Showing papers on "Fracture mechanics published in 1990"

Mechanics of Solid Materials

Abstract: 1. Elements of the physical mechanisms of deformation and fracture 2. Elements of continuum mechanics and thermodynamics 3. Identification and theological classification of real solids 4. Linear elasticity, thermoelasticity and viscoelasticity 5. Plasticity 6. Viscoplasticity 7. Damage mechanics 8. Crack mechanics.

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.

Direct Observation and Analysis of Indentation Cracking in Glasses and Ceramics

Abstract: A review of the observations of indentation-induced fracture suggests that there is no simple generalization which may be made concerning crack initiation sequences. Here, we investigate the material dependence of the initiation sequence of indentation cracks (cone, radial, median, half-penny, and lateral) using an inverted tester allowing simultaneous viewing of the fracture process and measurement of the indeter load and displacement during contact. Two normal glasses, two anomalous glasses, and seven crystalline materials are examined. Key results include (i) direct evidence that the surface traces of cracks observed at indentation contacts are those of radial cracks, rather than median-nucleated half-penny cracks (at least for peak contact loads <40 N) and (ii) that, in crystalline materials, radial cracks form almost immediately on loading of the indenter, in anomalous glasses at somewhat greater loads, but in normal glasses during unloading. A detailed consideration of the stress fields arising during indentation contact predicts material-dependent initiation sequences, in agreement with observations, particularly those of radial crack formation on loading for materials with large modulus-to-hardness ratios. In addition, a new, unexplored crack system is demonstrated, the shallow lateral cracks, which appear to be responsible for material removal at sharp contacts.

Crack Extension Force in a Piezoelectric Material

Abstract: A conservation law that leads to a path-independent integral of fracture mechanics is derived along with the governing equations and boundary conditions for linear piezoelectric materials. A closed-form solution to the antiplane fracture problem is obtained for an unbounded piezoelectric medium

The damage mechanics of brittle solids in compression

Abstract: The development of microcrack damage in brittle solids in compression is analyzed, using a simple model. The model is developed from recent detailed analysis of the initiation, propagation and linkage of microfractures from pre-existing cracks, voids, or other inhomogeneities. It describes the evolution of damage with strain and from it a criteria for failure can be established. The results are used to construct failure surfaces in stress space which combine information about brittle failure with data describing the onset of plastic yielding. Such failure surfaces are constructed for a number of rocks and are compared with previously published experimental data.

Determination of fracture energy, process zone longth and brittleness number from size effect, with application to rock and conerete

Abstract: The dependence of the fracture energy and the effective process zone length on the specimen size as well as the craek extension from the notch is analyzed on the basis of Ba

Random particle model for fracture of aggregate or fiber composites

Abstract: A particle model for brittle aggregate composite materials such as concretes, rocks, or ceramics is presented. The model is also applicable to the behavior of unidirectionally reinforced fiber composites in the transverse plane. A method of random computer generation of the particle system meeting the prescribed particle size distribution is developed. The particles are assumed to be elastic and have only axial interactions, as in a truss. The interparticle contact layers of the matrix are described by a softening stress‐strain relation corresponding to a prescribed microscopic interparticle fracture energy. Both two‐ and three‐dimensional versions of the model are easy to program, but the latter poses, at present, forbidding demands for computer time. The model is shown to simulate realistically the spread of cracking and its localization. Furthermore, the model exhibits a size effect on: (1) The nominal strength, agreeing with the previously proposed size effect law; and (2) the slope of the post‐peak l...

Numerical Fracture Mechanics

Abstract: This text bridges the gap between existing specialist books on theoretical fracture mechanics, and texts on numerical methods. It concentrates on the application of the boundary element method to fracture mechanics, although an account of recent advances in other numerical methods is presented.

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.

The analysis of interlaminar fracture in uniaxial fibre-polymer composites

Abstract: One of the most important mechanical properties of a fibre-polymer composite is its resistance to delamination. The presence of delaminations may lead not only to complete fracture but even partial delaminations will lead to a loss of stiffness, which can be a very important design consideration. Because delamination may be regarded as crack propa­gation then an obvious scheme for characterizing this phenomenon has been via a fracture mechanics approach. There is, therefore, an extensive literature on the use of fracture mechanics to ascertain the interlaminar fracture energies, G c , for various fibre-polymer composites using different test geometries to yield mode I, mode II and mixed mode I/II values of G c . Nevertheless, problems of consistency and discussions on the accuracy of such results abound. This paper describes a detailed study of the methods of analysing the experimental data obtained from fracture mechanics tests using double-cantilever beam, end loaded split and end notched flexure specimens. It is shown that to get consistent and accurate values of G c it is necessary to consider aspects of the tests such as the end rotation and deflection of the crack tip, the effective shortening of the beam due to large displacements of the arms, and the stiffening of the beam due to the presence of the end blocks bonded to the specimens. Analytical methods for ascertaining the various correction constants and factors are described and are successfully applied to the results obtained from three different fibre-polymer composites. These composites exhibit different types of fracture behaviour and illustrate the wide range of effects that must be considered when values of the interlaminar fracture energies, free from artefacts from the test method and the analysis method, are required.

Casting defects and the fatigue behaviour of an aluminium casting alloy

Abstract: — The fatigue properties of un-notched polished specimens of an aluminium casting alloy have been measured for various heat-treatment conditions and at various mean stresses. The relation between fatigue life and alternating stress is insensitive to heat-treatment and, apparently, to mean stress. It was observed that failure initiated at interdendritic shrinkage defects: evidence of classical crack initiation from persistent slip bands was also seen but such cracks, being less severe than the casting defects, never caused failure. A fracture mechanics analysis for the growth of fatigue cracks from the pores is described. It shows that the fatigue life can be quantitatively predicted from a knowledge of the size of casting defects: in particular it explains the lack of effect of heat-treatment and the apparent absence of a mean stress effect is shown to be caused by the variation in size of maximum defect present among the specimens tested. It is shown that reducing the size of shrinkage defects will increase the life, but only up to the stage at which initiation from persistent slip bands becomes operative.

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.

The fracture energy of bimaterial interfaces

Abstract: This article describes a framework applicable to the measurement and interpretation of the fracture energy of bimaterial interfaces. A major conclusion of this study is that the fracture energy, Γi, is not unique and usually exhibits values substantially larger than the thermodynamic “work of adhesion. ” The lack of uniqueness is related to mode mixity (shear/opening) effects experienced by interface cracks, as characterized by the phase angle of loading, ψ: typically, Γi, is found to increase as ψ increases. These trends are attributed to crack shielding caused by roughness of the interface fracture surface, to material nonlinearity,etc. The phase angle is, in turn, influenced by the choice of test specimen, resulting in values of Γi that differ between specimens in a manner attributed to the locus of Γi with ψ. Preliminary models that relate Γi to roughness, plasticity, segregation,etc., are described, leading to insights concerning microstructural aspects of “weaklrd and “strong” interfaces.

In Situ Measurements of Bridged Crack Interfaces in the Scanning Electron Microscope

Abstract: A device for in situ SEM examination of crack propagation during loading of compact tension specimens is described, with a specific demonstration on an alumina ceramic. The device facilitates direct qualitative observations of the inception and subsequent frictional pullout of grain-localized bridges at the crack interface. Quantitative data on the bridging mechanism are obtained from measurements of the crack-opening displacements behind the crack tip. The crack profile is found to be closer to linear than parabolic at the bridged interface. Deconvolution of these crack-opening data allow for an evaluation of the closure tractions operative at the crack walls within the bridging zone, and thence the R-curve.

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 Effects of Geometry, Rate and Temperature on the Mode I, Mode II and Mixed-Mode I/II Interlaminar Fracture of Carbon-Fibre/Poly(ether-ether ketone) Composites:

Abstract: A detailed study on the interlaminar failure of carbon-fibre/poly(ether-ether ketone) unidirectional composite (termed PEEK composite: "APC-2" from ICI (UK) plc) is presented. A fracture mechanics approach has been adopted and Mode I, Mixed-Mode I/II and Mode II tests have been conducted and the effects of specimen geometry, test rate and test temperature have been investigated. It is shown that for the interlaminar fracture of the PEEK composite the value of the interlaminar fracture energy, G,, generally in creases as the crack propagates through the composite, i.e., a rising "R-curve" is observed. Thus, it is not usually possible to assign one unique value to the interlaminar fracture energy, Gc, for any given Mode of loading for the PEEK composite. We have therefore defined both an initiation value, Gc(init), and a steady-state propagation value, Gc(s/s prop). The variation of these parameters with the Mode of loading, method of precracking and the test temperature is described in detail. From optical...

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.

Hypersingular integrals in boundary element fracture analysis

Abstract: A new general purpose boundary element method for domains with cracks has been recently developed. This technique avoids the use of a multi-domain decomposition by including an additional integral equation expressing the boundary condition on the crack. The principal requirement of this technique is the analytic determination of certain hypersingular integrals of the Green's function which arise from this equation. In order to establish the applicability of this method for fracture, these integrals are evaluated herein for the Kelvin solution of the three-dimensional Navier equations of linear elasticity. Numerical results for fracture problems using the single-domain boundary element analysis are also presented.

Crack initiation and growth toughness of an aluminum metal-matrix composite

Abstract: The effects of systematic changes in matrix microstructure on crack initiation and growth toughnesses were determined on an Al-Zn-Mg-Cu alloy containing 0, 15, 20 percent by volume of SiC particulates. Materials were heat treated to underaged (UA) and overaged (OA) conditions of equivalent matrix microhardness and flow stress. Although both the fracture initiation and growth toughnesses, as measured by JIc and tearing modulus, were similar for the unreinforced materials in the UA and OA conditions, significant effects of microstructure on both JIc and tearing modulus were observed in the composites. SEM and TEM observations of fracture paths in the two conditions are utilized to rationalize these observations in light of existing theories of ductile fracture propagation.

Micromechanical fracture strength of silicon

Abstract: In order to test the statistical influence of some process and micromachining parameters on the fracture strength of silicon microelements, arrays of identical microsized cantilever beams were bulk micromachined in single‐crystalline silicon wafers. The beams were exposed to various surface treatments (diamond polishing with different grades, oxidization, stripping of oxide) in different combinations. The influence on fracture strength was investigated by bending the beams to fracture in a micromanipulator mounted in situ in a scanning electron microscope while registering force‐versus‐deflection curves. Average fracture strengths, standard deviations, Weibull moduli, crack‐initiating flaw sizes, and in some cases elastic moduli were evaluated. Diamond polishing was found to decrease the fracture strength drastically, but polishing followed by oxidization not only restored the original strength, but actually increased it, due to crack healing. Polishing, oxidization, and subsequent stripping of oxide resu...

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.

Limits to adherence of oxide scales

Abstract: Strains can cause oxide scales to fracture, often leading to loss of protectiveness and creation of spalling debris. Fracture mechanics is used to identify a number of criteria under which uniform scales may be expected to fail as a result of rapidly applied strains. The failure mode most frequently found occurs when the strain ɛ builds up in the scale until the strain energy density per unit area exceeds the fracture surface energy γ of the oxide. This produces spalling when ɛ>(2·8 γ/hE)1/2, where h is the scale thickness and E is the Young's modulus of the oxide. Two further regimes are identified in thin scales. First, as the external strain is applied to the oxide via the metal substrate, it is obvious that no further stress can be applied to the oxide if the substrate has itself been stressed beyond yield. This condition gives rise to a second regime, that of extended oxide adherence on substrates under external tensile strains in which the oxide cracks and forms a series of islands, but rema...

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.

Size Effect in Fracture of Ceramics and Its Use To Determine Fracture Energy and Effective Process Zone Length

Abstract: The paper shows that a previously proposed size effect law can be used to identify nonlinear fracture properties solely from measured maximum loads of geometrically similar ce­ ramic fracture specimens of sufficiently different sizes. This law represents a first-order global approximation of the de­ viations from linear elastic fracture mechanics, independent of the type of the toughening mechanism in the fracture process zone. It provides a simple and unambiguous way to determine the size- and shape-independent values of the fracture energy, the effective length of the process zone, and the effective crack-tip opening displacement. It also yields the R curve, which is geometry (shape) dependent. The prox­ imity of response to linear elastic fracture mechanics is characterized by a brittleness number, which is shape in­ dependent. [Key words: mechanical properties, fracture, R curve, energy, modeling.]