Viscoplasticity based on overstress with a differential growth law for the equilibrium stress

Abstract

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...

A large strain hyperelastic viscoelastic-viscoplastic-damage constitutive model based on a multi-mechanism non-local damage continuum for amorphous glassy polymers

“…Most of them were initially used for metals and then extended to polymers. In this category, the Perzyna viscoplasticity theory (Perzyna, 1971) can be used to model the rate-dependent behavior of polymers as demonstrated by Van Der Sluis et al (2001); Kim and Muliana (2010); Abu Al-Rub et al (2015); the viscoplastic theory based on the overstress (VBO) concept (Krempl et al, 1986) can be considered for polymers as shown by Colak (2005); the Bodner and Partom viscoplastic model (Bodner and Partom, 1975) can be applied to polymers as also shown by Frank and Brockman (2001); Zaïri et al (2008). The complex behavior of polymers can thus be captured using a viscoelastic-viscoplastic constitutive model with a robust integration algorithm to be implemented in finite element codes (Miled et al, 2011) by combining a viscoelastic constitutive model with a phenomenological-based viscoplastic one.…”

High Temperature Advanced Structural Composites. Volume 3. Mechanics

“…It differs slightly from the formulation given by Krempl et al [1986] and these differences are delineated in the Appendix and in the Appendix of Lee & Krempl [1988].…”

“…To compare the growth la' 'or tht ,.quilibrium stress in the present theory with one in [Krempl et al, 1986], the t'…”

A mathematical representation of the multiaxial Bauschinger effect

“…etc. Many other unified cyclic viscoplastic theories were also under development in the same period, using similar concepts, attempting to reconcile cyclic plasticity and creep flow (e.g., refs [42][43][44][45][46]. One advantage of my own approach, mainly based on the very simple structure of the A-F rule, was that it was simple to integrate in closed form (for proportional cyclic conditions) and easily incorporated in a more fundamental thermodynamic framework.…”