Studies on Stress Concentration Using Experimental and Numerical Methods ABSTRACT

This paper presents the experimental and numerical studies that had been 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 longitudinal strain measurements in the vicinity of the hole can be performed. 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. A hole was located so 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.

METHODOLOGY

Stress Concentration in a Tensile Specimen

1. An aluminum plate with a central circular hole will be subjected to a tensile load. 2. Strain distributions are measured using strain gages attached to different positions on the plate. 3. Local tangent strains are measured at five positions along the ligament. 4. Load the plate in tension to a pressure of 500 psi.

5. Record data

Stress Concentration in a Cantilever Specimen

1. High-strength aluminum alloy beam, 1/4 x 1 x 12 ½ (3.2 x 25 x 318 mm), outfitted with preinstalled strain gages and a ¼” diameter stress concentration hole is used in the flexure frame. 2. Three very small strain gages are placed at varying distances from the hole, with one directly adjacent to the edge. 3. Plot strains on a graph sheet at the locations of the gage centerlines, and draw a smooth curve. 4. Extrapolate the data to the edge to obtain the peak strain. 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 far-field) stress, σnom as:

The theoretical stress concentration factor is a function of component geometry and loading. Stress concentration factor Kt for plate with hole under tension is shown as a function of the diameter to width ratio, d/b in Figure 1. For a plate with hole under bending the stress concentration factors as a function of the diameter to width ratio, d/b for various depth-to-thickness ratios d/h are shown in Figure 2. For the two specimen geometries used in the experiments, the experimental results as well as the results from the numerical solutions was compared with the corresponding analytical results displayed in Figures 1 and 2.

Figure 1: Stress Concentration Factor for a Plate with a Hole Loaded in...