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Research Papers

Use of a Continuum Damage Model Based on Energy Equivalence to Predict the Response of a Single-Crystal Superalloy

[+] Author and Article Information
P. Grammenoudis

Department of Civil Engineering and Geodesy, Institute of Continuum Mechanics, Darmstadt University of Technology, Hochschulstrasse 1, Darmstadt D-64289, Germany

D. Reckwerth

 Continental Teves AG & Co. oHG, Guerickestrasse 7, Frankfurt am Main D-60488, Germany

Ch. Tsakmakis

Department of Civil Engineering and Geodesy, Institute of Continuum Mechanics, Darmstadt University of Technology, Hochschulstrasse 1, Darmstadt D-64289, Germanytsakmakis@mechanik.tu-darmstadt.de

J. Eng. Mater. Technol 133(2), 021001 (Mar 03, 2011) (7 pages) doi:10.1115/1.4000666 History: Received May 05, 2008; Revised July 21, 2009; Published March 03, 2011; Online March 03, 2011

Anisotropic viscoplasticity coupled with anisotropic damage has been modeled in previous works by using the energy equivalence principle appropriately adjusted. Isotropic and kinematic hardenings are present in the viscoplastic part of the model and the evolution equations for the hardening variables incorporate both static and dynamic recovery terms. The main difference to other approaches consists in the formulation of the energy equivalence principle for the plastic stress power and the rate of hardening energy stored in the material. As a practical consequence, a yield function has been established, which depends, besides effective stress variables, on specific functions of damage. The present paper addresses the capabilities of the model in predicting responses of deformation processes with complex specimen geometry. In particular, multiple notched circular specimens and plates with multiple holes under cyclic loading conditions are considered. Comparison of predicted responses with experimental results confirms the convenience of the proposed theory for describing anisotropic damage effects.

Copyright © 2011 by American Society of Mechanical Engineers
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Figures

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Figure 1

Given global strain history over time

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Figure 2

Axis of the specimen and crystallographic axes

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Figure 3

Cylindrical multiple notched tensile specimen used in the experiments

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Figure 4

Finite element mesh of the cylindrical multiple notched tensile specimen used in the calculations

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Figure 5

Global force acting on the specimen (multiple notched circular specimen, as function of global strain) to realize the strain history

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Figure 6

Global force acting on the specimen (multiple notched circular specimen, as function of time) to realize the strain history

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Figure 7

Distribution of Dzz within the specimen (multiple notched circular specimen) after the eight load cycles

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Figure 8

Circumferential distribution of Dzz at z=34.5 mm and r=3.35 mm

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Figure 9

Circumferential distribution of Dzz at z=20 mm and r=3.35 mm

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Figure 10

Circumferential distribution of Dzz at z=5.5 mm and r=3.35 mm

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Figure 11

Distribution of Dzz at {x=−3.35, y=0, z=5.5} and {x=3.35, y=0, z=34.5} as a function of time

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Figure 12

Plate with multiple holes used in the experiments

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Figure 13

Finite element mesh of the plate with multiple holes used in the calculations

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Figure 14

Global force acting on the specimen (plate with multiple holes, as function of global strain) to realize the strain history

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Figure 15

Global force acting on the specimen (plate with multiple holes, as function of time) to realize the strain history

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Figure 16

Distribution of Dzz within the specimen (plate with multiple holes) after the eight load cycles

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Figure 17

Distribution of Dzz at z=9.9 mm and y=1 mm as a function of x

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Figure 18

Distribution of Dzz at z=7.5 mm and y=1.5 mm as a function of x

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Figure 19

Distribution of Dzz at z=5.1 mm and y=2 mm as a function of x

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Figure 20

Distribution of Dzz at {x=10.3, y=1, z=9.9} and {x=1.75, y=2, z=5.1} as a function of time

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