Showing papers on "Fracture toughness published in 1993"

Fracture of Brittle Solids

Abstract: This is an advanced text for higher degree materials science students and researchers concerned with the strength of highly brittle covalent–ionic solids, principally ceramics. It is a reconstructed and greatly expanded edition of a book first published in 1975. The book presents a unified continuum, microstructural and atomistic treatment of modern day fracture mechanics from a materials perspective. Particular attention is directed to the basic elements of bonding and microstructure that govern the intrinsic toughness of ceramics. These elements hold the key to the future of ceramics as high-technology materials - to make brittle solids strong, we must first understand what makes them weak. The underlying theme of the book is the fundamental Griffith energy-balance concept of crack propagation. The early chapters develop fracture mechanics from the traditional continuum perspective, with attention to linear and nonlinear crack-tip fields, equilibrium and non-equilibrium crack states. It then describes the atomic structure of sharp cracks, the topical subject of crack-microstructure interactions in ceramics, with special focus on the concepts of crack-tip shielding and crack-resistance curves, and finally deals with indentation fracture, flaws, and structural reliability.

The influence of plasticity on mixed mode interface toughness

Abstract: Calculations are reported for the mixed mode toughness of an interface joining an elastic-plastic solid to a solid which does not yield plastically. A potential function of the components of the crack face displacements is used to generate the tractions along the interface where the fracture processes causing separation occur. The two main parameters characterizing this potential are the work of separation per unit area and a peak normal stress. This description of the interface separation process is embedded within the continuum description as a boundary condition on the interface linking the adjoining solids. Small-scale yielding in plane strain is considered with the remote field specified by the magnitude and phase of the mixed mode stress intensity factors. Crack growth resistance curves are computed for a range of the most important nondimensional material parameters and for various combinations of remote mixed mode loading. Particular emphasis is placed on the ratio of the steady-state interface toughness to the “intrinsic” work of separation as it depends on plastic yielding and on the combination of modes 1 and 2. Plasticity enhances the interface toughness for all modes of loading, but substantially more so in the presence of a significant mode 2 component of loading than in near-mode 1 conditions.

Effect of electric field on fracture of piezoelectric ceramics

Abstract: Closed form solutions for all three modes of fracture for an infinite piezoelectric medium containing a center crack subjected to a combined mechanical and electrical loading were obtained. The explicit mechanical and electrical fields near the crack tip were derived, from which the strain energy release rate and the total potential energy release rate were obtained by using the crack closure integral. The suitability in using the stress intensity factor, the total energy release rate, or the mechanical strain energy release rate as the fracture criterion was discussed.

Fracture Mechanics: An Introduction

Abstract: Conversion table Preface to the Second Edition Preface 1: Introduction 1.1. Conventional failure criteria 1.2. Characteristic brittle failures 1.3. Griffith's work 1.4. Fracture mechanics References 2: Linear Elastic Stress Field in Cracked Bodies 2.1. Introduction 2.2. Crack deformation modes and basic concepts 2.3. Westergaard method 2.4. Singular stress and displacement fields 2.5. Stress intensity factor solutions 2.6. Three-dimensional cracks Examples Problems Appendix 2.1 References 3: Elastic-Plastic Stress Field in Cracked Bodies 3.1. Introduction 3.2. Approximate determination of the crack-tip plastic zone 3.3. Irwin's model 3.4. Dugdale's model Examples Problems References 4: Crack Growth Based on Energy Balance 4.1. Introduction 4.2. Energy balance during crack growth 4.3. Griffith theory 4.4. Graphical representation of the energy balance equation 4.5. Equivalence between strain energy release rate and stress intensity factor 4.6. Compliance 4.7. Crack stability Examples Problems References 5: Critical Stress Intensity Factor Fracture Criterion 5.1 . Introduction 5.2. Fracture criterion 5.3. Variation of Kc with thickness 5.4. Experimental determination of K1c 5.5. Crack growth resistance curve (R-curve) method 5.6. Fracture mechanics design methodology Examples Problems Appendix 5.1 References 6: J-Integral and Crack Opening Displacement Fracture Criteria 6.1. Introduction 6.2. Path-independent integrals 6.3. J-integral 6.4. Relationship between the J-integral and potential energy 6.5. J-integral fracture criterion 6.6. Experimental determination of the J-integral 6.7. Stable crack growth studied by the J-integral 6.8. Crack opening displacement (COD)fracture criterion Examples Problems References 7. Strain Energy Density Failure Criterion: Mixed-Mode Crack Growth 7.1. Introduction 7.2. Volume strain energy density 7.3. Basic hypotheses 7.4. Two-dimensional linear elastic crack problems 7.5. Uniaxial extension of an inclined crack 7.6. Ductile fracture 7.7. The stress criterion Examples Problems References 8: Dynamic Fracture 8.1. Introduction 8.2. Mott's model 8.3. Stress field around a rapidly propagating crack 8.4. Strain energy release rate 8.5. Crack branching 8.6. Crack arrest 8.7. Experimental determination of crack velocity and dynamic stress intensity factor Examples Problems References 9: Fatigue and Environment-Assisted Fracture 9.1. Introduction 9.2. Fatigue crack propagation laws 9.3. Fatigue life calculations 9.4. Variable amplitude loading 9.5. Environment-assisted fracture Examples Problems References 10: Micromechanics of Fracture 10.1. Introduction 10.2. Cohesive strength of solids 10.3. Cleavage fracture 10.4. Intergranular fracture 10.5. Ductile fracture 10.6. Crack detection methods References 11: Composite Materials 11.1. Introduction 11.2. Through4hickness cracks 11.3. Interlaminar fracture References 12: Thin Films 12.1. Introduction 12.2. Interfacial failure of a bimaterial system 12.3. Steady-state solutions for cracks in bilayers 12.4. Thin films under tension 12.5. Measurement of interfacial fracture toughness References 13: Nanoindentation 13.1. Introduction 13.2. Nanoindentation for measuring Young's modulus and hardness 13.3. Nanoindentation for measuring fracture toughness 13.4. Nanoindentation for measuring interfacial fracture toughness

Fracture of brittle solids: Atomic aspects of fracture

Abstract: Until now we have approached crack propagation from the continuum viewpoint. Nonetheless, repeated allusions have been made in chapters 3 and 5 to the fundamental limitations of any such approach that disregards the atomic structure of solids. There we argued for the incorporation of a lattice-plane range parameter as a critical scaling dimension in the brittle crack description. We noted that the Barenblatt cohesion-zone model avoids reference to the atomic structure by resorting to the Irwin slit description of cracks; yet estimates of the critical crack-opening dimensions using this same model confirm that the intrinsic separation process indeed operates at the atomic level. The Elliot lattice half-space model of sect. 3.3.2 represents one attempt to incorporate an essential element of discreteness. The phenomenological kinetic models of sect. 5.5, with their presumption of energy barriers, represent another. However, those models are at the very least quasi-continuous. In brittle fracture, as in any thermodynamic process, the final answers must be sought at the atomic or molecular level. On the other hand, while an atomistic approach provides greater physical insight into the crack problem, it inevitably involves greater mathematical complexity. Classically, solids may be represented as manybody assemblages of point masses (atoms) linked by springs (bonds). We will see that the mass–spring representation can lead us to a deeper understanding of brittle cracks. But even this representation is oversimplistic. In some cases, particularly when the crack interacts with environmental species, it is necessary to consider atoms as elastic spheres rather than point masses, to allow properly for molecular size effects.

Mechanical behavior of alumina-silicon carbide «Nanocomposites»

Abstract: The fracture behavior of Al2O3 containing 5 vol% 0.15μm SiC particles was investigated using indentation techniques. A significant increase in strength was achieved by the addition of SiC particles to the base Al2O3. Specifically, the strength increased from 560 MPa for Al2O3 to 760 MPa for the composite samples (average values for unindented hotpressed bars tested in four-point bending). After annealing for 2 h at 1300°C, the average strength of the composite samples increased to about 1000 MPa. Toughness was estimated using indentation-strength data. While there was a slight increase in toughness, the increase was not sufficient to account for the increase in the unindented strength on SiC particle addition. It is suggested that the observed strengthening and apparent toughening were due to a machining-induced compressive surface stress.

Fracture toughness testing of brittle materials

Abstract: Research within the past two decades has achieved a dramatic upsurge of improvements in the mechanical properties of engineering ceramics. These improvements have often been made through increased toughness by novel toughening mechanisms such as the stress induced phase transformation, microcracking, fibre/whisker crack bridging, etc. These may occur not only in the frontal process zone ahead of a sharp crack, but also in the following crack wake region. The consequences of these microfracture processes and mechanisms in the wake and the crack bridging regions are significant, for they result in very complex fracture processes and they create many critical issues and difficulties in the experimental determination of the fracture resistance of brittle materials. The lack of a physical basis for a fracture criterion in the present fracture mechanics framework adds further confusion to fracture mechanics studies. This paper is a state of the art review of the application of fracture mechanics to brit...

Ceramic Matrix Composites

Abstract: The present state of the knowledge of ceramic-matrix composites have been reviewed. The fracture toughness of present structural ceramics are not enough to permit design of high performance machines with ceramic parts. They also fail by catastrophic brittle fracture. It is generally believed that further improvement of fracture toughness is only possible by making composites of ceramics with ceramic fibre, particulate or platelets. Only ceramic-matrix composites capable of working above 1000 degree centigrade has been dealt with keeping reinforced plastics and metal-reinforced ceramics outside the purview. The author has discussed the basic mechanisms of toughening and fabrication of composites and the difficulties involved. Properties of available fibres and whiskers have been given. The best results obtained so far have been indicated. The limitations of improvement in properties of ceramic-matrix composites have been discussed.

Continuum and micromechanics treatment of constraint in fracture

Abstract: Two complementary methodologies are described to quantify the effects of crack-tip stress triaxiality (constraint) on the macroscopic measures of elastic-plastic fracture toughness J and Crack-Tip Opening Displacement (CTOD). In the continuum mechanics methodology, two parameters J and Q suffice to characterize the full range of near-tip environments at the onset of fracture. J sets the size scale of the zone of high stresses and large deformations while Q scales the near-tip stress level relative to a high triaxiality reference stress state. The material's fracture resistance is characterized by a toughness locus Jc(Q) which defines the sequence of J-Q values at fracture determined by experiment from high constraint conditions (Q∼0) to low constraint conditions (Q<0). A micromechanics methodology is described which predicts the toughness locus using crack-tip stress fields and critical J-values from a few fracture toughness tests. A robust micromechanics model for cleavage fracture has evolved from the observations of a strong, spatial self-similarity of crack-tip principal stresses under increased loading and across different fracture specimens. We explore the fundamental concepts of the J-Q description of crack-tip fields, the fracture toughness locus and micromechanics approaches to predict the variability of macroscopic fracture toughness with constraint under elastic-plastic conditions. Computational results are presented for a surface cracked plate containing a 6:1 semielliptical, a=t/4 flaw subjected to remote uniaxial and biaxial tension. Crack-tip stress fields consistent with the J-Q theory are demonstrated to exist at each location along the crack front. The micromechanics model employs the J-Q description of crack-front stresses to interpret fracture toughness values measured on laboratory specimens for fracture assessment of the surface cracked plate.

An Edge Crack Torsion Method for Mode III Delamination Fracture Testing

Abstract: A new fracture toughness test, the edge crack torsion method, has been developed for characterizing the mode III delamination behavior of composites. The test is based on a laminate specimen subjected to torsion to propagate an edge delamination crack in its midplane. The crack growth mode of the specimen has been deduced to be mode III from fracture mechanics principles. The torsional behavior and the corresponding fracture parameter GIIIC have been analyzed on the basis of plate torsion and laminate theory. Edge crack torsion tests were performed to measure GIIIC of several carbon fiber/epoxy composite systems. Laminate layups were optimized to yield linear elastic fracture behavior of the specimens. The specimens were also sufficiently compliant to allow GIIIC to be readily obtained by using the compliance calibration method. The deformation characteristics of the specimens were found to follow the laminate torsion description. SEM observations showed fracture surface morphology varying with resin microstructures and, for the case of an untoughened matrix, were consistent with what was reported in the literature for other proposed mode III fracture tests.

Fracture toughness and fracture mechanisms of PBT/PC/IM blend

Abstract: Scanning electron microscopy (SEM) and transmission electron microscopy (TEM) techniques were employed in the morphology and fracture mechanisms studies on a commercial polybutylene terephthalate/polycarbonate/impact modifier (PBT/PC/IM) blend. The fracture mechanisms involved at different temperatures under both impact and static loading were revealed. It was found that massive plastic deformation of the matrix material occurred after rubber particle cavitation; and it was this plastic deformation that was responsible for the drastic enhancement in fracture toughness although the widespread cavitation did absorb a considerable amount of energy as well. The major source of toughness was the same for both impact and static fracture tests, but the toughening processes became effective at a much lower temperature under static than impact conditions. The sequence of toughening events was also observed using TEM.

Effect of Grain Growth of β‐Silicon Nitride on Strength, Weibull Modulus, and Fracture Toughness

Abstract: [beta]-Si[sub 3]N[sub 4] powder containing 1 mol% of equimolar Y[sub 2]O[sub 3]-Nd[sub 2]O[sub 3] was gas-pressure sintered at 2,000C for 2 h (SN2), 4 h (SN4), and 8 h (SN8) in 30-MPa nitrogen gas. These materials had a microstructure of in-situ composites'' as a result of exaggerated grain growth of some [beta]-Si[sub 3]N[sub 4] grains during firing. Growth of elongated grains was controlled by the sintering time, so that the desired microstructures were obtained. SN2 had a Weibull modulus as high as 53 because of the uniform size and spatial distribution of its large grains. SN4 had a fracture toughness of 10.3 MPa[center dot]m[sup 1/2] because of toughening provided by the bridging of elongated grains, whereas SN8 showed a lower fracture toughness, possibly caused by extensive microcracking resulting from excessively large grains. Gas-pressure sintering of [beta]-Si[sub 3]N[sub 4] powder was shown to be effective in fostering selective grain growth for obtaining the desired composite microstructure.

Dependence of ceramic fracture properties on porosity

Abstract: A connected-grain model developed earlier to study the modulus of elasticity as a power-law of density was extended to study the dependence of the flexural strength of polycrystalline ceramics on porosity. Relations were derived for specific surface fracture energy, fracture toughness and flexural strength as power laws of (1 −p), wherep is porosity. Model validity was confirmed with data on α-alumina, UO2, Si3N4, and the YBa2Cu3O7−δ superconductor.

Particulate fracture during deformation of a spray formed metal-matrix composite

Abstract: The mechanisms of deformation and failure in a 2618 Al alloy reinforced with 15 vol pct SiC particilates were studied and compared with those of the unreinforced alloy, processed by spray forming as well. Tensile and fracture toughness tests were carried out on naturally aged and peak-aged specimens. The broken specimens were sliced through the middle, and the geometric features of fractured and intact particulates were measured. The experimental observations led to the conclusion that failure took place by the progressive fracture of the particulates until a critical volume fraction was reached. An influence of the particulate size and aspect ratio on the probability of fracture was found, the large and elongated particulates being more prone to fail, and the fracture stress in the particulates seemed to obey the Weibull statistics. The dif- ferences in ductility found between the naturally aged and peak-aged composites were explained in terms of the number of broken particulates as a function of the applied strain. Numerical simulations of the deformation process indicated that the stresses acting on the particulates are higher in the peak-aged material, precipitating the specimen failure. Moreover, the compressive residual stresses induced on the SiC during water quenching delayed the onset of particulate breakage in the naturally aged material.

Effect of electric fields on fracture behavior of PZT ceramics

Abstract: To obtain a better understanding of the effects of electric fields on the fatigue lifetime of PZT materials, specimens of poled and unpoled PZT-8 were either pre-indented to generate a pre- crack or indented in the presence of an applied static electric field. Significant differences in the crack growth behavior perpendicular and parallel to the poling direction were observed in static and time-varying electric fields leading to a reduction in the fracture toughness normal to the poling axis. Fatigue crack growth was significant at field amplitudes as low as 5% of the poling fields. These results are shown to be related to the effects of electrical fields on the stresses at the crack tip.© (1993) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.

Relationship between Fracture Surface Roughness and Fracture Behavior of Cement Paste and Mortar

Abstract: Fracture surfaces of cement and mortar specimens were characterized using a confocal microscope to create three-dimensional computer-based topographic maps. The texture of the fracture surfaces was quantified using image analysis techniques to compute a roughness parameter and fractal dimension. Total porosity, pore-size distribution, compressive strength, and fracture properties of the specimens were determined and compared with the roughness parameter. Fracture properties were determined by notched-beam tests and the results were analyzed both by using conventional linear elastic fracture mechanics as well as a compliance-based approach that incorporated R-curve type of behavior. A positive correlation between fracture surface roughness and fracture toughness was demonstrated.

Toughened plastics I : science and engineering

Abstract: Mechanisms of Toughening Thermoset Resins Fracture-Toughness Testing of Toughened Polymers Multiple-Phase Toughening-Particle Morphology: Effects on the Properties of Rubber-Toughened Poly(methyl methacrylate) Toughened Semicrystalline Engineering Polymers: Morphology, Impact Resistance, and Fracture Mechanisms Deformation and Fracture Toughness in High-Performance Polymers: Comparative Study of Crystallinity and Cross-Linking Effects The Damage Zone in Some Ductile Polymers Under a Triaxial Tensile Stress State Additive Effects on the Toughening of Unsaturated Polyester Resins Particle-Matrix Interfacial Bonding: Effect on the Fracture Properties of Rubber-Modified Epoxy Polymers Macroscopic Fracture Behavior: Correlation with Microscopic Aspects of Deformation in Toughened Epoxies Optimization of Mode-I Fracture Toughness of High-Performance Epoxies Using Designed Core-Shell Rubber Particles Toughening of Epoxy Resin Networks with Functionalized Engineering Thermoplastics Epoxy-Rubber Interactions The Synergistic Effect of Cross-Link Density and Rubber Additions on the Fracture Toughness of Polymers Rubber-Modified Epoxies: Analysis of the Phase Separation Process Thermal Shock Resistance of Toughened Epoxy Resins Toughening Epoxy Resin with Poly(methyl methacrylate)-Grafted Natural Rubber Toughening Epoxies Using Rigid Thermoplastic Particles: A Review Preparation of Poly(butylene terephthalate)-Toughened Epoxies Toughening of Epoxy Resins by Epoxidized Soybean Oil Structure-Property Relations of High-Temperature Composite Polymer Matrices Model Multilayer Toughened Thermosetting Advanced Composites Multiphase Matrix Polymers for Carbon Fiber Composites Thermal Characterization of the Cure Kinetics of Advanced Matrices for High-Performance Composites

Prediction of delamination in composite laminates subjected to low velocity impact

Abstract: A method for predicting impact-induced delamination in composite lami nates was proposed. This method is suitable for low velocity impact with heavy impactors. Static delamination fracture toughness was used to predict delamination crack growth under impact conditions. Curing stresses were also considered and found to play a signifi cant role in evaluating the fracture toughness of some laminates such as [905/05/90 5]. Ex periments were performed to obtain the impact force history from which the peak force was used to determine the extent of delamination crack length. The prediction of delami nation size using static fracture toughness was found to agree very well with the experi mental result.

Round Robin Testing for Mode I Interlaminar Fracture Toughness of Composite Materials

Abstract: This report summarizes the results of several interlaboratory “round robin” test programs for measuring the Mode I interlaminar fracture toughness of advanced fiber-reinforced composite materials. Double cantilever beam (DCB) tests were conducted by participants in ASTM Committee D-30 on High Modulus Fibers and Their Composites and by representatives of the European Group on Fracture (EGF) and the Japanese Industrial Standards Group (JIS). DCB tests were performed on three AS4 carbon fiber-reinforced composite materials: AS4/3501-6 with a brittle epoxy matrix, AS4/BP907 with a tough epoxy matrix, and AS4/PEEK with a tough thermoplastic matrix. Difficulties encountered in manufacturing panels, as well as conducting the tests, are discussed. Critical issues that developed during the course of the testing are highlighted. Results of the round robin testing used to determine the precision of the ASTM DCB test standard are summarized.

The brittle-to-ductile transition in silicon

Abstract: In order to better understand the brittle-to-ductile transition in silicon, details of different experimental and numerical studies are discussed. In the concept of elastical stress intensity factors, experiments with four-point-bending bars are not directly comparable with experiments done with tapered-double-cantilever-beam samples. The internal elastic and plastic conditions of the samples are different due to large differences of the load levels applied in both cases. A smooth transition from cleavage to semi-brittle fracture with small, relatively homogeneous plastic zones precedes a sharp transition to general plasticity. The fracture toughness between both transitions is independent of temperature, yielding a plateau region. Numerical simulations qualitatively show the same results. The plateau region is a direct consequence of the shielding dynamics, the sharp transition is a consequence of the assumed emission configuration of the dislocations. The simulations do not rely on a heterogeneous distribution of dislocation sources.

A model for lapping of glass

Abstract: Lapping of glass and other brittle materials is an important economic activity. Nevertheless, it has not received much scientific attention, despite the fact that it is also related to problems of wear (three-body abrasion). Therefore, lapping of glass has been analysed in terms of the concept of lateral fracture, by studying the influence of material parameters, namely Young's modulus, hardness and fracture toughness, on material removal and surface roughness for two different sets of experimental conditions. The concept was found to be well applicable, and was therefore used to develop a model of three-body abrasion by material removal via rolling and indenting abrasives. The model gives a good description of the two experiments. It allows an average normal force per abrasive to be determined from Preston's coefficient and the characteristics of the workpiece and abrasive.

Analysis of a mixed mode fracture specimen: the asymmetric double cantilever beam

Abstract: An asymmetric double cantilever beam (ADCB) is a simple but effective specimen for the measurement of polymer/polymer and polymer/non-polymer bimaterial interface fracture toughness. In order to characterize fully the bimaterial interface strength, and to control the crack trajectory, the critical energy release rate, G c, and the phase angle, ψ, of the applied stress field as functions of loading and geometry of the specimen should be obtained. For most practical cases, ψ has to be evaluated numerically. In this work, a boundary element analysis is carried out to obtain G and ψ for the ADCB specimen at different material and geometry combinations. An expression for the energy release rate, G, based on Kanninen's beam on elastic foundation model is compared with the numerical results. Limitations on the use of the ADCB specimen are also discussed.