Wide-Range Displacement Expressions for Standard Fracture Mechanics Specimens

Kapp, J. A.; Gross, Bernard; Leger, G. S.

doi:10.1520/stp34244s

Cited by 12 publications

(12 citation statements)

References 2 publications

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“…The first set of calculations deals with the form of U given by Eq. (2). The effects of rounding the U parameter are interesting.…”

Section: Crack Length As a Function Of Displacementmentioning

confidence: 99%

“…The first set of data uses U in the form of Eq. (2). Miscalculating the U parameter by 0.1 percent will introduce a maximum error of -0.0006 W in the calculation of a/W, a 1 percent miscalculation results n an error of about -0.004 W at all crack lengths, and a 5 percent miscalculation results in about a -0.02 W error at all crack lengths.…”

Section: Crack Length As a Function Of Displacementmentioning

confidence: 99%

See 1 more Smart Citation

Improved Wide Range Expressions for Displacements and Inverse Displacements for Standard Fracture Toughness Specimens

Wolfenden¹,

Kapp

1991

Journal of Testing and Evaluation

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Wide range expressions (interpolating polynomials) for displacements for standard ASTM fracture testing specimens have been developed. The strategy was to fit displacements as a function of crack length for all the specimens using a similar form of nondimensional displacement. Different forms appear in different ASTM standards for the same or similar specimens. The criterion used to establish the degree of polynomial fit and number of significant figures for the coefficients of the polynomial was for the polynomial to agree with the best available numerical displacement solutions to within 1% or better. Once the polynomials for displacement as a function of crack length were developed, inverted forms of the specific interpolating polynomials were obtained to determine relative crack length (a/W) as a function of displacement. Since the inverted polynomial will be used in tandem with the interpolating polynomial, the inverted polynomial was fit to the interpolating polynomial and not the numerical solution for displacement. Three forms of nondimensional displacements were used to invert the interpolating polynomials. The criterion used to establish the degree of polynomial and the number of significant figures of the coefficients of the polynomial was for the predicted relative crack length to agree with the actual relative crack depth to within 0.0005W. A sensitivity analysis was performed to suggest which form of interpolating polynomial should be used for standards.

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“…The first set of calculations deals with the form of U given by Eq. (2). The effects of rounding the U parameter are interesting.…”

Section: Crack Length As a Function Of Displacementmentioning

confidence: 99%

Section: Crack Length As a Function Of Displacementmentioning

confidence: 99%

Improved Wide Range Expressions for Displacements and Inverse Displacements for Standard Fracture Toughness Specimens

Wolfenden¹,

Kapp

1991

Journal of Testing and Evaluation

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“…Some authors, e.g. Kapp et al [6] take only bending deformation into account, resulting in C 0 = & ( i ) 3 which gives EBC, = 16 for S / W = 4. Equation (5a) underestimates the non-cracked compliance, since for relatively short bars the shear deformation cannot be neglected as, for example, noted by Haggag and Underwood [7].…”

Section: Load-line Compliancementioning

confidence: 99%

Compatible Compliance and Stress Intensity Expressions for the Standard Three‐point Bend Specimen

Bakker

1990

Fatigue Fract Eng Mat Struct

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Available expressions for load-line compliance and crack-mouth opening compliance expressions for standard three-point bend specimens (span over width ratio = 4) are assessed. It is concluded that none of the available expressions are able to reproduce the source data (boundary collocation results and theoretical limits for relative crack depths equal to 0 and 1) for the entire range of relative crack depth. New expressions for example are proposed and the accuracy of each is indicated. A by-product of the new expression for load-line compliance is a new, fully compatible stress intensity expression that is, consistent with the load line compliance expression as known from theoretical considerations. Also inverse expressions are presented which predicting the crack length from compliance. To improve the accuracy of such inverse expressions, a correction that results in a considerable error reduction is presented. NOMENCLATURE a = crack length B = specimen thickness C = load line compliance ( = A / P ) C, = load-line compliance of the uncracked specimen (= A J P ) C, = crack-mouth opening compliance ( = A m / P ) C,, = load-line compliance due to the presence of the crack only (= C -C,) E = modulus of elasticity E ' = effective modulus of elasticity [=E for plane stress, E/(l -v2) for plane strain] K = stress intensity factor (mode I) P = load S = specimen span W = specimen width a = relative crack depth ( = a / W ) 6,, =' transfer function used for inverse load-line compliance expressions 6 , = transfer function used for inverse crack-mouth opening compliance expressions A = load-line displacement Acr = load-line displacement due to the presence of the crack Anc = load-line displacement of uncracked specimen Acr = crack-mouth opening displacement v = Poisson's ratio

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“…Various methods, for example, unloading compliance, potential drop and image processing techniques are commonly employed to measure crack growth. The unloading compliance technique is the most commonly used and also the simplest method to measure crack growth during fracture test of small specimens, for example, CT and TPB . This technique allows crack growth to be inferred from the load and displacement transducers that are part of any fracture mechanics test.…”

Section: Introductionmentioning

confidence: 99%

New unloading compliance correlation for throughwall circumferentially cracked pipe to measure crack growth during fracture tests

Chattopadhyay

Venkatramana

Dutta

2014

Fatigue Fract Eng Mat Struct

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Crack growth is generally measured during fracture experiment of specimen or component. The unloading compliance technique is commonly used for this purpose because of its simplicity. It infers the crack length from unloading compliance of cracked component. The pre‐requisite of this technique is the availability of an equation that correlates crack length with unloading compliance. While such correlations are available for compact tension and three‐point bend specimens, it is not available for big components such as pipe or pipe bend. Development of such a correlation for throughwall circumferentially cracked (TCC) straight pipe under bending, therefore, forms the objective of the present study. However, the challenge to develop such correlation for TCC pipe is that the equation should contain not only crack length as a function but also the current deformation or load level as a parameter. This is attributed to the fact that the circular cross section of the pipe ovalizes during deformation leading to change of bending stiffness of the cracked body. New compliance correlations have been proposed for TCC pipe under bending load considering these complexities. Elastic‐perfectly plastic material behaviour has been assumed to characterize the material stress–strain response. However, it has been shown that error due to this approximation with respect to the actual stress–strain behaviour is negligible if one chooses flow stress equal to average of yield and ultimate strength. The proposed correlations are expressed in terms of normalized parameters to make them independent of specific values of geometric dimensions such as radius, thickness and span length of four‐point bending loading system. Effectiveness of this normalization has also been verified by carrying out a sensitivity study.

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Wide-Range Displacement Expressions for Standard Fracture Mechanics Specimens

Cited by 12 publications

References 2 publications

Improved Wide Range Expressions for Displacements and Inverse Displacements for Standard Fracture Toughness Specimens

Improved Wide Range Expressions for Displacements and Inverse Displacements for Standard Fracture Toughness Specimens

Compatible Compliance and Stress Intensity Expressions for the Standard Three‐point Bend Specimen

New unloading compliance correlation for throughwall circumferentially cracked pipe to measure crack growth during fracture tests

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