Stress Concentration Study: A plate with Holes
INTRODUCTION
Stress is the internal resistance to change in the shape of the body when the external load is applied. When the stress in the body exceeds the failure stress for the material, the structure can fail either by yielding or cracking. In ductile materials, necking phenomenon is noticed, while in brittle materials, necking is not seen but still fails by cracking. In either case, following three broad steps are involved,
1) Crack initiation
2) Crack Propagation
3) Failure
The cracks are typically initiated in the stress concentrated region. These are the regions where localised maximum stresses are generated either due to abrupt changes in geometry or irregularities. These changes and irregularities act as the stress raiser. These are the most common examples of the stress raisers.
1) Holes
2) Notches
3) Fillets
4) Sharp Shoulders
5) Grooves, Keyways, Threads
6) Internal defects
7) Load variabilities
8) Material changes
9) Temperature changes
Various methods and theories are used to determine the stress concentration fator. Following simple formula is used for determining the actual stress concentration fator
Kactual = 1 + q*(Ktheoretical - 1) where q is the notch sensitivity. Ktheoretical depends only on Size and type of the discontinuity whereas, q is dependent on material and nature of load.
Various geometric induced stresses could be mitigated by following means
1) Drilling additional holes
2) Use of fillets
3) Use of multiple notches
4) Removal of unwanted material to maintain smooth stress flow lines
This study is hence carried out to determine the stress due to hole in a plate and advantage of using the additional holes.
FEA SIMULATION
Geometry: Two geometries are used for two cases as shown below. Alloy steel is used as the material in both the cases
Case 1: Single hole
Case 2: Additional holes
MESHING: The auto meshing feature is utilised
SOLUTION SETUP AND INTIALISATION
One face is fixed and on the other face, load of 1000N is applied
RESULTS
Stress
Displacement
Strain
DISCUSSION ON RESULTS
1) This example deals with stress concentration raise due to presence of the hole in a plate
2) The maximum stress in a plate with one hole is 1.189MPa and for the plate with three holes 1.145MPa
3) The percentage reduction in the stress is around 3.7%
4) A simple change to the geometry reduced stress by almost 4%, similar changes to notches, grooves, shoulders brings about a significant improvement in Stress values in the structure
5) A simple table of comparison is as follows
| Geometry\Properties | Max Stress(MPa) | Max Disp | max Strain |
| Plate with one hole | 1.189 | 0.00052 | 4.187e-06 |
| Plate with three hole | 1.145 | 0.00057 | 4.023e-06 |