Investigations on the influence of the triaxial state of stress on the failure of polyurethane rigid foams
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O R I G I NA L A RT I C L E
Dan-Andrei Serban ¸ Liviu Mar¸savina
· Radu Negru · Hannelore Filipescu ·
Investigations on the influence of the triaxial state of stress on the failure of polyurethane rigid foams
Received: 24 March 2020 / Accepted: 28 August 2020 © Springer-Verlag GmbH Germany, part of Springer Nature 2020
Abstract This paper investigates the failure strain as a dependence of the stress triaxiality and the Lode angle parameter for polyurethane rigid foams (PUR) of two densities (100 and 300 kg/m3 ). Tests were carried out in tension for various configurations, resulting in different states of stress triaxiality at various Lode angles in the critical areas. The failure strain was determined for each setup using finite element analysis, as the tests were replicated with numerical models. The displacement at failure recorded in the experiments was imposed for the models, determining the failure strain as a function of stress triaxiality and the Lode angle parameter. The results were validated through the analysis of the failure of sandwich structures with aluminium faces and PUR cores. Keywords PUR foam · Failure · Stress triaxiality · Experiment · Numerical simulation List of symbols d D ec et I1 J2 J3 p pc pt q r sc st γ εc
Plastic displacement Damage evolution parameter Logarithmic compressive strain Logarithmic tensile strain First invariant of the stress tensor Second invariant of the deviatoric stress tensor Third invariant of the deviatoric stress tensor Hydrostatic pressure Yield stress in hydrostatic compression Yield stress in hydrostatic tension von Mises equivalent stress Normalized third invariant True compressive stress True tensile stress Bai–Wierzbicki Lode angle-dependent parameter Engineering compressive strain
Communicated by Luca Placidi and Emilio Barchiesi. D.-A. Serban ¸ (B)· R. Negru · L. Mar¸savina Department of Mechanics and Strength of Materials, Politehnica University Timi¸soara, Timisoara, Romania E-mail: [email protected] H. Filipescu Department of Mechatronics, Politehnica University Timi¸soara, Timisoara, Romania
D.-A. Serban ¸ et al.
εt pl ε¯ D ε¯ pl ε˙¯ pl η θ¯ ν ξ σ σ¯ σc σt σi j σi σ σij σy ψ ω
Engineering tensile strain Critical plastic strain Equivalent plastic strain Equivalent plastic strain rate Stress triaxiality Lode angle Poisson’s ratio Lode angle parameter Stress tensor Effective stress tensor Engineering compressive stress Engineering tensile stress Stress tensor components Principal stresses Deviatoric stress tensor Deviatoric stress tensor components Equivalent yield stress Yield function Dissipated plastic energy Damage initiation parameter
1 Introduction Polyurethane rigid (PUR) foams represent a class of lightweight materials that, due to their mechanical and thermal properties, are used in a wide range of applications such civil engineering (thermal insulating panels), naval industry (composite panels with good floatability), railway transportation, automotive and aerospace applications (composite panels with good mechanical properties at
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