Stress Intensity Factor Solutions Research Articles

Effect of fibre volume fraction and fibre direction on crack paths in flax fibre-reinforced composites

Mechanical and fracture mechanical behaviour of composites reinforced with unidirectionally aligned flax fibres is investigated experimentally and numerically. Thereby, the main points are the determination of crack paths in compact tension specimens with three different fibre directions under static as well as fatigue loading and their fatigue crack growth rate curves. Due to the pronounced orthotropic behaviour of those materials the crack path is not only governed by the stress state, but affected by the fibre direction and fibre volume fraction as well. Therefore, the well-known stress intensity factor solutions for the standard specimens are not applicable. Consequently, extensive numerical simulations have been carried out to evaluate the stress intensity factor evolution along the growing crack in order to be able to determine fatigue crack growth rate curves. An approach for calculating stress intensity factors analytically with geometry correction factor functions is conducted exemplified for one fibre direction.

Stress Intensity Factor Solutions for Welds in Lap-Shear Specimens under Clamped Loading Conditions

Stress Intensity Factor Solutions for Welds in Lap-Shear Specimens under Clamped Loading Conditions

Computations of stress intensity factors for semi-elliptical cracks with high aspect ratios by using the tetrahedral finite element (fully automated parametric study)

The stress intensity factor (SIF) solutions of semi-elliptical cracks with high aspect ratios in plate and thick wall cylinder have been investigated under various assumed stress distributions. The authors have developed an automated analysis procedure to perform parametric studies on crack shapes and loading conditions. It consists of programs to perform automatic mesh generation, analysis execution including assignments of boundary conditions and SIF evaluations by VCCM (virtual crack closure-integral method). It was also found that SIF solutions for the thick wall cylinder and for the complex structure could be estimated by those for the flat plate.

Evaluation of stress intensity factors from stress concentration factors for a crack embedded in dissimilar elliptic inclusion

This paper provides a solution for stress intensity factors for a crack embedded in an elliptic inclusion. The inclusion is bonded to an infinite matrix. The inclusion and the infinite matrix have different elastic properties. The crack is replaced by a very slender elliptic configuration. After this replacement, the stress concentration factor can be evaluated. The stress intensity factor at the crack tip can be evaluated from the stress concentration factor by using an available equation. In the solution, the complex variable function method, conformal mapping and the matrix transfer method are used.

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.

Geometric functions of stress intensity factor solutions for spot welds in coach-peel specimens

Stress intensity factor solutions for spot welds in two kinds of coach-peel specimens are investigated by finite element analyses. Three-dimensional finite element models are developed to obtain accurate solutions. Various ratios of sheet thickness, specimen width, flange length, and effective wall height to nugget radius are considered. The results confirm the functional dependence on the nugget radius and sheet thickness of Zhang’s analytical solution. Two geometric functions in terms of the normalized geometric parameters for Zhang’s solution are obtained. Based on the analytical and computational results, the dimensions of coach-peel specimens and the corresponding approximate stress intensity factor solutions are suggested.

Fatigue life prediction model for laser clad AISI 4340 specimens with multiple surface cracks

Fatigue test on laser clad AISI 4340 steel specimens show that multiple surface cracks initiate from the clad-toe region due to clad bead overlap features deposited in a raster scan pattern. A fatigue crack growth modeling algorithm capturing the observed fatigue behavior of periodic multiple co-planar semi-elliptical cracks initiating from these features was developed based on crack closure concepts for small cracks to predict the fatigue S–N curve of laser clad AISI 4340 steel specimens. New solutions for stress intensity factor and clad-toe magnification factor (Mk-factor) are presented for surface cracks propagating from the laser clad-toe region. The fatigue life prediction model is able to start from multiple clad-toe surface cracks propagating from the clad-toe region which coalesce into a dominant surface crack or edge crack before final failure. The fatigue life prediction result was compared to the experiment S–N curve test data and gave good agreement.

Influence of anisotropy, porosity and initial stresses on crack propagation due to Love‐type wave in a poroelastic medium

AbstractAn analytical solution has been attained to establish the closed form expression of stress intensity factor at the tip of a semi‐infinite crack, dynamically propagating in an initially stressed transversely isotropic poroelastic strip due to Love‐type wave for the case of concentrated force of constant intensity as well as for the case of constant load. The study presents the sound effect of various affecting parameters viz. speed of the crack, length of the crack, horizontal compressive/tensile initial stress, vertical compressive/tensile initial stress, porosity parameter and anisotropy parameter on the stress intensity factor. In order to delineate the effects of these aforementioned parameters on the stress intensity factor graphically, numerical simulations have been accomplished. One of the major highlight of the paper is the comparative study carried out for horizontal compressive/tensile initial stress, vertical compressive/tensile initial stress, porosity parameter and anisotropy parameter with the case when the strip is isotropic, non‐porous and free from initial stresses. Wiener–Hopf technique and the Fourier integral transform has been effectuated for the procurement of the closed form expression (exact solution) of stress intensity factor.

Solutions for a Circular Hole With Edge Cracks Under Shear Load

A 2D mechanical analysis was performed on an infinite plate containing a circular hole with two collinear edge cracks of unequal lengths, under uniformly distributed shear load at infinity. Based on the complex variable function method, the analytic solutions of stress functions and stress intensity factors were obtained. Through an numerical example, the stress distributions along the coordinate axes and the hole edge were given in the graphical form, and the stress intensity factors were also calculated. The results show that, there is obvious stress concentration near the hole and the cracks, and the stress values far from the defects tend towards the applied load, which conforms to the Saint-Venant’s principle. In addition, the results from the finite element simulation agree well with the analytic solutions, to prove the correctness of the theoretical derivation.

半円より奥に深い亀裂の応力拡大係数解の比較

半円より奥に深い亀裂の応力拡大係数解の比較

Effect of Specimen Geometry and Press-Fit on the Stress Intensity Factor Solution for Scaled Wheelset Axles under Bending

One problem in wheelset axles are the failures due to the propagation of fatigue cracks. To avoid those failures with sometimes catastrophic consequences analytical crack propagation simulations are used. For these simulations the knowledge of the crack propagation path and the corresponding stress intensity factor (SIF) is required. To calculate the SIF a numerical simulation, such as finite element method (FEM), is generally needed. To this end numerical simulations for shouldered solid shafts with elliptical surface cracks are done. In this work different influencing factors of the stress intensity factor expressions have been identified. Therefore, two different specimen types with three different stress concentration factors each were designed. The results represent an overview for the interaction of stress concentration factor, crack depth, crack aspect ratio, bending and press-fit load in shouldered solid shafts. To represent the rotation, different characteristic angular positions for one selected characteristic crack geometry have been considered.

SIF Determination with Thermoelastic Stress Analysis

This work is focused on the experimental determination of the stress intensity factor (SIF) using thermoelastic stress analysis (TSA) for a compact tension specimen during a fatigue crack growth test. A comparison of the stress field obtained with computational modelling, finite element method, against the experimental data obtained with the thermoelastic stress analysis under mode I loading in a fatigue test is presented. The stress field in front of the crack tip obtained with TSA, was used in William’s expansion, together with an overdetermined algorithm to calculate the SIF under mode I loading. The proposed methodology has a hybrid experimental-numerical nature where the stress intensity factor determination depends on a stress field obtained with an optical technique, TSA. The soundness of the experimentally obtained SIF solution was validated through finite element method computations.

Fatigue Life Prediction of Heavy-Duty Riveted Steel Gratings in Bridge Decks

AbstractHeavy-duty riveted steel gratings often occur as open-grid deck systems used in movable bridge construction and in rehabilitation projects due to their light weight compared with conventional systems. Open-grid decks have been used in a number of bridges, with the majority fabricated as welded decks. Field and laboratory experience with heavy-duty riveted steel gratings indicates improved fatigue performance compared with welded decks, but no specific provisions currently exist. This study explored a fatigue life prediction methodology for riveted gratings using fracture mechanics. The models involve crack growth rate relations and approximate stress intensity factor solutions for a crack in a bearing bar of the grating. Two failure modes of the riveted gratings were considered based on results of fatigue testing of both full-size and smaller-size samples of a 37R5 lite panel under various stress ranges. Results from the fracture mechanics approach compared well with experimental results. The prop...

Investigation of crack paths in natural fibre-reinforced composites

Nowadays, fibre-reinforced composite materials are widely used in many fields, e.g. automotive and aerospace. Natural fibres such as flax and hemp provide good density specific mechanical properties. Additionally, the embodied production energy in natural fibres is much smaller than in synthetic ones. Within this paper the fracture mechanical behaviour of flax fibre-reinforced composites is discussed. Especially, this paper focuses on the determination and investigation of crack paths in compact tension specimens with three different fibre directions under a static as well as fatigue load. Differences and similarities in the obtained crack paths under different loading conditions are presented. Due to the pronounced orthotropic behaviour of those materials the crack path is not only governed by the stress state, but practically determined by the fibre direction and fibre volume fraction. Therefore, the well-known stress intensity factor solutions for the standard specimens are not applicable. It is necessary to carry out extensive numerical simulations to evaluate the stress intensity factor evolution along the growing crack in order to be able to determine fatigue crack growth rate curves. Those numerical crack growth simulations are performed with the three-dimensional crack simulation program ADAPCRACK3D to gain energy release rates and in addition stress intensity factors.

A computational model for large deformations of composites with a 2D soft matrix and 1D anticracks

• Anticracks are rigid line inclusions in a two-dimensional deformable matrix. • For the first time, we present a meshfree method without remeshing for anticracks. • The matrix undergoes finite deformation, with anticracks moving rigidly. • The method matches available analytical solutions for stress intensity factors. • The method can handle nonlinear constitutive models and multiple anticracks. Anticracks (also known as rigid line inclusions) occur frequently in a variety of natural and engineered composites as very stiff and extremely sharp (almost zero-thickness) fibers or lamellae embedded in a softer matrix. In the linear elastic regime, similarly to cracks, anticracks generate a singularity in the stress distribution around the tip. Because of this similarity, existing analytical techniques and solutions (for simple cases) can be easily translated to anticracks. However, despite their importance in many biological and engineering composites, there has been surprisingly little development of numerical methods that would account simultaneously for the presence of multiple fibers or lamellae, arbitrary loadings and nonlinear behavior of the matrix. This paper presents the first numerical approach for rigid line inclusions, based on a meshfree scheme recently developed for multiple crack growth in elastic media. The inclusion of zero thickness is created as a crack, and a rigid motion (rotation and translation) is enforced at the anticrack faces. The equations of motion are solved according to a Total Lagrangian framework, and the matrix supposed hyperelastic. Contrarily to available analytical solutions, the degrees of freedom of the rigid motion are determined a posteriori as a consequence of the (discretized) elastic equilibrium, expressed in a variational approach. Results show that the proposed approach match well the analytical solutions and provides accurate stress intensity factors (SIFs) for relatively little computational cost. Moreover, the method can reproduce some peculiar features of the anticracks: unlike cracks, singularities also appear under compressive and parallel loads; moreover, for a certain combination of biaxial load, stress concentrations disappear. Finally, the paper presents examples drawn from biological and engineering composites: the reorientation of one or more fibers under large strains, resulting in a smart stiffening and strengthening mechanism. Reorienting towards the direction of applied load has structural importance since reinforcements can have the most effectiveness in withstanding loads. If the matrix is compliant, the reorientation is eased.

Cracks at elliptical holes: Stress intensity factor and Finite Fracture Mechanics solution

Abstract In this work crack initiation at elliptical holes in plates under uniaxial tension is studied by means of a closed form analytical Finite Fracture Mechanics approach. To allow for a detailed study of crack initiation, stress intensity factors available in literature are discussed and compared to extensive numerical results. Based on physical rationale, an improved stress intensity factor solution is proposed that shows a very good agreement with numerical results for a wide range of stress concentration factors of the ellipse and crack lengths. Using the exact solution of the stress field in the notched plate and the proposed stress intensity factor, an efficient Finite Fracture Mechanics solution is obtained. No empiric length parameters are introduced but only the strength and the fracture toughness are required for evaluation. The analysis comprises the case of a circular hole and the limiting cases of a crack tangential and normal to the loading direction. Typical notch size effects are covered by this coupled stress and energy approach. A continuous transition from strength of materials to Linear Elastic Fracture Mechanics can be rendered.

Stress Intensity Factor and Elastic Crack Opening Displacement Solutions of Complex Cracks in Pipe Using Elastic Finite-Element Analyses

In the present paper, the closed-form expressions for the stress intensity factors (SIFs) and the elastic crack opening displacements (CODs) of complex-cracked pipes are derived based on the systematic three-dimensional (3D) elastic finite-element (FE) analyses. The loading conditions that are evaluated include global bending moment, axial tension, and internal pressure. In terms of geometries, the geometric variables affecting the SIFs and the elastic CODs of complex-cracked pipes, i.e., the crack angle of through-wall cracks (TWCs), the crack depth of fully circumferential, internal surface cracks in the inner surface of pipe, and the ratio of pipe mean radius to thickness, are systematically considered in the present FE analyses. The FE analysis procedure employed in the present study has been validated against the existing solutions for the circumferential TWC pipes. Using the present FE results, the shape factors of SIF and elastic COD for complex-cracked pipes are tabulated as a function of geometric variables. The results are applied for closed-form expressions of SIF and elastic COD when the pipe is subjected to simple loading conditions of bending, axial tension, or internal pressure. The proposed closed-form expressions can estimate SIF and elastic COD of complex-cracked pipes within maximum differences of 2.4% and 5.9% with FE results, respectively.

Failure Mode and Fatigue Behavior of Dissimilar Friction Stir Spot Welds in Lap-Shear Specimens of Transformation-Induced Plasticity Steel and Hot-Stamped Boron Steel Sheets

Failure mode and fatigue behavior of dissimilar friction stir spot welds in lap-shear specimens of transformation-induced plasticity steel (TRIP780) and hot-stamped boron steel (HSBS) sheets are examined in this paper. Optical micrographs of the dissimilar TRIP780/HSBS friction stir spot welds made by a concave silicon nitride tool before and after testing are obtained and examined. These micrographs indicate that subject to quasi-static and cyclic loading conditions, the TRIP780/HSBS welds fail from cracks growing through the TRIP780 sheets where the tool was plunged into and the thickness was reduced. The bending moments and the transverse shear force near the welds are derived with consideration of the load offset, the weld gap, and the bend distance for calculation of analytical global stress intensity factor solutions for the welds in lap-shear specimens. A fatigue model of kinked crack growth is used to estimate fatigue lives based on the local stress intensity factor solutions for kinked cracks. The estimated fatigue lives with consideration of the weld gap and the bend distance are in agreement with the fatigue test results under low-cycle loading conditions and lower than the fatigue test results under high-cycle loading conditions. The estimated fatigue lives suggest that the weld gap and the bend distance can significantly affect fatigue lives of the friction stir spot welds in lap-shear specimens under cyclic loading conditions.

Stress Intensity Factor Solution for a Naturally Emanating Crack Out of a V-Notched Round Bar

During the estimation of Stress Intensity Factor (SIF) of a notched round bar, standard crack geometries such as elliptical, semi-circular, and straight crack fronts are commonly considered at the notch root region. In the present work, the SIF solution for a naturally initiating crack out of a V-notched round bar has been estimated experimentally and the results are compared with data obtained from 3D finite element analysis. The fractographic investigation of the fractured surface suggested a non-symmetric crack propagation and the strong influence of stress concentration factor on SIF, especially in the early stages of crack growth (up to a/d ratio of 0.15, where “a’” is crack length and “d” is notch root diameter). Four aspect ratios (a/c = 0.4, 0.5, 0.75, and 0.85, where “c” is semi-major axis of elliptical crack) and seven crack depth (a/d) ratios in the radial directions were considered with and without offset of surface crack origin to match experimental observations. It was noted that a naturally formed crack had an elliptic shape with aspect ratio of 0.75, with its center offset by 0.5 mm in an upward direction from the notch root region.

Corrected stress intensity factor solution for a British standard single edge notched tension (SENT) specimen

AbstractThis paper revisits a complicated analytical solution of the stress intensity factor K adopted in a newly published British standard BS 8571:2014 for clamped single edge notched tension (SENT) specimens. Comparison with existing numerical results of K shows that the analytical K solution in BS 8571 is correct only for the crack length to specimen width ratio a/W ≤ 0.6, but incorrect for a/W > 0.6. A reinvestigation is thus performed using the crack compliance method, and a corrected K solution is obtained for the BS 8571 clamped SENT specimens over the full range of a/W. On this basis, a simple closed‐form solution of K is obtained using the best curve fitting with an accuracy within 1% for crack sizes up to a/W = 0.98. Results show that the proposed closed‐form solution of K agrees well with the numerical results of K for the clamped SENT specimens.