Stress Intensity Factor KII Research Articles

Stress Concentration at Load-Carrying Fillet Welded Cruciform Joints Subjected to Tensile and Bending Loads

Abstract This article presents numerical finite element method (FEM) analysis of the stress concentration at toes and crack-like faults in load-carrying fillet welded cruciform joints with transversal slits resulting from non-fused root faces. Potential fatigue damage of such joints subjected to cyclic tensile and bending loads appears in the form of fatigue cracks starting from the weld roots or toes. The aim of this article is to find qualitative and quantitative relationships between geometrical parameters of the load-carrying fillet welded cruciform joint subjected to tensile and bending loads and the stress concentration at weld toes and roots. The results of the analysis represented by the stress concentration factors (SCFs) and the stress intensity factors KI and KII are shown in the form of tables, graphs and mathematical formulas, which may be applied for fatigue assessment of such joints.

Application of distributed dislocation method to curved crack moving near a press-fitted inclusion in a two-dimensional infinite plate

This paper describes the application of the distributed dislocation method to the problem of a curved crack moving near a press-fitted inclusion in a two-dimensional infinite plate which is subjected to a tensile loading. The formulation is based upon the superposition of the following three fundamental problems: a continuous distribution of edge dislocations along the crack line in an infinite plate with an inclusion, residual stress generated by the press-fitted inclusion without the crack, and stress field in the infinite elastic plate containing the circular inclusion, but without the crack, which is subjected to a uniform tensile loading. The superposition leads to simultaneous singular integral equations, which are introduced by relating the traction-free condition along the curved crack line to the dislocation density functions as unknown functions in the integral equations. The stress intensity factors can be derived directly from those dislocation density functions. In this study, the crack-propagation program, which is considered that the crack tip is automatically moved in a direction satisfying the restriction that the stress intensity factor KII is zero, was developed. The developed program is applied to the elastic problem including the press-fitted inclusion and crack, and the influence of the initial crack locations and residual stress generated by inserting the inclusion into the hole on the geometry of the crack path is discussed.

An insight into mode II fracture toughness testing using SCB specimen

AbstractThe effect of friction forces between the test specimen and its bottom supports on the mode II fracture toughness values obtained using the semicircular bend (SCB) specimen is investigated. First, a number of experiments were conducted on SCB specimen in order to determine the mode II fracture toughness of polymethyl methacrylate (PMMA) according to the conventional approaches available in the literature. Three different types of supports that have been frequently employed by researchers in recent years were used to evaluate the effect of support type on the fracture loads. It was found that the friction forces between the supports and the SCB specimen have a significant effect on the value of mode II fracture toughness measured using the SCB samples. Then, the specimen was simulated using finite element method for more detailed investigation on the near crack tip stress field evolution when friction forces increase between the supports and the SCB specimen. The finite element results confirmed that the type of support affects not only the stress intensity factors KI and KII but also the T‐stress. The experimental and numerical results showed that the use of the crack tip parameters available in literature for frictionless contact between the supports and the SCB specimen can result in significant errors when the mode II experiments are performed by using the fixed or roller‐in‐grove types of supports.

Determination of Stress Intensity Factors and J integral based on Digital Image Correlation

Digital image correlation (DIC) is a technique in experimental mechanics to acquire full-field measurement data of displacements and deformations from the surface of specimens or components. Especially for the investigations of cracks it provides additional benefits. The actually present deformation field in the vicinity of the crack tip can be obtained which directly reflects for example crack closure effects or plasticity. Against this background the paper summarizes a procedure to compute the J integral and the stress intensity factors KI and KII based on DIC data. For this purpose the J and interaction integral are computed as line and domain integrals. Through experiments it is shown that the domain integral is less affected by scatter of the DIC data. Furthermore, the specific domain, facet sizes and facet distances slightly influence the results.

Enhancement of fracture toughness under mixed mode loading of ABS specimens produced by 3D printing

Purpose The purpose of this paper is the application and the improvement of a previous method based on an acrylonitrile butadiene styrene thread deposition in fused deposition modeling. To gain up to 20 per cent of mechanical strength in comparison with a classical deposition, this method suggests a smart threads deposition in the principal stresses direction. Design/methodology/approach In this work, the authors use single edge notched bend specimens with mixed mode I+II loading cases to study the influence of the thread deposition on the fracture toughness of the specimens. For this purpose, finite elements simulations have been used to evaluate the fracture toughness of the specimens through the calculation of the J integral. The study presents a method to compare the optimized and classical specimens and also to gather data and suggest a numerical model for this optimized deposition. For this reason, tensile tests are carried out to characterize the mechanical behavior of the printed samples with respect to the raster angle. Extra attention has been paid to 45 per cent samples behavior that shows a pronounced plasticity before the fracture. This interprets partially the improvement in the fracture behavior of the single edge notched bend samples. Findings The results show an enhancement through this optimization which leads to an increase of the maximal force in fracture up to 20 per cent and the fracture toughness of the specimens with stress intensity factors KI and KII increases about 30 per cent. Originality/value Additive manufacturing is increasingly gaining importance not only in prototyping but also in industrial production. For this reason, the characterization and the optimization of these technologies and their materials are fundamental. An adaptive deposition through a smart material based on specific mechanical behaviors would be an advance.

Effect of crack position and loading conditions on SIF in SiC particles reinforced Al composite

In this paper the effect of reinforcement crack position and loading conditions (in mode I) on the stress intensity factors of the Al/SiCp metal matrix composite was examined using a finite element method. A simple cubic cell model with square reinforcement shapes was developed to investigate its effect on the mechanical properties of the MMC. The finite element technique was used to calculate the stress intensity factors KI and KII for crack in the matrix and in particle. The particle and matrix materials were modelled in linear elastic conditions. The obtained results show the important role on the stress intensity factors played by the relative elastic properties of the particle and matrix. The results also show that the loading conditions and inter-distance between two particles with two interfacial cracks has an important effect on the KI and KII stress intensity factors.

Cruciform specimens used for determination of the influence of T-stress on fatigue crack growth with overloads on aluminum alloy Al 6061 T651

The publication presents a cruciform specimen for the determination of cyclic crack growth data under biaxial loading. The design of the specimen with slotted loading arms allows good decoupling between the two loading directions. For different initial crack geometries, the solutions for the stress intensity factors KI and KII as well as the crack-parallel T-stress are calculated by linear elastic finite element analysis (FEA) with the program ABAQUS. For two specimens with the same geometry made of aluminum alloy 6061 T651, the crack growth behaviour is measured at different T-stresses at a stress ratio of R=0.7 and overloads. It is shown that the crack retardation after an overload with crack-parallel tensile stress is less than without it. The reason for this behaviour is considered to be the reduced plasticity at the crack tip due to the higher triaxiality of the stress state.

Analytical approach and numerical simulation to investigate the stress field and the dynamic stress intensity factors of a cracked tooth subjected to a periodic loading

A new analytical approach was developed in this paper to study the dynamic analysis of a cracked gear tooth subjected to a periodic loading. The finite elements method (FEM) based on the contour integral technique was used in order to validate the effectiveness and reliability of the analytical formulation. A three-dimensional (3D) model of a cracked tooth was designed where a refined mesh was applied in the crack region to better simulate the stress concentration. The main objective of this study was to investigate the influence of the crack depth and the external load on the variation of the stress intensity factors (SIF) KI and KII associated with the opening crack modes I and II, respectively, and on the stress field near the crack tip. The obtained results show a significant agreement between the analytical results and the FEM findings.

Investigation on fracture toughness and micro-deformation field of SCB sandstone including different inclination angles cracks

The increasing use of hydraulic fracturing in mining, petroleum engineering is boosting great interest in the fracture mechanism and fracture toughness of rock. A static loading device, Geotechnical Consulting & Testing Systems, was used to conduct three-point bending tests on semicircular bend (SCB) sandstone specimens, the results showed that the concentrated force plays a guiding role in crack propagation. With the increase of crack inclination angle β, the peak load of the specimen exponentially increases. The mode I stress intensity factor KI decreases gradually, and the mode II stress intensity factor KII increases first and then decreases. RFPA2D software can effectively simulate the failure process of rock, the obtained crack propagation path and peak load are basically consistent with the experimental results. The deformation field was analyzed based on the experimental and numerical results. It was found that the deformation field at crack tip varied continuously during the loading process, where the rate and range of variation show huge diversity for different β values. As shown in the analysis of displacement field evolution, a mode I crack specimen will exhibit a uniform symmetrical trend eventually. However, the transformations of I/II mixed mode cracks are more complex, exhibiting different degrees of “sliding cross” phenomenon at crack tip and asymmetrical distribution in general. The comprehensive method combined with GCTS, RFPA and DIC can be effectively applied to evaluate the fracture toughness of rock material.

On the special angle of surface cracks propagation in the railway rail heads

Investigation of crack-like surface defects on running surfaces of railway rails was carried out using the Keer-Bryant model scheme. For this purpose by singular integral equation method, the contact problem for an elastic half-plane with an edge crack was solved, taking into account the general conditions of crack faces interaction (slip, stick, opening). Dependence of the range of stress intensity factors KII in contact cycle on crack orientation angle for different service parameters, namely friction between the wheel and the rail, length of the crack and friction between its faces was investigated in detail. As a result, it has been shown that surface cracks on running surfaces of rails grow in the direction of the rolling stock traffic at shallow characteristic angle by transverse shear mechanism. This angle is a basis for formation of typical surface contact fatigue damages, such as pitting, squat, checks. The conditions for finding it have been put down. Characteristic angle values found theoretically agree with engineering data well.

Conditions of Self-Similarity of Edge Transverse Shear Cracks in a Square Plate

We determine the stress-strain state of a rectangular plate with edge crack under the conditions of transverse shear. The conditions of self-similar crack propagation are established. We deduce a formula for the evaluation of the stress intensity factors KII via the shear stresses.

Instability of cracks initiation from a mixed-mode crack tip with iso-stress intensity factors KI and KII

For a special case of mixed-mode crack with iso-stress intensity factors KI and KII, the instability of cracks initiation from a crack tip has been investigated based on the principle of the energy-based driving force. By using the Ji-integrals over the crack boundary, the fracture modelling and relevant energy release rate on the multiple-crack initiation have been formulized. It has been found that when stress intensity factors KI and KII close to each other, more possible forms of multiple-cracks initiation from a crack tip may occur theoretically including the crack side-branching and kinking, which is remarkable and conducive to better understand the complex fractural phenomena in engineering and fracture tests. By using the present method, which part of the crack tip boundary fracture can be identified and the relevant critical energy release rate can be found.

Application of singular integral equation to crack moving near an inclusion in two-dimensional infinite plate

This paper describes application of singular integral equation method to crack moving near an inclusion in two-dimensional infinite plate which is subjected to a tensile loading at infinity. The theoretical formulation is based upon the superposition of the problem of a continuous distribution of edge dislocations spread along the crack locus in an infinite plate with single inclusion and the problem for the same geometry without crack which is subjected to a tensile loading. The superposition leads to simultaneous singular integral equation, and they relate the surface zero-tractions to the dislocation densities along the curved crack locus. The stress intensity factors are derived directly from the crack-tip stress field. Then, the crack tip is automatically moved to a direction as satisfying the restriction that the stress intensity factor KII is zero, which was developed in this study. The direction search is conducted by rotating the tip of virtually incremented crack around the origin crack tip. The search and extension processes are repeated in sequence. In this numerical calculation, the influence of the initial crack locations on crack moving path is discussed.

Numerical simulation of kink angle prediction for non-lubricated surface crack subjected to Hertzian pressure

Analysis of determining linear fracture mechanics parameters for a surface crack loaded with Hertzian pressure without the presence of a lubricant in the crack is presented. For this purpose, the elements of Williams equation for describing stresses near the crack tip are determined: Stress intensity factors KI and KII, and T-stress, which were taken into account when determing the direction of crack propagation by means of Strain energy density (SED) criterion. The elements are determined based on the case of a gear tooth flank, with various friction coefficients on the free surface and friction in the crack being taken into account. The results show that friction on the free surface and, consequently, tangential forces have an impact on whether the crack will propagate along the free surface or into the depth.

Bodies described by non-monotonic strain-stress constitutive equations containing a crack subject to anti-plane shear stress

In this paper the state of stress and strain close to sharp cracks in bodies subjected to an anti-plane state of stress is studied within the context of a non-monotonic strain-stress relation within the context of a generalization of the Cauchy theory of elasticity, providing an exact analytical solution to the problem.A discussion is provided to highlight the main features of stress and strain distributions, and the implications of the new theory for fracture assessments. In particular, it is proved that the intensity of the complete stress field can be expressed as a function of the Stress Intensity Factor KIII, as in the case of conventional linearized elasticity theory, thus promoting a K based-approach to the fracture of elastic solids obeying a constitutive relation wherein the linearized strain is expressed as a non-linear function of the Cauchy stress.

Effect of notch on static and fatigue performance of multilayered composite structures under tensile loads

Fatigue failure of laminated composites containing circular or elliptical (vertical and horizontal) holes and subjected to tension was studied. This research investigates the stress components, the initiation and propagation of static and fatigue damage and failure in notched composite laminates by analytic method and FE model, both of which are validated by experimental tests. The major focus was to understand the failure mechanisms of composites induced by stress concentrations, and to determine the effects of ply orientations, material properties and geometry on the fatigue damage. It was demonstrated that the crack initiation and growth was connected with the interaction of the stress intensity factors (SIFs) KI and KII.

Mode III crack approaching the wedge-shaped elastic inclusion

The problem on an antiplane semi-infinite crack approaching an elastic wedge-shaped inclusion is considered. The problem has been solved exactly using the Mellin integral transformation and the Wiener–Hopf method. The asymptotic behavior of the stress intensity factor KIII in the crack tip was studied for short distances from the crack to the inclusion vicinity. Depending on the composition parameters, the crack was shown to be stable (KIII→0) or unstable (KIII→∞). Provided that the interface has a corner point, the crack growth can be unstable (unlike the smooth interface) for some parameter values even though the crack approaches, from a soft material, a relatively harder inclusion. Alternatively, the possibility of KIII→0 exists provided the crack approaching a soft inclusion from a hard material.

Minimum shear stress range: a criterion for crack path determination

For problems under proportional mixed-mode conditions, various criteria are used to predict fatigue crack growth directions, most achieving reasonable accuracy. The crack propagation angle is often obtained by maximizing a quantity (for instance, energy or stresses) as function of the stress intensity factors KI and KII. This maximization is generally performed at the instant of maximum fatigue loading and a stress analysis at this instant is sufficient to predict the crack propagation angle and thus the fatigue crack growth direction. However, under non-proportional loading, the maximum values of KI and KII may occur at different instants of the fatigue cycle and so a simple analysis at the maximum loading instant is not appropriate; it is necessary to consider the entire loading cycle history. One possible criterion to treat problems under these circumstances is the minimum shear stress range criterion (MSSR). This paper presents a brief discussion of the most common criteria used for determination of crack propagation direction, focusing on an implementation of MSSR. Its performance is assessed in different conditions and the results are compared to literature data.

Mixed mode fracture analysis using generalized averaged strain energy density criterion for linear elastic materials

A modified energy-based model called the generalized averaged strain energy density (ASED) criterion is proposed to predict the mixed mode I/II fracture resistance of brittle and quasi-brittle materials. The proposed criterion takes into account the effect of T-stress in addition to the stress intensity factors KI and KII when calculating the strain energy density averaged in a control volume around the crack tip. The effect of T-stress on the mixed mode fracture resistance of materials is investigated by using the generalized ASED criterion and the generalized SED criterion. The results predicted by these criteria are compared with the experimental results reported in the literature from fracture tests conducted on the Brazilian disc specimens and the semi-circular bend specimens made of Harsin marble and Guiting limestone. It is shown that the theoretical estimates of the generalized ASED criterion are consistent very well with the experimental results. The theoretical results also show that the specimens having a negative T-stress require higher loads in order their averaged strain energy density around the crack tip attains its critical value.

Calculation of the crack tip parameters in the holed‐cracked flattened Brazilian disk (HCFBD) specimens under wide range of mixed mode I/II loading

AbstractIn this paper, the crack tip parameters including the stress intensity factors (KI and KII), T‐stress and the third terms of the stress field (A3 and B3) are determined comprehensively for a disk‐type sample named holed‐cracked flattened Brazilian disk (HCFBD) under various combinations of mode I and mode II loading. The HCFBD specimen is a circular disk containing a central hole in which the initial cracks are created radially from the hole circumference. Moreover, the ends of HCFBD are flattened for the sake of convenient loading. Performing enormous finite element analyses and calculating the stress intensity factors KI and KII, the states of pure mode II are determined for different configurations of HCFBD. Furthermore, the sign and magnitude of parameter A3 which plays an important role to justify the geometry and size effects on the fracture toughness of quasi‐brittle materials are also determined for HCFBD with different geometrical ratios.