Primary and recency effects based on loading path in classical plasticity

Abstract

We have established an elastoplastic analysis model to explore the effect of loading path in an incompressible thin-walled tube under the combined action of axial force and torque based on Mises yield condition and isotropic linear hardening assumption. Further, four stress areas (σ_x, τ_x) are divided according to the characteristics of the final stress, and the plastic stress-strain relationship of twelve stress paths in different stress areas is derived. The “primary effect” of the stress path on plastic strain is demonstrated, namely, the plastic strain caused by the pre-loaded stress in path A (tensile stress is initially applied, followed by shear stress) is always greater than that caused by the post-loaded stress in path C (shear stress is initially applied, followed by tensile stress) irrespective of the value of final stress. The “recency effect” of the strain path on the stress is also established, which indicates that the stress caused by the post-loaded strain in path A is always greater than that caused by the pre-loaded strain in path C irrespective of the value of final strain. From the perspective of deformation, the “primary effect” of the stress path on the plastic strain and the “recency effect” of the strain path on the stress are unified. These effects are succinct and universal, and they provide useful insights on the plastic stress-strain relationship under different loading paths. Furthermore, they can serve as a useful reference for optimizing the processing technologies and construction procedures.

Keywords

isotropic linear hardening / stress path / strain path / primary effect / recency effect

References

[1] ZhanQ, YuZ. Comparison of the effects of primary effect and recency effect in different contexts [J]. Journal of Health Psychology, 2000, 8(3): 251-253(in Chinese)

[2] BaddeleyA D, HitchG. The recency effect: Implicit learning with explicit retrieval [J]. Memory & Cognition, 1993, 21(2): 146-155

[3] FolkeO, PerssonT, RickneJ. The primary effect: Preference votes and political promotions [J]. American Political Science Review, 2016, 110(3): 559-578

[4] LiZ, ZhouH, JiangY, HuD, ZhangC. Methodology for establishing comprehensive stress paths in rocks during hollow cylinder testing [J]. Rock Mechanics and Rock Engineering, 2019, 52(4): 1055-1074

[5] WangL, NiuC, ZhangB, MaY, YinS, XuX. Experimental study on mechanical properties of deep-buried soft rock under different stress paths [J]. Chinese Journal of Rock Mechanics and Engineering, 2019, 38(5): 973-981(in Chinese)

[6] LimA, OuC Y. Stress paths in deep excavations under undrained conditions and its influence on deformation analysis [J]. Tunnelling and Underground Space Technology, 2017, 63: 118-132

[7] WangJ, CaoW, JiangZ, ZhaoZ. Large-scale triaxial test study on deformation mechanical properties of soil-rock mixture under different stress paths [J]. Rock and Soil Mechanics, 2016, 37(2): 424-430(in Chinese)

[8] KawalkoJ, MuszkaK, GracaP, KwiecienM, SzymulaM, MarciszkoM, BalaP, BeyerleinI J. The effect of strain path changes on texture evolution and deformation behavior of Ti6Al4V subjected to accumulative angular drawing [J]. Materials Science and Engineering A, 2019, 764: 138168

[9] TangL, JiangF, TengJ, FuD, ZhangH. Strain path dependent evolutions of microstructure and texture in AZ80 magnesium alloy during hot deformation [J]. Journal of Alloys and Compounds, 2019, 806292-301

[10] BaiQ, YoungR. Numerical investigation of the mechanical and damage behaviors of veined gneiss during true-triaxial stress path loading by simulation of in situ conditions [J]. Rock Mechanics and Rock Engineering, 2020, 53(1): 133-151

[11] QiZ, XiaQ, QiC, QiuZ. Numerical simulation analysis of forming high strength steel sheet under different strain paths [J]. Forging Technology, 2013, 38(1): 35-39(in Chinese)

[12] LiD, ChenJ, ZhouY. Triaxial shear test and constitutive model of artificial frozen soil with complicated stress path [J]. China Coal Journal, 2016, 41(S2): 407-411(in Chinese)

[13] Taheri-BehroozF, KianiA. Numerical investigation of the macroscopic mechanical behavior of NiTi-Hybrid composites subjected to static load-unload-reload path [J]. Journal of Materials Engineering and Performance, 2017, 26(4): 1483-1493

[14] ZhuN, LiuC, ZhaoX, WangW. Experimental study on microstructure characteristics of K_(0) consolidated structural clay under different stress paths [J]. Rock and Soil Mechanics, 2020, 41(6): 1-12(in Chinese)

[15] GuoY, CaoL, HuoP. Study on the strength and microstructure of unsaturated polluted soil under two stress paths [J]. Journal of Applied Basics and Engineering Science, 2019, 27(3): 602-611(in Chinese)

[16] GuptaA, KhatirkarR K, KumarA, ThoolK, BibhanshuN, SuwasS. Microstructure and texture development in Ti-15V-3Cr-3Sn-3Al alloy—Possible role of strain path [J]. Materials Characterization, 2019, 156: 109884

[17] ChenJ, ChenG, WenJ. Multiaxial low cycle fatigue life prediction model considering strain paths [J]. Engineering Mechanics, 2012, 29(4): 84-89 in Chinese)

[18] EglyT A, LangK H, LöheD. Influence of phase shift and strain path on the thermomechanical fatigue behavior of CMSX-4 specimens [J]. International Journal of Fatigue, 2007, 30(2): 249-256

[19] ItohT, NakataT, SakaneM, OhnamiM. Nonproportional low cycle fatigue of 6061aluminum alloy under 14 strain paths [J]. European Structural Integrity Society, 1999, 2541-54

[20] QianJ, DuZ, LuX, GuX, HuangM. Effects of principal stress rotation on stress-strain behaviors of saturated clay under traffic-load-induced stress path [J]. Soils and Foundations, 2019, 59(1): 41-55

[21] SchwarzS, MauteK, RammE. Topology and shape optimization for elastoplastic structural response [J]. Computer Methods in Applied Mechanics and Engineering, 2001, 190(15–17): 2135-2155

[22] JanikM, DyjaH, BerskiS, BanaszekG. Two-dimensional thermomechanical analysis of continuous casting process [J]. Journal of Materials Processing Technology, 2004, 153–154: 578-582

[23] CermakM, KozubekT, SysalaS, ValdmanJ. A TFETI domain decomposition solver for elastoplastic problems [J]. Applied Mathematics and Computation, 2014, 231: 634-653

[24] ArtioliE, AuricchioF, BeiraoD V L. A novel ‘optimal’ exponential-based integration algorithm for von-Mises plasticity with linear hardening: Theoretical analysis on yield consistency, accuracy, convergence and numerical investigations [J]. International Journal for Numerical Methods in Engineering, 2006, 67(4): 449-498

[25] SzaboL. A semi-analytical integration method for J2 flow theory of plasticity with linear isotropic hardening [J]. Computer Methods in Applied Mechanics and Engineering, 2009, 198(27–29): 2151-2166

[26] SahinS, ToparliM, OzdemirI, SasakiS. Modelled and measured residual stresses in a bimaterial joint [J]. Journal of Materials Processing Technology, 2003, 132(1): 235-241

[27] ChenMElasticity and plasticity [M], 2007, Beijing, Science Press(in Chinese)

[28] XuB, LiuXApplied elastoplastic mechanics [M], 1995, Beijing, Tsinghua University Press(in Chinese)