In order to model steel material in finite element software, different types of hardening plasticity can be used. Using these methods lead to different response when the material undergoes cyclic loading. It seems the response would not differ if the material experience monotonic loading. How can it be described theoretically?
In other words, as it is known, the hardening rule determines when the material will yield again if the loading is continued or reversed. Hence, is it true to say “if the material does not experience reloading, hardening rule is not important.”?
I think this will only be true if the stress state is uniaxial - otherwise increasing the size of the von Mises cylinder is not the same as shifting it.
Hardening rule is important if the material undergoes plastic deformation (stress crosses the initial yield stress). As Martin rightly mentioned, isotropic hardening grows the yield size (keeping the origin/center unchanged) while kinematic hardening shifts the yield surface i.e. origin is changed (keeping the size same). When the material undergoes non proportional loading (or reverse loadings) then generally mixed isotropic kinematic hardening (or in some cases only kinematic hardening) must be taken into account. For monotonic loadings, generally, isotropic hardening suffice.
Dear Dr. Baeker, dear Dr. Niazi and dear Dr. Majidi,
Thank you for your responses.
Is there any reference which explains the path of stress-strain curve in both cases (i.e. when the yield size grows and when the yield surface shifts)?
I need to find the exact error between the stress-strain curves of the two mentioned cases when the material experiences yielding under monotonic load.
The theory s explained, for example, in our textbook
https://www.researchgate.net/publication/255723809_Mechanical_Behaviour_of_Engineering_Materials_Metals_Ceramics_Polymers_and_Composites_with_320_Figures_and_32_Tables?_sg=mkWk5im7XFHApaIuuGWTGRRqwAZE8kN-B8oGcHG9hu-5POS6ukJ14ZXfFr18ZD_e.jVOvOwYr-RLgyfbwSpp7wQ6uikfcttGqaWirBbQOC70O3mrXU_Jv30gpOrXeEPuB&_iepl%5BviewId%5D=p5uemCfk04T6mtR82CXYi4qP&_iepl%5BprofilePublicationItemVariant%5D=default&_iepl%5Bcontexts%5D%5B0%5D=prfpi&_iepl%5BtargetEntityId%5D=PB%3A255723809&_iepl%5BinteractionType%5D=publicationTitle
Book Mechanical Behaviour of Engineering Materials: Metals, Ceram...
Thank you again for your answers.
I employed both hardening rules in FE simulation of a high strength bolt which was previously tested under monotonic shear loading. As you mentioned, different hardening rules led to different responses. Comparing the numerical and experimental results showed that the material with kinematic hardening yields more reasonable results (related picture is attached). However, many references used isotropic hardening when material is subjected to monotonic load.
How can I justify this issue? Is it true to say “when material undergoes monotonic shear, kinematic hardening may lead to more accurate results”? Or using isotropic hardening in the case of monotonic loading is a requirement.
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