Variation Of Stress Intensity Factor Research Articles

Effect of Thermal Load Caused by Tread Braking on Crack Propagation in Railway Wheels on Long Downhill Ramps

To investigate the propagation behavior of thermal cracks on the wheel tread under the conditions of long downhill ramps, a three-dimensional finite element model of a 1/16 wheel, including an initial thermal crack, was developed using the finite element software ANSYS 17.0. The loading scenarios considered include mechanical wheel–rail loads, both with and without the superposition of thermal wheel–brake shoe friction loads. The virtual crack closure method (VCCM) is employed to analyze the variations in stress intensity factors (SIFs) for Modes I, II, and III (KI, KII, and KIII) at the 0°, mid, and 90° positions along the crack tip. The simulation results show that temperature is a critical factor for the propagation of thermal cracks. Among the SIFs, KII (Mode II) is larger than KI (Mode I) and KIII (Mode III). Specifically, the thermal load on the wheel tread during braking contributes up to 23.83% to KII when the wheel tread reaches the martensitic phase transition temperature due to brake failure. These results are consistent with the observed radial propagation of thermal cracks in wheel treads under operational conditions.

Influence of load ratio on fatigue life assessment of AZ31B magnesium alloy under different temperatures

First ever fatigue crack growth experiments were conducted under various load ratios (R = 0.1 to 0.8) at 300 K, and (R = 0.1, 0.3, 0.5, and 0.7) at 327 K and 473 K, respectively, on AZ31B magnesium alloy. The results reveal that temperature-dependent variations in both fatigue crack growth rates and stress intensity factor ranges (ΔK) across different load ratios. It was found that at relatively higher load ratio (R = 0.8) leads to a lower ΔK = 8.0287 MPa√m and a lower load ratio (R = 0.1) result in a higher ΔK = 15.5981 MPa√m, indicating that the material undergoes fatigue crack propagation at a higher level of stress intensity factor range at room temperature. A slower crack propagation was seen at higher load ratio (R = 0.8), whereas lower load ratio (R = 0.1) exhibits faster crack growth at 300 K. Similarly, crack growth generally increases at higher temperatures (i.e., 373 K and 473 K). The fatigue life of the magnesium alloy AZ31B increased from 12,410 to 87,031 cycles at 300 K, 9,620 to 32,667 cycles at 373 K, and 9,140 to 30,143 cycles at 473 K as the load ratio increases. The average fatigue life decreases to 59 % and 63 % as the temperature is varied from 300 K through 373 K to 473 K. The fractographic and surface roughness carried out by field emission scanning electron microscopy and 3D-Profilometer respectively, illustrate that roughness of fracture surfaces correlates with an increase in the fatigue crack growth rate for a specific value of ΔK.

Analysis of the Fracture Behavior of Orthopedic Cement Using Submodeling Technique

Orthopedic cement is an essential component of cemented Total Hip Replacements (THR). It must ensure three essential functions: very good implant-cement adhesion, good bone-implant load transfer, and good antibiotic transport. The main objective of the present work is to study the fracture behavior of orthopedic cement in total hip replacements. The analysis is performed using the submodel technique. Two cases are being considered. The first case involves ordinary cracks, while the second case involves cracks emanating from cavities in the cement of the THR acetabular part. The effects of crack position and implant orientation on the variation of stress intensity factors (SIF) in the three failure modes are discussed. It has also been shown that the circumferential positions of cracks present a major risk of loosening of the prosthesis, especially when the defect is aligned with its axis.

Stress intensity factors and full-field stresses for a hypocycloid-type crack within a thermo-elastic material

This study focuses on the failure analysis of a hypocycloid-type crack within a thermo-elastic material. Employing the conformal mapping method, analytical continuation theorem, and principle of superposition, the explicit general solution for stress intensity factors (SIFs) associated with an arbitrary-edged hypocycloid-type crack is determined analytically under the influence of remote homogeneous heat flux and mechanical load. The superposition method combines stress functions and SIFs for two distinct loading conditions. The outcomes of the normalized SIFs are affected by the magnitude and orientation of the heat flux and mechanical load. A full-field stress distribution is provided to account for variations in SIFs. Certain combinations of loads lead to maximum SIF values, rendering the system highly vulnerable to damage, while two specific scenarios inhibit crack propagation, thereby reducing the risk of structural failure.

SIF formula based on exact SIF distribution for semi‐elliptical surface cracks subjected to mode I, II, III uniform loading

AbstractThe stress intensity factor (SIF) distribution of a semi‐elliptical surface crack is often used for evaluating the fatigue strength of structures. Virtually exact distributions of SIFs can be provided along the crack front by solving the hypersingular integral equation of the body force method. In this paper, to create a very accurate SIF variation formula, the elliptical crack SIF solutions , , are used and the SIF ratios , , are mainly focused. Paying attention to the corner point singularity, by applying the least squares method to the ratio , in the whole range of parametric angle , and formulas can be proposed. Instead, formula can be proposed by applying the method of least squares to the ratio of in the range but applying directly to in the range . In this way, all of formulas proposed in this paper provide the SIFs with better than 1.0% accuracy.

Mechanics of Indentation for an Elastic Half-Space by Punches

The dynamic and static problems of finding stress components under four moving punches (a≤|X|≤b,c≤|X|≤d), located close to each other over an elastic half-plane (Y=0), are solved. Employing the Fourier integral transform, the problem is reduced to a set of integral equations in both cases. Using the Hilbert transform technique, the integral equations are solved to obtain the stress and displacement components. Finally, exact expressions for the stress components under the punches and the normal displacement component in the region outside the punches have been derived. Numerical results showing the variations in stress intensity factors (SIF) at the punch ends, and the absolute value of torque applied over the contact regions with different values of the parameters used in the problems have been presented in the form of graphs.

High cycle fatigue life assessment of notched components with induced compressive residual stress

A method for predicting the high cycle fatigue life of cyclically loaded components with induced residual stress based on standard S–N curve data, a fracture mechanics crack growth model, and Finite Element Analysis using the ANSYS SMART crack growth modelling tool is proposed. The method is appropriate to high cycle fatigue analysis of components in which the working stress cycle is linear elastic and the conditions required by LEFM and the SMART FEA method are satisfied. The total fatigue life of the component is calculated as the sum of the crack initiation life and crack propagation life. Crack initiation life is evaluated for an assumed initiation crack length by reference to an S-Ni curve relating stress amplitude to number of cycles to crack initiation, generated from standard S–N data and application of SMART FEA to determine the crack growth component of total test specimen life. Crack propagation life is evaluated by superposition of the individual applied load and residual stress fields, where variation in stress intensity factor with increasing crack length is obtained in the form of polynomial equations. Numerical and experimental investigation of double-notch 316L stainless steel tensile specimens show that the proposed method gives an improved estimate of fatigue life when compared to standard stress-life fatigue assessment for specimens both with and without induced compressive residual stress.

Interaction among interfacial offset cracks in composite materials under the anti‐plane shear loading

AbstractThe present article considers an anti‐plane stress problem of three cracks at different orthotropic materials' interfaces. According to the geometry of the problem, the governing equations and mixed boundary conditions have been formulated. Fourier integral transformation is used to convert the mixed boundary value problem into dual integral equations, which gives two equations containing infinite series. The investigation of the problem concerning anti‐plane cracks subjected to static loadings is done with the help of the Schmidt method to satisfy the given boundary conditions. The difference in displacements is expanded to proceed further in the problem, which becomes zero outside the cracks. Numerical computations are carried out for the graphical representation of stress intensity factors (SIFs) at all cracks' tips. The Interaction among the cracks as those are in close proximity to each other or move away are represented pictorially. Detailed numerical results and discussion are done for the considered materials, which include aluminium, epoxy and graphite epoxy. The novelty of the present article is the numerical analysis and pictorial presentation of SIFs at the tips of interfacial offset parallel cracks for various crack lengths and normalised heights for different combinations of materials. The authors have obtained variations in SIFs for the cracks at the interfaces of dissimilar composite materials.

Employment of Fracture Mechanics Criteria for Accurate Assessment of the Full Set of Elastic Constants of Orthorhombic/Tetragonal Mono-Crystalline YBCO

The effect of elastic constants, cij, on the nature (easy or difficult) of a cleavage system in mono-crystalline YBa2Cu3O7−δ is investigated by employing a novel three-dimensional eigenfunction expansion technique, based in part on the separation of the thickness variable and partly on a modified Frobenius-type series expansion technique in conjunction with Eshelby–Stroh formalism. Out of the three available, complete sets of elastic constants, only the experimental measurements using resonant ultrasound spectroscopy merit serious attention, despite reported values of c12 and, to a lesser extent, c66 being excessively high. The present investigation considers six through-thickness crack systems weakening orthorhombic mono-crystalline Yttrium barium copper oxide (YBCO) plates. More importantly, the present investigation establishes sufficient conditions for crack path stability/instability, which entail a cleavage system being easy or difficult, i.e., whether a crack would propagate in its original plane/direction or deflect to a different one. This criterion of fracture mechanics is then employed for accurate determination of the full set of elastic constants of superconducting mono-crystalline YBCO. Finally, heretofore unavailable results pertaining to the through-thickness variations of stress intensity factors and energy release rates for a crack corresponding to symmetric and skew-symmetric hyperbolic cosine loads, which also satisfy the boundary conditions on the plate surfaces, bridge a longstanding gap.

Energy evolution and crack development characteristics of sandstone under freeze-thaw cycles by digital image correlation.

Freeze-thaw erosion is the main reason for rock mass instability in cold regions and poses major threats to public safety. In this study, the stress threshold, energy, and strain field evolution of sandstone and the variation in stress intensity factor of fractures in various stress fields were all investigated after freeze-thaw cycles by uniaxial compression tests and digital image correlation technology. The results show that the elastic modulus, crack initiation stress, and peak stress all fell by 97%, 92.5%, and 89.9%, respectively, as the number of freeze-thaw cycles approaches 80. Elastic energy's storage capacity also dropped from 0.85 to 0.17. Sandstone's strain was increased by freeze-thaw erosion, which also improved ductility and shortened the cracking time. The stress intensity factor at the crack tip was positively correlated with the tip inclination angle and negatively correlated with the number of freeze-thaw cycles. This study provides a useful reference for understanding the stability of rock masses and the characteristics of crack derivation in cold regions.

An Analytical and Numerical Analysis for Hydraulic Fracture Propagation through Reservoir Interface in Coal-Measure Superimposed Reservoirs

Hydraulic fracturing technology can be used to jointly exploit unconventional natural gas such as coalbed methane and tight sandstone gas in coal-measure superimposed reservoirs for the enhancement of natural gas production. Hydraulic fracturing usually induces mixed fractures of I and II modes, but existing studies have not considered the influence of reservoir lithology on the stress intensity factor of I/II mixed fractures in coal-measure superimposed reservoirs. This paper develops an analytical stress model and a seepage-mechanical-damage numerical model for the vertical propagation of I/II mixed fractures in coal-measure superimposed reservoirs. The variation of stress intensity factor of I/II mixed fractures is analyzed when the fractures are close to the interface of different lithologic reservoirs and the effects of elastic modulus difference, stress state, fracturing fluid viscosity, shear and tensile failure modes on the vertical propagation of hydraulic fractures are investigated. Finally, the ratio of elastic modulus of adjacent reservoirs is proposed as an evaluation index for the fracture propagation through reservoir interface. These investigations revealed that hydraulic fracture propagation through the reservoir interface is a process of multi-physical interactions and is mainly controlled by the injection pressure and the elastic modulus ratio of adjacent reservoirs. A critical line is formed in the coordinates of elastic modulus ratio and injection pressure. A fracture can propagate through the reservoir interface when the combination of injection pressure and the elastic modulus ratio is in the breakthrough zone. These results can provide theoretical support for the site selection of horizontal wells in coal-measure gas exploitation.

Experimental and FEM Analysis for Fracture Performance Evaluation of Concrete Made with Recycled Construction and Demolition Waste Aggregates

Paper presents experimental and Finite Element Method (FEM) analysis of fracture behavior of concrete made using Recycled Aggregate (RA). Concrete mixes were prepared using Construction and Demolition Waste (CDW) as replacement of natural coarse aggregates. To study fracture performance, concrete mixes were prepared with water to cementitious content (w/b) ratios between 0.4 and 0.5. Beam specimens of size 100 mm x 100 mm x 500 mm were cast and tested as per method of Three-point bend test on notched beam proposed by RILEM. Fracture parameters like fracture energy, stress intensity factor, energy release rate and characteristic length were evaluated using Load-CMOD (Crack Mouth Opening Displacement) and load deformation curves. Mechanical properties of concrete such as compressive and flexural strength, modulus of elasticity and split tensile strength were also evaluated. The performance of concrete using RA has been compared with concrete using Natural Aggregate (NA) from literature. Results suggest slightly better fracture performance in case of concrete made using RA in comparison to conventional concrete in spite of having similar strength and w/b ratio. Fracture energy parameter in terms of stress intensity factor obtained from FEM analysis were similar to experimental results wherein no significant variation in stress intensity factor for concrete mixes with recycled and natural aggregate were observed. However, it can be stated that values of stress intensity factor of 0.47_NA was lowest and 0.5_RA was highest. There was no significant difference in average fracture energy of mixes and it lies in range of 180 N/m to 300 N/m.

Numerical simulation of pre-cracked thin aluminum alloy skin repaired with a FRP patch: Pre-crack length studies

The fatigue life of a thin pre-cracked aluminium-alloy panel, repaired with Carbon Fiber Reinforced Plastics (CFRP) patch on one side, is investigated using a numerical model. CFRP plies of different lengths are used to form patch which in turn repair pre-cracked aluminium skin. Numerical studies are performed to determine variation in stress intensity factor (SIF) range and bulging out deflection of specimen subjected to minimum and maximum fatigue load. Patch width to pre-crack and length to pre-crack ratio are kept constant for different pre-crack studies. Numerical simulations are carried out for three different pre-crack length. Three different patch configurations are studied for each pre-crack length. Maximum stress considered is at 50 % yield strength of aluminium skin. The numerical model is simulated by using ANSYS 15.0, a Finite Element Analysis package. The interface behaviour between the skin and the patch is simulated by using cohesive zone material model (CZM). Stress intensity factor (SIF) is determined from J-integral results. Relation between SIF range and crack length can be used to determine fatigue crack propagation by invoking the Paris law. It is found that with increasing the patch length, ΔKI decreased significantly which may result into the increase of the fatigue life.

Numerical Evaluation of Stress Intensity Factors in Functionally Graded CNTRC Plates

The numerical evaluation of stress intensity factors (SIFs) is presented for functionally graded CNT-reinforced composite (FG-CNTRC) plate. The 3-D linear elasticity of cracked orthotropic plate is formulated in terms of 2-D FEM and the (1,1,0) hierarchic model which is sort of the first-order shear deformation theory. Meanwhile, a 2-D thickness-wise plane within FG-CNTRC plate is taken for the numerical evaluation of SIFs. The thickness-wise mixed-mode SIFs are evaluated from the interaction integral by introducing the 2-D complex-valued orthotropic crack-tip singular fields. The numerical evaluation method is validated by comparing with the other reference methods, with the maximum relative difference equal to 31.43%. Moreover, the SIF characteristics of FG-CNTRC are numerically investigated. It is revealed that the thickness-wise volume fraction distribution of CNTs significantly influences the magnitude and variation of SIFs. However, the volume fraction magnitude of CNTs does not show an apparent consistent effect on the both items of SIFs.

Prediction of Mode I Fracture Toughness of Shale Specimens by Different Fracture Theories Considering Size Effect

In this study, mode I fracture tests on cracked straight-through Brazilian disc (CSTBD) and notched semi-circular bend (NSCB) shale specimens with different sizes were conducted to investigate the difference between maximum tangential stress fracture criterion and the size effect law (SEL) model in predicting apparent fracture toughness (Ka) of shale. In addition, the effects of specimen size and geometry on the Ka and the selection of fracture criterion on the prediction of the inherent fracture toughness (KIc) were also studied. The results show that the Ka increases with the increase of specimen size, and the difference between KIc of shale specimens with different sizes predicted by the fracture process zone length determined by the further improved maximum tangential stress (FIMTS) criterion is the smallest. For the prediction of Ka of NSCB specimen, the results predicted by the FIMTS criterion are the closest to the tested fracture toughness. However, the effect of SEL model applied to the prediction of Ka of NSCB specimens is poor. The effective establishment of SEL model requires high accuracy for test data, especially for the configuration with large variation of the dimensionless stress intensity factor (Y*) with normalized crack length (α).

Moving semi-infinite crack between dissimilarorthotropic strips

In this paper, we conceive a semi-infinite moving crack between two bonded dissimilar orthotropic strips. Fourier transform has been adopted to reduce the mixed boundary value problem to a standard Wiener–Hopf equation. To determine the stress intensity factor (SIF) and crack opening displacement (COD), the Wiener–Hopf equation is solved in asymptotic sense for stress free boundary. Finally, the variation of SIF and COD is demonstrated graphically with respect to several orthotropic material parameters.

A stabilized mixed-FE scheme for frictional contact and shear failure analyses in deformable fractured media

Simulation of fracture contact mechanics in deformable fractured media is of paramount important in computational mechanics. Previous studies have revealed that compressive loading may produce mode II fractures, which is quite different from mode I fractures induced by tensile loading. Furthermore, fractures can cross each other. This will increase the complexity of their network deformation under different loading types significantly. In this work, a stabilized mixed-finite element (FE) scheme with Lagrange multipliers is proposed in the framework of variational formulation, which is able to simulate frictional contact, shear failure (mode II) and opening (mode I) of multiple crossing fractures. A novel treatment is devised to guarantee physical solutions at the intersection of crossing fractures. A preconditioner is introduced to re-scale the saddle-point algebraic system and to preserve the numerical robustness. Then, a solution strategy is designed to calculate the unknowns, displacement and Lagrange multipliers, in one algebraic system. Later, numerical tests are conducted to study mechanical behaviors of fractured media. Benchmark study is performed to verify the presented mixed-FE scheme. A deformable medium with crossing fractures is simulated under mixed-mode loading types. The characteristics of fracture contact, surface sliding, opening and variation of stress intensity factor are analyzed. Simulation results show that the curve of slippage induced by compression, as well as the opening induced by internal fluid pressure, along the fracture length holds a parabolic shape. The diagonal contact point, at the intersecting position of the crossing fractures, is studied in detail, specially under different stress states. Finally, the impact of intersecting fractures on frictional contact mechanics is investigated for different loading conditions.

Phase-field modeling of continuous fatigue via toughness degradation

We present a phase-field formulation to model fatigue crack growth over large numbers of cycles. Building upon a recently introduced phase-field formulation by the authors, fatigue is modeled phenomenologically by degradation of the fracture toughness, treated as a spatiotemporally evolving material property, inside a region around the crack tip with size Rfatigue. The present formulation, however, treats cycle number N as a continuous variable, allowing for crack growth prediction over large numbers of cycles of experimental relevance in arbitrary geometries containing one or several cracks, as well as under various loading conditions. The phenomenological form of the degradation law is analytically motivated by first deriving a relationship between the crack growth rate per cycle da/dN and the stress intensity factor (SIF) variation amplitude ΔK in the sharp-interface limit where Rfatigue is much larger than the phase-field regularization length ξ. This relationship reproduces salient features of experimentally measured fatigue growth curves, including the existence of a minimum ΔK for growth, a power law over an intermediate range of ΔK, and a sharp increase of growth rate when the peak SIF value approaches the Griffith threshold Kc. Phase-field simulations are shown to reproduce similar growth curves with quantitative differences depending on the ratio Rfatigue/ξ. The ability of the model to predict realistic crack paths is demonstrated by various examples in two and three dimensions including crack kinking under mode I+II loading, “en-passant” interacting cracks, and crack twisting in a three-point bending geometry with mode I+II+III loading.

Variations of Stress Intensity Factors of Surface Cracks with Wrapping Location in Compression Coil Springs

This study has investigated the effects of coil turn position on the principal stresses and the correction factors, Fi (i=I, II and III) of the three modes of the stress intensity factors for a semi-elliptic surface crack on the outer surface of a compression coil spring. For this purpose, 3D finite element stress analyses have been made on a compression coil spring having a surface crack on the outer surface of its wire at every 0.5 turn from n=0.5 to n=4.5. The maximum principal stress, σ1, was also calculated by FEM and found to vary as cosine function of number of turns, n. The value of σ1 took maxima for half integer coil turns, i.e., n=0.5, 1.5, 2.5, …, whereas minima for every coil turn, i.e., n=1, 2, 3, … The principal stress fluctuation range was found as small as 4.6 % of its center value. The correction factor FI for the mode I stress intensity factors of the semi-elliptic surface crack also varied as cosine functions of n in the same manner as σ1 at all the positions of crack peripheries investigated. The largest mode I correction factor fluctuation range was as large as 22.9 % of its fluctuation center value. The variations of FI value with n can be distinguished into 5 groups according to the distance from the wire surface. This tendency was caused by the variations of FI value with the eccentric angle φ of the crack which are expressed as quartic functions of φ almost symmetric with the φ=90° (deepest point). The FI value took minima at the wire surface and second minima at the deepest point of the crack, and the value increased as the point got closer to the surface. The FI value varied from 0.47 to 0.69 with the geometrical parameters n and φ. The FI value was found dominant among the three modes of correction factors, since the values of the correction factors of the other modes, i.e., FII and FIII, were at most 8.3 % and 14.3 % of the FI value, respectively.

Mode dependent evaluation of fracture behaviour using cantilever bending

Fracture toughness measurement by cantilever bending has been widely used to study the fracture behaviour of different class of materials especially at the micro-scale. However, standard protocols of testing do not exist in these non-conventional geometries, leading to variable results. In this study we assess the geometric factors affecting the stress intensity factor solutions of a single edge notched cantilever bend specimen in different loading modes to propose suitable testing standards. Variation of stress intensity factor and mode mixity is analysed as a function of the relative position of the crack, beam cross-section, crack geometry, arm length of the cantilever and loading direction to discern the contributions of different loading states and boundary conditions on the same. During cantilever bending, state of mode I predominates for beams with length to width ratios above 4 whereas mode II and mode III predominates for shorter beams of length to width ratio of 0.5. Experimental validation is carried out both at the micro-scale and macro-scale using Barium Titanate and polymethyl methacrylate respectively.