Zone Fracture Model Research Articles

The effect of specimen thickness on the dislocation-free zone model of fracture

We use the method of continuously distributed dislocations to study the dislocation-free zone (DFZ) model of fracture in an infinite plate of finite thickness under externally applied uniform anti-plane shear stress. We formulate the equilibrium condition in terms of a set of two coupled singular integral equations using the representation of the total interaction force between two screw dislocations in a thin plate obtained by Eshelby and Stroh (1951). This set of singular integral equations is then solved numerically using the Gauss-Chebyshev integration formula resulting in the dislocation distribution functions in the crack and in the two plastic zones, the total number of screw dislocations in the plastic zone, the DFZ condition for a crack in a thin plate and the local mode III stress intensity factor at the crack tip.

Cohesive Zone Modeling of Crack Propagation in FCC Single Crystals via Atomistic Simulations

This paper presents a cohesive zone model of fracture in Cu and Ni single crystals under tension, based on an atomistic analysis. The molecular-statics approach based on the conjugate-gradient method was used to investigate the crack-growth behavior at the atomic level. The fracture toughness was evaluated on the basis of energy considerations, and the cohesive traction was calculated using the J integral and the atomic-scale separation in the cohesive zone. The cohesive traction and separation curves obtained using computational data from atomistic simulations were compared with the exponential form of continuum mechanics. The results showed that the exponential form satisfactorily represented the cohesive zone properties of Cu. However, the cohesive traction and separation curves for Ni were found to deviate from the exponential form in the softening stage, owing to small-scale nonlinear features near the cohesive zone.

A limit equilibrium fracture zone model to investigate seismicity in coal mines

This paper explores possible synergies between techniques used to minimise seismicity in deep South African gold mines and their applicability to control coal bumps. The paper gives a summary of the techniques used in the deep gold mines and a critical appraisal if these are useful in coal mines. The techniques typically include control of mining rate, preconditioning, optimisation of extraction sequences and centralised blasting. Of particular interest to the coal bump problem is an experimental limit equilibrium fracture zone model implemented in a displacement discontinuity code. This was recently developed for the gold mines to enable the interactive analysis of complex tabular mine layout extraction sequences. The model specifically accommodates energy dissipation computations in the developing fracture zone near the edges of these excavations. This allows the released energy to be used as a surrogate measure of ongoing seismic activity and addresses a number of the weaknesses in the traditional usage of this quantity as a criterion for the design of seismically active layouts. This paper investigates the application of the model to a hypothetical coal longwall layout and the specific problem of coal bumps.

Simulation of tabular mine face advance rates using a simplified fracture zone model

This paper describes a method to determine the time-dependent stability of the fracture zone near the edges of tabular excavation layouts when different mining rates and face advance increment lengths are scheduled. Some analytic properties of the proposed time-dependent fracture zone evolution model are presented initially for a simplified mining geometry. The implementation of the model in a general tabular layout setting is described next including a novel scheme to allow for partially fractured elements. The reef plane stress distribution in the fracture zone is solved using a fast marching method that is coupled to a displacement discontinuity solution of the excavation and fracture zone deformations. The numerical scheme is illustrated by considering the extraction of a hypothetical deep-level mining layout. The sensitivity of the results to changes in the mining rate schedule and the face advance step size are discussed. Further extensions to the solution scheme are noted.

How to Measure a Dislocation’s Breakthrough Stress to Estimate the Grain Boundary Resistance against Slip Transfer Based on the DFZ-Model of Fracture

Stage-I-fatigue-cracks are used as highly localized dislocation sources with well-known Burger’s vectors to study the interaction between dislocations and grain boundaries. This interaction in the plastic zone is of particular interest to understand the fluctuating crack growth in the very short crack regime. In the case of a blocked slip band the dislocations pile up at the grain boundary causing a local stress concentration. The resulting local stress distribution is calculated based on measurements of the dislocation density distribution in the plastic zone. For this purpose the slip line profiles were measured by AFM, the dislocation density distribution was determined and the dislocation-free zone model of fracture (DFZ) was validated. With this it is possible to quantify the grain boundary resistance and to combine geometric and stress approach for grain boundary resistance against slip transfer.

Quantifying the grain boundary resistance against slip transfer by experimental combination of geometric and stress approach using stage-I-fatigue cracks

In recent studies, many groups have investigated the interaction of dislocations and grain boundaries by bi-crystals and micro-specimen experiments. Partially, these experiments were combined with supplementary simulations by discrete dislocation dynamics, but quantitative data for the grain boundary resistance against slip transfer is still missing. In this feasibility study with first results, we use stage-I-fatigue cracks as highly localised sources for dislocations with well-known Burgers vectors to study the interaction between dislocations in the plastic zone in front of the crack tip and selected grain boundaries. The stress concentration at the grain boundary is calculated with the dislocation-free zone model of fracture using the dislocation density distribution in the plastic zone from slip trace height profile measurements by atomic force microscopy. The grain boundary resistance values calculated from common geometric models are compared to the local stress distribution at the grain boundaries. Hence, it is possible to quantify the grain boundary resistance and to combine geometric and stress approach for grain boundary resistance against slip transfer to a self-contained concept. As a result, the prediction of the grain boundary resistance effect based on a critical stress concept is possible with knowledge of the geometric parameters of the grain boundary only, namely the orientations of both participating grains and the orientation of the grain boundary plane.

Improving adhesion of copper/epoxy joints by pulsed laser ablation

The purpose of the present work is to analyze the effect of pulsed laser ablation on copper substrates (CuZn40) deployed for adhesive bonding. Surface pre-treatment was carried using an Yb-fiber laser beam. Treated surfaces were probed using Scanning Electron Microscopy (SEM) and X-Ray Photoelectron Spectroscopy (XPS). The mechanical performance of CuZn40/epoxy bonded joints was assessed using the T-peel test coupon. In order to resolve the mechanisms of failure and adhesive penetration within surface asperities induced by the laser treatment, fracture surfaces were surveyed using SEM. Finite element simulations, based on the use of the cohesive zone model of fracture, were carried out to evaluate the variation of bond toughness. Results indicated that the laser ablation process effectively modifies surface morphology and chemistry and enables enhanced mechanical interlocking and cohesive failure within the adhesive layer. Remarkable improvements of apparent peel energy and bond toughness were observed with respect to control samples with sanded substrates.

Investigation of longwall goaf gas flows and borehole drainage performance by CFD simulation

To reduce methane emissions into the workings of a longwall panel, the mechanisms of gas emissions and migration within the longwall goaf must first be understood. Additionally, high performance drainage boreholes must be designed. Many variables affect the goaf gas flow and borehole drainage efficiency, namely the gas release characteristics of gas sources, the heights of caved and fractured zones of the goaf, the location of the drainage borehole and the position of the effective drainage section (the portion of the perforated case and the uncased open hole). This paper illustrates how these variables influence the goaf gas flow patterns and borehole performances through CFD simulations. A permeability model and a gas release curve, which reflect observations from experiments, geomechanical modellings, mine site monitoring and borehole drainage data, were constructed for the mining-disturbed strata and incorporated into the CFD model. The CFD model was calibrated with the actual drainage data from the surface boreholes at a coal mine. Simulation results show that the gas drainage velocities around the perimeter of the panel goaf are higher than in the central goaf, which is consistent with the overlying annular fracture zone model established from CSIRO previous research. Boreholes located within the annular area drew methane at a higher flow rate than those located in the central area, leading to a significant reduction of methane emissions to the ventilation system. Goaf geometry with higher caved and fractured zones has lower pressure and methane concentration but higher gas flow velocity. The location of the effective drainage section of the borehole has significant influence on drainage performance. Boreholes with the bottom end located in the lower region of the fractured zone, (20m above the roof), can draw more methane than those located in the upper region of the fractured zone (70m above the roof) and those located in the caved zone (2m above the roof).

Stage-I fatigue crack studies in order to validate the dislocation-free zone model of fracture for bulk materials

Stage-I fatigue cracks are commonly described by the model of Bilby, Cottrell and Swinden (BCS model). However, since several experimental investigations have shown a dislocation-free zone (DFZ) in front of crack-tips, it is necessary to validate the new DFZ model and to examine the deviations to the BCS model. Therefore, the dislocation density distribution is derived from height profiles of slip lines in front of stage-I fatigue cracks in CMSX4® single crystals measured by contact-mode atomic force microscopy. This is possible, because the cracks are initiated at notches milled by focused ion beam technique directly on slip planes with a high Schmid factor. Consequently, the directions of the Burgers vectors are well known; it is possible to calculate the dislocation density distributions from the height profiles. The measured distributions are compared to the calculated distribution function of the DFZ model proposed by Chang et al. The additionally measured microscopic friction stress of the dislocations is then used to calculate the influence of grain boundaries on the dislocation density distribution in front of stage-I cracks. The calculation is done by the extended DFZ model of Shiue et al. and compared with the measured distribution function in polycrystalline specimens. Finally, the crack-tip sliding displacement as a measure for the crack propagation rate is compared for the DFZ model and the BCS model with the experimentally revealed values. The important result: the often used BCS model does not reflect the experimental measurements. On the contrary, the DFZ model reflects the measurements at stage-I cracks qualitatively and quantitatively.

Insights into the origin of the thermal springs of Bath and Bristol, England, from geophysical data

The thermal springs of Bath, England, produce 1.25 Ml day −1 of water at 46.5 °C. The spring at Hotwells, Bristol, England, 15 km to the west, is estimated to produce between 0.17 and 0.39 Ml day −1 of water at a temperature between 22.8 and 24.4 °C. Published research suggests that the waters originate in the Mendip Hills, SW of Bath and Bristol, and are heated by geothermal energy within the Carboniferous Limestone basin (‘The Mendips Model’). The exact paths of the waters to the springs have not been established. We interpreted seismic reflection data for the urban district of Bath and for the Radstock Basin to the south of Bath. By combining the geophysical interpretations with published geological data we have established a potential route through the Carboniferous Limestone reaching sufficient depths for the waters to attain the required temperatures. We imaged a steeply dipping, fractured region of Carboniferous Limestone coincident with the valley of the River Avon and propose that this is the feature by which the thermal waters can rise rapidly to the surface, providing an explanation for the existence of these unique springs. We have incorporated these new aspects of the Mendip Model into the ‘Mendip–Avon Fracture Zone Model’.

Evaluation of known-boundary and resistivity constraints for improving cross-borehole DC electrical resistivity imaging of discrete fractures

There is a need to better characterize discrete fractures in contaminated hard rock aquifers to determine the fate of remediation injections away from boreholes and also to evaluate hydraulic fracturing performance. A synthetic cross-borehole electrical resistivity study was conducted assuming a discrete fracture model of an existing contaminated site with known fracture locations. Four boreholes and two discrete fracture zones, assumed to be the dominant electrical and hydraulically conductive pathways, were explicitly modeled within an unstructured tetrahedral mesh. We first evaluated different regularization constraints starting with an uninformed smoothness-constrained inversion, to which a priori information was incrementally added. We found major improvements when (1) smoothness regularization constraints were relaxed (or disconnected) along boreholes and fractures, (2) a homogeneous conductivity was assumed along boreholes, and (3) borehole conductivity constraints that could be determined from a specific conductance log were applied. We also evaluated the effect of including borehole packers on fracture zone model recovery. We found that the fracture zone conductivities with the inclusion of packers were comparable to similar trials excluding the use of packers regardless of electrical potential changes. The misplacement of fracture regularization disconnects (FRDs) can easily be misinterpreted as actual fracture locations. Conductivities within these misplaced disconnects were near the starting model value, and removing smoothing between boreholes and assumed fracture locations helped in identifying incorrectly located FRDs. We found that structural constraints used after careful evaluation of a priori information are critical to improve imaging of fracture electrical conductivities, locations, and orientations.

Investigating Some Technical Issues on Cohesive Zone Modeling of Fracture

This study investigates some technical issues related to the use of cohesive zone models (CZMs) in modeling the fracture of materials with negligible plasticity outside the fracture process zone. These issues include: (1) why cohesive laws of different shapes can produce similar fracture predictions, (2) under what conditions CZM predictions have a high degree of agreement with linear elastic fracture mechanics (LEFM) analysis results, (3) when the shape of cohesive laws becomes important in the fracture predictions, and (4) why the opening profile along the cohesive zone length (CZL) needs to be accurately predicted. Two cohesive models were used in this study to address these technical issues. They are the linear softening cohesive model and the Dugdale perfectly plastic cohesive model. Each cohesive model uses five cohesive laws of different maximum tractions. All cohesive laws have the same cohesive work rate (CWR) defined by the area under the traction–separation curve. The effects of the maximum traction on the cohesive zone length and the critical remote applied stress are investigated for both models. The following conclusions from this study may provide some guidelines for the prediction of fracture using CZM. For a CZM to predict a fracture load similar to that obtained by an LEFM analysis, the cohesive zone length needs to be much smaller than the crack length, which reflects the small-scale yielding condition requirement for LEFM analysis to be valid. For large-scale cohesive zone cases, the predicted critical remote applied stresses depend on the shape of the cohesive models used and can significantly deviate from LEFM results. Furthermore, this study also reveals the importance of accurately predicting the cohesive zone profile for determining the critical remote applied load.

Three-dimensional cohesive zone model for fracture of cementitious materials based on the thermodynamics of irreversible processes

This paper presents the formulation and implementation of a new 3-D cohesive zone element (CZM) with mode I traction-displacement laws for cementitious materials. The separation model is based on a damage mechanics framework which accounts for the thermodynamics of irreversible processes. Unlike many existing cohesive models, this proposed irreversible cohesive constitutive model prevents previous cohesive states from occurring on the fracture surface upon external or local unloading through a scalar damage parameter. In the proposed formulation, the interpenetration upon compressive loading is also avoided without any special contact algorithm. The CZM formulation and implementation are first verified using a 3-D uniaxial tension problem under tension and compression loading, unloading, and reloading. The proposed approach converged with higher values of the penalty stiffness without generating instabilities or oscillations in the traction profile. The damage-based evolution cohesive law was characterized by physically-defined fracture parameters derived from standard fracture tests for concrete materials (KIC, CTODC, Gf, and GF) and tensile strength (ft′). The proposed model was validated by predicting the fracture behavior of SEN(B) specimen for a wide range of concrete materials including plain concrete mixtures containing virgin aggregates and recycled concrete aggregates (RCA), and concrete with RCA and fibers or nano-silica particles. The proposed model was further validated by predicting the load–deflection of 1.8m×1.8m by 0.15m concrete slabs experimentally tested on a soil foundation. The 3-D damage-based cohesive zone model simulations with bilinear softening, defined by small-scale fracture tests, were able to predict the concrete slab response and load capacity.

Study on the role of laser surface irradiation on damage and decohesion of Al/epoxy joints

In this work we investigate the effect of laser irradiation on the bond toughness of aluminum/epoxy bonded joints. The evolution of substrate surface morphology and wettability, for various sets of laser process parameters (i.e. laser power, line spacing, scan speed), was investigated by means of Scanning Electron Microscopy (SEM) and contact angle measurements. A proper combination of power, line spacing and scan speed was then selected and adhesive bonded Al/epoxy T-peel joints were prepared and tested. For comparison, similar samples were produced using substrates with classical grit blasting surface treatment. Finally, post-failure SEM analyses of fracture surfaces were performed, and in order to typify the increase in bond toughness of the joints, finite element simulations were carried out using a potential based cohesive zone model of fracture.

A combined dislocation–cohesive zone model for fracture in nanocrystalline materials

Abstract

Simulation of debonding in Al/epoxy T-peel joints using a potential-based cohesive zone model

In this work, a cohesive zone model of fracture is employed to study debonding in plastically deforming Al/epoxy T-peel joints. In order to model the adhesion between the bonded metal strips, the Park-Paulino-Roesler (PPR) potential based cohesive model (J Mech Phys Solids, 2009;57:891-908) is employed, and interface elements are implemented in a finite element com-mercial code. A study on the influence of the cohesive properties (i.e. cohesive strength, fracture energy, shape parameter and slope indicator) on the predicted peel-force versus displacement plots reveals that the numerical results are mostly sensitive to cohesive strength and fracture energy. In turn, these parameters are tuned until a match between experimental and simulated load displacement curves is achieved.

A combined dislocation—cohesive zone model for fracture in a confined ductile layer

The collective dislocation behavior near a crack tip in a ductile layer sandwiched between two brittle solids is analyzed via two-dimensional dislocation dynamics (DD) simulations that incorporate a cohesive zone (CZ) model. The cohesive crack tip is treated as part of a much larger finite crack confined in the ductile layer. The underlying boundary value problem is formulated with a set of boundary integral equations and numerically evaluated with a collocation method. The fracture energy of the layered composite material is shown to be strongly correlated with the layer thickness and is directly influenced by the cohesive strength of the ductile layer (Hsia KJ et al. (1994) J Mech Phys Solids 6 877–896).

Near threshold fatigue curve based on the dislocation free zone model of fracture

Dislocation pileup along an inclined direction from a crack tip has been observed in metals during tensile deformation in an electron microscope. Dislocations are emitted from the crack tip, move through a dislocation free zone, and pile up in the plastic zone. The problem of inclined pileup of screw dislocations at a crack tip with a dislocation free zone has been solved by applying the Wiener–Hopf method. The result can be used to calculate the crack tip blunting and the local stress intensity K for the applied stress intensity K 3. According to the fatigue theory of Laird or Neumann, the crack propagation per cycle has the order of magnitude of the blunting. The blunting versus K 3 is then plotted. It has the shape of the near threshold fatigue curve. To plot this curve, the local stress intensity K has been assumed to be the critical value K g for the dislocation emission at the crack tip.

Effect of grain boundary ledge on the dislocation-free zone model of fracture: Transgranular microcrack nucleated from a grain boundary ledge

The effect of grain boundary ledge on the dislocation-free zone model of fracture is investigated in the case of a transgranular microcrack nucleated from a grain boundary ledge. The dislocation distribution functions to simulate the crack and plastic zone, the numbers of dislocations in the crack and plastic zone, the stress field, and the stress intensity factor at the crack tip (or the energy barrier for the dislocation emission from the crack tip) are obtained. If the Burgers vector of dislocations comprising the grain boundary ledge has the same sign as that of plastic zone dislocations, the dislocation distributions to simulate the plastic zone, the number of dislocations in the plastic zone, the stress field in the dislocation-free zone, and the stress intensity factor at the crack tip increase with increasing number of grain boundary ledge dislocations, but increase with decreasing grain size. Both sides of the grain boundary ledge dislocations have different effects on the dislocation-free zone size, plastic zone size, and the applied stress to accumulate the plastic zone dislocations. The stress intensity factor at the crack tip increases with increasing dislocation-free zone size. When there is no dislocation-free zone in front of the crack tip, the stress intensity factor is zero regardless of whether the grain boundary ledge dislocations exist.

Dislocation-free zone model of fracture: The effect of transgranular microcrack nucleated from a grain-boundary ledge

The effects of transgranular microcrack nucleated from a grain-boundary ledge on a dislocation-free zone model of fracture are investigated by a continuous dislocation modeling method. The dislocation distribution functions to simulate the crack and plastic zone, the number of dislocations in the crack and plastic zone, the stress field, and stress intensity factor at the crack tip are obtained. If the Burgers vector of dislocations composing the grain-boundary ledge has the same sign as that of the plastic zone dislocations, all the dislocation distributions that simulate the crack and plastic zone, the number of dislocations in the crack and plastic zone, the stress field in the dislocation-free zone, the stress intensity factor at the crack tip, the dislocation-free zone size, and the plastic zone size increase with an increasing number of grain-boundary ledge dislocations, but the applied stress σ to accumulate the plastic zone dislocations decreases with an increasing number of grain-boundary ledge dislocations. The effects of transgranular microcrack nucleated from a grain-boundary ledge on a fracture without a dislocation-free zone are also considered. When there is no dislocation-free zone in front of the crack tip, the stress intensity factor is zero, regardless of whether the grain-boundary ledge dislocations exist.