Showing papers on "Crack closure published in 1996"

Mechanical properties of ceramics

Abstract: Preface. Acknowledgments. 1 Stress and Strain. 1.1 Introduction. 1.2 Tensor Notation for Stress. 1.3 Stress in Rotated Coordinate System. 1.4 Principal Stress. 1.4.1 Principal Stresses in Three Dimensions. 1.5 Stress Invariants. 1.6 Stress Deviator. 1.7 Strain. 1.8 True Stress and True Strain. 1.8.1 True Strain. 1.8.2 True Stress. Problems. 2 Types of Mechanical Behavior. 2.1 Introduction. 2.2 Elasticity and Brittle Fracture. 2.3 Permanent Deformation. 3 Elasticity. 3.1 Introduction. 3.2 Elasticity of Isotropic Bodies. 3.3 Reduced Notation for Stresses, Strains, and Elastic Constants. 3.4 Effect of Symmetry on Elastic Constants. 3.5 Orientation Dependence of Elastic Moduli in Single Crystals and Composites. 3.6 Values of Polycrystalline Moduli in Terms of Single-Crystal Constants. 3.7 Variation of Elastic Constants with Lattice Parameter. 3.8 Variation of Elastic Constants with Temperature. 3.9 Elastic Properties of Porous Ceramics. 3.10 Stored Elastic Energy. Problems. 4 Strength of Defect-Free Solids. 4.1 Introduction. 4.2 Theoretical Strength in Tension. 4.3 Theoretical Strength in Shear. Problems. 5 Linear Elastic Fracture Mechanics. 5.1 Introduction. 5.2 Stress Concentrations. 5.3 Griffith Theory of Fracture of a Brittle Solid. 5.4 Stress at Crack Tip: An Estimate. 5.5 Crack Shape in Brittle Solids. 5.6 Irwin Formulation of Fracture Mechanics: Stress Intensity Factor. 5.7 Irwin Formulation of Fracture Mechanics: Energy Release Rate. 5.8 Some Useful Stress Intensity Factors. 5.9 The J Integral. 5.10 Cracks with Internal Loading. 5.11 Failure under Multiaxial Stress. Problems. 6 Measurements of Elasticity, Strength, and Fracture Toughness. 6.1 Introduction. 6.2 Tensile Tests. 6.3 Flexure Tests. 6.4 Double-Cantilever-Beam Test. 6.5 Double-Torsion Test. 6.6 Indentation Test. 6.7 Biaxial Flexure Testing. 6.8 Elastic Constant Determination Using Vibrational and Ultrasonic Methods. Problems. 7 Statistical Treatment of Strength. 7.1 Introduction. 7.2 Statistical Distributions. 7.3 Strength Distribution Functions. 7.4 Weakest Link Theory. 7.5 Determining Weibull Parameters. 7.6 Effect of Specimen Size. 7.7 Adaptation to Bend Testing. 7.8 Safety Factors. 7.9 Example of Safe Stress Calculation. 7.10 Proof Testing. 7.11 Use of Pooled Fracture Data in Linear Regression Determination of Weibull Parameters. 7.12 Method of Maximum Likelihood in Weibull Parameter Estimation. 7.13 Statistics of Failure under Multiaxial Stress. 7.14 Effects of Slow Crack Propagation and R-Curve Behavior on Statistical Distributions of Strength. 7.15 Surface Flaw Distributions and Multiple Flaw Distributions. Problems. 8 Subcritical Crack Propagation. 8.1 Introduction. 8.2 Observed Subcritical Crack Propagation. 8.3 Crack Velocity Theory and Molecular Mechanism. 8.4 Time to Failure under Constant Stress. 8.5 Failure under Constant Stress Rate. 8.6 Comparison of Times to Failure under Constant Stress and Constant Stress Rate. 8.7 Relation of Weibull Statistical Parameters with and without Subcritical Crack Growth. 8.8 Construction of Strength-Probability-Time Diagrams. 8.9 Proof Testing to Guarantee Minimum Life. 8.10 Subcritical Crack Growth and Failure from Flaws Originating from Residual Stress Concentrations. 8.11 Slow Crack Propagation at High Temperature. Problems. 9 Stable Crack Propagation and R -Curve Behavior. 9.1 Introduction. 9.2 R-Curve (T-Curve) Concept. 9.3 R-Curve Effects of Strength Distributions. 9.4 Effect of R Curve on Subcritical Crack Growth. Problems. 10 Overview of Toughening Mechanisms in Ceramics. 10.1 Introduction. 10.2 Toughening by Crack Deflection. 10.3 Toughening by Crack Bowing. 10.4 General Remarks on Crack Tip Shielding. 11 Effect of Microstructure on Toughness and Strength. 11.1 Introduction. 11.2 Fracture Modes in Polycrystalline Ceramics. 11.3 Crystalline Anisotropy in Polycrystalline Ceramics. 11.4 Effect of Grain Size on Toughness. 11.5 Natural Flaws in Polycrystalline Ceramics. 11.6 Effect of Grain Size on Fracture Strength. 11.7 Effect of Second-Phase Particles on Fracture Strength. 11.8 Relationship between Strength and Toughness. 11.9 Effect of Porosity on Toughness and Strength. 11.10 Fracture of Traditional Ceramics. Problems. 12 Toughening by Transformation. 12.1 Introduction. 12.2 Basic Facts of Transformation Toughening. 12.3 Theory of Transformation Toughening. 12.4 Shear-Dilatant Transformation Theory. 12.5 Grain-Size-Dependent Transformation Behavior. 12.6 Application of Theory to Ca-Stabilized Zirconia. Problems. 13 Mechanical Properties of Continuous-Fiber-Reinforced Ceramic Matrix Composites. 13.1 Introduction. 13.2 Elastic Behavior of Composites. 13.3 Fracture Behavior of Composites with Continuous, Aligned Fibers. 13.4 Complete Matrix Cracking of Composites with Continuous, Aligned Fibers. 13.5 Propagation of Short, Fully Bridged Cracks. 13.6 Propagation of Partially Bridged Cracks. 13.7 Additional Treatment of Crack-Bridging Effects. 13.8 Additional Statistical Treatments. 13.9 Summary of Fiber-Toughening Mechanisms. 13.10 Other Failure Mechanisms in Continuous, Aligned-Fiber Composites. 13.11 Tensile Stress-Strain Curve of Continuous, Aligned-Fiber Composites. 13.12 Laminated Composites. Problems. 14 Mechanical Properties of Whisker-, Ligament-, and Platelet-Reinforced Ceramic Matrix Composites. 14.1 Introduction. 14.2 Model for Whisker Toughening. 14.3 Combined Toughening Mechanisms in Whisker-Reinforced Composites. 14.4 Ligament-Reinforced Ceramic Matrix Composites. 14.5 Platelet-Reinforced Ceramic Matrix Composites. Problems. 15 Cyclic Fatigue of Ceramics. 15.1 Introduction. 15.2 Cyclic Fatigue of Metals. 15.3 Cyclic Fatigue of Ceramics. 15.4 Mechanisms of Cyclic Fatigue of Ceramics. 15.5 Cyclic Fatigue by Degradation of Crack Bridges. 15.6 Short-Crack Fatigue of Ceramics. 15.7 Implications of Cyclic Fatigue in Design of Ceramics. Problems. 16 Thermal Stress and Thermal Shock in Ceramics. 16.1 Introduction. 16.2 Magnitude of Thermal Stresses. 16.3 Figure of Merit for Various Thermal Stress Conditions. 16.4 Crack Propagation under Thermal Stress. Problems. 17 Fractography. 17.1 Introduction. 17.2 Qualitative Features of Fracture Surfaces. 17.3 Quantitative Fractography. 17.4 Fractal Concepts in Fractography. 17.5 Fractography of Single Crystals and Polycrystals. Problems. 18 Dislocations and Plastic Deformation in Ductile Crystals. 18.1 Introduction. 18.2 Definition of Dislocations. 18.3 Glide and Climb of Dislocations. 18.4 Force on a Dislocation. 18.5 Stress Field and Energy of a Dislocation. 18.6 Force Required to Move a Dislocation. 18.7 Line Tension of a Dislocation. 18.8 Dislocation Multiplication. 18.9 Forces between Dislocations. 18.10 Dislocation Pileups. 18.11 Orowan's Equation for Strain Rate. 18.12 Dislocation Velocity. 18.13 Hardening by Solid Solution and Precipitation. 18.14 Slip Systems. 18.15 Partial Dislocations. 18.16 Deformation Twinning. Problems. 19 Dislocations and Plastic Deformation in Ceramics. 19.1 Introduction. 19.2 Slip Systems in Ceramics. 19.3 Independent Slip Systems. 19.4 Plastic Deformation in Single-Crystal Alumina. 19.5 Twinning in Aluminum Oxide. 19.6 Plastic Deformation of Single-Crystal Magnesium Oxide. 19.7 Plastic Deformation of Single-Crystal Cubic Zirconia. Problems. 20 Creep in Ceramics. 20.1 Introduction. 20.2 Nabarro-Herring Creep. 20.3 Combined Diffusional Creep Mechanisms. 20.4 Power Law Creep. 20.5 Combined Diffusional and Power Law Creep. 20.6 Role of Grain Boundaries in High-Temperature Deformation and Failure. 20.7 Damage-Enhanced Creep. 20.8 Superplasticity. 20.9 Deformation Mechanism Maps. Problems. 21 Creep Rupture at High Temperatures and Safe Life Design. 21.1 Introduction. 21.2 General Process of Creep Damage and Failure in Ceramics. 21.3 Monkman-Grant Technique of Life Prediction. 21.4 Two-Stage Strain Projection Technique. 21.5 Fracture Mechanism Maps. Problems. 22 Hardness and Wear. 22.1 Introduction. 22.2 Spherical Indenters versus Sharp Indenters. 22.3 Methods of Hardness Measurement. 22.4 Deformation around Indentation. 22.5 Cracking around Indentation. 22.6 Indentation Size Effect. 22.7 Wear Resistance. Problems. 23 Mechanical Properties of Glass and Glass Ceramics. 23.1 Introduction. 23.2 Typical Inorganic Glasses. 23.3 Viscosity of Glass. 23.4 Elasticity of Inorganic Glasses. 23.5 Strength and Fracture Surface Energy of Inorganic Glasses. 23.6 Achieving High Strength in Bulk Glasses. 23.7 Glass Ceramics. Problems. 24 Mechanical Properties of Polycrystalline Ceramics in General and Design Considerations. 24.1 Introduction. 24.2 Mechanical Properties of Polycrystalline Ceramics in General. 24.3 Design Involving Mechanical Properties. References. Index.

Fatigue Damage, Crack Growth and Life Prediction

Abstract: Some general concepts concerning fatigue. Cyclic stress-strain response. Phenomenological approach to fatigue life prediction under uniaxial loading. Fatigue failure under multiaxial states of stress. Multiaxial experimental facilities. Constitutive laws for transient and stable behaviour of inelastic solids. Fatigue crack growth. Fatigue of notched members. Growth and behaviour of small cracks. Probabilistic fatigue crack growth. References. Index.

Crack problems in fgm layers under thermal stresses

Abstract: In this study an unconstrained elastic layer under statically self-equilibrating thermal or residual stresses is considered. The layer is assumed to be a functionally graded material (FGM), meaning that its thermo-mechanical properties are assumed to be continuous functions of the thickness coordinate. The layer contains an embedded or a surface crack perpendicular to its boundaries. Using superposition the problem is reduced to a perturbation problem in which the crack surface tractions are the only external forces. The dimensions, geometry, and loading conditions of the original problem are such that the perturbation problem may be approximated by a plane strain mode I crack problem for an infinite layer. After a general discussion of the thermal stress problem, the crack problem in the nonhomogeneous medium is formulated. With the application to graded coatings and interfacial zones in mind, the thickness variation of the thermo-mechanical properties is assumed to be monotonous. Thus, the functions suc...

Dislocation based fracture mechanics

Abstract: Girffith-Inglis crack and Zener-Stroh-Koehler crack dislocation mechanics Hilbert transform and Muskhelishvili equations Bilby-Cottrell-Swinden-Dugdale (BCSD) crack crack tip shielding and antishielding by dislocations mode III crack in an elastic-plastic solid mode II crack in an elastic-plastic solid mode I crack in an elastic-plastic solid moving Yoffee crack interesting problems appendices.

Energy dissipation in dynamic fracture.

Abstract: Measurements in PMMA of both the energy flux into the tip of a moving crack and the total surface area created via the microbranching instability indicate that the instability is the main mechanism for energy dissipation by a moving crack in brittle, amorphous material. Beyond the instability onset, the rate of fracture surface creation is proportional to the energy flux into the crack. At high velocities microbranches create nearly an order of magnitude larger fracture surface than smooth cracks. This mechanism provides an explanation for why the theoretical limiting velocity of a crack is never realized. PACS numbers: 68.35.Gy, 62.20.Mk, 83.50.Tq Although the subject of much research over the past decades, the fracture of brittle amorphous materials remains in many ways not understood. Of particular interest is the mechanism by which energy in the system is dissipated. Experimental measurements of the flow of energy into the tip of a running crack [1] have indicated that the fracture energy (i.e., the energy needed to create a unit extension of a crack) is a strong function of the crack’s velocity and that the majority of the energy stored in the system prior to the onset of fracture ends up as heat [2]. In this Letter we present quantitative measurements indicating that this increased dissipation is due entirely to the onset of a microbranching instability [3,4] which occurs at a critical value yc of the velocity y .A s yincreases beyond yc we find that the energy needed to create microbranches is precisely enough to account for the velocity dependence of the fracture energy. The long-standing problem of the limiting velocity of a crack is also explained by this mechanism. While linear elastic theory predicts that a crack should continuously accelerate up to the Rayleigh wave speed VR, experiments in a number of brittle materials [5] show that a crack will seldom reach even half of this value. As we will show, the total amount of fracture surface created by both the main crack and the microbranches increases rapidly with y. Thus, rather than acceleration, increased driving results in increased ramification of structure below the fracture surface. There have been a number of suggestions for the velocity dependence of fracture energy. One view is that the energy flow into the tip of a single moving crack is dissipated by plastic deformation around the crack tip. Depending on the model used to describe the area of deformation around the tip, either a nonmonotonic or monotonically increasing function [6] of the velocity of the crack can result. An alternative view of the dissipation process was suggested by Ravi-Chandar and Knauss [7]. They viewed the fracture process as the coalescence of preexisting microvoids or defects situated in the path of the crack and activated by the intense stress field at the crack tip. An increase in the energy flux to the tip, in this picture, causes an increase in the number of microcracks formed and thereby enhanced dissipation. This picture suggests that crack propagation via interacting microvoids occurs as a randomly activated process.

Finite thermoelastic fracture criterion with application to laminate cracking analysis

Abstract: A stress energy criterion for the development of a new finite size crack surface under temperature and load input, in the presence of thermal residual stresses, is established on the basis of an energy release formulation. It is shown that if a fixed specific crack opening surface energy γ exists, an upper bound on the critical energy release can be established on the basis of the thermoelastic principle of minimum complementary energy. On the basis of a variational formulation of thermoelastic laminate analysis a relation is established which permits construction of thermoelastic solutions for cracked laminates by a simple replacement in the corresponding isothermal solution. The results described above are applied to establish relations between crack density and standard deviation of crack interdistances of crack distribution in a cross-ply laminate layer, and load/temperature inputs of the laminate. It is shown that for certain ranges of crack densities, one small to medium and one large, the standard deviation is not needed. The physical and experimental significance of the results obtained is discussed.

Numerical simulations of dynamic crack growth along an interface

Abstract: Dynamic crack growth is analyzed numerically for a plane strain bimaterial block with an initial central crack. The material on each side of the bond line is characterized by an isotropic hyperelastic constitutive relation. A cohesive surface constitutive relation is also specified that relates the tractions and displacement jumps across the bond line and that allows for the creation of new free surface. The resistance to crack initiation and the crack speed history are predicted without invoking any ad hoc failure criterion. Full finite strain transient analyses are carried out, with two types of loading considered; tensile loading on one side of the specimen and crack face loading. The crack speed history and the evolution of the crack tip stress state are investigated for parameters characterizing a PMMA/Al bimaterial. Additionally, the separate effects of elastic modulus mismatch and elastic wave speed mismatch on interface crack growth are explored for various PMMA-artificial material combinations. The mode mixity of the near tip fields is found to increase with increasing crack speed and in some cases large scale contact occurs in the vicinity of the crack tip. Crack speeds that exceed the smaller of the two Rayleigh wave speeds are also found.

Transition from pitting to fatigue crack growth—modeling of corrosion fatigue crack nucleation in a 2024-T3 aluminum alloy

Abstract: The nucleation of fatigue cracks from corrosion pits was investigated by conducting fatigue experiments on open-hole specimens of a 2024-T3 aluminum (bare) alloy in 0.5 M NaCl solution at room temperature and different load frequencies from 0.1 to 20 Hz. The maximum cyclic stresses applied at the hole ranged from 144 to 288 MPa and the load ratio, R , was 0.1. A specimen subjected to pre-corrosion in the NaCl solution prior to corrosion fatigue was also investigated. Pitting was found to be associated with constituent particles in the hole and pit growth often involved coalescence of individual particle-nucleated pits. Fatigue cracks typically nucleated from one or two of the larger pits, and the size of the pit at which the fatigue crack nucleates is a function of stress level and load frequency. The observations indicate that the nucleation of corrosion fatigue cracks essentially results from a competition between the processes of pitting and crack growth. Pitting predominates in the early stage of the corrosion fatigue process, and is replaced by corrosion fatigue crack growth. Based on these results, two criteria are proposed to describe the transition from pit growth to fatigue crack growth: (1) the stress intensity factor of the equivalent surface crack has to reach the threshold stress intensity factor, Δ K th , for fatigue crack growth, assuming that a corrosion pit may be modeled by an equivalent semi-elliptical surface crack, and (2) the time-based corrosion fatigue crack growth rate also exceeds the pit growth rate.

A Model of Anisotropic Damage by Mesocrack Growth; Unilateral Effect

Abstract: A three-dimensional model of anisotropic damage by mesocrack growth is first described in its basic version, employing a second-order tensorial damage variable The model—concerning rate-independen

A transferability model for brittle fracture including constraint and ductile tearing effects: a probabilistic approach

Abstract: This study describes a computational framework to quantify the influence of constraint loss and ductile tearing on the cleavage fracture process, as reflected by the pronounced effects on macroscopic toughness (J c , δc). Our approach adopts the Weibull stress σw as a suitable near-tip parameter to describe the coupling of remote loading with a micromechanics model incorporating the statistics of microcracks (weakest link philosophy). Unstable crack propagation (cleavage) occurs at a critical value of σw which may be attained prior to, or following, some amount of stable, ductile crack extension. A central feature of our framework focuses on the realistic numerical modeling of ductile crack growth using the computational cell methodology to define the evolution of near-tip stress fields during crack extension. Under increased remote loading (J), development of the Weibull stress reflects the potentially strong variations of near-tip stress fields due to the interacting effects of constraint loss and ductile crack extension. Computational results are discussed for well-contained plasticity, where the near-tip fields for a stationary and a growing crack are generated with a modified boundary layer (MBL) formulation (in the form of different levels of applied T-stress). These analyses demonstrate clearly the dependence of σw on crack-tip stress triaxiality and crack growth. The paper concludes with an application of the micromechanics model to predict the measured geometry and ductile tearing effects on the cleavage fracture toughness J c of an HSLA steel. Here, we employ the concept of the Dodds-Anderson scaling model, but replace their original local criterion based on the equivalence of near-tip stressed volumes by attainment of a critical value of the Weibull stress. For this application, the proposed approach successfully predicts the combined effects of loss of constraint and crack growth on measured J c -values.

Numerical modeling of ductile crack growth in 3-D using computational cell elements

Abstract: This study describes a 3-D computational framework to model stable extension of a macroscopic crack under mode I conditions in ductile metals. The Gurson-Tvergaard dilatant plasticity model for voided materials describes the degradation of material stress capacity. Fixed-size, computational cell elements defined over a thin layer at the crack plane provide an explicit length scale for the continuum damage process. Outside this layer, the material remains undamaged by void growth, consistent with metallurgical observations. An element vanish procedure removes highly voided cells from further consideration in the analysis, thereby creating new tractionfree surfaces which extend the macroscopic crack. The key micro-mechanics parameters are D, the thickness of the computational cell layer, and f 0 , the initial cell porosity. Calibration of these parameters proceeds through analyses of ductile tearing to match R-curves obtained from testing of deep-notch, through-crack bend specimens. The resulting computational model, coupled with refined 3-D meshes, enables the detailed study of non-uniform growth along the crack front and predictions of specimen size, geometry and loading mode effects on tearing resistance, here described by J-Δa curves. Computational and experimental studies are described for shallow and deep-notch SE(B) specimens having side grooves and for a conventional C(T) specimen without side grooves. The computational models prove capable of predicting the measured R-curves, post-test measured crack profiles, and measured load-displacement records.

A theory of local limiting speed in dynamic fracture

Abstract: A nonlinear continuum analysis is developed to show that stable, steady-state crack motion is limited not only by the macroscopic Rayleigh wave speed as asserted by the established theory of dynamic fracture, but also by a local wave speed governed by the elastic response near the crack tip. The local limiting speed ensures that a subsonic steady-state field can be established in highly nonlinear material regions prior to rupture. A two-dimensional triangular lattice with nearest-neighbor interatomic bonding is studied as a model nonlinear elastic solid that is isotropic under infinitesimal strains, but becomes anisotropic and nonlinear when the lattice is heavily stretched. The local limiting speed is determined by considering the most critical state of deformation on the verge of bond rupture. If the critical state is assumed to be under equibiaxial stressing, the local limiting speed is found to be v 1 = c s σ max μ , where cs is the macroscopic shear wave speed, μ is the shear modulus and σmax is the equibiaxial cohesive strength of the solid (i.e. the maximum equibiaxial tensile stress that a flawless solid can stand without spontaneous rupture). The generality of this result is discussed by relaxing the restrictions in the model problem. It is also shown that lattice dispersion in front of a crack tip can further reduce the speed of bond-breaking stress waves with wavelength on the order of a few atomic spacings. This study lends further support for a viewpoint previously discussed by the author that high speed dynamic fracture involves a competition between a high inertia local crack-tip field and the surrounding low inertia apparent crack field. Motivated by recent molecular dynamics simulations of crack propagation in a 6–12 Lenard-Jones lattice, a variational principle for steady-state deformation is used together with a conjugate gradient minimization algorithm to compute atomistic responses near the tip of a crack moving with constant speed in a similar Lenard-Jones lattice. The computation is performed over a block which moves with the crack and is subjected along the boundary to a low inertia displacement field based on existing solutions for cracks moving in linear elastic solids. The critical velocity at the onset of local crack branching is found to be 0.30cs, in almost exact agreement with the earlier molecular dynamics study. In this case, the local limiting speed is calculated to be v1 = 0.37cs, which is 20% larger than the observed value. This difference can be attributed to the effects of local lattice dispersion. The results are fully supportive of the notion that global-local inertia competition is a key to understanding dynamic fracture instabilities.

Early development of fatigue cracking at manual fillet welds

Abstract: — An experimental study within the Canadian Offshore Corrosion Fatigue Research Programme was performed on the early development of fatigue cracking along the wavy toe of manual fillet welds between structural steel plates. Stress relieved and as-welded cruciform joints were tested under R =−1 and R= 0 loading at different stress amplitudes. The depth and the opening level of cracks as small as 10–20 μm were monitored using miniature strain gauges installed along the toe apex, in combination with beach marking. Most of the “initiation life” (25% to 50% of total life), conventionally defined by a crack depth of 0.5 mm, is consumed in short crack propagation. Three types of short crack development for different combinations of local mean stress and stress range are identified and analyzed. Growth rates in as-welded specimens are faster than in stress relieved specimens, which results in shorter “initiation lives”. This is associated with a higher effective stress range, particularly under R = - 1 loading where cracks are open over nearly the full stress range. The V-notch stress intensity factor is a promising parameter to rationalize the crack “initiation life”. It takes into account the thickness effect experimentally observed. Under R = - 1 loading of as-welded joints, using R = 0 data and taking the whole stress range gives a reasonably conservative approximation of the crack “initiation life”.

Dynamic crack propagation in piezoelectric materials—Part I. Electrode solution

Abstract: An analysis is performed for the transient response of a semi-infinite, anti-plane crack propagating in a hexagonal piezoelectric medium. The mixed boundary value problem is solved by transform methods together with the Wiener-Hopf and Cagniard-de Hoop techniques. As a special case, a closed form solution is obtained for constant speed crack propagation under external anti-plane shear loading with the conducting electrode type of electric boundary condition imposed on the crack surface (a second type of boundary condition is considered in Part II of this work). In purely elastic, transversely isotropic elastic solids, there is no antiplane mode surface wave. However, for certain orientations of piezoelectric materials, a surface wave will occur—the BleusteindashGulyaev wave. Since surface wave speeds strongly influence crack propagation, the nature of antiplane dynamic fracture in piezoelectric materials is fundamentally different from that in purely elastic solids, exhibiting many features only associated with the indashplane modes in the elastic case. For a general distribution of crack face tractions, the dynamic stress intensity factor and the dynamic electric displacement intensity factor are derived and discussed in detail for the electrode case. As for inplane elastodynamic fracture, the stress intensity factor and energy release rate go to zero as the crack propagation velocity approaches the surface wave speed. However, the electric displacement intensity does not vanish.

Near-tip fields and intensity factors for interfacial cracks in dissimilar anisotropic piezoelectric media

Abstract: A complete form of stress and electric displacement fields in the vicinity of the tip of an interfacial crack, between two dissimilar anisotropic piezoelectric media, is derived by using the complex function theory. New definitions of real-valued stress and electric displacement intensity factors for the interfacial crack are proposed. These definitions are extensions of those for cracks in homogeneous piezoelectric media. Closed form solutions of the stress and electric displacement intensity factors for a semi-infinite crack as well as for a finite crack at the interface between two dissimilar piezoelectric media are also obtained by using the mutual integral.

A study of fatigue crack closure by elastic-plastic finite element analysis for constant-amplitude loading

Abstract: A comprehensive elastic-plastic constitutive model is employed in a finite element analysis of fatigue crack closure. An improved node release scheme is used to simulate crack growth during cyclic loading, which eliminates the associated numerical difficulties. New definitions of crack opening and closing stresses are presented in this paper. Special attention is paid to a discussion of some basic concepts of fatigue crack growth and crack closure behaviour. Residual tensile deformation and residual compressive stress are found to be two major factors in determining the crack opening stress. A comparison of crack tip node release at the maximum or minimum load of each cycle is made and the disadvantage of releasing crack tip node at the minimum load are pointed out.

Models of High‐Temperature, Environmentally Assisted Embrittlement in Ceramic‐Matrix Composites

Abstract: The intermediate-temperature oxidation embrittlement, or pest, effect found in ceramic-matrix composites (CMCs) is shown to have features analogous to stress corrosion cracking. The behavior involves crack growth upon oxidation of the fibers or the fiber coatings to form an oxide that weakens the fibers. It has reaction- and diffusion-controlled regimes. The former occurs at low stresses. The latter occurs at higher stresses. It is controlled by oxygen ingress through the matrix cracks. There is also a crack growth threshold. Expressions for the crack velocity above the threshold are derived as well as the stress dependence of the rupture life.

Numerical simulations of dynamic interfacial crack growth allowing for crack growth away from the bond line

Abstract: Dynamic crack growth is analyzed numerically for a plane strain bimaterial block with an initial central crack subject to impact tensile loading. The material on each side of the bond line is characterized by an isotropic hyperelastic constitutive relation. Potential surfaces of decohesion are interspersed in the material on either side of the bond line and along the bond line. The cohesive surface constitutive relation allows for the creation of new tree surface and dimensional considerations introduce a characteristic length into the formulation. Full transient analyses are carried out. The resistance to crack initiation, the crack speed history and the crack path are predicted without invoking any ad hoc failure criterion. Three calculations are carried out for a PMMA/Al bimaterial. The imposed loading and the properties of the adjacent materials are kept fixed, while the bond line strength is taken to be 1/4, 1/2, and 3/4 of the strength of PMMA. The nominal crack speed decreases with increasing bond line strength. When the bond line strength is 1/4 that of PMMA, the crack remains on the bond line although there is an attempt at branching off the bond line. For the intermediate case, a bond line strength 1/2 that of PMMA, repeated branching of the main crack off the bond line into the PMMA occurs, together with micro-crack nucleation on the bond line. The crack branches off the bond line into the PMMA when its strength is 3/4 that of PMMA, with the main direction of growth being parallel to the bond line, but with the crack progressively drifting further into the PMMA.

Dynamic crack propagation in piezoelectric materials—Part II. Vacuum solution

Abstract: In Part I of this work, antiplane dynamic crack propagation in piezoelectric materials was studied under the condition that crack surfaces behaved as though covered with a conducting electrode. Piezoelectric surface wave phenomena were clearly seen to be critical to the behavior of the moving crack. Closed form results were obtained for stress and electric displacement intensities at the crack tip in the subsonic crack speed range; the major result is that the energy release rate vanishes as the crack speed approaches the surface (Bleustein-Gulyaev) wave speed. In this paper, an alternative assumption is made that between the growing crack surfaces there is a permeable vacuum free space, in which the electrostatic potential is nonzero. By coupling the piezoelectric equations of the solid phase with the electric charge equation in the vacuum region, a closed form solution is again obtained. In contrast to the electrode case of Part I, this case allows both applied charge and applied traction loading. In addition, the work of Part I is extended to examine piezoelectric crack propagation over the full velocity range of subsonic, transonic and supersonic speeds. Several aspects of the results are explored. The energy release rate in this case does not go to zero when the crack propagating velocity approaches the surface wave speed, even if there is only applied traction loading. When the crack exceeds the Bleustein-Gulyaev wave speed, the character of the crack-tip singularities of the physical fields depends on both speed regime and type of loading. At the other extreme, the quasi-static limit of the dynamic solution furnishes a set of new static solutions. The general permeability assumptions made here allow for fully coupled conditions that are ruled out by the a priori interfacial assumptions made in previously published solutions.

Molecular statics simulation of fracture in -iron

Abstract: The behaviour of mode I cracks in -Fe is investigated using molecular statics computer simulation methods with an EAM potential. A double-ended crack of finite size embedded in a cylindrical simulation cell and fixed boundary conditions are prescribed along the periphery of the cell, whereas periodic boundary conditions are imposed parallel to the crack front. The displacement field of the finite crack is represented by that of an equivalent pile-up of opening dislocations distributed in a manner consistent with the anisotropy of the crystal and traction-free conditions of the crack faces. The crack lies on the plane and the crack front is located along , or directions. The crack tip response is rationalized in terms of the surface energy of the cleavage plane and the unstable stacking energies of the slip planes emanating from the crack front.

An Experimental Investigation of the Crack Growth Phenomenon for Drilling of Fiber-Reinforced Composite Materials

Abstract: An experimental study has been conducted to study the crack growth phenomenon that occurs while drilling fiber-reinforced composite materials (FRCM), specifically unidirectional (UD) carbon fiber/epoxy resin. It uses an experimental setup that exploits the technology of video to understand the complete crack growth phenomenon as the drill emerges from the exit side of the workpiece. Significant damage mechanisms are observed and defined, and correlations between the average exit drill forces and the crack tip position are shown. Instantaneous forces as they vary along the orientation of the cutting edges are identified in terms of their contribution to the crack propagation.