Showing papers on "Crack closure published in 1985"

Indentation fracture of WC-Co cermets

Abstract: Indentation fracture of a series of well-characterized WC-Co cermets was studied with a Vickers diamond pyramid indenter. The resulting crack length-indentation load data were analysed in terms of relations characteristic of radial (Palmqvist) and fully developed radial/median (half-penny) crack geometries. The radial crack model gave a better fit to the data on all the alloys studied. Crack shapes determined by repeated surface polishing confirmed the radial nature of the cracks. An indentation fracture mechanics analysis based on the assumption of a wedge-loaded crack is shown to be consistent with the observed linear relation between the radial crack length and the indentation load. The analysis also predicts a simple relation among the fracture toughness (K lc), the Palmqvist toughness (W) and the hardness (H) of the WC-Co alloys.

Compression-induced microcrack growth in brittle solids: Axial splitting and shear failure

Abstract: Micromechanisms of rock failure (axial splitting and shear failure) are examined in light of simple mathematical models motivated by microscopic observations. The elasticity boundary value problem associated with cracks growing from the tips of a model flaw is solved. It is shown that under axial compression, tension cracks nucleate at the tips of the preexisting model flaw, grow with increasing compression, and become parallel to the direction of the maximum far-field compression. When a lateral compression also exists, the crack growth is stable and stops at some finite crack length. With a small lateral tension, on the other hand, the crack growth becomes unstable after a certain crack length is attained. This is considered to be the fundamental mechanism of axial splitting observed in uniaxially compressed rock specimens. To model the mechanism of shear failure, a row of suitably oriented model flaws is considered and the elasticity boundary value problem associated with the out-of-plane crack growth from the tips of the flaws is solved. It is shown that for a certain overall orientation of the flaws the growth of the out-of-plane cracks may become unstable, leading to possible macroscopic faulting. On the basis of this model the variations of the “ultimate strength” and the orientation of the overall fault plane with confining pressure are estimated, and the results are compared with published experimental data. In addition, the results of a set of model experiments on plates of Columbia resin CR39 containing preexisting flaws are reported. These experiments are specifically designed in order to show the effect of confining pressure on the crack growth regime. The experiments seem to support qualitatively the analytical results.

Two Parameter Fracture Model for Concrete

Abstract: Attempts to apply linear elastic fracture mechanics (LEFM) to concrete have been made for several years. Several investigators have reported that when fracture toughness, Klc, is evaluated from notched specimens using conventional LEFM (measured peak load and initial notch length) a significant size effect is observed. This size effect has been attributed to nonlinear slow crack growth occurring prior to the peak load. A two parameter fracture model is proposed to include this nonlinear slow crack growth. Critical stress intensity factor, KIcS, is calculated at the tip of the effective crack. The critical effective crack extension is dictated by the elastic critical crack tip opening displacement, CTODc. Tests on notched beam specimens showed that the proposed fracture criteria to be size independent. The proposed model can be used to calculate the maximum load (for Mode I failure) of a structure of an arbitrary geometry. The validity of the model is demonstrated by an accurate simulation of the experimen...

Smeared Crack Approach and Fracture Localization in Concrete

Abstract: The possibilities of the smeared crack concept for simulating crack propagation and fracture in concrete is investigated. A smeared crack formulation is proposed which treats concrete constitutive behaviour separately from crack interface behaviour. In this study concrete is in most cases modelled as having linearly elastic characteristics. For the crack (or the band of micro-cracks) tensile-softening and shear transfer are allowed to take place but no interaction between these phenomena is taken into account. A crack closing option is included. The model has been evaluated by using the DIANA finite element package. Three types of example problems are considered. First, mode I fracture in unreinforced concrete is discussed. Emphasis is placed upon the effect of the basic concrete softening properties, such as the shape of the strainsoftening branch and the value of the fracture energy Gr. The way in which stable and mesh-insensitive solutions can be obtained is demonstrated. Next, mixed-mode fracture in unreinforced concrete is discussed. Here, the predicted post-peak response is shown to be unstable, which has to do with the existence of a considerable number of cracks of which only a limited number is active while the majority is arrested or closed. Again mesh-sensitivity of the results is examined, not only with respect to mesh refinements but also with respect to a change in the orientation of mesh lines. Very fine meshes seem to be most promising for reproducing curvilinear crack trajectories. Finally, mixed-mode fracture in two shear-critical reinforced beams is analysed, one of which fails in diagonal tension and one in shear-compression. Sudden extensive diagonal cracking is shown to be simulated quite correctly, although it should be added that corresponding genuine limit loads are not always attained. Further, comments are made on the crack shear representation adopted, involving a constant shear retention factor. The principal outcome of the project is that pronounced fracture localization can in principle be predicted by using a smeared crack strategy. However, problems are also encountered to which no definite answers can yet be given. Throughout the article possible future approaches are indicated which may help to solve them.

Non-orthogonal cracks in a smeared finite element model

Abstract: A new model for handling non‐orthogonal cracks within the smeared crack concept is described. It is based on a decomposition of the total strain increment into a concrete and into a crack strain increment. This decomposition also permits a proper combination of crack formation with other non‐linear phenomena such as plasticity and creep and with thermal effects and shrinkage. Relations are elaborated with some other crack models that are currently used for the analysis of concrete structures. The model is applied to some problems involving shear failures of reinforced concrete structures such as a moderately deep beam and an axisymmetric slab. The latter example is also of interest in that it confirms statements that ‘reduced integration’ is not reliable for problems involving crack formation and in that it supports the assertion that identifying numerical divergence with structural failure may be highly misleading.

Fatigue crack deflection and fracture surface contact: Micromechanical models

Abstract: The variation of cyclic crack propagation rates, under thecombined influence of crack kinking (deflection) and fracture surface contact (closure), is estimated from simple linear elastic analyses of tilted cracks. The predictions of the models are consistent with the experimental results of linear and kinked crack advance in high strength aluminum alloys testedin vacuo. Examples of crack deflection in various engineering alloy systems and some generalizations ofaverage deflection parameters based on microstructural and mechanical factors are discussed. The individual contributions to overall growth rates from deflection and closure processes are evaluated for different mechanical and metallurgical conditions. The significance, implications, and limitations of the models are outlined.

Subcritical crack growth, surface energy, fracture toughness, stick-slip and embrittlement

Abstract: It is proposed that the difficulties encountered with the meaning of subcritical crack growth arose from a misunderstanding of the Griffith equation. This equation is G=2γ for an equilibrium crack (stable or unstable) where γ is the intrinsic surface energy. When G>2γ the crack has a velocity v depending on the crack extension force G−2γ, even in a vacuum, and the following equation, well verified for adherence of elastomers, G−2γ=2γφT(v) where φT(v) is related to viscoelastic losses or internal friction at the crack tip, is generalized to other materials. At a critical speed vc, dφ/dv becomes negative; as a negative branch cannot be observed the velocity jumps to high values on a second positive branch, so that G=Gc is a criterion for crack speed discontinuity, not the Griffith criterion. The multiplicative factor 2γ on the right-hand side accounts for the shift of the v-K curves with environment. No stress corrosion is needed to explain subcritical crack growth. Subcritical crack growth in glasses and ceramics and velocity jump in brittle polymers are shown to agree with this proposal. This model can also explain stick-slip motion when a mean velocity is imposed in the negative branch. Occurrence of velocity jump or stick-slip depends on the geometry tested and the stiffness of the apparatus. A second kind of stick-slip associated with cavitation in liquid-filled cracks is discussed. When the surrounding medium can reach the crack tip and reduce the surface energy, even at the critical speed vc, the critical strain energy release rate Gc is reduced in the same proportion as γ, and a loading which would have given subcritical growth will give a catastrophic failure. Reduction of surface energy in the Rehbinder effect and in embrittlement by segregation is discussed. Finally, the evolution of ideas concerning the Irwin-Orowan formula and fracture toughness is examined.

Mechanics of crack curving and branching — a dynamic fracture analysis

Abstract: A comparative study on crack curving and branching criteria in dynamic fracture mechanics shows that the criteria based on “advanced cracking” concept correlated best with available experimental data. The crack branching criterion requires as a necessary condition, a critical dynamic stress intensity factor, K Ib, and a sufficient condition involving the crack curving criterion. The criteria are used to predict crack curving and crack branching in dynamic photoelastic experiments involving Homalite-100 and polycarbonate fracture specimens, as well as bursting steel and aluminum pipes.

Fracture indentation beneath flat and spherical punches

Abstract: The mechanics of crack initiation and propagation beneath an axisymmetric flat punch are investigated. The stress tensor given by Sneddon in 1946 is described. Numerical integration along stress trajectories gives the strain energy release rate as a function of both the crack length and its position relative to the indenter. Comparison with Hertzian fracture is made. The initiation of crack outside the circle of contact is shown to be due to the steepest gradient of stresses along the flaws near the circle of contact. The meaning of Auerbach's law is discussed. The Auerbach range is shown to correspond to the relatively flat maximum of the envelope of theG againstc/a curves for various starting radii. The influence of subcritical crack growth is also discussed. The model proposed in 1978 by Maugis and Barquins for kinetics of crack propagation between punches and viscoelastic solids is used. It is assumed that the static fatigue limit corresponds to the true Griffith criterion with intrinsic surface energy γ, and that the critical strain energy release rateG c corresponds to a criterion for crack speed instability and velocity jump, so that no stress corrosion is needed to explain subcritical crack growth for 2γ

High strain-rate crack growth in rate-dependent plastic solids

Abstract: At high crack velocities in metallic materials nearly all plastic strain accumulates at very high strain-rates, typically in the range 10 3 s −1 to 10 5 s −1 . At these rates, dislocation motion is limited by dynamic lattice effects and the plastic strain-rate increases approximately linearly with stress. The problem for a crack growing at high velocity is posed for steady-state, small scale yielding in elastic/rate-dependent plastic solids. A general expression is derived for the near-tip stress intensity factor in terms of the remote intensity factor, or equivalently for the near-tip energy release-rate in terms of the overall release-rate. An approximate calculation of the plastic strain-rates provides this relation in analytical form. Imposition of the condition that the near-tip energy release-rate be maintained at a critical value provides a propagation equation for the growing crack. A single, nondimensional combination of material constants emerges as the controlling parameter. Implications for dynamic crack propagation are discussed.

On macroscopic and microscopic analyses for crack initiation and crack growth toughness in ductile alloys

Abstract: Relationships between crack initiation and crack growth toughness are reviewed by examining the crack tip fields and microscopic (local) and macroscopic (continuum) fracture criteria for the onset and continued quasi-static extension of cracks in ductile materials. By comparison of the micromechanisms of crack initiationvia transgranular cleavage and crack initiation and subsequent growthvia microvoid coalescence, expressions are shown for the fracture toughness of materials in terms of microstructural parameters, including those deduced from fractographic measurements. In particular the distinction between the deformation fields directly ahead of stationary and nonstationary cracks are explored and used to explain why microstructure may have a more significant role in influencing the toughness of slowly growing, as opposed to initiating, cracks. Utilizing the exact asymptotic crack tip deformation fields recently presented by Rice and his co-workers for the nonstationary plane strain Mode I crack and evoking various microscopic failure criteria for such stable crack growth, a relationship between the tearing modulusTR and the nondimensionalized crack initiation fracture toughnessJIc is described and shown to yield a good fit to experimental toughness data for a wide range of steels.

On the measurement of dynamic fracture toughnesses — a review of recent work

Abstract: The influence of dynamic effects on test procedures for measuring the crack arrest toughness and the impact fracture toughness is analyzed. It is shown that these dynamic effects can be significant: For cracks at arrest the stress condition is still dynamic and not static although the crack velocity has become zero. Dynamic effects become small only for small crack velocities or small crack jumps or for specially designed specimens. It is shown that the stress intensity factor history for cracks under impact loading cannot be adequately derived from instrumented impact data via static evaluation procedures. Only for large times to failure, resulting for small impact velocities and/or ductile material behavior do static approaches represent acceptable approximations. Reliable crack arrest and impact fracture toughness data can only be obtained by evaluation procedures which take the dynamic effects into account, e.g. by utilizing the reduced dynamic effects crack arrest teat specimen or by applying the concept of impact response curves.

Closure and Repropagation of Healed Cracks in Silicate Glass

Abstract: Cracks in soda-lime-silica and vitreous silica glass close against a finite load at humidities between 0.01% and 100%. The force associated with crack closure (0.15 J/m/sup 2/) can be predicted by a model which involves hydrogen-bonded linkages of surfaceadsorbed water molecules. The fracture energy to reopen healed cracks in vitreous silica is also in the range of hydrogenbonding interactions. In the driest environments used, healed cracks in soda-lime-silica glass required 1.7 + or - 0.2 J/m/sup 2/ to reopen. This bonding energy can be attributed to the formation of either cationic bridges or siloxane bonds between fracture surfaces. Since crack healing was observed to be independent of the number of cycles, a cationic bridging model is favored to explain healing effects at room temperature.

Mechanism of Crack Growth in Lubricated Rolling/Sliding Contact

Abstract: In order to explain the mechanism of rolling-contact fatigue crack growth analytically, fracture mechanics are applied to a semicircular surface crack inclined at an angle to the elastic half-space loaded by Hertzian stresses. It is shown that the surface traction is the controlling factor for lubricant seepage into the crack and for shear mode crack growth rate. It is also clarified that the generation of pits results from tensile mode crack growth mainly due to the oil hydraulic pressure action.

Interpretation of the Griffith Instability as a Bifurcation of the Global Equilibrium

Abstract: The process zone at the crack tip of a concrete-like material can be simulated in two different alternative ways: (a) with a damage zone in front of the stress-free crack tip, or (b) with a cohesive force distribution behind a fictitious crack tip. Both these numerical models are able to simulate the slow crack growth and to reproduce the scale effects of fracture toughness testing. With large structural sizes the softening structural behaviour disappears and the global ductility drastically decreases. In the damage model, this is due to the priority of the crack instability over the traditional structural instability. On the other hand, in the cohesive model, this is revealed by a bifurcation of the global equilibrium, the stress-singularity being not included in such a model.

Mode II stress intensity factors for a crack parallel to the surface of an elastic half-space subjected to a moving point load

Abstract: The direction of propagation of rolling contact fatigue cracks is observed to depend upon the direction of motion of the load. In this paper approximate calculations are described of the variation of Mode II stress intensity factors at each tip of a subsurface crack, which lies parallel to the surface of an elastic half-space, due to a load moving over the surface. In particular the effect of frictional locking of the crack faces under the load is investigated. In consequence of frictional locking the range of SIF at the trailing tip ΔKT is found to be about 30% greater than that of the leading tip ΔKL, which is consistent with observations that subsurface cracks propagate predominantly in the direction of motion of the load over the surface. The effects on kt and klof crack length, crack face friction, traction forces at the surface and residual shear stresses are also investigated.

Analysis of Surface Crack Propagation in Lubricated Rolling Contact

Abstract: Growth behavior of surface cracks formed on lubricated rolling-sliding contact surfaces is studied by calculating three-dimensional mixed-mode stress intensity factors KI, KII, and KIII. It is shown from the viewpoint of the fatigue crack propagation that the hydraulic pressure effect pointed out by Way may be accepted as a possible mechanism of surface crack growth. Some of the experimental facts on pitting are also confirmed qualitatively.

Finite element analysis of void growth near a blunting crack tip

Abstract: Large deformation finite element analysis has been used to study the near crack tip growth of long cylindrical holes aligned parallel to the plane of a mode I plane strain crack. The near crack tip stress and deformation fields are analyzed. The results show that the holes are pulled towards the crack tip and change their shape to approximately elliptical with the major axis radial to the crack. They also grow faster directly ahead of the crack than at an angle to the crack plane. Several crack-hole coalescence criteria are discussed and estimates for the conditions for fracture initiation are given and compared with experimental results. The range of estimates now available from finite element calculations coincides quite well with the range of experimental data for materials containing inclusions which are only loosely bonded to the matrix.

A micro‐mechanics analysis for short fatigue crack growth

Abstract: Crack initiation and early growth of fatigue cracks in a fully annealed 0.4% carbon steel was investigated using plastic replicas and torsion loading. In a structure consisting of a 70/30 mixture of pearlite and ferrite the cracks are seen to develop and grow initially along slip bands in the ferrite phase. Energetic considerations lead to the formulation of a model which, while characterizing short crack growth rate, also considers those microstructural variables relevant to fatigue crack initiation and early crack growth. The driving force for crack growth is provided by the energy of the slip band; correspondingly crack growth per cycle is proportional to the strength of the slip band. In the short fatigue crack region, cracks grow initially at a fast rate but deceleration occurs quickly and, depending on the stress level, they either arrest or are temporarily halted at a critical length. This critical length is shown to coincide with the value of the threshold length for crack growth under LEFM conditions.

Microvoid growth and failure in the ligament between a hole and a blunt crack tip

Abstract: Large deformation finite element analysis has been used to study the near crack tip growth of a cylindrical void ahead of a blunting crack. Such voids are often nucleated at elongated inclusions in specimens cut from rolled steel plates in the long transverse direction. The presence of smaller-scale voids nucleated at carbides or precipitate particles was taken into account by using Gurson's equations to describe the constitutive behavior of the material. Using the modification to Gurson's model introduced by Tvergaard and Needleman [22] we have been able to study the formation and subsequent growth of the microcrack in the ligament between the hole and the crack. Estimates for the crack tip opening displacement for fracture initiation were obtained and compared with those of a fully dense elastic-plastic material.

Dynamics of an expanding fluid-filled crack

Abstract: The dike intrusion mechanism proposed recently by B. R. Julian and his colleagues for several large earthquakes at Long Valley caldera has stimulated new interest in the mechanics of fluid injection. This study is an attempt to resolve some of the questions raised by this interpretation by numerically simulating the dynamics of a propagating fluid-filled crack. The computations are based on the two-dimensional finite difference method applied by Aki and coworkers to a similar problem of a fluid-driven crack. We extend this earlier study by improving the boundary conditions applied in the plane of the crack and by analyzing a crack containing a viscous fluid that supports acoustic wave propagation. The problem has two time scales: the duration of the rupture, which is proportional to the distance the crack propagates, and the period of the acoustic resonance of the fluid, which is a function of the length of the crack and the acoustic velocity in the fluid. For a small extension of a long crack containing a fluid of low bulk modulus, these time scales are markedly different. The initial motion of the walls near the propagating crack tip is directed outward, so the radiated first motion is compressive everywhere. The increase of the crack tip volume, however, induces a pressure drop in the fluid which propagates over the length of the crack with the velocity of the acoustic wave, causing a partial collapse of the wall radiated as a long-period dilatation. The dilatation following the short compressional first arrival is well marked in the vicinity of the crack plane, and for a buried vertical crack it is a conspicuous feature of the near-field vertical ground motion close to the crack trace. These properties of the signal suggest that first motion studies of this frequency-dependent source may be delicate without broadband instruments. Inhomogeneous waves propagating at the liquid-solid interface produce high-frequency vibrations which are observed only in the immediate vicinity of the crack. The source duration depends strongly on the fluid viscosity and associated viscous damping at the crack wall; damping of the motion by the radiation of elastic waves is a comparatively small effect.

A normal stress criterion for crack extension direction in orthotropic composite materials

Abstract: A criterion for predicting the direction of crack extension in orthotropic composite materials is presented. The criterion is based upon the normal stress and the anisotropic tensile strength on arbitrary planes about the tip of a crack. Results are obtained, via finite element solutions, for: (1) isotropic mixed mode fracture, (2) cracks in unidirectional off-axis slotted composite tensile coupons and (3) cracks in cross plied laminates. Comparisons are made with other theories and experimental results.