Plastic Tension Failure

[aerohead56]

We are having an interesting debate here at our company. The debate stems from using linear FEM model stresses to predict failure of a material at Ftu. One side is arguing that the linear stress can be used to predict failure based on Ftu due to the example of an axially loaded bar. Obviously the stress in the bar is merely P/A, whether you are in the linear range or not. However, it can be argued that the part fails at a specific strain energy, not at a specific stress. Thus, until the integral stress/strain curve up to Ftu in deformation energy is achieved the part does not fail. This would mean that using a linear FEM model (or, even linear calculations) under-predicts the failure energy (since it is stiffer than a non-linear model above Fy) and thus the part still has some residual strength left before failure.

Any comments would be appreciated.

 

[Sparweb]

Others would phrase it more like: A material will "fracture" at a specific "strain". This definition applies to ductile materials capable of straining beyond the peak stress, having a Stress-strain curve with a peak and subsequent drop in stress at higher strains. Your first definition doesn't count that, while the other does so, tho not explicitly.

Strain energy can be calculated from the area under the Stress-strain curve, just like any function. If you stick to the linear part of the curve, the area is pretty small:

Stress*deflection/2

When you include the the plastic part of the curve, you get a big extra rectangular area added on.

But, energy may not be a part of the problem you are trying to solve. Energy is imparted through Work, hence:

F*d=E

If the applied force is dependent upon the deflection of the structure and vice-versa, then you run out of Work. Take, for example, a hydraulic ram that can exert 500 pounds, but can only extend 1 inch. It will do 500 inch-pounds of work. If it pushes on a cantilevered beam that can deflect 2" before reaching maximum strain, then the beam may plastically deform, but it won't fail, even if, in a static analysis, the beam couldn't hold a 500 pound load, anyway. If the 500 pounds kept being applied no matter how far the beam deflected, then it would fail.

A good explanation of fracture mechanics from the "big picture" point of view can be found in J.E. Gordon's books called "Structures (Why Things Don't Fall Down)" and "THE NEW SCIENCE OF STRONG MATERIALS". Gordon presents very detailed (and easily readable) discussions of fracture mechanics that the layman can understand and the engineer can use.



Steven Fahey, CET

 

[rb1957]

my 2c worth ...
a linear FE of a very simple structure (an axially loaded stick) would be reasonable, i think you could use the FE results (load or stress) and compare to Ftu. ... but then why use FE for such a simple problem ?

but a model that included bending loads/reactions probably wouldn't work (as linear FE doesn't include cozzone factors)

and a more complicated structure also wouldn't work, as you'd need to include plastic (ie large) deformations that would redistribute the loads between the element of the structure.

i'd answer the energy argument by saying that a linear FE probably can't calculate plastic strain energy, tho' i guess you could do some sort of fudge (like cozzone, and extrapolate the linear stress/strain curve (line?) up to Ftu and get an "elastic equivalent" failure energy) which should be similar to the linear FE results. ... which again should be as good as comparing the FE stress with Ftu

as for linear FE having stiffer elements, this is relevent at all stress levels (not just Ftu) and means that the FE is over-predicting stresses (as most elements these days are displacement-based).