Incrementally objective implicit integration of hypoelastic–viscoplastic constitutive equations based on the mechanical threshold strength model

Mourad, Hashem M.; Bronkhorst, Curt A.; Addessio, F. L.; Cady, Carl M.; Brown, Donald W.; Chen, Shuh Rong; Gray, George T.

doi:10.1007/s00466-013-0941-9

Cited by 13 publications

(10 citation statements)

References 43 publications

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“…The mechanical threshold stress (MTS) model (Follansbee and Kocks, 1988;Follansbee et al, 1990;Mourad et al, 2014) can be regarded as a complex, nonlinear isotropic hardening law, which accounts for strain-and strain-rate hardening, as well as thermal softening effects. It considers the combined effect of different types of barriers to dislocation glide, in order to characterize the material's resistance to inelastic deformation.…”

Section: The Mts Flow-stress Modelmentioning

confidence: 99%

“…The constitutive update procedure adopted herein is very similar to the algorithm described in detail in a previous publication (Mourad et al, 2014). The key difference is that, in the present work, we use a mid-point rule formulated in the corotational description to integrate the constitutive relations (14); viz.…”

Section: Integration Of the Constitutive Relationsmentioning

confidence: 99%

“…is solved in iteration (k + 1). Linearization of the MTS model equations is discussed in detail by Mourad et al (2014). Finally, the spatial Cauchy stress is obtained via the inverse of the transformation (15):…”

Section: Integration Of the Constitutive Relationsmentioning

confidence: 99%

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Modeling and simulation framework for dynamic strain localization in elasto-viscoplastic metallic materials subject to large deformations

Mourad

Bronkhorst

Livescu

et al. 2017

International Journal of Plasticity

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This paper describes a theoretical and computational framework for the treatment of adiabatic shear band formation in rate-sensitive polycrystalline metallic materials. From a computational perspective, accurate representation of strain localization behavior has been a long-standing challenge. In addition, the underlying physical mechanisms leading to the localization of plastic deformation are still not fully understood. The proposed framework is built around an enhanced-strain finite element formulation, designed to alleviate numerical pathologies known to arise in localization problems, by allowing a localization band of given finite width (weak discontinuity) to be embedded within individual elements. The mechanical threshold strength (MTS) model is used to represent the temperature and strain rate-dependent viscoplastic response of the material. This classical flow stress model employs an internal state variable to quantify the effect of dislocation structure evolution (work hardening and recovery). In light of growing evidence suggesting that the softening effect of dynamic recrystallization may play a significant role, alongside thermal softening, in the process of shear band formation and growth, a simple dynamic recrystallization model is proposed and cast within the context of the MTS model with the aid of the aforementioned internal state variable. An initiation criterion for shear localization in rate and temperature-sensitive materials is introduced and used in the present context of high-rate loading, where material rate-dependence is pronounced and substantial temperature increases are achieved due to the dissipative nature of viscoplastic processes. In addition, explicit time integration is adopted to facilitate treatment of the dynamic problems under consideration, where strain rates in excess of 10 4 s −1 are typically attained. Two series of experiments are conducted on AISI 316L stainless steel, employing the commonly used top-hat sample geometry and the Split-Hopkinson Pressure Bar dynamic test system. Axi-symmetric finite element simulation results are compared to cross-sectional micrographs of recovered samples and experimental load-displacement results, in order to examine the performance of the proposed framework and demonstrate its effectiveness in treating the initiation and growth of adiabatic shear banding in dynamically loaded metallic materials. These comparisons demonstrate that thermal softening alone is insufficient to induce shear localization behaviors observed in some materials, such as stainless steel, and support the hypothesis that dynamic recrystallization and/or other softening mechanisms play an essential role in this process.

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Section: The Mts Flow-stress Modelmentioning

confidence: 99%

Section: Integration Of the Constitutive Relationsmentioning

confidence: 99%

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Modeling and simulation framework for dynamic strain localization in elasto-viscoplastic metallic materials subject to large deformations

Mourad

Bronkhorst

Livescu

et al. 2017

International Journal of Plasticity

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“…is assumed where σ 0 is the yield at zero plastic deformation (ε p = 0) andσ is an internal state variable that represents the evolving yield stress component. The isothermal evolution ofσ follows an empirical modication for the Voce law (Kocks et al, 1998;Mourad et al, 2013) reading…”

Section: Materials Modelmentioning

confidence: 99%

Simultaneous estimation of boundary conditions and material model parameters

Rensburg

Kok

Wilke

2018

Struct Multidisc Optim

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Room temperature experimental compression test data is available for dierent hardmetals. This data indicates the presence of some spatial inhomogeneity due to a compression instability, eccentric loading or time varying equivalent bending moment. To account for this, an inverse analysis is employed that determines not only the constitutive material model parameter values but also the displacement boundary conditions that best replicate the experimental data. The unknown boundary displacement history is approached using a systematically rened piecewise linear approximation, determined alongside material parameter values. The systematic simultaneous estimation of material parameter values and boundary approximations is also investigated using a virtual problem for which the exact solution is known. This investigation conrms that known material parameter values and boundary conditions can be recovered without using any prior knowledge of the exact displacement boundary conditions.

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“…Hereinafter, the two latter strength models are briefly summarized as they will later be used as a comparison for the results obtained through symbolic regression. For the considered material, copper, the values of the parameters used by MTS and PTW are given in [33] and [16], respectively.…”

Section: Existing Strength Modelsmentioning

confidence: 99%

Data driven modeling of plastic deformation

Versino

Tonda

Bronkhorst

2017

Computer Methods in Applied Mechanics and Engineering

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In this paper the application of machine learning techniques for the development of constitutive material models is being investigated. A flow stress model, for strain rates ranging from 10 −4 to 10 12 (quasi-static to highly dynamic), and temperatures ranging from room temperature to over 1000 K, is obtained by beginning directly with experimental stress-strain data for Copper. An incrementally objective and fully implicit time integration scheme is employed to integrate the hypo-elastic constitutive model, which is then implemented into a finite element code for evaluation. Accuracy and performance of the flow stress models derived from symbolic regression are assessed by comparison to Taylor anvil impact data. The results obtained with the free-form constitutive material model are compared to well-established strength models such as the Preston-Tonks-Wallace (PTW) model and the Mechanical Threshold Stress (MTS) model. Preliminary results show candidate free-form models comparing well with data in regions of stress-strain space with sufficient experimental data, pointing to a potential means for both rapid prototyping in future model development, as well as the use of machine learning in capturing more data as a guide for more advanced model development.

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Incrementally objective implicit integration of hypoelastic–viscoplastic constitutive equations based on the mechanical threshold strength model

Cited by 13 publications

References 43 publications

Modeling and simulation framework for dynamic strain localization in elasto-viscoplastic metallic materials subject to large deformations

Modeling and simulation framework for dynamic strain localization in elasto-viscoplastic metallic materials subject to large deformations

Simultaneous estimation of boundary conditions and material model parameters

Data driven modeling of plastic deformation

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