Plastic Analysis vs. Satisfied Client 3

[trainguy]

Hi everyone.

I'm looking for some input on the usual approach taken by FEA professionals (which I "ain't&quot. I'm more a P/A + M/S type of guy. (and M/S is on a good day...)

Here's the dilemma:

Railcar stress analysis (of existing equipment)- linear static - showed very hot spots, i.e. Von-mises stress approx. 1.5 x Fy, locally.

The Spec. says no permanent deformation, which usually means, in our industry, no stresses over yield.

So we did an elasto-plastic analysis (non-linear material props, NE/Nastran) to show that after local yielding, the extent of yielded material is not large.

Another reason for pursuing this type of analysis, in our twisted minds, was to hopefully calculate residual plastic strain and compare it with 0.002. This can be used to confirm, on paper for our client, that the car meets the "it did not yield" Spec.

Any thoughts on what we should do with our results to satisfy the client?

Is it common practice to simply state what the total car shortening is after the load was removed (residual deformation)?

Once again, I hugely appreciate any input.

trainguy
(actual initials withheld in case my client realizes the true depth of my knowledge...)

 

[brad]

"Permanent set" measured in residual deflection, is commonly used in automotive.

Your approach to comparing with .2% yield is very reasonable, and is also used in automotive.

You haven't stated what the ultimate plastic strain was in your analysis. I have seen problems that were so localized that, upon introduce plasticity, one saw effectively no "plastic strain" based on the 0.2% yield assumption. I have justified and defended such analyses in the past.

However, I haven't seen the details of your analysis, and I don't know any of your approaches. I also am pretty much ignorant of railway design practices. While at the surface your approaches seem reasonable, I can't endorse them without a whole lot of details. (and please don't provide them--by "whole lot of details" I mean me much more than can be provided via this forum).

Brad

 

[corus]

Generally, 0.2% residual strain defines the yield stress of the material, however if you have previously had elastic stresses of 1.5Ys and now calculate residual plastic strains of less than 0.2%, I'd be suspicious. If you're inputting the stress-strain curve for the material then the turning point should reflect that true yield gives 0.2% plastic strain, ie. that the turning point of the curve is before the defined yield point of the material. If you're using a bilinear ideally plastic curve with the yield stress as the turning point then the 0.2% plastic strain calculated is really additional to the 0.2% strain defined by the material properties, I would have thought.
I would also consider in your analysis that for secondary stresses repeated loads can cause shakedown to occur and that the stresses will cycle in the elastic range after the first initial loads. Try running the analysis with the load apllied, removed, then re-applied to see if there is a difference in the reults for the third step.

 

[trainguy]

bradh,

Could you clarify your third paragraph (about ultimate plastic strain)? It seems I will need to do some justification and defence of my own.

Thanks again,
trainguy

 

[brad]

I meant "You haven't stated what the plastic strain was in your analysis" (ultimate merely referred to the final answer).

As corus suggests, you should also be pretty confident of your material curve.

If a steel has a 0.2% "yield strength" of 200MPa, one would expect a "true yield" (mechanics yield) lower than that--typically 5-10% lower than that. At a true stress of about 200MPa, one would see plastic strain of about 0.2%. If your curve utilizes 200MPa as "true yield", then you haven't actually modeled the material you are intending to, but rather a stronger material (hence a nonconservative assumption). I've seen this mistake made many times.

Brad

 

[trainguy]

As soon as the fine folks at NE/Nastran can inform me which of the 500 available output vectors I should get contour plots for, I will be able to nail down the actual plastic strain.

trainguy

 

[oso]

Hi, Bradh and corus:

This discussion is very helpful and I really appreciate you share your knowledge.

I am not a professional FEA analyst. However, my job involves making design decidion by using FEA analysis results. The company I am working for don't have non-linear analysis capability.

One thing I am doing is based on linear static analysis and judge by my knowledge that it's a local high stress or primary yield. I have been confirmed by experiment that local stress would not show any "permanent set".

In the mean time, my specifications quite often require that permanent deformation less than 4 mm (for example). I think non-linear analysis should be able to predict the permanent deformation amount by apply load and remove load. Is my thought correct?

I would appreciate very much if you could shed any light on this subject.

Thanks

Oso

 

[brad]

oso,
That is correct. Apply the load in one step, and unload it in the next. The total deflection at the end of this step is the permanent set. This is straightforward with a nonlinear code.
Brad

 

[corus]

You may find that the deformation is dominated by the elastic region around the plastic zone and no permanent deformation exists. You may also find, however, that the deformation grows with each load cycle, and thus although you may get less than 4mm on the first load you could get more than 4mm with successive loads (ratcheting). I'd try repeated cycles if you're not sure.

 

[oso]

corus:

Thanks for your post. I would agree with you and probably this kind of specification is not right in automotive industry. They should state very clearly that the permanent deformation is measured at the first time when extreme load is applied.

In addition, one interest question come to my mind. When material is yielded, stress hardening will occur. That means the yield stress has been increased when the second round over load is applied. This is the same reason why some pre-strained sheet material has very high yield stress.

This may bring another question: how should we evaluate stress in stamping or forging product. Stamping product all have been plastic deformed when the product is stamped. Actual yielded stress will be high than that stated in material manual.

Thanks.

Oso

 

[corus]

You're correct Oso, stress or strain hardening (I forget)does occur with yielding and this will be seen in FE results providing you don't use an ideally plastic stress-strain curve. From a design point of view it is better to use the material specificiation for the yield as you will always be sure from your analysis that stresses will not exceed yield even if that yield value does increase with successive loads. From that point of view the design will be safe from static loads. I would be concerned about residual plastic strains on fatigue though I'm not sure that design codes really consider this to my satisfaction.

I'm not sure of the automotive design criteria but I think the motive behind their thinking is to set a limit of yield on stresses, or more exactly, a limit of yield on primary stresses, which can be calculated in most cases by hand. For FE results this isn't so easy as they will throw up other stresses which can be classified differently from primary, and separating these components isn't straightforward. Design codes have yet to be written for 21st century methods, in my opinion.

 

[swainw]

Very interesting thread. I work in the aerospace industry and almost always we find the FEA von mises are high locally around mounting bolt holes where high stress concentrations exist. When we do plastic analysis of the area of interest, we are allowed to have local yeilding as the material minutely close (less than 1 inch away) to the stress concentration area prior to the onset was basically and usually underloaded and now takes up a bit of extra loading after the yield and subsequent material area reduction in the concentration area. Remember, the load you are calculating is probably a low percentage event that occurs only a fraction of the true cyclical loadings that the material should probably see over its life. If this is a common repeatitive load, I'd be worried that you've under designed the load area. In the first instance cited above though, we actually have to resort to hand calculations around the bolt hole to verify that we do not have a problem instead of relying on the FEA at this point.

Its still a little early in the morning here, but you may wish to review the modified Goodman rules, if my memory serves me correct.


If you have access to MIL-Handbook-5, this could be very comparable to the train and automotive rules, if not more restrictive.

Good Luck,
Bill

 

[brad]

corus and oso,
This approach IS common, at least in North American automotive. The rationale for this is twofold:
1) The loads are typically one-time (or very rare) peak loads such as potholes, curb impacts, etc.
2) The loads utilized are typically dynamic loads being addressed within a quasi-static analysis; hence they are more severe than reality.

The expectation is not that this is a regularly-occurring event. It is essentially a single case, and the engineering goals are:
1) The part survive the event intact;
2) There is a small enough amount of permanent set within the component(s) that functionality is not noticeably effected.

Brad

 

[oso]

corus:

Regarding your second paragraph, could you talk about it a little bit more?

It seems that any high stress except primary stress woundn't cause permanent set. Do you have any recommended reading or book talking about this topic?

I saw couple of post mentioned about ASME code. Is that a mainly Pressure Vessel design code?

How to separate priminary stress probably take some experience and also depends on the parts you are working on. Anybody have experience with plastic parts?

Thanks!

Oso

 

[swainw]

Oso,

Are you using the term primary stress as the same as principle stress where the stresses are resolved into directional coordinates within the body at any point where there are no shear stresses? If doing hand calculations, can't you get the principle stress, directions and strain from Mohr's circle, in three dimensions.

I am confused about your comment that only the primary stress can cause permanent deformation. Depending on the stress tensor, any stress in any direction that causes strain past the 2% offset with respect to the yielding onset would be permanent. I assume you may be refering to the "Maximum Principle STRESS Criterion" that states that yeilding begins at a point when the maximum principle stress reaches a value equal to the tensile yield stress, Y (also called Rankine's criterion).


However, since there are various yield criteria for multiaxial stress states and there is not one that can accurately predict yeilding for all materials. Depending on the loading in three dimensions, you could possibly have three dimensional yielding. From, "Advanced Mechanics of Materials": Boresi, Arthur, et al., "when a member is subjectedd to multiaxial state of stress in which a single stress component does not dominate, failure criteria must account for the multiaxial nature of the stress state".

A couple of other criterions to think about: Maximum principle STRAIN criterion or St. Venants; Strain Energy Density Criterion; Maximum shear stress (Tresca) criterion, ductile materials; and finaly Distortional Energy density (von Mises) Criterion. Esentially in the von Mises the criterion states that the total strain energy can be broken into two terms: volumetric change, and deformation change. The deformation change is related to G, the shear modulus of the material where G = E/[2(1 + v)], where v is the poisson's ratio. This would indicate that the principle stress is not the contributor to deformation, but shear stress.

If doing FEA, isn't the von Mises the main output of the software. Just to quote from again from the "Advanced Mechanics of Materials": "The Tresca and von Mises yield circle form a regular hexagon and circle, respectively, on the pi-plane. Representation of the Tresca and von Mises yield surfaces on th pi-plane is of ..fundamental importance to the theory of plasticty (which includes flow rules and hardeneing rules in addition to yield criteria)!!.... A statement about the Tresca criterion indicates that ductile materials deformation is mostly due to shear stress and not principle stress. This is supported by the fact that ductile materials have movement across the material's crystal lattice slip planes which is the result of permanet deformation.

I would suggest you review your basic engineering course work on principle axis of stress and strain and von Mises as well as the other criterion to ensure you have selected the correct criterion for yield onset. For instance the maximum principle strain criterion doesn't work very well with ductile materials, but may show better ability to predict fracture of brittle materials.

I hope we are not relying on FEA software to give us "the answer" as software still requires interpretive results and good boundry conditions and rules to follow from a qualified engineer to support the FEA outcome. As I mentioned in an earlier posting, for some localized areas we sometimes due better with a few hand calculations than problematic meshing and localized incongruities with the software's convergences especially in the plastic region.

I hope this isn't too much, just trying to get the thought process back into the basic theory to help you fimd a way to proceed.

Regards and good luck, I'd hope to hear about your results.
Bill

 

[Theanalyst]

Bill, that was a great post. I am a full time structural analyst and there are two rules that I follow: If the hardness of the part is in the HRC50 range, then I use the maximum principal stress to compare to the ultimate tensile stress of the material for brittle failure, and if the part does not really go through a hardening process, then I use Von Mises. Am I using the right approach? All I have been doing so far are linear static analyses. I'd like to get into non linear materials, and I would not know where to start...although I took some plasticity courses in college...I dont remember diddly squat.

Can you advice me of a good book or any online reading material that would help me get into plasticity, how to understand the non linear material properties and define them, and how to get into plasticity applied to FEA etc.. I would greatly appreciate any input from anyone in this regard. Thanks in advance, Sunny!

 

[swainw]

I haven't actually seen the book or the courses other than the advertisements, but the video's and handbooks look quite good about FEA from Algor;

http://www.algor.com.

They especially have dynamic loadings and plastic analyses well brought out for the FEA specialist, or any structural engineer for that matter.

Here is the link to their books and training material.

http://www.algor.com/news_pub/apd/default.asp

Looking at the cost, they do not appear to be that expensive for the education value that a couple of samples from the text that I've looked at before seems to indicate.

As to your specific question of are you doing it correct, I would hesitate to provide specific advise due to guiding principles for your specific field. In the Aerospace industry we have several MIL-specs that we use for guidelines. Also, my loading conditions are almost always dynamic and so I work mostly in the time frequency (PSD) of the loadings from an energy imparted into the structure point of view. We use a lot of different techniques to resolve some difficult load conditions and usually not one solution method is correct until verified through test.

The book that I mentioned in my previous submittal was my advanced mechanics class book. I always have found it to be a great reference to start a problem with, although I usually never end with the canned approach.

Regards,
Bill

Bill Swain
Ultra Electronics Precison Air Systems
Technical Coordination Manager-US Programs
swainw@asme.org