A numerical procedure enabling accurate descriptions of strain rate-sensitive flow of polycrystals within crystal visco-plasticity theory

Abstract

The plastic deformation of polycrystalline metals is carried by the motion of dislocations on specific crystallographic glide planes. According to the thermodynamics theory of slip, in the regime of strain rates, roughly from 10 -5 /s to 10 5 /s, dislocation motion is thermally activated. Dislocations must overcome barriers in order to move, and this concept defines critical activation stresses on a slip system s that evolve as a function of strain rate and temperature. The fundamental flow rule in crystal visco-plasticity theory that involves in order to activate slip has a power-law form:. This form is desirable because it provides uniqueness of solution for the active slip systems that accommodate an imposed strain rate; however, it also introduces astrain rate dependence, which in order to represent the actual behavior of polycrystalline materials deforming in relevant conditions of temperature and strainrate usually needs to be describedby a high value of the exponent n. However, since until now the highest value of n was limited by numerical tractability, the use of the power-law flow rule frequently introduced an artificially high rate-sensitivity.All prior efforts tocorrect thisextraneous rate sensitivity have only lessened its effect and unfortunatelyalso at the expense of substantial increases in computation time. To this day, a solutionfor the power-law exponent reflecting true material behavior is still sought. This article provides a novel method enablingthe use of realistic material strain rate-sensitivity exponents to be used within the crystal vico-plasticity theory without increasing computation time involved in polycrystal simulations. Calculations are performed for polycrystalline pure Cu and excellent agreement with experimental measurement is demonstrated.

Multiscale Modeling of Microstructure‐Property Relationships of Polycrystalline Metals during Thermo‐Mechanical Deformation

“…The first example found in Figure a, is Cu tested under different strain rates. The parameters that provided this good agreement have been reported in ref . A second example considers Haynes 25.…”

“…Comparison of measured (solid lines) and simulated (dashed lines) true stress–true strain responses for: a) pure Cu in compression at room temperature and strain rates as indicated in the plot Reproduced with permission, 2017, Elsevier, b) Haynes 25 in compression along the extrusion direction and at the temperate and strain rate indicated in the plots Reproduced with permission, 2017, Elsevier, c) AA6022‐T4 during monotonic tension to failure and several tension‐compression cycles along RD each followed by tension to failure at room temperature and 0.001 s −1 strain rate, and d) IN718 during monotonic tension to failure (the shorter curve) and compression and multiple tension‐compression cycles pre‐strained in tension to 0.01, 0.02, 0.03, and 0.04 strains and then pulled to failure at room temperature and 0.001 s −1 strain rate Reproduced with permission, 2017, Elsevier.…”

Towards Manufacturing of Ultrafine-Laminated Structures in Metallic Tubes by Accumulative Extrusion Bonding

“…Many material combinations have been reported as bonded using accumulative roll bonding (ARB) such as Cu/Ti [5], Al/Cu [6], Al/Zn [7], Mg/Al [8], Cu/Zn/Al [9], Cu/Zn [10], Zr/Nb [11,12], Mg/Nb [13,14] and Zn/Sn [15] in plate form. When the layering is pushed to the ultrafine micron, or ultimately nanometer scale, the multilayered bimetallic material exhibits significantly improved strength [16][17][18][19][20][21][22][23][24], thermal stability [25,26], resistance to shock damage [27], and resistance to radiation damage [28,29]. Beyond this, the authors of [30] summarize the history of laminated metal composites and other benefits of bimetallic materials, such as improved fracture resistance, delayed fatigue crack growth, and ballistic energy absorption.…”

The concept of control points in hybrid discontinuous Galerkin methods—Application to geometrically nonlinear crystal plasticity

“…This issue makes the convergence of the nonlinear equations more complex using the Newton scheme. Therefore, the enhancement of the power law material subroutine for crystals with high sensitivity exponents (nearly rate‐independent materials) has been recently investigated in order to improve solving the nonlinear system of equations() that will be extended in this work.…”