Cyclic plasticity across micro/meso/macroscopic scales

In this paper, a multi-scale modelling methodology of cyclic plasticity is proposed, which is effective for quantitatively analysing the relationships among variables at three scales as opposed to two. This methodology takes meso-cells (inclusions) as a means of linking these variables at micro/meso/macroscopic scales and it is exemplified for dual-phase materials with layered microstructures. Size laws of the effects of microstructure on material behaviour are developed through the analysis of effects of dislocation pile-ups on both yield stress and plastic tangential modulus. It is found that Hall-Petch relationship is valid and, most importantly, that the kinematic hardening material parameters depend even more on the layer thickness. This is due to the fact that, for a thinner layer, more intensive concentrations of stress at the tip of dislocation pile-ups are produced than for a thicker layer, which results in a larger kinematic hardening and back stress. A systematic experimental study and microstructure characterization were carried out to determine the size effects on cyclic creep. A comparison of experimental cyclic curves with numerical results obtained by the present three-scale methodology and size laws shows agreement qualitatively and quantitatively. Several significant findings resulted. These findings offer additional knowledge of both material behaviour and failure mechanisms, proving the value of the proposed methodology and size laws.

[1]  Quanshui Zheng,et al.  An explicit and universally applicable estimate for the effective properties of multiphase composites which accounts for inclusion distribution , 2001 .

[2]  James F. Shackelford,et al.  Introduction to materials science for engineers , 1985 .

[3]  David L. McDowell,et al.  Cyclic plasticity at pores and inclusions in cast Al-Si alloys , 2003 .

[4]  Huseyin Sehitoglu,et al.  Modeling of cyclic ratchetting plasticity, part i: Development of constitutive relations , 1996 .

[5]  K. Valanis,et al.  Endochronic Analysis of Cyclic Elastoplastic Strain Fields in a Notched Plate , 1983 .

[6]  G. Langford.  Deformation of pearlite , 1977 .

[7]  X. Peng,et al.  A microstructure-based description for cyclic plasticity of pearlitic steel with experimental verification , 2002 .

[8]  David L. McDowell,et al.  Stress state dependence of cyclic ratchetting behavior of two rail steels , 1995 .

[9]  Huseyin Sehitoglu,et al.  Modeling of cyclic ratchetting plasticity, Part II: Comparison of model simulations with experiments , 1996 .

[10]  David L. McDowell,et al.  Computational micromechanics analysis of cyclic crack-tip behavior for microstructurally small cracks in dual-phase Al–Si alloys , 2001 .

[11]  George J. Weng,et al.  The overall elastoplastic stress-strain relations of dual-phase metals , 1990 .

[12]  K. Valanis,et al.  FUNDAMENTAL CONSEQUENCES OF A NEW INTRINSIC TIME MEASURE-PLASTICITY AS A LIMIT OF THE ENDOCHRONIC THEORY , 1980 .

[13]  Y. Chou,et al.  The role of dislocations in the flow stress grain size relationships , 1970 .

[14]  Peng Xianghe,et al.  A physically based constitutive description for nonproportional cyclic plasticity , 1991 .

[15]  André Zaoui,et al.  An extension of the self-consistent scheme to plastically-flowing polycrystals , 1978 .

[16]  David L. McDowell,et al.  An engineering model for propagation of small cracks in fatigue , 1997 .

[17]  J. Fan.  A Micro/Macroscopic Analysis for Cyclic Plasticity of Dual-Phase Materials , 1999 .

[18]  J. D. Eshelby,et al.  XLI. The equilibrium of linear arrays of dislocations. , 1951 .

[19]  P. Dawson,et al.  On the spatial arrangement of lattice orientations in hot-rolled multiphase titanium , 2001 .

[20]  N. Ohno,et al.  Kinematic hardening rules with critical state of dynamic recovery. I - Formulation and basic features for ratchetting behavior. II - Application to experiments of ratchetting behavior , 1993 .

[21]  Robert E. Rudd,et al.  Concurrent Coupling of Length Scales in Solid State Systems , 2000 .

[22]  G. Weng,et al.  The influence of inclusion shape on the overall elastoplastic behavior of a two-phase isotropic composite , 1991 .

[23]  K. Tanaka,et al.  Average stress in matrix and average elastic energy of materials with misfitting inclusions , 1973 .

[24]  E. Kröner.  Zur plastischen verformung des vielkristalls , 1961 .

[25]  Rodney Hill,et al.  Continuum micro-mechanics of elastoplastic polycrystals , 1965 .