Objective

• To measure the average and concentrated strains on a mild steel specimen under tension due to the effect of circular hole by placing two strain guages one close to and another further away from the hole.​

• By estimating the ratio of concentrated stress and average stress, calculate the sress concentration (values are nominally in the range of 2-3) ratio. Verify that the Fig below is obtained as the experimental output.

Introduction

Stress concentration is the increase in stress along the cross-section that maybe caused by a point load or by any another discontinuity such as a hole which brings about an abrupt change in the cross sectional area. It is the ratio of the maximum to the average stress is called as stress concentration factor.

Stress concentration factor is denoted as k_t

 

Figure1 : Stress concentration and stress trajectories

Figure 2: Stress distribution around a circular hole 

Figure 2 above shows the stress distribution pattern around a circular hole for a rectangular plate when tensile load is applied at both the ends of the plate. 

The specimen

 

The specimen in consideration is a mild steel plate with thickness‘t’. The width of the specimen will be 2 times the diameter. As per S.Timoshenko and J.N. Goodier, at a depth below the top equal to one-quarter of the width, 

                

Fig 3: The 2-d View of specimen with physical dimension; Fig 2: Stress concentration due to a central hole in a plate subjected to a uni-axial loading.

 

Fig 4: Graph showing variation of stress concentration factor for various notch geometries

Figure obtained from “Engineering Mechanics of Solids”, Second edition by Egor P.Popov

 

The Tension test

In this experiment, we fix two strain gages around the circular hole, one below the circle and one adjacently on the side of the circle. The one fixed below the circle will pick up the average strains and the other strain gage will pick up the Concentrated strain value. The stress will be concentrated near the point of application of load, and hence care is taken to place the average strain gage away from load application point.  Since stress is proportional to strain, the measurement of strain can help us determine the stress at the respective points as our specimen is an isotropic material.  Although the average stress along the uniform cross section remains constant, at the discontinuity (hole), the stress is distributed as shown in fig.1. To perform the tension test, the UTM is switched on and the specimen subjected to tensile load. The respective strain values obtained from both the strain gages are measured and then plotted with respect to time.

 

Fig 5: Specimen of Circular hole experiment

Specimen details are as follows:

Specimen details:

Material : Mild steel

Hole diameter: 5.32 mm

Specimen width: 31.5 mm

Specimen gage length: 126 mm

Specimen thickness: 3.4 mm