Wing Crack Growth Research Articles

A complete three-dimensional continuum model of wing-crack growth in granular brittle solids

Failure of brittle materials containing embedded three dimensional pre-cracks and subjected to uniaxial compressive and tensile loading is considered here. The sliding crack (wing-crack) model of Ashby and Sammis (1990) is extended and further developed to formulate a 3D anisotropic continuum damage model.First, a frictional sliding condition of pre-cracks is formulated in three dimensions and a crack interaction function is proposed. To introduce inelastic strains due to cracking, crack opening displacements are derived from Castigliano's second theorem. Finally, a strain–stress relation is obtained from the Gibbs energy density equation.The model was implemented in Abaqus/Explicit finite element software. Material inhomogeneity was considered assuming that the pre-cracks are lognormally distributed between integration points.While testing the proposed model against experimental results of granular ice, the numerical simulations were in good agreement both under uniaxial compression and tension as a function of grain size and temperature-dependent kinetic friction. The model was able to predict qualitatively and quantitatively the brittle failure modes and strength both under compression and under tension. Due to the modelled inhomogeneity, the scatter in simulated strengths corresponded to that of the test results. Besides non-simultaneous and non-uniform damaging, the model revealed important phenomena observed during the experiments; e.g. under compression the sliding of the pre-cracks resembled “stick-slip” motion, and secondary cracks were observed to grow in a jerky manner. The effect of specimen end conditions on both the failure stress and failure mode was addressed in the simulations.

Crack initiation in asphalt mixtures under external compressive loads

Crack initiation was studied for asphalt mixtures under external compressive loads. High tensile localized stresses near the edges of compressed air voids lead to the growth of wing cracks in the direction of the external loads. A quantitative crack initiation criterion was derived using pseudostrain energy balance principle. Bond energy is determined and it increases with aging and loading rate while decreases with temperature. Cohesive and adhesive cracking occur simultaneously and a method was proposed to determine the individual percentage. The crack initiation criterion is simplified and validated through comparing the predicted and measured compressive strength of the asphalt mixtures.

Application of PDS-FEM for Simulating 3D Wing Crack Growth

3D wing crack growth is not a well understood phenomenon, although it is one of the key mechanisms of the failure of brittle materials under compression. Using PDS-FEM, we simulated the growth of 3D wing cracks emerging from pre-existing cracks in blocks of brittle linear elastic solids, under compression. The complex 3D wing crack profiles are reproduced with PDS-FEM, which uses non-overlapping shape functions of conjugate geometries to approximate functions and their derivatives. PDS-FEM provides numerically efficient failure treatment for modeling 3D cracks, making use of the numerous discontinuities in the approximated displacement field. Large scale models with several million elements are used to reproduce the experimentally observed details of wing crack profiles. The bending of crack surfaces at the tip of mode-I regions, extension of wing cracks and the growth of tensile openings or petal cracks at mode-III regions are reproduced, demonstrating the applicability of PDS-FEM for studying 3D wing crack growth phenomena.

The Wing Crack Growth Processes of Rock Induced by Hydraulic Pressure

The pre-existing fractures in rock can close, open and growth as it subjected to mechanical or environment loading, which can in turn change the structure of the rock and alter its fluid flow properties. In order to study the crack growth processes of pre-existing fracture in rock under the condition of hydraulic and mechanical coupling, a numerical tool, named F-RFPA2D which takes into account the growth of existing fractures and the formation of new fractures, is used for this purpose. By considering the effect of hydraulic pressure filling into the wing crack, the behavior of fluid flow, damage evolution and their coupling action in the pre-existing and the newly formed fractures are studied in detail. The modeling results suggest that the hydraulic pressure in the crack enhanced the tensile stresses at the crack tips, resulting in crack growth path is different from that without hydraulic pressure loading. The wing crack growth mechanism under the coupling of hydraulic and mechanical is discussed, which provides a good reference for studying on the hydraulic fracturing in rock masses.

Research on the process of micro-crack damage evolution and coalescence in brittle materials

Damage and failure of quasi-brittle materials are caused by evolution and coalescence of micro-cracks. To solve the problem of elliptical micro-crack growth at the elastic deformation stage, a method of complex potential functions is proposed and the effect of the initial orientation on micro-crack growth and deflection is discussed. The critical stress condition for the initial damage is derived according to the criterion of micro-crack growth. Based on energy conservation during wing-crack propagation, a damage constitutive model is developed with the strain criterion created in the condition of micro-crack coalescence. The stress–strain curves of quasi-brittle materials in uniaxial compression obtained based on this model are examined with the experimental results. In conclusion, (1) wing crack growth, propagation, and coalescence at the tips of micro-cracks eventually lead to the formation of an anisotropic effective compliance tensor in the damaged material; (2) a large number of micro-crack coalescence is a highly nonlinear phenomenon resulting in failure of materials; and (3) the effective elastic modulus of damaged material decreases with the wing crack propagation length increasing.

Evolution Procedure of Multiple Rock Cracks under Seepage Pressure

In practical geotechnical engineering, most of rock masses with multiple cracks exist in water environment. Under such circumstance, these adjacent cracks could interact with each other. Moreover, the seepage pressure, produced by the high water pressure, can change cracks’ status and have an impact on the stress state of fragile rocks. According to the theory of fracture mechanics, this paper discusses the law of crack initiation and the evolution law of stress intensity factor at the tip of a wing crack caused by compression-shear stress and seepage pressure. Subsequently, considering the interaction of the wing cracks and the additional stress caused by rock bridge damage, this paper proposes the intensity factor evolution equation under the combined action of compression-shear stress and seepage pressure. In addition, this paper analyzes the propagation of cracks under different seepage pressure which reveals that the existence of seepage pressure facilitates the wing crack’s growth. The result indicates that the high seepage pressure converts wing crack growth from stable form to unstable form. Meanwhile, based on the criterion and mechanism for crack initiation and propagation, this paper puts forward the mechanical model for different fracture transfixion failure modes of the crag bridge under the combined action of seepage pressure and compression-shear stress. At the last part, this paper, through investigating the flexibility tensor of the rock mass’s initial damage and its damage evolution in terms of jointed rock mass's damage mechanics, deduces the damage evolution equation for the rock mass with multiple cracks under the combined action of compression-shear stress and seepage pressure. The achievement of this investigation provides a reliable theoretical principle for quantitative research of the fractured rock mass failure under seepage pressure.

Melange: A viscoelastic lattice‐particle model applicable to the lithosphere

This article introduces the software Melange, a 3D lattice‐particle hybrid model. The software was specifically designed in order to simulate ductile visco‐elasto‐plastic deformation and can be used to study tectonic processes in the lithosphere from the micro to the macro scale. Melange is under an open source license. The code takes both relevant yield mechanisms for the deformation of lithospheric material into account: dynamic brittle failure and ductile creep, where ductile creep is modeled as viscoelasticity. The software considers effects of the local geology, of the inherent disorder of geomaterials, of rheological layering of the lithosphere and applies repulsion when the material fractures. Driving forces are the externally applied strain and the gravitational load. Melange applies an elastically isotropic regular 3D lattice with HCP geometry and next‐nearest neighbor interactions. Young's modulus, viscosity, material density and system size can be freely chosen. Poisson's ratio is restricted to values <0.25. The most important innovation of the software is a physically consistent scheme to model viscoelasticity in a lattice‐particle model. The scheme couples the local lattice‐geometry to the time‐dependent volume‐conservative viscoelastic deformation of particles. The procedure achieves the typical viscoelastic stress‐strain relationship. The article incorporates a number of benchmark simulations, where the model output is being tested and evaluated. The results obtained with Melange show strong similarities with the benchmark values, e.g., stress fields in crack vicinity. Geologically relevant examples include structures associated with the brittle‐ductile transition, growth of wing cracks and brittle graben formation.

Application of the expanded distinct element method for the study of crack growth in rock-like materials under uniaxial compression

The expanded distinct element method (EDEM) was used to investigate the crack growth in rock-like materials under uniaxial compression. The tensile-shear failure criterion and the Griffith failure criterion were implanted into the EDEM to determine the initiation and propagation of pre-existing cracks, respectively. Uniaxial compression experiments were also performed with the artificial rock-like samples to verify the validity of the EDEM. Simulation results indicated that the EDEM model with the tensile-shear failure criterion has strong capabilities for modeling the growth of pre-existing cracks, and model results have strong agreement with the failure and mechanical properties of experimental samples. The EDEM model with the Griffith failure criterion can only simulate the splitting failure of samples due to tensile stresses and is incapable of providing a comprehensive interpretation for the overall failure of rock masses. Research results demonstrated that sample failure primarily resulted from the growth of single cracks (in the form of tensile wing cracks and shear secondary cracks) and the coalescence of two cracks due to the growth of wing cracks in the rock bridge zone. Additionally, the inclination angle of the pre-existing crack clearly influences the final failure pattern of the samples.

Interaction and coalescence of nanovoids and dynamic fracture in silica glass: multimillion-to-billion atom molecular dynamics simulations

In this review, we present our recent results for atomistic mechanisms of damage nucleation and growth and dynamic fracture in silica glass. These results have been obtained with multimillion-to-billion atom, parallel, molecular dynamics simulations of (1) the interaction and coalescence of nanovoids in amorphous silica subjected to dilatational strain and (2) the nucleation, growth and healing of wing cracks and damage nanocavities in silica glass under impact loading. We also give an overview of our current efforts to perform dynamic fracture simulations over microsecond time scales and multiscale simulations of stress corrosion cracking in silica glass.

Transition in brittle failure mode in ice under low confinement

Compressively loaded ice deformed within the brittle regime fails by axial splitting under no confinement and by shear faulting under moderate confinement. This paper investigates the transition between these two failure modes using a novel very low-confinement loading device. It is found that, with increasing confinement, the orientation of the macroscopic failure plane rotates rapidly away from the direction of maximum compression until the confining stress reaches ∼1% of the maximum compressive stress, and then, under higher confinement, remains within the range of orientations generally attributed to Coulombic faulting. Quantitative modeling of the effect of confinement on wing crack growth and on the distribution of excess shear stress ahead of the wing crack tip results in predictions of the macroscopic fault orientation in good agreement with experimental observations.

Mechanical behaviors and damage constitutive model of ceramics under shock compression

One-stage light gas gun was utilized to study the dynamic mechanical properties of AD90 alumina subjected to the shock loading. Manganin gauges were adopted to obtain the stress-time histories. The velocity interferometer system for any reflector (VISAR) was used to obtain the free surface velocity profile and determine the Hugoniot elastic limit. The Hugoniot curves were fitted with the experimental data. From Hugoniot curves the compressive behaviors of AD90 alumina were found to change typically from elastic to “plastic”. The dynamic mechanical behaviors for alumina under impact loadings were analyzed by using the path line principle of Lagrange analysis, including the nonlinear characteristics, the strain rate dependence, the dispersion and declination of shock wave in the material. A damage model applicable to ceramics subjected to dynamic compressive loading has been developed. The model was based on the damage micromechanics and wing crack nucleation and growth. The effects of parameters of both the micro-cracks nucleation and the initial crack size on the dynamic fracture strength were discussed. The results of the dynamic damage evolution model were compared with the experimental results and a good agreement was found.

A Dynamic Damage Model for Uniaxial Compressive Response of AD90 Alumina

The dynamic response of polycrystalline alumina were investigated in the pressure range of 0-13Gpa by planar impact experiments. Manganin gauges were employed to obtain the stress-time histories. From the free surface particle velocity profiles indicate the dispersion of the “plastic” wave for alumina. Using path line principle of Lagrange Analysis the dynamic mechanical behaviors for alumina under impact loading are analyzed, such as nonlinear, strain rate dependence, dispersion and declination of shock wave in the material. A damage model applicable to ceramics subjected to dynamic compressive loading is developed. The model is based on the damage micromechanics and established on wing crack nucleation and growth. The results of the dynamic damage evolution model are compared to the experimental results and a good correlation is obtained.

Multimillion atom simulations of dynamics of wing cracks and nanoscale damage in glass, and hypervelocity impact damage in ceramics

We have developed scalable parallel algorithms for first-principles based predictive atomistic simulations of materials. We have achieved parallel efficiency 0.998 for 134 billion-atom molecular dynamics (MD), 1.06 billion-atom reactive force-field MD, and 11.8 million-atom (1.04 trillion electronic degrees-of-freedom) quantum-mechanical MD in the framework of the density functional theory on 131,072 BlueGene/L processors. We have performed up to 540 million-atom MD simulations to study: (1) initiation, growth and healing of wing cracks in confined silica glass; and (2) damage initiation during hypervelocity impact on advanced ceramics.

Numerical Simulation on 3-D Crack Coalescence in Rock-Like Materials Containing Pre-Existing Surface Closed Flaws

Using newly developed 3 dimensional Rock Failure Process Analysis code RFPA3D, numerical simulations on samples of rock-like material containing pre-existing surface closed flaws under uniaxial compressive loading are conducted to investigate the failure mechanism and crack coalescence modes. Friction in closed flaws is modeled by inserting ideal elasto-plastic materials into the flaws. The simulations replicate most of the phenomena observed in actual experiments, such as initiation and growth of wing and secondary cracks, crack coalescence, and the macro-failure of the sample. For the samples containing three pre-existing surface closed flaws, four different patterns of crack coalescence are obtained in our simulations. The four different patterns of coalescence are the combination of T mode, S mode, TS mode and C mode, i.e. type (C+S mode), (T+S mode), (S mode) and (C+S mode). A total of four types of samples containing three surface parallel inclined frictional flaws are numerically simulated.

Crack Propagation under Compressive Stress Influenced by Crack Face Asperity

The influence of surface roughness in crack face on the behavior of crack growth is studied. Numerical results derived from two kinds of mechanical models representing the macroscopic and microscopic asperity supposed to exist in the face of an initial crack are compared. In macro-asperity model, the influence of location and size of single-triangular asperity on the stress intensity factor is evaluated. In this model, it is found that the mode-I stress singularity appears in certain circumstances even under overall compression. In micro-asperity model, influence of friction coefficient on the trajectory of crack path is discussed. There exists a tendency that a path of wing crack growth becomes more straight and parallel to axis of compression as the friction coefficient increases.

2034 ウイングき裂の伝ぱ挙動に及ぼす自由境界の影響(J01-2 材料や構造の破壊/損傷/マルチスケール解析(2),J01 材料や構造の破壊/損傷/マルチスケール解析)

The behavior of wing crack growth influenced by free boundaries is studied. Compression of a plate with angled crack induces the propagation of wing cracks which grow almost parallel to the axis of compression. The mode- I stress intensity factor at the wing crack tip increases when the crack grows near a free boundary. In this study, the behavior of fracture under single axial compression of transparent material was investigated. A simulation of crack propagation was conducted for various cases in which the distance between free boundary and the location of initial crack and the crack inclination are different. The compression test using PMMA plates with centric and eccentric saw flaw were also demonstrated.

Dynamics of Wing Cracks and Nanoscale Damage in Glass

We investigate initiation, growth, and healing of wing cracks in confined silica glass by molecular dynamics simulations. Under dynamic compression, frictional sliding of precrack surfaces nucleates nanovoids which evolve into nanocrack columns at the precrack tip. Nanocrack columns merge to form a wing crack, which grows via coalescence with nanovoids in the direction of maximum compression. Lateral confinement arrests the growth and partially heals the wing crack. Growth and arrest of the wing crack occur repeatedly, as observed in dynamic compression experiments on brittle solids under lateral confinement.

The brittle compressive failure of fresh-water columnar ice loaded biaxially

New experiments have been performed on the brittle compressive failure of columnar-grained, S2 fresh-water ice, proportionally loaded biaxially across the columns at −10 °C at 4.5 × 10 −3 s −1. The results and analysis show that under higher confinement ( σ 22/ σ 11 > 0.2) where terminal failure occurs via across-column cleavage and spalling out of the loading plane, a combination of wing crack growth and Euler buckling of deformation-induced thin plates underlies the process.

Influence of lateral confinement on dynamic damage evolution during uniaxial compressive response of brittle solids

A dynamic damage growth model applicable to brittle solids subjected to biaxial compressive loading is developed. The model incorporates a dynamic fracture criterion based on wing-crack growth model with a damage evolution theory based on a distribution of pre-existing microcracks in a solid. Influences of lateral confinement pressure (dynamic or static) as well as frictional coefficient on the rate dependence of fracture strength of basalt-rock are investigated systematically. It is found that the failure strength, damage accumulation and wing-crack growth rate are strongly influenced by the nature and the magnitude of confinement pressure. It is also verified that the effect of strain rate on fracture strength of brittle solids is independent of confinement pressure in a certain range of strain rate.

Influence of shape and locations of initial 3-D cracks on their growth in uniaxial compression

Mechanisms of 3-D crack development in uniaxial compression have been studied. Several tests undertaken on different transparent casting resin, cement and mortar samples with single internal cracks of different shapes and sizes, produced by different techniques, demonstrated that 3-D crack growth in compression was qualitatively different from the two-dimensional case. Unlike 2-D cracking, there were intrinsic limits on 3-D growth of wing cracks produced by a single pre-existing crack. This limitation was related to the wrapping (curving) of emerging wings around the initial crack. On the other hand, in samples with few initial cracks, a special crack arrangement existed which could produce a large tensile fracture parallel to the direction of loading. Particularly, for two coplanar initial cracks, the tensile fracture was produced only when the inter-crack spacing was below a critical value. In samples where the initial cracks were present in high concentrations, the influence of interaction always generated a number of tensile fractures parallel to the direction of loading.