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Research Papers

Material Model for Creep-Assisted Microcracking Applied to S2 Sea Ice

[+] Author and Article Information
Kari Santaoja

Department of Mechanical Engineering,
School of Engineering,
Aalto University,
P.O. Box 14300,
Aalto FI-00076, Finland
e-mail: kari.santaoja@aalto.fi

J. N. Reddy

Fellow ASME
Department of Mechanical Engineering,
Texas A&M University,
College Station, TX 77843-3123
e-mail: jnreddy@tamu.edu

1Corresponding author.

Contributed by the Applied Mechanics Division of ASME for publication in the JOURNAL OF APPLIED MECHANICS. Manuscript received July 10, 2016; final manuscript received July 25, 2016; published online August 24, 2016. Editor: Yonggang Huang.

J. Appl. Mech 83(11), 111002 (Aug 24, 2016) (11 pages) Paper No: JAM-16-1346; doi: 10.1115/1.4034345 History: Received July 10, 2016; Revised July 25, 2016

A material model is presented that includes the following deformation mechanisms: the instantaneous response of ice due to distortion of crystal lattices, creep, the formation of microcrack nuclei due to creep, the formation of microcracks, and deformation due to microcracks. The new material model has a strict foundation on deformation mechanisms. This constitutive equation was applied to sea ice for engineering applications through implementation in the Abaqus explicit code by writing a VUMAT subroutine. The computed results show that the model correctly predicts the uniaxial tensile and the uniaxial compressive strengths of ice. The computed compressive strength versus strain-rate relation takes an almost linear relation when expressed in the log–log coordinates, which fits well with the data obtained from the literature. The material model shows the Hall–Petch type of strength dependency on the grain size.

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References

Figures

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Fig. 1

Two microcracks in a two-dimensional domain

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Fig. 2

(a) Surfaces of a microcrack penetrating each other. (b)Penetration is prevented by the Heaviside function H(nr ⋅ σ ⋅ nr).

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Fig. 3

(a) Uniaxial fiber model for evaluation of the stress σ and the effective stress σ̃ and (b) stress strain curves

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Fig. 4

Generated versus fitted creep curves

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Fig. 5

Stress–strain curves in tension and in compression at ε˙=2×10−4 1/s

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Fig. 6

Computed strength values versus number of potential microcrack orientations: (a) tension and (b) compression

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Fig. 7

Results by Jones [53] for “Baltic” sea ice (◻) compared to data in the literature, (○) and (+) Frederking and Timco [54]; (⋄) Schwarz [55]; (▪) Kuehn and Schulson [56]. Jones [53] Fig.3.

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Fig. 8

Strength diagram for columnar-grained ice (S2) in compression and tension at −10 °C (Ref. [57], Fig. 2.41)

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Fig. 9

Mode of failure observed and predicted as a function of applied strain rate and effective stress at failure at T=−10 °C (Ref. [28])

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Fig. 10

Computed tensile strength values σut versus strain rate. The range where the strength does not increase, is not included in the model and is marked “Not in model.”

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Fig. 11

The material model obeys the Hall–Petch equation under compression and under tension

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