Showing papers on "Fracture toughness 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.

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.

Mechanical behaviour of laminated metal composites

Abstract: Laminated metal composites (LMCs) are a unique form of composite material in which alternating metal or metal containing layers are bonded together with discrete interfaces. The mechanical properties of these materials are reviewed. The tensile properties at low and high temperatures are described. At low temperature, very high tensile strengths can be achieved in deposition processed laminates and very high tensile ductilities can be achieved in roll bonded laminates by layer thickness refinement. At high temperature, superplasticity has been observed and agrees with predictions from constitutive creep relations. Damage critical properties (such as fracture toughness, fatigue, and impact behaviour) and damping can be superior to those exhibited by the component materials. The damage critical properties are strongly influenced by local delaminations at layer interfaces. Mechanisms responsible for many of the unique properties of LMCs have been proposed. The influence of processing, laminate archit...

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.

Biaxial flexural strength and indentation fracture toughness of three new dental core ceramics

Abstract: The traditional gold and porcelain fused to metal crowns have been challenged by the esthetic all-ceramic crown materials. Only previous experience with poor mechanical properties, lack of standardized tooth preparation, and processing challenges have prevented universal acceptance of all-ceramic crowns. However, stronger and tougher ceramics and unique processing methods for ceramics have been developed in the past 20 years. In this study, three new ceramic crown core materials were tested to compare their biaxial flexural strength and indentation fracture toughness. Ten specimens of Empress, In-Ceram, and Procera AllCeram ceramics were prepared according to their manufacturers' recommendations. The results revealed significant differences in flexural strength for the three materials (p < or = 0.05). The average flexural strengths of AllCeram, In Ceram, and Empress ceramics were 687 MPa, 352 MPa, and 134 MPa respectively. There was no statistically significant difference between the fracture toughness of Procera (4.48 MPa x m1/2) and In-Ceram ceramics (4.49 MPa x m1/2); however, both ceramics had significantly higher fracture toughness (p < 0.005) than Empress ceramic (1.74 MPa x m1/2).

High-temperature refractory metal-intermetallic composites

Abstract: In this article, toughness, oxidation, and rupture behaviors of present-generation refractory metal-intermetallic composites are compared to the performance requisites necessary to make these materials a competitive choice for the jet engine turbine environment of the future.

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.

Effect of Heat Treatment on Grain Size, Phase Assemblage, and Mechanical Properties of 3 mol% Y‐TZP

Abstract: The effect of heat treatment on the grain size, phase assemblage, and mechanical properties of a 3 mol% Y-TZP ceramic was investigated. Specimens were initially sintered for 2 h at 1450 C to near theoretical density; some specimens were then heat-treated at 1550, 1650, 1750, or 1850 C to coarsen the microstructure. The average grain size increased with heat treatment from 1750 C. The maximum fraction of tetragonal phase that transformed during fracture corresponded with the largest tetragonal grain size of {approximately}5--6 {micro}m. Strength was on the order of 1 GPa, and was surprisingly insensitive to heat-treatment temperature and grain size, contrary to previous studies. The fracture toughness increased from 4 to 10 MPa{center_dot}m{sup 1/2} with increasing grain size, owing to an increasing transformation zone size. Grain sizes larger than 5--6 {micro}m spontaneously transformed to monoclinic phase during cooling. Such critical grain sizes are much larger than those found in past investigations, and may be due to the greater fraction of cubic phase present which decreases the strain energy arising from more » crystallographic thermal expansion anisotropy of the tetragonal phase. « less

Critical notch-root radius effect in SENB-S fracture toughness testing

Abstract: The brittle behaviour of ceramic materials makes imperative the development of accurate and reproducible methods of measuring their resistance to fracture. To this end, a European round robin was set up to investigate the relative merits of five different methods of fracture toughness testing. Of these the single edge notch bend — saw cut (SENB-S) method seemed to deliver the most reproducible results, both within and between laboratories. However, it has been observed empirically that if notches are cut too thick, the values of fracture toughness determined are systematically too high. An explanation and a theoretically based relationship to describe this behaviour are presented. It is suggested that this effect results from the interaction of the stress field around the notch tip and defects related to the microstructure or machining damage. Measured data from a number of materials seem to correlate well with the theory. It is shown that if correct values of fracture toughness are to be determined with the SENB-S method, the notch width must be of the order of the size of the relevant microstructural or machining-induced defects (e.g. large pores and weak grain boundaries).

Fracture toughness of micro-fiber reinforced cement composites

Abstract: Toughness and strength improvements in cementbased matrices due to micro-fiber reinforcement were investigated. Cement paste and cement mortar matrices were reinforced at 1, 2 and 3% by volume of carbon, steel and polypropylene micro-fibers, and these composites were then characterized in the hardened state under an applied flexural load. Both notched and unnotched specimens were tested in four-point bending. Considerable strengthening, toughening and stiffening of the host matrix due to micro-fiber reinforcement was observed. The test data from the notched specimens was used to construct crack growth resistance and crack opening resistance curves for these composites and to identify the conditions necessary for failure. This paper recognizes the potential of these composites in various applications and stresses the need for continued research.

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.

How does “phase transformation toughening” work in semicrystalline polymers?

Abstract: The possibility of phase transformation toughening is demonstrated by the example of the β-modification of isotactic polypropylene (β-iPP), which undergoes βα-transformation (i.e., from hexagonal to monoclinic) during mechanical loading. The resulting α-iPP exhibits a higher crystalline density than the initial β-modification. That, along with the exothermic character of the βα-recrystallization, is responsible for the improvement in toughness that occurs. The occurrence of this βα-transformation is evidenced by differential scanning calorimetry (DSC). Toughness of the α- and β-iPP is studied and compared with the “essential work of fracture” concept by using static-loaded deeply double-edge-notched tensile (DDEN-T) specimens. The main effect of the βα-transformation is a large increase in the specific plastic work consumed in the necked zone. Light microscopic (LM) and infrared thermographic (IT) pictures reveal that the plastic zone becomes larger and its shape more circular when βα-transformation takes place. It is suggested that the principle of mechanical stress-induced phase transformation from a less toward a more dense crystalline state may be a universal tool for toughness upgrading in semicrystalline polymers.

Ductile crack growth−III. Transition to cleavage fracture incorporating statistics

Abstract: The fracture resistance of ferritic steels in the ductile/brittle transition regime is controlled by the competition between ductile tearing and cleavage fracture. Under typical conditions, a crack initiates and grows by ductile tearing but ultimate failure occurs by catastrophic cleavage fracture. In this study the tearing process is simulated using void-containing cell elements embedded within a conventional elastic-plastic continuum; details of the cell model are discussed in Parts I and II of this article. Weakest link statistics is incorporated into the cell element model and this new model is employed to predict the onset of unstable cleavage fracture. Our approach differs from previous analyses in several important ways. The elastic-plastic field computed for crack growth by ductile tearing is fully integrated with a weakest link cleavage fracture model. The model also accounts for the competition between the nucleation of voids from carbide inclusions and the unstable cracking of inclusions precipitating catastrophic cleavage fracture. This model leads immediately to a natural definition of the Weibull stress measure pertinent to cleavage fracture. The model is not restricted by the extent of plastic deformation and ductile tearing. Two effects are associated with ductile crack growth: the cumulative sampling volume is increased and the crack tip constraint is altered. Both effects have important roles which are treated within the present cleavage fracture model. Load-displacement behavior, ductile tearing resistance and transition to cleavage fracture are investigated for several different test geometries and a range of microstructural parameters. It is found that certain variations in microstructure can result in pronounced effects on the cleavage fracture toughness though they have no effect on the ductile tearing resistance preceding cleavage. Rate effects on ductile tearing and transition to cleavage fracture are also discussed. The model predicts trends in ductile/brittle transition that are consistent with available experimental data.

Toughening of Layered Ceramic Composites with Residual Surface Compression

Abstract: Effects of macroscopic residual stresses on fracture toughness of multilayered ceramic laminates were studied analytically and experimentally. Stress intensities for edge cracks in three-layer, single-edge-notch-bend (SENB) specimens with stepwise varying residual stresses in the absence of the crack and superimposed bending were calculated as a function of the crack length by the method of weight function. The selected weight function and the method of calculation were validated by calculating stress intensities for edge cracks in SENB specimens without the residual stresses and obtaining agreement with the stress-intensity equation recommended in ASTM Standard E-399. The stress-intensity calculations for the three-layer laminates with the macroscopic residual stresses were used to define an apparent fracture toughness. The theoretical predictions of the apparent fracture toughness were verified by experiments on three-layer SENB specimens of polycrystalline alumina with 15 vol% of unstabilized zirconia dispersed in the outer layers and 15 vol% of fully stabilized zirconia dispersed in the inner layer. A residual compression of ∼400 MPa developed in the outer layers by the constrained transformation of the unstabilized zirconia from the tetragonal to the monoclinic phase enhanced the apparent fracture toughness to values of 30 MPa.m1/2 in a system where the intrinsic fracture toughness was only 5 to 7 MPa.m1/2.

Fracture Toughness of 2‐D Woven SiC/SiC CVI‐Composites with Multilayered Interphases

Abstract: Relations between fracture toughness and fiber/matrix interphases were examined on various SiC/SiC composites made by chemical vapor infiltration (CVI) and reinforced with woven fiber bundles. Strong and weak fiber/matrix bondings were obtained using multilayered interphases consisting of various combinations of carbon and SiC layers of different thickness and using fibers which had been previously treated. Fracture toughness was estimated using the J-integral and using strain energy release rate computed with a model taking into account the presence of a process zone of matrix microcracks. Both approaches evidenced similar trends. It appeared that higher toughness was obtained with those composites possessing strong interphases and subject to dense matrix microcracking.

A single leg bending test for interfacial fracture toughness determination

Abstract: A single leg bending test is described and its suitability for interfacial fracture toughness testing is evaluated. The test specimen consists of a beam-type geometry comprised of two materials, one ‘top’ and one ‘bottom’, with a split at one end along the bimaterial interface. A portion of the bottom material in the cracked section of the beam is removed and the geometry is loaded in three-point bending. Thus, the reaction force of the support at the cracked end is transmitted only into the material comprising the top portion of the beam. The test is analyzed by a crack tip element analysis and the resulting expressions for energy release rate and mode mixity are verified by comparison with finite element results. It is shown that, by varying the thicknesses of the two materials, the single leg bending test can be used to determine the fracture toughness of most bimaterial interfaces over a reasonably wide range of mode mixities.

Grain size and porosity dependence of ceramic fracture energy and toughness at 22 °C

Abstract: A review of the fracture energy and toughness data for dense ceramics at 22 °C shows maxima commonly occurring as a function of grain size. Such maxima are most pronounced for non-cubic materials, where they are often associated with microcracking and R-curve effects, especially in oxides, but often also occur at too fine a grain size for association with microcracking. The maxima are usually much more limited, but frequently definitive, for cubic materials. In a few cases only a decrease with increasing grain size at larger grain size, or no dependence on grain size is found, but the extent to which these reflect lack of sufficient data is uncertain. In porous ceramics fracture toughness and especially fracture energy commonly show less porosity dependence than strength and Young's modulus. In some cases little, or no, decrease, or possibly a temporary increase in fracture energy or toughness are seen with increasing porosity at low or intermediate levels of porosity in contrast to continuous decreases for strength and Young's modulus. It is suggested that such (widely neglected) variations reflect bridging in porous bodies. The above maxima as a function of grain size and reduced decreases with increased porosity are less pronounced for fracture toughness as opposed to fracture energy, since the former reflects effects of the latter and Young's modulus, which usually has no dependence on grain size, but substantial dependence on porosity. In general, tests with cracks closer to the natural flaw size give results more consistent with strength behaviour. Implications of these findings are discussed.

Hardness and fracture toughness of bulk single crystal gallium nitride

Abstract: Basic mechanical properties of single crystal gallium nitride are measured A Vickers (diamond) indentation method was used to determine the hardness and fracture toughness under an applied load of 2N The average hardness was measured as 12±2 GPa and the average fracture toughness was measured as 079±010 MPa√m These values are consistent with the properties of brittle ceramic materials and about twice the values for GaAs A methodology for examining fracture problems in GaN is discussed