General Mechanical

General Mechanical

Calculating alternating strain / strain amplitude / mean strain

    • maddes
      Subscriber

      Hey,


      I am doing a static structural analysis with ANSYS Workbench R19.0. This analysis contains 2 load steps. In my opinion there are nodes which change from a (main) load under tension [load step 1] to a (main) load under pressure [load step 2]. How can I calcute the mean strain and the strain amplitude / alternating strain between these 2 load steps? Is there a way to get the results automatically or do I have to calculate it by myself?


      It would be best to compare the resulting (alternating and mean) von Mises strains and principal strains. It is unknown whether the material can be described by von Mises strains or principal strains.


      ---


      I tried the following approaches to calculate the strain amplitude for one examplary node. It would be nice to get feedback. I dont know whether I am totally wrong, but here are my thoughts:



      • First I compared the von Mises strain in both load steps for one examplary node: As the von Mises strain only calculates an absolute strain, tension and pressure can not be distinguished. The von Mises strain is not changing much between both load steps (equivalent von Mises strain load step1=5%, load step2=6,5%). This is clear as it is a matter of the formula to calculate the von Mises strain, but in my mind it pretends a strain amplitude (1,5%) which is too small (I calculated: strain amplitude = v.M. strain load step 1 - v.M. strain load step2).

      • Then I compared the principal strains in this exemplary node:

        • load step 1: epel1= 5%, epel2= 1%, epel3= -4%

        • load step 2: epel1= 4%, epel2= 0,5%, epel3= -7%

        • As you can see the highest absolute value changes from 5% (load step1, epel1) to -7% (load step2, epel3). In my mind this is an evidence that the load is changing from tension to pressure. I found 2 hypotheses to calculate the equivalent principal strain, but I am not sure about the english names, so I just describe the hypotheses:

          • if the material is critical to principal stresses and you want to calculate the equivalent strain:

            • principal strain hypothesis 1:

            • equivalent strain= 1/(1+poissons ratio)*[ε1+poissons ratio/(1-2*poissons ratio)*{ε1+ε2+ε3}]. I am not sure: is ε1 the max strain (=4% in load step 2) or absolute max strain (= -7% in load step2). I think it should be -7 % if you look at a unidirectional case.

            • this would result in a equivalent strain(load step 1)= 8,56 % and a equivalent strain(load step 2)= -11,23% (alternatively -3,59 %). So I could calculate a strain amplitude of 8,56+11,23=19,79% (alternatively 8,56+3,59=12,18%). This sounds reasonable.



          • if the material is critical to principal strains and you want to calculate the equivalent strain:  


            • principal strain hypothesis 2:

            • equivalent strain= max(ε1, ε2, ε3)

            • this would result in a equivalent strain(load step 1)= 5 % and a equivalent strain(load step 2)= 4%. So I could calculate a strain amplitude of 5% - 4%= 1%. This sounds too small.








      Thanks in advance! Why are the results so different? I am excited to get to know about your thoughts.


      Regards,


      maddes

    • peteroznewman
      Subscriber

      Maddes, I like that you have focused on one node and I find this evidence the best for fatigue calculations:



      • load step 1: epel1= 5%, epel2= 1%, epel3= -4%

      • load step 2: epel1= 4%, epel2= 0,5%, epel3= -7%

      • As you can see the highest absolute value changes from 5% (load step1, epel1) to -7% (load step2, epel3).


      The strain range is 12% (5% to -7%) so the strain amplitude is 6% and the mean strain is -1%


      This is a conservative approach. I will be interested to hear what others may say.


      Regards,
      Peter


       

    • maddes
      Subscriber

      Hi Peter,


      thank you for your answer. I thought about your approach and I found one example where it could cause problems. If you keep load step 1 as I mentioned before and the load in the step 2 is changing a little bit, the following results could be calculated:



      • load step 1: epel1= 5%, epel2= 1%, epel3= -4%

      • load step 2: epel1= 4%, epel2= 1%, epel3= -4%


      In case the directions of the principal strains keep the same, the strain amplitude could be 1%. In the worst case, the direction of the principal strains are changing and the strain amplitude could be up to 9%. So there is a big difference in the results.


      Anyway there should be a way to calculate the von Mises strain amplitude. How do they do for steel constructions for example?


      How is the calculation done in "real" fatigue calculations?

    • peteroznewman
      Subscriber

      Hi Maddes,


      Yes, if the Principal directions don't move, then the true amplitude is small. That is why I said that for a conservative approach, you assume the worst. That way you predict the shortest life. The true life may well turn out to be longer, but you don't want to over predict the life and have an in-service failure which may be a safety issue.


      I read about signed von Mises as a way to characterize if the material point was in tension or compression, without regard to a principal direction.


      Real fatigue is done experimentally where the actual cycles to failure are counted and a large number of samples map out the mean and standard deviation for each load level.

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