iMechanica - failure - Comments

Re: what material is this?

Biswajit Banerjee — Sat, 19 Jul 2008 02:06:09 -0400

Linhua,

There is no attachment. Just the two images that you see in the post.

-- Biswajit

what material is this?

Lianhua Ma — Thu, 17 Jul 2008 00:53:42 -0400

I can not see the attachment, can you upload again?

Re: Puzzle - Ajit's guess

Biswajit Banerjee — Wed, 16 Jul 2008 22:55:53 -0400

Ajit,

You analysis is amost absolutely correct. The bottom picture doesn't have any glue on it - that's what the surface looks like just after it's cut (before joining). The ridges are gone in the failed specimen precisely because of dissolution. I took the photographs while testing a light microscope that can (supposedly) magnify to 40x. But given the vibrations in our lab only around 25x is possible.

I took the unfailed picture at a higher magnification to give you an indication of the material. What do you think it is?

-- Biswajit

Michael, You're spot on

Biswajit Banerjee — Wed, 16 Jul 2008 22:50:42 -0400

Michael,

You're spot on about the torsion bit. But I'll leave the experiment with ovine lactic fluid to you and then we can compare images on iMechanica.

-- Biswajit

Re: Oreo

Biswajit Banerjee — Wed, 16 Jul 2008 22:48:55 -0400

Chad,

I assure you that the next time it'll be an Oreo. That thought had never crossed my mind.

-- Biswajit

Re: Puzzle

Biswajit Banerjee — Wed, 16 Jul 2008 22:48:11 -0400

Mike,

I was hoping that some of the younger members of iMechanica would give it a shot before I provided more details.

The failed image has been magnified 6 times, the unfailed one 16 times (my mistake).

The joint is not a weld and the material is not a metal. The unfailed material does not have cracks - those are ridges generated during the cutting process.

-- Biswajit

Wow, Ajit's analysis is very good,I am inclined to accept it!

Mike Ciavarella — Wed, 16 Jul 2008 00:43:23 -0400

michele ciavarella
www.micheleciavarella.it

That seems reasonable.

Mike Graham — Tue, 15 Jul 2008 14:39:20 -0400

I think this is spot on. You can see telltale signs of the torsional failure of the bond between the alternating organic materials. My guess from the failure pattern is that the outer shell was twisted fast, causing a relatively clean failure of the binder. Perhaps this was some sort of preperation for a chemical treatment in a bath of ovine lactic fluid?

Re: Puzzle - My Guess

Ajit R. Jadhav — Tue, 15 Jul 2008 13:51:45 -0400

I will do as best as this flaky Drupal and Internet connection allow me to do.

I bet it's a polymer glue and that the failure occurred in torsion (of a rotating rod), sure, but that primarily this happened because the actual cross section failed short of the required strength in torsion.

In the top picture, the circles appearing in the grayish background are due to air entrapment or perhaps, even gas release during polymer setting. The whitish patches in the center is the glue material fractured suddenly in shear. However, it may carry inclusions like crud or dust particles. The glue in the bottom also shows sudden brittle mode fracture. The bottom picture shows the glue applied with a brush, just before the two parts are axially pressed together.

I would bet that the rod material itself was non-polymeric---otherwise, one would expect dissolution of surface layers, and no gas release of this nature.

A reasonable guess would be that either wood or ceramic or metal (likelihood in that order) rods were joined using a synthetic glue, e.g., two parts of the axis of a motor or a hairdrier or a turbine or so, and that the joint failed due to above reason.

-----

No mention of scale, material, whether it's a micro/meso/macro-graph, method of preparation of micrograph... And what else do you expect?

-----

I also felt initially that it could be fatigue. But, fatigue, it's not. There are no progressions characteristics of beach marks. Plus, typically, fatigue cracks grow from only one dominant point on the circumference. Here, the top picture shows a lot of shear walls. So, sure, it's a sudden and brittle failure. But not involving fatigue even in its history. (Plus, the top bubbles are not stretched in one direction, and are too big. So, they can't be dimples. They have to be gas bubbles. My best guess is air entrapment during mixing of the base and the hardner.

Up to you, Biswajit.

My guess is that it's an Oreo.

Chad Landis — Tue, 15 Jul 2008 10:08:11 -0400

Not even close huh?

for sure failure under torsion --- but

Mike Ciavarella — Tue, 15 Jul 2008 08:51:40 -0400

but I am unsure about fatigue, I do not see clearly beach marks

plus what are these buttered circles? corrosion?

tell us more about it. What do you mean joint? Which type of joining? Welding?

Also what are the scales, they seem different in the two pictures?

What is the material -- looks a metal. Why the second 'unfailed' seems neverthless to have cracks?

Many more details for a reasonable descprition are needed to raise the case!

Thanks

Konstantin Volokh — Wed, 14 Mar 2007 09:25:34 -0400

Thanks, though I did not understand much in your post. Probably, you can be more specific about my very specific points.

Kind regards,

Kosta

Stress analysis, Griffith's theory, and the related points

Ajit R. Jadhav — Wed, 14 Mar 2007 08:20:52 -0400

I have a few points to make--some very obvious.

1. Size does matter--Griffith or no Griffith.

Consider the following simplest example. Take a plate having its center at the origin. Apply compressive loading via two point-forces, say, -100j at the point (0,10) and +100j N at the point (0,-10), where 'j' denotes the unit vector along the y-axis.

(a) Compute/Calculate the stress field for an infinite plate.

(b) Then, assume finite dimensions for the plate, say, 100 units square, and compute the solution again.

The stress fields in situations (a) and (b) are inherently different, whether:
(i) the loading is singular or not (i.e. involves point forces or not),
(ii) we are able to give analytic solutions for the stress field or not and
(iii) our numerical solution method gives proper results at the free boundaries, surfaces and edges, or not.

The stress field in (b) becomes different from that in (a) because:
(i) normal stresses can only be zero at the free surfaces/edges, and
(ii) the effect of each boundary theoretically reaches to infinite lengths.

Note, the predicted difference in (a) and (b) is exclusively based on the premises of the classical stress analysis theory.

As an aside, also note, St. Venant's principle only states what happens in the limiting scenario. But there is also an opposite aspect to it. Domain connectivity necessarily implies a modulation of the field everywhere within the domain.

Further also note, FEM is inherently wrong inasmuch as it predicts nonzero normal stresses at free surfaces. Thus, any FE analysis for (b) would have to be taken with a pinch of salt.

2. About the unboundedness increase in the critical failure stress with the decreasing defect size.

But why isolate Griffith alone here?

Why not include the whole field of elasticity? (Indeed, also all other branches of stress analysis?) After all, the same criticism would apply equally well to the simple linear stress-strain relationship too, out of the reason that this line terminates so suddenly at the yield/failure point.

Griffith's specific insight is to acknowledge the existence of the surface energy--something that didn't occur to any mechanician before him because apparently they all thought that only liquids had surface energy, not solids. To them, creation of a crack surface would take nothing, provided enough of a stress was created. To correct this misconception is Griffith's primary achievement. The fact that he could also quantitatively predict the overall failure loads for glass fibers is almost secondary in importance. The fact that the quantitative model he employed is essentially hybrid--Inglis' stress analysis thrown awkwarldy together with energetics--is of almost no consequence or significance in comparison.

Griffith's basic insight has by now been well-justified by those QM-based descriptions. We have already seen ample simulations that our "intuitions" too have become better developed. Really, wouldn't one expect that the ionic cores got ever so slightly shifted from their regular positions and that the electron cloud suffered some local density changes, whenever a free boundary/surface was introduced into an otherwise infinite lattice? Isn't this what you would "naturally" expect?

From another point of view, this issue actually is a "killer-app" for the QM-based theories of solid state physics. They should seize this opportunity to compute the surface energy due to the finite size of the stressed objects (I mean, in case they haven't, already!) and develop further along these lines.

3. Overall, Volokh's basic point seems to be that the very concept of stress at a point does not include the effects due to surface. To remedy this, apparently, he would like to distribute the effects due to the finitude or surfaces right inside each and every infinitesimal element all through the domain volume.

Now, by itself, this can be quite valuable. In fact, this is what many approaches such as the continuum damage mechanics have attempted to do in the past. Research proposals like these are welcome as descriptions of certain *particular* type of material behavior. Volokh's particular theory in the above paper is valuable from this angle.

But when this or such schemes are stretched too far and proposed as fundamental descriptions of the mechanics of solids, then the proposals must face some tough questions: Why include only the cavitation-related phenomena--say, as in the quasi-static contexts? Why not include impact-related behavior right in that infinitesimal element? Can you include the entire range for such behavior? How about the shock-related behavior? And the ductile-to-brittle transition with cooler temperature? The fatigue-related behavior? And, how about hysteresis and dissipation--in each and every one of the aforementioned phenomena? ... So on and so forth...

If the very definition of stress attempted to incorporate all such effects, the theory would become hopelessly complicated. Proper epistemology includes paying respect to the crow-principle. For further details, please see the American philosopher Ayn Rand's book: "An Introduction to the Objectivist Epistemology." Incidentally, I first read this book in 1981, and so, in a sense, there is nothing new to this point either! Yet, I think crow-epistemology is a relevant point here. Fundamentally, that's only how one could say that the continuum theoretical definition of stress (whether Cauchy's or Kirchhoff and Piola's) ought to be kept intact.

Here are the problems with Griffith

Konstantin Volokh — Wed, 14 Mar 2007 00:34:21 -0400

1. If the failure process is controlled by stresses/strains at the edge of the void then the critical load should not depend on the void size for small voids because the stresses/strains at the edge of the void do not depend on the void size for small voids. This simple physical notion is not in peace with Griffith.

2. In my opinion, the Griffith prediction of the unbounded increase of the critical failure load with the decrease of the defect size is unphysical.

3. Griffith solves the problem in two steps. He finds stresses/strains at the first step and considers the failure criterion at the second step. Griffith is inconsistent because he ignores the surface energy at the first step and he includes the surface energy at the second step. If the surface energy is important it should be a part of stress analysis - the first step. If the surface energy is not important in stress analysis why should we include it in the failure criterion?

size-independent or dependent?

Rui Huang — Tue, 13 Mar 2007 19:17:40 -0400

Hi Kosta:

I don't really agree with your point in this paper. First, the conclusion from the Griffith energy method, i.e., the critical tension tends to infinity when the cavity radius approaches zero is not necessarily meaningless. Without any defects (cavity or crack), the material does not fail. The failure analysis (Griffith and yours) is based on the assumption that defects pre-exist. Larger defects give lower failure stress, and smaller defects give higher failure stress. I don't see why this critical stress has to be length independent. In fact, one of the reasons that Griffith approach is so successful is the prediction for size-dependent fracture strength: thin glass fibers fail at a much higher stress than thick glass rod. This is indeed one of the puzzles Griffith wanted to resovlve at his time.

Second, you criticized the introduction of a characteristic length due to surface energy. I don't see what is wrong with it. Yes, it is not in peace with the length-independent classical continuum mechanics. So what? The physical world is length dependent. Size matters!

Finally, the Griffith approach has its base in the principle of thermodynamics. It applies to cracks, voids, and many other problems. It is simple (to some of us), but more importantly, it has a solid foundation. So far I don't see any controversy.