Brittle Failure Criterion Research Articles

Shear thinning and brittle failure in crystal-bearing magmas arise from local non-Newtonian effects in the melt

Crystal-bearing magmas are often assumed to be intrinsically non-Newtonian, but the mechanism underlying suspension shear thinning remains unconstrained. Here, we test the hypothesis that shear thinning in these suspensions arises solely from unrelaxed shear thinning in the melt phase or from viscous heating or both. We compile existing data for the rheology of high-temperature crystal-bearing silicate magmas across a wide range of conditions. In order to test this, we define a ‘lever’ function L(ϕ) which scales the strain rate in the melt phase between crystals relative to the bulk strain rate of the suspension as a function of crystal volume fraction ϕ. We show that, in general, the parameterisation of the amplification of strain rates via the L(ϕ) factor coupled with a shear-thinning law for the melt phase fully accounts for the non-Newtonian behaviour of the suspension. Next, we use the Brinkman number Br to demonstrate that some existing data derive from experiments that were subject to viscous heating, resulting in a further manifestation of apparent shear thinning. Taken together, our results provide a theoretical framework that predicts microphysical regimes for shear thinning. This implies that crystal-bearing magmas are Newtonian except where the scaled conditions for viscous heating are met, or when the strain rates in the melt phase approach the inverse of the structural relaxation timescale. This shear thinning due to non-Newtonian behaviour of the melt between crystals occurs very close to the brittle threshold, yielding an extension of the brittle failure criterion to crystal-bearing magmas, with direct implications for volcanic eruption dynamics.

A numerical study of the mechanical and fracture properties of ZTA (zirconia toughened alumina)p/40Cr steel spatial spherical dot matrix composite

In this work, the geometrical characteristics of ZTA reinforcement particles were obtained, and a three-dimensional numerical model of ZTAp/40Cr steel spatial spherical dot matrix composite, similar to the actual structure, was established. In addition, the matrix toughness and shear fracture criterion, the brittle failure criterion of reinforcement particles, and the interfacial traction splitting criterion were all established. Under uniaxial compression, the influence of constitutive factors (volume fraction of spatial spherical dot matrix composite zone - VFB, and particle size - RPS) on the mechanical characteristics and fracture behavior of spatial spherical dot matrix composites was investigated. The elastic modulus, the compressive strength, and elongation in the stress–strain curves were calculated to assess the mechanical properties of the composites, and the particle average Mises stress and particle stress concentration coefficient were introduced to quantify the load carrying capacity of the composites. Furthermore, the fracture behavior of the secondary interface damage, the internal isotropic strain, and the macroscopic failure behavior were used to study the composites' fracture behavior. A new approach and theoretical foundation for following composites conformal design were established.

Simulation of hard rock pillar failure using 2D continuum-based Voronoi tessellated models: The case of Quirke Mine, Canada

The Quirke Mine, ON, Canada, is a typical example of a mine that experienced a chain reaction of pillar failure. In this mine, the rib pillars were initially laid out with their long axis parallel to the dip direction of the orebody. In the central part of the mine, the pillars were re-aligned at 45° to the orebody true dip. This realignment resulted in adverse shear loading conditions that led to their failure. In this study, a two-dimensional finite element program was used to simulate the failure of Quirke Mine pillars under compressive and shear loading conditions. The pillars were simulated as a heterogeneous material, consisting of randomly generated Voronoi blocks. The calibration of this model, referred to as a Voronoi Tessellated Model (VTM), was conducted against the rock mass strength estimated based on a tri-linear, brittle failure criterion. The calibrated VTM was then employed to investigate the pillar behavior during drift development and stope excavation. It was found that the pillar under shear loading experiences higher confinement loss and tensile stress at its core and, therefore, fails at a lower stress level than that under compression. The simulated pillar failure process was found to agree with documented field observations.

A two-level strategy for simplification of fracture prediction in notched orthotropic samples with nonlinear behavior

In this paper, the load bearing capacity of U-notched specimens made of Russian pine wood, as a natural orthotropic material with nonlinear behavior, is investigated under pure mode I loading. The load bearing capacity of the orthotropic specimens with nonlinear behavior is predicted adopting a novel combination of the Equivalent Material Concept (EMC) and the Virtual Isotropic Material Concept (VIMC) in conjunction with the brittle failure criteria. By applying the EMC, the orthotropic material with nonlinear behavior is equated with a virtual linear one. Subsequently, using the VIMC, the orthotropic material with linear behavior obtained from the previous step is equated with a virtual isotropic material with linear behavior. Eventually, the load bearing capacity of the orthotropic nonlinear notched samples is predicted using two common brittle failure criteria, so-called the point stress criterion and the mean stress criterion. It is shown that both criteria employed for predicting the notch fracture toughness of the wood specimens are of good accuracy.

Wellbore stability in high-temperature granite under true triaxial stress

Supercritical/superhot geothermal success depends on successful drilling. However, wellbore stability in supercritical environments has not been investigated because imposing sufficient stress on high-temperature granite with true triaxial loading is difficult. We conducted wellbore failure experiments on 200–450 °C granite under true triaxial stress, including deformation and acoustic emission measurements, and post-experiment thin section observations. Wellbore failure initiated at stress states consistent with existing brittle failure criterion at the studied temperatures. Using breakout geometry for in situ stress estimation may be difficult as shear failure propagation is suppressed at high temperatures; however, boreholes may be inherently stable in high-temperature environments.

An Alternative Brittle Failure Criterion and Methodology for Predicting Fracturing around Underground Excavations

An Alternative Brittle Failure Criterion and Methodology for Predicting Fracturing around Underground Excavations

Deformation behavior and damage in B4Cp/6061Al composites: An actual 3D microstructure-based modeling

The influence of particle size on the mechanical behavior of B4Cp/6061Al composites prepared by powder metallurgy is investigated by combining the tensile test with finite element method (FEM) simulation. The experimental results show that increasing the particle size from 20 μm to 80 μm deteriorates the tensile property and work hardening rate of the B4Cp/6061Al composites. The actual three-dimensional (3D) microstructure obtained by synchrotron radiation X-ray computed microtomography (SR-μCT) is incorporated into finite element models to study the deformation behavior and internal damage of the composites. The matrix ductile damage, particle brittle failure criterion, and interface traction–separation law which are associated with particle sizes are employed to predict the tensile properties. The deformation behavior and damage mechanism in the B4Cp/6061Al composites are revealed by analyzing the stress and strain distributions. Furthermore, stress concentration factor is considered to evaluate the load-bearing capability of the composites reinforced by various particle sizes. This work provides a reference for studying the mechanical behavior of heterogeneous microstructural materials via actual microstructure-based modeling.

Brittle failure criteria of CNRB specimen for fracture toughness test

Brittle failure criteria of CNRB specimen for fracture toughness test

Multi-parameters mechanical modeling to derive a confinement model for masonry columns

Abstract Increments of the axial capacity of existing masonry elements can be provided by confinement. Assessment methodologies with general validity to assess the behavior of confined masonry columns with strengthening systems are not available in the technical literature, in fact, the strong variability and heterogeneity of masonry material did not allow to develop generalized models. For brittle materials damage mechanics and failure criteria allow to do this in the framework of solid mechanics. However, the recent scientific researches provided relevant information about the experimental behavior of masonry confined with composites. In this paper, an analytical model able to assess the behavior of the confined masonry with composite is proposed. It was developed according to a failure criterion based on mechanical parameters representative of masonry. It can be applied to masonry cross sections of any shape also under a non-uniform lateral stress field (i.e. generic stress fields). To confirm the flexibility of the proposed model some existing experimental results have been used. The comparison between model predictions and experimental results in terms of axial strength showed that the proposed model is a valid tool to assess the confinement properties of strengthened masonry elements.

Pure mode III fracture of U-notched specimens made of PMMA and GPPS polymers: Experimental and theoretical evaluations

In this paper, a new set of fracture experiments are conducted on the U-notched components made of Polymethyl-methacrylate (PMMA) and general-purpose Polystyrene (GPPS) under pure out-of-plane shear (mode III) loading by using an anti-symmetric four-point bend (ASFPB) configuration. For exploring the influence of the notch tip radius, the specimens with four different radii are tested. Two well-known brittle failure criteria, namely the point stress (PS) and mean stress (MS) criteria, are then employed to assess the fracture behavior of the tested U-notched specimens. Stress analyses needed for determining the notch stress intensity factors (NSIFs) are performed by means of the finite element modeling of the test configuration. A good agreement is revealed between the predictions of the PS and MS criteria and the experimental results, confirming their suitability for estimating pure mode III fracture of U-notched components made of brittle materials. No meaningful difference is observed between the theoretical predictions of the PS and MS criteria. It is revealed that the fracture toughness enhancement of PMMA-made U-notched specimens is more sensitive to increasing the notch tip radius than that of U-notched GPPS samples.

Numerical Simulation for the Dynamic Breakout of a Borehole Using Boundary Element Method

Borehole breakouts are formed by spalling of fragments in a direction parallel to the least horizontal stress. As the breakouts falling into the wellbore or being scoured by the drilling mud piece by piece, the stress concentration on the wellbore will release gradually. The wellbore is not circular or elliptical, which requires a numerical method to determine the redistributed stress around the irregular borehole. In this article, boundary element method associated with the brittle rock failure criterion is deployed to simulate the dynamic breakout of a borehole. The borehole shape is updated step by step during the time-dependent breakout. The first breakout volume is smaller than the analytical solution (Gholami et al. in J Rock Mech Geotech Eng 8:521–532, 2016). However, the total breakout volume is larger than the analytical solution because our model considers the subsequent failure of the irregular wellbore. The stress distribution around the irregular wellbore after each step of breakout is investigated and the maximum cohesive strength at which the rock will fail is figured out. These results provide new insights to understand the dynamic process of borehole breakout.

Effect of carbonate platform morphology on syndepositional deformation: Insights from numerical modeling

We use finite element numerical modeling to show that carbonate platform morphology is a control on syndepositional deformation in steep-walled carbonate platforms. We simulate gravity application on three end-member carbonate platform margin morphologies: (1) a mixed planar-concave up shaped shelf margin from Tobacco Cay, Belize, (2) a concave up shaped system representing the Capitan Profile, Guadalupe Mountains West Texas, and (3) a sigmoidal, Jurassic Amellago ramp. We model the platform material with a brittle failure criteria that captures tensile and shear failure. We show that the presence of a vertical reef wall and, thereby, lack of lateral confining stress seaward leads to a tensile stress state in the middle of the shelf and the shelf edge, promoting the development of opening-mode (Mode I) tensile fractures. Fractures occur in the absence of additional loading or burial, indicating that their formation is consistent with a syndepositional setting. Overall, our results demonstrate that carbonate platforms with a near vertical reef wall are routinely modified by syndepositional deformation and failure in the absence of compaction. We show that zones of high tensile stress can result in brittle, tensile failure and confirm that tensile failure is a critical element of building and may contribute to maintaining steep-walled carbonate platform systems.

Brittle failure criteria for components containing U-notches under Mode I loading

In this study, a modified fracture criterion which satisfies the necessary stress and energy conditions is proposed for brittle materials. The criterion is based on the assumption that fracture is generated by the initiation of a crack with a finite length lcm. In the proposed criterion, it is assumed that the crack length lcm is an intrinsic material parameter, with a value between 0.8d0m⩽lcm⩽d0m(=2(KIC/σC)2/π). Here,d0m is the characteristic length used in the mean stress criterion, and KIC and σC are the fracture toughness and the tensile strength for the considered material, respectively. The stress and energy conditions for estimating the brittle fracture behaviour can be fulfilled progressively not simultaneously. However, both conditions must ultimately be fulfilled. Following tests on brittle materials, it has been shown that the predicted values of ultimate stress, based on the necessary stress and energy conditions, agree well with the experimental data.

Experimental study on the confinement-dependent characteristics of a Utah coal considering the anisotropy by cleats

Characterizing a coal from an engineering perspective for design of mining excavations is critical in order to prevent fatalities, as underground coal mines are often developed in highly stressed ground conditions. Coal pillar bursts involve the sudden expulsion of coal and rock into the mine opening. These events occur when relatively high stresses in a coal pillar, left for support in underground workings, exceed the pillar's load capacity causing the pillar to rupture without warning. This process may be influenced by cleating, which is a type of joint system that can be found in coal rock masses. As such, it is important to consider the anisotropy of coal mechanical behavior. Additionally, if coal is expected to fail in a brittle manner, then behavior changes, such as the transition from extensional to shear failure, have to be considered and reflected in the adopted failure criteria. It must be anticipated that a different failure mechanism occurs as the confinement level increases and conditions for tensile failure are prevented or strongly diminished. The anisotropy and confinement dependency of coal behavior previously mentioned merit extensive investigation. In this study, a total of 84 samples obtained from a Utah coal mine were investigated by conducting both unconfined and triaxial compressive tests. The results showed that the confining pressure dictated not only the peak compressive strength but also the brittleness as a function of the major to the minor principal stress ratio. Additionally, an s-shaped brittle failure criterion was fitted to the results, showing the development of confinement-dependent strength. Moreover, these mechanical characteristics were found to be strongly anisotropic, which was associated with the orientation of the cleats relative to the loading direction.

On combination of the equivalent material concept and J‐integral criterion for ductile failure prediction of U‐notches subjected to tension

AbstractThe aim of the present research is to check the capability of the equivalent material concept (EMC) combined with the J‐integral failure criterion, called EMC‐J criterion, in predicting the load‐carrying capacity (LCC) of U‐notched ductile aluminium plates subjected to tension by considering the 2 moderate and large‐scale yielding regimes. For this purpose, first, a set of experimental results on LCC of 2 groups of thin U‐notched rectangular plates made of Al 7075‐T6 and Al 6061‐T6 are gathered from the recent literature. Then, because the Al 7075‐T6 and Al 6061‐T6 plates have ductile behaviour, EMC is employed to avoid performing elastic‐plastic failure analysis for LCC predictions. Up to now, different failure models in the context of the linear‐elastic notch fracture mechanics have been successfully utilized in combination with EMC for ductile failure prediction of notched members. However, this is the first time in this research that J‐integral, as a well‐known brittle failure criterion, is linked to EMC for predicting LCC of the U‐notched rectangular aluminium plates. Finally, it is shown that EMC‐J criterion can predict well the experimental results of tensile LCC.

Study on brittle failure criteria for components containing U-notches under mode I loading

Study on brittle failure criteria for components containing U-notches under mode I loading

Application of the incubation time criterion for dynamic brittle fracture

The complex issue of penetration and perforation of brittle plates subjected to normal impact is addressed. Fracture and fragmentation are simulated numerically by using simultaneously two failure criteria: ductile and brittle failure. A new brittle failure criterion, which is based on incubation time, is proposed. The criterion, inspired from the Tuler–Butcher criterion, is implemented in a commercial finite element code by means of a user subroutine. It is validated by comparing numerical predictions to experimental ballistic results of normal impact on polymethylmethacrylate plates. It is shown that the projectile's exit velocity and the timing of the penetration are faithfully reproduced. It is also verified visually that the experimental damage/fracture pattern, namely radial cracking and dishing, are both well captured by the proposed criterion.

Analysis of spalling failure in marble rock slope: a case study of Neyriz marble mine, Iran

The expansion of the Neyriz marble mine into deeper levels caused an unexpected failure particularly in the toes of lower benches. This phenomenon can impact the overall stability of the quarry and results in undesirable environmental and technical consequences. To understand the failure mechanism, a comprehensive study including—laboratory testing, in situ field testing and theoretical analyses are carried out. The theory of the brittle failure which was mainly developed based on the experiences gained during excavation in granite rocks is adopted and augmented in this study to explain the governing mechanism of failure. Mechanical properties of the marble are determined using conventional rock mechanics tests, and the in situ stress field was evaluated using a modified under coring test. Analyzing the laboratory and field data with the available empirical criteria for brittle failure shows that the level of stress in the lower bench is high enough to initiate the brittle failure. Finally, constitutive models developed for this failure mode are adopted in conjunction with numerical modeling to investigate the observed failure in the quarry. Two modeling strategies, based on elastic and elastic–plastic analyses, are considered. Comparing the predicted failure surface with the observed failure profile, it can be concluded that the brittle failure criteria can very well capture the failure mechanism in this marble quarry. This shows that the criteria proposed to describe spalling failure around underground excavation in granite can be effectively employed for assessing the brittle failure in deep open cast and quarry mines in good quality rocks such as marble.

Fracture mechanical analysis of open cell ceramic foams under multi-axial mechanical loading

Ceramic foams made by replica techniques contain sharp edged cavities, which are potential crack initiators. This paper presents an approach to analyse such structures with respect to their fracture mechanical properties. A fundamental domain of an open cell Kelvin foam is used to model the geometry including the cavities and to generate a finite element model of the structure. Sub-models containing crack tip elements are used to resolve the local stress fields at the vicinity of the sharp-edged cavities. The interaction integral is used to compute the local stress intensity factors under multi-axial loading. Using a homogenization approach, a criterion for brittle failure based on the effective stress state is presented. The failure criteria can be extended to account for the anisotropic behaviour of the foam structure.

A linear elastic-brittle interface model: application for the onset and propagation of a fibre-matrix interface crack under biaxial transverse loads

A new linear elastic and perfectly brittle interface model for mixed mode is presented and analysed. In this model, the interface is represented by a continuous distribution of springs which simulates the presence of a thin elastic layer. The constitutive law for the continuous distribution of normal and tangential initially-linear-elastic springs takes into account possible frictionless elastic contact between adherents once a portion of the interface is broken. A perfectly brittle failure criterion is employed for the springs, which enables the study of crack onset and propagation. This interface failure criterion takes into account the variation of the interface fracture toughness with the fracture mode mixity. A unified way to represent several phenomenological both energy and stress based failure criteria is introduced. A proof relating the energy release rate and tractions at an interface point (not necessarily a crack tip point) is introduced for this interface model by adapting Irwin’s crack closure technique for the first time. The main advantages of the present interface model are its simplicity, robustness and computational efficiency, even in the presence of snap-back and snap-through instabilities, when the so-called sequentially linear (elastic) analysis is applied. This model is applied here in order to study crack onset and propagation at the fibre-matrix interface in a composite under tensile/compressive remote biaxial transverse loads. Firstly, this model is used to obtain analytical predictions about interface crack onset, while investigating a single fibre embedded in a matrix which is subjected to uniform remote transverse loads. Then, numerical results provided by a 2D boundary element analysis show that a fibre-matrix interface failure is initiated by the onset of a finite debond in the neighbourhood of the interface point where the failure criterion is first reached (under increasing proportional load); this debond further propagates along the interface in mixed mode or even, in some configurations, with the crack tip under compression. The analytical predictions of the debond onset position and associated critical load are used for several parametric studies of the influence of load biaxiality, fracture-mode sensitivity and brittleness number, and for checking the computational procedure implemented.