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Combined Creep and Plasticity
 
  1. One can perform combined creep and plasticity analysis using ANSYS 5.5. The way to do that is defining the creep equation by table command TB, CREEP and plasticity by using commands TB, BISO or TB, MISO.
  2. So far we (ANSYS) haven't received or aware of incorrect results when combined creep and plasticity is used. However if you have an example for the contrary, please contact your ASD and file a bug report. Following that, we will investigate it.
  3. Both performance and functionality of creep have been addressed in the coming release 5.6. The improvements include:
    1. performance has been greatly improved,
    2. creep constant defined through TBDATA can now be temperature-dependent,
    3. a new command has been added to performance or bypass a creep analysis in a load step.
  4. ANSYS 5.5 does combination of creep and plasticity by superposition of creep and plasticity, since an explicit algorithm is used for integration of creep equation. However ANSYS has enforced a relative small ratio of creep strain rate to ensure the accuracy.
  5. In ANSYS 5.6, we have used an implicit algorithm for integration of creep equation so that combination of creep and plasticity is simultaneous. We believe this will provide more accurate results and improve performance.
  Posted by Guoyu Lin (ANSYS, Inc.) on 10.19.1999
 
Creep and Plasticity
 

Q: I have used a temperature dependent BISO table for my material, and activated the "Modified Rational Polynomial Creep Equation" of Table 2.4-6. Thank you for the feedback; I didn't realize that I should not use BKIN for the plastic deformation in this combined effects model.

A: Since you are using explicit creep, you *can* use BKIN or BISO. The choice will probably be dictated by cyclic loading applications (inclusion or omission of the Bauschinger effect).
As a side note, although isotropic hardening is also used for finite strain applications because of the expansion rather than shifting of the yield surface, I am not sure how suitable finite strain is with creep. I am not saying that BISO shouldn't be used with creep but, rather, that if the application involves finite (large) strains, I am not sure how valid the relationship would be by treatment of plastic (rate-independent and rate-dependent) in a decoupled fashion. Both explicit and implicit (5.6) creep handle plastic and creep strain terms independently, although they are evaluated at the (current) stress state. Unified theories try to treat all inelastic strains together in a coupled fashion, although I've come across so many different models (from customers) that it can get tricky to figure out which is most applicable (based on strain rates, temperatures, type of cyclic loading, etc.). Anyways, I bring this up simply because I don't know enough about it whether it is a concern or it but just wanted to point it out.
Since you are using 5.5, explicit creep is the only option available. (Implicit creep was introduced at 5.6) From your problem description, it does not seem like you are dealing with finite strain for the initial load, and it seems that you are looking at relaxation effects separately. So maybe the above paragraph was too much rambling, but I just wanted to point it out, anyway.

Q: I am using ANSYS 5.5 -- sounds like 5.6 would be better.

A: If your characteristic relaxation times are much shorter than the period of interest, implicit creep would definitely be much more efficient. To me, solving problems with explicit creep is really like solving it in 'real-time'. :)

Q: -- I don't understand why there is a comment on "creep constant defined through TBDATA" and its temperature dependence. I have a spatially varying temperature... is not creep within each element calculated with respect to that element's temperature? Is the built-in creep model that I am using (Table 2.5-6, ANSYS 5.5) appropriate for a spatially varying temperature in a structure during creep analysis? Does a spatially varying temperature in structure analysis of creep require a temperature dependent creep constant table as implemented in ANSYS 5.6 -- I hope not.

A: In 5.6, implicit creep includes the provision to include temperature-dependent constants. This means that temperature can be included in two ways:

  • usually, via the Arrhenius eqn which is the term w/ the activation energy: exp(-Q/RT). This is just like explicit creep, and it includes the temperature-dependency as part of the equation.
  • For implicit creep, all constants C1-Cx can also be temperature-dependent. This feature could've been included for a number of reasons, but I'm guessing that it has been included for more simple models (strain- or time-hardening terms only) which don't include the Arrhenius function but require temperature-dependency, such as a common equation of the form:
        d(ecr)/dt = C1 * sigma(C2) * epsilon(C3)
    where C1, C2, or C3 can be temperature-dependent since temperature is not explicitly included in the above equation.
As usual, I probably digressed too much, but in answer to your question, at 5.5, there is no temperature-dependent creep constants allowed. In 5.6, for implicit creep, you can include them, but you don't have to. It all depends on your creep equation and the material constants you have available.

Q: in 5.5, with explicit creep, the creep and plasticity are treated sequentially within each iteration, if you do them separately you can see the potential for inaccuracies if the time step is too large, this is one of the reasons why the crplim has to be small and explicit creep analysis takes so long
with implicit creep, the calculations are done simultaneously (within the same subroutine) which can partially explain the 20X+ solution speed increase that you see between using implicit vs explicit (for the same material law)

A: In a separate posting by Carlos (above), it seemed that it was implied that explicit creep is slower than implicit creep because of the treatment of the plastic strain (plastic and creep calculations done sequentially or simultaneously). I probably misread this or the intent of the author, but I don't believe this to be true. Even if rate-independent plasticity was not included in the calculations, if the time domain of interest is much longer than the characteristic relaxation times, the solution using the explicit creep method will take much longer than the implicit creep method (i.e., it doesn't matter if you include plasticity or not). This is because creep is defined by the strain rate d(ecr)/dt. How one determines this calculation (dt) can be either forward- or backward-Euler method. That time integration term is what tends to make explicit creep longer (what I referred to as solving the problem in 'real time') since forward-difference method is only conditionally stable (we're assuming the slope of the function is the same at time=t+dt and time=t, so dt has to be small for explicit creep).
The treatment of plastic and creep strain terms (calculations done sequentially or simutaneously) probably also affects the overall solution time, but not as much as the fact that explicit creep requires much smaller time steps. The treatment of the plastic and strain terms affect accuracy, however.

Anyways, as usual, feel free to correct any of my misinformation since I am known to spread them like wildfire. :) I am definitely not a material science person, so I often obtain this information off of the back of cereal boxes.

  Posted by Sheldon Imaoka (CSI) on 11.15.2000
 
Creep and Plasticity
  In addition to recent discussions on creep and plasticity, followings are a few of comments I would like to make:
  1. Why not BKIN with implicit creep?
    this is really a resource issue, since any combination of creep and plasticity is an independent work, as we now solve equations simultaneously. however, we are going to address this issue in the time frame of 5.7.?-5.8.
  2. Explicit creep and plasticity
    What we do here is we first do plasticity integration (here we use backward Euler integration), get stresses and plastic strains, and then we do creep strain calculation using the stresses obtained from plasticity. This is what we mean superposition. We don't go back and adjust the plastic strain and others. This is what we mean we don't adjust plastic strains in some places of the documents. As the nature of the algorithm, we need to restrict time increment to insure the accuracy and a stability of algorithm, however the trade off is then too time-consuming for a lot of applications.
  3. Explicit creep vs. implicit creep
    In general, explicit algorithm take advantage only when the inverse calculation of stiffness matrix is not needed or say modified Newton-Raphson algorithm is used. When plasticity is involved, the efficiency of MNR becomes questionable, by default we use full Newton-Raphson scheme. In this case, explicit integration algorithm for creep almost doesn't have any more advantage.
  4. Quite a few creep functions, such as the rational polynomial creep function in documented in 5.5 theory manual (table 2.5-6), are specific to certain materials under certain conditions. Therefore, the parameters as well as their dependency on temperature and stress are already built-in in ansys, for example, A, B, and epsilonmdot in table 2.5-6. So for these specific creep functions the temperature dependency is taking care inside ansys program. This is also one of reason that in 5.5 and earlier we don't have a temperature dependent creep data table like plasticity. For implicit creep equations in 5.6, we don't provide these functions for specific materials and conditions, instead you are now able to define creep equations at different temperatures.
  5. Unified creep approach (mentioned in Sheldon's post) is now available in 5.7, there one could combine creep with either isotropic plasticity (documented in 5.7) or bilinear kinematic plasticity (not documented in 5.7). Contact your ASD for requesting the detailed info.
  Posted by Guoyu Lin (ANSYS, Inc.) on 11.20.2000