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Research Papers: Design and Analysis

Analytical Prediction of Fatigue Crack Growth Behavior Under Biaxial Loadings

[+] Author and Article Information
Ragupathy Kannusamy

Honeywell Technology Solutions Lab,
Bangalore 560076, India

K. Ramesh

Applied Mechanics Department,
Indian Institute of Technology Madras,
Chennai 600036, India

Contributed by the Pressure Vessel and Piping Division of ASME for publication in the JOURNAL OF PRESSURE VESSEL TECHNOLOGY. Manuscript received May 22, 2012; final manuscript received September 22, 2013; published online January 29, 2014. Assoc. Editor: Hardayal S. Mehta.

J. Pressure Vessel Technol 136(2), 021204 (Jan 29, 2014) (11 pages) Paper No: PVT-12-1067; doi: 10.1115/1.4025611 History: Received May 22, 2012; Revised September 22, 2013

Aircraft and pressure vessel components experience stresses that are negative biaxial or multiaxial in nature. Biaxiality is defined as the ratio of stress applied parallel and normal to the crack front. In recent years, many experimental studies have been conducted on fatigue crack growth (FCG) under various biaxial loading conditions. Biaxial loadings affect crack front stresses and strains, fatigue crack growth rate and direction, and crack tip plastic zone size and shape. Many of these studies have focused on positive biaxial loading cases. No conclusive study has been reported out yet that accurately quantifies the influence of negative biaxiality on fatigue crack growth behavior. Lacking validation, implementation on real life problems remains questionable. To ensure safe and optimum designs, it is necessary to better understand and quantify the effect of negative biaxial loading on fatigue crack behavior. This paper presents the results of a study to quantify the effect of biaxial load cases ranging from B = −0.5 to 1.0 on fatigue crack growth behavior. Also, a simplified approach is presented to incorporate the effect of biaxiality into da/dN curves generated from uniaxial loading using an analytical approach without conducting expensive biaxial crack growth testing. Sensitivity studies were performed with existing test data available for AA2014-T6 aluminum alloy. Detailed elastic-plastic finite element analyses were performed using the different stress ranges and stress ratios with various crack sizes and shapes on notched and unnotched geometries. Constant amplitude loads were applied for the current work and comparison studies were made between uniaxial and different biaxial loading cases. It was observed from the study that negative biaxiality has a very pronounced effect on the crack growth rate and direction for AA2014-T6 if the externally applied load equal to 30% of the yield strength as compared with 40% of externally applied load for steel alloy quoted in the literature.

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References

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Figures

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Fig. 1

True stress–strain curve for AA2014-T6 material

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Fig. 2

Geometry and FE model for 2D (1/4th symmetry FE model)

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Fig. 3

3D geometry and FE model (1/4th symmetry FE model)

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Fig. 4

Spider web mesh patterns for 2D crack tip and 3D crack front region

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Fig. 5

Contact elements between two traction free contact surfaces

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Fig. 7

da/dN curves with biaxiality corrections for AA2014-T6 material for R = 0

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Fig. 6

da/dN curves for AA2014-T6 material for two different R ratios [16]

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Fig. 8

Paris constant C′ for three different biaxiality loading cases

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Fig. 9

(a) Crack front at 90 deg and (b) crack front at 0 deg. 3D FE model represents the location of 0 and 90 deg.

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Fig. 10

Plastic zone sizes and shapes under B = −0.5, 0, and 1 for externally applied load equal to 40% of yield strength

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Fig. 11

Representation of virtual crack extension directions in angular positions (θ) at the 3D crack front

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Fig. 12

Schematic representation of 3D crack front profile

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Fig. 13

Energy release rate in angular position (θ) for different crack extension directions at the crack front

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Fig. 14

(a) FE model with initial crack for B = 1 and (b) crack path with plastic zone at the crack tip. Crack growth path in cruciform specimen for B = 1 for externally applied load equal to 50% of yield strength for R = 0.

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Fig. 15

(a) FE model with initial crack for B = 0 and (b) crack path with plastic zone at the crack tip. Crack growth path in cruciform specimen for B = 0 (uniaxial) for externally applied load equal to 50% of yield strength for R = 0.

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Fig. 16

(a) FE model with initial crack for B = −0.5 and (b) crack path with plastic zone at the crack tip. Crack growth path in cruciform specimen for B = −0.5 for externally applied load equal to 50% of yield strength for R = 0.

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Fig. 17

(a) FE model with initial crack and (b) crack path with plastic zone at the crack tip for B = −0.5. Crack growth path in half symmetry cruciform specimen for B = −0.5 for externally applied load equal to 50% of yield strength for stress ratio (R) = 0.

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Fig. 18

Crack growth rate for flat plate model for externally applied load equal to 20% of yield strength under R = 0

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Fig. 19

Crack growth rate for flat plate model for externally applied load equal to 40% of yield strength under R = 0

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Fig. 20

Crack growth rate for 3D middle tension specimen model for externally applied load equal to 40% of yield strength for stress ratio (R) = 0

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Fig. 21

Crack growth rate for flat plate model for externally applied load equal to 30% of yield strength for R = 0.5

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Fig. 22

Crack growth rate from FE analysis for cruciform specimen compared with experimental results from Ref. [1] for AA2024-T351 material for externally applied load equal to 17% of yield strength under R = 0.1

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Fig. 23

Variation of Jmax values for three different biaxial ratios under three different loading conditions (20%, 30%, and 40% of yield strength)

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Fig. 24

Jmax values for three different biaxial ratios for flat plate model with hole for loading condition of 30% yield strength

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Fig. 25

Crack opening displacement (COD) behind crack front at 0 deg for 20% of yield strength

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Fig. 26

COD behind crack front at 90 deg for 20% of yield strength

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Fig. 27

COD behind crack front at 0 deg for 40% of yield strength

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Fig. 28

COD behind crack front at 90 deg for 40% of yield strength

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