Showing papers on "Fracture mechanics 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.

Dynamic fracture using element-free galerkin methods

Abstract: The element-free Galerkin method for dynamic crack propagation is described and applied to several problems. This method is a gridless method, which facilitates the modelling of growing crack problems because it does not require remeshing; the growth of the crack is modelled by extending its surfaces. The essential feature of the method is the use of moving least-squares interpolants for the trial-and-test functions. In these interpolants, the dependent variable is obtained at any point by minimizing a weighted quadratic form involving the nodal variables within a small domain surrounding the point. The discrete equations are obtained by a Galerkin method. The procedures for modelling dynamic crack propagation based on dynamic stress intensity factors are also described.

A unified approach to the evaluation of linear elastic stress fields in the neighborhood of cracks and notches

Abstract: The problem of evaluating linear elastic stress fields in the neighborhood of cracks and notches is considered. An analytical solution valid for cracked and notched components is given in general terms, according to Muskhelishvili's method based on complex stress functions. The solution is particularly useful for V-shape notches in wide and finite plates under uniform tensile loading. It will be demonstrated that some remarkable solutions of fracture mechanics and notch analysis already reported in the literature can be considered special cases of this general solution, as soon as appropriate values of the free parameters are adopted.

Fracture toughness of re-entrant foam materials with a negative Poisson's ratio: experiment and analysis

Abstract: Fracture toughness of re-entrant foam materials with a negative Poisson's ratio is explored experimentally as a function of permanent volumetric compression ratio, a processing variable. J IC values of toughness of negative Poisson's ratio open cell copper foams are enhanced by 80 percent, 130 percent, and 160 percent for permanent volumetric compression ratio values of 2.0, 2.5, and 3.0, respectively, compared to the J IC value of the conventional foam (with a positive Poisson's ratio). Analytical study based on idealized polyhedral cell structures, approximating the shape of the conventional and re-entrant cells, disclose for re-entrant foam, toughness increasing as Poisson's ratio becomes more negative. The increase in toughness is accompanied by an increase in compliance, a combination not seen in conventional foam, and which may be useful in some applications such as sponges.

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.

Some basic fracture mechanics concepts in functionally graded materials

Abstract: In this paper, the crack-tip fields in a general nonhomogeneous material are summarized. The fracture toughness and R-curve of functionally graded materials (FGMs) are studied based on the crack-bridging concept and a rule of mixtures. It is shown that the fracture toughness is significantly increased when a crack grows from the ceramic-rich region into the metal-rich region in an alumina-nickel FGM. By applying the concept of the toughening mechanism to the study of the strength behavior of FGMs, it is found that the residual strength of the alumina-nickel FGM with an edge crack on the ceramic side is quite notch insensitive.

Strengthening of concrete prisms using the plate-bonding technique

Abstract: This paper presents the use of fracture mechanics for the plate bonding technique. Plates of steel or carbon-fibre reinforced plastic are bonded with an epoxy adhesive to rectangular concrete prisms and loaded in shear up to failure, what is normally known in fracture mechanics as mode II failure. In this special application a linear and a nonlinear approach are presented. The nonlinear equation derived for a realistic shear-deformation curve can only be used for numerical calculations. However, for simplified shear-deformation curves, the derived formula can be solved analytically. Results from tests, which are compared with the theory, are also presented.

Microbranching instability and the dynamic fracture of brittle materials.

Abstract: We describe experiments on the dynamic fracture of the brittle plastic, PMMA. The results suggest a view of the fracture process that is based on the existence and subsequent evolution of an instability, which causes a single crack to become unstable to frustrated microscopic branching events. We demonstrate that a number of long-standing questions in the dynamic fracture of amorphous, brittle materials may be understood in this picture. Among these are the transition to crack branching, ``roughness'' and the origin of nontrivial fracture surface, oscillations in the velocity of a moving crack, the origin of the large increase in the energy dissipation of a crack with its velocity, and the large discrepancy between the theoretically predicted asymptotic velocity of a crack and its observed maximal value. Also presented are data describing both microbranch distribution and evidence of a new three-dimensional to two-dimensional transition as the ``correlation width'' of a microbranch diverges at high propagation velocities. \textcopyright{} 1996 The American Physical Society.

On the toughness of ductile adhesive joints

Abstract: Crack propagation along one of the interfaces between a thin ductile adhesive layer and the elastic substrates it joins is considered. The layer is taken as being elastic-plastic, and the fracture process of the interface is modeled by a traction-separation law, characterized by the peak separation stress 6 and the work of separation per unit area To. Crack growth resistance curves for mode I loading of the adhesive joint are computed, with emphasis on steady-state toughness, as a function of three extrinsic effects : layer thickness, layer-substrate modulus mismatch, and initial residual stress in the layer. Conditions under which separation first occurs well ahead of the initial crack tip are discussed. 1. SPECIFICATION OF THE MODEL This paper continues the study begun by Tvergaard and Hutchinson (1994) in which an embedded fracture zone model is applied to the mode I fracture of an adhesive joint comprised of a thin elastic-plastic metal layer joining two elastic substrates. The present work employs the model to investigate the influence on joint toughness of both the elastic mismatch between the layer and the substrates and the residual stress in the layer. As in the earlier study, the thickness of the ductile layer is another extrinsic variable which comes into play. The approach adopted was first introduced by Needleman (1987) to study particle debonding in metal matrices and subsequently by Tvergaard and Hutchinson (1992, 1993) to model crack growth resistance in homogeneous solids and along interfaces. A traction-separation law simulating the fracture process is embedded within an elastic-plastic continuum as a boundary condition along the line extending ahead of the crack. In the case of an interface joining dissimilar materials, the separation law necessarily involves both the normal and shear tractions and the two associated relative displacements of the surfaces across the interface.

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.

The essential fracture work concept for toughness measurement of ductile polymers

Abstract: The essential work of fracture method is explored. The method was used to determine the fracture toughness of a series of toughened polymer blends and the crack resistance of a thin ductile polymer film, which could not be tested using the J-integral method. A comparison between J-integral and the specific essential work of fracture was carried out to test the equivalence of the two methods. The effects of geometry on the essential work of fracture and the plane-stress/plane-strain transition were studied. It has been shown that the specific essential work of fracture is a material constant, independent of sample geometry, and equivalent to the critical J-integral. The plane-stress/plane-strain transition is found to depend on the nature of the material tested. The sample thickness requirement for valid plane-strain specific essential work of fracture is discussed, and it Is proposed that the size requirement for the plane-strain specific essential work of fracture may be less rigorous than that for plane-strain J IC measurement.

Quantitative Prediction of Environmentally Assisted Cracking

Abstract: It has long been recognized that the stress corrosion cracking (SCC) and corrosion fatigue cracking susceptibility of various alloy and environment systems is dependent upon complex interactions between stress, material, and environmental parameters. This complexity can lead to scatter in cracking responses that, in turn, leads to difficulty in predicting the life of engineering structures. F.P. Ford was the 1995 recipient of the W.R. Whitney Award sponsored by NACE International. The present work is taken from his award lecture at CORROSION/95 held in March 1995 in Orlando, Florida. His lecture focused on how these interactions may be predicted quantitatively for ductile alloys in aqueous environments with knowledge of the cracking mechanism. This capability may lead to life prediction of critical structures in, for instance, boiling-water nuclear reactors (BWR).

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.

In Situ Toughened Silicon Carbide with Al‐B‐C Additions

Abstract: “In situ toughened” silicon carbides, containing Al, B, and C additives, were prepared by hot pressing. Densification, phase transformations, and microstructural development were described. The microstructures, secondary phases, and grain boundaries were characterized using a range of analytical techniques including TEM, SEM, AES, and XRD. The modulus of rupture was determined from fourpoint bend tests, while the fracture toughness was derived either from bend tests of beam-shaped samples with a controlled surface flaw, or from standard disk-shaped compact-tension specimens precracked in cyclic fatigue. The R-curve behavior of an in situ toughened SiC was also examined. A steady-state toughness over 9 MPa·m1/2 was recorded for the silicon carbide prepared with minimal additives under optimum processing conditions. This increase in fracture toughness, more than a factor of three compared to that of a commercial SiC, was achieved while maintaining a bend strength of 650 MPa. The mechanical properties were found to be related to a microstructure in which platelike grain development had been promoted and where crack bridging by intact grains was a principal source of toughening.

Modeling and simulation of crack propagation in mixed-modes interlaminar fracture specimens

Abstract: A study of mixed-mode crack propagation in bending-based interlaminar fracture specimens is here presented. A numerical scheme to simulate full crack propagation is proposed which makes use of interface laws relating interlaminar stresses to displacement discontinuities along the plane of crack propagation. The relation between interface laws and mixed-mode failure loci in terms of critical energies is discussed and clarified. Numerical simulations are presented and compared with analytical and experimental results.

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 investigation of 3-D constraint effects on brittle fracture in SE(B) and C(T) specimens

Abstract: Specimen size and geometry effects on cleavage fracture of ferritic steels tested in the ductile-to-brittle transition region remain an important technological impediment in industrial applications of fracture mechanics and in the on-going development of consensus fracture testing standards. This investigation employs 3-D nonllinear finite element analyses to conduct an extensive parametric evaluation of crack front stress triaxiality for deep notch SE(B) and C(T) specimens and shallow notch SE(B) specimens, with and without side grooves. Crack front conditions are characterized in terms of J-Q trajectories and the constraint model for cleavage fracture toughness proposed previously by Dodds and Anderson. An extension of the toughness scaling model suggested here combines a revised ‘in-plane’ constraint correction with an explicit thickness correction derived from extreme value statistics. The 3-D analyses provide ‘effective’ thicknesses for use in the statistical correction which reflect the interaction of material flow properties and specimen aspect ratios, a/W and W/B, on the varying levels of stress triaxiality over the crack front. The 3-D computational results imply that a significantly less strict size/deformation limit, relative to the limit indicated by previous plane-strain computations, is needed to maintain small-scale yielding conditions at fracture by a stress-controlled, cleavage mechanism in deep notch SE(B) and C(T) speciments. Moreover, the analyses indicate that side grooves (20 percent) should have essentially no net effect on measured toughness values of such specimens. Additional new results made available from the 3-D analyses also include revised η-plastic factors for use in experimental studies to convert measured work quantities to thickness average and maximum (local) J-values over the crack front. To estimate CTOD values, new m-factors are included for use in the expression 131-1.

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.

Basic issues in the mechanics of high cycle metal fatigue

Abstract: Mechanics issues related to the formation and growth of cracks ranging from subgrain dimension to up to the order of one mm are considered under high cycle fatigue (HCF) conditions for metallic materials. Further efforts to improve the accuracy of life estimation in the HCF regime must consider various factors that are not presently addressed by traditional linear elastic fracture mechanics (LEFM) approaches, nor by conventional HCF design tools such as the S-N curve, modified Goodman diagram and fatigue limit. A fundamental consideration is that a threshold level for ΔK for small/short cracks may be considerably lower than that for long cracks, leading to non-conservative life predictions using the traditional LEFM approach. Extension of damage tolerance concepts to lower length scales and small cracks relies critically on deeper understanding of (a) small crack behavior including interactions with microstructure, (b) heterogeneity and anisotropy of cyclic slip processes associated with the orientation distribution of grains, and (c) development of reliable small crack monitoring techniques. The basic technology is not yet sufficiently advanced in any of these areas to implement damage tolerant design for HCF. The lack of consistency of existing crack initiation and fracture mechanics approaches for HCF leads to significant reservations concerning application of existing technology to damage tolerant design of aircraft gas turbine engines, for example. The intent of this paper is to focus on various aspects of the propagation of small cracks which merit further research to enhance the accuracy of HCF life prediction. Predominant concern will rest with polycrystalline metals, and most of the issues pertain to wide classes of alloys.

Three-dimensional cell model analyses of void growth in ductile materials

Abstract: Three-dimensional micromechanical models were developed to study the damage by void growth in ductile materials. Special emphasis is given to the influence of the spatial arrangement of the voids. Therefore, periodical void arrays of cubic primitive, body centered cubic and hexagonal structure are investigated by analyzing representative unit cells. The isotropic behaviour of the matrix material is modelled using either v. Mises plasticity or the modified Gurson-Tvergaard constitutive law. The cell models are analyzed by the large strain finite element method under monotonic loading while keeping the stress triaxiality constant. The obtained mesoscopic deformation response and the void growth of the unit cells show a high dependence on the value of triaxiality. The spatial arrangement has only a weak influence on the deformation behaviour, whereas the type and onset of the plastic collapse behaviour are strongly affected. The parameters of the Gurson-Tvergaard model can be calibrated to the cell model results even for large porosity, emphasizing its usefulness and justifying its broad applicability.

Size Effect and Fracture Characteristics of Composite Laminates

Abstract: Measurements of the size effect on the nominal strength of notched specimens of fiber composite laminates are reported. Tests were conducted on graphite/epoxy crossply and quasi-isotropic laminates. The specimens were rectangular strips of widths 6.4, 12.7, 25.4 and 50.8 mm (0.25, 0.50, 1.00 and 2.00 in.) geometrically similar in two dimensions. The gage lengths were 25, 51, 102 and 203 mm (1.0, 2.0, 4.0 and 8.0 in.). One set of specimens had double-edge notches and a [0/92{sub 2}]{sub s} crossply layup, and another set had a single-sided edge notch and a [0/{+-}45/90]{sub s} quasi-isotropic layup. It has been found that there is a significant size effect on the nominal strength. It approximately agrees with the size effect law proposed by Bazant, according to which the curve of the logarithm of the nominal strength versus the logarithm of size represents a smooth transition from a horizontal asymptote, corresponding to the strength criterion (plastic limit analysis), to an inclined asymptote of {minus}0.5 slope, corresponding to linear elastic fracture mechanics. Optimum fits of the test results to identify the material fracture characteristics, particularly the fracture energy and the effective length of the fracture process zone. Finally, the R-curves are also identified on themore » basis of the maximum load data. The results show that in design situations with notches or large initial traction-free cracks the size effect on the nominal strength of fiber composite laminates must be taken into account.« less

Fracture mechanics for the design of ceramic multilayer actuators

Abstract: In a multilayer actuator, each internal electrode terminates an edge inside the active ceramic. Around the edge, the nonuniform electric field generates an incompatible strain field, which, in its turn, generates stresses and may cause the ceramic to crack. The industry has been exploring alternative electrode configurations to alleviate the stress concentration. The effort has been empirical and benefited little from numerical simulations. An inherent difficulty is that the actuator ceramics have nonlinear electro-mechanical interactions, of which no unified mathematical description is now available. In this paper, we develop a crack nucleation model that includes essential features of this nonlinearity. The model applies to both paraelectrics and ferroelectrics. Attention is focused on situations where the small-scale saturation conditions prevail. That is, the driving voltage is low enough so that the bulk of the ceramics is linearly dielectric, except for a cylinder of a small radius around the electrode edge. Inside the cylinder, large strains result from electrostriction or polar rotation. We identify a parameter group that determines the cracking condition; details in the material description only affect a dimensionless coefficient. Everything else being fixed, a critical layer thickness exists, below which a multilayer actuator will not crack around its internal electrode edges. Merits and limitations of the small-scale saturation model are discussed. We analyze this model analytically for a paraelectric with perfect polarization saturation, and estimate the value of the dimensionless coefficient in the model.

Mechanical properties of reactive powder concretes

Abstract: Reactive Powder Concretes (RPC) are a set of ultrahigh-strength concretes reinforced with steel fibers. Their compressive strength is between 200 and 800MPa, and their flexural strength can reach 140MPa.RPC200 has been studied with respect to compressive strength and two-point loading strength to define its mechanical behavior.RPC800, which has been mostly studied from the point of view of compressive strength, displays hardening elastic non-linear behavior at low stress. This behavior is similar to that of some natural rocks. The critical stress intensity factorKIc, and the average fracture energy,\(\bar G_F \), ofRPC200 andRPC800 have been studied experimentally by applying the theory of linear fracture mechanics (compliance method). The fracture energy, which is a measurement of ductility, can reach 40,000 J/m2 forRPC200, as compared to 100 to 150 J/m2 for ordinary concretes. Fracture energy depends on the volume of fibers added to the concrete. The optimum content is between 2 and 3% by volume.