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Research Papers: Design and Analysis

Dimensionless Compliance With Effective Modulus in Crack Length Evaluation for B × B Single Edge Bend Specimens

[+] Author and Article Information
Guowu Shen

CanmetMATERIALS,
Minerals and Metals Sector,
Natural Resources Canada,
183 Longwood Road South,
Hamilton, ON L8P 0A5, Canada
e-mail: gshen@nrcan.gc.ca

William R. Tyson

CanmetMATERIALS,
Minerals and Metals Sector,
Natural Resources Canada,
555 Booth Street,
Ottawa, ON K1A 0G1, Canada
e-mail: btyson@nrcan.gc.ca

James A. Gianetto

e-mail: jgianett@nrcan.gc.ca

Jie Liang

e-mail: jliang@nrcan.gc.ca
CanmetMATERIALS,
Minerals and Metals Sector,
Natural Resources Canada,
183 Longwood Road South,
Hamilton, ON L8P 0A5, Canada

Steenkamp [8] as well as Perez Ipina and Santarelli [14] also studied the effects of other variables on the compliance, and concluded that the rotation of the specimen accompanying crack growth and plastic deformation had the largest effect. In fact, the effect of rotation on compliance accompanying crack growth and plastic deformation has been evaluated by Steenkamp [8] using large deformation elastic-plastic finite element analysis. However, the present study is focused only on evaluation of the effective modulus to be used in the relation between crack size and compliance. Hence, the effects of both rotation of the specimen accompanying crack growth and plastic deformation were not included although these effects are important and will be investigated in future work.

1Corresponding author.

Contributed by the Pressure Vessel and Piping Division of ASME for publication in the Journal of Pressure Vessel Technology. Manuscript received July 24, 2012; final manuscript received May 13, 2013; published online October 10, 2013. Assoc. Editor: Haofeng Chen.

J. Pressure Vessel Technol 135(6), 061209 (Oct 10, 2013) (8 pages) Paper No: PVT-12-1104; doi: 10.1115/1.4024688 History: Received July 24, 2012; Revised May 13, 2013

In ASTM standard E1820, the crack size, a, may be evaluated during J-integral or crack-tip opening displacement (CTOD) resistance testing using the measured crack-mouth opening displacement (CMOD) elastic unloading compliance C (UC). The equation given to relate a to dimensionless compliance BCE (the product of thickness B, the compliance C and the modulus of elasticity E) in E1820 incorporates Young's modulus E rather than the plane-strain modulus E/(1 − υ2) where υ is Poisson's ratio. However, the three-dimensional (3-D) single edge bend (SE(B)) specimens used in fracture toughness tests are in neither plane-stress nor plane-strain condition, especially for B×B SE(B) specimens which are popular in characterizing fracture toughness of pipes with surface notches. In the present study, 3-D finite element analysis (FEA) was used to evaluate the CMOD compliance of plain- and side-grooved B×B SE(B) specimens with shallow and deep cracks. Crack sizes evaluated using plane-stress and plane-strain assumptions with the CMOD compliance calculated from FEA for the 3-D specimen were compared with the actual crack size of the specimens used in FEA. It was found that the errors using plane-strain or plane-stress assumptions can be as high as 5–10%, respectively, especially for shallow-cracked specimens. In the present study, an effective modulus with value between plane-stress and plane-strain is proposed and evaluated by FEA for the 3-D B×B SE(B) specimens for use in estimating the dimensionless compliance for crack size evaluation of B×B SE(B) specimens. It is shown that the errors in crack size evaluation can be reduced to 1% and 2% for plain-sided and side-grooved specimens, respectively, using this effective modulus. The effect of material removal to accommodate integral knife edges on the CMOD compliance was studied and taken into account in the crack length evaluations in the present study. Elastic unloading tests were conducted to measure the compliance of SE(B) specimens with two widths W and notch depths a/W from 0.1 to 0.5. Notch depths of the specimens evaluated by using the measured compliance and assumptions of plane stress, plane strain, and effective moduli were compared with the notch depths of the specimens used in the tests. It was found that best agreement of notch depth was achieved using the effective modulus.

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References

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Clarke, G. A., Andrews, W. R., Paris, P. C., and Schmidt, D. W., 1976, “Single Specimen Tests for JIc Determination,” Mechanics of Crack Growth, J. R.Rice and P. C.Paris, eds., ASTM STP 590, American Society for Testing and Materials, West Conshohocken, PA, pp. 27–42.
Clarke, G. A., 1981, “Single-Specimen Tests for JIc Determination-Revisited,” Fracture Mechanics: 13th Conference, R.Roberts, ed., ASTM STP 743, American Society for Testing and Materials, Philadelphia, PA, pp. 553–575.
Tada, H., Paris, P. C., and Irwin, G. R., 1985, The Stress Analysis of Cracks Handbook, 2nd ed., Del Research Corporation, Hellertown, PA.
Wu, S. X., 1984, “Crack Length Calculation Formula for Three-Point Bend Specimens,” Int. J. Fract., 24, pp. R33–R35. [CrossRef]
Joyce, J. A., 1992, “J-Resistance Curve Testing of Short Crack Bend Specimens Using Unloading Compliance,” Fracture Mechanics: Twenty-Second Symposium, Vol. 1, H. A.Ernst, A.Saxena, and D. L.McDowell, eds., ASTM STP 1131, American Society for Testing and Materials, West Conshohocken, PA, pp. 904–924.
Steenkamp, P. A. J. M., 1988, “JR-Curve Testing of Three-Point Bend Specimens by the Unloading Compliance Method,” Fracture Mechanics: Eighteenth Symposium, D. T.Read, and R. P.Reed, eds., ASTM STP 945, American Society for Testing and Materials, West Conshohocken, PA, pp. 583–610.
Shih, C. F., De Lorenzi, H. G., and Andrews, W. R., 1977, “Elastic Compliances and Stress-Intensity Factors for Side-Grooved Compact Specimens,” Int. J. Fract., 13, pp. 544–548. [CrossRef]
Neale, B. K., Curry, D. A., Green, G., Haigh, J. R., and Akhurst, K. N., 1985, “A Procedure for the Determination of the Fracture Resistance of Ductile Steels,” Int. J. Pressure Vessels Piping, 20, pp. 155–179. [CrossRef]
Shivakumar, K. N. and Newman, J. C., Jr., 1992, “Verification of Effective Thickness for Side-Grooved Compact Specimens,” Eng. Fract. Mech., 43, pp. 269–275. [CrossRef]
Gudas, J. P., and Davis, D. A., 1982, “Evaluation of the Tentative JI-R Curve Testing Procedure by Round Robin Tests of HY-130 Steel,” J. Test. Eval., 10, pp. 252–262. [CrossRef]
Shen, G., Bouchard, R., and Tyson, W. R., 2002, “Estimation of 3-D SE(B) Fracture Parameters Using 2-D Equations,” Proceeding of the 14th European Conference on Fracture (ECF14), A.Neimitz, D.Rokanda, and K.Golos, eds., EMAS Publishing, Warrington, UK, pp. 281–290.
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Figures

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Fig. 1

Finite element meshes for B × B SE(B) specimens: (a) plain-sided, a/W = 0.5, (b) side-grooved, a/W = 0.3, and (c) with integral knife edge

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Fig. 2

Stress state parameter in the ligament of a B × B SE(B) specimen: (a) a/W = 0.5 plain-sided, (b) a/W = 0.5 side-grooved, and (c) a/W = 0.1, plain-sided

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Fig. 3

CMOD along the thickness direction: (a) plain-sided and (b) side-grooved

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Fig. 4

Parameter β as a function of (a) a/W and (b) u

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Fig. 5

Errors in crack size estimates using plane stress, plane strain, and effective moduli for B × B SE(B) specimens: (a) plain-sided and (b) side-grooved

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Fig. 6

Flowchart for evaluation of a/W from measured compliance C

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Fig. 7

Effect of material removal for integral knife edges on CMOD compliance

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Fig. 8

CMOD compliance evaluated by experiments and FEA

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Fig. 9

Ratio of crack length evaluated using unloading compliance to actual length by measurements: PSS-plane stress, PSN-plane strain, and EFM-effective modulus

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