Collinear Microcrack Research Articles

Multiple snap-back instabilities in progressive microcracking coalescence

This work describes an application of the Crack Length Control Scheme to analyze the damage evolution in solids containing a distribution of collinear microcracks. By means of a Dual Boundary Element Method numerical procedure, a model of crack growth is developed according to Linear Elastic Fracture Mechanics. A controlled crack propagation is obtained increasing the macrocrack length in the loading process. Some illustrative problems are shown, related to finite plates in plane strain conditions with one row of evenly spaced collinear cracks. The snap-back branches of the load-displacement curve are numerically plotted, and the interaction effects of the microcracks on damage evolution are analyzed.

Oil-Gas Transformation Induced Subcritical Crack Propagation and Coalescence in Petroleum Source Rocks

The present work describes a multi-physics model to investigate subcritical propagation of initially oil-filled, sub-horizontal collinear microcracks driven by the excess pressure induced by the conversion of oil to gas in a petroleum source rock under continuous burial. The crack propagation distance, propagation duration, crack coalescence and excess pressure in the crack are determined using a finite difference scheme that couples linear elastic fracture mechanics, oil-gas transformation kinetics and an equation of state for the gas. The numerical results for a shale source rock with typical properties show that when the crack spacing parameter b/a0 is greater than 3, where a0 is the half crack length and b the half distance between the crack centers, the cracks do not coalesce, and the duration of gas-driven crack propagation is governed by the transformation kinetics because the oil-gas conversion rate is much slower than the subcritical crack propagation rate. The collinear cracks coalesce for smaller crack spacing and the crack propagation duration may reduce significantly due to crack interactions. The multi-physics model presented in this work together with our previous model for crack propagation during the conversion of solid kerogen to oil indicates that self-propagating microcracks resulting from the buildup of excess fluid pressure during hydrocarbon generation may serve as effective pathways for primary migration of hydrocarbons.

On collinear microcrack–inclusion arrays interaction and related problems

Investigated is a crack problem for an array of collinear microcracks in composite matrix. Inclusions are situated in between the neighbouring microcracks tips and exhibit different elastic properties than matrix. The problem is solved using the technique of distributed dislocations. A developed approximate fundamental solution for a single dislocation lying in a general point between inclusions is employed in the distribution of continuously distributed dislocation to cracks modelling. Stress intensity factor is calculated for various cracks/inclusions geometries and elastic moduli mismatches. Stability and/or instability of the straight microcrack paths is investigated for slowly growing microcracks with inclusions located in between the neighbouring microcracks tips. Applications to periodic microcrack tunnelling and microcracks weakening ahead of the main crack are discussed.

On the Interaction of an Array of Collinear Microcracks with a Periodic Array of Inclusions

On the Interaction of an Array of Collinear Microcracks with a Periodic Array of Inclusions

Critical linkages of coalescing microcracks under stress loading

The fracture process of brittle materials with randomly orientated microcracks critically depends on strong interactions among microcracks and the coalescence path that leads to a fatal crack. In this paper, a model based on the coalescence process for planar orientated microcracks is presented. An energy ratio is defined as the competition between the potential energy release and the new crack surface energy in each coalescence step, which is a token of the excessive driving force for microcrack propagation. A critical linkage dictates the coalescence of microcracks under stress loading. Probabilities of microcrack coalescence dominated by the first linkage and subsequent linkages are analysed for collinear and wavy microcrack arrays in detail.

Expected coalescing length of displacement loading collinear microcracks

Under displacement loading, brittle material softens due to the coalescence of statistically distributed microcracks. Microcracks propagate, coalesce, and eventually reach a stable configuration. The situation is simulated in the present work by a collinear microcrack configuration with the attention focused on the expected crack length. The results indicate that the expected crack length increases by higher microcrack density, less microcrack randomness, and a larger specimen size (scale effect).

Effective toughness for bridged crack interacting with an arbitrary oriented and located microcrack

The fracture problem for a brittle matrix reinforced by ductile particles is considered. As a crack propagates through the brittle matrix, it circumvents ductile particles which are left to form isolated bridges capable of supporting tractions across the crack faces and thus improve the fracture toughness of the matrix. The stress induced microcracking, which can provide another important toughening mechanism, is assumed to also take place. More specifically, a single microcrack arbitrary oriented and located ahead of the main crack tip is considered and the resulting combined toughening effect of crack bridging and crack–microcrack interaction is investigated. To make the problem mathematically tractable the restraining effect of bridging discrete forces is approximated by a continuum with an effective yield stress acting over a specified multiligament zone behind the crack tip. This zone is further simulated by an unknown continuous distribution of edge dislocations. The present work then proposes a self-consistent scheme, which relies on using a point-source representation for the microcrack and a simultaneous solution of integral equation for the unknown dislocation distribution. Both, the stress intensity factor (SIF) and crack opening displacement (COD) are derived for general orientation and position of microcrack and an effective fracture toughness of composite is assessed. This approximative solution is further tested using the exact solution for a collinear microcrack.

Remarks on Macrocrack - Microcrack Interaction and Related Problems

An analytical solution representing the interaction of a macrocrack with a collinear microcrack is re-examined. The purpose of the analysis is to separate the singular term and to represent the remaining part of the solution as a bounded function in the form of a uniformly convergent power series. Some aspects of the solution in application to fracture development in composites are discussed.

Statistical strength of brittle materials with strongly interacted collinear microcracks

The coalescing process from microcracks to a fatal macroscopic crack is dominated by the strong interaction among neighbouring microcracks. The distribution of microcracks modifies the strength and toughness of a brittle material. The present paper focuses on the case of strongly interacting collinear microcracks, and quantifies the influence by the statistical distributions of crack lengths and ligament sizes. The strength of a brittle solid decreases as the standard deviation of those distributions increases. Furthermore, we predict the scale dependency of brittle materials: a specimen of large size would have lower strength than a small specimen with the same microcrack density. The analysis indicates that the statistical strength of a brittle material with strongly interacting collinear microcracks can be correlated by a three-parameter Weibull distribution.

Macrocrack extension by connecting statistically distributed microcracks

The present paper explores the extension of a macrocrack by connecting statistically distributed microcracks. Two issues are discussed: (1) how long a semi-infinite crack can extend by connecting collinear microcracks of equal length but distributed ligament sizes; (2) how far the crack tip can shift vertically from the original crack extension line by connecting randomly positioned and oriented microcracks. Statistical analysis is employed to calculate the expected crack extension length and the vertical shift of the crack tip. The implication of the present study for the problem of a macrocrack linking to a parallel fault is addressed.

Interaction between microcracks and a main crack in a semi-infinite medium

A very efficient numerical scheme for solving fracture problems involving two-dimensional elastic interaction between multiple microcracks and a main crack in a semi-infinite medium is proposed. The analysis is based on a singular integral equation method in which the microcracks and main crack are represented by distributions of edge dislocations. It is seen that this interaction could produce either an enhancement or a shielding effect on the stress intensity factors depending on the positions and orientations of the microcracks relative to the main crack in a semi-infinite medium. Typical examples are presented for one parallel microcrack, two equal microcracks and a semi-infinite array of periodically distributed collinear microcracks subjected to a remote mode I loading. For one collinear microcrack, the present solutions are compared with the exact solutions given in terms of elliptic integral; very good agreement is obtained.

Analysis of crack-microcrack interactions and doubly kinked cracks using multiple singular points elements

The problems of crack-microcrack interactions and doubly kinked cracks have been analysed by the finite element method. In the first case the main crack tip SIF has been evaluated for different length of a collinear microcrack, which is located at a fixed distance. Through another case study the influence of a pair of stacked parallel microcracks on the SIF of a main crack has been studied by varying the spacing of the two microcracks. The third example deals with a doubly kinked crack. The SIF at the crack tip has been determined for various angles of the second kink. All the three examples have been studied employing the multiple point singularity elements and their degenerate forms. The finite element computations have been compared, whenever possible, with analytical solutions available in the literature. The accuracy of the finite element computations are good. This has been achieved using a relatively coarse discretisation.

General solution to the problem of microcracks near the tip of a main crack

A general solution is obtained to the two-dimensional problem of the interaction between a main crack and multiple microcracks. Analysis is based on the method of pseudo-tractions, which is a general method for interaction problems. The stress intensity factors at the tips of both the main crack and microcracks are obtained in asymptotic forms and approximate closed-form solutions are also derived. Typical examples are presented for one collinear microcrack, one arbitrarily located microcrack and two arbitrarily located microcracks near the tip of the main crack. For one collinear microcrack the present solution is shown to coincide with the Taylor expansion of the exact solution, and inconsistencies in several previous solutions are compared. For arbitrarily located microcracks, the effects of the main crack—microcrack interaction and the microcrack—microcrack interaction are investigated. Application of the present model to the fracture process zone problem is discussed.

Microcrack interaction with a main crack

It is noted that calculations of the interaction between a main crack and two-dimensional microcracks surrounding the main-crack tip can be considerably simplified by using a point-source representation for the microcracks and a self-consistent scheme to determine the strength of these point sources. The procedure is illustrated by a detailed analysis for two basic configurations: (i) a single microcrack of arbitrary orientation near a main crack which is subjected to combined mode I and mode II loading; (ii) two microcracks symmetrically disposed about a main crack which is subjected to purely mode I loading. By comparing the result for configuration (i) with the exact result which is available for the special case of a collinear microcrack, it is found that the point-source representation for that case is accurate to within 5 percent over the range 0 <s/r1 < 2/3, where 2s is the length of the microcrack and r1 the distance from the main-crack tip to the mid-point of the microcrack. Over this range of s/r1, the neutral-shielding angle for configuration (ii), using the point-source representation, is found to vary from 70 to 69.4 deg, when the microcracks are parallel to the main crack.

Effective Fracture Toughness of Microcracked Materials

Explicit analytical formulas are derived for the stress intensity factors at the tips of a main crack and of a microcrack for the two‐dimensional case of a collinear microcrack. This configuration is used to derive an estimate of the toughness degradation due to microcracks linking up with an advancing main crack. The implications of this estimate for theoretical predictions of the toughening due to stress‐induced micro‐cracking are discussed.