Vicinity Of Crack Tip Research Articles

A Griffith Crack at the Interface of an Isotropic and Orthotropic Half Space Bonded Together

In the past 53 years, many efforts have been contributed to develop and demonstrate the properties of reinforced composite materials. The ever-increasing use of composite materials through engineering structures needs the proper analysis of the mechanical response of these structures. In the proposed work, we have an exact form of Stress components and Displacement components to a Griffith crack at the interface of an Isotropic and Orthotropic half-space bounded together. The expression was evaluated in the vicinity of crack tips by using Fourier transform method but here these components have been evaluated with the help of Fredholm integral equations and then reduce to the coupled Fredholm integral equations. In this paper, we use the problem of Lowengrub and Sneddon and reduce it to dual integral equations. Solution of these equations through the use of the method of Srivastava and Lowengrub is reduced to coupled Fredholm integral equation. Further reduces the problem to decoupled Fredholm integral equation of 2nd kind. We get the solution of dual integral equations and the problem is reduced to coupled Fredholm integral equation. We find the solution of the Fredholm integral equation and reduce it to decoupled Fredholm integral equation of 2nd kind. The Physical interest in fracture design criterion is due to Stress and crack opening Displacement components. In the end, we can easily calculate the Stress components and Displacement components in the exact form.

Dynamic effects and an oscillator model of a spatio-temporal representative volume describing fracture process at the crack

An analytical investigation of a fundamental dynamic fracture effect observed in samples with a crack under shock-wave pulse load is provided. Particular attention is paid to the phenomenon of delayed fracture. The effect can be described in the following way: the fracture in the crack tip vicinity can possibly take place after the local stresses reached their maximum value. A number of important features of dynamic fracture under the threshold and beyond threshold loads, observed in various experiments, are discussed. It was found that the experimentally registered fracture delay can be clearly explained within the framework of the structural-temporal approach based on the concept of the incubation time of fracture. The conditions for the delay are found and the corresponding analytical formulas are given. Additionally, a simple analogy based on a mass-spring model is discussed. Analytical formulas available for the oscillator model help to find some non-obvious similarities between the crack behaviour under short pulse loads and the oscillator failure due to analogous loads. It is concluded that it is essential to study threshold cases in which the most important time effects appear that do not fit into the classical concepts of strength and crack resistance – the concepts that rely on local ultimate stress and/or critical intensity factor parameters.

A fracture mechanics approach to hydrogen assisted microdamage and failure analysis of high-strength pearlitic steel wires: Resembling Michelangelo Stone Sculpture Texture

A fracture mechanics approach to hydrogen-assisted microdamage and failure analysis of high-strength pearlitic steel wires is presented. Fractographic analysis revealed micromechanical effects of hydrogen in the form of tearing topography surface(TTS). The progress of this microdamage is modelled as a macroscopic crack that extends the original fatigue precrack and involves linear elastic fracture mechanics (LEFM) principles. In this case, the change from hydrogen-assisted microdamage (HAMD) in the form of TTS (subcritical mode) to cleavage-like topography (critical regime associated with failure) takes place when a critical stress intensity factor (KH) is reached, and this value depends on the amount of hydrogen which penetrated the vicinity of the actual crack tip (the fatigue precrack plus the TTS extension). It is seen that the crack growth by TTS corresponds to the horizontal part (plateau) in the crack growth kinetics (CGK) curve da/dt-K until reaching the critical level KH.

Crack root radius effect on stress fields under nonlinear

The influence of crack root radius and plastic material properties on the crack tip fields was evaluated by strain gradient plasticity theory, and classical plasticity theory. A conventional mechanism-based strain gradient (CMSG) plasticity theory was used in the study. The stress fields in single edge tension specimen are investigated numerically for a wide range of the crack tip radius variations. Five values of the crack tip curvature radius ρ = 0 (mathematical notch); ρ = 25 nm, ρ = 30 nm, ρ = 60 nm and ρ = 100 nm were investigated. The strain hardening exponent varied from N = 0.075 to N = 0.4. A stress analysis by CMSG plasticity was performed for two values of the Taylor’s length parameter l = 1μm and l = 10μm. The boundaries of the local areas, where the influence of the crack tip radius is realized were determined for both HRR and CMSG plasticity. The sizes of the dominance area of the strain gradient plasticity were established and their approximation equations were presented. The influence of the plastic properties and the Taylor’s length scale parameter on the stress fields in the vicinity of rhe crack tip was estimated for the strain gradient plasticity.

Effect of machining on near surface microstructure and the observation of martensite at the fatigue crack tip in PWR environment of 304L stainless steel

This work highlighted that a ground surface finish and the exposure to a pressurised water reactor (PWR) environment result in a decreased low-cycle fatigue lifetime, an enhanced fatigue crack initiation and an accelerated fatigue crack growth rate of 304 L austenitic stainless steel. A ground surface finish promotes fatigue crack initiation and short crack growth especially in a water environment, due to the highly deformed underlying microstructure with high-angle grain boundaries and the grinding marks on surface. Martensite was observed in the vicinity of secondary crack tips in specimens tested in a simulated PWR primary side environment. The aggregated presence of α′- and ε-martensite in the vicinity of the fatigue crack tip can enhance the material's susceptibility to hydrogen-assisted fatigue cracking. Martensite formation was rarely observed in specimens exposed to high temperature air. The phase transformation from γ-austenite to αꞌ-martensite in the PWR primary environment occurred via the intermediate ε-martensite phase.

On the topological enrichment for crack modeling via the generalized/extended FEM: a novel discussion considering smooth partitions of unity

Purpose It has been usual to prefer an enrichment pattern independent of the mesh when applying singular functions in the Generalized/eXtended finite element method (G/XFEM). This choice, when modeling crack tip singularities through extrinsic enrichment, has been understood as the only way to surpass the typical poor convergence rate obtained with the finite element method (FEM), on uniform or quasi-uniform meshes conforming to the crack. Then, the purpose of this study is to revisit the topological enrichment strategy in the light of a higher-order continuity obtained with a smooth partition of unity (PoU). Aiming to verify the smoothness' impacts on the blending phenomenon, a series of numerical experiments is conceived to compare the two GFEM versions: the conventional one, based on piecewise continuous PoU's, and another which considers PoU's with high-regularity. Design/methodology/approach The stress approximations right at the crack tip vicinity are qualified by focusing on crack severity parameters. For this purpose, the material forces method originated from the configurational mechanics is employed. Some attempts to improve solution using different polynomial enrichment schemes, besides the singular one, are discussed aiming to verify the transition/blending effects. A classical two-dimensional problem of the linear elastic fracture mechanics (LEFM) is solved, considering the pure mode I and the mixed-mode loadings. Findings The results reveal that, in the presence of smooth PoU's, the topological enrichment can still be considered as a suitable strategy for extrinsic enrichment. First, because such an enrichment pattern still can treat the crack independently of the mesh and deliver some advantage in terms of convergence rates, under certain conditions, when compared to the conventional FEM. Second, because the topological pattern demands fewer degrees of freedom and impacts conditioning less than the geometrical strategy. Originality/value Several outputs are presented, considering estimations for the J–integral and the angle of probable crack advance, this last computed from two different strategies to monitoring blending/transition effects, besides some comments about conditioning. Both h- and p-behaviors are displayed to allow a discussion from different points of view concerning the topological enrichment in smooth GFEM.

TEM investigation of SCC crack tips in high Si stainless steel tapered specimens

ABSTRACT The stress corrosion cracking (SCC) mechanism is investigated in high Si duplex stainless steel in a simulated PWR environment based on TEM analysis of FIB-extracted SCC crack tips. The microstructural investigation in the near vicinity of SCC crack tips illustrates a strain-rate dependence in SCC mechanisms. Detailed analysis of the crack tip morphology, that includes crack tip oxidation and surrounding deformation field, indicates the existence of an interplay between corrosion- and deformation-driven failure as a function of the strain rate. Slow strain-rate crack tips exhibit a narrow cleavage failure which can be linked to the film-induced failure mechanism, while rounded shaped crack tips for faster strain rates could be related to the strain-induced failure. As a result, two nominal strain-rate-dependent failure regimes dominated either by corrosion or deformation-driven cracking mechanisms can be distinguished.

V-notch crack toughness of PMMA by strain gages and its comparison with caustics results under impact loading

Strain gages and dynamic caustics were used in this experiment to measure the V-notch crack initiation toughness and propagation toughness of polymethyl methacrylate (PMMA) specimens. Furthermore, a method of pasting strain gages on V-notch PMMA specimens for three-point bending test was proposed. The specimens were divided into five groups according to the opening angle (ω), and each group corresponded to two pasting methods: acute-angle pasting method and obtuse-angle pasting method. The results of notch stress intensity factors (NSIFs) obtained by strain gage measurement were consistent with the results calculated using the dynamic caustics method. The concept of the dimensionless notch stress intensity factor (DNSIF) was introduced for a better analysis of the effect of opening angles on cracking. The experimental results revealed that the initiation of V-notch crack in the specimens were inhibited more when ω was larger than 90° than for small opening angles. Under this condition, the specimens displayed higher cracking initiation toughness. Furthermore, the time required for crack initiation was longer, and the cracking was instantaneous. An analysis of the vicinity of the V-notch crack tip showed that with the increase in ω, the stress component decreased, and the rate of decrease became higher. This also explains the phenomenon wherein the specimens transformed from being easy to crack to not being so as ω increased. The experimental results showed that the crack propagation velocity and propagation toughness were also affected by the opening angle of the V-notch crack.

Analysis of Hydrogen-Induced Changes in the Cyclic Deformation Behavior of AISI 300–Series Austenitic Stainless Steels Using Cyclic Indentation Testing

The locally occurring mechanisms of hydrogen embrittlement significantly influence the fatigue behavior of a material, which was shown in previous research on two different AISI 300-series austenitic stainless steels with different austenite stabilities. In this preliminary work, an enhanced fatigue crack growth as well as changes in crack initiation sites and morphology caused by hydrogen were observed. To further analyze the results obtained in this previous research, in the present work the local cyclic deformation behavior of the material volume was analyzed by using cyclic indentation testing. Moreover, these results were correlated to the local dislocation structures obtained with transmission electron microscopy (TEM) in the vicinity of fatigue cracks. The cyclic indentation tests show a decreased cyclic hardening potential as well as an increased dislocation mobility for the conditions precharged with hydrogen, which correlates to the TEM analysis, revealing courser dislocation cells in the vicinity of the fatigue crack tip. Consequently, the presented results indicate that the hydrogen enhanced localized plasticity (HELP) mechanism leads to accelerated crack growth and change in crack morphology for the materials investigated. In summary, the cyclic indentation tests show a high potential for an analysis of the effects of hydrogen on the local cyclic deformation behavior.

Effect of ageing on microstructure and fracture behavior of cortical bone as determined by experiment and Extended Finite Element Method (XFEM)

Bone fracture is a severe health concern; therefore, understanding the causes of bone fracture are crucial. This paper investigates the microstructure and fracture behaviour of cadaveric cortical bone of two different groups (Young, n= 6; Aged, n=7). The microstructure is obtained from µ-CT images, and the material parameters are measured with nanoindentation. Fracture behaviour in transverse and longitudinal orientations is investigated experimentally and numerically. The results show that the Haversian canal (HC) size increases and the osteon wall thickness (OWT) decreases significantly in the aged group, whereas a nonsignificant difference is found in tissue properties. The crack initiation (Jic) and crack growth (Jgrow) toughness of the aged group are found to be significantly lower (p<0.01) than the young group in the transverse orientation; however, for the longitudinal orientation, only the value of Jic in the aged group is found significantly lower. Further, a 4-phase XFEM (based on micro-CT image) model is developed to investigate the crack propagation behaviour in both orientations. For the transverse orientation, results show that in the aged group, the crack initially follows the cementline and then penetrates the osteon, whereas, in the young group, it propagates along the cementline. These results are in agreement with experimental results where the decrease in Jgrow is more significant than the Jic in the aged group. This study suggests that ageing leads to a larger HC and reduced OWT, which weakens the crack deflection ability and causes fragility fracture. Further, the XFEM results indicate that the presence of a small microcrack in the vicinity of a major crack tip causes an increase in the critical stress intensity factor.

J - Integral Tearing Modulus Analysis for Cracked Plates under Biaxial Bending.(Dept.M)

This paper presents a J - integral - tearing modulus analysis for thick plates containing uniform through cracks and subjected to biaxial bending stresses. The solutions are derived for various crack length ratios and applied stress conditions. They are useful for predicting stability of crack propagation in plates with limited plasticity in the vicinity of crack tip. The results are then applied to a carbon steel plate to predict the onset of crack growth instability. Similar applications may be made for other materials, plate geometry and stress conditions.

Evaluation of fracture parameters in cracked plates using an extended meshfree method

In this paper, an extended meshfree method approach is developed for numerical analysis of cracked plates using the First order Shear Deformation Theory — FSDT. Extrinsic enriched functions are employed to capture the jump in deflection and rotation fields, as well as the stress singularity in the vicinity of crack tip. Meshfree approximation of field variables is done by the Radial Point Interpolation Method, which possesses the desirable Kronecker-delta property, unlike many other meshfree methods. Numerical integration is conducted by the Cartesian Transformation Method (CTM), which turns a domain integration into a 1D integration and a boundary integration. As alternative to conventional Gaussian Quadrature (GQ), CTM is advantageous in the context of meshfree analysis, such that background cells are no longer required, forming a truly meshfree formulation. Furthermore, crack surfaces are viewed as part of the domain boundaries and thus, it is guaranteed that no discontinuities exist within the integration domain. The accuracy of the present approach is demonstrated by various numerical examples, in which Stress Resultant Intensity Factors (SRIFs) are evaluated. Obtained numerical results are compared with reference solutions derived from analytical, experimental and other existing numerical methods. It is also exhibited that CTM is more suitable to the meshfree context than GQ.

Damage micromechanisms of stress corrosion cracking in Al-Mg alloy with high magnesium content

Al-10Mg alloys, which are highly susceptible to SCC, were prepared with various β precipitate morphologies. Interrupted in-situ tensile tests were conducted under synchrotron X-ray radiation, employing a recently developed X-ray microtomography technique that combines high-energy, applicability to metallic materials, and ultra-high resolution. Preferential dissolution of the β phase along grain boundaries, and incidental intergranular and transgranular fracture, were observed in 3D. A drastic decrease in SCC resistance was measured after hydrogen charging. The additional effect of external hydrogen absorbed from an aqueous solution during loading was also revealed, by directly measuring crack-tip plasticity. The aquatic environment, one of the most extreme conditions for hydrogen uptake, caused continuous crack-tip corrosion. Catastrophic failure was observed when an alloy had both a relatively high areal grain boundary coverage by film-like β phase, and a reticulately interconnected plate-like β phase in the grain interior. Hydrogen bubble formation was also observed, in relation to the progress of crack-tip corrosion. The main corrosion product was identified as Al(OH)3, based on its linear absorption coefficient. The respective amounts of corrosion products and hydrogen gas in the gas bubbles, and the pH value of the aqueous solution, were accurately measured during in-situ tensile testing, enabling estimation of the local elevation of hydrogen content in the crack-tip vicinity. Finally, a quantitative criterion for the occurrence of hydrogen embrittlement in inter-β ligaments is discussed, together with the applicability of the findings to the prevention of SCC.

On the failure analysis of cracked plates within the strain gradient elasticity in terms of the stress concentration

We consider the fracture mechanics problem for the finite and semi-infinite cracks in the gradient elasticity. Local stress fields that define the fracture the strength of materials are found as solutions of the inhomogeneous Helmholtz equations in which the inhomogeneity is determined by classical stresses. To construct solutions, the radial multipliers method and the Papkovich-Neuber representation are used. We show that the use of the gradient theory of elasticity is carried out simultaneously with the identification of the scale parameter and an indication of its physical meaning and fundamental role in fracture mechanics. We established that the local stresses in the vicinity of crack tips are regular, have the form characteristic of stress concentration, and depend only on the level of acting stresses and the scale parameter, which is found as a result of mechanical testing of material sample

Influence of stress state volume on limit equilibrium of elasto-plastic plate with regular system of internal cracks

The problem of the limit equilibrium of an elasto-plastic plate with internal cracks is reduced to a system of nonlinear singular integral equations, and an algorithm for the numerical solution of such systems together with the conditions of plasticity, single-valued displacements and limited stresses in the vicinity of crack tips is constructed. Cite as: M. M. Nykolyshyn, T. M. Nykolyshyn, “Influence of stress state volume on limit equilibrium of elasto-plastic plate with regular system of internal cracks,” Prykl. Probl. Mekh. Mat. , Issue 18, 74–82 (2020) (in Ukrainian), https://doi.org/10.15407/apmm2020.18.74-82

Error estimation for 2-D crack analysis by utilizing an enriched natural element method

This paper presents an error estimation technique for 2-D crack analysis by an enriched natural element (more exactly, enriched Petrov-Galerkin NEM). A bare solution was approximated by PG-NEM using Laplace interpolation functions. Meanwhile, an accurate quasi-exact solution was obtained by a combined use of enriched PG-NEM and the global patch recovery. The Laplace interpolation functions are enriched with the near-tip singular fields, and the approximate solution obtained by enriched PG-NEM was enhanced by the global patch recovery. The quantitative error amount is measured in terms of the energy norm, and the accuracy (i.e., the effective index) of the proposed method was evaluated using the errors which obtained by FEM using a very fine mesh. The error distribution was investigated by calculating the local element-wise errors, from which it has been found that the relative high errors occurs in the vicinity of crack tip. The differences between the enriched and non-enriched PG-NEMs have been investigated from the effective index, the error distribution, and the convergence rate. From the comparison, it has been justified that the enriched PG-NEM provides much more accurate error information than the non-enriched PG-NEM.

Modelling interfacial cracking and matrix cracking in particle reinforced composites using the extended Voronoi cell finite element method

In this paper, a new extended Voronoi cell finite element method (X-VCFEM), in which two new elements in the crack propagation process are proposed and a remeshing algorithm is constructed, is proposed to model the initiation and propagation of the interface crack and the matrix crack in particulate reinforced composites. In order to accurately capture crack-tip stress concentrations, some singular stress terms of Williams expansion in the vicinity of crack tips are introduced in the stress functions in X-VCFEM. The direction of the crack propagation in matrix is determined by the maximum energy release rate and the interface crack propagation along the interface or into the matrix is assessed on the base of a series of criteria relating to the critical normal stress and the critical hoop stress. Then several numerical examples are used to demonstrate the effectiveness of X-VCFEM by comparing with results obtained by the commercial software ABAQUS. At last, a numerical example is given for a complex structure with 20 randomly distributing inclusions to model the interfacial cracking and matrix cracking. It is certain that this method is a powerful way to model the interfacial and matrix damage of composites containing a great deal of inclusions and cracks.

Extended Voronoi cell finite element method for multiple crack propagation in brittle materials

This paper introduces a new extended Voronoi cell finite-element method (X-VCFEM) for modelling the propagation of multiple cracks in brittle materials. The direction of the crack propagation is adaptively determined in terms of the maximum energy release rate near the crack tip, and we apply a remeshing strategy that a node at a last incremental crack tip in the crack advance process is replaced by a node pairs to realize the gradual crack propagation. In order to accurately capture crack-tip stress concentrations, some singular stress terms of Williams expansion in the vicinity of crack tips are introduced in the assumed stress hybrid formulation which also includes the polynomial terms and the reciprocal terms. Then several numerical examples are used to demonstrate the effectiveness and accuracy of X-VCFEM enriched by some singular stress terms of Williams expansion by comparing X-VCFEM results with those computed by the commercial finite element package ABAQUS or established results in the literature. At last, two numerical examples are given to simulate multiple crack propagation in brittle media. The effects of morphological distributions such as length, orientation and dispersion on the crack propagation are studied. It is obvious that the X-VCFEM has great advantage of analyzing large regions of the microstructure with multiple growing and interacting cracks.

Fracture toughness of self-similar hierarchical material

Two-dimensional materials with self-similar second-order hierarchy are considered. The microstructure with fourfold cubic symmetry is generated by a periodic system of voids in brittle parent material, in one case, macrovoids are filled by a microvoided phase, and in the second one, this phase surrounds hollow macrovoids. A crack is embedded in a rectangular periodic domain subjected to the K-field boundary conditions, and the fracture toughness is determined by the analysis of stresses in the crack-tip vicinity. A novel approach based on the discrete Fourier transform reduces the computational cost of the problem. The analysis of the domain, consisting of several hundreds repeating patterns, is reduced to the multiple analysis of a single representative cell in the Fourier transform space.A parametric study is carried out and, in particular, the influence of parent material redistribution between the hierarchical levels is examined. It is found that for the material with filled macrovoids increasing the relative stiffness at the second hierarchical level diminishes the fracture toughness, while for the second layout the effect is opposite. A comparison with non-hierarchical voided materials of the same relative density emphasizes the role of the length scale parameter of a layout.

Interaction of surface cracks on an egg-shaped pressure shell

This paper is focused on the interaction of surface cracks of an egg-shaped pressure shell of manned deep-sea submersibles. The surface cracks of the egg-shaped shell were subjected to the combined action of uniform external pressure and welding residual stress. The stress intensity factors were calculated using the M-integral method as an important parameter to characterize the stress and displacement fields in the vicinity of crack tips. The study is to evaluate the influence degree of the disturbing crack on the main crack and investigate the interaction between multiple cracks. The results provide references for optimizing the design and manufacture of egg-shaped pressure shells.