Constraint-corrected fracture failure criterion based on CTOD/CTOA

In engineering design, a difficulty has always existed in those standard laboratory tests that cannot accurately predict the behavior of large structures like pipelines due to the different constraint levels. At present, extensive work has been done to characterize the constraint effects on fracture toughness by introducing a second parameter, while the systematic research on constrained transformation is inadequate. To address this issue, the ductile fracture process of X65 SENB specimen is simulated through the finite-element method coupled with the Gurson–Tvergaard–Needelman model. The parameters crack tip opening displacement (CTOD) and crack tip opening angle (CTOA) are chosen to characterize the fracture behaviors. The effects of specimen thickness on fracture toughness based on CTOD/CTOA and constraints ahead of crack tips in SENB specimen are studied. The results indicate that the critical values of CTOD/CTOA decrease with the increase of specimen thickness, but the constraint parameters are opposite. Furthermore, it finds that there is a near linear relationship between critical values of CTOD/CTOA and the stress constraint ahead of the crack tip. Thus, a constraint-corrected fracture failure criterion based on CTOD/CTOA is proposed, which can be used for the prediction and simulation of stable tearing crack growth in specimens and structures, made of this steel with any thickness value.     

The non-constant CTOD/CTOA in stable crack extension under plane-strain conditions

Contrary to the previous work that successfully applied the constant CTOD/CTOA fracture criteria to relatively thin structures, this paper demonstrates that the initial non-constant portion of the CTOD/CTOA plays an essential role in predicting fracture behavior under plane-strain conditions. Three- and two-dimensional finite element analyses indicate that a severe underestimation of the load would occur as the crack extends if a constant CTOD/CTOA criterion were used. However, the use of a simplified, bilinear CTOD/CTOA criterion to approximate its non-constant portion will closely duplicate the test data. Furthermore, using the experimental data from J-integral tests with various crack length to specimen width ratios (a/W), it is demonstrated that the critical CTOD/CTOA is crack tip constraint dependent. The initial high values of the CTOD/CTOA are in fact a natural consequence of crack growth process that is reflected by, and consistent with, the J-resistance (J-R) curve and its slope (tearing modulus).     

Determination of the CTOA and J integral by fracture surface topography analysis

In order to investigate the causes of material fracture, a new method is proposed that uses only the fracture surfaces for determining the fracture parameters in terms of the Cract-tip opening angle (CTOA) and the J integral. This method is based on the principle of fracture-surface topography analysis (FRASTA). In FRASTA, the fracture surfaces are scanned by laser microscope and the elevation data is recorded. Based on this recorded elevation data, the J integral can be calculated. The J integral calculated by the new method agrees well with that calculated by the elastic compliance method. FRASTA allows easy determination of the crack opening deformation (CTOA and COA) and the variation in CTOA and COA through specimen thickness.     

CTOA of a stable crack in a thin aluminum fracture specimen

A crack tip opening angle (CTOA) resistance curve was generated from the moiré interferometry data of thin single edge notched (SEN) and central notched (CN), 2024-T3 aluminum fracture specimens. This CTOA resistance curve, which has a steady state value of 6°, was then used to propagate the cracks in elastic–plastic finite element models of the CN specimen and a CN specimen with a simulated multiple site damage. The CTOA of curved crack growth in a biaxial fracture specimen scattered between 4° and 8° but the resultant crack tip opening displacement, which is the vector sum of the mode-I and the mode-II crack tip sliding displacement, remained a constant 0.18 mm. The CTOA of a rapidly propagating crack in 1.6 mm thick, 7075-T6 SEN specimens increased from 4.5° at a low-crack velocity to a constant 7° at the terminal crack velocity.     

A criterion for the time dependence of dynamic fracture

Dynamic fracture is a time-dependent phenomena-in which the spall stress depends on the stress pulse duration. It is shown that the empirical relation between the spall stress and the square root of the stress gradient is equivalent to a simple impulse criterion. A more general criterion based on the concept of cumulative damage is proposed, and good agreement is obtained between calculated and observed values of the spall layer thickness in aluminum.

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Zusammenfassung Ein dynamischer Bruch ist eine zeitabhängige Erscheinung, wo die Absplitterspannung von der Dauer des Stosses abhängt. Es wird gezeigt, dass die empirische Beziehung zwischen der Absplitterspannung und der Quadratwurzel des Spannungsgefälles einem einfachen Impulskriterium equivalent ist. Ein allgemeineres Kriterium wird aufgestellt und vorgeschlagen, das auf den Begriff eines Sammelschadens beruht, und eine gute Übereinstimmung wird erlangt zwischen den berechneten und experimentell beobachteten werten der Ahsplitterungsschichtdicke im Aluminium.

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Résumé Une rupture dynamique est un phénoméne qui dépend du temps et dans lequel la contrainte d'écaillage est une fonction de la durée du choc. II a été démontré que la relation empirique entre la contrainte d'écaillage est la racine carrée du gradient d'écaillage équivaut un simple critère d'impulsion. Nous proposons un critère plus général, basé sur le concept d'un dommage cumulatif, ayant obtenu un bon raccordement entre les valeurs calculées et expérimentalement observées de l'épaisseur d'une couche d'écaillage dans l'aluminium.

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This work was supported by the United States Atomic Energy Commission.     

A criterion for the time dependence of dynamic fracture

Dynamic fracture is a time-dependent phenomena in which the spall stress depends on the stress pulse duration. It is shown that the empirical relation between the spall stress and the square root of the stress gradient is equivalent to a simple impulse criterion. A more general criterion based on the concept of cumulative damage is proposed, and good agreement is obtained between calculated and observed values of the spall layer thickness in aluminum.

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Zusammenfassung Ein dynamischer Bruch ist eine zeitabhängige Erscheinung, wo die Absplitterspannung von der Dauer des Stosses ab:hangt. Es wind gezeigt, dass die empirische Beziehung zwischen der Absplitterspannung und der Quadratwurzel des Spannungsgefälies einem einfachen Impulskriterium equivalent ist. Ein allgemeineres Kriterium wird aufgestellt and vorgeschlagen, das auf den Begriff eines Sammelschadens beruht, und eine gute Ubereinstimmutag wird erlangt zwischen den berechneten und experimentell beobachteten Werten der Absplitterungsschichtdicke im Aluminium.

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Résumé Une rupture dynamique est un phénomène qui dépend du temps et dans lequel la contrainte d'déaillage est une fonction de la duree du choc. II a été démontre que la relation empirique entre la contrainte d'écaillage est la racine carrée du gradient d'décaillage équivaut un simple critère d'impulsion. Nous proposons un critère plus général, basè sur le concept d'un dommage cumulatif, ayant obtenu un bon raccordement entre les valeurs calculées et expérimentalement observées de l'épaisseur d'une couche d'écaillage dans l'aluminium.

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This work was supported by the United States Atomic Energy Commission.     

Two-parametrical fracture criterion

We demonstrate that semi-brittle or semi-plastic solids require more comprehensive fracture interpretation, than brittle or plastic ones. Application of two-parametrical fracture criterions make it possible to solve this problem and to provide more reliable estimation of mechanical behavior of materials. __________ Translated from Problemy Prochnosti, No. 4, pp. 56–63, July–August, 2006.     

A fracture criterion for three-dimensional crack problems

A criterion for predicting the growth of three-dimensional cracks is developed on the basis of the strain energy density concept which has been used successfully for treating two-dimensional crack problems. Fracture is assumed to initiate from the nearest neighbor element located by a set of spherical coordinates (r, θ, φ) attached to the crack border. The new fracture surface is described by a locus of these elements whose locations correspond to the strain energy function, dW/dV, being a minimum. The function dW/dV is found to be singular of the type 1/r and is of quadratic form in the three stress intensity factors k₁, k₂ and k₃ expressed through the strain energy density factor S. It is postulated that unstable crack propagation initiates from a region where S reaches a critical value S_cr = r₀(dW/dV)_cr. The locations of failure lying on the fracture surface is determined by holding (dW/dV)_cr = S_min/r₀ constant. The quantity S_min stands for the value of S minimized with respect to θ and φ and r₀ is a radial distance measured from the crack border.

An example of failure prediction for an embedded elliptical crack subjected to both normal and shear loads is presented. According to the S-criterion, fracture initiation takes place at the ends of the minor axis. An unexpected result is that for a narrow elliptical crack and Poisson's ratio of 1/3 the lowest failure load occurs when the uniaxial tensile load makes an angle of approximately 60° with the crack surface and is in the plane of the major axis. This is in contrast to the expectation that the lowest critical load occurs when the uniaxial tension is perpendicular to the crack surface. In the limit as the elliptical crack becomes increasingly narrower, the result reduces to the two dimensional line crack case of Mode I and III loading. The S-criterion is also applied to the failure prediction of three dimensional cracks under compressive loads.     

A fracture criterion for sharp V-notched samples

The objective of this paper is to show the advantages of the cohesivecrack model for predicting fracture of V-notched components. Criticalvalues of the generalized stress intensity factor can be obtained fromthe knowledge of the material softening function and the elastic parameters,avoiding a cumbersome experimental work. The results were checked successfullyagainst experimental ones, from other authors, in different materials: steel,aluminium, PMMA and PVC. A non dimensional formulation of the fracturecriterion for sharp V-notched components was obtained and a simpleapproximate expression derived for easy appication.     

A criterion for dynamic fracture strength of materials

A phenomenological criterion for damage to materials due to short duration stresses is proposed. Based on the proposed criterion, an equation is obtained to find the time to failure corresponding to an applied stress history. It is shown that the equation is in agreement with several experimental and theoretical studies. The criterion is generalized to the case of repeated loading and an equation is derived to calculate cumulative damage under repeated loading. The predictions of the equation are in qualitative agreement with some test data.     

Method of constraint loss correction of CTOD fracture toughness for fracture assessment of steel components

This paper presents a procedure for transferring the CTOD fracture toughness obtained from laboratory specimens to an equivalent CTOD for structural components, taking constraint loss into account. The Weibull stress criterion is applied to correct the CTOD for constraint loss, which leads to an equivalent CTOD ratio, β, defined as β = δ/δ_WP, where δ and δ_WP are CTODs of the standard fracture toughness specimen and the structural component, respectively, at the same level of the Weibull stress. The CTOD ratio β is intended to apply to the fracture assessment of ferritic steel components to stress levels beyond small-scale yielding. Nomographs are given to determine the β-value as a function of the crack type and size in the component, the yield-to-tensile ratio of the material and the Weibull shape parameter m. Examples of the fracture assessment using β are shown within the context of a failure assessment diagram (FAD). An excessive conservatism observed in the conventional procedure is reduced reasonably by applying the equivalent CTOD ratio, β.     

A modified thickness criterion for fracture toughness testing

A modified criterion is developed on an empirical basis for the minimum thickness $\text{B}{}_{\min }$ of a plane strain fracture toughness test specimen: $\text{B}{}_{\mathrm{<mtext>min</mtext>}}\text{= 400}\text{K}{}_{\mathrm{Ic}}{}^2\text{Eδ}{}_{\mathrm{Y}}$ where $\text{K}{}_{\mathrm{Ic}}$ is the plane strain fracture toughness, $\text{E}$ is the Young's modulus and δ_Y is the yield stress of the material. The modified criterion is tested alongside the ASTM thickness criterion against published data on the variation of $\text{K}{}_{\mathrm{c}}$ with thickness, and shows significantly the better agreement with observed values of $\text{B}{}_{\mathrm{<mtext>min</mtext>}}$ for a wide range of materials.An attempt has been made to rationalise this criterion. The expression is considered to take into account two major factors which determine $\text{B}{}_{\mathrm{<mtext>min</mtext>}}$, the attainment of plane strain in the specimen interior ahead of the crack tip, and the role of microstructure in determining how far the quasi-plane strain fracture (square fracture) extends beyond the region of true plane strain.