Effect of crack curvature on stress intensity factors for ASTM standard compact tension specimens

The stress intensity factors (SIF) are calculated using the method of lines for the compact tension specimen in tensile and shear loading for curved crack fronts. For the purely elastic case, it was found that as the crack front curvature increases, the SIF value at the center of the specimen decreases while increasing at the surface. For higher values of crack front curvatures, the maximum value of the SIF occurs at an interior point located adjacent to the surface. A thickness average SIF was computed for parabolically applied shear loading. It is assumed that it reflects the average stress environment near the crack edge. These results were used to assess the requirements of ASTM standards E399-71 and E399-81 on the shape of crack fronts.     

Coefficients of the crack tip asymptotic field for a standard compact tension specimen

The coefficients of the crack tip asymptotic field of a standard compact tension (CT) specimen are computed using a hybrid crack element (HCE). It allows the direct calculation (without post-processing) of not only the stress intensity factor (SIF) but also the coefficients of higher order terms of the crack tip asymptotic field. Approximate closed-form expressions for the first five terms for the CT specimen that are accurate for shallow to very deep cracks are obtained by fitting the computed data. The SIF formula proposed by Brown and Srawley (1966) is shown to be accurate when the crack length to depth ratio () ranges from 0.35 to 0.75. The formula proposed by Newman (1974) and Srawley (1976) is accurate for 0.15. However, the accuracy of available formulas for the second T-term in the literature is quite disappointing. Numerical results also show that, unlike the notched three-point bend beam and the wedge splitting specimen, the second T-term of the CT specimen is always positive.     

Measuring residual stress and the resulting stress intensity factor in compact tension specimens

The measurement of residual stress through the remaining ligament of a compact tension specimen was studied. In the crack compliance method, a slot or notch is successively extended through the part, and the resulting strain is measured at an appropriate location. By using a finite element simulation of a specimen preloaded beyond yield, three techniques for determining the original residual stress from the measured strains were compared for accuracy and sensitivity to measurement errors. A common beam-bending approximation was substantially inaccurate. The series expansion method proved to be very versatile and accurate. The fracture mechanics approach could determine the stress intensity factor caused by the residual stresses with a very simple calculation. This approach offers the exciting possibility of determining the stress intensity factor prior to a fatigue or fracture test by measuring strains during the specimen preparation.     

Back-face strain compliance relation for compact specimens for wide range in crack lengths

A back-face strain (BFS) compliance relation has been developed for the standard compact C(T) specimen for a very wide range in crack-length-to-width (a/W) ratios. Both finite-element and boundary-element methods were used to develop the BFS relation for a/W ratios from 0.2 to 0.95. In addition, experimentally determined compliance values on four metallic materials compared well with the new relation over nearly the complete a/W range. The new relation can be used to monitor crack-length-against-cycles using computerized crack-monitoring systems that are currently used with the crack-mouth-opening-displacement (CMOD) gage method, and the relation has been cast in a standard form compatible with existing compliance crack length monitoring systems.     

An improved analysis of the potential drop method for measuring crack lengths in compact tension specimens

A single-parameter logarithmic equation is suggested for the calibration of the potential drop method for measuring crack length in compact tension specimens. This equation follows the correct asymptotic solution for long crack lengths and is shown to hold for even very short crack lengths for specimens with a small notch. Use of this equation provides a first step towards evaluation of calibration fata for anomalies such as those associated with variation of electrical conductivity due to plasticity of the crack tip and with uneven crack growth. In addition, use of this equation as a two-parameter model allows determination of the electrical resistivity of the specimen from the calibration data. Data are presented for specimens with large notches which support the results obtained in a previous paper by a numerical method coupled with conformal mapping.

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Résumé On suggère une équation logarithmique à paramètre simple pour l'étalonnage de la méthode de la chute potentielle, applicable à la mesure des longueurs de fissure dans des éprouvettes de traction compactes. Cette équation est conforme à la solution asymptotique correcte pour les fissures longues, et on montre qu'elle est applicable même pour des fissures très courtes dans la cas d'éprouvette comportant une petite entaille.L'utilisation de cette équation permet l'évaluation des données d'étalonnage dans le cas d'anomalies telles que celles qui sont associées à une variation de la conductibilité électrique due à la plasticité à l'extrémité de la fissure, et en présence d'une croissance inégale de celle-ci.En outre, l'utilisation de cette équation comme modèle à deux paramètres permet la détermination de la résistivité électrique d'une éprouvette au départ de données d'étalonnage.Des données sont présentées pour des éprouvettes à grande entaille. Elles viennen àa l'appui des résultats obtenus dans un article précédant par une méthode numérique associée à une représentation conforme.

     

Quantitative characterization of creep constraint induced by crack depths in compact tension specimens

In this paper, the C(t) and C∗ integrals, stress redistribution time t_red and creep crack-tip stress distributions in the CT specimens with various crack depths have been calculated by the finite element method (FEM), and the creep constraint induced by crack depths are quantitatively investigated in detail. The results show that the creep constraint could be characterized by the new constraint parameter R. The constraint effect induced by crack depths at non-steady-state creep is more pronounced than that at steady-state creep. The effects of the crack depths, load levels (C∗) and distances from the crack tips on the creep constraint parameter R are analyzed.     

Explicit calculation of the crack tip stress intensity factor for the double slip plane model crack

A more rigorous analysis is presented for the stationary double slip plane (DSP) crack loaded in mode III with constant friction stress on the slip planes. This analysis gives the dislocation distributions on the slip and crack planes. More important, the analysis leads to an explicit calculation of the crack tip stress intensity factor K_t without resort to use of the J-integral or the Rice-Thompson expression for dislocation crack tip shielding/antishielding factor. It is shown that K_t ≈ K for the stationary crack. With the results of this paper there are now essentially three independent methods of obtaining K_t for a DSP crack.     

An analysis of the crack tip stress field in DCB adhesive fracture specimens

The problem of a cracked adhesive bonded DCB-type fracture specimen has been analyzed using a hybrid stress model finite element analysis which incorporates an advanced crack tip element. Stresses in the near and far fields have been studied as a function of adherend/adhesive modulus ratio and adhesive thickness. The results are compared to monolithic systems with regard to the stress intensity factor and the localization of the singular stress domain associated with the crack tip.

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Résumé Le problème d'une éprouvette de rupture Double Poutre Cantilever comportant une liaison par adhésif fissurée a été analysée en utilisant un modèle de contrainte hybride et une analyse par élément fini qui incorpore un élément particulier à la pointe de la fissure. Les contraintes dans le champ proche et dans le champ éloigné ont été étudiées en fonction du rapport des modules de l'adhésif et de l'adhérent, et de l'épaisseur de l'adhésif. Les résultats sont comparés à un système monolitique en ce qui regarde le facteur d'intensité des contraintes et la localisation du domaine singulier des contraintes associé à l'extrémité de la fissure.

     

Distributions of stress and plastic strain in circumferentially notched tension specimens

Distributions of stress and plastic strain at the minimum diameter in circumferentially notched bars with three different notch profiles are deduced from observation of the displacements of bands within the material and a modified Bridgman analysis. The strain distributions were found to be non-linear; the degree of non-linearity being dependent on the degree of straining and strongly dependent upon notch geometry, which cannot be described only by the ratio of the minimum radius to the profile radius.

For two of the three profiles studied the longitudinal stress distributions were found to be nearly uniform across the minimum diameter whilst the third was found to be extremely non-uniform. Qualitative confirmation of the strain distribution results were obtained by use of transversely orientated specimens.     

Characterization of crack tip stress fields in test specimens using mode mixity parameters

The aim of this study is to represent the combined effect of mode mixity, specimen geometry and relative crack length on the $T$ -stress, elastic–plastic stress fields, integration constant $I_{n}$ , angle of initial crack extension, and the plastic stress intensity factor. The analytical and numerical results are obtained for the complete range of mixed modes of loading between mode I and mode II. For comparison purposes, the reference fields for plane mixed-mode problems governing the asymptotic behavior of the stresses and strains at the crack tip are developed in a power law elastic–plastic material. For the common experimental fracture mechanics specimen geometries considered, the numerical constant of the plastic stress field $I_{n}$ and the $T$ -stress distributions are obtained as a function of the dimensionless crack length and mode mixity. A method is also suggested for calculating the plastic stress intensity factor for any mixed-mode I/II loading based on the $T$ -stress and power law solutions. It is further demonstrated that in both plane stress and the plane strain, the plastic stress intensity factor can be used to characterize the crack tip stress fields for a variety of specimen geometries and different mixed-mode loading. The applicability of the plastic stress intensity factor to analysis of the in-plane and out-of-plane constraint effect is also discussed.     

On the use of the crack tip opening angle parameter to explain the ductile crack growth behavior of miniature compact specimens

Experimental crack resistance curves obtained from miniature compact tension, MC(T), specimens were found to be significantly less tough than those obtained on standard one inch 1T-C(T) specimens. In order to investigate the fundamental reasons behind this unexpected result, local approaches to fracture based on the Rice and Tracey void growth model and the crack tip opening angle (CTOA) concept are used. Local crack growth criteria are identified on test results obtained from 1T-C(T) and are used to predict the MC(T) behavior. Results demonstrate that the CTOA parameter is very effective as it allows transferring results from MC(T) to larger specimens, it is easy to implement in a finite element code, it is mesh size insensitive and can be actually measured although its experimental determination is not straightforward. The β parameter derived from the Rice and Tracey void growth model is unable to explain the experimental results. The possible reasons for the poor performance of the β parameter are discussed.     

Effect of loadline shift on applied crack tip stress intensity in WOL specimens

A change in applied stress intensity due to shifting of load line from the pin hole to a wedge located on the outside edge of the notch has been investigated by: (1) finite element analysis, (2) measurements of front face crack opening displacement and (3) strain relaxation near the crack tip.

Results show that this wedge loading procedure will result in a significant drop, up to a factor of two, in applied stress intensity. The drop in stress intensity is inversely related to the crack length (expressed by a/W). This drop in stress intensity is due to overall specimen distortion because of load line shift and local deformation of the wedge and notch surfaces. Implications of this drop on Stress Corrosion Cracking results are discussed. For reliable stress corrosion testing, modifications in specimen geometries and loading procedures are suggested.     

Fracture energy and strain softening of concrete as determined by means of compact tension specimens

Fracture mechanics parameters of concrete are determined by means of the compact tension (CT) test. The effects of ligament length, rate of loading and concrete composition on the specific fracture energy G_F and the strain-softening diagram are investigated. As a first approximation of the real softening behaviour of concrete, a bilinear strain softening diagram is used in a finite-element analysis. A parameter study shows that several bilinear diagrams can represent the real behaviour equally well. With the bilinear softening diagram, a good agreement between both calculated and measured load-displacement curves and G_F-values is obtained. The determined strain-softening diagrams are transformed into a normalized presentation. For each investigated testing condition, characteristics shapes of this normalized strain-softening diagram are obtained.     

Measurement of fatigue crack growth in large compact tension specimens using an AC magnetic field method

Fatigue crack growth rate data are required in order to carry out a numerical analysis of the fatigue performance of complex structural components. These data are obtained by measuring crack growth in standard fracture mechanics specimens. A new method for measuring fatigue crack growth in compact tension specimens has been developed. The technique is based on the measurement of the surface magnetic fields produced when passing a high-frequency alternating current through the specimen. Fatigue crack growth data recorded using this method indicated an accuracy of ±0.02 mm when compared with optical measurements. The technique is suitable for computer-controlled operation and could easily be applied to other standard specimen geometries.     

Coefficients of the crack tip asymptotic field for wedge splitting specimens

The stress intensity factor (SIF) and the coefficients of higher order terms of the crack tip asymptotic field of typical wedge splitting specimens with two different loading arrangements are directly computed using a hybrid crack element. Accurate analytical expressions for the first five terms are obtained by fitting the computed data. Numerical results show that the coefficients of terms higher than three are negligibly small, this may explain that the wedge splitting specimen is more stable than other geometries. The first five terms are not sensitive to support conditions. However, for short cracks coefficients of terms, except the SIF, are quite sensitive to the loading arrangement even when the loads are statically equivalent.