Journal of Materials Science

, Volume 43, Issue 6, pp 1783–1794

Fatigue crack orientation in NR and SBR under variable amplitude and multiaxial loading conditions


DOI: 10.1007/s10853-007-2398-8

Cite this article as:
Harbour, R.J., Fatemi, A. & Mars, W.V. J Mater Sci (2008) 43: 1783. doi:10.1007/s10853-007-2398-8


The orientations of cracks as they develop in a material indicate the planes that have experienced the maximum damage. For the purpose of fatigue life analysis and prediction, these planes are referred to as the failure or critical planes. In order to study the planes on which cracks develop for different types of loading, the development of cracks was observed during constant and variable amplitude experiments using the multiaxial ring specimen. Two filled rubber materials were compared in this study: NR, which strain crystallizes, and SBR, which does not. Multiaxial test signals composed of alternating blocks of axial and torsion cycles (each of which acts on different critical planes) produced crack orientations that fell between those occurring for signals composed only of axial or of torsion cycles. Plane-specific fatigue damage parameters of cracking energy density and normal strain were evaluated for their ability to predict the experimentally observed planes of crack development.


\( {\overrightarrow{r}} \)

Unit normal vector


Energy release rate based on cracking energy density


Strain energy density


Strain energy density based on Neo–Hookean model


Cracking energy density


Raw computed cracking energy density


Angle of crack orientation from horizontal plane

ε, ε

Strain tensor, state of strain


Normal strain


State of stress


Angle of crack plane in material thickness direction

Copyright information

© Springer Science+Business Media, LLC 2008

Authors and Affiliations

  1. 1.The University of ToledoToledoUSA
  2. 2.Goodyear Tire and Rubber CompanyAkronUSA
  3. 3.Mechanical, Industrial and Manufacturing Engineering DepartmentThe University of ToledoToledoUSA
  4. 4.Research DepartmentCooper Tire and Rubber CompanyFindlayUSA

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