Hi Michael, Thanks. I have made some videos on Rainflow cycle counting now. It is good to catch up with an alum of UIUC Theoretical and Applied Mechanics.
Excellent content i can feel the passion trought the lesson. Just wath i was looking for undertsant what i am learning. Take care and keep uploading videos
@@mbarkey.mechanics hi again. I'm studying from fatigue of material book by surish I'm having a doubt. He talk on one part about cycle creep or ratcheting when the mean stress is different from 0 value. The question is, this is the same or similar behavior of Hardening or softening under cycle strain?
Not necessarily the same thing. The presence of the non-zero stress (or strain in strain controlled loading) beyond the yield causes an accumulation of plastic strains in mean strain direction, similar to advancing a screw happens in the linear direction by rotating it (thus ratcheting behavior). That said, the materials transient behavior such as hardening and softening can influence the ratcheting rate since the materials microstructure affects both issues.
@@mbarkey.mechanics I have another question. what happen with the bauschinger effect on a cyclic load with mean stress is different from 0 value ? i understan that if we have a difference of two time the yield stress the material will yield and have reverse plasticity, but i cant imagine what happend when the material reload (like on zero-tension-zero load or tension-tension load). My common sence say that the material will be on a higher yield point until stabilization (like in monotonic loading-unloading-reloading) is that correct? or im messing up concepts and bauschinger effect only applied with reversed loads?
To first order you can apply a uniaxial cyclic plasticity model with the Bauschinger effect and use Masing's hypothesis. But materials can do all sorts of variations on that basic concept, such as you have mentioned with cyclic softening or hardening, or multiaxial ratcheting. If you really need to know what your material does, you will have to test it.
Thank you, Professor Mark for these great set of lectures. Could you please let me know how these hysteresis loops are affected when the concepts of elastic and plastic shakedown are applied?
Hi professor Barkey great lecture, I have a doubt though, in some cases I've seen very similar relationships, but instead of stress and strain is Moment-rotation/curvature, how are those developed? Do you have any lecture on this topic ?
Hi Ing. Erick Osorio, moment/curvature/deflection is here: ua-cam.com/video/uSzgr8R2Z1Q/v-deo.html but I am not sure I would be able to make an parallels to Masing Hypothesis/cyclic stress strain curves but I can take a look. Take care!
@@mbarkey.mechanics yeah, I was basically asking what would be the procedure to construct a hysteresis loop but in terms of moment and curvature and not stress and strain. Regards
@@ing.erickosorio2887 Ah, I see. There are many nice cases in earthquake analysis for nonlinear bending behavior of beams, in which there would be hysteresis. I do not have any other information on that, but I've seen dissertations involved in that subject.
@@ing.erickosorio2887 I think any load term can be substituted for stress, and any deformation term (that includes some permanent set) can be substituted for strain to be able to develop hysteresis plots. Note however, this would lose some information--we use true stress in hysteresis plots, and the moment would be more like an engineering stress that is directly proportional to load. (There are also some stress equilibrium issues that may not be able to be accounted for with only using the moment at the location.) You would also want to be careful about the curvature term, as that is probably associated with the mid-plane. The maximum strains occur away from the mid-plane--at first thought, I am not sure how you would overcome that issue without just using the strain on the outer fiber, but there may be a way.
From what I understand, the curvature can be developed using the strain in the outer fiber, so that could be a way. Am I right? But using moment rotation, would be probably easier, what do you think? Thanks for your help professor Mark.
Hi Dr Mark, In FE we define the material behaviour with a uniaxial stress-strain curve that we get from the uniaxial cyclic/monotonic tests. However, the stress state in FE model is not uniaxial as the deviatoric stress. in similar way, when we have amultiaxial state of loading, do we need to modify the input stress-strain or not, please? if yes, how we modify the test data of stress-strain to simulate the case of combined loading.
Your FE code should take care of making the conversion from the uniaxial input into an equivalent stress-strain curve for use in general multiaxial loading. Now, you also need to to be aware of what assumptions and options you select--for example if the material is anisotropic, then you must also enter the coefficients of anisotropy. If you do not specify these, the default is to usually assume your material is isotropic. I have not gotten to that part in my class yet (so no video yet) but this is where the yield criterion and flow rule enter as well. If you have some time, I think you can find a good discussion in the ABAQUS user and theory manuals.
I am currently working on my thesis and this series has been of great help. Thank you dr. Barkley! I have a couple of questions on hysteresis loops. I seem to understand that since the cyclic curve can be expressed using a RO equation (K',n') then the loading and unloading reference points (edges) should be symmetric about zero. However, when modelling the loop (strain control) in excel, I notice that if for stress σ I have a strain ε then for stress -σ, the strain will not be -ε. This is backed up by the branch equations since they are simply RO equations with the start set at the reversal point . Am I doing something wrong? The K1 and n1 parameters I'm using for the branches are different from those i used in the cyclic curve itself (K',n'). Could this be the problem? All parameters were determined through experiments. Thank you very much, in advance for your help and in general for your contribution!!!
Yes, if you use the same parameters with the Massing hypothesis, the calculations will be (should be) symmetric. Experiments will not often give symmetric results though, due to a mean stress bias in strain control (tension first cycle or compression first cycle) and all kinds of other good reasons that materials don't really behave in the idealized way.
@@mbarkey.mechanics Thank you, I implemented Massing's hypothesis to the model and it did actually yield the results you're describing. If I may ask for some follow up questions, will the cyclic curve then be the one connecting the edges of the loops and therefore asymmetric or the theoretical one? And is it possible to get any information about the transient stages, by the shape of the cyclic stress-strain, the shape of the monotonic stress-strain and the shape of the hysteresis loops by comparing then with the one's suggested by Massing's hypothesis?
How you choose to model the plasticity depends on what your needs are--for example, to use this information to calculate fatigue life, only a coarse model is needed so you can usually get away with the symmetric type of model (because the scatter in variable amplitude fatigue life predictions are often large). But there are a lot of models out there, and they can be used for transient behavior, such as the behavior shown in the video, and I suspect for non-symmetric loops as well (search for papers on nitinol modelling). From a predictive use of a model, though, the trick is always how to model it in a meaningful way with as few parameters as necessary--and for those to be mechanism based where possible.
That information comes from a monotonic tension test. You would have to make too many assumptions about the material behavior to get that from cyclic data. Most researchers would conduct a tension test before starting a cyclic/fatigue testing effort.
start with the tip of the loop (epsilon, sigma) point and then calculate delta_epsilon for each delta_sigma from the tip to the ending point at various intervals using the hysteresis branch equation
Is "material memory" a term commonly used in literature to describe the phenomenon you're describing? Because I cannot seem to find many articles on that.. thank you
By definition, the primes are cyclic values. However, if you know your material neither cyclically hardens nor cyclically softens, and can assume a perfect Massing behavior, then they would be the same as the monotonic values. But that is not often the case for real materials.
@@mbarkey.mechanics yes i want to plot energy dissipation vs deformation. I did quasi static loading test on RC shear walls. I need to find energy dissipation of wall but i dont know the procedure
My recommendation is that you look in journals related to Civil Engineering, particularly those that deal with earthquake engineering and structures. You will find it.
Excellent illustration about the Bauschinger effect, Massing's hypothesis, and Hysteresis loop, etc.
Hi Michael, Thanks. I have made some videos on Rainflow cycle counting now. It is good to catch up with an alum of UIUC Theoretical and Applied Mechanics.
Excellent content i can feel the passion trought the lesson. Just wath i was looking for undertsant what i am learning. Take care and keep uploading videos
Thanks David, happy studies!
@@mbarkey.mechanics hi again. I'm studying from fatigue of material book by surish I'm having a doubt. He talk on one part about cycle creep or ratcheting when the mean stress is different from 0 value. The question is, this is the same or similar behavior of Hardening or softening under cycle strain?
Not necessarily the same thing. The presence of the non-zero stress (or strain in strain controlled loading) beyond the yield causes an accumulation of plastic strains in mean strain direction, similar to advancing a screw happens in the linear direction by rotating it (thus ratcheting behavior). That said, the materials transient behavior such as hardening and softening can influence the ratcheting rate since the materials microstructure affects both issues.
@@mbarkey.mechanics I have another question. what happen with the bauschinger effect on a cyclic load with mean stress is different from 0 value ? i understan that if we have a difference of two time the yield stress the material will yield and have reverse plasticity, but i cant imagine what happend when the material reload (like on zero-tension-zero load or tension-tension load). My common sence say that the material will be on a higher yield point until stabilization (like in monotonic loading-unloading-reloading) is that correct? or im messing up concepts and bauschinger effect only applied with reversed loads?
To first order you can apply a uniaxial cyclic plasticity model with the Bauschinger effect and use Masing's hypothesis. But materials can do all sorts of variations on that basic concept, such as you have mentioned with cyclic softening or hardening, or multiaxial ratcheting. If you really need to know what your material does, you will have to test it.
Thank you, Professor Mark for these great set of lectures. Could you please let me know how these hysteresis loops are affected when the concepts of elastic and plastic shakedown are applied?
Hi professor Barkey great lecture, I have a doubt though, in some cases I've seen very similar relationships, but instead of stress and strain is Moment-rotation/curvature, how are those developed? Do you have any lecture on this topic ?
Hi Ing. Erick Osorio, moment/curvature/deflection is here: ua-cam.com/video/uSzgr8R2Z1Q/v-deo.html but I am not sure I would be able to make an parallels to Masing Hypothesis/cyclic stress strain curves but I can take a look. Take care!
@@mbarkey.mechanics yeah, I was basically asking what would be the procedure to construct a hysteresis loop but in terms of moment and curvature and not stress and strain.
Regards
@@ing.erickosorio2887 Ah, I see. There are many nice cases in earthquake analysis for nonlinear bending behavior of beams, in which there would be hysteresis. I do not have any other information on that, but I've seen dissertations involved in that subject.
@@ing.erickosorio2887 I think any load term can be substituted for stress, and any deformation term (that includes some permanent set) can be substituted for strain to be able to develop hysteresis plots. Note however, this would lose some information--we use true stress in hysteresis plots, and the moment would be more like an engineering stress that is directly proportional to load. (There are also some stress equilibrium issues that may not be able to be accounted for with only using the moment at the location.) You would also want to be careful about the curvature term, as that is probably associated with the mid-plane. The maximum strains occur away from the mid-plane--at first thought, I am not sure how you would overcome that issue without just using the strain on the outer fiber, but there may be a way.
From what I understand, the curvature can be developed using the strain in the outer fiber, so that could be a way. Am I right? But using moment rotation, would be probably easier, what do you think? Thanks for your help professor Mark.
Hi Dr Mark,
In FE we define the material behaviour with a uniaxial stress-strain curve that we get from the uniaxial cyclic/monotonic tests. However, the stress state in FE model is not uniaxial as the deviatoric stress. in similar way, when we have amultiaxial state of loading, do we need to modify the input stress-strain or not, please? if yes, how we modify the test data of stress-strain to simulate the case of combined loading.
Your FE code should take care of making the conversion from the uniaxial input into an equivalent stress-strain curve for use in general multiaxial loading. Now, you also need to to be aware of what assumptions and options you select--for example if the material is anisotropic, then you must also enter the coefficients of anisotropy. If you do not specify these, the default is to usually assume your material is isotropic. I have not gotten to that part in my class yet (so no video yet) but this is where the yield criterion and flow rule enter as well. If you have some time, I think you can find a good discussion in the ABAQUS user and theory manuals.
Thanks ..its appreciated
I am currently working on my thesis and this series has been of great help. Thank you dr. Barkley! I have a couple of questions on hysteresis loops. I seem to understand that since the cyclic curve can be expressed using a RO equation (K',n') then the loading and unloading reference points (edges) should be symmetric about zero. However, when modelling the loop (strain control) in excel, I notice that if for stress σ I have a strain ε then for stress -σ, the strain will not be -ε. This is backed up by the branch equations since they are simply RO equations with the start set at the reversal point . Am I doing something wrong? The K1 and n1 parameters I'm using for the branches are different from those i used in the cyclic curve itself (K',n'). Could this be the problem? All parameters were determined through experiments. Thank you very much, in advance for your help and in general for your contribution!!!
Yes, if you use the same parameters with the Massing hypothesis, the calculations will be (should be) symmetric. Experiments will not often give symmetric results though, due to a mean stress bias in strain control (tension first cycle or compression first cycle) and all kinds of other good reasons that materials don't really behave in the idealized way.
@@mbarkey.mechanics Thank you, I implemented Massing's hypothesis to the model and it did actually yield the results you're describing. If I may ask for some follow up questions, will the cyclic curve then be the one connecting the edges of the loops and therefore asymmetric or the theoretical one? And is it possible to get any information about the transient stages, by the shape of the cyclic stress-strain, the shape of the monotonic stress-strain and the shape of the hysteresis loops by comparing then with the one's suggested by Massing's hypothesis?
How you choose to model the plasticity depends on what your needs are--for example, to use this information to calculate fatigue life, only a coarse model is needed so you can usually get away with the symmetric type of model (because the scatter in variable amplitude fatigue life predictions are often large). But there are a lot of models out there, and they can be used for transient behavior, such as the behavior shown in the video, and I suspect for non-symmetric loops as well (search for papers on nitinol modelling). From a predictive use of a model, though, the trick is always how to model it in a meaningful way with as few parameters as necessary--and for those to be mechanism based where possible.
@@mbarkey.mechanics I see. Once again thank you
Sir how to find initial stiffness and ultimate strength from hysterisis curve
That information comes from a monotonic tension test. You would have to make too many assumptions about the material behavior to get that from cyclic data. Most researchers would conduct a tension test before starting a cyclic/fatigue testing effort.
Please explain how to calculate intermediate points on the hysteresis loop
start with the tip of the loop (epsilon, sigma) point and then calculate delta_epsilon for each delta_sigma from the tip to the ending point at various intervals using the hysteresis branch equation
Is "material memory" a term commonly used in literature to describe the phenomenon you're describing? Because I cannot seem to find many articles on that.. thank you
you can look for the word "hysteresis"
is it possible to get 'n' Prime and 'K' prime values from monotonic curve ?
By definition, the primes are cyclic values. However, if you know your material neither cyclically hardens nor cyclically softens, and can assume a perfect Massing behavior, then they would be the same as the monotonic values. But that is not often the case for real materials.
how to find the Energy dissipation during cyclic loading
plastic energy dissipation per volume is the area enclosed by stress vs plastic strain hysteresis loop
yes sir but i have data of all cycles how to find out energy dissipation curve?
I am not exactly sure what you want to do, but perhaps you want to find the plastic energy dissipation for each cycle and plot it vs cycle number.
@@mbarkey.mechanics yes i want to plot energy dissipation vs deformation. I did quasi static loading test on RC shear walls. I need to find energy dissipation of wall but i dont know the procedure
My recommendation is that you look in journals related to Civil Engineering, particularly those that deal with earthquake engineering and structures. You will find it.