Microcrack Shielding Research Articles

Exceptional fracture toughness in a high-strength Mg alloy with the synergetic effects of bimodal structure, LPSO, and nanoprecipitates

Addressing the strength-toughness trade-off issue has been highly desirable for high strength Mg alloys. Herein, an Mg-9Gd-4Y-1Zn-0.5Zr (wt %) alloy is designed, and a yield strength of 430 MPa and plane-strain fracture toughness KIc of 23.1 MPa·m1/2 are achieved. Intrinsically, significant stress dissipation is induced by interactions between the tensile twinning and the kinking of the lamellar γ' phase, leading to increased KIc. Owing to the residual stress release, the fracture resistance is remarkably improved by the non-basal 〈a〉 and 〈c + a〉 dislocations activated in the fine dynamic recrystallized (DRXed) grains. Extrinsically, the microcracks initiated along the interfaces between lamellar γ' phase and α-Mg matrix facilitate the reduction of local crack-driving forces, resulting in an enhanced KIc. Moreover, the underlying toughening mechanisms were revealed, including the crack propagation path deflection caused by coarse deformed grains and microcrack shielding by the long-period stacking ordered (LPSO) and lamellar γ' phases.

Investigation of the Thermal Shock Behavior of Mo‐Containing TiAl Alloys

TiAl alloys undergo cyclic temperature changes during use, the process of which can be simulated by the thermal shock test. A systematic investigation of the thermal shock behavior of four Mo‐containing TiAl alloys is conducted. The increase in Mo content from 1.0% to 4.0% causes the gradual decrease in the volume fraction of γ/α2 lamellar colony, while the volume fraction of equiaxed γ and βo phases gradually increases. At the same time, the thermal shock resistance of the TiAl alloys decreases as the Mo content increases. After thermal shock, cracks often occur within the lamellae and extend in a zigzag manner for TiAl−1.0Mo and TiAl−1.5Mo alloys. Their thermal shock resistance is enhanced by crack deflection, bridging, and microcrack shielding. For TiAl−2.0Mo and TiAl−4.0Mo alloys, cracks occur at the grain boundaries or within the γ phase and extend straight, with the result that these two alloys have worse thermal shock resistance than the other two alloys due to the limited effect of microcrack shielding. In addition, the microstructure stability of TiAl alloys after thermal shock is discussed, and there is a critical value of Mo content between 3.13% and 5.67%, which inhibits the βo → ω phase transition.

Meso-scale mixed-mode fracture modelling of reinforced concrete structures subjected to non-uniform corrosion

Corrosion-induced concrete cracking is a significant problem affecting the durability of reinforced concrete structures. Considerable research has been carried out in addressing this problem but few have considered the cracking process of concrete as a mixed-mode fracture and the concrete as a multi-phase material. This paper develops a meso-scale mixed-mode fracture model for the cracking of concrete structures under non-uniform corrosion of reinforcement. Concrete is treated as a three-phase heterogeneous material, consisting of aggregates, mortar and interfaces. An example is worked out to demonstrate the application of the derived model and is then partially verified against previously published experimental results. In agreement with experimental results, the new model reproduces the observation that microcracks tend to form first at the interfaces before they connect to generate a discrete crack. Toughening mechanisms, e.g., microcrack shielding, crack deflection, aggregate bridging and crack overlap, have been captured in the model. Further, effects of aggregate randomness on the crack width development of concrete structures, differences between uniform and non-uniform corrosion and a comprehensive parametric study have been investigated and presented.

Promoting the mechanical properties of Ti42Al9V0.3Y alloy by hot extrusion in the α+β phase region

Hot extrusion was conducted in the α+β phase region for promoting mechanical properties of Ti42Al9V0.3Y. The microstructures and tensile properties before and after hot extrusion were studied. The results show that the microstructure of the as-cast alloy mainly consists of massive γ phase in β matrix and the as-extruded alloy mainly consists of lamellar α2/γ, lamellar β/γ, and strip γ propagating from elongated β phase. In the as-cast alloy, the predominantly observed fracture mode is transgranular cleavage failure at room temperature and intergranular fracture at 650–750 °C. After hot extrusion, it transforms into transgranular cleavage-like failure, including translamellar cleavage and delamination. The excellent tensile properties of the as-extruded material are attributed to the obvious refined microstructure with broken YAl2 particles and the micro-crack shielding action of the TiAl lamellasome.

On the mechanism of crack propagation resistance of fully lamellar TiAl alloy

The study was done using notched two-colony thick tensile specimens of a directionally solidified cast fully lamellar TiAl alloy. In-situ observations of fracture processes in scanning electron microscope (SEM) were combined with section-to-section related observations of fracture surfaces to investigate the crack growth process. Finite element method (FEM) calculations are carried out to evaluate the stresses for propagating cracks. The results reveal that: (1) the reason why enhancement of applied load is required to propagate the main crack, was attributed to that the main crack observed at the surface did not extend all the way through the specimen's thickness thus the stress field was still controlled by the notch, in which a definite stress required for extending a crack tip should be kept by increasing the applied load. (2) Crack propagation resistance is enhanced at colony boundaries, only when a change occurs from an inter-lamellar propagation to a trans-lamellar propagation (3) Ligament bridging toughening phenomena can be integrated into aforementioned mechanism. As a whole the processes of new crack nucleation with bridging ligament formation decreases the crack propagation resistance rather than increasing it. (4) In case the majority of microcracks are surface cracks, the effect of microcrack shielding is not obvious.

A Brief Evaluation of Approximation Methods for Microcrack Shielding Problems

This note can be regarded as a supplement of a paper entitled “On the Use of Approximation Methods for Microcrack Shilding Problems” (H. Cai and K. T. Faber, 1992, ASME J. Appl. Mech. 59, 497–501). In this note, an effective approximation method for microcrack shielding problems is introduced briefly and is further used to study the examples given in the Cai and Faber paper for the interaction of a macrocrack with microcracks. It is found that the applicability range of the present approximation method in which the errors are acceptably small is much larger than that of the approximation methods listed in the Cai and Faber paper.

Near‐tip microcrack shielding in advanced ceramics

ABSTRACTRecent manufacturing of advanced ceramics has developed phase transformation and cracks tilted or bridged to enhance ceramic‐inherent toughness. However, main crack and near‐tip microcracks interaction is another prominent means in toughening of the ceramic materials. In this study, mechanics of discrete model combined with alternative iterating numerical technique is developed and applied in assessment of main–microcrack interaction. Consequences of main–microcrack interaction can either shield or amplify the resulting main crack stress intensity factor, which accounts for the increase or decrease of ceramic toughness. Numerical outcomes show good agreement with the available solutions in the literatures; in addition results also reveal that the toughness shielding or amplification is dependent on the type of loadings as well as location/orientation of the microcrack. Nevertheless, residual normal stress plays an important role in shielding/amplification region trade‐off. This work may provide a useful quantitative tool in ceramic design and a valuable insight into main–micro interaction phenomenon.

An investigation of contact deformation, fracture, and fatigue behavior in bulk metallic glasses

This article presents the results of a study of the contact-induced deformation, fracture/resistance-curve behavior, and fatigue-crack-growth behavior of two bulk metallic glasses (BMGs), one in the fully amorphous condition and the other containing a dispersion of microscale crystallites. Hertzian contact indentation experiments were performed on both materials under monotonic loading conditions. The contact-induced deformation characteristics observed in the Hertzian experiments are then compared with the stress distribution determined from finite-element analyses. In addition, the cracking patterns associated with resistance-curve behavior in single-edge notched bend (SENB) specimens are incorporated into a fracture-mechanics framework for the estimation of toughening due to microcrack shielding. The predicted steady-state toughness values are shown to be comparable to the measured values obtained from resistance-curve experiments. Subsequently, fatigue-crack-growth rare data obtained at stress ratios of 0.1 and 0.5 are presented and analyzed using a crack-tip opening displacement (CTOD) model. The implications of the results are then discussed.

A semi-infinite interface crack interacting with subinterface matrix cracks in dissimilar anisotropic materials. I. Fundamental formulations and the J-integral analysis

The J-integral analysis is presented for the interaction problem between a semi-infinite interface crack and subinterface matrix microcracks in dissimilar anisotropic materials. After deriving the fundamental solutions for an interface crack subjected to different loads and the fundamental solutions for an edge dislocation beneath the interface, the interaction problem is deduced to a system of singular integral equations with the aid of a superimposing technique. The integral equations are then solved numerically and a conservation law among three values of the J-integral is presented, which are induced from the interface crack tip, the microcracks and the remote field, respectively. The conservation law not only provides a necessary condition to confirm the numerical results derived, but also reveals that the microcrack shielding effect in such materials could be considered as a redistribution of the remote J-integral. It is this redistribution that does lead to the phenomenological shielding effect.

Interaction between an interface crack and subinterface microcracks in metal/piezoelectric bimaterials

A semi-infinite interface macrocrack interacting with multiple oriented subinterface microcracks in the process zone near the macrocrack tip in metal/piezoelectric bimaterials is studied. After deriving the elementary solutions for a semi-infinite interface crack and a special subinterface crack under various loading conditions, the present interaction problem is deduced to a system of integral equations with the aid of the pseudo-traction-electric-displacement method. The integral equations are then solved numerically by using the Chebyshev numerical integration technique. After doing so, the variable tendencies of the stress intensity factors at the interface macrocrack tip versus the location angle and the orientation angle of the subinterface cracks, and the distance between the interface crack tip and the center of the subinterface microcrack are derived and discussed. The numerical results are shown in the figures. Detailed comparisons between the results under the compound mechanical-electric loading conditions and those derived under purely mechanical loading conditions are performed. Some conclusions are given which are certain to be useful for investigating the microcrack shielding problems in metal/piezoelectric bimaterials.

Further investigation of interaction between interface macrocrack and parallel microcracks in bimaterial anisotropic solids

In this paper, with the aid of superimposing technique and the Pseudo Traction Method (PTM), the interaction problem between an interface macrocrack and parallel microcracks in the process zone in bimaterial anisotropic solids is reduced to a system of integral equations. After the integral equations are solved numerically, a conservation law among three kinds ofJ-integrals is obtained which are induced from the interface macrocrack tip, the microcrack and the remote field, respectively. This conservation law reveals that the microcrack shielding effect in such materials could be considered as the redistribution of the remoteJ-integral.

Strengthening contribution arising from residual stresses in Al 2O 3/ZrO 2 composites: a piezo-Spectroscopy investigation

Piezo-spectroscopy measurements have been performed in order to obtain information about the internal stresses in a series of (2 mol% Y 2O 3-stabilized) ZrO 2 ceramics added with fine Al 2O 3 dispersoids. These composites were previously reported to fracture at remarkably high strength levels. Residual stresses arising from the thermal mismatch between the ZrO 2 matrix and the Al 2O 3 dispersoids were found to be of the order of several hundreds MPa, in agreement with the predictions of an elastic stochastic stress analysis. Taking into consideration the results of the present piezo-spectroscopic analysis, a micromechanism of microcrack shielding by residual microstresses has been proposed, which overlaps with the effect of phase transformation on strength. A theoretical assessment is given which enables one to explain the presence of a maximum of strength at 0·2–0·4 volume fraction of Al 2O 3 dispersoid.

Effect of the T-Stress in Microcrack Shielding Problems

The effect of the T-stress in microcrack shielding problems is studied by solving the interaction problem of a macrocrack with near tip microcracks applying a discrete model. The T-stress has no effect on the results for the parallel microcrack cases; however, it plays an important role for the oriented microcrack cases, especially for large values of the T-stress and large distances of the microcrack center from the macrocrack tip. In determining the shielding or amplification effect of the oriented microcracks, it is necessary to consider the effect of the T-stress. The effect of the T-stress on microcrack shielding or amplification is substantially dependent on the sign and magnitude of the T-stress as well as on the geometry of the microcrack arrangement. The contribution to the J-integral induced from the microcracks is reexamined by considering the T-stress and shown to be still in a consistent relation with those induced from the macrocrack tip and the remote stress field.

Explicit formulation of theJ 2-integral in anisotropic materials and its application in microcrack shielding problems

The explicit formulation of theJ 2-integral in anisotropic bodies and its application in microcrack shielding problems are discussed. With analytical treatments and numerical examinations, it is proved that there is a redistribution law for the remoteJ-integral in a discrete model of microcrack shielding problems, i.e. the projected conservation law of theJ k -vector. In this law, theJ 2-integral which was disregarded by Herrmann (1981) is proved to be of the same significance as theJ 1-integral. It is also concluded that the two energy dissipative processes due to the microcrack damage, i.e. the reduction in the effective moduli and the release of residual stresses, can be described by using the dissipation of the remoteJ-integral spreading across the microcrack damage zone.

On the contribution of subinterface microcracks near the tip of an interface macrocrack to the J-integral in bimaterial solids

The J-integral analysis is performed for the plane problems of multiple subinterface microcracks near the tip of an interface macrocrack in bimaterial solids. The analysis starts from a general solution based on the “pseudo-traction” method which has been addressed thoroughly in homogeneous cases. The contribution to the J-integral induced from the subinterface microcracks is shown in a consistent relation with those induced from an interface macrocrack tip and the remote stress field. A new technique is developed to evaluate the second component (being expressed by J2∗ in this paper) of the well-known Jk-vector of a subinterface crack for considering a contour enclosing the whole crack, which is necessary to evaluate the contribution to the J-integral arising from the subinterface microcracks. The consistency of the J-integral for numerical examples is proved, where two kinds of material combinations presented by Hutchinson et al. [ASME J. Appl. Mech., 1987, 54, 828–832] are considered. Some discussion and conclusions are then given which seem very useful in the investigation of microcrack shielding problems in bimaterial cases.

Toughening mechanisms in titanium aluminides

The relevant toughening mechanisms in two-phase titanium aluminides are reviewed in order to elucidate microstructure/fracture toughness relationships. Both intrinsic and extrinsic toughening mechanisms are present in Ti3Al- and TiAl-base alloys. The former affects the initiation toughness(i.e., KIC value) at the onset of crack extension, while the latter leads to crack growth toughness by instigating a resistance-curve behavior. Intrinsic toughening arises from matrix slip and ductile-phase blunting. In contrast, extrinsic toughening originates from crack deflection, ductile-phase bridging, shear ligament toughening, microcrack shielding, twin toughening, and the growing crack singularity. The influence of microstructure on toughening mechanisms in two-phase Ti3Al- and TiAl-base alloys is discussed, with particular emphasis on the need to control the microstructure in order to achieve the desired mechanical properties.

On the Use of Approximation Methods for Microcrack Shielding Problems

There is experimental evidence that stress-induced microcracking near a macrocrack tip enhances the fracture toughness of brittle materials. In considering the interaction of the macrocrack with multiple microcracks using a discrete model, it is essential to use approximation methods in order to keep the amount of the computation to a tractable level. However, when crack distances are small, the results of the approximation methods can be significantly different from the numerical solution based upon the exact formulation. The results obtained by these approximation methods will be compared with the numerical solution to show the applicability ranges in which the errors are acceptably small. The use of results obtained by the approximation methods outside applicability ranges in literature is shown to lead to incorrect conclusions concerning microcrack shielding.

An experimental study of toughening and degradation due to microcracking in a ceramic composite

An experimental investigation has been carried out to study the effects of controlled microcracking on the fracture resistance of brittle solids. The material chosen as a model system for the experimental study is an aluminum oxide reinforced with 33 vol.% SiC whiskers. The experimental program involves the determination of fracture toughness at room temperature on four-point flexure specimens containing sharp, through-thickness precracks where different amounts of microcrack damage are introduced a priori at different elevated temperatures and tensile load levels. The room temperature fracture initiation toughness of the pre-damaged material with a controlled amount of small-scale microcracking ahead of the stationary macrocrack is compared and contrasted with that of the undamaged material and the enhancement or reduction in fracture initiation toughness is estimated. Detailed transmission electron microscopy of the crack-tip damage zone has been conducted in an attempt to examine the mechanisms of permanent degradation and of microcrack formation. These observations reveal that the mechanism of microcracking by the coalescence of intergranular/interfacial cavities in the ceramic composite exposed to the high-temperature environment dominates over any other possible source of permanent deformation such as dislocation plasticity for the conditions of the experiments of this study. The fracture test results suggest that some toughness gains can be achieved, in certain cases, despite the creation of damage which primarily involves microcracking ahead of the crack-tip; however, significant increases in microcrack density, in fact, lead to a deterioration in the resistance of the material to fracture. The experiments of this study are discussed in the context of available theories of microcrack shielding, material degradation, and crack-microcrack interactions, as well as possible effects of dislocation plasticity and residual stresses.

Influence of microstructure on intrinsic and extrinsic toughening in an alpha-two titanium aluminide alloy

The toughening mechanisms in the Ti-24A1-11Nb (Ti-24-11) alloy have been identified previously to include crack-tip blunting, bridging, and deflection by the ductileβ phase, while the fracture mechanisms involve the nucleation, growth, and linkage of microcracks with the main crack. By performing appropriate theoretical analyses and critical experiments, the relative contributions of intrinsic and extrinsic toughening mechanisms, including microcrack shielding, crack-tip blunting, bridging, and deflection by theβ phase, to the initiation and crack growth toughness values of the Ti-24-11 alloy have been studied for three microstructures. The results indicate that the microstructure affects not only the amount of toughness enhancement, but also the type of toughening mechanisms present in the Ti-24-11 alloy. The initiation toughness in Ti-24-11 arises from the matrix toughness, crack-tip blunting, and, occasionally, from crack deflection by the ductile phase. As a result, theKIC values increase with the volume fraction of the ductile phase. In contrast, the resistance curve behavior originates from (1) a change of crack-tip singularity, which occurs when the blunted crack extends into the plastic zone, (2) crack bridging by ductile phase and shear ligaments, and (3) microcrack shielding, which occurs mostly at elevated temperatures.

A numerical simulation of the R-curve behavior in microcracking materials

We propose several models for crack propagation in ceramic materials with microcrack formation and coalescence. The models differ in the relative time scales involved in the internal relaxation processes and the external loading rate. We find that when the external loading rate is very high, a rising R-curve is obtained. For slow external loading, the results depend upon the relative rate of the different internal relaxation processes and upon the distribution of the critical stresses needed to form the microcracks. In this regime, the existence of a rising R-curve behavior is found to be primarily due to microcrack shielding.