Excessive Elastic Deformation

You can't expect an answer to such a vague question.

"safety factor close to 1"

"excessive elastic deformation"

How about, maybe.

I doubt that it could fail to fail.

Nick Name, Esq.,

Thank you for your critique. It's enlightening. It has squeezed me (to exude) as follows:-

Why, Excessive Elastic Deformation ?

It's deflection, dicey though, could still be within the elastic range of the material (of which the component is made).

And therefore, there is mentioned Young's Modulus (which is defined by the elastic range of the stress-strain curve).

Consequently, Excessive Elastic Deformation could not be referred to Ultimate Tensile Strength.

Excessive Deformation at UTS would sure be catastrophic failure.

Excessive Elastic Deformation could have meant to be tensile or compressive deflection.

Otherwise, Excessive Elastic Deformation could also be deflection subject to bending (in which case, the component is at stake due to shear stress).

By Excessive Elastic Deformation, the component, under bending, could have exceeded Shear Yield Stress (and therefore, Ultimate Shear Strength) of the material (Could it be shown mathematically ?).

In practice, one could conjure up (though not mentioned by the query) the following:-

a. Cyclic loading (that would cause fatigue of the material, work-hardening and brittle failure, compounded by crack propagation).

b. Differential range of thermal conditions (that could cause cyclic loading as above).

The (design) safety factor being close to 1, should have been written,

Safety Factor = 1. It should not be less than Unity.

With Safety Factor = 2, Excessive Elastic Deformation would not be manifest.

Regards.

Failure-mechanism models for excessive elastic deformation ...

You seem singularly focused upon fracture as the method of failure.

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Brittle fracture as well as ductile fracture are certainly paths to structural failure, but those aren't the only paths. Excessive deformation, elastic or otherwise, can be sufficient for failure.

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Of course, the various requirements of a component can introduce novel routes to failure, but even assuming strictly structural demands, fracture and failure are not interchangeable terms.

Nick Name, Esq.,

Thank you for your critique. It's enlightening. It has squeezed me (to exude) as follows:-

Why, Excessive Elastic Deformation?

Question: When an excessive deformation does occur? Answer: When the applied load increases

It's deflection, dicey though, could still be within the elastic range of the material (of which the component is made).

If the stress (equivalent according to one of the accepted criteria) does not go over the limit the structure still is in the elastic range

And therefore, there is mentioned Young's Modulus (which is defined by the elastic range of the stress-strain curve).

Young's modulus is only the slope of the curve strain-load in a unidirectional test. Do not forget that physically only strain is real stress is a convention

Consequently, Excessive Elastic Deformation could not be referred to Ultimate Tensile Strength.

Excessive Deformation at UTS would sure be catastrophic failure.

Yes

Excessive Elastic Deformation could have meant to be tensile or compressive deflection.

Yes

Otherwise, Excessive Elastic Deformation could also be deflection subject to bending (in which case, the component is at stake due to shear stress).

No since shear is directly related to tension-compression due to the material deformation.

You consider the Tresca criterion but for elastic materials the most accepted is the von Mises and according to it shear limit is tension limit*3^-0.5

By Excessive Elastic Deformation, the component, under bending, could have exceeded Shear Yield Stress (and therefore, Ultimate Shear Strength) of the material (Could it be shown mathematically?).

See above, in general in bending the shear values are due to the cutting force in the section and are maximal at the section center line (parabolic distribution) tension-compression is maximal at the outmost fiber.

In practice, one could conjure up (though not mentioned by the query) the following:-

a. Cyclic loading (that would cause fatigue of the material, work-hardening and brittle failure, compounded by crack propagation).

Fatigue does not go over the brittle state, cracks can appear at the inter-crystal border due to other lattice disturbances or at the peak of a roughness trace

b. Differential range of thermal conditions (that could cause cyclic loading as above).

The (design) safety factor being close to 1, should have been written,

Safety Factor = 1. It should not be less than Unity.

With Safety Factor = 2, Excessive Elastic Deformation would not be manifest.

The safety factor in stress is not a solution for a structure which is dynamically loaded and has to be stiff enough to avoid resonances.

I can give you an example. Consider a cantilever beam with a mass at the free end. Statically the load will ne F=M*g and the stress at the root σ=F*L/W with W= b*h²/6 for a rectangular section. Mass + beam are a system with a spring constant C= 3*E*J/L^3

and an own frequency of fo=(0.5/π)*sqrt(C/M),end travel a= F/C

Dynamically a force is applied F1= Fo*sin (2*π*f1*t) is small enough so that the stress level does not reach yield limit. But f1 is near to fo, there is a resonance risk and the structure can be destroyed. Its stiffness has to be increased via a bigger J= W*h/2 but this decreases σ! Usually it is recommended to have a ratio fo/f1 around 3 for a safe system. Let say when the system was dimensioned it was made the choice for Cs=2 but the system is to weak and the stiffness has to be increased with a factor of 3 so that J1=3*J assuming same ration h/b geometrically the stress will decrease with 1/ 2.28 and you will obtain a safety factor "statically" of 4.56.

I hope this will help for a clearer image.

Regards.

Of course it will fail, by defintion of the term 'excessive'.

Mind, it also depends on your definition of 'fail'...
I'm currently building a Yew warbow of 130 pound draw weight at a draw of 32".
I currently have it back to 130# at 28" of draw... the bow has taken a little permanent bend...what us bowyers call 'set'.
Is this a failure?
It's obviously pushing the limits of the material, but the wood doesn't behave like a simple material and a longbow isn't covered by your physics books with equations for 'small angle of deflection'

I laugh in the face of small angles of deflection!

Will it make it back to 32"? I dunno... I won't be able to draw the sucker anyhow... my limit is about 100#.
Maybe I need to break out the hard hat before trying for those last 6" of draw?

Del

Is that cat math?

_{last 6" of draw}

'....Could that component fail....'

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You haven't specified so many things. Also your use of excessive elastic deformation is curious.

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I'll say yes a component could fail due to 'excessive elastic deformation'. A good example would be a shear pin, that fails to shear when appropriate and instead undergoes elastic deformation beyond expected/design, failing to allow separation.

The way you put it.

With that excessive elastic deformation IT WILL FAIL without doubt.