Mixed mode fracture analyses of deflected surface cracks in solid cylindrical structures under tension, bending and torsion loads

Initial defects or cracks and/or crack initiation and propagation under fatigue loads may occur in mechanically designed machine and structural parts due to manufacturing defects. Fracture occurs as a result of damage to a certain part of the structure. Fracture occurs in two parts as crack formation and crack propagation. Ductile fracture and brittle fracture occur in materials. While plastic deformation consists a remarkable amount in ductile fracture, sudden breaking is formed in brittle fracture without high deformation. In order for structural parts to maintain its function safely, safety and life calculations need to be done using the principles of strength of materials and fracture mechanics. Bars, beams and shafts with circular cross-section are also quite widely used mechanical parts in practice. Therefore, it is fairly important to perform fracture analysis of an initial surface crack that may occur in cylindrical parts subjected to such loads, and to make safety and life evaluations. The finite element method is used to present numerical solutions to structural mechanics, heat transfer, electromagnetic and computational fluid dynamics problems. Because engineering problems involve mathematical models of their physical states, most of them have differential equations with boundary and/or initial conditions. Practical engineering problems for which exact solutions are difficult to obtain consist of differential equations to have complex boundary or initial conditions. One of the ways to be able to solve these equations goes through the implementation the numerical methods called the finite element method. On the contrary to analytical solutions, numerical solutions converge to exact solutions at nodes. The region of the problem is divided into a series of small sub-items and nodes. ANSYS Parametric Design Language (APDL) is one of the most powerful features of ANSYS. It ensures to be able to define a part or all of the model (geometry, material properties, loads, boundary conditions, etc.) parametrically. It's pretty easy to create and solve a new variable of a parametric model, by changing a few parameter values, and rerun the model. This makes ANSYS a powerful tool for engineering analysis, optimization, root cause analysis, and design of new systems and technologies. APDL also allows to build and execute macros, run macros as ANSYS commands, operate on parameter arrays, and do simple logic. FCPAS (Fracture and Crack Propagation Analysis System) software makes calculation of the stress intensity factor in geometric structures containing two and three dimensional cracks. There is no modelling interface in FCPAS software. The information in the finite element model is element, node, load and boundary conditions. The necessary finite element model information was transferred to the FCPAS software, which contains the enriched finite element solver FRAC3D, and fracture analyses were performed. Among the parameters needing attention is the number of elements, the number of nodes and the processing power of the computer. While the solid cylinder modellings are carried out in the ANSYS Mechanical APDL interface, the cylinders are divided into sections in order to be able to obtain finer finite element mesh structure. As a result of the analyses, the stress intensity factor values are presented in graphs as non-dimensional distributions. The effects of variations in parameters such as crack depth/cylinder diameter (a/D), crack depth/crack width (a/c), the angle () at which the deflected surface crack is positioned with respect to the horizontal axis, on stress intensity factors were explained. The uniform axial tensile load was created by defining constant distributed pressure load on the lower and upper surfaces of the solid cylinders. The bending moment was created by defining the linear surface load gradient, provided that it is zero at the center of the cylinder. In surface crack problems where the angle with respect to the horizontal axis is zero in both load types, only the dimensionless KI values that constitute the opening mode are calculated. In deflected crack problems, in cases where the angle with respect to the horizontal axis is different from zero, in addition to the opening mode, the sliding (in plane shear) and tearing (out of plane shear) modes also become active. The dimensionless KI values obtained for the tensile load increase as the diameter decreases (the depth of the dimensionless crack increases) and decreases as the angle of deflection between the crack and the horizontal axis increases. The dimensionless KII values calculated for the sliding (in plane shear) mode are usually negative. In the sliding (in plane shear) mode analysis, the highest dimensionless KII values are in the plane with the maximum shear stress for tensile and bending loads. For the tensile load, the dimensionless KII values are close to each other at angles that usually complement each other to 90 degrees (15°-75° and 30°-60°). In graphs with respect to the depth point for tearing (out of plane shear) mode, usually one region is positive and one region is negative. The torsional moment was created by defining the force from the nodal points on the lines surrounding the lower and upper circular area of the solid cylinders. In cases where the surface crack is angled at zero degree with respect to the horizontal axis, while the opening mode does not occur, the sliding (in plane shear) and tearing (out of plane shear) modes are active. In cases, where the angle with respect to the horizontal axis is different from zero, the opening mode is also activated. As expected, the dimensionless KI values at the depth point are zero. The distributions seen in the positive regions in the graphs represent the opening of the crack, and the distributions in the negative regions represent the closure of the crack. Since the contact mechanics is not modeled in FCPAS analyses, the values given in the graphs do not represent the real physical conditions. In order to observe the physics of the problem more clearly, structural analyses were made in ANSYS software and the results were shared as contour pictures. It has been seen that closure of crack surfaces occurred in the regions with negative KI values. It is also seen that the dimensionless KI distributions obtained for the torsional load are similar to the dimensionless KIII distributions obtained for the tensile and bending loads. In order for the obtained solutions to be used in practice, mixed mode stress intensity factor empirical equations of the depth and free surface points, which are valid in the defined ranges of the relevant parameters, are also generated. Different sets of equations have been developed for the crack aspect ratios between 0.25 and 2.0 in order to increase the accuracy levels of the empirical equations. Empirical equations were developed with the help of Minitab software. While making the equation solution, insignificant coefficients were eliminated in order to make a more practical solution instead of developing solutions with too many coefficients. By looking at the T-values of the coefficients and generally containing a large number of terms, the coefficients were included in the scope of elimination. Equation creation processes were completed by using the dimensionless stress intensity factor values at the free surface and depth points obtained for tension and bending loads. Because the contact mechanics is not modelled in the opening mode cases for the torsional load, the equations were not created for the torsional load cases. Finally, validation studies of empirical equations have been carried out for many different problems that are not included in the analysis library, by including many different combinations of intermediate values of the parameters defining the problem. It has been observed that the dimensionless KI and KII values calculated in the depth region and the empirical equation results are quite consistent. It has been also detected that the results of the empirical equations with the dimensionless KI values in the free surface region are also quite consistent, while for the dimensionless KII and KIII values, the approximate value predictions cannot be done by empirical equations with as much accuracy as the above cases.