Showing papers on "Fracture toughness published in 1980"

High-strength silicon carbide fibre-reinforced glass-matrix composites

Abstract: Silicon carbide fibre-reinforced glass-matrix composites have been fabricated and tested. Two fibre forms, a 140 μm diameter monofilament and a 10 μm diameter filamentary yarn, were incorporated into a matrix of borosilicate glass. The hot-pressing fabrication procedure resulted in fully dense unidirectionally reinforced specimens with excellent flexural strength and fracture toughness over the temperature range 22 to 700° C. In addition, composite thermal expansion was found to be nearly independent of fibre orientation indicating that multiaxially reinforced composites should be readily fabricable without the occurrence of extensive cracking.

Crack blunting mechanisms in polymers

Abstract: A quantitative model has been developed to account for the degree of blunting that occurs at crack tips in epoxy materials prior to the onset of crack propagation. This mechanism controls the subsequent mode of crack growth and, to a large extent, the toughness as defined by the stress intensity factor for crack initiation. From this model a unique fracture criterion is derived which is applicable over all modes of crack propagation.

Initiation and Growth of Transverse Cracks and Edge Delamination in Composite Laminates Part 1. An Energy Method

Abstract: This paper is concerned with the basic fracture mechanisms involved in matrix-dominated failures in fibrous composite laminates, Specifically, interlaminar fracture in the form of free-edge ply delamination and intra- laminar fracture in the form of multiple transverse cracks are investigated. In each case, a theory is formulated based on the classical linear fracture mechanics concept of strain energy release rate as a criterion for crack growth. A finite element technique incorporating the virtual crack-closure procedure is developed to generate numerical results. Simultaneously, an experimental study is conducted using a series of graphite epoxy laminates in the form of (±25/90n)s, n = 1,2,3. Part 1 of this paper presents the development of the method from the conceptual, physical and numerical considerations, while Part 2 provides for a comparison between the analyti cal and experimental results.

Fracture Toughness Determination of A12O3 Using Four‐Point‐Bend Specimens with Straight‐Through and Chevron Notches

Abstract: Fracture toughness of a sintered A12O3 was determined with four-point-bend specimens having either straight-through or chevron notches. For the straight-through notched specimens, measured KIc decreased with decreasing notch width. For the smallest notch width (66 μm) KIc= 3.42±0.13 MN m−¾. For specimens with chevron notches, a crack initiates and extends from the tip of the notch under increasing load. KIc is calculated from the maximum load without measuring crack length, under the assumption that the derivative of the compliance is the same as that for a specimen with a straight-through crack. A refined calculation accounts for the truncated chevron crack shape at maximum load using Bluhm's slice model. For the chevronnotch configuration, a value of KIc= 3.49±0.11 MN m−¾ was measured, which appears to be independent of the initial notch length a0 (distance from the crack mouth to the tip of the triangular notch). An effect of a1 (length of the chevron notch at the surface) on KIc was observed, independent of whether the calculation of KIc was based on the straight-through crack assumption or on the slice model.

Cumulative-strain-damage model of ductile fracture: simulation and prediction of engineering fracture tests

Abstract: A cumulative-strain-damage criterion is used to predict the initiation and propagation of fracture in ductile materials. The model is consistent with a model of ductile rupture that involves void growth and coalescence. Two- and three-dimensional finite difference computer codes, which use incremental-plasticity theory to describe large strains with rotation, are used to trace the history of damage in a material due to external forces. Fracture begins when the damage exceeds a critical value over a critical distance and proceeds as the critical-damage state is reached elsewhere. This unified approach to failure prediction can be applied to an arbitrary geometry if the material behavior has been adequately characterized. The damage function must be calibrated for a particular material using various material property tests. The fracture toughness of 6061-T651 aluminum is predicted.

Fatigue of polymers

Abstract: The general nature of fracture in polymers, when subject to alternating loads as distinct from static or steadily increasing loads, is reviewed; and the molecular mechanisms and micromechanics aspects of the fatigue fracture process are discussed. Some attention is given to thermal fatigue, where fracture results primarily from a large specimen temperature rise due to hysteresis heating. However, primary emphasis is devoted to mechanical fatigue, in which fracture is a result of initiation and propagation of a crack, as a result of the periodic nature of the applied load.

Micromechanisms of crack growth in ceramics and glasses in corrosive environments

Abstract: At normal temperatures and pressures water is known to have a strong influence on the strength of ceramics and glasses. Behaving as a stress corrosion agent, water causes these materials to fail prematurely as a consequence of subcritical crack growth. A basic premise of this paper is that stress corrosion cracking of ceramics is a chemical process which involves a stress-enhanced chemical reaction between the water and the highly stressed ceramic near the crack tip. Plastic deformation is believed to play no role in this fracture process. After a brief survey of chemical reaction rate theory, the basic rate equation from this theory is modified to reflect physical and chemical processes which occur at crack tips. Modification of the rate equation is based on the assumption thatl the crack tip can be modelled as an elastic continuum, an assumption that is supported by a simple atomistic model of crack growth. When tested against experimental data collected on glass the theory was found to be consi...

Grain Boundary Segregation and Intergranular Fracture in Molybdenum

Abstract: The refractory group VIA metals generally exhibit intergranular brittleness when they are in the recrystallized condition. This causes severe problems in their fabrication and places major limitations on their practical application. The phenomenon, generally referred to as recrystallization embrittlement, results in large increases in the ductile-to-brittle transition temperature and a change in fracture mode in the lower shelf regime from cleavage to intergranular with a significant decrease in ductility. The embrittlement is widely considered to be associated with interstitial impurities but there have been few systematic studies to elucidate their effects. The present paper reports results from a systematic study of segregation and intergranular embrittlement in binary molybdenum-oxygen and ternary molybdenum-oxygen-carbon alloys. The experiments were carried out on ‘bamboo’ specimens containing a series of identical single grain boundaries traversing their cross-sections. Measurements have been made of the activation energy for oxygen segregation to grain boundaries in the binary molybdenum-oxygen alloys. The influence of carbon additions on the level of oxygen segregation has also been determined. In addition, the influence of oxygen segregation on the energy to fracture has been studied and this has involved quantitative measurements of the work of fracture and the contribution made by plastic deformation. Results from metallographic studies are also presented, showing the effects of segregation on fracture surface topography and dislocation structures immediately adjacent to the fracture surfaces. In discussing the results we consider the thermodynamics of oxygen segregation to grain boundaries and the role played by carbon in inhibiting segregation. It is proposed that carbon either increases the effective solubility of oxygen in molybdenum or acts as a trap for oxygen atoms. In either case the effect is to reduce the driving force for segregation. We also consider the influence of segregation on the work of fracture and show that the reduction in oxygen segregation resulting from the addition of carbon produces small increases in fracture energy. This increases the local stress to propagate a crack sufficiently to promote plastic deformation which blunts the crack tip. The consequent change in geometry reduces the stress concentration at the crack tip, thereby resulting in a large increase in the applied fracture stress and the work to fracture.

Optimizing fracture toughness and abrasion resistance in white cast irons

Abstract: A series of twelve Cr-Mo white irons varying in carbide volume from 7 to 45 pct were tested for dynamic fracture toughness and wet sand abrasion resistance. Carbon content was varied from 1.4 to 3.9 pct. Two matrix microstructures were employed, and the compositions (copper and chromium content) were varied to assure constant matrix compositions. Chromium was varied from 11.6 to 25.7 pct. In addition, one composition of white iron was subjected to thirty different heat treatments to define the effect of matrix microstructure on dynamic fracture toughness and abrasion resistance. It was shown that for the abrasive wear system used, a carbide volume of about 30 pct represented an optimum quantity, above which abrasion resistance decreased. Martensitic irons provided consistently better abrasion resistance than austenitic irons. Dynamic fracture toughness decreased with carbide volume, as expected. Higher toughness values were obtained with predominantly austenitic matrix microstructures than with predominantly martensitic matrix microstructures. Considering both abrasion resistance and fracture toughness, it was shown that heat treated irons could provide an optimal combination of these properties.

The mechanical properties of epoxy resins

Abstract: Crack propagation in a series of epoxy resins described in Part 1 has been studied as a function of testing rate and temperature. It has been found that crack propagation is continuous at low temperatures but that as the temperature is raised the mode of propagation becomes unstable (stick/slip). Features on the fracture surfaces at the crack arrest lines have been shown to be of the same dimensions as those expected for a Dugdale plastic zone. It has been suggested that the “slip” process takes place by slow growth of a crack through the plastic zone followed by rapid propagation through virgin material. It has been shown that the stick/slip behaviour is due to blunting of the crack which is controlled by the yield behaviour of the resin. A unique fracture criterion has been shown to be applicable to epoxy resins which is that a critical stress of the order of three times the yield stress must be achieved at a critical distance ahead of the crack. Electron microscope replicas of the fracture surfaces have been obtained and an underlying nodular structure can be resolved. However, no direct correlation between the nodule size and fracture properties has been found.

Strain-rate dependent fracture initiation

Abstract: The theory of linear elastic dynamic fracture mechanics for Heaviside loading of an isolated crack is employed to formulate the response to constant strain-rate loading of a single crack. Numerical integration of the Heaviside solution is shown to lead to fracture initiation stresses that are dependent upon the imposed strain rate. These fracture initiation stresses are also shown to be relatively independent of the crack size and crack shape. The results are used to explain the strain-rate dependent fracture stress observed in some rocks as being a structural response, rather than a basic material property.

Fracture toughness of silicon

Abstract: The paper presents a study to determine the fracture toughness and to characterize fracture modes of silicon as a function of the orientation of single-crystal and polycrystalline material. It is shown that bar specimens cracked by Knoop microhardness indentation and tested to fracture under four-point bending at room temperature were used to determine the fracture toughness values. It is found that the lowest fracture toughness value of single crystal silicon was 0.82 MN/m to the 3/2 in the 111 plane type orientation, although the difference in values in the 111, 110, and 100 planes was small.

Compliance and stress intensity coefficients for short bar specimens with chevron notches

Abstract: For the determination of fracture toughness especially with brittle materials, a short bar specimen with rectangular cross section and chevron notch can be used. As the crack propagates from the tip of the triangular notch, the load increases to a maximum then decreases. To obtain the relation between the fracture toughness Kic and maximum load Pmax, calculations of Srawley and Gross for specimens with a straight-through crack were applied to the specimens with chevron notches. For the specimens with a straight-through crack, an analytical expression was obtained. This expression was used for the calculation of the Kic−Pmax relation under the assumption that the change of the compliance with crack length for the specimen with a chevron notch is the same as for a specimen with a straight-through crack.

Composites with high work of fracture

Abstract: [Plates I and 2] Results obtained when investigating the fracture behaviour of wood have suggested the possibility of making composite materials with high work of fracture and low density, at the expense of moderate loss of stiffness. The reinforcing elements of the composite are made in the form of cylindrical tubes with helically wound walls of glass or carbon fibres, simulating, to a certain extent, the structure of wood cells. The hollow tubes, under tensile stress and in certain circumstances, are capable of deforming pseudo-plastically absorbing large amounts of energy in a manner which is effectively similar to that of ductile fibres Work of fracture in excess of 4 x 105 J/m2 has been obtained, comparable to that of ductile metals. The dependence of the work of fracture on various parameters will be discussed together with some suggestions for compensating for the loss of stiffness without reducing the energy absorbing capacity of the system.

Cleavage micromechanisms of crack extension in steels

Abstract: The micromechanisms of cleavage fracture in ferritic steels are reviewed. Mechanisms of crack nucleation by dislocation interaction are compared with those involving the formation of stable microcracks. It is concluded that cleavage in steels containing discrete carbide particles is nucleated by microcracks formed in the carbide particles when fracture obeys a critical tensile stress criterion. The cleavage fracture stress in these steels is seen to depend largely upon the size of the cracked carbide particle. No micromechanisms have been established for cleavage in martensitic or low-carbon bainitic steels but the packet size seems to control cleavage fracture in these materials.Two models of the relationship between the micromechanism of cleavage and fracture toughness are discussed in some detail. The statistical competition between different sized crack nuclei at a loaded crack tip can be represented by the requirement that the fracture stress be exceeded over a microstructurally determined ch...

Incomplete self‐similarity of fatigue in the linear range of crack growth

Abstract: —The application of dimensional analysis and similarity methods to the study of the speed of fatigue crack growth is considered. It is shown that the Paris range of the crack propagation diagram is an intermediate-asymptotic stage of the crack growth process. Over this stage the influence of the initial conditions on the process of fatigue crack growth has disappeared but the influence of the instability has not yet intruded. So-called incomplete self-similarity prevails at this stage with respect to a basic similarity parameter, equal to the ratio of the stress intensity factor amplitude to the fracture toughness. It is shown that for a certain material under fixed external loading conditions the exponent in the Paris power law is a universal function of the ratio of specimen thickness to the ultimate size of the cyclic plastic zone. Processing of available experimental data confirmed the results obtained by this approach.

Statistical Characterization of Fracture in the Transition Region

Abstract: Fracture toughness results are measured in the transition region for an ASTM A471 Ni-Cr-Mo-V steel on two specimen sizes IT compact tension (CT) and 4T-CT. The results are typical for steels in the transition in that the smaller specimen toughness values are greater than the larger specimen results. Two explanations are given for this behavior. One explanation, based on loss of constraint, suggests that small specimens cannot be used to characterize the toughness of a large structure in the transition region. A second explanation, based on a statistical model, suggests that small specimen results when properly analyzed can be used to characterize the toughness of large structures. The results of these tests and others support the statistical model as the proper explanation for the observed difference in toughness between small and large specimens in the transition. The model gives a method for analyzing small specimen results to properly predict the toughness of a large structure.

Effects of pre-strain on plane stress ductile fracture in α-brass

Abstract: The effects of pre-strain on plane stress ductile fracture in a 70/30 alpha brass Austral 207 have been studied using the deep-edge-notched tension (DENT) specimens. The amount of pre-strain varies between 5 and 35%. It is found that both the specific essential work of fracture (w e) and the critical crack opening displacement (δc) decrease with increasing pre-strain. A simple theory for estimating the specific essential work of fracture in the presence of pre-strain is suggested and it gives good agreement with experimental results. Elongations to fracture in the DENT specimens are also predictable from a simple deformation analysis which considers the plastic elongations due to crack initiation, crack propagation and final stretch of a ligament that has reached a necking strain equal to that in a simple plain tension test. Micro-hardness measurements show that the strain localization is more intense near the fracture surface as the pre-strain level is increased and this is suggested to be an explanation for the low δc values obtained in pre-strained specimens.

Crack velocity dependence of longitudinal fracture in bone

Abstract: An evaluation of the fracture characteristics of bovine tibia compact tension specimens associated with controlled crack propagation in the longitudinal direction has been made. The fracture mechanics parameters of critical strain energy release rate (G c) and critical stress intensity factor (K c) were determined for a range of crack velocities. A comparative fracture energy (W) was also evaluated from the area under the load-deflection curve. It was found that an increase in the average crack velocity from 1.75 to 23.6×10−5 m sec−1 produced increases in G c (from 1736 to 2796 J m−2), K c (from 4.46 to 5.38 MN m−3/2) and W. At crack velocities >23.6×10−5 m sec−1, W decreased appreciably. Microstructural observations indicated that, for crack velocities <23.6 m sec−1, relatively rough fracture surfaces were produced by the passage of the crack around intersecting osteons (or lamellae), together with some osteon pull-out. In contrast, at a higher crack velocity, fracture was characterized by relatively smooth surfaces, as the crack moved indiscriminately through the microstructural constituents.

Solute segregation and brittle fracture in an alloy steel

Abstract: Using an Sb doped Ni-Cr steel as a model material, the mechanism of intergranular brittle fracture was studied by means of tests on smooth, notched, and precracked specimens, in conjunction with statistically analyzed, selected area Auger electron spectroscopy.The critical local stress for fracture of a grain boundary was determined as a function of the Sb concentration on that boundary. The Sb effect can be understood in terms of its influence on cohesive energy, which controls the plastic work associated with brittle fracture. The results indicate that the optimum method for assessing embrittlement behavior of such a steel with minimum ambiguity is to use a notched specimen at a fixed test temperature in the appropriate temperature range for that material. The conditions which govern brittle crack nucleation in steel and the factors which influence the plastic work are discussed.