Showing papers on "Fracture toughness published in 1990"

Dynamic Fracture Mechanics

Abstract: Preface List of symbols 1. Background and overview 2. Basic elastodynamic solutions for a stationary crack 3. Further results for a stationary crack 4. Asymptotic fields near a moving crack tip 5. Energy concepts in dynamic fracture 6. Elastic crack growth at constant speed 7. Elastic crack growth at nonuniform speed 8. Plasticity and rate effects during crack growth Bibliography Index.

Ductile Fracture of Metals

Abstract: An account of the recent developments in research into ductile fracture in metals and alloys. Aspects covered include localized fracture at the root of notches and sharp cracks, and fracture in bulk plastic-deformation processes of the metal and metal forming type. Also discusses various theoretical

Experimental determination of interfacial toughness curves using Brazil-nut-sandwiches

Abstract: A Brazil-nut-sandwich with a crack on a substrate/interlayer interface is developed for fracture testing. The fracture loading phase is controlled by the angle of diametral compression. Interfacial fracture mechanics is summarized and adopted in reporting data. Experiments are conducted with aluminum, brass, steel and plexiglass as substrates and epoxy as interlayer. Interfacial toughness curves are measured for large range of loading phase. Effects of the roughness of the surfaces prior to bonding on the interfacial toughness are demonstrated. Failure patterns for the adhesive structure under different loading modes are observed with a scanning electron microscope. For the metal/epoxy systems, when the remote loading is predominantly mode I, cracks tend to kink out of interfaces and run within the epoxy layer, although the bulk epoxy fracture energy is much higher than the interfacial toughness. At large loading phases, abnormally high apparent toughness is measured. These observations are discussed in the light of crack path selection criteria in adhesive joints and large scale contact zone of crack faces.

Fracture Mechanisms in Ferroelectric‐Ferroelastic Lead Zirconate Titanate (Zr: Ti=0.54:0.46) Ceramics

Abstract: Fracture toughness, KIC, of a single-phase commercial lead zirconate titanate (PZT) ceramic (Zr/Ti=0.54/0.46) of tetragonal structure (c/a=1.019) was measured using the single edge notched beam method above and below the Curie temperature. Domain switching (poling) under electrical and mechanical loading was examined using X-ray diffraction. Surface grinding, electrical poling, and mechanical poling caused crystallographic texture. Similar texture, indicative of domain switching, was also observed on fracture surfaces of some saples fractured at room temperature. At room temperature, the highest KIC measured was 1.85 MPa·m1/2, while above the Curie temperature it was about 1.0 MPa·m1/2. Cracks emanating from Vickers indents in poled samples were different in the poling and the transverse directions. The difference in crack sizes is explained on the basis of domain switching during crack growth. These results indicate that ferroelastic domain switching (twinning) is a viable toughening mechanism in the PZT materials tested.

Buoyancy-driven fluid fracture: the effects of material toughness and of low-viscosity precursors

Abstract: When buoyant fluid is released into the base of a crack in an elastic medjura the crack will propagate upwards, driven by the buoyancy of the fluid. Viscous fluid flow in such a fissure is described by the equations of lubrication theory with the pressure given by the sum of the hydrostatic pressure of the fluid and the elastic pressures exerted by the walls of the crack. The elastic pressure and the width of the crack are further coupled by an integro-differential equation derived from the theory of infinitesimal dislocations in an elastic medium. The steady buoyancy-driven propagation of a two-dimensional fluid-filled crack through an elastic medium is analysed and the governing equations for the pressure distribution and the shape of the crack are solved numerically using a collocation technique. The fluid pressure in the tip of an opening crack is shown to be very low. Accordingly, a region of relatively inviscid vapour or exsolved volatiles in the crack tip is predicted and allowed for in the formulation of the problem. The solutions show that the asymptotic width of the crack, its rate of ascent and the general features of the flow are determined primarily by the fluid mechanics; the strength of the medium and the vapour pressure in the crack tip affect only the local structure near the advancing tip of the crack. When applied to the transport of molten rock through the Earth's lithosphere by magma-fracture, this conclusion is of fundamental importance and challenges the geophysicist's usual emphasis on the controlling influence of fracture mechanics rather than that of fluid mechanics.

The brittle compressive fracture of ice

Abstract: The brittle compressive fracture under uniaxial loading of fresh-water, granular ice Ih has been studied. Measurements are reported of the fracture stress at temperatures from −10 to −50°C at strain rates of 10 −3 and 10 −1 s −1 for grain sizes from approximately 1 to 10 mm. Also a summary is reported of measurements by Jones et al . (unpublished) of the kinetic coefficient of friction for ice on ice at temperatures from −10 to −40°C at sliding velocities from 5 × 10 −7 m s −1 to 5 × 10 −2 ms −1 . Observations via high speed photography of internal cracking during loading are included. The strength, albeit scattered, increases with decreasing grain size, with decreasing temperature and at −10°C with decreasing strain rate. Similarly, the coefficient of friction increases with decreasing temperature and at −10°C with decreasing sliding velocity. Wing cracks were observed on some inclined cracks nucleated during loading. The results are explained in terms of the frictional crack sliding-wing crack model [as developed by Ashby and Hallam, Acta metall. 34, 497 (1986)] of compressive fracture. Finally, a simple model is presented for the transition from ductile to brittle behavior. It is based upon the competition between the building up and the relaxation of internal stresses within the vicinity of the internal cracks, and it leads to a transition strain rate which can be expressed in terms of the fracture toughness, the creep rate, the kinetic coefficient of friction and the microstructural scale of the material.

Cyclic Fatigue-Crack Propagation in Magnesia-Partially-Stabilized Zirconia Ceramics

Abstract: The subcritical growth of fatigue cracks under (tension-tension) cyclic loading is demonstrated for ceramic materials, based on experiments using compact C(T) specimens of a MgO-partially-stabilized zirconia (PSZ), heat-treated to vary the fracture toughness Kc from ∼3 to 16 MPa·m1/2 and tested in inert and moist environments. Analogous to behavior in metals, cyclic fatigue-crack rates (over the range 10−11 to 10−5 m/cycle) are found to be a function of the stress-intensity range, environment, fracture toughness, and load ratio, and to show evidence of fatigue crack closure. Unlike toughness behavior, growth rates are not dependent on through0-thickness constraint. Under variable-amplitude cyclic loading, crack-growth rates show transient accelerations following low-high block overloads and transient retardations following high-low block overloads or single tensile overloads, again analogous to behavior commonly observed in ductile metals. Cyclic crack-growth rates are observed at stress intensities as low as 50% of Kc, and are typically some 7 orders of magnitude faster than corresponding stress-corrosion crack-growth rates under sustained-loading conditions. Possible mechanisms for cyclic crack advance in ceramic materials are examined, and the practical implications of such “ceramic fatigue” are briefly discussed.

Effect of grain size on brittle and semibrittle strength: Implications for micromechanical modelling of failure in compression

Abstract: Triaxial experiments were performed at room temperature and confining pressures up to 450 MPa on four pure, dense calcite rocks whose average grain sizes range over four orders of magnitude. Volumetric strain was measured during some of the experiments and microstructural studies were conducted to identify the active deformation mechanisms. The brittle fracture strength and macroscopic initial “plastic” yield stress in the semibrittle field follow empirical Hall-Petch relations. The confining pressure at the brittle-ductile transition depends inversely on grain size, but the stress ratio σ3/σ1 at the transition is nearly the same for the different rocks. We assume that the initial flaw size scales with grain size and compare our experimental data to the fracture mechanics models of Ashby and Hallam (1986) for brittle fracture and Horii and Nemat-Nasser (1986) for the brittle-plastic transition in compression. The first model predicts that small confining pressures are sufficient to inhibit work softening behavior; however, our data indicate that localization occurs for significantly higher values of confining pressure than predicted. Furthermore, we find that localization is inhibited with increased confining pressure because of the increased activity of plastic flow mechanisms, rather than because of the increased difficulty of crack propagation alone. With certain assumptions, the model predicts the experimentally determined slope of the Hall-Petch relation in the brittle field, although it underestimates the compressive strength of the rocks. The second model predicts that the stress ratio σ3/σ1 at the brittle-plastic transition scales with the, square root of the grain size; however, the experimental data do not corroborate the model unless the square of the ratio of the mode I fracture toughness to the plastic yield stress in shear scales with the grain size. The stress ratio at the brittle-ductile transition is apparently a constant for many different rock types; we suggest that the physical basis for this relationship is that the ductility of most mineral aggregates falls within a small range.

Crack Spacing in Brittle Films on Elastic Substrates

Abstract: An approximate, analytical solution is derived for the minimum spacing that can exist between a series of parallel cracks propagating in a thin film. The analysis is pertinent to the specific case of a film and substrate having identical elastic properties. In the absence of plasticity, only three parameters govern the minimum crack spacing. The cracks are predicted to be more closely spaced if the film stress or the film thickness is increased, or if the fracture toughness of the film is decreased.

Mixed-mode fracture toughness of ceramic materials

Abstract: An experimental technique whereby pure mode I, mode II, and combined mode I-mode II fracture toughness values of ceramic materials can be determined using four-point bend specimens containing sharp, through-thickness precracks is discussed. In this method, notched and fatigue-precracked specimens of brittle solids are subjected to combined mode I-mode II and pure mode II fracture under asymmetric four-point bend loading and to pure mode I under symmetric bend loading. A detailed finite element analysis of the test specimen is performed to obtain stress intensity factor calibrations for a wide range of loading states. The effectiveness of this method to provide reproducible combined mode I-mode II fracture toughness values is demonstrated with experimental results obtained for a polycrystalline Al2O3. Multiaxial fracture mechanics of the Al2O3 ceramic in combined modes I, II, and III are also described in conjunction with the recent experimental study of Suresh and Tschegg (1987). While the mode II fracture toughness of the alumina ceramic is comparable to the mode I fracture toughness KIc, the mode III fracture initiation toughness is 2.3 times higher than KIc. The predictions of fracture toughness and crack path based on various mixed-mode fracture theories are critically examined in the context of experimental observations, and possible effects of fracture abrasion on the apparent mixed-mode fracture resistance are highlighted. The significance and implications of the experimental methods used in this study are evaluated in the light of available techniques for multiaxial fracture testing of brittle solids.

Grain growth in nanocrystalline TiO2 and its relation to vickers hardness and fracture toughness

Abstract: This paper reports on scientific interest in ultra-fine grained powders for processing of ceramic components motivated by the possibilities for the enhancement of sintering rates, reduction in flaw sizes and low-temperature superplastic deformation. Previous works have developed a technique, which combines the methods established of inert gas condensation of small particles and in situ powder compaction, for synthesizing materials with grain sizes {lt}10 nm. It has been shown that this method can be adapted for the production of ceramic nanocrystalline particles. Subsequent work has demonstrated that enhanced sintering and superplastic deformation is possible in nanocrystalline ceramics (TiO{sub 2}), but not without significant grain growth. Control of grain growth, however, is necessary if the capability for synthesizing nanoscale powders is to have benefit for structural applications. It is well known that the initial particle size in green body compacts is not always indicative of the final grain sizes in fully sintered ceramic bodies. This study was initiated to examine grain growth kinetics in nanocrystalline materials. TiO{sub 2} was selected for this initial study since sintering, deformation and diffusion data are available.

Evaluation by indentation of fracture toughness of ceramic materials

Abstract: A transition fracture mode from Palmqvist to median has been observed in a number of ceramic materials A new expression to determine the fracture toughness (KIC) by indentation is presented The KIC values calculated by this formula are independent of the crack profile (median or Palmqvist) and of the applied load This formula has been obtained by modifying the universal curve of Evans and Charles to incorporate Palmqvist and median cracks over a wide range of loads in the case of brittle materials with different mechanical properties (elastic properties: E, v, KIC)

The effect of cell size on the mechanical behavior of cellular materials

Abstract: The Young's modulus, strength and fracture toughness, of a brittle reticulated vitreous carbon foam, was measured as a function of cell size at a constant density and compared to a theoretical model Image analysis was used to characterize the macrostructure of the samples and provided a basis for evaluating the mechanical behavior It was determined that both the compressive and bend strength scale inversely with cell size The change in compressive strength is due to a change in the strut strength with cell size The bend strength behavior may be due to a reduction in the critical flaw size, as well as the increasing strut strength at smaller cell sizes The fracture toughness and elastic modulus were found to be independent of cell size Comparison of these results with previous work on open cell alumina clearly indicates a very different behavior and is attributed to a change in the microstructure of the solid phase with cell size in the alumina materials

Experimental study on propagation of liquid-filled crack in gelatin: Shape and velocity in hydrostatic stress condition

Abstract: The three-dimensional shape and velocity of propagating cracks in the hydrostatic stress condition were studied by using gelatin, the physical properties of which were controlled to be constant. Various liquids (with various densities, viscosities, and volumes as the governed parameters) were injected in gelatin to form liquid-filled cracks. The directions of the crack growth and the propagation of an isolated crack are governed by the density difference between injected liquid and gelatin (Δρ), that is, a buoyancy. The propagation of a crack has two critical values: the first is the transition value to brittle fracture; the second is the value where segmentation begins to occur. The condition of a stable isolated crack formation is discussed. The crack shape of an isolated crack in the direction perpendicular to the crack plane is different from that of a growing crack with a fat tear drop form: the former has an elliptical top and a nearly flat bottom. The upper termination of an isolated crack in the vertical cross section has an elliptical shape, and the lower termination has a cusped shape. The lower part of the crack occupies the preexiting fracture which has formed by fracturing at the crack top. The crack thickness (w)/crack height (h) ratio is proportional to Δρ A, if the elastic moduli are constant. The crack length l/h ratio increase with h in the primary fracture, while the l/h ratio decreases with h in the preexisting fracture except for air-filled cracks. The ascending velocity of an isolated crack is proportional to Δρ3 h4, that is, Δρ w2, if the other physical properties are constant. The height and length of a growing penny-shaped crack are approximately proportional to A 3d1/3t4/9, so that the growth rate of height is in proportion to A3d3t−5/9 (A3d is constant injection rale). Some comparisons with the two-dimensional crack theory and applications for magma-filled cracks are discussed on the basis of these results.

Effect of Ta2O5, Nb2O5, and HfO2 Alloying on the Transformability of Y2O3-Stabilized Tetragonal ZrO2

Abstract: The addition of Ta{sub 2}O{sub 5}, Nb{sub 2}O{sub 5}, and HfO{sub 2} enhanced the transformability of Y{sub 2}O{sub 3}-stabilized tetragonal ZrO{sub 2} polycrystal (Y-TZP), which was indicated by an increase in phase transformation temperatures and fracture toughness of Y-TZP. Comparison of the alloying effects of these oxides on the transformability and crystal structure of Y-TZP suggested that an alloying oxide which increases the c/a axial ratio (tetragonality) of TZP also increases the transformability. Empirical equations to predict the tetragonality are proposed. Calculated tetragonalities showed good agreement with measured values in the systems ZrO{sub 2}-Y{sub 2}O{sub 3}-Ta{sub 2}O{sub 5}, -Nb{sub 2}O{sub 5}, and -HfO{sub 2}.

Behavior of surface and corner cracks subjected to tensile and bending loads in Ti-6Al-4V alloy

Abstract: The behavior of part-through flaws with regard to failure under monotonic loading and their growth under fatigue loading was studied experimentally and analytically. Comparisons are made of experimental values of toughness obtained using surface and corner cracked specimens with those obtained using standard test specimens, and also experimental growth cycles were compared with numerical predictions using the NASA/FLAGRO computer program. Tests were conducted on various types of surface and corner cracks under tensile and bending loads. Room temperature lab air provided the test environment. The material used in this study was the Ti-6Al-4V alloy in the solution treated and aged (STA) and stress relieved condition. Detailed tabulation of the fracture toughness data and results of life prediction using the NASA/FLAGRO program are presented. Fatigue crack growth rates for the part-through cracked specimens are compared with a base curve fitted from the data obtained using standard specimens. The fatigue loading used in the crack growth testing was constant-amplitude sinusoidal type.

The toughening of alumina with nickel inclusions

Abstract: Brittle solids can be toughened by the introduction of ductile metallic inclusions. In the present study, the mechanical properties and oxidation resistance of Al2O3/Ni composites are investigated. The oxidation resistance of the ceramic/metal composite (8 × 10−11 g2 cm−4 s−1 at 1300° C) is comparable to that of many silicon nitrides. The fracture toughness of the composite containing 13 vol.% nickel is twice that of alumina alone. The square of the toughness enhancement for composites containing various amounts of nickel exhibits a linear relationship with the product of volume fraction and inclusion size, as predicted in theoretical models. For the alumina/nickel composite system, it is demonstrated that dissolved oxygen in the nickel increases the yield strength of nickel and enhances the toughness of the composite.

Whisker Toughening: A Comparison Between Aluminum Oxide and Silicon Nitride Toughened with Silicon Carbide

Abstract: Two whisker-toughened materials have been studied, with the objective of identifying the mechanisms that provide the major contribution to toughness. It is concluded that, for composites with randomly oriented whiskers, bending failure of the whiskers obviates pullout, whereupon the major toughening mechanisms are the fracture energy consumed in creating the debonded interface and the stored strain energy in the whiskers, at failure, which is dissipated as acoustic waves. The toughening potential is thus limited. High toughness requires extensive pullout and, hence, aligned whiskers with low fracture energy interfaces.

Fracture toughness and brittle-ductile transition controlled by grain boundary character distribution (GBCD) in polycrystals

Abstract: The structural dependence of intergranular fracture processes in bicrystals and polycrystals of metals and alloys is first reviewed. It is shown that even in polycrystals, grain boundary structure plays a significant role in controlling the fracture properties of the material. Next, we evaluate quantitatively the effect of different types, frequencies and configurations of grain boundaries, so-called the grain boundary character distribution (GBCD), on the toughness of a three-dimensional (3D) polycrystals. The results show that the toughness of a polycrystals increases monotonically with increasing overall fraction of fracture-resistant low-energy boundaries in the material. A brittle-ductile transition, corresponding to a change of fracture mode from predominantly intergranular with low toughness to predominantly transgranular with high toughness, is observed when the overall fraction of low-energy boundaries reaches a critical value. For a 3D polycrystals with a non-random GBCD such that the fraction of low-energy boundaries on the inclined boundary facets is maximised, a smaller critical overall fraction of low-energy boundaries is needed to bring about the brittle-ductile transition. Similar effect is also found if the grains are made elongated and aligned with the stress axis. The results are discussed in relation to the concept of grain boundary design for strong and tough polycrystals proposed by one of the present authors (T.W.).

Structure-property relationships in bainitic steels

Abstract: Bainitic microstructures can be produced in a variety of steels either as a result of a deliberate attempt to achieve a particular combination of strength and toughness or in response to welding during fabrication. In addition, such microstructures can offer advantages in terms of their resistance to creep or fatigue deformation or susceptibility to hydrogen embrittlement. The relationships among chemical composition, processing, microstructure, and the mechanical properties will be reviewed. Particular emphasis will be placed on recent advances in alloy design. These developments rely on an improved understanding of the mechanisms of bainitic transformation, and the relevance of recent research in this area to the design of new alloy systems will be discussed. Bainitic structures which arise during welding can have a significant and sometimes detrimental effect on the fracture toughness of the welded joint. The fracture toughness of bainitic microstructures in so-called “local brittle zones” in the heat-affected zone and in weld metals and the importance of controlling the bainitic morphology will be considered and the transformation mechanisms discussed. In summary, the aim of this review will be to indicate the prospects for improved microstructural control of structure-property relationships in steels containing a significant proportion of bainite.

An Analytical Investigation of Delamination Front Curvature in Double Cantilever Beam Specimens

Abstract: An analytical investigation is conducted to determine the shape of a growing delamination and the distribution of the energy release rate along the delamination front in a laminated composite double cantilever beam specimen. Distributions of the energy release rate for specimens with straight delamination fronts and delamination front contours for delaminations whose growth is governed by the fracture criterion that G = Gc at all points are predicted as a function of material properties and delamination length. The predicted delamination front contours are utilized to ascertain the effect of the changing shape of the delamination front on the value of the critical strain energy release rate as computed from double cantilever beam fracture toughness test data.

Grain Growth During Gas‐Pressure Sintering of β‐Silicon Nitride

Abstract: The microstructures of gas-pressure-sintered materials from β-Si3N4 powder were characterized in terms of the diameter and aspect ratio of the grains. The size distributions of diameters in materials fabricated by heating for 1 h at 1850° to 2000°C were nearly constant when they were normalized by average diameters because of normal grain growth. The rate-determining step in the densification and grain growth was expected to be the diffusion of materials through the liquid phase. The activation energy for grain growth was 372 kJ/mol. The average aspect ratio of the grains was 3 to 4, whereas that of large grains was smaller because of shape accommodation. The fracture toughness was about the same as that of material from α-Si3N4 powder despite the smaller aspect ratio of the grains

Dynamic fracture initiation and propagation in 4340 steel under impact loading

Abstract: Dynamic fracture initiation and propagation in 4340 steel was investigated experimentally using the optical method of reflected caustics combined with high speed photography. A new crack propagation testing configuration consisting of a three point bend specimen loaded in a drop weight tower was used. It was found that prior to crack initiation the stress intensity factor time record calculated using the dynamic tup load and a static formula disagrees with the actual stress intensity factor measured by caustics. During crack propagation, the crack tip velocity and stress intensity factor time records varied smoothly and repeatably allowing for a straightforward interpretation of the data. The experiments show that for the particular heat treatment of 4340 steel used, the dynamic fracture propagation toughness depends on crack tip velocity through a relation that is a material property.