Fracture toughness and hydrogen embrittlement of pipes with notches

A technique for experimental determination of fracture toughness and hydrogen embrittlement of pipes made of API 5L X52 steel is described. The tests were performed using arc-shaped specimens with a notch cut out from pipes under the conditions of a three-point bend. The fracture toughness was determined in terms of the J-integral and the stress intensity factor at the notch tip. The value of K _ρ,c was established using the volumetric method based on the experimentally measured critical load and the results of the FEM calculation of the distribution of elastic-plastic stresses ahead of the notch tip, and J _ρ,c was determined using the method of separable functions. The effect of hydrogen embrittlement was studied using electrolytically prehydrogenated specimens.     

Plastic notch stress intensity factors for pointed V-notches under antiplane shear loading

The paper deals with a work-hardening, elastic–plastic, stress analysis of pointed V-notches under antiplane shear deformation loading both under small and large scale yielding. Stress and strain field intensities are expressed in terms of plastic Notch Stress Intensity Factors, which are analytically linked to the corresponding linear elastic ones under small scale yielding. The near tip stress and strain fields are then used to give closed-form expressions for the Strain Energy Density over a circular sector surrounding the notch tip, and for the J-integral parameter, both as a function of the relevant plastic NSIFs, these expressions being valid both under small and large scale yielding.     

J-integral evaluation for U- and V-blunt notches under Mode I loading and materials obeying a power hardening law

The paper deals with calculations of the J-integral for a plate weakened by U- and V-blunt notches under mode I loading in the case of a linear and nonlinear elastic material. The main aim of the study is to suggest simple equations suitable for rapid calculations of the J-integral. The semicircular arc of the notch, which is traction free, is assumed as integration path and the J-integral is given as a function of the strain energy over the notch edge. For a numerical investigation of the strain energy density distribution on the notch edge the equation W(θ)=W_max cos^δ(θ) has been assumed, where δ has been determined from finite element analyses. In particular, the following values of the notch acuity a/ρ and the opening angle 2α have been analyzed: 4 ≤ a/ρ ≤ 400 and 0 ≤ 2α ≤ 3π /4. Considering plates weakened by lateral and central notches under symmetric mode I loading, the approximate relationships for the strain energy density, which require the presence of a non zero notch radius for their application, and the J-integral are discussed firstly considering a linear elastic material and then a material obeying a power hardening law during the loading phase. The predicted results of the J-integral are consistent with those directly obtained from finite element analyses.     

A new path independent integral applied to notched components under mode I loadings

In the present work, the J-integral is applied to rounded V-shaped notches subjected to mode I loading. The material is thought of as obeying a purely linear elastic law. Both numerical and analytical solutions are presented, after careful study of the principal stress along the notch-free edge. When the notch depth-to-radius ratio tends toward infinity, this stress assumes a cosine-type form. Indeed, some analogies with respect to sharp V-shaped notches are highlighted. If an appropriate integration path is chosen, an operator, J _Lρ, is defined, which is invariant with respect to the integration radius and coincides with that pertaining to a sharp V-shaped notch of the same depth. This operator allows estimation of stress concentration factor K _t for V-shaped notches under mode I loading on the basis of the relevant Notch Stress Intensity Factors (N-SIF). A sound agreement is achieved, in particularly in U-notch cases, since the notch depth-to-radius ratio is taken into account as well as the real notch profile.     

The use of the JV parameter in welded joints: Stress analysis and fatigue assessment

This paper investigates the use of the J_V parameter, a path-independent integral, for the evaluation of the elastic local stress parameters in welded details and for the estimation of their fatigue life.First, the stress intensity factors (SIF) of an embedded crack lying along the bisector of a sharp V-notch is calculated by means of the J_V without modelling the crack and by keeping the same external load and boundary conditions of the cracked model. Furthermore, the notch stress intensity factors (NSIFs) of the welds can be calculated after a post processing procedure of FE analysis with the advantage of using coarse meshes.Second, a correlation between the fatigue life of welded details and the J_V parameter is shown. In fact, careful analysis of the fracture surface of fillet welds taken from literature and of new fatigued joints indicates that the first stage of fatigue crack propagation follows the bisector line of the local V-notch as only mode I would be present. Therefore, since the J_V evaluated on a suitable integration path represents the SIF of an embedded crack lying along the bisector, the J_V is used for the fatigue life assessment of welded details. The critical characteristic length of a suitable integration path for welded joints made of steel and aluminium alloys has been calculated. These critical characteristic lengths were used for the evaluation of two fatigue general scatter bands, mainly based on fatigue data of non-load-carrying cruciform joints characterised by a V-notch angle of 135°. Further, fatigue life data of steel and aluminium alloy welded connections have also been investigated when both mode I and mode II loadings are singular.     

A general weight function for inclined cracks at sharp V-notches

A general method for evaluating the Stress Intensity Factors of an inclined edge crack originated at the tip of a sharp V-notch in a semiplane is presented. An analytical Weight Function with a matrix structure was derived by extending a method developed for an inclined edge crack in an unnotched semi-plane. The effects of the principal geometrical parameters governing the problem were studied through a parametric finite element analysis, carried out for different reference loading conditions. The Weight Function can be used to produce efficient and accurate evaluations of the stress intensity factors for cracks with inclination angle in the range −72°, +72° emanating from V-notches with opening angle in the range from 18° to 144°. For a crack length up to the 10% of the characteristic notch dimension, the maximum estimated error of the Stress Intensity Factor is lower than 2% (typical errors less than 1%) in the whole ranges of the angular parameters. The capability of the proposed method to analyse cracked notches in finite-size bodies was also considered. The agreement between the results with those obtained by accurate Finite Element solutions suggests that the proposed Weight Function can be used as a general tool for evaluating the Fracture Mechanics parameters of a short crack at any V-notch tip.     

Analysis of the driving force for a generally oriented crack in a functionally graded strip sandwiched between two homogeneous half planes

The driving forces for a generally oriented crack problem embedded in a Functionally Graded strip sandwiched between two half plane are analyzed using singular integral equations with Cauchy kernels, and integrated using Lobatto-Chebyshev collocation. Mixed-mode Stress Intensity Factors (SIF) and Strain Energy Release Rates (SERR) are calculated. The Stress Intensity Factors are compared for accuracy with previously published results. Parametric studies are conducted for various non-homogeneity ratios, crack lengths, crack orientation and thickness of the strip. It is shown that the SERR is more complete and should be used for crack propagation analysis.     

Analytical modeling of imperfect bond between coated fibers and matrix material

The present study is intended to find the stress intensity factors (SIF) and strain energy release rates (SERR) at the tips of an interface crack in a non-homogeneous medium. The boundary-value problem governing a three-phase concentric cylinders model is used to analyze annular interfacial crack problems with Love's strain functions. The complex form of a singular integral equation of second kind is formulated using Bessel's functions in Fourier domain. Stress intensity factors (SIF) and total strain energy release rates (SERR) are calculated using Jacoby polynomials. For validity of the equations of Stress Intensity Factors, the Singular Integral Equation (SIE) of a three concentric cylinders model is reduced to the SIE for a two concentric cylinders model and results are compared with previous results of Erdogan.     

Arbitrarily oriented microcracks near the tip of an interface macrocrack in bonded dissimilar anisotropic materials

It is well known that microcracking in brittle materials results in a reduction of the stress intensity factor (SIF) and energy release rate (ERR). The reduced SIF or ERR represents crack tip shielding which is of significant interest to micromechanics and material science researchers. However, the effect of microcracking on the SIF and ERR is a complicated subject even for isotropic homogeneous materials, and becomes much more formidable in case of interface cracks in bonded dissimilar solids. To unravel the micromechanics of interface crack tip shielding in bonded dissimilar anisotropic solids, an interface crack interacting with arbitrarily oriented subinterface microcracks in bonded dissimilar anisotropic materials is studied. After deducing the fundamental solutions for a subinterface crack under concentrated normal and tangential tractions, the present interaction problem is reduced to a system of integral equations which is then solved numerically. A J‐integral analysis is then performed with special attention focused on the J₂‐integral in a local coordinate system attached to the microcracks. Theoretical and numerical results reassert the conservation law of the J‐integral derived for isotropic materials 1 , 2 also to be valid for bonded dissimilar anisotropic materials. It is further concluded that there is a wastage when the remote J‐integral transmits across the microcracking zone from infinity to the interface macrocrack tip. In order to highlight the influence of microstructure on the interfacial crack tip stress field, the crack tip SIF and ERR in several typical cases are presented. It is interesting to note that the Mode I SIF at the interface crack tip is quite different from the ERR in bonded dissimilar anisotropic materials.     

Comparison of DBEM and FEM crack path predictions in a notched shaft under torsion

The rather complex 3D fatigue crack growth behaviour of two anti-symmetric “bird wing” cracks, initiated from the two crack front corner points of a notched shaft undergoing torsion, is investigated by the Dual Boundary Element Method (DBEM) and by the Finite Element Method (FEM). Different criteria for the crack path assessment (Minimum Strain Energy Density, Maximum Principal Stress and Approximate Energy Release Rate) and for the Stress Intensity Factor (SIF) evaluation (COD and J-integral) are adopted. The SIF’s and the crack path, calculated by such different approaches, turn out to be well consistent with each other. Moreover the simulated crack path qualitatively agrees with experimental findings available from literature.     

Hypersingular quarter-point boundary elements for crack problems

The present paper deals with the study and effective implementation for Stress Intensity Factor computation of a mixed boundary element approach based on the standard displacement integral equation and the hypersingular traction integral equation. Expressions for the evaluation of the hypersingular integrals along general curved quadratic line elements are presented. The integration is carried out by transformation of the hypersingular integrals into regular integrals, which are evaluated by standard quadratures, and simple singular integrals, which are integrated analytically. The generality of the method allows for the modelling of curved cracks and the use of straight line quarter-point elements. The Stress Intensity Factors can be computed very accurately from the Crack Opening Displacement at collocation points extremely close to the crack tip. Several examples with different crack geometries are analyzed. The computed results show that the proposed approach for Stress Intensity Factors evaluation is simple, produces very accurate solutions and has little dependence on the size of the elements near the crack tip.     

Size effect in beams with rounded-tip V-notch

Stresses and strains in a beam with a single-edge rounded-tip V-notch subjected to bending were analyzed by the method of finite elements by using nonconforming quadrilateral elements under the assumption that the material is linearly elastic. We studied the influence of the depth of the notcha, its radius of curvature ρ, the angle of the notch ω, and the height of the beamh on the stress intensity factorK _t . It is established that the relative depth of the notch ζ=a/h causes practically no influence if the notch angle ω lies within the range 0°–135°. The influence of the notch rapidly weakens as the relative radius of curvature ρ _d =ρ/h increases from 0.01 to 1.0 and becomes insignificant for ρ _d ≤ 1. For small ρ _d (ρ _d ≤ 1), the quantityK _t attains its maximum value provided that ζ lies within the range 0.1–0.3. As the height of the beam increases, the quantityK _t first remains practically constant, then increases, and finally, ash infinitely increases, approaches a certain constant value. Dipartimento di Ingegneria Civile, Universita di Parma Viale delle Scienze, 43100 Parma, Italy. Published in Fizyko-Khimichna Mekhanika Materialiv, Vol. 32, No. 3, pp. 73–79, May–June, 1996.     

Stress intensity factors for a wide range of long-deep semi-elliptical surface cracks, partly through-wall cracks and fully through-wall cracks in tubular members

To calculate the rate of fatigue crack growth in tubular members, one approach is to make use of the fracture mechanics based Paris law. Stress intensity factors (SIF) of the cracked tubular members are prerequisite for such calculations. In this paper, stress intensity factors for circumferential deep semi-elliptical surface crack (a/t > 0.8), semi-elliptical partly through-wall crack and fully through-wall crack cracks in tubular members subjected to axial tension are presented. The work has produced a comprehensive set of equations for stress intensity factors as a function of a/T, c/πR and R/T for deep surface cracks. For the partly through-wall cracks and fully through-wall cracks, two sets of bounding stress intensity factor equations were produced based on which all stress intensity factors within the range of parameters can be obtained by interpolation.     

Weld magnification factors for semi-elliptical surface cracks in fillet welded T-butt joint models

The weld magnification factor method has been widely used in the determination of the stress intensity factor (SIF) for weld-toe cracks in welded structural components. Weld magnification factors M _kare normally derived from two-dimensional crack models with fillet weld profiles to take account of the effect of weld-notch stress concentration at the deepest point of the crack front. This paper presents a detailed three-dimensional analysis of weld-toe surface cracks in fillet welded T-butt joint models using the finite element method. Effects of the weld notch and the welded attachment stiffness on the SIFs of the weld-toe surface cracks have been studied quantitatively. Weld magnification factors applying to the whole surface crack fronts have been estimated. Numerical results show two contradictory effects; that the effect of weld notch increases SIF values throughout the shallow surface crack fronts which are in the region of notch stress concentration, while the effect of local structural constraint reduces the SIF values. The increase in the SIF values mainly depends upon the relative crack front depth and the decrease in the SIF values mainly depends upon the crack shape aspect ratio for a specific weld profile. Both effects on the weld magnification factors can be estimated separately. A simple approach for deriving the weld magnification factors for various weld-toe surface crack problems is proposed for engineering applications.     

Use of J-integral to predict static failures in sharp V-notches and rounded U-notches

In the present paper, the physical meaning of J_V (namely, the classic J-integral applied to either sharp V-notch) is discussed. Consider a Cartesian reference frame having the x-axis parallel to the notch bisector, each mode of J_V, for a given circular path, is proportional to the correspondent mode of the classic J-integral of a virtual crack having length equal to the path radius and emanating from the tip of the V-notch. Analytical and numerical results have been performed for linear elastic materials. Additionally, in order to verify the formulations of J_V, experimental result of embedded cracks of sharp V-notch was considered.Then, by introducing a characteristic path radius ρ^∗, assumed to be dependent only on the material properties, the J_V parameter was used for the estimation of the static failure load of sharp V-notches specimens under mode I loading.Furthermore, the J_Vρ parameter (namely, the classic J-integral applied to U-rounded notches) was used to analyze the static failure of two new series of specimens with double U-notches made of brittle material (PMMA and PVC glass) subjected to tensile loading. This method allowed us to prove that when the ratio between the notch tip radius and ρ^∗ is small the approach agrees with the classic J-integral, whereas when ρ^∗ becomes small with respect to the notch tip radius, the J_Vρ method agrees with the classic peak stress approach.     

Stress intensity factors for large aspect ratio surface and corner cracks at a semi-circular notch in a tension specimen

Stress intensity factor solutions for semi-elliptic surface and quarter-elliptic corner cracks emanating from a semi-circular notch in a tension specimen are presented. A threedimensional finite-element analysis in conjunction with the equivalent domain integral was used to calculate stress intensity factors (SIF). SIF solutions for surface or corner crack (crack length to depth ratio of 2) at a notch are presented for a wide range of crack sizes and notch radii. Results showed that the SIF are larger for larger crack lengths and for larger notch radii. The SIF are nearly constant all along the crack front for deep surface cracks and for all corner cracks analysed.     

Mixed mode plane stress ductile fracture

Mixed mode ductile fractures in thin sheets are shown to be possible. The staggered deep edge notch tension specimen enablesJ _p , the plane stress propagation value of theJ integral, and dJ/d, the rate of increase inJ with crack growth to be measured from the specific work of fracture. TheJ integral can also be separated into its two component modesJ ₁ andJ _n.For the particular low alloy steel testedJ _p is virtually independent of the mode of fracture, but for other materialsJ _p may be dependent on the fracture mode.

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Résumé On montre que des ruptures mixtes de mode ductile dans des feuillards minces sont possibles. En utilisant une éprouvette de traction comportant deux entailles latérales, profondes et décalées, on peut mesurerJ _p composante de propagation de l'intégraleJ en état plan de tension et dJ/d _a , le taux d'accroissement deJ en fonction de la croissance de la fissure à partir du travail spécifique de rupture. L'intégraleJ peut également être séparée en ses deux composantes des modesJ ₁ etJ _n.Dans le cas de l'acier faiblement allié particulier qui a été traité,J _p est virtuellement indépendant du mode de rupture; cependant, pour d'autres matériaux,J _p peut dépendre du mode de rupture.

     

Stress intensity factors in spot welds

This paper looks at stress intensity factors of cracks in resistance spot welded joints. Stress intensity factors have been used in the past to predict fatigue crack propagation life of resistance spot welds. However, the stress intensity factors from all previous work was based on assumed initial notch cracks at the nugget, parallel to the sheets. Physical evidence shows, however, that fatigue cracks in spot welds propagate through the thickness of the sheets rather than through the nugget. In this work, stress intensity factors of assumed notch cracks and through thickness cracks in tensile shear (TS) and modified coach peel (MCP) specimens were determined by the finite element method. The finite element results from the assumed notch cracks were compared with the results in the literature and were found to be in agreement with the results from Zhang’s equations [Int. J. Fract. 88 (1997) 167]. The stress intensity factors of assumed notch cracks were found to be different from those of through thickness cracks. To date, no analytic equations for stress intensity factors of through thickness cracks in spot welds have been published. In the current work, simple equations are proposed to estimate the K_I and K_II values of through thickness cracks in TS and MCP specimens.     

Prediction of fracture toughness for heat-resistant steels considering specimen dimensions. Report 2. Ductile fracture

A model of ductile failure of a body with a crack has been developed which enables predicting fracture toughness on the upper shelf of the fracture toughness temperature dependence taking into account the influence of the stress state. The model is based on the physical-mechanical model of ductile failure which is controlled by the critical value εf reached by plastic strain at the crack tip ε _i ^ρ . In this case it is assumed that both the ε _i ^ρ value, which precedes the crack growth onset by the mechanism of pore coalescence, and the critical strain εf are functions of specific stress state parameters, namely: the critical strain is a function of the stress state triaxiality σ _m /σ _n (σ _m is the hydrostatic stress, σ _i is the stress intensity), and ε _i ^ρ is a function of the parameter χ introduced, which is an explicit function of all three principal local stresses in the process zone at the crack tip and which defines the degree to which the stress state approaches the plane strain conditions for a body of specified thickness. The model developed has two modifications one of which enables predicting fracture toughness of large-size bodies from the results of testing only small cylindrical specimens without cracks (smooth and with a circular recess) and the other from the results of testing small cylindrical specimens and small specimens with a crack. Translated from Problemy Prochnosti, No. 2, pp. 5–19, March–April, 1997.     

MODE I STRESS INTENSITY FACTOR EQUATIONS FOR CRACKS AT NOTCHES AND CAVITIES

Abstract— In this paper, the notch-crack problem is treated in two different ways: if the non-dimensional crack length l /ρ ( l = crack length; ρ= notch root radius) is smaller than the transition crack length l _T/ρ, it is treated as an edge crack lying within the local stress field around the notch tip; if l/ ρ is larger than l _T/ρ, the notch-crack is considered as a simple flat crack problem subjected to remote loading, the flat crack size being the sum of notch depth and the real crack length. Based on currently available numerical data, expressions for the transition crack length, l _T, and for the geometric factor F = K _I/(1.1215K_tσ√π l ) are developed for various notch problems for the crack length range l ≦ l _T. It is found that the stress (σ_yy) normalized by the peak stress (σ_peak), σ_yy/σ_peak, for the pre-cracked component is very similar to the geometric factor for short cracks.