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Two coupled,nonlinear differential equations are proposedfor the modelingof the elasticand rate (time)-dependent inelastic behavior of structural metalsin the absenceof recoveryand aging. The structure of the model is closeto the unifiedtheoriesbut containsessential differences.The properties of the modelare delineated by analytical meansand numericalexperiments.It is shownthat the model reproduces almostelasticregionsupon initialloadingand in the unloading regionsof the hysteresis loop. Under loading,unloadingand reloading in straincontrolthe model simulated the experimentally observedsharptransition fromnearly elasticto inelastic behavior. Theseproperties are essential for modelingmean stresseffectsin tenslon-tenslon straincycling. When a formulation akin to existingunifiedtheoriesis adoptedthe almost elasticregionsreduceto pointsand the transition upon reloading is very gradual.For differentformulations the behaviorundersuddenin(de)creases of the strainrate by two ordersof magnitudeis simulated by numerical experiments and differences are noted.The modelpresentlyrepresents cyclically neutralbehaviorand containsthreeconstants and two positive 3 decreasing functions.It is described how theseconstants and functions can be determinedfrom testsinvolving monotonic loadingwith strainrate changesand relaxation periods. INow at NASA,Houston, Texas. 25https://ntrs.nasa.gov/search.jsp?R=19850023219 2018-05-11T09:09:24+00:00Z INTRODUCTIONWithinthe last decadethe modelingof inelastic deformation through unifiedconstitutive equations has made conslderable progress [1][2][3][4][5][6]. Wlth the exception of [5],yieldsurfacesare not used in these approaches and creepand time independent plasticity are not considered separately.It is shownin [6]that theseconstitutive equations have similarmathematical structure but that they differwith regardto the specificchoicesof materialfunctions.The modelsmake the inelastic strainrate a functionof the effective stressdefinedas stressminussome quantityreferredto as kinematic stress,rest stressor back stress. In examining the mathematicalproperties of a flrst-order nonlinear differential constitutive equationit was shown [7] thatmakingthe inelastic strainrate solely dependent on the overstress givesqualitative solution properties of the differential equations foundin corresponding experiments.The overstress is the difference betweenthe stressand the equilibri_a stressand is equivalent to the effective stressmentionedabove.This approachhas beenverifiedfor monotonicloadingof Type 304 SS [8]and of a Ti alloy [9]. The purposeof the present paperis to presenta furtherdevelopment of the theoryof viscoplasticity basedon overstress for cyclicloading. It will be shown thatthis development is similarto the unifiedtheoriesbut contains essential modifications whichare necessaryfor reproducing regionsof nearlyelasticbehaviorand realistic reloading behavior. Thesepropertiesare basic for the modelingof mean stresseffectsin zero to maximumstrainstraincontrolled cycling. THEMAINPROPOSED MODEL DifferentialFo...

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