Cracking energy density for rubber materials: Computation and implementation in multiaxial fatigue design

Abstract

This article proposes a heuristic model to predict the fatigue life of rubber parts. The developed model is mainly based on the Cracking Energy Density (CED), originally developed by Mars, for the study of rubber parts fatigue. The main contribution consists in the integration of the theoretical framework of the critical plane analysis proposed by Mars with Saintier's experimental research carried out in tension and torsion modes. The CED parameter, derived from the Strain Energy Density (SED), can predict the occurrence of the first crack and its possible orientation depending on the type of loading path. In this context, an analytical analysis of this parameter is carried out for typical loading cases. Furthermore, the variation of CED by SED ratio (WC/W), as a function of the probable crack angle θ and the principal stretch λ1 is investigated. A finite element (FE) model is, then, developed to measure the performance and efficiency for some basic criteria used to investigate rubber fatigue life in literature. The pertinence of such criteria is evaluated in terms of a determination coefficient. The CED parameter can be considered as the most effective criterion for describing the multiaxial fatigue life of rubbers.

Research Progress on Fatigue Life of Rubber Materials

“…The theory of cracking energy density has two key points: the critical plane and the energy release rate. Zine et al [ 41 ] compared the strain energy density and cracking energy density to predict the multiaxial fatigue life of carbon-filled styrene–butadiene rubber and found that the cracking energy density standard was indeed better than the strain energy density; Belkhiria et al [ 42 ] and Pan [ 40 ] reached the same conclusion. Poisson et al [ 43 ] studied the multiaxial fatigue behavior of polychloroprene rubber based on the dissipative energy density criterion and compared the predictive ability of the dissipative energy density criterion with the strain energy density and the first principal stress regarding multiaxial fatigue.…”

FE and probabilistic analysis for rubber life estimation considering cracking energy density as a fatigue predictor

“…Furthermore, Verron 33 used the minimum configurational stress, used by le Cam et al 33 to evaluate fatigue damage. Elsewhere, energy-based criteria were also utilized 2,11,12,[14][15][16][23][24][25][26][27][28] to judge elastomeric fatigue life. Energy parameters may be Strain Energy Density (SED) 2,15,34 cracking energy density, 11,12,14,16,19,21,[23][24][25][26][27][28]37,38 and dissipation energy density.…”

“…Elsewhere, energy-based criteria were also utilized 2,11,12,[14][15][16][23][24][25][26][27][28] to judge elastomeric fatigue life. Energy parameters may be Strain Energy Density (SED) 2,15,34 cracking energy density, 11,12,14,16,19,21,[23][24][25][26][27][28]37,38 and dissipation energy density. [39][40][41][42][43][44] The main objective of the current work consists in developing a generalized methodology to calculate the reliability of a predictive fatigue model considering the cracking energy density as a damage parameter.…”

“…Elsewhere, energy-based criteria were also utilized 2,11,12,14–16,23–28,3437–44 to judge elastomeric fatigue life. Energy parameters may be Strain Energy Density (SED) 2,15,34 cracking energy density, 11,12,14,16,19,21,23–28,37,38 and dissipation energy density. 39–44…”

The prediction methodology for tire durability regulation test using FEA

“…[7] Belkhiria et al proposed a model to predict the fatigue life of rubber parts based on cracking energy density (CED) by combining finite element analysis (FEA) with MATLAB scripts through Abaqus software. [8] Xu et al predicted the fatigue life of the rubber bushing stud shear joints by FEA and investigated the effect of the rubber bushing and concrete properties on the fatigue life. [9] The tire is one of the most complex rubber products, and its fatigue life prediction has been a hot research topic.…”