Crack Tip Radius Research Articles

Numerical modeling of the nucleation of facets ahead of a primary crack under mode I + III loading

A numerical study of crack front segmentation under mode I + III loading is proposed. Facets initiation ahead of a parent crack is predicted through a tridimensional application of the coupled criterion. Crack initiation shape, orientation and spacing are determined for any mode mixity ratio by coupling a stress and an energy criterion using matched asymptotic expansions. The stress and the energy conditions are computed through a 3D finite element modeling of a periodic network of facets ahead of the parent crack. The initiation shape, loading and spacing of facets depend on the blunted parent crack tip radius. A good estimate of facet orientations is obtained based on the direction of maximum tensile stress. The facet shapes, determined using the stress isocontours, are qualitatively similar to those observed experimentally. The order of magnitude of numerical predictions of facets spacing is very close to experimental measurements.

Effect of specimen notch quality on the essential work of fracture of ductile polymer films

The essential work of fracture approach has been employed to analyse the effect of notch sharpening on the fracture toughness of a semicrystalline multiphase ethylene-propylene block copolymer. Double edge notched tension specimens were sharpened using different techniques: femtolaser ablation, razor blade sliding at room and liquid nitrogen temperatures, saw cutting, plastically deformed saw cutting, and scalpel sliding. The notch sharpening techniques provide notches of different quality in relation to both the notch tip radius and the plastic deformation in front of the crack tip. The best quality notches were produced by the femtolaser ablation technique, which provides very sharp notches without plastic deformation ahead of the crack tip. The effects of the non-collinearity of the notches and tilted specimens on the testing machine grips were also analysed. The shape of the registered stress–displacement curves shows differences, but only in the range comprised between the displacements corresponding to the maximum stress and the onset of crack initiation. A larger crack tip radius and/or larger extent of plastic deformation in front of the notch root leads to larger values of the displacement at the onset of crack initiation, resulting in higher values for the specific essential work of fracture. Yet on the other hand, the values of the slope of the essential work of fracture plot remain unchanged. A lower value for the specific essential work of fracture was obtained for the specimens sharpened using the femtolaser ablation technique.

Influence of the notch‐sharpening technique on styrene–acrylonitrile fracture behavior

ABSTRACTThe Centre Català del Plàstic and Universidad Rey Juan Carlos laboratories joined forces to investigate the effect of the notch‐sharpening technique on the fracture parameters of styrene–acrylonitrile. Contact notch‐sharpening techniques, such as razor tapping, razor sliding, and razor broaching, and a noncontact procedure, femtolaser, were analyzed. The fracture values of the samples with notches sharpened via contact techniques were divided into two groups: one with pop‐in and the other with no pop‐in in the load–displacement records; this resulted in the lowest and highest fracture toughnesses, respectively. The fracture parameters of the specimens with notches sharpened via a femtolaser were between those of the samples with notches sharpened via contact procedures in which pop‐in occurred and those in which it did not. To explain these results, the crack front of the nontested specimens after sharpening was investigated in depth, we identified the type of damage and measured its size and the crack tip radii. The morphology of the crack front was related to the fractographic study. © 2016 Wiley Periodicals, Inc. J. Appl. Polym. Sci. 2016, 133, 43775.

Fatigue crack propagation in short-fiber reinforced plastics

The influence of fiber orientation on the crack propagation behavior was studied with single edgenotched specimens which were cut from an injection-molded plate of short-fiber reinforced plastics of polyphenylenesulphide (PPS) reinforced with 30wt% carbon fibers. Specimens were cut at five fiber angles relative to the molding direction, i.e. ??= 0° (MD), 22.5°, 45°, 67.5°, 90° (TD). Fracture mechanics parameters derived based on anisotropic elasticity were used as a crack driving force. Macroscopic crack propagation path was nearly perpendicular to the loading axis for the cases of MD and TD. For the other fiber angles, the crack path was inclined because the crack tended to propagate along inclined fibers. For mode I crack propagation in MD and TD, the resistance to crack propagation is improved by fiber reinforcement, when the rate is correlated to the range of stress intensity factor. The crack propagation rate, da/dN, was slowest for MD and fastest for TD. For each material, the crack propagation rate is higher for larger R ratio. The effect of R ratio on da/dN diminished in the relation between da/dN and the range of energy release rate, ?GI. Difference among MD, TD and matrix resin becomes small when da/dN correlated to a parameter corresponding the crack-tip radius, H?GI, where H is compliance parameter. Fatigue cracks propagated under mixed loading of mode I and II for the fiber angles other than 0° and 90°. The data of the crack propagation rate correlated to the range of total energy release rate, ?Gtotal, lie between the relations obtained for MD and TD. All data of crack propagation tend to merge a single relation when the rate is correlated to the range of total energy release rate divided by Young’s modulus.

GS0224-406 異方性破壊力学パラメータによる短織維強化CFRPにおける疲労き裂進展の評価

The influence of fiber orientation on the crack propagation behavior was studied with single edge notched specimen which were cut from an injection molded plate of thermoplastic polyphenylenesulphitde (PPS) reinforced with 30wt% carbon fibers. Specimens were cut at five angles relative to the molding direction, i.e. θ=0°(MD), 22.5°, 45°, 67.5°, 90°(TD). Fracture mechanics parameters derived based on anisotropic elasticity were used as a crack driving force. Macroscopic crack path was nearly perpendicular to the loading direction for the cases of MD and TD, while inclined for the other angles. For modeIcrack propagation in MD, TD and resin, the crack propagation rate is expressed as a power function of a parameter corresponding to the crack-tip radius, H_IΔG_I, where H_I is a compliance parameter. The crack propagation rate under mixed mode I and II was correlated to the range of the total energy release rate, ΔG_<total> divied by Young's modulus.

Effect of cooperative grain boundary sliding and migration on dislocation emitting from a semi-elliptical blunt crack tip in nanocrystalline solids

A theoretical model is established to investigate the interaction between the cooperative grain boundary (GB) sliding and migration and a semi-elliptical blunt crack in deformed nanocrystalline materials. By using the complex variable method, the effect of two disclination dipoles produced by the cooperative GB sliding and migration process on the emission of lattice dislocations from a semi-elliptical blunt crack tip is explored. Closed-form solutions for the stress field and the force acting on the dislocation are obtained in complex form, and the critical stress intensity factors for the first dislocation emission from a blunt crack under mode I and mode II loadings are calculated. Then, the influence of disclination strength, curvature radius of blunt crack tip, crack length, locations and geometry of disclination dipoles, and grain size on the critical stress intensity factors is presented detailedly. It is shown that the cooperative GB sliding and migration and the grain size have significant influence on the dislocation emission from a blunt crack tip.

Blunt Cracks and Two Parameter Fracture Criteria

There is a concern in the fracture testing community about the influence of crack sharpness on measured toughness values. The notion of sufficiently sharp is intrinsic in the standards but does not define how sharp is sharp enough. This requires a definition of a crack tip radius below which the toughness will be Gc. A proposal is made here to modify the stress at a distance criteria in line with cohesive zones such that G GC and a critical stress σC is achieved. This provides a critical radius, ρC, below which, G = Gc. A comparison with FEA cohesive zone results supports the idea and comparison with data on uPVC conforms well to the suggested scheme to determine ρC. Some comments on self-blunting are also included.

Effect of special rotational deformation on dislocation emission from a semielliptical blunt crack tip in nanocrystalline solids

Abstract

Effect of Vacancy Defects on the Young's Modulus and Fracture Strength of Graphene: A Molecular Dynamics Study

AbstractThe Young's modulus of graphene with various rectangular and circular vacancy defects is investigated by molecular dynamics simulation. By comparing with the results calculated from an effective spring model, it is demonstrated that the Young's modulus of graphene is largely correlated to the size of vacancy defects perpendicular to the stretching direction. And a linear reduction of Young's modulus with the increasing concentration of mono‐atomic‐vacancy defects (i.e., the slope of −0.03) is also observed. The fracture behavior of graphene, including the fracture strength, crack initiation and propagation are then studied by the molecular dynamics simulation, the effective spring model, and the quantized fracture mechanics. The blunting effect of vacancy edges is demonstrated, and the characterized crack tip radius of 4.44 Å is observed.

On Crack-Tip Stresses as Crack-Tip Radii Decrease

In classical elasticity, when cracks are modeled with stress-free elliptical holes, stress singularities occur as crack-tip root radii go to zero. This raises the question of when crack-tip stresses first start to depart from physical reality as radii go to zero. To address this question, here, cohesive stress action is taken into account as radii go to zero. To obtain sufficient resolution of the key crack-tip fields, two highly focused numerical approaches are employed: finite elements with successive submodeling concentrated on the crack-tip and numerical analysis of a companion integral equation with considerable discretization refinement at the crack-tip. Both numerical approaches are verified with convergence checks and test problems. Results show that for visible cracks, classical elasticity analysis leads to physically sensible stresses, provided that crack-tip radii are accounted for properly. For microcracks with smaller crack-tip radii, however, cohesive stress action also needs to be included if accurate crack-tip stresses are to be obtained. For cracks with yet smaller crack-tip radii, cracks close and stresses throughout the crack plane become uniform.

The role of notching damage on the fracture parameters of ethylene-propylene block copolymers

The influence of the notching procedure on the fracture toughness measured via Elastic-Plastic Fracture Mechanics has been analyzed on four different ethylene-propylene block copolymers with two distinct dimensions, paying special attention to the morphology of the area surrounding the crack tip front. Two sharpening techniques were evaluated: the traditional steel razor blade and the femtolaser ablation process. The fracture toughness of the razor blade sharpened samples was always higher than that of the femtolaser sharpened specimens. Also, the fracture toughness of the razor blade samples was dependent on the thickness of the samples, whereas the fracture toughness of the femtolaser sharpened specimens was not influenced by the dimensions of the test specimens. The microscopic analysis of non-tested samples showed that the crack tip radii were similar for both type of sharpened samples but the damage and its extension ahead of the crack tip was dependent on the notching technique, the copolymer type and the dimensions of the analyzed specimen. The femtolaser sharpened samples presented a very tiny heat affected zone ahead of the crack tip, the size of which was independent of the copolymer type and the dimensions of the test specimen. On the other hand, the steel razor blade sharpened samples showed an area surrounding the crack tip formed by plastic deformation, the length of which increased for the smaller size of sample and for higher ethylene content in the copolymer.

Shielding effect and emission condition of a screw dislocation near a blunt crack in elliptical inhomogeneity

The shielding effect and emission condition of a screw dislocation near a blunt crack in elastic elliptical inhomogeneity is dealt with. Utilizing the Muskhelishvili complex variable method, the explicit series form solutions of the complex potentials in the matrix and the inclusion regions are derived. The stress intensity factor and critical stress intensity factor for dislocation emission are also calculated. The influences of the orientation of the dislocation and morphology of the blunt crack as well as the material elastic dissimilarity upon the shielding effect and emission criterion are discussed in detail. As a result, numerical analysis and discussion show that the positive screw dislocation can reduce the stress intensity factor of the crack tip (shielding effect) only when it is located in the certain region. The shielding effect increases with the increase of the shear modulus of the matrix and the curvature radius of the blunt crack tip, but decreases with the increase of dislocation azimuth angle. The critical loads at infinity for dislocation emission increases with the increment of the emission angle and the curvature radius of the blunt crack tip, and the most probable angle for screw dislocation emission is zero. The present solutions contain previous results as the special cases.

Modelling of Environmentally Assisted Crack Growth in Ceramics

We describe slow crack growth in ceramics within a cohesive zone methodology. Stress corrosion being thermally activated, a rate and temperature dependent formulation is considered to mimic the chemical reaction-rupture mechanism underlying failure. The effect of humidity is incorporated through a dependence of the activation energy, that facilitates the fracture process with increasing humidity. As a cohesive zone provides an intrinsic length scale, size effects due to the initial crack tip radius on the onset of crack propagation are addressed, opening the route to study the grain size effect on the slow crack growth observed in ceramics polycrystals.

Behavior of an Extended Dislocation near an Elliptical Blunt Crack

The behavior of an extended dislocation near an elliptical blunt crack is investigated. The equilibrium separation between Shockley partials and the critical value of stacking fault energy for the formation of extended dislocations by dissociation reaction as well as the extended dislocation emission criterion are developed. The results show that the equilibrium separation increases as the extended dislocation tends to the blunt crack. If the stacking fault energy is comparable to the critical energy for dissociation in a perfect medium, complete dislocations can dissociate to form extended dislocations near the blunt crack. The critical stress intensity factor (SIF) for extended dislocation emission increases with the stacking fault energy and the curvature radius of the blunt crack tip. Moreover, the critical SIF for extended dislocation emission is far lower than the critical SIF for edge dislocation emission.

Shielding effect and emission criterion of a screw dislocation near an interfacial blunt crack

Shielding effect and emission criterion of a screw dislocation near an interfacial blunt crack are dealt with in this paper. Utilizing the conformal mapping technique, the closed-form solutions are derived for complex potentials and stress fields due to a screw dislocation located near the interfacial blunt crack. The stress intensity factor on the crack tips and the critical stress intensity factor for dislocation emission are also calculated. The influence of the orientation of the dislocation and the morphology of the blunt crack as well as the material elastic dissimilarity on the shielding effect and the emission criterion is discussed in detail. The results show that positive screw dislocations can reduce the stress intensity factor of the interfacial blunt crack tip (shielding effect). The shielding effect increases with the increase of the shear modulus of the lower half-plane, but it decreases with the increase of the dislocation azimuth angle. The critical loads at infinity for dislocation emission increases with the increase of emission angle and curvature radius of blunt crack tip, and the most probable angle for screw dislocation emission is zero. The present solutions contain previous results as special cases.

The prediction of crack growth rates from total endurances in high strain fatigue—thirty years on

McClintock1, 2 was one of the first to model continuous-cycling fatigue crack growth by assuming a succession of miniature low-cycle-fatigue (LCF) specimens at the crack tip. Elements ahead of the crack amass damage until the arrival of the tip itself. Such models had been summarized by Majumdar and Morrow,3 but the author was unaware of these papers at the time. The ideas were pursued further by Chakrabortty4 whose paper, again unknown to the author, was published in the same issue (1979, Vol. 2) of FEMS. In the original paper5 crack propagation is represented by successive regeneration at the crack tip, the process becoming progressively easier as the crack grows owing to an increase in strain concentration. These ‘initiation’ cycles were related to the ‘Coffin’ expression for crack initiation, thereby introducing two empirical constants k and α. The paper is of the class ‘ρ/N’ where ρ is the assumed size of a crack-tip process zone and N is the cycles required to traverse that zone. Expressions had been previously derived linking LCF with linear-elastic fracture-mechanics (LEFM) crack growth, using the parameter ΔJ.6 (It was later shown that this was identical to using an equivalent stress intensity parameter.7) It has been shown that the approach does not apply for crack depths < 180 μm.6 At elevated temperature the ΔJ approach was successful for describing crack growth in the range 0.2–1.2 mm for the cobalt-based alloy MAR-M509 at 600 °C.8 Other studies have in fact shown9 that crack growth rates are approximately constant below a depth of 200 μm. Even to this day short crack growth relations in LCF and their practical use are not as familiar as those in LEFM. It may justifiably be argued that for every paper published on LCF short crack growth, several hundred have appeared dealing with LEFM crack growth in terms of the ‘Paris’ law. One of the original referees' comments was that the paper5 should have been presented in terms of LEFM. The author nevertheless defended his approach because for small cracks it was thought useful to retain the crack depth explicitly. It will be shown that LCF crack growth data have a definite part to play in the assessment of components and structures. The paper assumes that the elastic stress concentration at the tip of a crack of depth a is of the form 2(a/r)1/2 where r is an effective crack tip radius. Because it was known that the crack opening displacement increases with increasing crack depth, so too does the effective radius. This was achieved via a power law, which introduced two empirical constants G and n. Exponential crack growth in 316 steel at 600 °C, see Eq. (7). Adapted from tabulated data in Ref. 13. Values of parameter B (circles) adapted from Fig. 1 compared with upper bound relation given by Eq. (6). It is appropriate to record that the original paper5 and this last reviewed paper13 were both published by permission of the former Central Electricity Generating Board.

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.

Tensile strength and fracture toughness of brittle materials

The fracture properties of brittle materials under tension have been explained by many authors; however, questions such as the dependence of the tensile strength on the crack tip radius of curvature and the scatter of fracture toughness are still not well explained from fundamental principles. This work aims to address this question by using a force-atomistic approach: we analyze the forces that act in the solid down to the smallest dimensions in an atomistic context, verifying the satisfaction of the static equilibrium condition given by Newton’s second law up to the beginning of the rupture. We take into account the forces due to the applied stress, which may be very large at crack tips, and the material cohesion forces, particularly at the point of largest local strain and stress concentration, where the local hyperelasticity of the material plays a governing role. By considering and connecting microstructure and atomicity, and using an experimentally proved maximum tensile-stress criterion for fracture, here we obtain an expression for the tensile strength of the brittle materials, where an effective local cohesive stress is defined. Thus, we explain in a unified framework from fundamental principles a set of established experimental results of brittle fracture of materials under tension, including the dependence of the tensile strength on the crack tip radius of curvature and some scatter in reported values of fracture toughness and cleavage surface energy. This work can be useful to make more realistic predictions of fracture properties of brittle materials taking into account microstructure and atomicity.

A scheme for finite element analysis of mode I and mixed mode stable crack growth and a case study with AISI 4340 steel

A new scheme for elastic–plastic finite element analysis has been proposed for the study of stable crack growth (SCG) from initiation to instability in both mode I and mixed modes (I and II). The scheme is based on node-release technique and helps to determine the variation of fracture load with crack extension without requiring much computer storage and time. The scheme permits predictions of load variation with load line displacement (LLD), maximum fracture load, crack tip current plastic zone and crack edge profile. In the analysis the condition for crack extension at every stage of the SCG is considered to be governed by CTOA/COD reaching a critical value. The scheme of analysis is different from the ones proposed by earlier investigators. The whole SCG is analysed in a few stages using the ANSYS software and a single discretization. Element arrangement in the discretization is decided from the very beginning; it has a capability of accommodating changes in boundary conditions arising out of crack extension in the later stages. Each stage is analysed afresh ignoring state of stress–strain reached at a material point at the end of the previous stage. Case studies on both mode I and mixed mode presented considering AISI 4340 steel, which is widely used in nuclear power industry, indicate that the SCG through it can be characterized in terms of a single COD or CTOA. Predictions for the initiation and maximum fracture loads in both the cases compare very closely with the experimental data reported. The results presented also include the value of critical COD/CTOA (0.035 mm/0.0875 rad) characterizing the SCG through the steel and show that the initiation load is not significantly affected by crack tip radius up to 0.05 mm.

The brittle fracture criterion based on the maximum tensile stress on the surface of blunt crack tip

The brittle fracture criterion is developed for a blunted crack. The curvature radius of the blunt crack tip is suggested as a characteristic length for brittle materials, and then the fracture toughness of the brittle materials can be determined from the cohesion strength and the characteristic length of the materials.