A New Approach to More Realistic Rolling Texture Simulation

Engler, Olaf

doi:10.1002/1527-2648(200204)4:4<181::aid-adem181>3.0.co;2-3

Cited by 17 publications

(19 citation statements)

References 21 publications

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“…They also show that the D c in each crystal have approximately the same spherical component trðD c Þ % trðDÞ. Engler (2002) and Ma et al (2004) show that varying the D c according to a normal distribution in a meanfield polycrystal plasticity model provides an improved description of the polycrystal behavior. We presume that this improvement is because varying the D c according to a normal distribution statistically mimics the effects of the crystal interactions.…”

Section: Stochastic Polycrystal Plasticity Methodsmentioning

confidence: 99%

“…We presume that this improvement is because varying the D c according to a normal distribution statistically mimics the effects of the crystal interactions. In this section, we build on the work of Engler (2002) and Ma et al (2004) to develop two methods that approximate the L c with stochastic variation, the stochastic Taylor model and the stochastic no-constraints model. For both stochastic methods we treat the deviatoric component of the crystal strain rate D c in each crystal as a normally distributed random tensor D c0 while the spherical component is equal to the spherical component of D as indicated by the CPFEM results, i.e.…”

Section: Stochastic Polycrystal Plasticity Methodsmentioning

confidence: 99%

“…In Engler (2002) and Ma et al (2004), CPFEM results motivate the application of stochastic variations of L to obtain L c . Indeed, Sarma and Dawson (1996) found that the components of the crystal strain rates D c ¼ 1 2 ðL c þ L cT Þ predicted by the CPFEM follow a normal distribution with mean approximately equal to their aggregate macroscale counterpart, i.e.…”

Section: Introductionmentioning

confidence: 96%

“…Indeed, Sarma and Dawson (1996) found that the components of the crystal strain rates D c ¼ 1 2 ðL c þ L cT Þ predicted by the CPFEM follow a normal distribution with mean approximately equal to their aggregate macroscale counterpart, i.e. l D c ¼ D. Using this information, Engler (2002) presents the stochastic GIA (SGIA) model in which the D c obtained from the GIA model are randomly perturbed according to a normal distribution, resulting in more accurate results. Ma et al (2004) modify the FCM so that the D c are selected from a normal distribution with mean equal to D. This model appears to give more accurate texture predictions than the FCM with little increase in computational cost.…”

Section: Introductionmentioning

confidence: 99%

“…The methods define the covariance tensors similarly, but in the STM the mean tensors are equal to D 0 while in the SNCM the mean tensors are determined by scaling values of D c0 calculated using the NCM. Effectively, the SNCM is complementary to the SGIA model (Engler, 2002). Finally, in Section 4 we perform calibration and validation of the STM and SNCM using data from compression experiments of tantalum specimens.…”

Section: Introductionmentioning

confidence: 99%

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Two stochastic mean-field polycrystal plasticity methods

Tonks

Bingert

Bronkhorst

et al. 2009

Journal of the Mechanics and Physics of Solids

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a b s t r a c tIn this work, we develop two mean-field polycrystal plasticity models in which the crystal velocity gradients L c are approximated stochastically. Through comprehensive CPFEM analyses of an idealized tantalum polycrystal, we verify that the L c tend to follow a normal distribution and surmise that this is due to the crystal interactions. We draw on these results to develop the stochastic Taylor model (STM) and the stochastic noconstraints model (SNCM), which differ in the manner in which the crystal strain rates D c ¼ 1 2 ðL c þ L cT Þ are prescribed. Calibration and validation of the models are performed using data from tantalum compression experiments. Both models predict the compression textures more accurately than the fully constrained model (FCM), and the SNCM predicts them more accurately than the STM. The STM is extremely computationally efficient, only slightly more expensive than the FCM, while the SNCM is three times more computationally expensive than the STM.Published by Elsevier Ltd.

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Section: Stochastic Polycrystal Plasticity Methodsmentioning

confidence: 99%

Section: Stochastic Polycrystal Plasticity Methodsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 96%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Two stochastic mean-field polycrystal plasticity methods

Tonks

Bingert

Bronkhorst

et al. 2009

Journal of the Mechanics and Physics of Solids

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Measurement of In‐Grain Orientation Gradients by EBSD and Comparison with Finite Element Results

Delannay¹,

Logé²,

Chastel³

et al. 2003

Adv Eng Mater

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The electron backscatter diffraction (EBSD) technique allows rapid orientation mapping over large sample areas. This enables the analysis of tendencies that can only be derived from the averaged behavior of many grains. In this communication, we present a recent study based on this feature, in order to gather statistically relevant information about the orientation gradients that developed within grains of a coldrolled aluminum plate. We also check whether the orientation gradients observed can be attributed to the interaction of adjacent grains. We rely on the finite element (FE) technique to simulate plane strain compression of an aggregate of 1200 grains. Twelve of these grains have an identical initial orientation that has been selected, either close to {001}<100>, or along the b-fiber (i.e., {110}<112>, {123}<634>, and {112}<111>). Every one of the 12 grains has a distinct neighborhood and follows thereby a different deformation path. In concordance with experimental measurements, the FE simulations lead to a larger average orientation spread within grains oriented near {001}<100>. However, the amplitude of the orientation spread is underestimated, whatever the initial orientation of grains.Owing to its influence on the mechanical anisotropy of metal sheets, the crystallographic texture developed in rolling operations has been the object of considerable interest in the past few decades. In cubic metals, most of the stable texture components can be identified by relying on the Taylor± Bishop±Hill (TBH) plasticity theory, which presupposes a uniform deformation field over the polycrystalline aggregate. [1,2] However, this unsophisticated theory does not provide a quantitative prediction of texture development. A comparison of the modeling results with diffraction measurements shows that the TBH theory predicts too rapid a rotation for too many grains towards some of the stable texture components. [2,3] It has been known for a long time that only a heterogeneous strain field can fulfill the stress balance condition across grain boundaries. [1,2] It has also been shown that strain heterogeneity retards the development of texture, leading to a closer match between prediction and experiment. [4±9] However, much uncertainty persists about the origin, the type, and the amplitude of local strain heterogeneities. The purpose of the EBSD study and the FE is to address the following questions.l To what extent is the direct neighborhood of a grain influential? If two grains have an identical initial orientation but a different surrounding, will they take different deformation paths, leading to distinct texture components?

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