Crack Tip Shape Research Articles

Corrosive Influence of Carbon Dioxide on Crack Initiation in Quartz: Comparison With Liquid Water and Vacuum Environments

AbstractThe stimulation of crack growth in quartz and siliceous materials by injecting carbon dioxide (CO2) represents a key technology in long‐term carbon storage and in the development of natural gas wells. While this technology is widely used, the molecular impact of CO2 interactions on the solid matrix is only incompletely understood. In this work, we employ reactive molecular dynamics simulations to study how the CO2 fluid environment affects the mechanical properties of pre‐cracked single‐crystal quartz. The thermodynamic conditions of interest are those relevant to subsurface reservoirs. We report how structural properties of quartz—bond length distribution and crack tip shape—evolve upon introduction of a fluid. These properties are directly related to macroscopic quantities of the global stress–strain curves, thus reaffirming the inherent coupling across multiple scales for fluid–solid interactions in the subsurface. We find that CO2 reduces the fracture toughness of quartz by 12.1% compared to that of quartz in vacuum, thereby promoting crack growth and enhancing fluid transport in the subsurface.

Role of Initial Crack Tip Shape, Plastic Compressibility and Strain Softening on Near-Tip Stress-Strain State in Fatigue Cracks during Simulation of a Finite Deformation based Elastic-Viscoplastic Constitutive Model

This paper deals with the effect of initial crack tip shape, plastic compressibility, and strain softening on near-tip stress-strain fields for a mode I crack subjected to fatigue loading under plane strain and small scale yielding. A finite strain-based elastic-viscoplastic constitutive equation with bilinear hardening and hardening-softening-hardening hardness functions is taken up for simulation. It is observed that plastic compressibility and strain softening have a significant impact on crack tip opening displacement (CTOD) and tip propagation. Furthermore, it has been viewed that the initial shape of a crack tip can significantly influence both the CTOD and the crack tip extension for the bilinear hardening material; however, with identical conditions for the hardening-softening-hardening material, the initial crack tip shape affects the fatigue crack growth much lesser though the CTOD is influenced considerably. In comparison to the crack growth in the plastically incompressible hardening-softening-hardening solids, the variation of the crack growth (with respect to the tip curvature radius) is more and peculiar in the corresponding plastically compressible solid. To explain and to get a better insight of the crack tip deformation, the near-tip plastic strain and hydrostatic stress have been illustrated.

Calibration of Paris law constants for crack propagation analysis of damaged steel plates strengthened with prestressed CFRP

Paris law constants, C and m, are two vital parameters of the Paris law for fatigue crack propagation of steel structures. Traditionally, the constants are determined through a linear regression of experimental crack growth curve under tension-to-tension cyclic loading. However, the direct linear regression would provide the value of C with larger error under negative stress ratios (tension-to-compression cyclic loading) probably caused by prestress. This study firstly proposed a reverse-reasoning methodology to obtain and calibrate Paris law constants based on the notched specimens with non– and prestressed CFRP (Carbon Fiber-reinforced Polymer) reinforcement under a wider range of stress ratios. Finite element (FE) modeling was then performed using a combination of the programs FRANC3D and ANSYS to compute the stress intensity factors (SIF) as well as crack tip shape evolution of the respective specimens. A sensitivity analysis was also made to investigate the variety of the constants affected by crucial factors. The comparison of experimental and theoretical results confirms excellent accuracy of the proposed method. The results indicated that the constant m is stable around 3.15 and prestress effect is significant not only on reduction of effective SIF range but also on change of the constant C. Moreover, the suggested value of m and C are 3.15 and 1.08E-12 for prestressed CFRP reinforced steel structures under negative stress ratio (R ≤ 0), and are 3.15 and 2.17E-13 for the positive stress ratio (R > 0) in the unit of mm and MPa, respectively.

Distribution of crack-tip stresses during fatigue loading with an overload event: role of initial crack-tip shape, plastic compressibility and material softening

Distribution of crack-tip stresses during fatigue loading with an overload event: role of initial crack-tip shape, plastic compressibility and material softening

Anisotropic stress-softening effect on fast dynamic crack in filler-reinforced elastomers

Deformation of filler-reinforced elastomers is accompanied by a complex internal damage due to stress softening (Mullins effect). The crack growth behavior of filler-reinforced elastomers is made significantly complex by the occurrence of a simultaneous directional stress softening. The influences of the directional stress softening on fast crack propagation normal to the pre-stretching direction are revealed by the comparison using three types of specimens: (I) a low-filled elastomer with almost no stress softening, (II) a pristine highly filled elastomer with a pronounced stress-softening feature, and (III) an elastomer obtained by imposing before uniaxial loading–unloading cycles with a large maximum stretch of specimen (II). The previous directional softening causes a reduction in the threshold tearing energy for velocity transition, and an increase in local strain in the softening direction. In contrast, the previous directional softening has no appreciable effect on the tearing energy dependence of velocity, crack-tip shape, strain field behind the crack-tip, and the strain singularity near the crack-tip.

The mechanism of thermal corrosion fatigue (TCF) on nickel-based single crystal superalloy and the corresponding structure shape effect

The thermal fatigue behavior under hot corrosion is studied at 25 ℃ - 900 ℃. The whole process of thermal corrosion fatigue (TCF), including crack initiation and propagation, is analyzed in detail from the perspective of driving force and the intensity factor for cracking. By controlling the Cr content in nickel-based single crystal superalloy, different hot corrosion degrees and reaction products are obtained, and its influence on the thermal fatigue mechanism of the alloy is analyzed comprehensively. It can be concluded from the research that hot corrosion has a great influence on thermal fatigue. Firstly, severe hot corrosion which induces spallation can lead to crack initiation dominantly. Secondly, the thermal mismatch between the hot corrosion products and the matrix provides a high driving force for thermal fatigue. Subsequently, the driving force can influence the thermal corrosion fatigue (TCF) process by stress concentration generated by crack tip and products shape. Finally, the loose and fragile nature of the hot corrosion products can provide a channel for crack propagation. These characteristics of thermal corrosion fatigue (TCF) behaviors are obvious in low Cr content Nickel-based single crystal superalloy.

Stress Intensity Factor Expression for Welded Butt Joint with Undercut and Inclined Lack of Penetration Defects considering the Effect of Joint Shape

In this paper, the stress intensity factor (SIF) expression for defected butt welds containing undercut and inclined lack of penetration (LOP) subject to far-field tensile stress is derived. Some of the standards such as ISO 5817 and BS EN 25817 have specified allowable limits for the length of the undercut and LOP defects and for the height of the weld. In addition, EN 29692 standard has determined an acceptable range for the groove angle. In this paper, the effect of these acceptable geometries on stress intensity factor (SIF) of butt welded joint is investigated through following steps: i) elastic analyses to predict crack tip stress intensity (KI, KII) and shape factors, ii) approximation of shape factors by Response Surface Method (RSM). These expressions provide design guidelines for welded butt joint containing unavoidable undercut and inclined lack of penetration (LOP) defects.

A study on residual ultimate strength of steel unstiffened plate with a crack

Crack damage is commonly found in aged hull structure severely affecting the ultimate compressive strength. A numerical study is comprehensively carried out to reveal the ultimate strength reduction behaviors of steel unstiffened cracked plate. The parameters such as crack length, angle and positions as well as the plate aspect and slenderness ratios were taken into account in the FE models. The crack was assumed to be through-thickness with no faces contact and propagation. Reasonable element type and size, crack width and tip shape were adopted based on a series of sensitivity analyses. It is concluded that the real length of longitudinal crack, projected lengths of transverse and inclined cracks, their transverse positions and slenderness ratio significantly influence the plate ultimate strength, while effects of aspect ratio and longitudinal position are not crucial. Based on the numerical results, two empirical formulas as a function of the critical parameters were proposed for predicting the residual ultimate strength of ship plates with longitudinal crack, transverse or inclined cracks, respectively.

A numerical study of the effects of overload on fatigue crack growth in plastically compressible hardening and hardening-softening-hardening solids

Variation of cyclic loading effect on fatigue crack growth is investigated under plane strain and small scale yielding (SSY) conditions. The material is characterized by a finite strain elastic viscoplastic constitutive model with hardening and hardening-softening-hardening hardness functions. Displacements corresponding to the isotropic linear elastic mode I crack field are prescribed on a remote boundary. The influence of cyclic stress intensity factor range (), load ratio (R), number of cycles (N), plastic compressibility ( overload and material softening on near tip deformation was studied in detail. For comparison purpose, a few results pertaining to plastically incompressible solids are also considered. The crack tip opening displacement (CTOD), plastic crack growth, deformed crack tip shape, plastic zone shape and size near the crack tip appear to depend significantly on R, N, overload and material softening. The overload produces strong plastic deformation ahead of the crack tip and decreases the fatigue crack growth substantially. Highlights Variation of cyclic loading effect on fatigue crack growth is investigated for materials characterized by a finite strain elastic viscoplastic constitutive model with hardening and hardening-softening-hardening hardness functions. Both plastically compressible and incompressible solids are considered. The influence of cyclic stress intensity factor range (), load ratio (R), number of cycles (N), plastic compressibility ( overload and material softening on near tip deformation was studied in detail. The crack tip opening displacement, plastic crack growth, plastic zone shape and size near the crack tip appear to depend significantly on R, N, overload and material softening. The combination of softening or softening-hardening material response and plastic compressibility leads to major deviations in crack tip blunting and fatigue crack growth from those that prevail for a hardening material.

Crack-Tip Strain Field in Supershear Crack of Elastomers.

We characterize the crack-tip strain field in the high-speed (supershear) crack in the elastomers propagating faster than the shear wave speed of sound (Cs). The dependence of steady-state crack velocity (V) on input tearing energy exhibits a crossover at V ≈ Cs between the subsonic (V < Cs) and supershear cracks (V > Cs). Several features of the crack-tip strain field such as strain-magnitude, extent boundary, and singularity exponent also change substantially accompanying the transition from subsonic to supershear cracks. The definite crossover of these characteristics at V ≈ Cs reflects the variations in the crack-growth mechanism: The inertia effect comes into play in the supershear crack. We also demonstrate that the azimuthal distribution of the local crack-tip strain has a close correlation with the macroscopic crack-tip shape, regardless of the regime of V.

Effect of crack tip shape on near-tip deformation and fields in plastically compressible solids

In the present study, the crack tip shape effect on near-tip deformation and fields is numerically investigated for a mode I crack under plane strain and small-scale yielding conditions. We explore here the quasi-static deformations of solids characterized by finite strain elastic–viscoplastic material model with bilinear hardening and hardening–softening–hardening hardness functions. For comparative analyses, both plastically incompressible and plastically compressible solids have been considered. It has been observed that the crack tip shape can have great consequence on the near-tip deformation and plastic fields. As the crack tip radius is increased, the plastic strain and stresses advance more to the tip of a crack as compared to the crack surface. It has also been revealed that the combination of crack tip curvature radius, material softening and plastic compressibility provides some useful and fundamental information for the near-tip deformation and plastic fields.

Crack tip shape effect on stress-strain fields in plastically compressible materials

In the present study, the effects of crack tip shape on near tip deformation and fields are numerically investigated for a mode I crack under plane strain and small scale yielding conditions. The material is characterized by finite strain elastic-viscoplastic constitutive relation with bi-linear hardening and hardening-softening-hardening hardness functions. Both plastically incompressible and compressible solids have been considered for analyses. It has been observed that the combination of crack tip profile and plastic compressibility has significant effect on the near tip deformation and plastic fields.

Experimental methodology for the quantification of crack tip plastic zone and shape from the analysis of displacement fields

The current work presents a novel methodology for the experimental quantification of the crack tip plastic zone during fatigue crack growth. This methodology is based on the application of yield criteria to estimate the area and the shape of the plastic zone at the crack tip. The implementation of the proposed methodology requires the use of strain maps calculated from the differentiation of the displacement fields obtained by digital image correlation (DIC). Stress maps can subsequently be inferred from both von Mises and Tresca yield criteria. Fatigue tests and associated measurements of plastic zone size and shape were conducted on a compacttension specimen made from commercially pure titanium at R ratio of 0.6. In addition, the ability to predict the shape and size of the experimentally observed crack tip plastic zone has been explored using three different analytical elastic crack tip models [Westergaard, Williams and Christopher- James-Patterson (CJP)]. This analysis indicated that the CJP model provided the most accurate prediction of the plastic zone and shape.

Crack-tip shape in the crack-growth rate transition of filled elastomers

The velocity transition in crack-growth dynamics and the accompanying changes in crack tip shapes are investigated for the elastomers composed of styrene-butadiene rubber and silica filler (SBR/SI). The concentrations of filler and cross-link (ϕf and cx, respectively), and temperature (T) are extensively varied in order to change the degree of nonlinearity in elasticity of the elastomers. The shapes of the crack tip are characterized by three parameters, i.e., the deviation δ from the parabolic one expected by the linear elastic fracture mechanics (LEFM), the parabolic curvature a, and the non-dimensional quantity aδ. The dependence of these parameters on the input tearing energy Γ is successfully explained by the weakly nonlinear theory of dynamic fracture (WNLT), which considers the contribution of the second-order shear modulus μ(2) to the strain field in addition to that of the first-order shear modulus μ(1), independently of ϕf, cx and T, unless δ exceeds a limit value (δC). SBR/SI shows an appreciably larger value of δC than the carbon-black filled acrylonitrile butadiene (NBR/CB) elastomers. The smaller value of δC for NBR/CB is attributed to that the contribution of the third-order nonlinear modulus μ(3)/μ(1), which is not considered in WNLT, is appreciably higher than that in SBR/SI. The magnitude of the threshold tearing energy Γc for the onset of the velocity transition shows a good correlation with the fracture toughness Wc normalized by the nonlinear elastic constant μ(1)3/μ(2)2 in WNLT. This result indicates that the magnitude is governed by the combined effect of the degree of nonlinearity in elasticity and the fracture toughness.

Proposal for a new CTOD calculation formula

A new CTOD calculation method is investigated in this work, considering the variation of crack tip blunting due to strain hardening. The calculation formula is constructed assuming that CTOD45FEM based on three-dimensional elasto-plastic FEM is the target CTOD to be calibrated. A new factor f is introduced to correct the plastic term. In this factor, the blunted crack tip shape is considered to depend on the strain hardening exponent, and f is given as a function of the yield-to-tensile ratio (YR) of the material and the specimen thickness. The appropriateness of the investigated CTOD calculation is verified numerically and experimentally.

Calculation of the influence of plastic deformation on the evolution of crack stress intensity factors in a body-centered cubic crystal

The evolution of stress intensity factors in a mixed loading mode has been calculated for different cleavage planes, the direction of the crack front, and the easy slip systems near the crack tip in a body-centered cubic (bcc) crystal. Calculations take into account the mutual influence of the plastic deformation and crack tip shape as well as T stress. The dependence of screening the crack tip by dislocations on the crack orientation, easy slip system, and fracture modes is found.

GS0601-372 初期不整を有する円板状き裂の応力拡大係数

GS0601-372 初期不整を有する円板状き裂の応力拡大係数

Influence of Re on the propagation of a Ni/Ni3 Al interface crack by molecular dynamics simulation

The influence of Re on the propagation of a (0 1 0)[1 0 1] crack in the Ni/Ni3Al interface, including crack propagation velocity, crack-tip shape, and dislocation emission, is investigated using a molecular dynamics method with a Ni–Al–Re embedded-atom-method potential. The propagation velocity of the crack noticeably decreases at 5 K when 3 or 6 at% Re atoms are added into the Ni matrix. At 1033 K, the crack tip becomes blunter and emission of dislocations becomes easier with Re addition, owing to the larger bond strength between Re and Ni atoms. Furthermore, we calculate the unstable stacking energy (γus), surface energy (γs), and adhesion work (Wad) of the interface. When Re atoms are randomly doped into a Ni matrix, γs/γus increases correspondingly. This means that Re addition decreases brittleness and improves ductility. The calculation also shows that γus is not affected by Re–Ni atomic interaction, and that Re–Re atomic interaction has some effect on γus. In addition, Wad increases with Re addition, and a small increase in Wad results in a larger decrease in crack velocity. This indicates that Re–Ni atomic interaction restrains crack propagation velocity at low temperature.

Effect of crack-tip shape on the near-tip field in glassy polymer

The physical nature of a crack tip is not absolutely sharp but blunt with finite curvature. In this paper, the effects of crack-tip shape on the stress and deformation fields ahead of blunted cracks in glassy polymers are numerically investigated under Mode I loading and small scale yielding conditions. An elastic–viscoplastic constitutive model accounting for the strain softening upon yield and then the subsequently strain hardening is adopted and two typical glassy polymers, one with strain hardening and the other with strain softening–rehardening are considered in analysis. It is shown that the profile of crack tip has obvious effect on the near-tip plastic field. The size of near-tip plastic zone reduces with the increase of curvature radius of crack tip, while the plastic strain rate and the stresses near crack tip enhance obviously for two typical polymers. Also, the plastic energy dissipation behavior near cracks with different curvatures is discussed for both materials.

On the dynamic interaction between a penny-shaped crack and an expanding spherical inclusion in 3-D solid

Three-dimensional stress investigation on the interaction between a penny-shaped crack and an expanding spherical inclusion in an infinite 3-D medium is studied in this paper. The spherical transformation area (the inclusion) expands in a self-similar way. By using the superposition principle, the original physical problem is decomposed into two sub-problems. The transient elastic filed of the medium with an expanding spherical inclusion is derived with the dynamic Green's function. A time domain boundary integral equation method (BIEM) is then adopted to solve the current problem. The numerical scheme applied here uses a constant shape function for elements away from the crack front, and a square root crack-tip shape function for elements near the crack tip to describe the proper behavior of the unknown quantities near the crack front. A collocation method as well as a time stepping scheme is applied to solve the BIEs. Numerical examples for the Mode I stress intensity factor are presented to assess the dynamic effect of the expanding inclusion.