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Research Papers

Higher-Order Thermomechanical Gradient Plasticity Model With Energetic and Dissipative Components

[+] Author and Article Information
George Z. Voyiadjis

Boyd Professor
Computational Solid Mechanics Laboratory,
Department of Civil and Environmental
Engineering,
Louisiana State University,
Baton Rouge, LA 70803
e-mail: cegzv1@lsu.edu

Yooseob Song

Computational Solid Mechanics Laboratory,
Department of Civil and Environmental
Engineering,
Louisiana State University,
Baton Rouge, LA 70803
e-mail: ysong17@lsu.edu

Taehyo Park

Professor
Computational Solid and Structural
Mechanics Laboratory,
Department of Civil and Environmental
Engineering,
Hanyang University, 222 Wangsimni-ro,
Seongdong-gu,
Seoul 04763, South Korea
e-mail: cepark@hanyang.ac.kr

1Corresponding author.

Contributed by the Materials Division of ASME for publication in the JOURNAL OF ENGINEERING MATERIALS AND TECHNOLOGY. Manuscript received May 29, 2016; final manuscript received October 6, 2016; published online February 7, 2017. Assoc. Editor: Xi Chen.

J. Eng. Mater. Technol 139(2), 021006 (Feb 07, 2017) (12 pages) Paper No: MATS-16-1154; doi: 10.1115/1.4035293 History: Received May 29, 2016; Revised October 06, 2016

The thermodynamically consistent framework accounting for the thermomechanical behavior of the microstructure is addressed using the finite-element implementation. In particular, two different classes of the strain gradient plasticity (SGP) theories are proposed: In the first theory, the dissipation potential is dependent on the gradient of the plastic strain, as a result, the nonrecoverable microstresses do not have a value of zero. In the second theory, the dissipation potential is independent of the gradient of the plastic strain, in which the nonrecoverable microstresses do not exist. Recently, Fleck et al. pointed out that the nonrecoverable microstresses always generate the stress jump phenomenon under the nonproportional loading condition. In this work, a one-dimensional finite-element solution for the proposed strain gradient plasticity model is developed for investigating the stress jump phenomenon. The proposed strain gradient plasticity model and the corresponding finite-element code are validated by comparing with the experimental data from the two sets of microscale thin film experiments. In both experimental validations, it is shown that the calculated numerical results of the proposed model are in good agreement with the experimental measurements. The stretch-passivation problems are then numerically solved for investigating the stress jump phenomenon under the nonproportional loading condition.

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References

Figures

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Fig. 1

The schematic illustration of the spatial lattice of two contiguous grains, G1 and G2, along with a single slip in grain G1

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Fig. 2

The schematic illustration of a one-dimensional model for a single grain with two grain boundaries

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Fig. 3

The specimen dimensions for the experimental validation of the proposed model [29]

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Fig. 4

The validation of the proposed strain gradient plasticity model by comparing the numerical results from the proposed model with that from Ref. [30] and the experimental measurements from Ref. [29] on the stress–strain response of Ni thin films

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Fig. 5

The schematic illustration of the plane-strain bulge test technique for Cu thin Films [19]

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Fig. 6

The validation of the proposed strain gradient plasticity model by comparing the numerical results from the proposed model with the experimental measurements from Ref. [19] on the stress–strain response of the electroplated Cu thin films with the passivated layers on both sides

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Fig. 7

The stress–strain behaviors of Ni thin films for the model with the dissipative potential dependent on ε˙ij,kp, i.e., QijkNR≠0, according to the variation of the temperature, i.e., T=25 °C, 75 °C, 145 °C, and 218 °C. The solid lines and dot lines represent the responses of the thin films under the abrupt passivation and unpassivation conditions, respectively, and the circles on the curve indicate the passivation point.

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Fig. 8

Comparison of the numerical results between the SGP model with the dissipative potential dependent on ε˙ij,kp, i.e., QijkNR≠0 and the one with the dissipative potential independent on ε˙ij,kp, i.e., QijkNR=0

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