Understanding Compressive Stresses in a Plate with a Hole Under Uniaxial Loading

[kajalschopra]

Is t right that, in a plate with a hole, subjected to uniaxial loading, along one of the axis, one gets compressive stresses around the crack tip (in the same direction as that of the applied load ). I'm not able to understand this intuitively. Can someone help?

I believe, intuitively, these compressive stresses (See sketch below) are due to Poisson's effect, although the magnitude might be greater because of the hole. There is 'nothing special' concerning the these compressive stresses as such.

Any comments?

 

[Nidum]

Not entirely sure what you are asking ?

 

[kajalschopra]

1) IF you look at the problem with a plate with a hole., around the hole you have a state of biaxial stress developed, see figure below. This can be proved mathematically if I look into the book by Timoshinko. But can't sense the biaxial stresses physically? Can you? How?

2) IT is not shown in the figure below, but adjacent to the hole some distance away, there will also be a compressive stress in horizontal direction, again , I can't sense it physically.

 

[Nidum]

Greatly magnified views of distortion of a thick plate with a hole . Uniform stress applied to top and bottom edge faces . The plate is not infinite but it is relatively big compared to hole diameter .

Can you see how the distorted shape of the hole relates to the stress distribution around the hole ?

 

[kajalschopra]

No, I think you didn't get my question still.See figure below. I have given the expression for σ_θθ

If you put θ = 0, you get σ_θθ = - σ_xx

That is compressive stress . This is what I'm trying to sense physically