Determining parametrical functions defining the deformations of a plane strain tensile rubber sample

Abstract

The plane strain (PS) tensile sample, which is very often named as pure shear sample, featured prominently in classic studies of fracture mechanics of rubbers while investigating fatigue crack growth (FCG) behaviour. A PS sample is shaped as a thin, rectangular strip. For the FCG investigation it is held by rigid clamps along its long edges. While straining in-plane, deformation of the sample originates mainly along the loading direction except in the regions near the free edges. Thus, when using the PS sample for FCG characterization while applying simple fracture mechanics, the crack growth is required to be investigated within the region, where the deformation of the sample originates mainly along the loading direction. Parametrical functions defining the region of PS sample, where the orientation of strain in the plane is in the loading direction or orthogonal to the crack growth, have experimentally been determined using a digital image correlation (DIC) system. In detail, the parametrical functions firstly describe the narrowing towards the edges and secondly the width of the region in which the FCG analysis should take place. This was observed over a broad range of the aspect ratio `width/ length' of the sample (<1/2, 10>) and the strain was varied in the interval 2 <0, 0.5>. The strain over the complete horizontal axis across all applied aspect ratios has experimentally proven that no pure shear deformation (deformation strictly originating along the loading direction) is present in the PS sample in reality. Thus, thanks to the exponential character of the contraction over the complete horizontal axis of the PS sample, a novel criterion considering a deviation from the maximum achieved contraction in proportion 2 <0.01, 0.05> has been established and it was included to the parametrical function defining the width of the region of deformation originating near the loading direction. Besides, it has been demonstrated that the deformation over the complete horizontal axis of sample is nearly independent of the applied rubber type. To conclude, based on the determined parametrical functions, the equation for calculating the minimal notch length required for FCG analyses within the region of deformation originating near the loading direction has been defined.