A model of thermal aging of hyper-elastic materials with an application to natural rubber
Understanding the degradation of material properties and stress-strain behavior of rubber-like materials that has been exposed to elevated temperature is essential for rubber among components design and lifetime prediction. The complexity of the relationship between hyper-elastic materials, crosslinking density, and chemical composition present a difficult problem for the accurate prediction of mechanical properties under thermal aging. In the first part of the current research, a new and relatively simple mathematical formulation is presented to expresses the change in material properties of natural rubber subjected to various elevated temperatures and aging times. The aging temperatures ranged from 76.7 °C to 115.0 °C, and the aging times ranged from 0 to 600 hours. Based on the experimental data, the natural rubber mechanical properties under thermal aging showed a similar behavior to the rate of change of the crosslinking density (CLD) with aging time and temperature as determined as of the research. Three mechanical properties have been chosen to be studied: the ultimate tensile strength, the fracture stretch value, and the secant modulus at 11.0% strain. The proposed phenomenological model relates the mechanical properties with the rate of change of the CLD based on a form of Arrhenius equation. The proposed equations showed promising results compared to the experimental data with an acceptable error margin of less than 10% in most of the cases studied. In the second part of the current research, a closed form set of equations that was based on basic continuum mechanics assumptions has been proposed to define the material stress-strain behavior of natural rubber as an application of hyper-elastic materials. The proposed formulas include the influence of aging time and temperature. The newly proposed “Wight Function Based” (WFB) method has been verified against the historic Treloar’s test data for uni-axial, bi-axial and pure shear loadings of Treloar’s vulcanized rubber material, showing a promising level of confidence compared to the Ogden and the Yeoh methods. Tensile testing was performed on strip specimens that were thermally aged then subjected uni-axial tension and hardness tests. A non-linear least square optimization tool in Matlab (Lscurvefitt) was used for all fitting purposes.