Failure Mode Transition Research Articles

Specific Energy as an Index to Identify the Critical Failure Mode Transition Depth in Rock Cutting

Rock cutting typically involves driving a rigid cutter across the rock surface at certain depth of cut and is used to remove rock material in various engineering applications. It has been established that there exist two distinct failure modes in rock cutting, i.e. ductile mode and brittle mode. The ductile mode takes precedence when the cut is shallow and the increase in the depth of cut leads to rock failure gradually shifted to brittle-dominant mode. The threshold depth or the critical transition depth, at which rock failure under cutting changes from the ductile to the brittle mode, is associated with not only the rock properties but also the cutting operational parameters and the understanding of this threshold is important to optimise the tool design and operational parameters. In this study, a new method termed the specific cutting energy transition model is proposed from an energy perspective which is demonstrated to be much more effective in identifying the critical transition depth compared with existing approaches. In the ductile failure cutting mode, the specific cutting energy is found to be independent of the depth of cut; but in the brittle failure cutting mode, the specific cutting energy is found to be dependent on the depth of cut following a power-law relationship. The critical transition depth is identified as the intersection point between these two relationships. Experimental tests on two types of rocks with different combinations of cutting velocity, depth of cut and back rake angle are conducted and the application of the proposed model on these cutting datasets has demonstrated that the model can provide a very effective tool to analyse the cutting mechanism and to identify the critical transition depth.

Carbon Nanotube Reinforced Composites: The Smaller Diameter, the Higher Fracture Toughness?

Carbon nanotube (CNT) reinforced composites have been drawing intense attentions of researchers due to their good mechanical and physical properties as well as potential applications. The diameter, as an important geometric parameter of CNTs, significantly affects the performance of CNTs in the reinforced composites, not only in a direct way but also in an indirect way by influencing the effective modulus and strength of reinforcing CNTs. This paper investigates the comprehensive effect of CNT diameter on the fracture toughness of CNT reinforced composites by accounting for both direct and indirect influences of CNT diameter based on the three-level failure analysis. The criteria for failure modes are established analytically, and the types of failure mode transition with the corresponding optimal CNT diameter are obtained. It is found that reducing CNT diameter can cause a sudden drop in fracture toughness of composites due to the transition of dominant failure mode. Therefore, the CNTs with smaller diameter do not definitely confer a better fracture toughness on their reinforced composites, and the optimal CNT diameter may exist in the transition between failure modes, especially from interfacial debonding to CNT break. In addition, according to the results, the failure mode of CNT break is suggested to be avoided in the composite design because of the low fracture toughness enhancement of CNTs in this mode. This study can provide guiding reference for CNT reinforced composite design.

Necking and notch strengthening in metallic glass with symmetric sharp-and-deep notches.

Notched metallic glasses (MGs) have received much attention recently due to their intriguing mechanical properties compared to their unnotched counterparts, but so far no fundamental understanding of the correlation between failure behavior and notch depth/sharpness exists. Using molecular dynamics simulations, we report necking and large notch strengthening in MGs with symmetric sharp-and-deep notches. Our work reveals that the failure mode and strength of notched MGs are strongly dependent on the notch depth and notch sharpness. By increasing the notch depth and the notch sharpness, we observe a failure mode transition from shear banding to necking, and also a large notch strengthening. This necking is found to be caused by the combined effects of large stress gradient at the notch roots and the impingement and subsequent arrest of shear bands emanating from the notch roots. The present study not only shows the failure mode transition and the large notch strengthening in notched MGs, but also provides significant insights into the deformation and failure mechanisms of notched MGs that may offer new strategies for the design and engineering of MGs.

Notch strengthening or weakening governed by transition of shear failure to normal mode fracture

It is generally observed that the existence of geometrical discontinuity like notches in materials will lead to strength weakening, as a resultant of local stress concentration. By comparing the influence of notches to the strength of three typical materials, aluminum alloys with intermediate tensile ductility, metallic glasses with no tensile ductility, and brittle ceramics, we observed strengthening in aluminum alloys and metallic glasses: Tensile strength of the net section in circumferentially notched cylinders increases with the constraint quantified by the ratio of notch depth over notch root radius; in contrast, the ceramic exhibit notch weakening. The strengthening in the former two is due to resultant deformation transition: Shear failure occurs in intact samples while samples with deep notches break in normal mode fracture. No such deformation transition was observed in the ceramic, and stress concentration leads to its notch weakening. The experimental results are confirmed by theoretical analyses and numerical simulation. The results reported here suggest that the conventional criterion to use brittleness and/or ductility to differentiate notch strengthening or weakening is not physically sound. Notch strengthening or weakening relies on the existence of failure mode transition and materials exhibiting shear failure while subjected to tension will notch strengthen.

Failure mode transitions of corroded deep beams exposed to marine environment for long period

This paper presents an investigation of the residual structural response of corroded, deep, reinforced concrete (RC) beams. A three-point loading test was carried out on two corroded deep beams that had been stored in a natural corrosive environment for 28years. Two uncorroded beams with the same steel configuration and span were tested to understand the impact of corrosion on the residual mechanical performance of the deep beams. The distribution of corrosion and gravimetric cross-section loss of the tension bars were measured. The corroded tension bars were extracted from the beams to study the residual mechanical properties. The load-bearing capacities of the corroded beams were assessed using the measured mechanical properties and the residual cross-section of the bars according to different failure mechanisms. The results show that, in this case, the corrosion of steel reinforcing bars could change the failure mode of the reinforced concrete beams from shear to flexure.

Metallurgical characteristics and failure mode transition for dissimilar resistance spot welds between ultra-fine grained and coarse-grained low carbon steel sheets

We studied the microstructure and mechanical characteristics of spot welded specimens, fabricated from low carbon steel sheets with different microstructures. Both ultra-fine grained (UFG) steel sheet and coarse grained (CG) steel sheet were used. The refined microstructure of the UFG steel has been produced by severe plastic deformation (SPD) using the constrained groove pressing (CGP) method. The grain size of the base metals was approximately 260nm and 30µm in diameter, respectively, in the UFG and CG steels. Examining the microstructure of a cross section cut through the spot weld reveals a similar grain size and phase distribution in the nugget on both the sides of the initial interface between sheets. Some recrystallization is observed in the heat affected zone on the UFG side as previously reported after the welding of symmetrical UFG–UFG spot welded specimens. The same energy deposit produces larger nuggets after the spot welding of UFG steels. Moreover, the hardness distribution across the nugget changes after welding on both sides of the initial (UFG/CG) interface. This effect is presently attributed to a change in the solidification, cooling rate and tempering after welding, likely because the higher resistance of UFG steel sheets increases the heat release by the Joule effect during spot welding. These changes in the mechanical behavior modify the transition between the interfacial failure (IF) and pull out failure (PF) mode with respect to energy deposit.

Changes in structural style of normal faults due to failure mode transition: First results from excavated scale models

The effects of failure mode transition from tensile to shear on structural style and fault zone architecture have long been recognized but are not well studied in 3D, although the two modes are both common in the upper crust of Earth and terrestrial planets, and are associated with large differences in transport properties. We present a simple method to study this in physical scale models of normal faults, using a cohesive powder embedded in cohesionless sand. By varying the overburden thickness, the failure mode changes from tensile to hybrid and finally to shear. Hardening and excavating the cohesive layer allows post mortem investigation of 3D structures at high resolution. We recognize two end member structural domains that differ strongly in their attributes. In the tensile domain faults are strongly dilatant with steep open fissures and sharp changes in strike at segment boundaries and branch points. In the shear domain fault dips are shallower and fault planes develop striations; map-view fault traces undulate with smaller changes in strike at branches. These attributes may be recognized in subsurface fault maps and could provide a way to better predict fault zone structure in the subsurface.

Influence of heat treatment on bond strength and corrosion resistance of sol–gel derived bioglass–ceramic coatings on magnesium alloy

In this study, bioglass–ceramic coatings were prepared on magnesium alloy substrates through sol–gel dip-coating route followed by heat treatment at the temperature range of 350–500°C. Structure evolution, bond strength and corrosion resistance of samples were studied. It was shown that increasing heat treatment temperature resulted in denser coating structure as well as increased interfacial residual stress. A failure mode transition from cohesive to adhesive combined with a maximum on the measured bond strength together suggested that heat treatment enhanced the cohesion strength of coating on the one hand, while deteriorated the adhesion strength of coating/substrate on the other, thus leading to the highest bond strength of 27.0MPa for the sample heat-treated at 450°C. This sample also exhibited the best corrosion resistance. Electrochemical tests revealed that relative dense coating matrix and good interfacial adhesion can effectively retard the penetration of simulated body fluid through the coating, thus providing excellent protection for the underlying magnesium alloy.

Dynamic crack propagation in a heterogeneous ceramic microstructure, insights from a cohesive model

A 2D plane-strain dynamically propagating crack under tensile loading is simulated with cohesive elements. Information of the main crack is extracted from a diffuse crack network with the use of graph properties. Micro-transgranular fracture properties are calibrated by comparing the crack path transgranular fracture percentage of numerical simulations with experimental data. Results show that although weaker grain boundaries cause more deflections in the crack path and consequently increase the crack length and roughness, the overall toughness is decreased due to reduction of transgranular fracture. The main crack failure mode transition at grain boundaries is compared to static (Hutchinson and Suo, 1992) and dynamic (Xu et al., 2003) classical analytical predictions. It is observed that in many cases, before the arrival of a transgranular fracture at a grain boundary, a micro-daughter crack starts to propagate on the interface. The crack tip extension through this daughter crack/mother crack mechanism complicates the interpretation of the main crack speed in dynamic regime. Yet, the dynamic analysis brings a more accurate prediction of the crack path in microstructures compared to the static one when the data are segregated according to this mechanism.

A discriminatory mechanical testing performance indicator protocol for hand-mixed glass-ionomer restoratives

ObjectivesTo identify a reproducible and discriminatory mechanical testing methodology to act as a performance indicator for hand-mixed glass-ionomer (GI) restoratives. MethodsGroups of 20 (five batches of four) cylinders (6.0±0.1mm height, 4.0±0.1mm diameter) for compressive fracture strength (CFS) and compressive modulus (CM) testing, bars (25.0±0.1mm length, 2.0±0.1mm width, 2.0±0.1mm thickness) for three-point flexure strength (TFS) and tensile flexural modulus (TFM) testing, discs (13.0±0.1mm diameter, 1.0±0.1mm thickness and 10.0±0.1mm diameter, 3.10±0.03mm thickness) for biaxial flexure strength (BFS) and Hertzian indentation (HI) testing, respectively, were prepared using a hand-mixed GI restorative manipulated with 100–20% (in 10% increments) of the manufacturers recommended powder content for a constant weight of liquid. Data were statistically analyzed at p<0.05, the coefficient of variation (CoV) was assessed for the four tests at each powder:liquid mixing ratio investigated (n=9) and a Weibull analysis performed on the CFS, TFS and BFS data to assess the reliability of the data sets. The failure mode and fracture origin of the HI specimens was assessed by fractography. ResultsFor the hand-mixed GI restorative, a progressive reduction in the powder content (by 10% for a constant weight of liquid) resulted in a progressive linear deterioration (p<0.001) in the CFS (R2=0.957), CM (R2=0.961) and TFM (R2=0.982) data. However, no linear deterioration (p>0.05) was identified for the TFS (R2=0.572), BFS (R2=0.81) and HI (R2=0.234). The CoV and Weibull data identified distinct regions – three for the CFS and TFS data and two for the BFS data sets, within the range of powder:liquid mixing ratios investigated. Fractographic analysis of HI specimens revealed a transition in failure mode from bottom-initiated radial cracking to top-initiated cone cracking on reducing the powder content for a constant weight of liquid. SignificanceThe CFS test is the only discriminatory performance indicator for hand-mixed GIs from amongst the four mechanical testing approaches (CFS, TFS, BFS and HI) investigated. The CM and TFM represent an intrinsic material property independent of specimen dimensions and may be used as an adjunct to a mechanical testing approach when investigating hand-mixed GIs.

Phase field modeling of fracture in multi-physics problems. Part II. Coupled brittle-to-ductile failure criteria and crack propagation in thermo-elastic–plastic solids

This work presents a generalization of recently developed continuum phase field models from brittle to ductile fracture coupled with thermo-plasticity at finite strains. It uses a geometric approach to the diffusive crack modeling based on the introduction of a balance equation for a regularized crack surface and its modular linkage to a multi-physics bulk response developed in the first part of this work. This evolution equation is governed by a constitutive crack driving force. In this work, we supplement the energetic and stress-based forces for brittle fracture by additional forces for ductile fracture. These are related to state variables associated with the inelastic response, such as the amount of plastic strain and the void volume fraction in metals, or the amount of craze strains in glassy polymers. To this end, we define driving forces based on elastic and plastic work densities, and barrier functions related to critical values of these inelastic state variables. The proposed thermodynamically consistent framework of ductile phase field fracture is embedded into a formulation of gradient thermo-plasticity, that is able to account for material length scales such as the width of shear bands. It is applied to two constitutive model problems. The first is designed for the analysis of brittle-to-ductile failure mode transition in the dynamic failure analysis of metals. The second is constructed for a quasi-static analysis of crazing-induced fracture in glassy polymers. A spectrum of simulations demonstrates that the use of barrier-type crack driving forces in the phase field modeling of fracture, governed by accumulated plastic strains in metals or crazing strains in polymers, provide results in very good agreement with experiments.

Geometric control of failure behavior in perforated sheets.

Adding perforations to a continuum sheet allows new modes of deformation, and thus modifies its elastic behavior. The failure behavior of such a perforated sheet is explored, using a model experimental system: a material containing a one-dimensional array of rectangular holes. In this model system, a transition in failure mode occurs as the spacing and aspect ratio of the holes are varied: rapid failure via a running crack is completely replaced by quasistatic failure, which proceeds via the breaking of struts at random positions in the array of holes. I demonstrate that this transition can be connected to the loss of stress enhancement, which occurs as the material geometry is modified.

Dynamic shear punch behavior of tungsten fiber reinforced Zr-based bulk metallic glass matrix composites

Dynamic shear punch tests were carried out on the tungsten fiber reinforced Zr-based bulk metallic glass composites. The experimental results show that with the increasing fiber volume fraction, the failure mode of the composites switches from shear to tensile fracture. A new failure criterion, based on the Tsai-Hill criterion and the unified failure criterion for bulk metallic glasses, is proposed to characterize fracture behavior of this bulk metallic glass composite. It is found that the shear-to-normal strength ratio α controls the transition of failure mode of this metallic glass composite. The underlying mechanism of the transition of failure mode is discussed as well.

Ultra-strong collagen-mimic carbon nanotube bundles

In spite of worldwide research, carbon nanotubes (CNTs) still have not fully realized their original promise as ideal reinforcements for composite materials due to a number of challenging issues such as weak interface, poor dispersion, misalignment and lack of optimized design. Here we propose a bio-inspired structure of CNT bundles with controllable crosslink density and staggered pattern of organization that mimic the architecture of natural collagen fiber. Molecular mechanics (MM) simulations show that, under tensile loading, the bio-inspired CNT bundles undergo a transition in failure mode from CNT pull-out to CNT break as the crosslink density increases, with strength an order of magnitude higher than that of the existing strongest conventional carbon fibers. Based on the MM simulations, a generalized tension-shear chain model with four dimensionless parameters is developed to guide the design of CNT bundles for optimized mechanical properties.

Modeling the ductile–brittle failure mode transition in rock cutting

Rock cutting represents a class of problems that exhibits ductile–brittle failure mode transition. Using the depth of cut as a structure size measure, this transition has been shown to follow Bažant’s simple size effect law for quasibrittle material. This study showed that the finite element analysis with the adoption of a continuum damage material model could capture the ductile–brittle transition in rock cutting, and produced the size effect law. One of the major defining characteristics of rock cutting modeling is that no pre-existing notches were introduced, and that the crack grow path was not known a priori. The trend of how nominal stress-relative displacement varied with sizes was found similar to those of notched plates under simple tension or three point bending tests. That might imply a common response feature for mechanisms that satisfy the simple size effect law.

An Improved Heat Equation to Model Ductile-to-Brittle Failure Mode Transition at High Strain Rates Using Fully Coupled Thermal-Structural Finite Element Analysis

In this paper a universal heat equation for fully coupled thermal structural finite element analysis of deformable solids capable of predicting ductile-to-brittle failure mode transition at high strain rates is presented. In the problem mathematical formulation appropriate strain measures describing the onset and the growth of ductile and total damage and heat generation rate per unit volume to model dissipation-induced heating have been employed, which were extended with the heat equation. The model was implemented into a finite element code utilizing an improved weak form for updated Lagrangian formulation, an extended NoIHKH material model for cyclic plasticity of metals applicable in wide range of strain rates and the Jaumann rate in the form of the Green-Naghdi rate in the co-rotational Cauchy’s stress objective integration. The model verification showed excellent agreement with the modelled experiment at low strain rates. Plastic bending of a cantilever has been studied at higher strain rates. A few selected analysis results are presented and briefly discussed.

The effect of nanosized (Ti,Mo)C precipitates on hydrogen embrittlement of tempered lath martensitic steel

Nanosized (Ti,Mo)C precipitates in a high-strength tempered lath martensitic steel are shown to increase resistance to hydrogen embrittlement. The hydrogen-induced failure mode transitions from failure along lath and prior austenite boundaries in the absence of the (Ti,Mo)C precipitates to a mixed failure mode of microvoid coalescence and lath boundary failure in their presence. In the absence of hydrogen and regardless of the presence or absence of the (Ti,Mo)C precipitates, failure occurs via ductile microvoid coalescence. By correlating the macroscale mechanical properties, the fractography of the resulting failure surfaces and observation of the evolved deformation structure immediately beneath the fracture surfaces, a hydrogen-enhanced and plasticity-mediated failure mechanism is proposed in which the role of the nanosized (Ti,Mo)C precipitates is to serve as effective traps for hydrogen.

Characterization of Strength of Intact Brittle Rock Considering Confinement-Dependent Failure Processes

As technologies for deep underground development such as tunneling underneath mountains or mass mining at great depths (>1,000 m) are implemented, more difficult ground conditions in highly stressed environments are encountered. Moreover, the anticipated stress level at these depths easily exceeds the loading capacity of laboratory testing, so it is difficult to properly characterize what the rock behavior would be under high confinement stress conditions. If rock is expected to fail in a brittle manner, behavior changes associated with the relatively low tensile strength, such as transition from splitting to the shear failure, have to be considered and reflected in the adopted failure criteria. Rock failure in tension takes place at low confinement around excavations due to tensile or extensional failure in heterogeneous rocks. The prospect of tensile-dominant brittle failure diminishes as the confinement increases away from the excavation boundary. Therefore, it must be expected that the transition in the failure mechanism, from tensile to shear, occurs as the confinement level increases and conditions for extensional failure are prevented or strongly diminished. However, conventional failure criteria implicitly consider only the shear failure mechanism (i.e., failure envelopes touching Mohr stress circles), and thus, do not explicitly capture the transition of failure modes from tensile to shear associated with confinement change. This paper examines the methodologies for intact rock strength determination as the basic input data for engineering design of deep excavations. It is demonstrated that published laboratory test data can be reinterpreted and better characterized using an s-shaped failure criterion highlighting the transition of failure modes in brittle failing rock. As a consequence of the bi-modal nature of the failure envelope, intact rock strength data are often misinterpreted. If the intact rock strength is estimated by standard procedures from unconfined compression tests (UCS) alone, the confined strength may be underestimated by as much as 50 % (on average). If triaxial data with a limited confinement range (e.g., σ3 ≪ 0.5 UCS due to cell pressure limitations) are used, the confined strength may be overestimated. Therefore, the application of standard data fitting procedures, without consideration of confinement-dependent failure mechanisms, may lead to erroneous intact rock strength parameters when applied to brittle rocks, and consequently, by extrapolation, to correspondingly erroneous rock mass strength parameters. It follows that the strength characteristics of massive rock differ significantly in the direct vicinity of excavation from that which is remote with higher confinement. Therefore, it is recommended to adopt a differentiated approach to obtain intact rock strength parameters for engineering problems at lower confinement (near excavation; e.g., excavation stability assessment or support design), and at elevated confinement (typically, when the confinement exceeds about 10 % of the UCS) as might be encountered in wide pillar cores.

Phase Field Modeling of Brittle and Ductile Fracture

AbstractThe phase field modeling of brittle fracture was a topic of intense research in the last few years and is now well‐established. We refer to the work [1‐3], where a thermodynamically consistent framework was developed. The main advantage is that the phase‐field‐type diffusive crack approach is a smooth continuum formulation which avoids the modeling of discontinuities and can be implemented in a straightforward manner by multi‐field finite element methods. Therefore complex crack patterns including branching can be resolved easily. In this paper, we extend the recently outlined phase field model of brittle crack propagation [1‐3] towards the analysis of ductile fracture in elastic‐plastic solids. In particular, we propose a formulation that is able to predict the brittle‐to‐ductile failure mode transition under dynamic loading that was first observed in experiments by Kalthoff and Winkler [4]. To this end, we outline a new thermodynamically consistent framework for phase field models of crack propagation in ductile elastic‐plastic solids under dynamic loading, develop an incremental variational principle and consider its robust numerical implementation by a multi‐field finite element method. The performance of the proposed phase field formulation of fracture is demonstrated by means of the numerical simulation of the classical Kalthoff‐Winkler experiment that shows the dynamic failure mode transition. (© 2013 Wiley‐VCH Verlag GmbH &amp; Co. KGaA, Weinheim)

On the Failure Behavior of Highly Cold Worked Low Carbon Steel Resistance Spot Welds

Highly cold worked (HCW) low carbon steel sheets with cellular structure in the range of 200 to 300 nm are fabricated via constrained groove pressing process. Joining of the sheets is carried out by resistance spot welding process at different welding currents and times. Thereafter, failure behavior of these welded samples during tensile-shear test is investigated. Considered concepts include; failure load, fusion zone size, failure mode, ultimate shear stress, failure absorbed energy, and fracture surface. The results show that HCW low carbon steel spot welds have higher failure peak load with respect to the as-received one at different welding currents and times. Also, current limits for failure mode transition from interfacial to pullout or from pullout to tearing are reduced for HCW samples. Fusion zone size is the main geometrical factor which affects the failure load variations. Ultimate shear stress of spot welds is increased with decreasing the heat input and for HCW samples at a specific welding current and time, it is lower than that of the as-received ones. Before pullout mode, failure absorbed energy (FAE) for HCW low carbon steel spot welds is higher than that of the as-received one, but after failure mode transition, trend would be vice versa and FAE of the as-received spot welds is extremely higher (about 3 times). In addition, spot welds fracture surface (in interfacial failure mode) for HCW sample is more dimpled which indicates higher energy absorption than that of the as-received one.