![]() Given the nominal stress and strain only (in case of tension specimen as you see in the charts above), how do we get corresponding true stress and true strain for tension specimen?Īssume incompressiblity during plastic deformation to get the deformed area. But each element will have a different damage state unless the deformation is homogeneous.ģ) We know that true stress involves area of the deformed specimen and nominal stress involves area of the undeformed specimen. The JC damage model can be used to decide when something will break. You can break your specimen in a finite element calculation only if you explictly specify when it breaks and what happens after that. The analysis terminates when your have reached your applied load. Whether this reflects the physical world is another question altogether.Ģ) Suppose we do not include the model for fracture then when will the analysis terminate? We mean there has to be limiting strain or limiting stress? If the displacement decreases so that the stress state goes back inside the surface, the plastic strain will remain constant. If the displacement increases monotonically (or is constant) and the stress state is on the yield surface, the plastic strain will increase. Non-linear finite element analyis of solids is usually displacement driven (see Chapter 6 of Belytschko et al, Nonlinear Finite Elements on how one such algorithm works and how the displacement increment is estimated from the applied load.) #HOW TO USE EXCEL SOLVER FUNCTION TO FIT A CONSTITUVE MODEL SERIES#We say above: When the stress state lies on the surface the material is said to have reached its yield point and the material is said to have become palsticĭoes that mean, if we plot the above cylinder on a graph, then calculate the principal stresses sigma_1,sigma_2,sigma_3 at a point in my structure ,then if we go to the cylinder plotted above and obtain on the graph the point corresponding to sigma_1,sgma_2,sigma_3 ,then, if this point is on the yield surface it indicates that the material has yielded and if inside the yield surface it means that material is elastic.ġ) Non-linear analysis involves a series of load increments- will the effective plastic strain be different at every load increment? Now, my question is that (in undestanding the above definition itself): When the stress state lies on the surface the material is said to have reached its yield point and the material is said to have become palstic (Reference: ) Von Mises yield surface is a circular cylinder of infinite length with its axis inclined at equal angles to the three principal stresses.Īlso, by the definition of the yield surface we can say that: The flow stress given by the Johnson-Cook model gives you a way of calculating S_y under various conditions.Ī very fundamental question from Von Mises yield surface (not going into Johnson Cooks model at the moment: ![]() The only way you can change the size of the cylinder is by changing the radius. The radius of the cylinder is S_y in your notation. If you take the square of both sides of the von Mises criterion you will notice that you get the equation of an infinite cylinder in 3D (the axes are the principal stresses). ![]() The Johnson-Cook model gives you a way of finding what the size of the yield surface is under different conditions. The material may also be rate dependent, in which case the surface has a different size at different strain rates. If there is strain hardening or thermal softening the size of the surface can change, allowing you to achieve larger stresses. However, the surface does does not have fixed dimensions except for perfect plasticity. The von Mises criterion is a yield condition which says that you cannot have stress states outside the surface defined by that criterion. ![]() Sorry oif the question is not mature / intelligent enough. What is the relation between Von Mises yield criteria and Johnson cooks constiitutive relation? Is the above constitutive relation as given by Johnson Cook an extension of Von Mises yield criteria (As satted above in this post of mine) in order to incorporate effect of strain rate and tem[perature? Where the first set of braclets gives the stress as a function of strain.The second set of brackets represents effect of strain rate and third effect of temperature. The Johnson cook model states that Von Mises flow stress is The von Mises yield criterion suggests that the yielding of materials begins when the second deviatoric stress invariant J2 reaches a critical value k Thank you very much for the response.Before starting my exercise, I just want to revisit my fundamentals so that my project is just not a mathematical jugglery!
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