×
INTELLIGENT WORK FORUMS
FOR ENGINEERING PROFESSIONALS

Log In

Come Join Us!

Are you an
Engineering professional?
Join Eng-Tips Forums!
  • Talk With Other Members
  • Be Notified Of Responses
    To Your Posts
  • Keyword Search
  • One-Click Access To Your
    Favorite Forums
  • Automated Signatures
    On Your Posts
  • Best Of All, It's Free!
  • Students Click Here

*Eng-Tips's functionality depends on members receiving e-mail. By joining you are opting in to receive e-mail.

Posting Guidelines

Promoting, selling, recruiting, coursework and thesis posting is forbidden.

Students Click Here

Jobs

Nonlinear FEA with Von Misses Plasticity in 17-4 PH900 Stainless Steel

Nonlinear FEA with Von Misses Plasticity in 17-4 PH900 Stainless Steel

Nonlinear FEA with Von Misses Plasticity in 17-4 PH900 Stainless Steel

(OP)
Software: Cosmos Advanced Professional
Purpose:  To find the residual displacement of the tip.
Model: Plasticity Von Mises Model

Material: 17-4 PH900 Stainless Steel
Modulus of Elasticity: 28,500 ksi
Poisson's Ratio: .272
Density: .282 lbm/in^3
UTS: 210 ksi
.2% YS: 200 ksi

Approximate Stress Strain Curve:
TrueStrain    TrueStress (psi)
0.00700        200000
0.00779        204101
0.00858        207878
0.00936        211383
0.01015        214658
0.01094        217733
0.01173        220633
0.01251        223380
0.01330        225990
0.01409        228478
0.01488        230855
0.01566        233133
0.01645        235320
0.01724        237424
0.01803        239451
0.01881        241408
0.01960        243299
0.02039        245130
0.02118        246905
0.02196        248627
0.02275        250300
0.02354        251926
0.02433        253509
0.02511        255051
0.02590        256554
0.02669        258021
0.02748        259453
0.02826        260852
0.02905        262220
0.02984        263559
0.03063        264869
0.03141        266152
0.03220        267409
0.03299        268642
0.03378        269851
0.03456        271037
0.03535        272202
0.03614        273346
0.03693        274470
0.03771        275574
0.03850        276660
0.03929        277728
0.04008        278780
0.04086        279814
0.04165        280832
0.04244        281835
0.04323        282823
0.04401        283797
0.04480        284757
0.04559        285703
0.04638        286635
0.04716        287555
0.04795        288463
0.04874        289359
0.04953        290243
0.05031        291116
0.05110        291978
0.05189        292829
0.05268        293670
0.05346        294500
0.05425        295321
0.05504        296132
0.05583        296934
0.05661        297727
0.05740        298511
0.05819        299286
0.05898        300052
0.05976        300811
0.06055        301561
0.06134        302304
0.06213        303039
0.06291        303766
0.06370        304486
0.06449        305199
0.06528        305905
0.06606        306604
0.06685        307296
0.06764        307982
0.06843        308661
0.06921        309334
0.07000        310001


Loading Conditions:
8 pound load at the tip is loaded and unloaded.  The load is always vertical.  Symmetry condition.  Fixed at back end.  See picture below.


Questions:
1.  What are the difference between kinematic hardening and isotropic hardening? How does it affect the solution?
2.  What is the proper control to use of these: Incremental Load Control Method, Incremental Displacement Control Method or Incremental Arc-Length Control Method?
3.  Should I use large strain formulation along with large displacement formulation?  Should I leave one out?
4.  How do I troubleshoot when the model fails?

Currently I can't get the problem to solve with Incremental Load Control Method and the stress strain information above.  We have tested this on exact problem on an Instron machine but I cannot get Cosmos to solve.  I checked for buckling and it doesn't occur before yielding (load factor of 4). I am missing something. HELP!!!

-Jason Nicholson
 

RE: Nonlinear FEA with Von Misses Plasticity in 17-4 PH900 Stainless Steel

I do not know much about Cosmos any more, its been a long long time..

But I can say one thing, your figures do not quite match.
You give 0.2% YS at 200KSI do you mean 0.2% proof stress? Then you have the stress strain curve with 200ksi at 0.7% stress? Most FE packages like stuff to match up so if these numbers have been input then you might be confusing the solver.  

RE: Nonlinear FEA with Von Misses Plasticity in 17-4 PH900 Stainless Steel

Does this problem solve with linear-elastic properties ? You should do that first. Then I'd simplify the plasticity problem to a yield stress and post yield stiffness if Cosmos lets you do that. If this all works then in my experince its the input of the stress-strain curve that causes the problem (I have no experience of Cosmos by the way). The other thing to do is a simple cantilever with your material properties and take it post yield using a large strain formulation.

Hope this helps.

RE: Nonlinear FEA with Von Misses Plasticity in 17-4 PH900 Stainless Steel

Isotropic hardening is where the material yield surface changes uniformly in all drections. Kinematic hardening is used for cylic loading with a constant rate of hardening. A combination of the two is commonly used.  
I'm not sure what the difference is between large strain and large displacment methods so how you can leave one out I have no idea. Use large displacement if the displacements are expected to be significant enough to change the load distribution, ie. the rod bends to such an extent that the bending moment will alter with displacement. I'd leave it out if possible as it adds a further non-linearity into the problem.
If you're applying a point load then you'll have problems getting a solution directly under the load position. Try and smooth it out a little. The stress strain curve you have isn't so non-linear as to cause problems in my opinion.  

corus

RE: Nonlinear FEA with Von Misses Plasticity in 17-4 PH900 Stainless Steel

The picture is too large to see the whole thing.  You may want to "Red Flag" yourself and upload the file using the engineering.com attachment feature instead of embedding it into the post.

I thought isotropic hardening would only allow you to enter a post-yield modulus where kinematic hardening lets you put in the full stress-strain curve, but that may just be my software, which isn't COSMOS.

Looks like UTS should have been listed as 310ksi, but I think that is just a typo.

Like JordanLaw says, you need to run it through a linear analysis first and see how much displacement you get.  If it is large compared to the dimensions of the part, you need to use a LaGrangian technique (Large Displacement) formulation.  Not sure what a "Large Strain" Formulation is mathematically.

What error are you getting when the model fails?  You say you "can't get it to solve", but what error are you getting?

RE: Nonlinear FEA with Von Misses Plasticity in 17-4 PH900 Stainless Steel

I think you can think of isotropic and kinematic hardening as part of the constitutive law that describes the stress-strain behavior of the material; examples of constitutive laws are 'linear elasticity', 'elastic-plastic,' 'Mooney Rivlin rubber'. There are an infinite number, since many laws are merely curve fits of experimental data.

The decision to use isotropic or kinematic hardening (for a plastically deforming material) depends on which (isotr. or kinem.) appears to fit the data best. How could you find out? For aluminums and steels, one way might be to run a simple tension-compression test, one cycle--take a simple dogbone (ASTM standard) coupon, watch the stress-strain curve as you load the coupon up in tension until the stress-strain curve starts 'bends' over--the material can be said be deforming plastically or 'becomes plastic.' Then load in compression with the same load. Now the question is how to interpret what you observed? If the stress when the coupon becomes plastic is greater in tension than compression (that is, the magnitude of the stress when it goes plastic in tension is greater than the magnitude of the stress when it goes plastic in compression), then the material is undergoing kinematic hardening. In isotropic hardening material, you might see a couple of behaviors--perhaps this stress in compression when the curve starts to deviate from a straight line is the same as tension, but the slope of the stress-strain curve after this stress is higher than the corresponding tension side. When someone says "isotropic hardening is when the yield surface expands the same amount in all directions'--this increased slope in the stress strain curve corresponds to this expanding yield surface.

The 'isotropic vs. kinematic' hardening decision will have great influence on your finite element results. As a rule of thumb, isotropic hardening rules work very well for single loadings. Kinematic hardening is generally needed when you for multiple (or cyclic) loadings.

There is something called the 'Bauschinger effect' which is a kinematic hardening related term. That's probably a whole 'nuther thread, which I am not qualified to talk about, since I have little experience with the Bauschinger effect. If I am not mistaken, you can observe the Bauschinger effect with some materials that undergo kinematic hardening, or perhaps you don't observe it.

Please feel free to chime in to correct me. I am just getting started with this, so my understanding is perhaps more meager than the plasticity experts on this panel.

RE: Nonlinear FEA with Von Misses Plasticity in 17-4 PH900 Stainless Steel

To use large strain formulations in FE software, you're going to need a material constitutive relation that uses compatible stress-strain measures. If you've ever had a continuum mechanics class, you might recognize these terms for large strain measures: Eulerian, Cauchy, Almansi, Lagragian, Green, St. Venant. Similarly, you have corresponding stress measures: First Piola-Kirchoff, 2nd Piola-Kirchoff, and Cauchy. What's the difference between all of them? Coordinate systems! Are your strains (or deformation gradients) in terms of a global (spatial) coordinate system, in which the coordinate system is stationary, or are strains in terms of a material coordinate system, in which the coordinate system follows the deformation of the material? These strain and stress measures are valid for arbitrarily large strains and displacements.

The key here is what stress and strain measures does the constitutive law of your material use? If you have a Mooney Rivlin rubber, the strain energy is function of two parameters, and two deformation tensor invariants. Stresses are derivatives of this strain energy function relative to the various deformation tensor invariants. This is all quite complicated if you've never seen it before, but the bottom line is if you have large strains and displacements, you need to use a nonlinear material in your FE with the appropriate constitutive law. For instance, I used ADINA circa 1994, had my own constitutive law to use, but had to use a large strain measure that ADINA could give me--I had to program a Fortran subroutine that returned 2nd Piola-Kirchoff stress stress, given a Lagrange strain--these both used a material coordinate system, so were completely compatible (consistent? I forget the precise term for stress and strain measures that use the same coordinate system).

RE: Nonlinear FEA with Von Misses Plasticity in 17-4 PH900 Stainless Steel

1.  What are the difference between kinematic hardening and isotropic hardening? How does it affect the solution?
2.  What is the proper control to use of these: Incremental Load Control Method, Incremental Displacement Control Method or Incremental Arc-Length Control Method?
3.  Should I use large strain formulation along with large displacement formulation?  Should I leave one out?
4.  How do I troubleshoot when the model fails?

Jason
1. Use Isotrpoic hardening. Kinematic is used for cyclical loading. In your case both will give similar results.
2. Use incremental disp control. Whenever you are trying to find load-deflection curve in the non-linear range apply displacement. Load can decrease displacement cannot.
3. start out with small-strain and small-displacement. You dont need large disp formulation. A good example of large displacement is a "fishing rod" when displaced at the tip it has a very large curvature.
4. troubleshoot :?? change variables slightly to see the difference in answers. For example : loading direction, loading location....

Red Flag This Post

Please let us know here why this post is inappropriate. Reasons such as off-topic, duplicates, flames, illegal, vulgar, or students posting their homework.

Red Flag Submitted

Thank you for helping keep Eng-Tips Forums free from inappropriate posts.
The Eng-Tips staff will check this out and take appropriate action.

Reply To This Thread

Posting in the Eng-Tips forums is a member-only feature.

Click Here to join Eng-Tips and talk with other members!


Resources