Crack-tip Model Research Articles

On the Cohesive Zone Model for a Finite Crack

The paper concentrates on the development of the crack tip model with the cohesive zone in an infinite plate with a finite crack of mode I. The estimation of the length of the cohesive zone and the crack tip opening displacement is based on the comparison of the local stress concentration according to Westergaard's theory with the cohesive stress. To calculate the cohesive stress, von Mises yield condition at the boundary of the cohesive zone is employed for plane strain and plane stress. The model of the stress distribution with the maximum stress within the cohesive zone is discussed. The calculation results of the crack tip opening displacement are compared with the Dugdale solution for the plane stress.

Crack modeling in FE analysis of circular tubular joints

By mapping circles in two-dimensional planes to three-dimensional intersection curves between tubular members, a complicated three-dimensional mesh generating procedure for tubular joints is changed to a procedure similar to a two-dimensional case. More detailed modeling of welds and cracks can be included to analyze the fracture behavior of cracked tubular joints. Different types of crack tip models are discussed and a four-tip crack model is introduced to model crack propagation. These crack models can be applied to both through-thickness cracks and surface cracks. A procedure for transforming crack elements around a plane curve into crack elements for a doubly curved semi-elliptical surface crack around an intersection is also introduced. High-quality meshes can be obtained.

Numerical evaluation of elastodynamic energy fracture parameters in 2-D heterogeneous media

The elastodynamic energy fracture parameters for a stationary crack in 2-D heterogeneous media are evaluated with a presented generalized Domain Integral Method (DIM). The method, incorporated with the finite element solutions, is demonstrated to be patch-independent in a generalized sense. In the context of dynamic response, the near-tip region is always involved in the calculation. The method is used for determination of the associated Energy Release Rate (ERR) for the cases when the crack tip is away from the material interface, with the formulation valid for both small and large elastic deformations. Numerical results for such problems appear to be very insensitive to the crack-tip finite element models. As to the instances when the tip terminates normally at the material interface, the ERR is not feasible for use as a fracture criterion. The generalized DIM is then applied for calculation of the alternative elastodynamic energy parameter J/Rλ0. The exponential order λ, with regard to the strength of stress singularity, is also properly evaluated in the calculation. No particular singular finite element is required throughout the study. © 1998 John Wiley & Sons, Ltd.

Crack dynamics and crack surfaces in elastic beam lattices

The dynamics of propagating cracks is analyzed in elastic two-dimensional lattices of beams. At early times, inertia effects and static stress enhancement combine so that the crack-tip velocity is found to behave as ${t}^{1/7}.$ At late times a minimal crack-tip model reproduces the numerical simulation results. With no disorder and for fast loading, a ``mirror-mist-mirror'' crack-surface pattern emerges. Introduction of disorder leads, however, to the formation of the ``mirror-mist-hackle''--type interface typical in many experimental situations.

Energy based approach for crack initiation and propagation in viscoelastic solid

The development of simple and computationally efficient analytical models for predicting the time-dependent initiation and propagation of cracks in linear viscoelastic materials is of paramount importance in practical structural design using polymeric materials. A crack tip model similar to that of Schapery is adapted (R. A. Schapery, A theory of crack initiation and growth in viscoelastic media I. Theoretical development. International Journal of Fracture, 1975, 11(1), 141–159), in which the failure zone is assumed to be of highly-damaged material preceding the physical crack tip. In the spirit of Wnuk's total energy release formulation of elasto-plastic solid (M. P. Wnuk, Subcritical growth of fracture (inelastic fatigue). International Journal of Fracture Mechanics, 1971, 7(4), 383–407), the theoretical expression for the total energy release rate of viscoelastic materials has been derived through the application of the correspondence principle. The derived theory has been applied to three specific case studies: (i) an infinite plate with central crack subjected to remote tension, (ii) an edge crack in a semi-infinite plate subjected to a pair of equal and opposite concentrated forces, and (iii) a pre-notched three-point bending beam. The significance of the influence of the plastic energy dissipation (due to viscoelasticity) on the crack initiation and propagation in these three cases has been examined and discussed in this paper.

Elastoplastic crack analysis for pressure-sensitive dilatant materials-Part II: Interface cracks

The problem of a plane strain crack lying along an interface between a rigid substrate and an elastic-plastic material has been studied. The elastic-plastic material exhibits pressure-sensitive yielding and plastic volumetric deformation. Two-term expansions of the asymptotic solutions for both closed frictionless and open crack-tip models have been obtained. The Mises effective stress in the interfacial crack-tip fields is a decreasing function of the pressure-sensitivity in both open and closed-crack tip models. The variable-separable solution exists for most pressure-sensitive materials and the limit values for existence of the variable-separable solution vary with the strain-hardening exponents. The governing equations become singular as the pressure-sensitivity limit is approached. Strength of the leading stress singularity is equal 1/(n+1) for both crack-tip models, regardless of the pressure-sensitivity. The second-order fields have been solved as an additional eigenvalue problem and the elasticity terms do not enter the second-order solutions as n≥2. The second exponents for the closed crack model are negative for the weak strain hardening, whereas the negative second-order eigenvalue in the open crack model slightly grows with the pressure-sensitivity. The second-order solutions are of significance in characterising the crack-tip fields. The leading-order solution contains the dominant mode I components for both open and closed crack-tip models when the materials do not have substantial strain hardening. The second-order solutions are generally mode-mixed and depend significantly on the pressure-sensitivity.

Effects of dissipation and driving on chaotic dynamics in an atomistic crack-tip model

An analysis of the dynamic behaviour associated with a simple atomistic model of a crack tip is presented. The model consists of a linear array of four atoms, with nearest neighbours interacting via a Morse-function potential. Energy exchange with the surroundings is simulated by driving the two outer atoms, that is, forcing them to oscillate sinusoidally with time, and by allowing the motion of the two inner atoms to be damped. The damping may be at least qualitatively related to dissipative mechanisms that may occur at the tip of a crack. Emphasis is placed on determining conditions under which the two inner atoms, which represent the crack tip, oscillate in a chaotic or aperiodic manner in response to the driving and damping. The amplitude of tile driving oscillation and the damping constant are treated as variable parameters in this regard. As expected, chaotic behaviour is to be found associated with larger driving amplitudes and smaller damping constants. Extreme sensitivity of chaotic motions to minute changes in initial conditions is explored. The temperature associated with the two inner atoms, calculated in terms of their time-averaged kinetic energy, can undergo a large increase when the transition from periodic to chaotic oscillations takes place. In addition, the non-linear dynamics is, under some conditions, found to be characterized by hyperchaos, that is, by the existence of two positive Lyapunov exponents. Qualitative implications of the results, relative to actual fracture processes, are discussed.

A dislocation shielding model for the fracture of semibrittle polycrystals

Using a dislocation mechanics-based crack-tip shielding model, a zeroth-order estimate of the grain size and yield strength dependence of fracture toughness is made for mild steel. This model, appropriate to cleavage fracture in the lower shelf regime, is shown to predict the fracture toughness determined over a temperature regime of 100 to 240 K in both quasi-static and dynamic tests and for two different grain sizes. Two grain size terms in the proposed model result. One is associated with grain boundary blockage effects on crack-tip shielding, while the other is proposed to affect the far-field stresses and, indirectly, the local crack-tip stress field. Differences between the present approach and the classic Cottrell-Petch model are in how the friction stress and grain size affect local stresses at the crack tip rather than at a carbide or a grain boundary.

Crack tip modelling for a geometrically non-linear plate bending problem

Crack tip modelling for a geometrically non-linear plate bending problem

Analysing a mixed-mode plane problem by using Jk integrals

The J 1 and J 2 integrals are used in conjunction with the superposition technique in fracture mechanics via finite-element stress analysis to obtain the stress intensity factors ( K I and K II ). Direct evaluation of the J 2 integral yields results that are very sensitive to the type of crack tip modelling employed. A superposition technique is used to overcome the difficulty that results from evaluating the J 2 integral at the crack faces. A simple and efficient solution procedure is developed involving only a known auxiliary solution for evaluating the J 1 and J 2 integrals. The finite-element solution converges to an accurate solution for contours remote from the crack tip. Numerical examples are presented to demonstrate the accuracy of the proposed approach.

Linear elastic crack tip modelling by the displacement discontinuity method

A special crack tip element is developed to model the feature of a stress singularity at a crack tip, based on an elastic solution for an arbitrary displacement discontinuity. By incorporating this crack tip element into the conventional displacement discontinity method, the propagation of a crack with an arbitrary configuration can be modelled using the Griffith-Irwin energy criterion in a linear elastic medium. The accuracy and consistency of the method is illustrated by various examples; the results are seen to be in excellent agreement with the exact analytical solutions and the known experimental evidence. The study shows that the displacement discontinuity method is efficient and has a potential for modelling the behaviour of a complex crack.

Crack tip modeling of hydrogen environement embrittlement: Application to fracture mechanics life prediction

An integrated fracture mechanics life prediction prodedure has been advanced over the past 20 years to mitigate hydrogen-environment-enhanced subcritical crack propagation in steels. Extensive date define monotonic load threshold stress intensities and corrosion fatigue growth kinetics for ferritic and martensitic steels of a wide variety of strengths and exposed to gaseous and aqueous environments. Broadly predictive crack tip models are evolving based on advances in elastic-plastic fracture mechanics, micromechanics and occluded crack chemistry. Hydrogen environment sensors, in sity crack propagation monitors and prototype testing enable evaluations and modifications of fracture mechanisc predictions. While the approach provides major advances towards reliable material usage in energy systems, uncertainties remain; specific issues are identified for future research.

DETERMINATIONS OF JIC FOR 2024‐T351 ALUMINIUM ALLOY

Abstract— The J‐integral is an elastic‐plastic fracture mechanics parameter which can be regarded as a measure of the intensity of the crack tip stress and strain fields, irrespective of the plastic zone size. The value of J at the onset of stable crack extension, JIC, has been suggested as a fracture criterion for both large‐and small‐scale yielding conditions. In this work the value of JIC for an extruded, medium‐strength aluminium alloy, 2024‐T351 bar, was determined using; (i) the Hutchinson‐Rice‐Rosengren crack tip model and experimentally‐determined crack tip strain profiles; and (ii) the ASTM standard multiple‐specimen technique. Knowing the critical load for initial crack extension from the crack tip strain profile method also enabled JIC to be computed using a finite element‐hybrid contour method and a modified linear elastic fracture mechanics approach. Agreement between the JIC values obtained by the various methods was good.

An improved method for computing the [formula omitted] integral

The J 2 integral, used in conjunction with the well-known J (or J 1 ) integral, can assist the analyst in the prediction of in-plane mixed-mode stress intensity factors via finite element stress analysis. However, direct evaluation of J 2 yields results which are very sensitive to the crack tip modeling employed, thus reducing the efficacy of the J 2 integral. A new technique is proposed to circumvent this problem. This new technique also permits one to easily calculate the non-singular stress component σ x0 which is known to be important in predicting crack kinking angles.

Calculation of the saddle-point configuration for an atomistic crack-tip model

Calculation of the saddle-point configuration for an atomistic crack-tip model

The effects of aluminum alloy microstructure on fatigue crack growth

Measurements of the fatigue crack tip opening displacement and strain for the aluminum alloys 7075 and 7091 have been used together with a crack tip model to infer the relevant microstructural parameters affecting fatigue crack growth rate. The two alloys studied are metallurgically quite different: alloy 7075 is an ingot metallurgy material with large pancake grains, while alloy 7091 is prepared by powder metallurgy techniques, resulting in small tubular-shaped grains. However, careful microstructural measurements showed that the dispersoid mean free path for the two alloys was nearly the same and of the same magnitude as the relevant microstructural parameter derived using the model. It is concluded that dispersoids in aluminum alloys play a larger role in fatigue crack growth rate than is commonly recognized. The effects of environment are also considered in this paper.

Correlation of microstructure and fracture toughness in two 4340 steels

A correlation is made of plane strain fracture toughness and microstructure in two steels corresponding to AISI 4340 composition. The steels were deoxidized with aluminum and titanium-aluminum additions, respectively. In the case of the aluminum killed steel, austenitizing at temperatures above 950 °C led to large austenite grain sizes, whereas in the titanium steel grain sizes were maintained below about 70 μm even after austenitizing at temperatures approaching 1200 °C. This allowed a comparison of variations in plane strain fracture toughness with austenitizing temperature between microstructures that underwent large increases in grain size and those that did not. The results are interpreted using a simple fracture model which indicated that particle spacing is of primary importance in controlling toughness. The overall observed phenomenology, however, is not explainable using simple models that essentially require that either critical stresses or critical strains be achieved over distances scaling with microstructure. This finding suggests that more detailed crack tip models than presently exist are required if the full effects of heat treatment are to be understood and explained.

Description of an atomistic model of environmentally assisted fracture in terms of catastrophe theory

A simple atomistic crack-tip model was developed by Hirth [1] and subsequently extended in detail by Markworth and Hirth [2] to describe the extension of a .crack by kink propagation, including effects that result from bond decohesion. It is demonstrated here that additional important insights pertaining to this model can be obtained in terms of the catastrophe-theory formalism discussed by Poston and Stewart [3] and others. The model for crack extension consisted of a linear chain of four atoms, with interactions occurring only between adjacent atoms and being described in terms of a Morse-function potential, v(s), of the form

3-D elastic-plastic fracture mechanics with ADINA

This paper gives an overview of the techniques used for the 3-D elastic-plastic fracture mechanics work at the General Electric Corporate Research and Development Center. The ADINA program is being used for the bulk of the numerical work, but it has been necessary to make certain modifications to the program. A description of the incorporation of the deformation theory of plasticity and of a new procedure for calculating the energy release rate is given in the paper together with a short discussion of the crack-tip modeling. The application of the techniques to a 3-D compact specimen is also presented.

A brief survey of the advances of fracture mechanics in china

A brief survey was made of the recent advances of macro-fracture mechanics in China up to December 1979. Topics dealt with included; (1) The stress field near the crack tip and fracture models; (2) The J- integral ; (3) The calculation of the stress intensity factor; (4) Fracture criteria for mixed mode cracks; and (5) Fracture crack propagation.