Dislocation density informed eigenstrain based reduced order homogenization modeling: verification and application on a titanium alloy structure subjected to cyclic loading

Abstract

This manuscript presents a dislocation density informed eigenstrain based reduced order homogenization model (DD-EHM), and its application on a titanium alloy structure subjected to cyclic loading. The eigenstrain based reduced order homogenization (EHM) approach has been extended to account for the presence of HCP (primary α phase) and BCC (β phase) grains, within which the deformation process is modeled using a dislocation density based crystal plasticity formulation. DD-EHM has been thoroughly verified to assess the accuracy of the reduced order model in capturing local and global behavior compared with direct crystal plasticity finite element method simulations. A structural scale study of titanium alloy Ti-6242S is performed using DD-EHM to quantify and characterize the spatial distribution and evolution of the dislocation pile-ups subjected to cyclic loading. The evolution of pileups at two Modelling and Simulation in Materials Science and Engineering

A comparative study on fatigue indicator parameters for near‐α titanium alloys

“…Here, the p = 0.8 is chosen to obtain the relatively low dislocation debris density 49 for near-α titanium alloys from the TEM observations. 27 k κ 1 and k κ 2 are the dislocation generating coefficient and the annihilation coefficient due to dynamic recovery, respectively and their relationship have been reported in Liu et al 30 The evolution of reversible forest dislocations are expressed as a function of the local resolved shear stress where symbol {} is the Macaulay brackets. ρ κ 0 is the value of the total dislocation density at the point of load reversal, and b m is the dislocation density recombination coefficient taken to be 0.4 for HCP and BCC crystals.…”

“…Here, the reversible dislocation is accounted for now to describe the back stress in the strength hardening rule for capturing the Bauschinger effect, which shows good prediction of heterosis loop. 30 Intrinsically during load reversal, partial stored dislocation is erased and is independent of the dislocation structure formed by the irreversible forest dislocations. 49 To incorporate the intrinsic dislocation interaction during load reversal, the forest dislocation density are divided into two parts, that is, forward (irreversible) forest dislocation ρ κ fwd and reversible dislocation ρ κAE rev 30,49 :…”

“…Former works focused on the microstructure effect and uncertainty quantification of this FIP in the reduced order and multiscale framework. 30,32,34,83 Here, it is incorporated in the CPFE framework and studied against other FIPs and experimental observations. The proposed FIP is a function of the maximum dislocation density discrepancy computed at all grain boundaries within the near-α titanium alloy microstructure, which is noted as MD 3 .…”

“…Enlightened by experimental observations in TEM and associated discrete dislocation work showing a high density mismatch of dislocations at hard-soft grain boundary in near-α titanium alloys, 26,27 a new FIP was recently proposed based on the maximum dislocation density discrepancy among all grain pairs in near-α titanium alloys. 30 In addition to its physical basis, this FIP is well suited for implementation in reduced order and multiscale models to predict fatigue initiation at both microstructure and component scales, [30][31][32][33] as well as in uncertainty quantification associated with fatigue crack nucleation. 34 In this study, the new FIP solely based on dislocation density is first validated with experimental data and then compared with a number of existing FIPs within one CPFE framework aiming to test their predictive capability of fatigue crack nucleation over statistical volume elements (SVEs).…”

“…However, till now, dislocation density alone has not been directly linked to the fatigue crack nucleation in near‐ α titanium alloys. Enlightened by experimental observations in TEM and associated discrete dislocation work showing a high density mismatch of dislocations at hard–soft grain boundary in near‐ α titanium alloys, 26,27 a new FIP was recently proposed based on the maximum dislocation density discrepancy among all grain pairs in near‐ α titanium alloys 30 . In addition to its physical basis, this FIP is well suited for implementation in reduced order and multiscale models to predict fatigue initiation at both microstructure and component scales, 30–33 as well as in uncertainty quantification associated with fatigue crack nucleation 34 …”