Prediction of Constraint Parameters Along the 3D Crack Front Under Negative Biaxial Loadings

Conference paper
Part of the Conference Proceedings of the Society for Experimental Mechanics Series book series (CPSEMS)


In the recent past, the effect of constraint parameter along the 3D crack front under different biaxial ratios has received huge attention due to its practical importance for complex structures. A large amount of information is available in the literature for predicting in-plane and out-of-plane constraint effects along the 3D crack front subjected to different biaxial loadings but majority of them are based on positive biaxial or uniaxial loading conditions which has considerable amount of plane strain effect. Linear elastic fracture mechanics (LEFM) from finite element(FE) analysis using J-integral method confirms that far-field stress applied parallel to the crack front does not contribute anything to the stress intensity factor (SIF) as biaxiality has no effect on singular term. However the biaxiality affects the non-singular terms and it can be predicted by using elastic–plastic FE analysis. Some aircraft components operate under negative biaxial loadings up to −0.5. In this work, attempts have been made to quantify the effect of in-plane and out-of-plane constraints along the 3D crack front under different biaxial loadings using elastic–plastic FE analysis approach for AA2014-T6 alloy. Aluminum alloy is used for current study considering its wide range of applications in the aerospace industry. In the aircraft industry, more than 40% of the components are manufactured with various aluminum alloys. J-Q two-parameter fracture mechanics approach has been considered to quantify the constraint effect along the 3D crack front. A comprehensive study was carried out on constraint parameters with 3D Flat plat models with different a/c and a/t ratios under three different biaxial loadings from −0.5 to +1. Also the effect of negative biaxiality on constraint parameter was investigated using three different far-field loadings to address from small scale yielding to large scale yielding (20%, 50% and 70% of yield strength). In order to determine Q parameter, the reference stress has to be calculated under plane strain condition. Therefore the modified boundary layer (MBL) approach is modeled with T=0 condition to determine the reference stress. It was observed from the study that negative biaxiality has significant influence on constraint parameters along the 3D crack front even at lower loading cases due to the nature of excess yielding. According to the yielding criteria, tension-compression is the worst load combination and it reduces the hydrostatic stress to the lowest level as compared to the positive and uniaxial loadings. Plotting of photoelastic fringe patterns using commercial FE package like ANSYS is demonstrated and numerical validation has been done with the cruciform specimen. A new methodology is proposed to quantify the impact of constraint parameters under negative biaxial loadings along the 3D crack front.


Constraint parameter MBL J-Q Biaxial loading Plane strain J-integral 


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Copyright information

© The Society for Experimental Mechanics, Inc. 2013

Authors and Affiliations

  1. 1.Applied Mechanics DepartmentIndian Institute of TechnologyMadrasIndia

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