Studies On Stress Concentration Using Experimental And Numerical Methods

The experimental and numerical studies were conducted to investigate the stress concentration around a circular cutout in an isotropic material. Test specimens with circular holes were loaded in tension and bending. The tension test specimen was loaded in an Instron test machine. By mounting a set of strain gages orthogonal to the applied loading direction, the students performed the longitudinal strain measurements in the vicinity of the hole. The strains obtained by the series of strain gages placed at varying distances from the hole were extrapolated to the edge of the hole to determine the peak stress at the hole. These peak stresses were divided by the corresponding nominal far field stresses to obtain the stress concentration factors for specimen loaded in tension. The bending case was investigated with a cantilever beam with a hole at its mid span. The Flexor setup by Vishay Instruments was used for this purpose. The hole was located in such a way that the nominal stress at the fixed end was the same as the one at the location of the hole. Strain gages were placed at varying distances from the edge of the hole, one being directly adjacent to the edge. Known amounts of load were applied at the free end of the beam. The peak strains at the hole were extrapolated from the strain gage readings similar to what was done for the tension case. The stress concentration factor is the peak strain at the hole divided by the nominal strain at the same location. The experimental results on stress concentrations were compared with finite element solutions performed on the specimen geometries and loadings similar to the ones used in the experiments. A mesh of quadrilateral elements was used to model both the tensile bar and the cantilevered beam specimens with holes. The tensile and the bend specimen geometry and loadings were used to calculate the stress concentration factors. The two dimensional finite element simulations were performed using ANSYS general-purpose computer program. The nodal stresses were used to calculate the stress concentration factors. The stress concentration factors obtained by the experimental and numerical methods were compared with the corresponding closed form solutions. INTRODUCTION This study constitutes a laboratory component of the strength of materials courses taught to both engineering and engineering technology students. It is important that engineering students learn the detrimental effects of stress raisers such as notches, holes, and sharp corners in machine members. Such discontinuities can cause a large rise in stress above the nominal value. This topic is introduced in the strength of materials course in the design of a stepped shaft with keyways subjected to bending, torsion, as well as axial loads. The nominal axial stress, the bending stress, and the shear stress due to torsion in the shaft are each multiplied by the corresponding stress concentration factors obtained from the literature. This approach does not generally present a convincing argument to the engineering student so there is a need to provide a different perspective to reinforce the concept of stress concentration. This issue is addressed through an experimental method as well as a numerical method. The experimental method uses strain gages in which the actual strains and also stresses can be measured in the laboratory. The numerical method is based on a finite element solution. In a tensile specimen, a discontinuity P ge 15137.1 such as a through-the-thickness circular hole is a stress raiser, and its effect on the stress is through a stress concentration factor. Similarly, a circular hole drilled through a beam loaded in bending is also a stress raiser with its own stress concentration factor. In this study the analytical solutions to the stress concentration factors for both the tensile and cantilever specimens due to a circular hole have been compared with experimental and numerical methods. First, the students are introduced to the concept of stress concentration factor and the analytical results of stress concentration factors for various test specimen geometries are outlined. Experimental studies on stress concentration factors are conducted for (a) bar with a hole in tension and (b) cantilever beam with hole in bending. Then the numerical solutions for the stress concentration factors for the test specimen geometries are conducted using finite element analyses. STRESS CONCENTRATION FACTORS Any physical discontinuity in a structural member or a sudden change in the geometric form of a part leads to a region of stress concentration. The abrupt change in cross sections cause the stress “flow lines” to crowd causing high stress concentration. To mitigate this phenomenon, smoother changes such as fillet radii are introduced in structural members that make the “flow lines” less crowded causing lower stress concentrations. The theoretical stress concentration factor, Kt is defined in terms of maximum (or peak) stress, σmax and nominal (or average or farfield) stress, σnom as: