Three-dimensional Stress Intensity Factors Research Articles

Study on mixed-mode fracture behavior of TC4 titanium alloy

Mixed mode fracture behaviors of TC4 titanium alloy are studied by finite element method, testing and theoretical analysis systematically. Results show that there exists II-III coupling effect ahead of crack tip for mixed mode crack, based on which three-dimensional stress intensity factors are defined and calculated; The crack under I-II mixed mode loading exhibits a planar propagation state, the deflection angle increases with mode II component increasing; I-II mixed mode fracture of TC4 shows the characterization of brittle fracture mechanism, and brittle fracture criteria are in agreement with test results with some conservative. While the crack under I-III mixed mode loading exhibits a spatial propagation state, the deflection angle firstly increases then decreases with mode III component increasing; It is due to that the fracture mechanism is from brittle to brittle-ductile mixed fracture mode, as mode III component increases. The brittle criterion has a good prediction on I-III mixed mode brittle fracture behavior, with mode III component lower enough. The conclusions in this paper are of great significance to the mixed mode fracture evaluation of TC4 titanium alloys.

3-Dimensional analysis of fatigue crack fields and crack growth by in situ synchrotron X-ray tomography

The propagation rate of a fatigue crack in a nodular cast iron, loaded in cyclic tension, has been studied in situ by X-ray computed tomography and digital volume correlation. The semi-elliptical crack initiated from an asymmetric corner notch and evolved to a semi-circular shape, initially with a higher growth rate towards one edge of the notch before the propagation rate along the crack front became essentially independent of position. The phase congruency of the displacement field was used to measure the crack shape. The three-dimensional stress intensity factors were calculated via a linear elastic finite element model that used the displacement fields around the crack front as the boundary conditions. Closure of the crack tip region was observed. The cyclic change in the local mode I opening of the crack tip determined the local fatigue crack propagation rate along the crack front.

The sloshing effects on the crack instability of the spherical tank under the simultaneous effect of internal pressure and earthquake

Spherical tanks have an important function in the industry due to the internal pressure of their contents. Also, the supporting structure of the spherical tank controls stability and damage to the tank One of the damages that can lead to a critical situation is an unstable crack in the column-vessel joint. In this study, the sloshing effects on the instability of 10 mm and 20 mm long semi-elliptical cracks with three aspect ratios in the connection zones of the supporting structure under the effect of internal pressure and eleven earthquakes have been investigated. Furthermore, using the finite element sub-modeling method around the crack area and part of the structure, the effect of fluid–structure interaction has been considered for three liquid levels to calculate the stress intensity factors along the crack front. Since the tank is under the simultaneous effect of internal pressure, earthquake, and sloshing motion, a three-dimensional mixed-mode stress intensity factor needed to be considered to study the crack instability. The results show that earthquakes and sloshing motions can have various effects on the equivalent stress intensity factors. For almost two-thirds of the studied cases, the equivalent stress intensity factor for the 50% filled vessel was 10%–70% greater than the 98% filled vessel. This finding shows that the crack located in the connection zones of the supporting structure under the simultaneous effect of internal pressure, earthquake, and sloshing motion, could lead to failure.

HR-EBSD analysis of in situ stable crack growth at the micron scale

Understanding the local fracture resistance of microstructural features, such as brittle inclusions, coatings, and interfaces, at the microscale is critical for microstructure-informed design of materials. In this study, a novel approach has been formulated to decompose the J-integral evaluation of the elastic energy release rate to the three-dimensional stress intensity factors directly from experimental measurements of the elastic deformation gradient tensors of the crack field by in situ high (angular) resolution electron backscatter diffraction (HR-EBSD). An exemplar study is presented of a quasi-static crack, inclined to the observed surface, propagating on low index {hkl} planes in a (001) single crystal silicon wafer.

Three-dimensional weight function analyses and stress intensity factors for two eccentric and asymmetric surface cracks and surface-corner cracks at a circular hole

Stress intensity factors (SIFs) of two eccentric and asymmetric surface cracks and surface-corner cracks at a hole are rare in the literature, since the problem is too complicated to be tackled by analytical methods and too costly by numerical approaches. A 3D slice synthesis weight function method (SSWFM) is developed to compute their 3D SIFs. The results agree well with those from finite element method (FEM). The SSWFM is about 450 times faster in calculation of the SIFs than FEM/Franc3D, and is very useful for 3D fatigue crack growth analyses of complicated surface and corner cracks at a hole.

Three-dimensional weight function analyses and stress intensity factors for two unsymmetric surface cracks and surface-corner cracks at a circular hole

Two unsymmetric surface cracks and a combination of surface and corner cracks emanating from a circular hole are frequently encountered in many engineering structures, especially in airframes. Their stress intensity factors are critical for damage tolerance analyses. However, compared to cases of a single crack and symmetric double cracks that have been extensively analyzed in the literature, the present unsymmetric surface cracks and surface/corner cracks emanating from a circular hole are much more complicated because more geometric variables are involved. In this paper, the slice synthesis weight function method for two unsymmetric hole-edge corner cracks developed recently by the present authors is further extended to calculate the stress intensity factors (SIFs) of two unsymmetric surface cracks and a combination of surface and corner cracks at a hole. The obtained SIFs are verified by comparing to limited solutions in the existing literature and also extensive finite element analysis. Very good agreements are achieved. Compared to 3D finite element analysis, the present slice synthesis weight function analysis is remarkably more efficient, and therefore can enhance the current capability of fatigue and fracture analyses for structures with unsymmetric surface and corner cracks at a circular hole.

In situ characterisation of the strain fields of intragranular slip bands in ferrite by high-resolution electron backscatter diffraction

High angular resolution electron backscatter diffraction has been used to quantify the local elastic field at the tip of mechanically loaded intragranular slip bands observed in situ in the ferrite grains of an age-hardened duplex stainless steel (Zeron 100). The surface elastic strain field was integrated to calculate in-plane and out-of-plane surface displacements. This allowed the elastic fields to be parameterised in a finite element analysis, which used the displacement field as the boundary conditions, to obtain the potential strain energy release rate (J-integral) and three-dimensional stress intensity factors (KI,II,III).This new analysis method is demonstrated by examining the elastic fields around the tip of an incipient slip band, an array of slip bands and the loading of a slip band. Direct measurement of the stress tensor in the grain identified the active slip systems with the highest Schmid factor. The stress intensity factors ahead of the slip band, measured under load, were directly affected by the magnitude of loading and the inclination angle of the slip band to the observed surface.

Three-dimensional sharp V-notch stress intensity factor and strain energy rate density under creeping conditions

Fracture evaluation of three dimensional (3D) notches in creeping solids have drawn considerable attention due to their potential application in structural integrity assessment. In this paper, the notch stress intensity factor (NSIF) and the strain energy rate density (SERD) rule are extended to 3D sharp V-notch tip under creeping conditions. In particular, the out-of-plane factor Tz is introduced to describe the 3D NSIF of creeping sharp V-notch tip field. The out-of-plane effect on the SERD is also studied based on the KN(t)-Tz solution. A method to evaluate the 3D sharp V-notch NSIF was proposed based on the concept of SERD. The link between the NISF and SERD of 3D sharp V-notch is established and discussed. It is found that the SERD is obviously influenced by the out-of-plane factor. The variations of NSIF along the thickness direction of 3D sharp V-notch front and the effect of creep time are also discussed. The accuracy of the presented evaluation form is also validated. The solution given in this paper could provide a new perspective and theoretical foundation on understanding the NSIF and SERD for sharp V-notch.

Combined evaluation of Young modulus and fracture toughness in small specimens of fine grained nuclear graphite using 3D image analysis

The fracture toughness of the fine-grained nuclear graphite SNG742 has been investigated by observation of stable crack propagation in double cleavage drilled compression specimens. The three-dimensional displacement fields were obtained by digital volume correlation (DVC) of in situ laboratory X-ray computed tomographs. The crack tip location and crack opening displacements were determined using an image edge detection algorithm based on the wavelet modulus maxima. The Young modulus was estimated by fitting a finite element model to DVC displacement field data measured before crack initiation. Using the 3D crack geometry and the surrounding full-field 3D displacement fields as boundary conditions, the elastic strain energy release rate J and the three-dimensional stress intensity factors KI to KIII were then evaluated via the contour integral method. Constant mode I critical stress intensity factor was obtained along the curved crack fronts, with negligible shearing modes. This method allows evaluation of the fracture toughness without prior knowledge of elastic properties, and has potential applications to assess the effects of high temperature, oxidation and irradiation in small specimens of nuclear graphite.

Three-dimensional mixed-mode stress intensity factors for deflected external surface cracks in thin and midsize-thick-walled spherical pressure vessels

Normalized three-dimensional mixed-mode stress intensity factor (SIF) distributions are presented for deflected external surface cracks in thin- and midsize-thick-walled spherical pressure vessels. With an aim to build a library of SIF solutions, values of the governing parameters of the problem, namely crack deflection angle, normalized crack depth and crack shape aspect ratio, are changed within their practical ranges. The obtained results show that for a given case, increasing the deflection angle yields a decrease in mode-I SIFs and increases in mode-II and mode-III SIFs. It is also observed that as the normalized crack depth increases, SIFs generally increase along the crack front. The results also show that magnitudes of the normalized mixed mode stress intensity factors at the depth location for midsize-thick-walled vessels are lower than those of thin-walled spherical vessels. The crack deflection angle has the highest effect among all parameters, emphasizing the importance of this study. It is concluded that the presented SIF solutions can be used to assess damage tolerance of a spherical vessel with a deflected external surface crack.

On through-thickness distribution of stress intensity factors and energy release rates in the vicinity of crack fronts

First, an eigenfunction expansion method is presented to obtain three-dimensional asymptotic stress fields in the vicinity of the front of a semi-infinite crack, subjected to the far-field extension/bending, in-plane shear/twisting and antiplane shear loadings, distributed through the plate thickness. A complex variable approach in conjunction with this eigenfunction expansion technique is employed here to derive the heretofore-unavailable through-thickness distribution of stress intensity factors and energy release rates for a center-crack weakening an infinite plate. Interesting numerical results for three-dimensional stress intensity factors and energy release rates for five different far-field loading scenarios are also presented.

Three-dimensional mixed-mode stress intensity factors for deflected internal surface cracks in thin and midsize-thick-walled spherical pressure vessels

In this paper, three-dimensional mixed-mode stress intensity factor solutions are obtained for deflected inner surface cracks contained in thin- and midsize-thick-walled spherical pressure vessels. In an effort to build a library of stress intensity factor solutions for different realistic cases, main parameters affecting the problem, which are crack deflection angle, normalized crack depth and crack shape aspect ratio, are changed systematically to cover all combinations. The results show that as the deflection angle increases, mode-I stress intensity factors decrease and mode-II and mode-III stress intensity factors increase for a given case. It is also observed that as the normalized crack depth increases, stress intensity factors increase along the crack front. The results show that magnitudes of the normalized mixed mode stress intensity factors for midsize-thick-walled vessels are higher than those of thin-walled spherical vessels. Crack deflection angle is shown to have the highest influencing effect among all parameters. It is also observed that especially for higher crack deflection angles, which have higher mode-mixity, crack surfaces may come into contact partially or fully.

Applications on Three-Dimensional Mixed Mode Fatigue Crack Propagation Using Fracture and Crack Propagation Analysis System (FCPAS)

In this study, results from two applications on three-dimensional fatigue crack propagation using the in-house developed “Fracture and Crack Propagation Analysis System (FCPAS)” are presented. FCPAS uses finite element models to calculate three-dimensional mixed mode stress intensity factors and other sub-modules to predict shapes of the incrementally growing crack fronts and the resulting fatigue crack propagation lives. The evolving crack surfaces are generated by successively adding the incremental growth surfaces and re-meshing and re-solving the finite element model using the standalone program FRAC3D, a finite element-based standalone program employing three-dimensional enriched finite elements. The results show that the fracture surfaces evolve into a mode-I type three-dimensional crack as expected. Very good agreements are obtained between the results of the current studies and those of numerical applications in terms of both evolving crack surfaces and crack propagation lives. Therefore, it is concluded that the applied method is capable of accurately predicting linear elastic three-dimensional mixed mode fatigue crack propagation problems.

Three-dimensional stress intensity factor computations for cracks in functionally graded materials (FGM)

Three-dimensional stress intensity factor computations for cracks in functionally graded materials (FGM)

Crack arrest behavior of central-cracked stiffened plates under uniform tensions

The magnitude and distribution of three-dimensional stress intensity factor are affected by out-of-plane bending and loading modes in stiffened plates, and the influences are studied externally under uniform tensile stresses. Based on theoretical analysis of linear elastic fracture mechanics, crack propagation behavior is investigated with three-dimensional finite element method. The crack arrest effects of stiffeners and the influences of out-of-plane bending are analyzed in three typical stiffened plates. Then relative stiffness is proposed to reflect the difference of crack arrest effects of the stiffeners, and mathematical models are developed for the fracture parameters of stiffened plates. Lastly, the effects of loading modes on crack propagation are discussed. The results indicate that stiffened plates generally have better crack arrest effects than flat (unstiffened) plates, and the relative stiffness, location, integrity and load sharing of the stiffeners play significant roles in crack arrest behavior. In some situations, the influence of out-of-plane bending cannot be negligible and should be considered carefully.

Stress intensity factors for fatigue analysis of weld toe cracks in a girth-welded pipe

This paper addresses the lack of three-dimensional stress intensity factor solutions for small to large surface cracks located at the weld toe region of welded pipes. A methodology was developed to model and calculate the stress intensity factors and weld toe magnification factors for semi-elliptical surface cracks in a circumferentially welded pipe. Three-dimensional finite element models were developed for a wide range of surface crack geometries. The stress intensity factors for surface cracks in a plain pipe were benchmarked with reported results and showed good agreement to within 2.6%. Stress intensity factors and weld toe magnification factors solutions were determined for weld toe surface cracks located at a circumferentially welded pipe. The weld toe semi-elliptical surface cracks geometries vary from small crack depth-to-thickness (a/t) ratios of 0.05 to large crack depth-to-thickness (a/t) ratio of 0.5. Three semi-elliptical surface crack shape aspect ratios (a/c) were modelled for values of 1.0, 0.5 and 0.25. The stress intensity factor and weld toe magnification factors solutions are reported in this paper for a wide range of semi-elliptical surface crack geometries with crack depth-to-thickness ratios (a/t) from 0.05 to 0.5 and crack shape aspect ratios (a/c) from 0.25 to 1.0 subject to pipe wall tension and bending loading. The stress intensity factor and weld toe magnification factors solutions are used for fatigue crack growth prediction assessment of weld toe surface cracks propagating in a circumferentially welded pipe.

Three-dimensional stress intensity factors for ring cracks and arrays of coplanar cracks emanating from the inner surface of a spherical pressure vessel

Certain spherical pressure vessels are composed of two hemispheres joined together by a girth weld. These vessels are susceptible to multiple cracking along the weld resulting in one or more cracks developing from the inner surface of the vessel and creating either a ring (circumferential) crack, or an array of coplanar cracks on the equatorial-weld plane. In order to assess the fracture endurance and the fatigue life of such vessels it is necessary to evaluate the Stress Intensity Factors (SIFs) distribution along the fronts of these cracks. However, to date, only two solutions for the SIF for an internal ring crack as well as two 3-D solutions for a single internal semi-elliptical crack prevailing in various spherical pressure vessels are available. In the present analysis, mode I SIF distributions for a wide range of ring, lunular, and crescentic cracks are evaluated. The 3-D analysis is performed, via the FE method employing singular elements along the crack front. SIFs for numerous ring cracks of different depths prevailing in thin, moderately thick, and thick spherical vessels are evaluated first. Subsequently, three-dimensional mode I SIF distributions along the crack fronts of a variety of lunular and crescentic crack array configurations are calculated for three spherical vessel geometries, with outer to inner radii ratios of R0/Ri=1.01, 1.1, and 1.7. SIFs are evaluated for arrays of density δ=0–0.99; for a wide range of crack-depth to wall-thickness ratios, a/t, from 0.025 to 0.95; and for various lunular and crescentic cracks with ellipticities, i.e., the ratio of crack-depth to semi-length, a/c, from 0.2 to 1.5. The obtained results clearly indicate that the SIFs are considerably affected by the three-dimensionality of the problem and by the following parameters: the crack density of the array-δ, the relative crack depth-a/t, crack ellipticity-a/c, and the geometry of the spherical vessel-η. Furthermore, it is shown that in some cases the commonly accepted approach that the SIF for a ring crack of any given depth is the upper bound to the maximum SIF occurring in an array of coplanar cracks, of the same depth, is not universal.

Three-dimensional singular stress/residual stress fields at crack/anticrack fronts in monoclinic plates under antiplane shear loading

A recently developed eigenfunction expansion technique, based in part on separation of the thickness-variable, is first developed to derive three-dimensional asymptotic stress field in the vicinity of the front of a semi-infinite through-thickness crack/anticrack weakening/reinforcing an infinite monoclinic plate, of finite thickness and subjected to far-field antiplane shear loading. Crack/anticrack-face boundary conditions and those that are prescribed on the top and bottom (free or fixed) surfaces of the anisotropic (monoclinic) plate are exactly satisfied. Five different through-thickness crack/anticrack-face boundary conditions are considered: (i) slit crack, (ii) anticrack or perfectly bonded rigid inclusion, (iii) transversely rigid inclusion (longitudinal slip permitted), (iv) rigid inclusion in part perfectly bonded, the remainder with slip, and (v) rigid inclusion located alongside a crack. The three-dimensional stress intensity factor for a center-crack, and stress singularity coefficients for/on a center-anticrack are then derived by incorporating an extension of the Stroh type approach in the present analysis. Through-thickness distribution of stress intensity factor and stress singularity coefficient for a crack and an anticrack, respectively, is also presented. Additionally, singular residual stress fields in the vicinity of the fronts of these cracks, anticracks and similar discontinuities are also discussed. Hitherto unavailable expressions for three-dimensional energy release and absorption rates for center-cracks and anticracks are derived by using Irwin’s crack closure and Eshelby’s eigenstrain approach, respectively. A heretofore unavailable expression for the energy release rate on the super-rigid inclusion is derived, using an approach which is analogous, in a reverse sense, to Irwin’s crack closure method. Finally, a new mode III crack deflection/bifurcation criterion is also derived. The crack deviation under antiplane shear loading is strongly correlated with the elastic stiffness constant, c45, of the monoclinic single crystal or off-axis composite lamina concerned.

Three-dimensional stress intensity factor calibration for a stiffened cracked plate

Three-dimensional finite element analyses are used in this paper to calibrate the stress intensity factor in a cracked stiffened plate subjected to remote uniform traction. An accurate numerical determination of the stress field and stress intensity variation through the thickness of a central cracked plate was first carried out in order to evaluate three-dimensional effects. A stiffened cracked plate was then analysed, taking into account the results and the conclusions obtained in the previous study. Such a structure was chosen due to the growing interest for large integral metallic structures for aircraft applications, following the continuous need for low cost and the emergence of new technologies. The J-Integral technique was used to calculate the values of the stress intensity factor along the plate thickness. The plane strain behaviour near the crack front and the variation of the opening stress are discussed.

Three-dimensional mixed-mode stress intensity factors for cracks in functionally graded materials using enriched finite elements

Three-dimensional enriched finite elements are used to compute mixed-mode stress intensity factors (SIFs) for three-dimensional cracks in elastic functionally graded materials (FGMs) that are subject to general mixed-mode loading and constraint conditions. The method, which advantageously does not require special mesh configuration/modifications and post-processing of finite element results, is an enhancement of previous developments applied so far on isotropic homogeneous and isotropic interface cracks. The spatial variation of FGM material properties is taken into account at the level of element integration points. To validate the developed method, two- and three-dimensional mixed-mode fracture problems are selected from the literature for comparison. Two-dimensional cases include: inclined central crack in a large FGM medium under uniform tensile strain and stress loadings, a slanted crack in a finite-size FGM plate under exponentially varying tensile stress loading and an edge crack in a finite-size plate under shear traction load. The three-dimensional example models a deflected surface crack in a finite-size FGM plate under uniform tensile stress loading. Comparisons between current results and those from analytical and other numerical methods yield good agreement. Thus, it is concluded that the developed three-dimensional enriched finite elements are capable of accurately computing mixed-mode fracture parameters for cracks in FGMs.