive law for an isotropic hyperelastic material is decomposed into volumetric and deviatoric parts. The deviatoric part is defined by an equation relating the strain energy density of the material to the three invariants of the strain tensor. By assuming the incompressible behavior of the

Nonlinear viscoelastic model for high strain rates

Having established the rate-independent hyperelastic model for polyurea under static loading conditions, we are now focusing on the rate-dependent characteristic of polyurea. A viscoelastic constitutive law is a good choice for capturing its rate-dependent behavior. For viscoelastic materials, the stress state depends on the strain and strain rate histories. Here, we assume the material is isotropic and subjected to small strains under an isothermal condition. But different from a linear

Results and discussions

In this study, the data for the unconfined uniaxial compression test at strain rate of 2250 s^− 1 from Sarva et al. [4] is used to determine the parameters A₁ and A₂. The parameters determined from the fitting are A₁ = 0.1435 and A₂ = 0.1098. Fig. 3 displays the comparison between the test data and our prediction from the present model. The symbols triangle, square, pentagon, hexagon and circle represent, respectively, the test data under the strain rate 0.0016/s, 80/s, 800/s, 2250/s and 6500/s. The

Conclusions

This letter presents a new constitutive model for polyurea by including both its hyperelastic and viscoelastic behavior. The Ogden model is used for the hyperelastic part and its parameters are curve fitted using the quasi-static test data. A nonlinear viscoelastic model is proposed to characterize its viscoelastic part and the relaxation time is determined based on the test data of the shear relaxation modulus. A special form of Zapas kernel for the damping function is found to be very

Acknowledgement

This work is supported by the Office of Naval Research under Contract N00014-08-C-0614 with Dr. Roshdy Barsoum as the Program Manager.

References (18)

J. Yi et al.
Polymer
(2006)
S.S. Sarva et al.
Polymer
(2007)
H.J. Qi et al.
Mech Mater
(2005)
S. Reese et al.
Int J Solids Struct
(1998)
L.M. Yang et al.
Int J Impact Eng
(2000)
W.G. Knauss, Final report to the Office of Naval Research. (ONR Grant No. N00014-03-1-0539), CIT, Pasadena,...
A.V. Amirkhizi et al.
Philos Mag
(2006)
T.M. Elsayed, PhD dissertation, California Institute of Technology...
E. Arruda et al.
J Mech Phys Solids
(1992)

There are more references available in the full text version of this article.

Cited by (108)

Redesign an aircraft windshield to improve its mechanical resistance against simultaneous bird impacts
2024, International Journal of Impact Engineering
The bird impact on aircraft components is one of the most serious accidents which can happen in the aviation industry. Among the various parts of an aircraft, the bird impact on the windshield is more important due to the possibility of causing injury to the pilot. Standard windshields are designed to withstand a bird strike, however, in a group flight of birds, several birds can strike the windshield at the same time. The results of practical tests and simulations show that the current windshields are seriously damaged in the simultaneous collision of several birds and the possibility of birds penetrating the cabin is very high. In this research the mechanical properties of standard windshield constituent materials are obtained. Initially practical tests are carried out and simulation results are verified for single bird strike. Using these results, the simultaneous impact of three birds on a windshield is simulated. It was shown that the resistance of the standard windshield against simultaneous collisions is insufficient. So the thicknesses of the windshield layers are determined in such a way that the new windshield is resistant and bird penetration into the cabin does not happen.
Elucidating the impact of microstructure on mechanical properties of phase-segregated polyurea: Finite element modeling of molecular dynamics derived microstructures
2024, Mechanics of Materials
Phase-segregated polyureas (PU) have received considerable interest due to their use as tough, impact-resistant coatings. Polyureas are favored for these applications due to their mechanical strain rate sensitivity and energy dissipation. Predicting and tailoring the mechanical response of PU remains challenging due to the complex interaction between its elastomeric and glassy phases. To elucidate the role of PU microstructure on its mechanical properties, we developed a finite element modeling framework in which each phase is represented by a volume fraction within a representative volume element (RVE). Critically, we used separate constitutive models to describe the elastomeric and glassy phases. We developed a plasticity-driven breakdown process in which we model the glassy phase disaggregating into a new phase. The overall contribution of each phase at a material point is determined by their respective volume fractions within the RVE. We applied our modeling methods to two compositions of PU with differing elastomeric segment lengths derived from oligoether diamines, Versalink P650 and P1000. Our simulations show that a combination of microstructural differences and elastomeric phase properties accounts for the difference in mechanical response between P650 and P1000. We show our model’s ability to predict PU behavior in various loading conditions, including low-rate cyclic loading and monotonic loading over a wide range of strain rates. Our model produces microstructure transformations that mirror those indicated by small-angle X-ray scattering (SAXS) experiments. Fourier transform analysis of our RVEs reveals glassy phase fibrillation due to deformation, a finding consistent with SAXS experiments.
Numerical investigation on polyurea coated aluminum plate subjected to low velocity impact
2023, International Journal of Impact Engineering
A novel three-dimensional model was established for analyzing the impact response and fracture of polyurea-coated aluminum plates using the LS-DYNA finite element code. Hyperelastic and viscoelastic constitutive models were established to characterize the impact response of polyurea, and a modified Johnson-Cook model was used to characterize the impact response of aluminum. The constitutive models of polyurea and aluminum were characterized and validated by comparing their results with those of tensile experiments under different strain rates. The simulation results of polyurea-coated aluminum plates were analyzed using the impact responses for different coating methods. Moreover, the effects of the polyurea stiffness, aluminum strength, bonding strength, and polyurea thickness on the impact resistance of polyurea-coated aluminum plates are discussed in detail.
The impact peak force, energy absorption, and deformation results of the simulation of polyurea-coated aluminum plates for different coating methods were within 5% of the experimental results. Accordingly, the established model can accurately predict the fracture modes, thus demonstrating that the proposed methodology is more suitable for polyurea-coated aluminum plates under low-velocity impact than the existing methods.
Impact resistance analysis and multi-objective optimization of polyurea-coated auxetic honeycomb sandwich panels
2023, Materials Today Communications
To investigate the protective capacity and mechanism of polyurea-coated auxetic honeycomb sandwich structures under impact loading. The mechanical properties of a sandwich panel under the action of a cylindrical punch is numerically simulated by LS-DYNA. Firstly, the impact of different coating positions on the protective properties of sandwich panels is analyzed and concluded which coating method is most effective. Then, the mechanism of the impact resistance of sandwich panels strengthened by the thickness, grading and orientation of the auxetic honeycomb cores is discussed by outline volume analysis. Finally, a multi-objective optimization of the sandwich panel's internal concave hexagonal structural parameters with the best impact resistance is carried out. It is shown that the coating of polyurea elastomers can effectively increase the impact protection performance of sandwich panels. The best impact resistance is achieved by the back side coated sandwich panel (type B). Increasing the wall thickness of auxetic honeycomb and the thickness of the upper graded honeycomb core can effectively increase the impact resistance of the type B sandwich panel. Optimized type B sandwich panel has a 6.2% reduction in maximum deflection (D) compared to the unoptimized version. The findings of this research provide a reference for the study and design of polyurea-coated sandwich panels.
Approach for the simulation of the load-deformation behaviour of hyperelastic bonded joints using strain and strain rate dependent tangent moduli
2023, International Journal of Adhesion and Adhesives
In structural glass, Structural Sealant Glazing (SSG) systems are often used to realise facades with maximum transparency. The used silicone adhesives are currently designed in accordance to the European Technical Approval Guideline 002 (ETAG 002) by a simplified two-dimensional stress calculation concept. For a more precise calculation of the adhesive stresses and deformations, finite element analyses are used. The quality of the results, however, strongly depends on the calculation concept and material model used. In this paper, a practice-oriented viscoelastic approach using strain and strain rate dependent tangent moduli within FEA is presented. Required material parameters can be determined with a simple uniaxial tension test only. The proposed model is validated with numerous FE calculations of reality-based adhesively bonded component tests with different geometric ratios that include complex multiaxial stress states. The proposed approach allows a precise prediction of the strain state- and time-dependent stress behaviour of hyperelastic silicone bonds. The prediction quality is significantly more accurate than often used linear-elastic material models or commonly available hyperelastic models.
Constitutive modeling of polyurea properties
2023, Polyurea: Synthesis, Properties, Composites, Production, and Applications
With the increasing use of polyurea in different applications, numerical modeling has also been the focus of concurrent research efforts. Mechanical behavior of the material including strain rate effects are important in the constitutive modeling of hyperelastic materials such as polyurea. The constitutive behavior of polyurea is discussed in this chapter using a case study. The development of a strain rate sensitive behavior of polyurea based on the well-known Mooney-Rivlin (MR) model is presented. A strain rate correction factor was introduced based on the strain energy density function. Derivation of the nine-parameter MR constitutive equations, including the rate correction factor is presented. The stress-strain behavior and internal energy of polyurea at different strain rates are predicted by the proposed model in close agreement with the experimental values. The proposed constitutive model can be implemented as a user-defined material in commercial finite element software such as LS-DYNA and ABAQUS.

View all citing articles on Scopus

View full text

A hyper-viscoelastic constitutive model for polyurea

Abstract

Introduction

Section snippets

Hyperelastic model for low strain rates

Nonlinear viscoelastic model for high strain rates

Results and discussions

Conclusions

Acknowledgement

Polymer

Polymer

Mech Mater

Int J Solids Struct

Int J Impact Eng

Philos Mag

J Mech Phys Solids