Constitutive Relations for the Nonelastic Deformation of Metals

Hart, Edward W.

doi:10.1115/1.3443368

Cited by 426 publications

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“…Withinthe 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.…”

Section: Introductionmentioning

confidence: 99%

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

Krempl

McMahon

Yao

1986

Mechanics of Materials

134

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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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Section: Introductionmentioning

confidence: 99%

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

Krempl

McMahon

Yao

1986

Mechanics of Materials

134

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“…In order to obtain creep rates from stress relaxation tests, a method that first was presented by Hart [26] and later also used by Woodford [27] have been used. During the TMF stress relaxation testing, the total strain is kept constant during the dwell time:…”

Section: Evaluation Of Creep Ratesmentioning

confidence: 99%

Creep and Stress Relaxation Anisotropy of a Single-Crystal Superalloy

Segersäll

Moverare

Leidermark

et al. 2014

Metall Mater Trans A

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In this study, the TMF stress relaxation and creep behavior at 1023 K and 1223 K (750°C and 950°C) have been investigated for a Ni-based single-crystal superalloy. Specimens with three different crystal orientations along their axes were tested; h001i, h011i, and h111i, respectively. A highly anisotropic behavior during TMF stress relaxation was found where the h111i direction significantly shows the worst properties of all directions. The TMF stress relaxation tests were performed in both tension and compression and the results indicate a clear tension/compression asymmetry for all directions where the greatest asymmetry was observed for the h001i direction at 1023 K (750°C); here the creep rate was ten times higher in compression than tension. This study also shows that TMF cycling seems to influence the creep rate during stress relaxation temporarily, but after some time it decreases again and adapts to the pre-unloading creep rate. Creep rates from the TMF stress relaxation tests are also compared to conventional constant load creep rates and a good agreement is found.

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“…Their unified theory described an approach that inelastic behavior of plasticity and viscoplasticity was not separated. M iller, (1976), Robinson et al (1976), Hart (1976), Krempl (1979) studied this theory, and Chaboche (1977) developed a viscoplastic constitutive model with nonlinear kinematic hardening, and Chaboche and Rousselier (1983) applied this model to the 316 stainless steel. Ellyin and Zia (1991) then used this viscoplasticity model for stainless steel 304 and 316.…”

Section: Introductionmentioning

confidence: 99%