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.     

Plane-Strain Propagation of a Fluid-Driven Crack in a Permeable Rock with Fracture Toughness

A solution to the problem of a plane-strain fluid-driven crack propagation in elastic permeable rock with resistance to fracture is presented. The fracture is driven by injection of an incompressible Newtonian fluid at a constant rate. The solution, restricted to the case of zero lag between the fluid front and the fracture tip, evolves from the early-time regime when the fluid flow takes place mostly inside the crack toward the large-time response when most of the injected fluid is leaking from the crack into the surrounding rock. This transition further depends on a time-invariant partitioning between the energy expanded to overcome the rock fracture toughness and the energy dissipated in the viscous fluid flow in the fracture. A numerical approach is used to compute the solution for the normalized crack length and crack opening and net-fluid pressure profiles as a function of two dimensionless parameters: the leak-off/storage evolution parameter and the toughness/viscosity number. Relation of this solution to the various available asymptotic solutions is discussed. Obtained mapping of the solution onto the problem parametric space has a potential to simplify the tasks of design, modeling, and data inversion for hydraulic fracturing treatments and laboratory experiments.     

Decomposition of Damage Tensor in Continuum Damage Mechanics

The principles of continuum damage mechanics are reviewed first for the case of uniaxial tension. The damage variable is then decomposed into two variables called crack damage variables and void damage variables. A consistent mathematical formulation is presented to decompose the damage tensor into two parts: one caused by voids and the other caused by cracks. In the first part of this work, isotropic damage in the uniaxial tension case is assumed. However, the generalization to three-dimensional states of damage is presented in the second part of this work, using tensorial damage variables. It is shown that the components of tensorial crack damage variables and void damage variables are not independent of each other, implying a coupling between the two damage mechanisms. This coupling may be obvious based on the physics of the problem, but a rigorous mathematical proof is given for it. Also, explicit relations governing the components of the crack and void damage variables are derived.     

不同张开度裂隙类岩体循环加卸载下滞回环特征与损伤变形分析

为探究张开度和不同应力等级循环加卸载复合影响下裂隙岩体的损伤特性和裂纹演化规律,利用水泥砂浆制备不同张开度单裂隙类岩石材料,基于RMT-150B岩石力学试验机对类岩石材料开展了3种等级的应力循环加载试验,分析了裂隙类岩石材料的应力—应变曲线特征、滞回环面积变化规律、动弹性模量变化规律及损伤特性.试验结果表明:类岩石材料...     

Distributed Thermal Cracking of AC Pavement with Frictional Constraint

This paper develops a model to simulate the distributed thermal cracking of concrete structures with frictional constraint. This model is developed primarily for the thermal cracking asphalt-concrete (AC) pavement structures; however, with some modifications, it is also applicable to similar problems such as shrinkage cracking of concrete and cracking of reinforced concrete in uniaxial tension. This model reflects the multiscale nature of these problems: microcracking or damage on the mesoscale and localization or redistribution on the macroscale. Randomly distributed fictitious cracks are introduced to represent the inhomogeneities and damage in the material at the mesoscale. Friction is recognized as the mechanism leading to stress redistribution and, therefore, damage localization on the macroscale. When the problem is assumed to be 1D and Coulomb friction is used, a semianalytical numerical scheme is developed. The formation of stress-free open cracks is due to the combination of continuous crack growth and unstable jumps, which involve a nonlinear stability analysis. Equilibrium solutions and stability conditions are given in the paper. Displacement controlled analysis is used to follow the unstable equilibrium path after the structure has lost stability. Numerical simulations clearly show that, with slight mesoscale inhomogeneities and in the presence of a constraining frictional force, microcracking or damage on the mesoscale localizes and finally leads to open cracks distributed at a spacing on the order of the macroscale.     

Damage Modeling of Saturated Rocks in Drained and Undrained Conditions

A new anisotropic damage model is proposed to describe the mechanical and poromechanical behavior of brittle rocks in drained and undrained conditions. Although phenomenological, the model is based on physical grounds of micromechanical analysis. Induced damage is represented by a second rank tensor, which is related to the density and orientation of microcracks. Damage evolution is related to propagation of the microcracks. The effective elastic compliance of the damaged material is obtained from a specific form of the Gibbs free enthalpy function. Irreversible damage-related strain due to residual opening of microcracks after unloading is also captured. The originality of our approach is that a poromechanical model of a saturated medium is constructed by extension of the mechanical model for dry material using micromechanical relationships. All the model parameters are determined from triaxial compression tests performed on dry material. The proposed model is applied to coupled poromechanical tests performed on typical brittle rock in saturated conditions. Comparison between test data and numerical simulations shows overall good agreement. The model proposed is able to describe the main features of poromechanical behavior related to microcracks induced in brittle geomaterials.     

Homogenization Approach of Advection and Diffusion in Cracked Porous Material

The present paper aims at studying the effect of microcracks opening on the diffusion and advection processes in a saturated porous medium. It is based on a micromechanical homogenization approach. The effects of porosity and microcracks are addressed in microscopic and mesoscopic levels to yield estimates of the effective diffusion and permeability tensors. Closed-form expressions and numerical results are obtained. For instance, the effect of the crack density parameter ε on the overall properties is discussed: (1) for a given value of ε, the maximum overall diffusion coefficient decreases for increasing values of crack radius; and (2) for large crack opening, the overall permeability is mainly controlled by ε and almost independent of the applied stress and the crack radius.     

Direct Tensile Tests on Concretelike Materials: Structural and Constitutive Behaviors

The complete stress-strain and stress-crack opening response of a concretelike material loaded in tension is examined starting from a series of displacement-controlled tests on notched cylinders, whose end sections were prevented from rotating (fixed platens). The test results refer to two very high-strength cementitious composites (tensile strength fc ≈ 160–165 MPa) and one “reference” high-strength concrete (fc ≈ 90 MPa). Their behavior (pseudoelastic up to first cracking and cohesive after crack localization) is analyzed to identify the nonlinear stress-strain and stress-crack opening response and to distinguish it from the structural behavior of the specimens. The ascending branch is modeled by studying the stresses at the notch tip by means of Neuber's approach based on stress concentration factors. As for concrete softening (falling branch), an appropriate cohesive law is introduced. Finally, the structural response associated with progressive cracking is systematically analyzed, and once more, it is shown that the load-displacement relationship obtained in a test is hardly a material property.     

Micromechanical Analysis of Anisotropic Damage in Brittle Materials

A general three-dimensional micromechanical approach to modeling anisotropic damage of brittle materials such as concrete, rocks, or certain ceramics is presented. Damage is analyzed as a direct consequence of microcracks growth. Following a rigorous scale change methodology, the macroscopic free energy of the microcracked medium is built considering either open and closed microcracks. Moreover, the microcracks opening/closure criterion as well as the moduli recovery conditions (unilateral effects) are addressed in stress-based and strain-based formulations. An alternative derivation of the homogenized properties, based on the well-known Eshelby method, is also presented and extended here to closed cracks. From the micromechanical analysis, an energy-based yield condition is formulated and illustrated in various stress subspaces. Assuming that the normality rule applies, we then present the damage evolution law and the rate form of the constitutive model. The main capabilities and advantages of the micromechanical model are illustrated through various examples in which material microstructure evolutions are presented.     

Damage Approach for the Prediction of Debonding Failure on Concrete Elements Strengthened with FRP

In this study, experimental and numerical procedures are proposed to predict the debonding failure of concrete elements strengthened with fiber-reinforced polymers (FRPs). Such debonding is modeled as a damage process, which takes place in a band along the bond line (crack band). Three-point bending tests were designed to obtain the softening curve of the crack band. The numerical simulations are conducted using a plastic-damage model. In this approach, the damage resulting in debonding is defined using the softening curve of the crack band. Numerical results are validated against experimental results obtained from single-lap shear tests. The numerical models were capable of predicting the experimentally observed load versus strain behavior, failure load, and failure mechanism of the single-lap shear specimens. The predictive capabilities of the numerical approach presented here were further investigated by means of a parametric study of the single-lap shear test. Results from this study indicate the applicability of the crack band approach to predict the behavior of concrete–FRP joints; they also indicate that the failure load determined from a single-lap shear test is geometry dependent.     

Porothermoelastic Analysis of the Response of a Stationary Crack Using the Displacement Discontinuity Method

Thermally induced volumetric changes in rock result in pore pressure variations, and lead to a coupling between the thermal and poromechanical processes. This paper examines the response of a fracture in porothermoelastic rock when subjected to stress, pore pressure, and temperature perturbations. The contribution of each mechanism to the temporal variation of fracture opening is studied to elucidate its effect. This is achieved by development and use of a transient displacement discontinuity (DD) boundary element method for porothermoelasticity. While the full range of the crack opening due to the applied loads is investigated with the porothermoelastic DD, the asymptotic crack opening is ascertained analytically. Good agreement is observed between the numerical and analytical calculations. The results of the study show that, as expected, an applied stress causes the fracture to open while a pore pressure loading reduces the fracture width (aperture). In contrast to the pore pressure effect, cooling of the crack surfaces increases the fracture aperture. It is found that the impact of cooling can be more significant when compared to that of hydraulic loading (i.e., an applied stress and pore pressure) and can cause significant permeability enhancement, particularly for injection/extraction operations that are carried out over a long period of time in geothermal reservoirs.     

Damage Quantification in Metal Matrix Composites

An experimental procedure is presented to quantify damage in terms of microcrack density. This is accomplished by experimentally evaluating the components of a second-order damage tensor for a metal matrix composite material. The procedure involves the use of a scanning electron microscope and image analyzing software to quantify physical damage features found on a representative volume element. These features are quantified in terms of crack density, which is used in developing the second-order damage tensor. The procedure could be applied to voids in a similar fashion. This procedure is applied to the following two different balanced symmetric layups: (1) (0∕90)S; and (2) (±45)S. Uniaxial tensile loads are used to induce damage in test specimens for each of the layups. Damage evolution is obtained by loading specimens over a range of load intensities from rupture load down to 70% rupture load. A good comparison is obtained between experimentally evaluated and numerically calculated damage values. A companion paper by Voyiadjis and Deliktas used the experimental data presented here in order to verify their proposed formulation for a coupled anisotropic damage model for the inelastic response of composite materials. A physical interpretation of the second-order damage tensor, ;qf, is presented in their work.     

The influence of applied stress,crack length,and stress intensity factor on crack closure

Experimental and analytical evidence for the influence of applied stress, crack length, and stress intensity factor on crack closure is critically compared and evaluated. Fatigue crack opening behaviors are broadly catalogued into three classes. Class I comprises “near-threshold” behavior, where crack closure levels increase with decreasing stress intensity factor. In class II, the “stable” regime, the crack opening level is independent of the stress intensity factor and crack length but is influenced by the applied stress. Class III is characterized by the loss of elastic constraint accompanying extensive yielding at the crack tip or in the remaining ligament, especially with further crack growth. Here, the crack opening level decreases with increasing crack length until little or no closure occurs. These three different classes of closure behavior are extensively illustrated with both experimental data and the results of numerical closure simulations, particularly original finite element (FE) analyses. No single relationship between crack opening levels and the fundamental fatigue parameters is found to hold universally, due to the wide range of mechanisms which cause or influence closure.     

块石对充填体损伤演化影响的声发射表征

块石胶结充填体中块石含量是决定承载能力的关键因素,在RMT-150C材料试验机上进行不同块石含量的尾砂胶结充填体单轴压缩实验,利用1 MHz的宽频声发射传感器采集峰值破坏前各阶段声发射参量,试验结果显示了块石对充填体不同承载阶段应力-应变水平的影响。对比应力-应变-累计声发射事件数关系,发现块石的掺入有利于降低充填体裂纹产生与扩展的速率从而使其承载能力得到加强。分析试验数据得到用累计声发射事件数表征充填体损伤程度的关系式,并得到2组试件的损伤-应变水平关系曲线。分析表明,块石的加入有效抑制充填体前期的损伤增长速率,并使得损伤激增段出现后延趋势。     

Propagation Regimes of Fluid-Driven Fractures in Impermeable Rocks

This paper reviews recent results of a research program aimed at developing a theoretical framework to understand and predict the different modes of propagation of a fluid-driven fracture. The research effort involves constructing detailed solutions of the crack tip region, developing global models of hydraulic fractures for plane strain and radial geometry, and identifying the parameters controlling the fracture growth. The paper focuses on the propagation of hydraulic fractures in impermeable rocks. The controlling parameters are identified from scaling laws that recognize the existence of two dissipative processes: fracturing of the rock (toughness) and dissipation in the fracturing fluid (viscosity). It is shown that the two limit solutions (corresponding to zero toughness and zero viscosity) are characterized by a power law dependence on time and that the transition between these two asymptotic solutions depends on a single number, which can be chosen to be either a dimensionless toughness or a dimensionless viscosity. The viscosity- and toughness-dominated regime of crack propagation are then identified by comparing the general solutions with the asymptotic solutions. This analysis yields the ranges of the dimensionless parameter for which the solution can be approximated for all practical purposes either by the zero toughness or by the zero viscosity solution.     

Fatigue oxidation interaction in a superalloy—application to life prediction in high temperature low cycle fatigue

A study of the interaction between fatigue and oxidation has been carried out in the case of a cast cobalt base superalloy MARM 509 tested in laboratory air at 900 °C. The influence of fatigue cycling on oxidation of this alloy has been studied by quantitative metallography on polished specimens exposed to air in a furnace and on strain-cycled low-cycle fatigue specimens. The oxidation kinetics were determined by thickness measurements for matrix oxidation and by oxidized depth measurements for the preferential oxidation of MC carbides. In both cases the oxidation kinetics were found to be dramatically enhanced by cycling for the matrix oxidation according to a linear relationship with plastic strain amplitude and less dramatically for carbides according to an exponential relationship with the maximum cyclic stress. From these observations a damage equation which describes fatigue damage as a crack growth process has been proposed: the elementary crack advance is a summation of a mechanical contribution due to the fatigue process itself which is described by Tomkins’ equation and of an oxidation contribution which has been evaluated from metallographic measurements. Integration of this crack growth equation gives predicted fatigue lives which are in good agreement with experimental results within a factor of two.     

Processing,Microstructure, and Mechanical Properties of B4C ― TiB2 Particulate Sintered Composites. Part II. Fracture and Mechanical Properties

The fracture response of pressureless sintered boron carbide ceramics containing 5-25 vol.% TiB₂ phase produced via the in-situ chemical reaction between B₄C, TiO₂ and elemental carbon was studied. Both strength and fracture toughness depend on TiB₂ volume fraction, reaching their maximum values of 500 MPa and 4.6 MPa·m^1/2, respectively, at 15 vol.% TiB₂. The observed increase in strength and fracture toughness was ascribed to the interaction between the propagating crack front and local thermal mismatch stress associated with TiB₂ particles. Induced circumferencial microcracking and crack impedance are discussed as the major toughening mechanisms. Spontaneous circumferencial microcracking due to thermal mismatch stress in TiB₂ particles was found to occur when the particle size exceeds its critical value. The theoretical interpretation of spontaneous circumferencial microcracking, toughening via induced microcracking, and crack impedance was justified experimentally.     

Nondestructive Assessment of Damage in Concrete Bridge Decks

Impact-echo tests were performed on a precast, reinforced concrete bridge slab that was removed from a maintenance bridge built in 1953 in South Carolina. Impact-echo tests were first performed to nondestructively assess the initial condition and the distribution of damage throughout the slab by analyzing the variation in propagation wave velocity. It was found that the velocity varied by as much as 900?m/s throughout the slab. After the in-service condition was assessed, the slab was subjected to a full-scale static load test in the laboratory and impact-echo tests were again performed, this time to evaluate the initiation and progression of damage (stiffness loss and crack development) within the slab. After structural failure of the slab, a reduction in propagation wave velocity up to 6% was observed correlating to a reduction in slab stiffness. Cracks were detected within the concrete slab that were not visible from the surface. Areas with preexisting damage experienced more crack growth when subjected to the load test than those that were initially intact. Locations exhibiting stiffness loss, crack propagation, and localized damage can be differentiated such that the method can be used to make decisions between rehabilitating and replacing concrete bridge decks depending upon the severity of damage.