Ratio Of Stress Intensity Factor Research Articles

Transient thermal fracture analysis of a honeycomb layer with a central crack

Auxetic honeycomb materials with negative Poisson’s ratio received rapidly growing attention in recent years owing to their exceptional thermomechanical properties in constructing sandwich composites. The objective of this article is to investigate the transient thermal behavior and fracture risk of a honeycomb layer with a central crack subject to a sudden thermal shock by theoretical modeling. Two different material configurations along both orthogonal directions, as well as the conventional and auxetic hexagonal alumina honeycomb cells, are examined to illustrate their effects on the thermal stress intensity factors. To solve the thermoelastic governing equations subject to complex boundary conditions, the methodology of integral transform with singular integral equation is employed. The numerical results demonstrate that the auxetic honeycombs can reduce the thermal stress intensity factors significantly compared to their conventional counterparts. The ratio of stress intensity factors in auxetic to non-auxetic honeycombs under the same absolute value of the internal cell angle θ decreases monotonically with increasing |θ|. In addition, the effects of the relative density, crack length, and crack position are investigated. Our findings would provide a more comprehensive understanding of the honeycomb’s fracture behaviors and contribute to the material design of the sandwich composites with honeycomb cores.

Cross-Crack Interaction and Initiation Mechanism Under Hydro-Mechanical Coupling

In this paper, the equation for computing the maximum Stress Intensity Factor (SIF) of cross-crack under hydraulic-mechanical coupling was derived by the dislocation method and the integral equation, and the influence of cross-crack geometric parameters (branch-crack length, pinch angle, inclination angle) on the interacting SIF was analyzed, and its influence law was obtained. Using the maximum shear and tensile SIF ratio criterion as a basis, the fracture criterion of hydraulic-mechanical coupling cross-crack was established, and the initiation process of hydraulic-mechanical coupled red sandstone cross-crack was predicted (including the cross-crack initiation angle, initiation load, and initiation mechanism). Results showed that for cross-crack with the inclination angle fixed ([Formula: see text]), [Formula: see text] of crack tip C decreases slowly. For cross-crack with change of [Formula: see text]. [Formula: see text] of crack tip A increases, and crack tip C decreases with [Formula: see text]. For the cross-crack hydraulic-mechanical coupling test, as the cross-crack angle [Formula: see text] grows, the fracture initiation stress first reduces before increasing. Initiation mechanisms are Mode I fracture and initiation angles are usually negative. The hydraulic-mechanical coupling cross-crack initiation criterion is validated by the experimental findings, which align with the expected outcomes.

Fatigue crack growth test and characteristics analysis for ultra-thick crack-arrest steel

The fatigue crack growth rate of materials is an essential aspect of the fatigue life prediction. Within the container ship industry, crack-arrest thick steel plates are extensively utilized to mitigate the fracture risks caused by the increasing vessel dimensions. However, it remains deficient in comprehensive investigations into its fatigue crack growth characteristics. This study conducted a sequence of experiments on 85 mm crack-arrest steel (EH47BCACOD) plates. The experiments include tension tests, through-thickness crack growth tests, and surface crack growth tests, while various thickness-based sampling locations, directions, and stress intensity factor ratios are designated. The results illustrate that the crack-arrest steel exhibits better crack growth resistance than conventional marine steels. Regarding non-homogeneity in the thickness direction, variations are observed among ultra-thick plates situated at different thickness locations. The crack growth rate near the surface of plate is lower than that at interior of plate, resembling the behavior exhibited by the tensile test. Furthermore, evident anisotropy is identified in the resistance of fatigue crack growth.

Compatibilization of Polyamide 6/Cyclic Olefinic Copolymer Blends for the Development of Multifunctional Thermoplastic Composites with Self-Healing Capability.

This study investigated the self-healing properties of PA6/COC blends, in particular, the impact of three compatibilizers on the rheological, microstructural, and thermomechanical properties. Dynamic rheological analysis revealed that ethylene glycidyl methacrylate (E-GMA) played a crucial role in reducing interfacial tension and promoting PA6 chain entanglement with COC domains. Mechanical tests showed that poly(ethylene)-graft-maleic anhydride (PE-g-MAH) and polyolefin elastomer-graft-maleic anhydride (POE-g-MAH) compatibilizers enhanced elongation at break, while E-GMA had a milder effect. A thermal healing process at 140 °C for 1 h was carried out on specimens broken in fracture toughness tests, performed under quasi-static and impact conditions, and healing efficiency (HE) was evaluated as the ratio of critical stress intensity factors of healed and virgin samples. All the compatibilizers increased HE, especially E-GMA, achieving 28.5% and 68% in quasi-static and impact conditions, respectively. SEM images of specimens tested in quasi-static conditions showed that all the compatibilizers induced PA6 plasticization and crack corrugation, thus hindering COC flow in the crack zone. Conversely, under impact conditions, E-GMA led to the formation of brittle fractures with planar surfaces, promoting COC flow and thus higher HE values. This study demonstrated that compatibilizers, loading mode, and fracture surface morphologies strongly influenced self-healing performance.

Fatigue Crack Propagation of 51CrV4 Steels for Leaf Spring Suspensions of Railway Freight Wagons.

Leaf springs are critical components for the railway vehicle safety in which they are installed. Although these components are produced in high-strength alloyed steel and designed to operate under cyclic loading conditions in the high-cyclic fatigue region, their failure is still possible, which can lead to economic and human catastrophes. The aim of this document was to precisely characterise the mechanical crack growth behaviour of the chromium-vanadium alloyed steel representative of leaf springs under cyclic conditions, that is, the crack propagation in mode I. The common fatigue crack growth prediction models (Paris and Walker) considering the effect of stress ratio and parameters such as propagation threshold, critical stress intensity factor and crack closure ratio were also determined using statistical methods, which resulted in good approximations with respect to the experimental results. Lastly, the fracture surfaces under the different test conditions were analysed using SEM, with no significant differences to declare. As a result of this research work, it is expected that the developed properties and fatigue crack growth prediction models can assist design and maintenance engineers in understanding fatigue behaviour in the initiation and propagation phase of cracks in leaf springs for railway freight wagons.

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.

Estimation of the stress intensity factor of an interface crack by the scattered SH-far field

The diffraction of the plane elastic SH-wave from a semi-infinite interface crack on junction of two elastic semi-infinite media is studied. The crack is modelled by the mathematical cut with no stress on its faces. The displacement and the stress fields are continuous outside of the crack. The wave diffraction problem is reduced to the solution of the mixed boundary value problem for Helmholtz equation. We search the solution which satisfies the Neumann boundary condition on the crack faces and the continuity condition for the stress and displacement fields outside of the crack. The radiation condition at the infinity and the Meixners condition at the crack tip must be also satisfied. Using the Fourier integral transform, the mixed boundary value problem is reduced to the Wiener-Hopf functional equation which is valid in the given strip of regularity in the complex plane. The method of factorization and decomposition, as well as the Liouvilles theorem, are used to solve this equation. Its kernel function is factorized and represented as a product of two split functions that are regular in the overlapping half-planes. These ones allow for the simple poles outside of the regularity regions. The solution of the Wiener-Hopf equation is presented in analytical form. The scattered displacement field is found for an arbitrary frequency and sounding angle by applying an inverse Fourier integral transform to the solution. The asympŹtotic formula for the stress intensity factor (SIF) at the crack tip is obtained. The correlation between complex amplitude of the SH-wave far scattered displacement field and the SIF caused by this field is obtained for an arbitrary radiation angle, frequency and medium parameters. This allows us to express the SIF through the amplitude of the far field if the radiation frequency, sounding angle as well as the physical characteristics of materials are known. It is shown that in the plane that is normal to the tip of the crack the ratio of SIF for the given junction and two fixed values of the sounding angle or two sounding frequencies is proportional to the ratio of the scattered fields. It is found that under above mentioned condition the proportionality rate does not depend on material properties. The obtained relations can be applied for estimation of the SIF with changing frequency and sounding angle.

Effects of Residual Stress Induced by Laser Shock Peening on Fatigue Crack Propagation Behavior in Directed Energy Deposition Stainless Steel

To investigate the effect of laser shock peening (LSP) on the fatigue crack propagation behavior of 316L stainless steel fabricated by directed energy deposition (DED), three‐dimensional finite element models of DED and compact tensile specimens before and after LSP are developed. The residual stress fields induced by DED and LSP are simulated, as well as the effects of different residual stresses on the stress intensity factor and effective stress ratio based on the contour integral method are also analyzed. The microstructure of the LSP region is observed by scanning electron microscope. When the crack length increases from 12 to 22.5 mm, the average effective stress ratio of the DED specimen is 0.133, and the average effective stress ratio of the DED specimen after LSP decreases to 0.110, which decreases by 17.3%. The fatigue lives of the DED specimen before and after LSP are 62.7% and 105.2% of that of the hot‐rolled plate. After LSP treatment, the fatigue life of the DED specimen is increased by about 1.68 times. The fracture morphology in the transient fracture zone changes from ductile and brittle mixed fracture to ductile fracture.

The Improved Irwin’s Model for Crack Problems in Power-Law Hardening Materials

In this paper, an improved Irwin’s model for power-law hardening materials is established through the static equivalence between the linear elastic stress solution and the stress redistribution in the plasticity-affected zone (PAZ) under small-scale yielding (SSY) conditions. HRR solution is adopted to describe the stress field within the crack-tip plastic zone (CTPZ). Analytical expressions of the effective stress intensity factor (SIF) and the size of PAZ are derived to illustrate the effect of CTPZ on the fracture behavior for power-law hardening materials. Influences of external load and hardening exponent on fracture behavior are explored. The proposed model can assess the toughening effect of CTPZ accurately using the SIF ratio, which is always smaller than 1. This model can be applied to various materials obeying power-law hardening constitutive equations. It will reduce to the extended Irwin’s model for elastic-perfectly plastic materials in the limiting case.

Study on the Initiation of Interface Crack in Rock Joints.

The interfacial fracture of rock joints is an important although easily ignored issue in jointed rock engineering. To conduct this study, an interface crack model of rock joints was proposed. By analyzing the ratio of stress intensity factor to fracture toughness, the fracture mode of the interface crack was studied. Based on the Mohr-Coulomb criterion, an interface fracture criterion considering T-stress was established. To verify the proposed fracture criterion, laboratory and numerical tests were conducted. Finally, the effect of relative critical size α, internal friction angle φ and cohesion c on the initiation of an interface crack was comprehensively discussed. It is concluded that the proposed fracture criterion can predit the initiation of the interface cracks properly. With an increase in cohesion c, mode II fracture toughness KIIC also clearly increases. When the absolute value of KI is small, the effect of α is much larger than that of φ. In addition, with an increase in the absolute value of the mode I stress intensity factor, the φ of the joint plays a more important role in the initiation of the interface crack.

Dynamic Propagation Characteristics of a Mode-III Interfacial Crack in Piezoelectric Bimaterials

This article presents the dynamic behavior of a semi-infinite interfacial crack in piezoelectric bimaterials under impact loading. With the help of the transform methods (the Laplace transforms and Fourier transforms), the problem is studied with the Wiener–Hopf technique. This strict proof guarantees the feasibility of this approach. The dynamic stress intensity factor and dynamic electric displacement intensity factor of the interfacial crack propagation characteristics are expressed. Finally, several classic numerical examples are mentioned and discussed to demonstrate that the theoretical deduction is highly accurate for interfacial crack analysis of piezoelectric bimaterials. The results show that the crack propagation is affected by the electromechanical coupling coefficient. In addition, if the velocity of the dynamic crack propagation reaches the generalized Raleigh wave speed, the dynamic stress intensity factor will disappear. Furthermore, for a given time, the ratio of the dynamic stress intensity factor to load increases with the electromechanical coupling coefficient decreasing. Numerical examples are presented to highlight the result.

On the prediction of fatigue crack growth based on weight functions in residual stress fields induced by laser shock peening and laser heating

AbstractThis study deals with fatigue crack growth prediction for thin sheet AA2024 specimens with residual stresses introduced through laser shock peening and laser heating treatments. Different weight functions are used to calculate the stress intensity factor due to the presence of residual stresses. A superposition principle is used by calculating the total stress intensity factor considering the applied loads and residual stresses. The fatigue crack growth is predicted using the Paris' law based on the effective stress intensity factor range, in that the effect of residual stresses is considered by changing the total stress intensity factor ratio. It is concluded, that weight functions are a powerful tool to predict fatigue crack growth in AA2024 containing residual stress fields, as long as the gradient in the loading direction, as induced by laser shock peening and laser heating, is moderate.

Convenient and accurate formulas for stress intensity factor distribution of semi-elliptical surface crack

In this paper, the stress intensity factor (SIF) formula [Formula: see text] along the crack front of a semi-elliptical surface crack is studied. The exact SIF solution [Formula: see text] is used by solving the hypersingular integral equation of the body force method discussed in the previous paper. To obtain the accurate formula, the SIF ratio [Formula: see text]/[Formula: see text] is focused considering the exact solution [Formula: see text] of an elliptical crack. By applying the least squares method to the ratio [Formula: see text]/[Formula: see text], accurate and convenient formula is proposed. The proposed formulas may provide the accurate SIF distributions for the aspect ratio [Formula: see text]–4 better than 0.2% accuracy.

Stress intensity factor and interaction analysis of offset parallel cracks in brittle solids

The analytical solutions for the mode-I and mode-II stress intensity factor (SIF) of arbitrary distributed offset parallel cracks in brittle solids were generated based on the Kachanov method and superposition principle. By analyzing the SIF ratio, effects of the horizontal interval, vertical interval, crack inclination angle and crack length on the interaction of offset parallel cracks were estimated, and the interference area of the crack was determined theoretically. Numerical models were established using the finite element method (FEM) to show the performance of the present method, and the relationship between crack propagation and crack interaction was discussed. The results show that the SIFs obtained from the present method agree well with the accurate ones. The interaction of offset parallel cracks contains three types, i.e. reinforcing effect, shielding effect and null-effect, which can convert mutually with the change in interval, crack inclination angle and crack length. The interference area of the crack can be divided into reinforcing, shielding area and null-effect area which are symmetric about the crack. The reinforcing effect facilitates crack propagation while the shielding effect inhibits crack propagation.

Study on Fracture Mode Mixity Under Impact Loading Based on SHTB

Mode mixity plays an essential role in the criteria of mixed mode fracture. In this paper, a novel approach for precisely controlling mode mixity under dynamic loading is proposed. Numerical simulation of all fracture mode (AFM) specimen and modified compact tension shear (MCTS) specimen loaded by split Hopkinson tension bar (SHTB) apparatus is carried out. With a constraint on MCTS specimen on the direction perpendicular to the incident bar, the dynamic stress intensity factor (DSIF) ratio of mode I to mode II remains constant during the loading process. When the constraint is absent, the DSIF ratio varies due to the vibration of clamps and specimen. The DSIF of MCTS specimen under different loading angles is also studied, and the ratio [Formula: see text] approximately equals the tangent of loading angle, which is also proven in experiments. Moreover, numerical results indicate that the influence of the shape of clamps is significantly reduced by applying a constraint on the specimen. It is concluded that AFM specimen is not suitable for dynamic fracture tests owing to over complicated clamps.

Observation of Crack Growth Behavior of Various Cracks in 4.762mm Diameter Silicon Nitride Balls under Cyclic Compressive Load

In order to investigate the effect of pre-crack lengths on strength of silicon nitride balls under cyclic pressure loads, growth behavior of 600~700μm pre-cracks were compared to those of 200μm~300μm and 400~500μm pre-cracks. Furthermore, the change in initial threshold limit of the maximum stress intensity factor was discussed. It was found that the increasing ratio of stress intensity factor during N=0 and N=1000 distinguished the failure and non-failure, and pre-crack length had strong effect on the threshold limits of the increasing ratio.

Investigation on the crack fracture mode and edge quality in laser dicing of glass-anisotropic silicon double-layer wafer

This work puts forward numerical and experimental investigations on laser dicing of glass-anisotropic single-crystal silicon double-layer wafer using laser induced thermal-crack propagation (LITP). A semiconductor continuous wave laser working at the defocusing mode serves as volumetric heat source for glass layer while as surface heat source for silicon layer. Based on the classical fracture theory, a static seam-type crack is introduced under the circumstance of ABAQUS to simulate the crack fracture modes in glass layer as well as silicon layer with crystal planes of (100), (110) and (111) during laser dicing in different dicing directions. In the experiments, processing parameters are kept the same as the simulations and typical dicing directions obtained from simulations are also used. The surface morphologies of crack edges are measured by the optical microscope and surface profiler. Through the comparison of numerical and experimental results it is discovered that for the specific substrate, the evolution of crack edge qualities in different dicing directions and different layers can be interpreted based on the corresponding stress distribution and stress intensity factor (SIF) ratio explicitly. And most important of all, the anisotropy of silicon layer has significant influence on the fracture mode and edge quality of crack in both layers.

Fracture toughness of CTBN modified PF particleboard based on equal deflection rigidity

The fracture toughness of particleboard should be evaluated when it was intended to use in the structure system. Single edge notched beam (SENB) test method was employed to measure stress intensity factor (SIF) of the internal middle layer of the PF and CTBN modified PF particleboard. Equal deflection rigidity algorithm (EDRA) was used to homogenized the sandwich bi-material beam in order to make the test procedure match ASTM E399-2017. The results shown that the optimized CTBN addition was among 8% to 12% and the improve ratio of SIF of the particleboard middle layer was 27.27 %. Owing to the different broken mechanism, the tested fracture performance show more stability compared to the traditional internal bonding (IB) test. But the fracture test strongly depend on the notched incision morphology.

The impact of various crack geometrical parameters on stress field over tip under different mixed loading conditions and inclination angles

Mixed mode fracturing behaviors in brittle materials are ubiquitous occurring in practicing engineering. Especially for rocks, tensile-shear loadings are one type of basic factors inducing failures. This paper presented analytical and numerical solutions to investigate the variations of stress field over crack front vicinity under different complex loading conditions and geometrical parameters. An analytical solution for crack under mixed loadings and various geometrical parameters (i.e. inclination angle α and shape parameter m of crack) was proposed, which also considers shear loadings both applying on internal boundary (i.e. crack surface) and external boundary (i.e. distance far away crack). The analytical solution for the model by complex potential method has been suggested. Numerical simulations have been carried out to verify the analytical solution of stress distribution adjacent to crack tip, in which the analytical solutions show good agreement with the numerical results. Three dimensionless loading coefficients (λ1,λ2,λ3) were defined to reflect the magnitudes of biaxial loading, external shearing and internal shearing, respectively. The characteristics of stress distribution, shearing effects and initiation stress were studied deeply under different λ1,λ2,λ3 with various α,m, and the effects of varied conditions on stress magnitude variations have been discussed. According to the solution, we derived the explicit expressions of stress intensity factor (SIF) under different loading situations. Considering the effects of various crack inclination angles and shear loadings, the variations of normalized SIF ratio 2πarctanKI/KII with various conditions also have been discussed. In conclusion, loadings and geometrical variations both have strongly effects on stress distributions around the tip, and the influences have the relationship with different situations.

Crack forbidden area in the anisotropic fracture toughness medium

In some rocks and crystals, the fracture toughness in one direction would be lower than the other directions, and the fracture behavior in the materials with anisotropic fracture toughness profile may be very different from the isotropic materials. The weak plane model is suitable to describe the fracture toughness property in such materials. Because of the attraction of weak plane direction, the fracture might never enter a sector of directions near the weak plane, instead, these kinds of fracture would deflect to the weak plane direction immediately. Such material-level crack forbidden area, which is protected by the weak plane, is demonstrated in this paper. The size of the forbidden area is found to be only related to one material constant, the fracture toughness ratio, and is independent of the angle between the fracture and the weak plane, or the ratio of stress intensity factors near the crack tip. An approximate expression of the crack forbidden area is also derived in this paper for the simplified model. The study on the crack forbidden area would be helpful to control the crack path in the anisotropic fracture toughness materials and protect parts of the medium by designing the material properties.