Validation of the applicability of a creep model for directionally solidified eutectics with a lamellar microstructure

Albiez, J.; Sprenger, Ioannis; Weygand, D.; Heilmaier, Martin; Böhlke, Thomas

doi:10.1002/pamm.201610137

Cited by 1 publication

(3 citation statements)

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“…In Figure 9A, the creep curves for the simulations in the yz-plane are shown. The curve for the load in growth direction agrees well with the computational and experimental results reported by Albiez et al 80 Up to a load angle of 45 • , we observe an increase in the overall creep rate and a less pronounced softening behavior, that is, an increase of the creep rate at increasing strains. This signifies that, in case of aligned load and growth direction, a large amount of stress is carried by the creep resistant Cr(Mo) lamellae which in turn activates their softening behavior.…”

Section: Discussion Of the Effective Creep Behaviorsupporting

confidence: 91%

“…NiAl is assumed to behave perfectly plastic, that is,

τ^{F} = τ_{0}^{F}

. The material parameters and volume fractions for NiAl‐31Cr‐3Mo are taken from Albiez et al, cf. Table .…”

Section: Numerical Demonstrationsmentioning

confidence: 99%

“…Simulating such a creep loading is a challenging problem for the investigated solution schemes, as a load transfer from the softer NiAl to the more creep resistant Cr(Mo) occurs as a viscous effect after the initial loading, cf. Albiez et al Thus, the loading in the single phases is nonmonotone, especially in the first few load steps after the initial loading.…”

Section: Numerical Demonstrationsmentioning

confidence: 99%

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On Quasi‐Newton methods in fast Fourier transform‐based micromechanics

Wicht

Schneider

Böhlke

2019

Numerical Meth Engineering

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SUMMARY This work is devoted to investigating the computational power of Quasi‐Newton methods in the context of fast Fourier transform (FFT)‐based computational micromechanics. We revisit FFT‐based Newton‐Krylov solvers as well as modern Quasi‐Newton approaches such as the recently introduced Anderson accelerated basic scheme. In this context, we propose two algorithms based on the Broyden‐Fletcher‐Goldfarb‐Shanno (BFGS) method, one of the most powerful Quasi‐Newton schemes. To be specific, we use the BFGS update formula to approximate the global Hessian or, alternatively, the local material tangent stiffness. Both for Newton and Quasi‐Newton methods, a globalization technique is necessary to ensure global convergence. Specific to the FFT‐based context, we promote a Dong‐type line search, avoiding function evaluations altogether. Furthermore, we investigate the influence of the forcing term, that is, the accuracy for solving the linear system, on the overall performance of inexact (Quasi‐)Newton methods. This work concludes with numerical experiments, comparing the convergence characteristics and runtime of the proposed techniques for complex microstructures with nonlinear material behavior and finite as well as infinite material contrast.

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Section: Discussion Of the Effective Creep Behaviorsupporting

confidence: 91%

“…NiAl is assumed to behave perfectly plastic, that is,