Spacing Of Flaws Research Articles

Numerical Analysis of Fracture Behaviour on Marble Samples Containing Two Flaws

Uniaxial compression tests were conducted on marble specimens containing two flaws. There are coplanar flaws and noncoplanar flaws. The inclination angle and spacing of flaws were considered of the coplanar flaws model, and the step angle and spacing of flaws were considered of the noncoplanar flaws model. Strength failure and crack coalescence behaviour were analysed in the paper. The crack evolution process containing microcrack initiation, coalescence, and failure is focused on the rock bridge coalescence and the extent of the pre‐existing flaws. There are four forms of rock bridge coalescence: tensile crack coalescence, shear crack coalescence, mixed tensile and shear crack coalescence, and no coalescence. Also, there are four forms of the rock failure mode: tensile failure, shear failure, mixed tensile and shear failure, and split fracture. The outer end of the critical stress values were used to compare with the crack initiation strengths, and the crack initiation strengths were slightly larger than the critical stress. In addition, energy dissipation laws were analysed during the model fracturing process. The crack evolution mechanisms around the pre‐existing flaw in the model were revealed by the distribution of microcrack and energy dissipation.

Experimental study and numerical simulation of propagation and coalescence processes of pre-existing flaws in a transparent rock-like material

Flaws in the rock play an important role in the failure of rock engineering. In this article, some rock-like specimens prepared by transparent resin material were used to investigate the propagation and coalescence processes of pre-existing closed three-dimensional flaws, and a series of uniaxial compressive tests were carried out to study the effects of flaw dip, flaw area, flaw friction coefficient, and composite flaw spacing on mechanical properties and flaw propagation and coalescence processes. Based on the particle flow method, the experimental results were verified by numerical simulation. The results show that there is a good agreement on flaw propagation rule revealed by the experiments and numerical simulations. In the case of the specimens with single-flaw, with the increase of the inclination angle, the peak stress of the specimen first decreases and then increases, when the inclination angle is 45°, the peak stress is the smallest. Meanwhile, the peak stress decreases with the increase of flaw area but increases with the increase of flaw friction coefficient. The spacing of the composite flaw has a significant influence on the strength, and the impact on the elastic modulus is not obvious. The results can provide a reference for the mechanism of flaw propagation and coalescence.

Crack Propagation and Coalescence of Step-Path Failure in Rocks

To provide insight into the understanding of step-path failure in rocks, gypsum specimens containing various configurations of preexisting flaws are used to investigate the crack behaviors of step-path failure in rock slopes under compression in terms of the inclination angle and number of flaws. The results show that step-path failure is usually caused by wing cracks (or tensile cracks) when the preexisting flaws are isolated or when two preexisting flaws are adjacent. Additionally, with an increase in the number of flaws, step-path failure is more likely to be caused by mixed wing-secondary crack formation (or tensile–shear crack formation), indicating that the mechanism of step-path failure is associated with the characteristics of the flaw (including the number of flaws, flaw inclination angle, flaw spacing, etc.). In the process of step-path cracking and failure, wing cracks can initiate at or near the middle of a preexisting flaw when the preexisting flaw has a small inclination angle (e.g., 0° or 15°), and secondary cracks usually propagate in three directions: (1) in the horizontal direction of the specimen; (2) coplanar or quasi-coplanar to the preexisting flaw; (3) in the direction perpendicular to that of wing crack propagation. Additionally, the closer the inclination angle is to 90°, the harder the secondary crack initiates. In addition, four types of coalescence cracks are identified from the specimens containing two preexisting flaws. The peak load of the specimen is influenced by the inclination angle; the closer the inclination angle is to 90°, the greater the peak load of the specimen. Furthermore, the equation describing the wing crack path of an isolated flaw, two types of spalling formations and the characteristics of the wing and secondary crack surfaces are determined and discussed.

Effect of collinear flaws on flexural strength and fracture behavior of ZrB2-SiC ceramic

Abstract As a typical kind of multiple flaws, collinear flaws are particularly detrimental to the mechanical properties of ceramics. Here, two identical collinear micron-sized flaws with controllable length and spacing were successfully fabricated in ZrB2-20 vol% SiC (ZS) ceramic using femtosecond laser, and the effect of flaw length and spacing on flexural strength as well as fracture behavior (i.e., load-displacement curve and fractography) of ZS ceramic were investigated. The flexural strength almost remained constant when the flaw spacing was less than the critical value, which strongly depended on the flaw length, then increased gradually with increasing flaw spacing and reached a plateau. If the ratio between flaw spacing and flaw length was small enough, flaws would tend to coalescence first before fracture, owing to the strong interaction between flaws. If the ratio was too large, the center of the mirror area in fracture surface would be offset.

Isogeometric Implementation of High-Order Microplane Model for the Simulation of High-Order Elasticity, Softening, and Localization

In this paper, a recently developed higher-order microplane (HOM) model for softening and localization is implemented within a isogeometric finite-element framework. The HOM model was derived directly from a three-dimensional discrete particle model, and it was shown to be associated with a high-order continuum characterized by independent rotation and displacement fields. Furthermore, the HOM model possesses two characteristic lengths: the first associated with the spacing of flaws in the material internal structure and related to the gradient character of the continuum; the second associated with the size of these flaws and related to the micropolar character of the continuum. The displacement-based finite element implementation of this type of continua requires C1 continuity both within the elements and at the element boundaries. This motivated the implementation of the concept of isogeometric analysis which ensures a higher degree of smoothness and continuity. Nonuniform rational B-splines (NURBS) based isogeometric elements are implemented in a 3D setting, with both displacement and rotational degrees-of-freedom at each control point. The performed numerical analyses demonstrate the effectiveness of the proposed HOM model implementation to ensure optimal convergence in both elastic and softening regime. Furthermore, the proposed approach allows the natural formulation of a localization limiter able to prevent strain localization and spurious mesh sensitivity known to be pathological issues for typical local strain-softening constitutive equations.

Dynamic fragmentation of brittle materials: analytical mechanics-based models

Two analytical mechanics-based models of dynamic fragmentation in brittle materials are proposed and solved to predict fragment size and time to fragmentation onset in terms of fundamental material properties and the applied strain rate. Previous widely adopted analytical models of dynamic fragmentation are based on relatively simple energy balance arguments, and assume that the fragmentation event occurs instantaneously. The present models account for the actual time-varying dynamic deformation that occurs prior to fragmentation onset. One of the models treats the fragmenting material as initially flaw-free, and determines the minimum fragment size predicted by a dynamic instability analysis. The second model accounts for initial flaw spacing (which may correlate physically with, for example, grain size), and a dynamic instability analysis is employed to determine which flaws become critical. The fragment size predictions of the present models and two previous energy-based models are found to agree at extremely high strain rates (≈5×10 7/s for dense alumina), but the present, more realistic analysis indicates that the regime of validity of the energy-based models is rather restricted. The predictions of the present models are also shown to agree with those of a recent numerical finite element simulation of dynamic fragmentation which applies to a lower strain rate regime. Comparisons of the two new models show that if a material contains initial flaws whose spacing is smaller than the predicted fragment size of an equivalent “unflawed” material, the fragment size of the preflawed material will be smaller in general, but usually not as small as the initial flaw spacing. The analysis also permits determination of the evolution of the strain rate distribution in a prospective fragment before and after fragmentation initiation; results are presented for some example cases. Finally, closed-form analytical results are derived for minimum fragment size and time to fragmentation for strain rates in the quasi-static regime; these show the fragment size to be independent of strain rate in this regime, and the time to fragmentation initiation to be inversely proportional to the strain rate.