Jorgen
2007-08-28, 19:34
http://polymerfem.com/polymer_files/topics/bbmodel.gif
The Bergstrom-Boyce (BB) model has been shown to successfully model many different elastomers. An interesting generalization of this model capable of explicitly predicting the behavior of particle filled elastomers is discussed in this pdf-file (http://polymerfem.com/polymer_files/timeDepFilled03.pdf).
Title: Large Strain Time-Dependent Behavior of Filled Elastomers
Abstract:The mechanical behavior of elastomeric materials is known to be rate-dependent and to exhibit hysteresis upon cyclic loading. Although these features of the rubbery constitutive response are well-recognized and important to its function, few models attempt to quantify these aspects of response. Based on a detailed experimental investigation a constitutive model for the time-dependence of unfilled elastomers has recently been proposed. The foundation of the model is that the mechanical behavior can be decomposed into two parts: an equilibrium network corresponding to the state that is approached in long time stress relaxation tests; and a second network capturing the non-linear rate-dependent deviation from the equilibrium state. The time-dependence of the second network is further assumed to be governed by the reptational motion of molecules having the ability to significantly change conformation and thereby relaxing the overall stress state. In this paper, the proposed constitutive model is extended to specifically account for the effect of filler particles such as carbon black on the time-dependent, hysteretic stress-strain behavior. The influence of filler particles is found to be well-modeled by amplification of the first stretch invariant of the matrix as well as the equivalent shear stress of the matrix. The amplification factor is dependent on the volume fraction of filler particles; three-dimensional stochastic micromechanical models are presented and verify the proposed amplification of matrix stretch and stress. A direct comparison between the new model and experimental data for two series of filled elastomers (a chloroprene rubber series and a natural rubber series) indicates that the new model framework successfully captures the observed behavior. The success of the model implies that the effects of filler particles on the equilibrium, rate and hysteresis behavior of elastomers mainly requires a rigorous treatment of the composite nature of the microstructure and not microlevel concepts such as alteration of mobility or effective crosslinking density of the elastomeric phase of the material.
The Bergstrom-Boyce (BB) model has been shown to successfully model many different elastomers. An interesting generalization of this model capable of explicitly predicting the behavior of particle filled elastomers is discussed in this pdf-file (http://polymerfem.com/polymer_files/timeDepFilled03.pdf).
Title: Large Strain Time-Dependent Behavior of Filled Elastomers
Abstract:The mechanical behavior of elastomeric materials is known to be rate-dependent and to exhibit hysteresis upon cyclic loading. Although these features of the rubbery constitutive response are well-recognized and important to its function, few models attempt to quantify these aspects of response. Based on a detailed experimental investigation a constitutive model for the time-dependence of unfilled elastomers has recently been proposed. The foundation of the model is that the mechanical behavior can be decomposed into two parts: an equilibrium network corresponding to the state that is approached in long time stress relaxation tests; and a second network capturing the non-linear rate-dependent deviation from the equilibrium state. The time-dependence of the second network is further assumed to be governed by the reptational motion of molecules having the ability to significantly change conformation and thereby relaxing the overall stress state. In this paper, the proposed constitutive model is extended to specifically account for the effect of filler particles such as carbon black on the time-dependent, hysteretic stress-strain behavior. The influence of filler particles is found to be well-modeled by amplification of the first stretch invariant of the matrix as well as the equivalent shear stress of the matrix. The amplification factor is dependent on the volume fraction of filler particles; three-dimensional stochastic micromechanical models are presented and verify the proposed amplification of matrix stretch and stress. A direct comparison between the new model and experimental data for two series of filled elastomers (a chloroprene rubber series and a natural rubber series) indicates that the new model framework successfully captures the observed behavior. The success of the model implies that the effects of filler particles on the equilibrium, rate and hysteresis behavior of elastomers mainly requires a rigorous treatment of the composite nature of the microstructure and not microlevel concepts such as alteration of mobility or effective crosslinking density of the elastomeric phase of the material.