Oore-Burns Function of Form Application in Numerical Treatment of Mode I Flat Crack Problem in Infinite Body

The general approach of numerical treatment of integro-differential equation of the flat crack problem is considered. It consists in presenting the crack surface loading as the set of the polynomial functions of two Cartesian coordinates while the corresponding crack surface displacements are chosen as the similar polynomials multiplied by the function of form (FoF) which reflects the required singularity of their behavior. To find the relations matrixes between these two sets a new effective numerical procedure for the integration over the area of arbitrary shape crack is developed. In based on the classical hyper-singular method, i.e. Laplace operator is initially analytically applied to the integral part of equation and the resulting hyper singular equation is subsequently considered. The presented approach can be implemented with any variant of FoF, but Oore-Burns FoF, which was earlier suggested in their famous 3D weight function method, is supposed to be the most accurate and universal. It takes into account all points of crack contour, which provides perfect physical conditionality of the solution, but such FoF is relatively heavy in implementation and of low computational speed. The special procedure is developed for the approximation of the crack contour of arbitrary shape by the circular and straight segments. It allows to easily obtain analytical expression for Oore-Burns FoF, which greatly increases the calculation speed and accuracy. The accuracy of the considered method is confirmed by the examples of the circular, elliptic, semicircular and square cracks at different polynomial laws of loading. The developed methods are used in the implemented procedure for crack growth simulation. It allows to model growth of crack of arbitrary shape at arbitrary polynomial loading, at that all contour points are taken into account and can expand with their own speeds each. Procedure has high accuracy and don’t need complex and high-cost re-meshing process between the iterations unlike FEM or other numerical methods. At that usage of Oore-Burns FoF provides high flexibility of the presented approach: unlike similar theoretical methods, where FoF calculation procedure is rigidly connected with the crack shape, which complicates the adequate crack growth modeling, the used FoF automatically takes into account all points of crack contour, even if its shape became complex during the growth. Presented crack growth procedure can be effectively used to test accuracy and correctness of correspondent numerical methods, including the newest XFEM approach.

A Crack Segmentation Approach Using the Combination of Gray Thresholds and Fractal Feature

A segmentation method of combining gray-level threshold and fractal feature for crack images is proposed, and the fractal law for the perimeter and area of the target is introduced as the constraint condition for the image segmentation of crack. At first, Otsu algorithm is used for the initial segmentation of the crack image, and then the edge of crack is optimized in accordance with fractal law. At last, boundary of crack is determined, and the final result of the image segmentation is obtained. This method makes full use of the fractal geometry law and image information, to effectively solve the problems such as crack contour detection, regional connection and cross crack identification. Several typical examples are analyzed, and the results show that this method has a good segmentation effect on crack images, and it can also be used to identify the other images which have fractal feature.

Research on the Propagation Pattern of 3-D Initial Crack in Rock-Like Material under Uniaxial Tension

Experiments and numerical simulations were conducted to investigate the propagation patterns of pre-existing 3-D elliptical crack in rock-like material under uniaxial tension. Research results demonstrated that as the load was increased, the wrapping wing cracks initiated near the front of long axis of crack, with the lateral growth of initial crack close to the front of short axis. A distortion surface formed from the growth of initial crack leaded to the macro fracture of samples. The distribution laws of mixed-mode stress intensity factor (SIF) along crack contour were derived with FRANC3D, and propagation process of 3-D crack under tension was simulated. It was concluded that propagation patterns of 3-D crack under tension were quite different from compressive cases, mainly in aspects of growth orientation and velocity.

Effect of Crosslink Density on Cut Growth in Gum Natural Rubber Vulcanizates

Conventional sulfur-cured, gum natural rubber vulcanizates of various crosslink densities were prepared. Dumbbell test pieces with and without edge precuts were tested in uniaxial tension. Relative strengths of the different vulcanizates depended on cut size. Lightly crosslinked specimens exhibited an abrupt drop in strength at a critical cut size, ccr, which became smaller as crosslink density increased because of reduced strain crystallizability. At all cut depths, crack growth was simply perpendicular to the loading direction and crack surfaces were smooth. A moderately crosslinked composition exhibited crack deviation prior to rupture. This was associated with an unusual increase in strength with increasing cut size. Densely crosslinked networks exhibited lateral fracture, like the lightly crosslinked gums, but produced a jagged crack contour path reflective of a rough fracture surface. Moreover, for the highly crosslinked samples, a critical cut size was not found. Rather, log-log plots of strength versus cut depth were linear and had slopes slightly greater than minus one-half.

A Procedure for Estimating the Stress Intensity Factor of a Flattened Surface Crack at a Nozzle Corner

A flattened surface crack at a nozzle corner is modeled by a segment of a semi-elliptical crack in a finite thickness plate with matching crack contour and crack pressure corresponding to the normal stresses in the uncracked nozzle corner. Lacking other solutions for comparison, a qualitative comparison was made between nondimensionalized stress intensity factors at the deepest crack penetration with those obtained experimentally for similar corner cracks in epoxy models.