Pole Figure Inversion Using Finite Elements Over Rodrigues Space

Barton, Nathan R.; Boyce, Donald E.; Dawson, Paul R.

doi:10.1080/073033002100000182

Cited by 35 publications

(34 citation statements)

References 16 publications

(20 reference statements)

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“…As described in various other works (for example [30][31][32]44]) the use of finite elements over Rodrigues space has several attractive properties for working with ODFs. Treatment of crystal symmetries is straightforward, resulting in planar boundaries to the fundamental region.…”

Section: The Use Of Discrete Harmonics For Texture Evolutionmentioning

confidence: 99%

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The use of discrete harmonics in direct multi-scale embedding of polycrystal plasticity

Barton

Lebensohn

Boyce

2015

Computer Methods in Applied Mechanics and Engineering

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We describe an approach for directly embedding polycrystal plasticity models in component scale calculations, with an emphasis on computational tractability. Previously, we have employed adaptive sampling to mitigate the computational cost of direct embedding, achieving two or more orders of magnitude in wall-clock speedup compared to more traditional approaches. However, in our previous work the crystal orientation distribution function (crystallographic texture) was not allowed to evolve significantly. Here we discuss an approach that allows for evolving texture by employing discrete harmonics, effectively decoupling considerations related to accuracy of integrals in the homogenization from those related to adequate representation of the evolving texture. We discuss the basic behaviors and convergence of the new polycrystal plasticity framework. Specific applications focus on the deformation of titanium, including the effects of twinning. Overall, the discrete harmonic based framework offers an attractive path forward for computationally efficient multi-scale embedding of polycrystal plasticity.

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Section: The Use Of Discrete Harmonics For Texture Evolutionmentioning

confidence: 99%

“…6 shows the reconstructed pole figures from ODFs with discrete harmonic expansions to degree d pf = 6 and d pf = 9. The pole figures are constructed using operators based on path integrals through the finite element discretization of Rodrigues space [44,43,61]. As seen in Fig.…”

Section: Convergencementioning

confidence: 99%

The use of discrete harmonics in direct multi-scale embedding of polycrystal plasticity

Barton

Lebensohn

Boyce

2015

Computer Methods in Applied Mechanics and Engineering

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“…However, the tensor nature of the LSDF and the need to apply mechanics-based constraints to the inversion operation put additional emphasis on the representation of orientation space. A different finite element framework, which was originally used for texture evolution simulations [11] has been shown to be especially effective for the inversion of both SPFs and orientation density pole figures [12][13][14]. Fig.…”

Section: Determining Orientation-dependent Stress Tensorsmentioning

confidence: 99%

Understanding local deformation in metallic polycrystals using high energy X-rays and finite elements

Miller

Dawson

2014

Current Opinion in Solid State and Materials Science

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a b s t r a c tA methodology for understanding the stress and elastoplastic deformation responses within a loaded polycrystal is presented along with illustrative examples. High energy synchrotron X-rays are used to penetrate bulk metallic samples and produce diffracted intensity from each deforming crystal -revealing the evolving internal structure. A virtual representation of the microstructure is constructed using the finite element method (FEM) to simulate the evolution of the elastoplastic deformations, stress fields, and lattice orientations within the deforming crystals as the polycrystal is loaded. Simulations are compared directly to experimental diffraction data. In the case of powder experiments, lattice strain pole figures (SPFs) measured experimentally are compared to SPFs calculated by projecting X-rays through the finite element mesh. During in situ loading experiments, the stress states are found to differ from one crystal to the next and to vary from the stress being applied at the macroscale. A SPF/FEM-based methodology for quantifying residual stress fields within processed polycrystalline components is described. SPFs were measured at many points within a shrink-fit sample. Finite element discretizations of both the sample and orientation space of each diffraction volume were used to formulate an optimization for the distribution of the stress tensor within the sample. A different experiment, one in which the X-ray beam and the crystals are closer to the same size, is used to investigate the aggregate crystal by crystal. The Debye-Scherrer rings reduce to a set of spots associated with each crystal within the diffraction volume. This method is demonstrated by tracking deformation of four grains within a deforming BCC titanium aggregate loaded in situ within the elastic regime to determine the single crystal elastic moduli. Plastic deformation can also be investigated by monitoring the size and shape of individual diffraction spots. Each spot contains geometrically exact information regarding the internal structure of the crystal. Instead of reconstructing the crystal structure by inverting the diffraction data, virtual diffraction experiments are performed on the finite element mesh and the resulting simulated diffraction patterns are compared directly to the experimental results. Once the experimental/simulation methodology is validated, the approximation of the subgrain distribution of stress and lattice orientation from the finite element model can be used to construct theories for failure phenomena such as microcrack initiation. As opposed to other methods of discretizing a polycrystalline aggregate, the finite element framework enables a seamless transition to analyses associated with mechanical design.

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“…The Rodrigues' parametrization was chosen over pole figures or Euler angle spaces because of its several advantages, discussed in detail in Kumar and Dawson (1996). The conversion of ODF data in Rodrigues' space to conventional pole figure data is a relatively simple affair and is dealt in Barton et al (2002). In fact, if the initial texturing is known, and the re-orientation of the crystal orientations is computed during deformation, then the current mapping or the current Lagrangian ODF can be evaluated using Eq.…”

Section: Overview Of Microstructure In Polycrystalline Materialsmentioning

confidence: 99%

“…The reference fundamental region, the deformed fundamental region, corresponding Lagrangian ODF and the corresponding h1 1 0i pole figure (at plastic strain of about 10%) obtained from the simple shear test of fcc Al (Example 1). The pole figure is obtained using the approach described in Barton et al (2002). manner the performance and accuracy of the material point simulator.…”

Section: Example 1: Validation Of the Constitutive Model For Fcc Matementioning

confidence: 99%

Modeling the thermoelastic?viscoplastic response of polycrystals using a continuum representation over the orientation space

Ganapathysubramanian

Zabaras

2005

International Journal of Plasticity

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Pole Figure Inversion Using Finite Elements Over Rodrigues Space

Cited by 35 publications

References 16 publications

The use of discrete harmonics in direct multi-scale embedding of polycrystal plasticity

The use of discrete harmonics in direct multi-scale embedding of polycrystal plasticity

Understanding local deformation in metallic polycrystals using high energy X-rays and finite elements

Modeling the thermoelastic?viscoplastic response of polycrystals using a continuum representation over the orientation space

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