Showing papers on "Crack closure published in 1992"

Fracture mechanics for piezoelectric ceramics

Abstract: We Study cracks either in piezoelectrics, or on interfaces between piezoelectrics and other materials such as metal electrodes or polymer matrices. The projected applications include ferroelectric actuators operating statically or cyclically, over the major portion of the samples, in the linear regime of the constitutive curve, but the elevated field around defects causes the materials to undergo hysteresis locally. The fracture mechanics viewpoint is adopted—that is, except for a region localized at the crack tip, the materials are taken to be linearly piezoelectric. The problem thus breaks into two subproblems: (i) determining the macroscopic field regarding the crack tip as a physically structureless point, and (ii) considering the hysteresis and other irreversible processes near the crack tip at a relevant microscopic level. The first Subproblem, which prompts a phenomenological fracture theory, receives a thorough investigation in this paper. Griffith's energy accounting is extended to include energy change due to both deformation and polarization. Four modes of square root singularities are identified at the tip of a crack in a homogeneous piezoelectric. A new type of singularity is discovered around interface crack tips. Specifically, the singularities in general form two pairs: r1/2±ieand r1/2±ie, where e. and k are real numbers depending on the constitutive constants. Also solved is a class of boundary value problems involving many cracks on the interface between half-spaces. Fracture mechanics are established for ferroelectric ceramics under smallscale hysteresis conditions, which facilitates the experimental study of fracture resistance and fatigue crack growth under combined mechanical and electrical loading. Both poled and unpoled fcrroelectrie ceramics are discussed.

Linear electro-elastic fracture mechanics of piezoelectric materials

Abstract: The concepts of linear elastic fracture mechanics, generalized to treat piezoelectric effects, are employed to study the influence of the electrical fields on the fracture behavior of piezoelectric materials The method of distributed dislocations and electric dipoles, already existing in the literature, is used to calculate the electro-elastic fields and the energy-release rate for a finite crack embedded in an infinite piezoelectric medium which is subjected to both mechanical and electric loads The energy-release rate expressions show that the electric fields generally tend to slow the crack growth It is shown that the stress intensity factor criterion and the energy-release rate criterion differ when the energetics of the electric field is taken into account The study of crack tip singular stress field yields a possible explanation for experimentally observed crack skewing in the presence of a strong electric field

Experimental and numerical analysis of micromechanisms of fracture of cement-based composites

Abstract: In this paper experimental evidence of fracture toughening of concrete and mortar through a mechanism called crack face bridging is presented. The classical explanation for softening of concrete, viz. the formation of a zone of discontinuous microcracking ahead of a continuous macrocrack seems only partially true. Instead, crack face bridging in the wake of the macrocrack tip seems a physically sounder explanation. The crack face bridges are flexural ligaments between ovelapping crack tips. The failure of the flexural ligaments occurs in a stable and controlled manner because the two overlapping crack tips shield each other. The cohesive stress over the macrocrack is directly related to the size of the crack face bridges, which depends on the heterogeneity of the material. The typical failure mechanism can be simulated using a simple numerical lattice model. First the grain structure of the material is generated either by manual methods or by adopting a random generator. Secondly a tringular lattice of brittle breaking beam elements is projected on the grain structure. Aggregate, matrix and bond properties are assigned to the lattice elements at the respective locations, and a simple algorithm allows for crack growth simulation. The main conclusion is that the crack patterns and the associated load-deformation response are largely governed by the properties of the constituents. The bond between aggregates and matrix is the weakest link in the system, and variation of this parameter leads to profoundly different crack patterns.

Asymmetric Shielding in Interfacial Fracture Under In-Plane Shear

Abstract: The toughness of a glass/'epoxy interface was measured over a wide range of mode mixes. A toughening effect was associated with increasing positive and negative in-plane shear components. Optical interference measurements of normal crack opening displacements near the crack front and complementary finite element analyses were used to examine near-front behavior during crack initiation. Estimates of the tough­ening based on plastic dissipation, bulk viscoelastic dissipation, and interface asperity shielding did not fully account for the measured values. The results suggest that the inelastic behavior of the epoxy, frictional, and, perhaps, three-dimensional effects should be considered. 1 Introduction Interfacial crack growth occurs in a number of applications of technological importance. Because of the fact that the frac­ture path is constrained irrespective of the orientation of the globally applied loads and also because of the mismatch of material properties across the interface, crack growth is in­herently mixed mode. Critical and subcritical crack growth must then be governed by some combination of mode I, II, and III fracture parameters. The simplest approach, using one parameter, seeks to determine an effective parameter that can account for all mode mixes in a unifying manner. This is particularly useful for subcritical crack growth where corre­lations of crack growth rates fall on one curve for all mode mixes when the proper parameter is found. An alternative is to consider a two-parameter approach where one parameter represents the mode mix or direction and the other a magni­tude. For critical crack growth, the magnitude will generally be a function of mode mix. The form the function is usually determined experimentally but may, as mechanisms are better understood, even be predicted. The most common approach for examining interfacial crack initiation has been to consider the interfacial fracture tough­ness, G

Instability in the propagation of fast cracks

Abstract: We report on experimental investigations of the propagation of cracks in the brittle plastic polymethyl methacrylate (PMMA). Velocity measurements with resolution an order of magnitude better than previous experiments reveal the existence of a critical velocity (330\ifmmode\pm\else\textpm\fi{}30 m/s) at which the velocity of the crack tip begins to oscillate, the dynamics of the crack abruptly change, and a periodic pattern is formed on the crack surface. Beyond the critical point the amplitude of the oscillations depends linearly on the mean velocity of the crack. The existence of this instability may explain the failure of theoretical predictions of crack dynamics and provides a mechanism for the enhanced dissipation observed experimentally in the fracture of brittle materials.

Slow crack growth in single-crystal silicon.

Abstract: Time-dependent crack growth has been measured on a precracked, single-crystal silicon cantilever beam 75 micrometers long that was excited at resonance. Growth of the precrack changes the resonant frequency of the beam, which is correlated to crack length. The measured steady-state crack growth rate was as slow as 2.9 x 10–13 meter per second, although the apparatus can measure crack growth rates as low as 10–15 meter per second. It is postulated that static fatigue of the native surface silica layer is the mechanism for crack growth. These experiments demonstrate the possibility of rate-dependent failure of silicon devices and the applicability of linear elastic fracture mechanics to small-scale micromechanical devices. The results indicate that slow crack growth must therefore be considered when evaluating the reliability of thin-film silicon structures.

Cyclic Fatigue-Crack Growth in a SiC-Whisker-Reinforced Alumina Ceramic Composite: Long- and Small-Crack Behavior

Abstract: The ambient-temperature subcritical growth behavior of both long and microstructurally small cracks is investigated during cyclic-fatigue loading in a SiC-whisker-reinforced alumina (Al2O3–SiCw) ceramic composite (fracture toughness, Kc∼ 4.5 MPa · m1/2). Based on long-crack experiments using compact C(T) specimens, cyclic fatigue-crack growth rates (over the range 10−11 to 10−5 m/cycle) are found to be sensitive to the applied stress-intensity range and load ratio, and to show evidence of fatigue crack closure. Similar to other ceramic materials, under tension–tension loading the “long”(>3 mm) crack fatigue threshold, ΔKTH, was found to be on the order of 60% of Kc. Conversely, “small”(1 to 300 μm) cracks grown from micro-indents on the surface of cantilever-beam specimens were observed to grow at applied ΔK levels some 2 to 3 times smaller than ΔKTH. similar to behavior widely reported for metallic materials. The observed small-crack behavior is rationalized in terms of the residual stress field associated with the indent, and the restricted role of crack-tip shielding (from mechanisms such as crack bridging, closure and deflection) with cracks of limited wake, analogous to closure effects with small fatigue cracks in metals. Consistent with the lack of zone-shielding mechanisms in Al2O3–SiCw, under variable-amplitude cyclic loading crack-growth rates do not exhibit the marked transient response following block overload sequences as do transformation-toughened ceramics or ductile metallic materials. Possible mechanisms for cyclic crack advance in reinforced ceramic-matrix composite materials are discussed.

Intergranular crack tip oxidation mechanism in a nickel-based superalloy

Abstract: This paper is concerned with the intergranular crack tip oxidation mechanism in alloy 718 at elevated temperatures. The basic concept is based on the ability of the oxygen partial pressure to control the preferential formation of oxide layers at the crack tip. The time required to complete the build-up of the protective oxide type at the metal-oxide interface is considered a measure of the limits of the oxidation process. Identification by transmission electron microscopy of oxide scale formed along fracture surfaces during a low frequency fatigue crack process in alloy 718 at 650°C supports the proposed model concepts. An experimental program was carried out to investigate the role of passivation time in controlling the progressive process of crack tip oxidation. This was achieved by testing the influence of oxide buil-up during hold time at minimum load, as well as the effect of a minor high frequency cycle imposed on the hold time period. It was established that an increase in fatigue crack growth rate accompanies the increase in passivation time period. These results were interpreted on the basis of the oxidation formation concepts.

Cyclic Plasticity and Low Cycle Fatigue Life of Metals

Abstract: 1 Introduction 2 Stress and Strain in Cyclic Loading Monotonic stress-strain curve Stress-strain relationship in cyclic loading Hysteresis loop Cyclic hardening/softening curves Cyclic stress-strain curve 3 Cyclic Plasticity and Microstructure Metals and simple alloys with fcc structure Metals and single phase alloys with bcc structure Other metals and single phase alloys Multiphase materials 4 Dislocation Mechanisms in Cyclic Plastic Straining Athermal mechanisms in fcc metals Thermally activated cyclic straining Dislocation mechanisms in particle strengthened metals 5 Statistical Description of Cyclic Stress-Strain Response Internal and effective stress in an elementary volume Statistical approach 6 Experimental Investigation of the Dynamics of Cyclic Plastic Straining Stress-dip method Stress and strain relaxation Strain rate changes Analysis of hysteresis loop shape Evaluation of results using individual methods 7 Cyclic Creep Relevant experimental investigations Dislocation arrangements Mechanisms and models 8 Fatigue Crack Initiation Observation of surface relief evolution Models of surface relief evolution Mechanisms of crack initiation Role of grain boundaries Role of inclusions 9 Growth of Fatigue Cracks Fracture mechanics approach to fatigue crack growth Crack growth under small scale yielding General yield fatigue crack growth Short crack growth 10 Fatigue Life of Smooth Bodies Strain controlled cycling Plastic strain controlled cycling Stress controlled cycling Energy criterion Evaluation of fatigue life of a smooth body using the fatigue process model 11 Fatigue Life of Notched Bodies Stress and strain concentration in a notched body Fatigue life evaluation 12 Variable Amplitude Loading Phenomenological description Analysis of load history Sudden changes of strain amplitude Cyclic plasticity in repeated block loading Hypothesis of cumulative damage Fatigue life prediction 13 Effect of Depressed Temperature Cyclic plasticity Fatigue life 14 High Temperature Low Cycle Fatigue Cyclic plasticity at elevated temperatures Fatigue life and its evaluation Damage mechanisms Fatigue life prediction 15 Thermal and Thermomechanical Fatigue The effect of temperature changes under constraint Reversed plasticity and thermal cracking Thermal ratchetting 16 Multiaxial Loading Multiaxial stress and strain Cyclic stress-strain response Fatigue life 17 Computer Controlled Fatigue Testing Role of the digital computer Low cycle fatigue test Crack growth test Variable amplitude test Other tests 18 Characterisation of Low Cycle Fatigue Resistance of Metallic Materials Basic characteristics Review of materials properties References Subject Index

Fatigue crack growth in metals and alloys: mechanisms and micromechanics

Abstract: Fatigue crack growth has been studied using several new experimental tools in the past ten years. The observation of fatigue cracks during growth under high resolution conditions has shown that crack advance is an intermittent process. These results, when combined with measurements of crack opening, displacements, crack closure, crack tip strains, fractography, and other information, leads to a reasonable understanding of many intrinsic aspects of fatigue crack growth at ambient temperature in a number of metallic alloys. Models of fatigue crack growth are reviewed from the perspective of this understanding. No model has achieved the capability of predicting fatigue crack growth from a description of microstructural and mechanical properties. The factors limiting a deeper understanding of fatigue crack growth are also more clearly defined, which gives some direction for future research. This paper is a critical review of crack growth mechanisms, mainly for large fatigue cracks subject to constant ...

Depth of intergranular oxygen diffusion during environment-dependent fatigue crack growth in alloy 718

Abstract: The elevated-temperture fatigue crack growth behavior in alloy 718, when subjected to a loading frequency lower than the transitional frequency of this alloy, is viewed as fully environment dependent. In this process, the crack growth increment per loading cycle is assumed to be equal to the intergranular oxygen diffusion depth at the crack tip during the cycle effective oxidation time. In order to identify the trend of this diffusion depth an experimental program was carried out on compact tension specimens made of alloy 718 at 650 °C in which fatigue crack growth measurements were made for cyclic load conditions with and without hold time periods at minimum load level. This work resulted in establishing a relationship correlating the intergranular oxygen diffusion depth and the value of the stress intensity factor range ΔK. This relationship, when integrated over the cycle effective oxidation time, results in a closed-form solution describing the environment-dependent fatigue crack growth rate. A comparison is made between the results of this solution when applied to different loading frequencies and the corresponding experimental results. This comparison shows good agreement between the two sets of results. Furthermore, by combining the parabolic rate law of diffusion and the equation for the intergranular oxygen diffusion depth, an explicit expression for the oxygen diffusivity of grain boundaries is derived. It is found that this diffusivity is both a ΔK- and a frequency-dependent parameter.

Mode-III cracks in piezoelectric materials

Abstract: The stress and electric fields around a mode‐III crack containing a dielectric medium are formulated. Mechanical equilibrium requires that the crack surfaces be traction free. Previous solutions have used the electrical boundary condition that the electric displacement component perpendicular to the crack surfaces should be zero. However, cracks that are filled with a dielectric medium, such as vacuum or air, require that the electric displacement be continuous across the crack faces. Using the boundary condition appropriate for an insulating crack, the stress, strain, and electric‐field strength are found to exhibit r−1/2 singularities while the electric displacement does not. The singularity in the electric‐field strength arises from piezoelectricity. The driving force for crack growth is only related to the effective level of applied stress. Under constant displacement, the applied field may increase or decrease the effective applied stress depending on its direction. As a result the electric field may...

Effects of sic content on fatigue crack growth in

Abstract: An experimental study has been conducted with the purpose of examining the fatigue crack growth characteristics of cast aluminum alloy matrix composites reinforced with different vol- ume fractions of silicon carbide particles. Particular attention has been paid to developing com- posite microstructures with similar matrix aging condition, precipitation, matrix strength, reinforcement particle size distribution, and interfacial characteristics but with different con- trolled amounts of reinforcement particles. Fatigue crack growth experiments have been con- ducted using constant stress amplitude methods with a fixed load ratio as well as constant Kmax control involving a varying load ratio. The development of crack closure and the microscopic path of the crack through the composite microstructure are monitored optically and using the electron microscope in an attempt to examine the mechanisms of fatigue fracture. The results indicate that an increase in SiC content results in the suppression of striation formation in the ductile matrix. Although ductile matrix failure involving the formation of striations in the low SiC content composite or of void growth in the high SiC content composite is evident, the results also show that fracture of the reinforcement particles plays a significant role in dictating the rates of fatigue crack growth. Detailed quantitative analyses of the extent of particle fracture as a function of the reinforcement content have been performed to elucidate the mechanistic origins of fatigue resistance. The propensity of particle fracture increases with particle size and with the imposed value of stress intensity factor range. While discontinuously reinforced metal- matrix composites with predominantly matrix cracking are known to exhibit superior fatigue crack growth resistance as compared to the unreinforced matrix alloy, the tendency for particle fracture in the present set of experiments appears to engender fatigue fracture characteristics in the composite which are inferior to those seen in the unreinforced matrix material. Particle fracture also results in noticeable differences in the microscopic fracture path and causes a reduction in crack closure in the composites as compared to that in the matrix alloy. The results of this work are discussed in light of other related studies available in the literature in an attempt to develop a mechanistic perspective on fatigue crack growth resistance in metal-matrix composites.

Fatigue crack growth modelling by successive blocking of dislocations

Abstract: Work hardening and the study of instability is incorporated into the description of the growth of a crack in terms of the successive blocking of the plastic zone by slip barriers, such as grain boundaries, and the subsequent initiation of the slip in neighbouring grains. A simple equation is derived to determine the critical position of the crack tip in relation to the grain boundary where the plastic zone is blocked at the moment of slip transmission. The intermittent pattern of decelerating and accelerating behaviour of short cracks and the existence of non-propagating cracks is explained. Instability in crack growth is seen to occur when the rate of hardening is insufficient to compensate for the increase in crack driving force in relation to the increase in crack length. This is associated with fracture toughness. The transition point between the short and long crack regimes is seen to occur when the size of the plastic zone is of the order of the microstructural parameter.

Crack healing behavior of hot pressed silicon nitride due to oxidation

Abstract: It is shown that limited oxidation of an MgO-containing, hot-pressed silicon nitride ceramic at 800 deg C and above results in increased strength due to crack healing. Slight oxidation of the surface produces enstatite and cristobalite which fills in cracks. More extensive oxidation leads to strength degradation due to the formation of new flaws by the evolution of N2 gas at the surface. The apparent fracture toughness also increased at 800 deg C and above due to oxidation. Bonds formed between the two surfaces of the crack during oxidation leads to a reduction in stress intensity at the crack tip, suggesting that valid high-temperature toughness values cannot be obtained in an air environment. The increase in strength due to crack healing by oxidation can be achieved without compromising the fatigue properties of the silicon nitride ceramic.

The structure of the near-tip field during transient elastodynamic crack growth

Abstract: T he process of dynamic crack growth in a nominally elastic malerial under conditions of plane strain or plane stress is considered. Of particular concern is the influence of the transient nature of the process on the stress field in the immediate vicinity of the crack tip during nonsteady growth. Asymptotically, the crack tip stress field is square root singular at the crack tip, with the angular variation of the singular field depending weakly on the instantaneous crack tip speed and with the instantaneous stress intensity factor being a scalar multiplier of the singular field. However, for a material particle at a small distance from the moving crack, the local stress field depends not only on instantaneous values of crack speed and stress intensity factor, but also on the past history of these lime-dependent quantities. A representation of the crack tip field is obtained in the form of an expansion about the crack up in powers of radial coordinate, with the coefficients depending on the time rates of change of crack tip speed and stress intensity factor. This representation is used to interpret some experimental observations, with the conclusion that the higher-order expansion provides an accurate description of crack tip fields under fairly severe transient conditions. In addition, some estimates are made of the practical limits of using a stress intensity factor field alone to characterize the local fields.

Interaction between crack deflection and crack bridging

Abstract: The potential of crack deflection and crack bridging as competing toughening mechanisms is reviewed. Available measurement techniques take a crucial role where it is required to distinguish between toughening increments associated with crack tip processes and crack wake processes near the crack tip. Particular emphasis is placed on measurements of the crack opening displacement. It is concluded that crack deflection has only small potential as a toughening mechanism compared to crack bridging, but is required to activate crack closure stresses associated with bridging ligaments. This simple realization defines a window of microstructural parameters in which crack deflection is active and where crack bridging parameters can be optimized.

Effect of crack meandering on dynamic, ductile fracture

Abstract: Dynamic crack growth is analyzed numerically for a plane strain edge cracked specimen subject to impulsive tensile loading at one end. An elastic—viscoplastic constitutive relation for a porous plastic solid is used to model ductile fracture by the nucleation and subsequent growth of voids to coalescence. Two populations of second-phase particles are represented: large inclusions with low strength, which result in large voids near the crack tip at an early stage, and small second-phase particles, which require large strains before cavities nucleate. Adiabatic heating due to plastic dissipation and the resulting thermal softening are accounted for in the analyses. Various two-dimensional distributions of the larger inclusions in front of the crack tip are considered, while the small second-phase particles are taken to be uniformly distributed. It is found that in most cases cracks grow in a zig-zag manner, dependent on the distribution of larger inclusions. Predictions for the dynamic crack growth behavior and for the time variation of crack tip characterizing parameters are obtained for each case analyzed. The computed crack growth paths and speeds are entirely based on the ductile failure predictions of the material model, so that the present study is free from ad hoc assumptions regarding appropriate dynamic crack growth criteria.