Variation Of Stress Intensity Factor Research Articles

Three-dimensional singular stress field near the interfacial bond line of a tapered jointed plate either free-standing (notch) or (fully/partially) attached to a super-rigid inclusion (antinotch)

A three-dimensional eigenfunction expansion approach is employed for determining singular stress fields in the vicinity of interfacial bond line of a tapered jointed plate either free-standing (notch) or (fully/partially) attached to a super-rigid inclusion (antinotch). The tapered jointed bi-material plate is subjected to extension/bending (mode I) and shear/twisting (mode II) far field loading (extension and shear being in the plane of the cross-section and bending/twisting about mid-width). Hitherto unavailable results, pertaining to the width-wise variations of stress intensity factors corresponding to symmetric and skew-symmetric (about mid-width) cosine function loads, in the vicinity of the interfacial bond line, are presented.

Crack propagation in elastic solids using the truss-like discrete element method

The crack propagation simulation is still an open problem in the mechanical simulation field. In the present work this problem is analyzed using a version of truss-like Discrete Element Method, that here we called DEM. This method has been used with success in several applications in solid mechanical problems where the simulation of fracture and fragmentation is relevant. The formulation of DEM explaining the way the process of rupture could be simulated in consistent form is showed. Also are described details about how the dynamical fracto-mechanical stress intensity factors are computed. The main aim of this paper is to show the ability of this method in simulating fracture and crack propagation in solids, for this, three examples with different levels of complexity are analyzed. The obtained results are presented in terms of the variation of dynamic stress intensity factor in the fracture process, the stress map and geometric configuration on different steps in the simulation of the fracture process, the crack speed and the energetic balance during all the process. These results are compared with experimental and numerical results obtained by other researchers and published in recognized scientific papers. Final commentaries about the performance of the version of lattice model considered are carried out.

On XFEM Applications to Crack Surface under External Force

The extended finite element method is applied to modeling growth of arbitrary crack with crack surface tractions. Firstly, the extended finite element method is investigated for the stress intensity factor solution of surface traction problems. Secondly, for different water pressure acting on the crack surfaces and different crack length, the variation of the stress intensity factors is investigated. Finally, the process of hydraulic fracturing is simulated with the method. Numerical simulations illustrate that the method can effectively model the fracture problems with surface tractions.

Research on Stress Intensity Factor of Gear Crack and its Variation with Changes of Gear Parameters

Used the theory of linear fracture mechanics and FEM, the two-dimensional model of single-tooth gear is established under the environment of ANSYS. The stress intensity factor(SIF) is analyzed when gear crack occurs and the variation of SIFs is discussed with changes of crack length, gear module, number of teeth, load when gear crack emerges at the pitch circle and tooth root respectively, and the influence of different cracked directions on tooth root is studied; The pragmatic expression of SIFs KI, KII have been brought forth with the results obtained by FEM. These establishes a good foundation on the fracture analysis and diagnosis of gear

Welding Defect Analysis in Thin-Walled Steel Tube under Bending Moment

The linear elastic problem for two welded thin-walled steel tubes containing circular arc weld defect subjected to bending load is analyzed in the present paper. The welding defect is firstly simplified as a circular arc crack and then the finite element based technique is used to calculate the corresponding energy release rate (J-integral), which is related to stress intensity factor directly. Finally, the arc length of welding defect is changed to investigate the variation of stress intensity factors.

Three-dimensional asymptotic mode I/II stress fields at the front of interfacial crack/anticrack discontinuities in trimaterial bonded plates

An eigenfuntion expansion method is employed for obtaining three-dimensional asymptotic displacement and stress fields in the vicinity of the front of a crack/anticrack discontinuity weakening/reinforcing an infinite pie-shaped trimaterial plate, of finite thickness, formed as a result of bimaterial (matrix/ARC plus reaction product/scatterer) deposit over a substrate (fiber/semiconductor). The wedge is subjected to mode I/II far field loading. Each material is isotropic and elastic, but with different material properties. The material 2 or the substrate is always taken to be a half-space, while the wedge aperture angle of the material 1 is varied to represent varying composition of the bimaterial deposit. Numerical results pertaining to the variation of the mode I/II eigenvalues (or stress singularities) with Young’s moduli ratio, as well as with the wedge aperture angle of the material 1 (reaction product/scatterer) are presented. Hitherto generally unavailable results, pertaining to the through-thickness variations of stress intensity factors or stress singularity coefficients for symmetric exponentially growing distributed load and its skew-symmetric counterpart that also satisfy the boundary conditions on the top and bottom surfaces of the trimaterial plates under investigation, bridge a longstanding gap in the stress singularity/interfacial fracture mechanics literature.

Three-dimensional asymptotic stress fields at the front of a trimaterial junction

A recently developed eigenfunction expansion method is employed for obtaining three-dimensional asymptotic displacement and stress fields in the vicinity of the junction corner front of an infinite pie-shaped trimaterial wedge, of finite thickness, formed as a result of bimaterial (matrix plus reaction product or contaminant) deposit over a substrate or reinforcement. The wedge is subjected to extension/bending (mode I), inplane shear/twisting (mode II) and antiplane shear (mode III) far field loading. Each material is isotropic and elastic, but with different material properties. The material 2 (substrate) is always taken to be a half-space, while the wedge aperture angle of the material 1 is varied to represent varying composition of the bimaterial deposit. Numerical results pertaining to the variation of the mode I, II, III eigenvalues (or stress singularities) with various moduli ratios as well as the wedge aperture angle of the material 1 (reaction product/contaminant), are also presented. Hitherto unavailable results, pertaining to the through-thickness variations of stress intensity factors for symmetric exponentially decaying distributed load and its skew-symmetric counterpart that also satisfy the boundary conditions on the top and bottom surfaces of the trimaterial plates under investigation, bridge a longstanding gap in the stress singularity/interfacial fracture mechanics literature.

XFEM simulation of cracks, holes and inclusions in functionally graded materials

The present work aims at the numerical simulation of inhomogeneities/discontinuities (cracks, holes and inclusions) in functionally graded materials (FGMs) using extended finite element method (XFEM). A FGM with unidirectional gradation in material properties is modeled under plane strain condition. The domain contains a major crack either at the center or at the edge of the domain along with multiple minor discontinuities/flaws such as minor cracks and/or voids/inclusions distributed all over the domain. The effect of the variation in stress intensity factor (SIF) of the major crack due to the presence of the minor cracks and voids/inclusions is studied in detail. The simulations show that the presence of minor discontinuities significantly affects the values of SIFs.

The effect of material combinations and relative crack size to the stress intensity factors at the crack tip of a bi-material bonded strip

Several types of singular stress fields may appear at the corner where an interface between two bonded materials intersects a traction-free edge depending on the material combinations. Since the failure of the multi-layer systems often originates at the free-edge corner, the analysis of the edge interface crack is the most fundamental to simulate crack extension. In this study, the stress intensity factors for an edge interfacial crack in a bi-material bonded strip subjected to longitudinal tensile stress are evaluated for various combinations of materials using the finite element method. Then, the stress intensity factors are calculated systematically with varying the relative crack sizes from shallow to very deep cracks. Finally, the variations of stress intensity factors of a bi-material bonded strip are discussed with varying the relative crack size and material combinations. This investigation may contribute to a better understanding of the initiation and propagation of the interfacial cracks.

Coplanar perturbation of a crack lying on the mid-plane of a plate

Several groups have studied experimentally the deformation of the front of mode I cracks propagating quasistatically along the interface between bonded plates. The theoretical interpretation of such experiments has always been based up to now on a formula of Rice (ASME J Appl Mech 52:571–579, 1985); this formula provides the first-order variation of the local mode I stress intensity factor resulting from some small, but otherwise arbitrary coplanar perturbation of the front of a semi-infinite crack in an infinite body. To be applicable to bonded plates, this formula requires that the characteristic distance of variation of this perturbation in the direction of the crack front be small compared to all other characteristic dimensions of the problem, and first of all the thickness of the plates. This condition is unfortunately frequently violated in practice. The purpose of this paper is therefore to provide a more exact formula for the variation of the local stress intensity factor, for the specific cracked geometry and boundary conditions used in experiments; this should allow for more accurate theoretical interpretations. This is done in two steps. The first one consists in adapting Rice’s (ASME J Appl Mech 52:571–579, 1985) treatment, applicable to the extreme case of plates of infinite thickness, to the other extreme one of plates of infinitesimal thickness, using the standard Love-Kirchhoff plate theory. An interesting outcome of the analysis is that the distance from the crack front to the boundary of the plate acts as a “cutoff length”, in the sense that when the distance between two points on the crack front gets larger than it, the influence of the crack advance at the first point upon the stress intensity factor at the second diminishes quickly; the plate thickness, however, plays no similar role. The second step consists in supplementing the theoretical expressions applicable to extreme values of the plate thickness with finite element computations providing results for intermediate values. These computations lead to the definition of a simple, approximate but accurate “interpolation formula” for the variation of the local stress intensity factor, applicable to plates of arbitrary thickness.

A three-dimensional eigenfunction expansion approach for singular stress field near an adhesively-bonded scarf joint interface in a rigidly-encased plate

A three-dimensional eigenfunction expansion approach for determination of the singular stress field in the vicinity of an adhesively-bonded scarf joint interface in a plate, with its top and bottom surfaces being encased, fully or partially, between infinitely rigid blocks is presented. The plate is subjected to extension/bending (mode I) and in-plane shear/twisting (mode II) far-field loading. Both the adhesive layer and plate materials are assumed to be isotropic and elastic. The boundary conditions that are prescribed on the end-faces (free, fixed and lubricated) of the plate as well as those, prescribed at the bottom or top surface of the scarf-bonded plate on either side of the interface between the plate and adhesive layer materials (fixed-fixed, free-fixed and fixed-free), are exactly satisfied. Numerical results include the dependence of the lowest eigenvalue (or most severe stress singularity) on the wedge aperture angle of the plate material. Variation of the same with respect to the shear moduli ratio of the constituent plate and adhesive layer materials is also an important part of the present investigation. Hitherto unobserved interesting and physically meaningful conclusions in regards to the fixed edge singularity and delamination type flaw sensitivity of an adhesively bonded plate surface are also presented. Finally, hitherto unavailable results, pertaining to the through-width variations of stress intensity factors corresponding to symmetric and skew-symmetric sinusoidal loads that also satisfy the boundary conditions on the end-faces of the adhesively bonded plate, in the vicinity of the scarf joint interface, under investigation, bridge a longstanding gap in the bonded joint stress singularity/fracture mechanics literature.

Variation of Stress Intensity Factor through the Thickness of Plate

Stress intensity factor (SIF) is one of the most important parameters in fracture mechanics. Therefore there is essential request on investigation of the behavior of SIF. Due to extensive and practical usage of plate structures in components, hence the behavior of SIF through the thickness of plate has been done. The three dimensional (3D) plate has simulated in ABAQUS finite element software. Crack tip has been meshed by 20 quarter node elements. The results presented that the SIF in free surfaces of plate had minimum value and variation of SIFs approximately was constant through the thickness of plate except on free surface.

Crack growth study of dissimilar steels (Stainless - Structural) butt-welded unions under cyclic loads

The research shows the study of the mechanisms of emergence and propagation of fatigue cracks caused by mechanical tension stress fluctuations in dissimilar steels butt-welded joints; structural steel ASTM A537 (I), austenitic stainless steel ASTM A240 (304L), through GMAW with argon as protecting gas and ASTM A240 (E308L) as supplier material, without pre and post welding thermal treatment. Samples were evaluated through optical and scanning electron microscopy and inspected by not destructive test with penetrating liquids and ultrasound, to discard surface and internal defects. The following mechanical tests were completed; Vickers microhardness profile, tension, impact Charpy, bending guided, axial fatigue, and speed of propagation of fatigue cracks. The phenomenon of initiation and crack growth was characterized from pre-cracked specimens, using the curve of the crack size vs. the number of fatigue cycles, and the curve of crack growth rate, vs. the variation of stress intensity factor. Results showed a proper mechanical steel behavior under cyclic loads, in spite of showed high values of microhardness, mainly in the fusion line between the welding and 304L stainless steel, as well inclusions between the structural and the stainless one. Pre-cracked test evidence a faster growth of crack in the fusion line between structural steel and stainless steel.

Numerical analysis of the effect of thermal residual stresses on the performances of bonded composite repairs in aircraft structures

In this study the finite element method is used to analyse the effect of the thermal residual stresses resulting from adhesive curing on the performances of the bonded composite repair in aircraft structures. The stress-intensity factor at the crack tip is chosen as fracture criterion in order to estimate the repair performances. The obtained results show that the presence of the thermal residual stresses reduces considerably the repair performances and consequently decreases the fatigue life of cracked structures. The effects of the curing temperature, the adhesive properties and the adhesive thickness on the stress-intensity factor (SIF) variation with thermal stresses are also analysed.

Finite Element Fracture Mechanics Study of Web Connections with Tapered Beam Flange Plates

Brittle fracture was identified in many of prequalified weld joints in steel moment frames in the 1994 Nothridge earthquake. Then analyses of response and damage mechanism of beam-to-column connections under seismic load were widely studied in the world, but few people conduct the research on seismic-resistant behavior of beam-to-column web connections. To quantify the variation of stress intensity factor to weld root flaw sizes beam-to-column web connections with tapered beam flange plates, detailed 3D finite element analyses is used to study fracture toughness requirements in beam-to-column web connections, considering the large deformation, large strain, bolts pretension, bolt contact-slide, as well as material harden and soften. Fracture toughness demands are evaluated in terms of the mode I stress intensity factor. The stress intensity factor is calculated through a J-integral approach. The fracture toughness demands are studied for the flaw on the top of the beam flange and the bottom surface, respectively. Results indicate that the likelihood of top flange fractures is smaller than that of bottom flange fracture. Stress intensity factor is not uniform and is largest in the edge of beam flange. The fracture toughness in the edge of beam flange for web connections with step beam flange plates is 15% less than that for tapered beam flange plates.

Three-dimensional asymptotic antiplane shear stress fields at the front of interfacial crack/anticrack type discontinuities in trimaterial bonded plates

An eigenfuntion expansion method is employed for obtaining three-dimensional asymptotic displacement and stress fields in the vicinity of the front of a crack/anticrack type discontinuity weakening/reinforcing an infinite pie-shaped trimaterial plate, of finite thickness, formed as a result of bimaterial (matrix/semiconductor/ARC plus reaction product/scatterer) deposit over a substrate (fiber/ARC/semiconductor). The wedge is of general (unsymmetric) geometrical configuration, and is subjected to antiplane shear (mode III) far field loading. Each material is isotropic and elastic, but with different material properties. The material 2 or the substrate is always taken to be a half-space, while the wedge aperture angle of the material 1 is varied to represent varying composition of the bimaterial deposit. Numerical results pertaining to the variation of the mode III eigenvalues (or stress singularities) with various wedge aperture angles of the material 1 (reaction product/scatterer), are also presented. Hitherto generally unavailable results, pertaining to the through-thickness variations of stress intensity factors for symmetric parabolic load and its skew-symmetric counterpart that also satisfy the boundary conditions on the top and bottom surfaces of the trimaterial plates under investigation, form also an important part of the present investigation.

Analysis of Crack Propagation in Fixed-Free Single-Walled Carbon Nanotube Under Tensile Loading Using XFEM

Fracture mechanics at the nanoscale level is a very complex phenomenon, whereas the macroscale fracture mechanics approach can be employed for nanoscale to simulate the effect of fracture in single-walled carbon nanotubes (SWCNTs). In this study, an extended finite element method is used to simulate crack propagation in carbon nanotubes. The concept of the model is based on the assumption that carbon nanotubes, when loaded, behave like space frame structures. The nanostructure is analyzed using the finite element method, and the modified Morse interatomic potential is used to simulate the nonlinear force field of the C–C bonds. The model has been applied to single-walled zigzag, armchair, and chiral nanotubes subjected to axial tension. The contour integral method is used for the calculation of the J-integral and stress intensity factors (SIFs) at various crack locations and dimensions of nanotubes under tensile loading. A comparative study of results shows the behavior of cracks in carbon nanotubes. It is observed that for the smaller length of nanotube, as the diameter increased, the stress intensity factor is linearly varied while for the longer nanotube, the variation in stress intensity factor is nonlinear. It is also observed that as the crack is oriented closer to the loading end, the stress intensity factor shows higher sensitivity to smaller lengths, which indicates more chances for crack propagation and carbon nanotube breakage. The SIF is found to vary nonlinearly with the diameter of the SWCNT. Also, it is found that the predicted crack evolution, failure stresses, and failure strains of the nanotubes correlate very well with molecular mechanics simulations from literature.

Three-dimensional singular stress field at the front of a crack weakening a unidirectional fiber reinforced composite plate

Abstract An eigenfunction expansion technique, based in part on separation of the thickness-variable and partly on the Eshelby–Stroh type affine transformation, is employed to derive hitherto unavailable three-dimensional asymptotic stress field in the vicinity of the front of a semi-infinite through-thickness crack weakening an infinite transversely isotropic unidirectional fiber reinforced composite plate, of finite thickness and subjected to far-field mode I/II loadings. Crack-face boundary conditions and those that are prescribed on the top and bottom (free, fixed or lubricated) surfaces of the lamina are exactly satisfied. The present investigation considers mainly two through-crack systems – (i) (0 1 0)[0 0 1] with the [1 0 0] propagation direction, and (ii) ( 1 ¯ 0 0 ) [ 0 0 1 ] with the [0 1 0] propagation direction. Explicit expressions for the singular stresses in the vicinity of the front of a through-thickness crack weakening a transversely isotropic unidirectional fiber reinforced composite plate, subjected to far-field mode I/II loadings, are presented. Hitherto unavailable numerical results, pertaining to the through-thickness variations of stress intensity factors for saw-tooth load and its skew-symmetric counterpart that also satisfy the boundary conditions on the top and bottom surfaces of the cracked unidirectional fiber reinforced composite (transversely isotropic) plates under investigation, bridge a longstanding gap in the fracture mechanics literature.

Effect of composite hygrothermal aging on the SIF variation in bonded composite repair of aircraft structures

In this study, the finite element method is used to analyze the effect of hygrothermal aging of composite on the stress intensity factor variation for the crack repaired with bonded composite patch. The obtained results show that moisture absorption has a negative effect on the repair performance. Indeed, the stress intensity factor increases with an increase in the water absorption in both mode I and mixed mode of crack propagation. The fatigue life of the repaired structures decreases with the increase in water absorption by the composite patch.

Variation of the Fatigue Lifetime with the Initial Notch Geometry of Circular Notched Bar Specimens

Circular notched bar (CNB) specimens are often used for studying the brittle failure of pipe-grade polymeric materials such as polyethylene (PE). However, there are some technical difficulties, such as the alignment of the centreline of a CNB specimen with that of a circular notch, the installation of a razor blade to fabricate a circular notch, etc., in making the axisymmetric initial notch for CNB specimens. Though a slightly asymmetric initial notch is fabricated for a CNB specimen, the final failure of the CNB specimen under fatigue loads can be severely eccentric. In this case, the fatigue lifetime of the CNB specimen with asymmetric crack growth is varied significantly comparing with that of the CNB specimen with symmetric crack growth. In this study, the effect of two cases of non-circular initial notch geometry, i.e., (a) an asymmetric circular notch (Case I) and (b) an elliptical notch (Case II), of the CNB specimen on the fatigue lifetime is investigated using finite element analysis. The variation of stress intensity factors during crack growth is investigated to understand the fatigue crack growth of the CNB specimen with two cases of slightly asymmetric initial notch geometries.