A numerical and experimental study of aggregate-induced shrinkage cracking in cementitious composites

Aggregates in cementitious composites subject to drying lead to mechanical restraint of the matrix shrinkage, which under certain conditions may lead to internal microcracking. In the present work this phenomenon is investigated using a two-dimensional (2D) numerical model and an approximate 2D experimental approach. Experimental and simulated samples with simplified and matching spatial aggregate distributions were produced to make a quantitative comparison between experiments and model predictions. In particular, the effects of aggregate size and volume fraction on the degree of internal microcracking are assessed. The main challenges of performing a quantitative comparison are highlighted and discussed. These are related to: (i) the difficulty of designing experiments without moisture gradient effects; (ii) the experimental crack detection limit; and (iii) the role of the creep response of the matrix phase in the model. The results suggest the existence of a critical aggregate size below which aggregate-restraint does not cause detectable microcracking.     

Effect of Nucleation on Transformation Toughening

A simple model is presented to account for the effect of martensitic nucleation in ZrO₂ particles on theoretical predictions of toughness enhancement during transformation toughening. The model allows for shear and volumetric strain contributions during nucleation, whereas only volumetric strain contributes to toughness enhancement. It is predicted that toughness enhancement results for both stationary and growing cracks. The predicted toughness enhancement exceeds the theoretical prediction for the case when only volumetric strain is allowed to operate. The important material property is identified to be the ratio of volumetric to shear strain during nucleation of the martensitic product in the transformation from tetragonal to monoclinic symmetry of the ZrO₂ particles.     

A Simple Calculation of Process-Zone Toughening by Microcracking

The method introduced by Evans and colleagues to calculate transformation toughening resulting from a dilatant transformation is extended, using the Eshelby "equivalent inclusion" approach, to treat the case of toughening resulting from microcracking.     

Synergism of Toughening Mechanisms in Whisker-Reinforced Ceramic-Matrix Composites

The improved fracture resistance of whisker-reinforced ceramic-matrix composites involves more than one energy-absorbing mechanism. The possible mechanisms are reviewed and a micromechanical model evaluating the relative contributions to the overall toughness is presented. The mechanisms involve microcracking, load transfer, bridging, and crack deflection. The synergism of these mechanisms is examined using an energy release rate balance equation. The basic assumption of the proposed model is that the load transfer between the matrix and the whiskers is due to Coulomb friction. The model has been applied to an Al₂O₃/SiC whisker composite and shows reasonable agreement with reported experimental results. The role of the thermal residual stresses is also examined in light of the frictional load transfer assumption.     

Modeling deformation of a melt-infiltrated SiC/SiC composite under fatigue loading

Results from fatigue experiments done on a SiC/SiC composite are presented. A micromechanics-based model is used to study the observed behavior under cyclic loading. The model includes consideration of progressive damage, creep and oxidation of the fiber and matrix. Comparison of model predictions with test data showed that the deformation during fatigue in this material is explained primarily by damage in the form of matrix microcracking and interface debonding, in combination with creep under the cyclic load. Stiffness of the material was observed to not change significantly during fatigue indicating that the contribution of fiber fracture to deformation is limited. Fiber fracture however was found to determine final failure of the composite. Failure under cyclic fatigue loading was found to be affected by load transfer from the matrix to the fiber due to damage and creep, and by progressive degradation of the load-carrying fibers due to the combined effect of oxidation and load cycling.     

On modeling of microstresses and microcracking generated by cooling of polycrystalline porous ceramics

Motivated by experimental observations on the temperature dependence of the effective Young's modulus and thermal expansion of porous polycrystalline ceramics, we model microstresses generated by cooling, and resulting microcracking. These microstresses are due to the mismatch in the thermal expansion and elastic properties between anisotropic randomly oriented grains. In the example of cordierite, the thermal expansion anisotropy is very strong, and one of the three principal values of the thermal expansion tensor is even negative. This necessitates tensor treatment of the problem. Model results shed light on the strength of interfaces, by relating the onset of microcracking observed at certain temperature (identified by the onset of stiffness reduction) to maximal tensile stresses at this temperature. The model also provides a possible explanation of the fact that, at a certain temperature drop, microcracking stops (as indirectly implied by thermal expansion data).     

On the Thermoelastic Martensitic Transformation in Tetragonal Zirconia

Recent evidence is summarized showing that the tetragonal ( t ) → monoclinic ( m ) martensitic transformation in ZrO₂ can occur thermoelastically in certain ZrO₂-containing ceramics, and that microcracking accompanying the transformation is more common than had previously been recognized. The implications of these new data for the conditions under which the stress-induced transformation is irreversible, and for the particle size dependence of the transformation start ( M _s), temperature, are discussed.     

Dynamic Stress-Induced Transformation and Texture Formation in Uniaxial Compression of Zirconia Ceramics

Transformation plasticity in Mg-PSZ and Y-TZP ceramics is investigated using a novel stress reversal Hopkinson bar technique recently developed at the University of California–San Diego (UCSD) for dynamic recovery experiments.¹ The longitudinal and transverse strains are measured by strain gauges mounted on the specimen. The specimens are loaded until transformation reaches saturation. Reloading of the same specimens to higher stress levels does not reveal additional inelasticity. Cuboid specimens which have been loaded initially to attain transformation saturation are then reloaded in a direction perpendicular to the first loading. The second loading produces additional inelasticity and microcracking, indicating the formation of transformation texture in each loading under uniaxial compression. Microscopic observations, and the results of ultrasonic and X-ray diffraction measurements, as well as micromechanical modeling of the damage evolution are discussed.     

Crack-Growth Resistance of Microcracking Brittle Materials

A mechanics model of microcrack toughening is presented. The model predicts the magnitude of microcrack toughening as well as the existence of R -curve effects. The toughening is predicated on both the elastic modulus diminution in the microcrack process zone and the dilatation induced by microcracking. The modulus effect is relatively small and process-zone-size-independent. The dilatational effect is potentially more substantial, as well as being the primary source of the R curve. The dilatational contribution is also zone-size-dependent. The analysis demonstrates that microcrack toughening is less potent than transformation toughening.     

Modeling the effects of thermal and mechanical load cycling on a C/SiC composite in oxygen/argon mixtures

Analytical solutions of and experimental results on the strain response of a carbon fiber reinforced SiC matrix composite under thermal and mechanical load cycling in O₂/Ar are presented. Thermal strain and mechanical strain were shown to approximately sustain linear relationships with temperature T and stress σ, respectively; whereas baseline strain was considered to be damage-dependent, resulting from a combination of two major contributing mechanisms: (a) a physical mechanism in the form of matrix microcracking accompanied by fiber debonding, sliding or fracture and (b) a chemical mechanism in the form of the fiber oxidation associated with longitudinally increased compliance. Based on these analyses a theoretical model, taking into account the thermal strain, mechanical strain and baseline strain, was theoretically formulated with respect to the contribution of each on the overall total strain and to their generation mechanisms. The proposed model gave correct and reliable predictions.     

Stress–Strain Behavior of Alumina, Magnesia-Partially-Stabilized Zirconia, and Duplex Ceramics and Its Relevance for Flaw Resistance, KR-Curve Behavior, and Thermal Shock Behavior

The stress–strain behavior for Al₂O₃ of different grain size, for three different Mg-PSZ grades, and for various differently composed duplex structures is investigated and compared with their flaw resistance, K^R -curve behavior, and thermal shock behavior measured in previous works. The experimental results seem to reveal that, for most materials, quasi ductility increases with increasing flaw resistance, increasingly pronounced K^R -curve behavior, and increasing thermal shock retained strength. However, brittle ceramics can exhibit rising K^R -curves, whereas pronounced quasiductile materials can exhibit flat K^R -curves. An explanation for the apparent pseudo relationship between quasi ductility and K^R -curve behavior may be that, apart from genuine transformation ductility, most quasi-ductile effects such as microcracking have only a minor contribution to rising R -curve behavior, but require the existence of strong residual stresses, which are, on the other hand, responsible for the occurrence of most toughening mechanisms. Also discussed is the influence of microcracking on flaw resistance and thermal shock strength degradation.     

R-Curve Behavior of a Polycrystalline Graphite: Microcracking and Grain Bridging in the Wake Region

The contributions of nonlinear fracture processes both in the microcracking frontal process zone and in the following wake region and of grain bridging to crack-growth resistance parameters are discussed in terms of the R-curve behavior of an isotropic polycrystalline graphite. The R-curve behavior of the graphite is characterized by rapidly increasing values at the initial stage of crack extension (Δa≤1 to 2 mm) followed by a steady-state plateaulike region and then a distinct decrease when the primary crack tip approaches the end surface of the test specimen. Scanning electron microscopy of fracture mechanics specimens revealed a dominant role of grain bridging in the following wake regions on the rising R-curve behavior and confirmed the significant size effect of the large-scale microcracking process zone on the falling R-curve behavior. The stress-derived fracture toughness (K_R) and the energy fracture toughness (R_c) are discussed in relation to the micro-cracking residual strain.     

水泥稳定碎石早期损伤自愈合疲劳特性试验研究

为了使水泥稳定碎石基层微裂技术在实际工程应用中的理论依据得到进一步完善,对水泥稳定碎石早期损伤自愈合疲劳性能进行全面和深入的研究.使用振动压实仪成型水泥稳定碎石梁式试件,并在不同微裂时间对梁式试件进行不同程度的微裂;在龄期为90d时,通过弯拉强度试验和疲劳试验测定微裂前后水泥稳定碎石材料的弯拉强度和疲劳寿命次数,并对试验结果进行分析.研究微裂后水泥稳定碎石材料早期损伤自愈合疲劳寿命的变化规律,并且应用Weibull分布建立了水泥稳定碎石微裂疲劳方程.研究结果表明:微裂前后的水泥稳定碎石材料疲劳寿命随应力水平增加均呈现出线性递减的规律;微裂程度为20％和30％时,水泥稳定碎石材料的疲劳寿命与未微裂时水平基本一致,微裂程度为40％的水泥稳定碎石材料的疲劳寿命相对降低,但仍在使用要求范围内;微裂时间对疲劳试验结果无显著性影响.     

Micromechanics of Failure Waves in Glass: II, Modeling

In an attempt to elucidate the failure mechanism responsible for the so-called failure waves in glass, numerical simulations of plate and rod impact experiments, with a multiple-plane model, have been performed. These simulations show that the failure wave phenomenon can be modeled by the nucleation and growth of penny-shaped shear defects from the specimen surface to its interior. Lateral stress increase, reduction of spall strength, and progressive attenuation of axial stress behind the failure front are properly predicted by the multiple-plane model. Numerical simulations of high-strain-rate pressure-shear experiments indicate that the model predicts reasonably well the shear resistance of the material at strain rates as high as 1 × 10₆/s. The agreement is believed to be the result of the model capability in simulating damage-induced anisotropy. By examining the kinetics of the failure process in plate experiments, we show that the progressive glass spallation in the vicinity of the failure front and the rate of increase in lateral stress are more consistent with a representation of inelasticity based on shear-activated flow surfaces, inhomogeneous flow, and microcracking, rather than pure microcracking. In the former mechanism, microcracks are likely formed at a later time at the intersection of flow surfaces. in the case of rod-on-rod impact, stress and radial velocity histories predicted by the microcracking model are in agreement with the experimental measurements. Stress attenuation, pulse duration, and release structure are properly simulated. It is shown that failure wave speeds in excess to 3600 m/s are required for adequate prediction in rod radial expansion.     

Crack Initiation in Borosilicate Glass-SiC Fiber Composites

The initiation of matrix microcracking was investigated in unidirectional glass matrix composites having controlled fiber spacing. Observations were taken from composites consisting of regular arrays of TiB₂-coated SIGMA 1240 and carbon-coated SCS-6 monofilament SiC fibers in a series of borosilicate glasses. The thermal expansion mismatch between the fibers and glass matrix was varied such that the resulting radial stresses after processing ranged from tensile to compressive. The glass strongly bonds to the TiB₂-coated SIGMA 1240 fiber but weakly bonds to the carbon coating of the SCS-6 fiber, allowing the investigation of the effects of bonding at the fiber/matrix interface. The observed crack initiation stresses of the various composites are compared to predictions based on a previously developed semiempirical model and used to study the influence of the volume fraction of fibers, residual stress state and interface strength.     

Implications of Transformation Plasticity in ZrO2-Containing Ceramics: I, Shear and Dilatation Effects

Transformation plasticity in ZrO₂-containing ceramics generally exhibits shear and dilatation effects of comparable magnitude. The coupling between external stresses and crystallographic strains assists the tetragonal-monoclinic transformation, which, via shear localization, gives rise to macroscopic shear and dilatant deformation. Application of a yield criterion based on both shear and dilatation effects correctly correlates deformation data from tension, compression, bending, and indentation, and further delineates a crack-tip process zone comparable to the one observed experimentally. Similar shear and dilatation effects in microcracking due to transformation plasticity are explored. These findings suggest that the strength of the ultimate transformation-toughened structural ceramics should be yield limited and sensitive to the stress state. Strategies for fracture control are recommended.     

Dual mechanism model for fluid particle breakup in the entire turbulent spectrum

This work provides an in-depth understanding of different breakup mechanisms for fluid particles in turbulent flows. All the disruptive and cohesive stresses are considered for the entire turbulent energy spectrum and their contributions to the breakup are evaluated. A new modeling framework is presented that bridges across turbulent subranges. The model entails different mechanisms for breakup by abandoning the classical limitation of inertial models. The predictions are validated with experiments encompassing both breakup regimes for droplets stabilized by internal viscosity and interfacial tension down to the micrometer length scale, which covers both the inertial and dissipation subranges. The model performance ensures the reliability of the framework, which involves different mechanisms. It retains the breakup rate for inertial models, improves the predictions for the transition region from inertia to dissipation, and bridges seamlessly to Kolmogorov-sized droplets.     

High‐temperature fracture toughness of mullite with monoclinic zirconia

Reactive sintering of zircon and alumina and zirconia additions to mullite are well‐established methods for improving the poor fracture toughness of mullite. While it is clear that transformation toughening is responsible for the improved toughness by addition of partially stabilized zirconia, it is not clear why adding unstabilized zirconia increases the toughness although microcracking and crack deflection have been suggested. Therefore, the fracture toughness of a mullite composite with 20 vol% unstabilized zirconia and a monolithic mullite were investigated at ambient conditions and at temperatures up to 1225°C. It was found that monoclinic zirconia increases the toughness at ambient conditions from the monolithic mullite value of 1.9 to 3.9 MPa·m^1/2. The toughness of the composite with zirconia remains relatively constant from ambient to 600°C but then decreases rapidly. The mechanism for the toughness enhancement as well as the reason for its variation with temperature are explained using changes in residual stress state as deduced using the sphere in shell model from the measured thermal expansion behavior.     

Fatigue Deformation Mechanisms of Zirconia Ceramics

Two distinct fatigue deformation mechanisms, microcracking and transformation plasticity, have been identified in 3Y-TZP and Mg-PSZ. Microcracking is dominant in 3Y-TZP, while transformation plasticity is more evident in Mg-PSZ. However, the proportion of these two mechanisms is dependent on the frequency and stress amplitude, with transformation plasticity favored at low frequency and high stress. Generally, microcracks form in the tensile half-cycle and partly close in the compressive half-cycle, whereas transformation from the tetragonal to the monoclinic phase, as well as the reverse transformation, can occur in both tension and compression. Under stress-controlled cycling, although the initial hysteresis loop is highly asymmetric with respect to the stress, cyclic softening and the development of an internal stress cause it to gradually evolve to yield an essentially symmetric cyclic stress–strain curve.