Mechanik einzelner kolloidaler Strukturen unter Einfluss von Nanopartikelwechselwirkungen: integrative Mehrskalen-Untersuchung
Final Report Abstract
The objective of the project was to describe the mechanical state of single clusters under deformation in the absence of a dispersion medium. The results of this study were to be incorporated into constitutive models of filled rubbers. This has been achieved through the following steps. 1) Non-linear elasticity of aggregates: In order to characterize the influence of filler particles in rubbers, mechanics of single aggregates and inter-aggregate interactions were studied. Aggregates when subjected to external loading tend to have a single chain path of particles which carries most of this transmitted external load. This chain path is known as a backbone chain. The forces between the particles of this backbone are further divided into tangential and centro-symmetric ones. Accordingly, the strain energy of the backbone chain in a three-dimensional space is formulated in terms of the tensile, bending and torsional moduli. 2) Yield behavior of aggregates: In order to characterize the yielding behavior of aggregates, yielding of an inter-particle bond is first considered where this bond is represented by an isotropic, homogeneous solid-like beam with a constant cross section. Bond failure is described in two ways: failure upon exceeding the critical bending moment in the absence of tensile forces, or failure upon exceeding the critical tensile force in the absence of a bending moment. Failure of the weakest bond in the backbone chain has been shown to be accompanied by massive breakage of further bonds, which leads to the whole aggregate failure. This yielding model has been verified against available experimental data. Unfortunately, experimental validations could not be improved due to the lack of detailed experimental data from the partner institute. 3) Re-aggregation: Stress softening in filled rubbers is partly a result of the recovery of filler aggregates which is due to the recreation of bonds between debonded filler particles. Recreated bonds are weaker than the virgin ones which results in weaker stiffness against the original bond. Thus, the elastic behavior of these recreated aggregates is the same as that of the original ones, except that their yield force is considerably less. Once this force becomes less than the internal forces of the network, the aggregate will no longer recreate. 4) Application of these concepts of elasticity, yielding and re-aggregation to constitutive modelling of filled rubbers: The filled rubber matrix is decomposed into five subnetworks. The above concepts form the basis of the so called CP network (its contribution provides the description of the hysteresis phenomenon). This network is decomposed into tiny micro-cells (each with a single aggregate inside) undergoing affine deformation. Considering an appropriate probability distribution of such cell sizes, the subnetwork energy is formulated which when added to the other subnetwork energies, yields accurate prediction of the mechanical response of filled rubbers under uniaxial tensile cyclic response.
Publications
- (2012) Yield behavior of colloidal aggregates due to combined tensile-bending loads, Physical Review E 85(5), 051406
Dargazany, R. and Itskov, M.
(See online at https://doi.org/10.1103/PhysRevE.85.051406) - (2013) Constitutive modeling of cyclic stress softening in filled elastomers, in Proceedings in Applied Mathematics and Mechanics, 13(1), 143-144
Khiem, V.N., Dargazany, R., and Itskov, M.
- (2013) Constitutive modeling of the Mullins effect and cyclic stress softening in filled elastomers, Physical Review E 88(1), 012602
Dargazany, R. and Itskov, M.
(See online at https://doi.org/10.1103/PhysRevE.88.012602) - (2013) Elasticity of colloidal clusters with application to carbon-black aggregates in filled rubbers, Constitutive Models for Rubber VIII, 261-266
Dargazany, R., Rege, A., and Itskov, M.
- (2014) A generalized network decomposition model for the quasi-static inelastic behavior of filled elastomers, International Journal of Plasticity 63, 94-109
Dargazany, R., Khiem, V.N., and Itskov, M.
(See online at https://doi.org/10.1016/j.ijplas.2013.12.004) - (2014) Micro-mechanics of inelastic effects in filled rubbers: a generalized network decomposition, 11th Fall Rubber Colloquium (KHK), Hannover, Germany, November 26-28
Itskov, M., Dargazany, R., and Khiem, V.N.
