Showing papers on "Crack closure published in 1980"

Elastic/Plastic Indentation Damage in Ceramics: The Median/Radial Crack System

Abstract: A theory for describing the evolution of the median/radial crack system in the far field of sharp-indenter contacts is developed. Analysis is based on a model in which the complex elastic/plastic field beneath the indenter is resolved into elastic and residual components. The elastic component, being reversible, assumes a secondary role in the fracture process: although it does enhance downward (median) extension during the loading half-cycle, it suppresses surface (radial) extension to the extent that significant growth continues during unloading. The residual component accordingly provides the primary driving force for the crack configuration in the final stages of evolution, where the crack tends to near-half-penny geometry. On the hypothesis that the origin of the irreversible field lies in the accommodation of an expanding plastic hardness impression by the surrounding elastic matrix, the ensuing fracture mechanics relations for equilibrium crack growth are found to involve the ratio hardness-to-modulus as well as toughness. Observations of crack evolution in soda-lime glass provide a suitable calibration of indentation coefficients in these relations. The calibrated equations are then demonstrated to be capable of predicting the widely variable median and radial growth characteristics observed in other ceramic materials. The theory is shown to have a vital bearing on important practical areas of ceramics evaluation, including toughness and strength.

Slightly curved or kinked cracks

Abstract: A solution is presented for the elastic stress intensity factors at the tip of a slightly curved or kinked two-dimensional crack. The solution is accurate to first order in the deviation of the crack surface from a straight line and is carried out by perturbation procedures analogous to those of Banichuk [1] and Goldstein and Salganik [2, 3]. Comparison with exact solutions for circular arc cracks and straight cracks with kinks indicates that the first order solution is numerically accurate for considerable deviations from straightness. The solution is applied to fromulate an equation for the path of crack growth, on the assumption that the path is characterized by pure Mode I conditions (i.e., K II=0) at the advancing tip. This method confirms the dependence of the stability, under Mode I loading, of a straight crack path on the sign of the non-singular stress term, representing tensile stress T acting parallel to the crack, in the Irwin-Williams expansion of the crack tip field. The straight path is shown to be stable under Mode I loading for T 0.

Tensile Cracks in Creeping Solids

Abstract: The aim of the paper is to answer the question: which loading parameter determines the stress and strain fields near a crack tip, and thereby the growth of the crack, under creep conditions? As candidates for relevant loading parameters, the stress intensity factor K I , the path-independent integral C*, and the net section stress σ n e t have been proposed in the literature. The answer, which is attempted in this paper, is based on the time-dependent stress analysis of a stationary crack in Mode I tension. The material behavior is modeled as elastic-nonlinear viscous, where the nonlinear term describes power law creep. At the time t = 0, load is applied to the cracked specimen, and in the first instant the stress distribution is elastic. Subsequently, creep deformation relaxes the initial stress concentration at the crack tip, and creep strains develop rapidly near the crack tip. These processes may be analytically described by self-similar solutions for short times t. An important result of the analysis is that small-scale yielding may be defined. In creep problems, this means that elastic strains dominate almost everywhere except in a small "creep zone" which grows around the crack tip. If crack growth ensues while the creep zone is still small compared with the crack length and the specimen size, the stress intensity factor governs crack growth behavior. If, however, the calculated creep zone becomes larger than the specimen size, the stresses become finally time-independent and the elastic strain rates can be neglected. In this limiting case, the stress field is the same as in the fully-plastic limit of power law hardening plasticity that has been treated in the literature. The loading parameter that determines the near tip fields uniquely is then the path-independent integral C*. It should be emphasized that K 1 and C* characterize opposite limiting cases. Which case applies in a given situation can be decided by comparing the creep zone size with the specimen size and the crack length. Criteria for small-scale yielding are worked out in several alternative forms. Besides several methods of estimating the creep zone size, a convenient expression for a characteristic time is derived also, which characterizes the transition from small-scale yielding to extensive creep of the whole specimen.

J integral applications for short fatigue cracks at notches

Abstract: Elastic and elastic-plastic fracture mechanics solutions are modified to predict the behaviour of short cracks. An effective crack length, l 0 is introduced into the solutions for both the linear elastic stress intensity factor and the J integral. Crack growth results for short cracks, in both elastic and plastic strain fields of unnotched specimens, when interpreted in terms of the modified solutions, show excellent agreement with elastic long crack data. The modified J integral solutions are extended to plastically strained notches, and the solutions obtained are tested in the correlation of data for growth of sort cracks near notches of varying severity with data for long crack under elastic loading. Although constant stress amplitude tests of these notches gave crack growth rate versus crack length curves which varied from monotonically increasing for blunt notches, to an initial decrease followed by an increase of sharp notches, all the data fell within the long crack data when correlated by the J integral solutions. Conversely, these solutions can be used to predict elastic and inelastic short crack growth curves for notches of various severities.

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.

Some formulas for the crack opening stress level

Abstract: Crack growth data for 2024-T3 sheet material were analysed with different formulas for ΔK eff as a function fo the stress ratio R . The data covered R values from −1.0 to 0.54. A good correlation was obtained for ΔK eff / ΔK = 0.55 + 0.33 R + 0.12 R 2 The relation between log d a/ d n and log ΔK eff was non-linear for high crack rates (> 1 μm/c).

Rough cracks in reinforced concrete

Abstract: Equations derived are which relate the normal and shear stresses transmitted across a crack due to aggregate interlock to the opening and slip displacements. Average strains due to a system of parallel continuous cracks are superimposed on the strains due to the solid concrete between the cracks. The response of cracked concrete reinforced by a regular net of bars is then calculated using an incremental loading procedure. The stress-displacement relations exhibit a singularity at the initial state of zero displacements and the initial crack opening must begin at zero slip. Responses to various types of loading are calculated and the variation of the secant friction coefficient, crack dilatancy due to slip and the effect of crack opening are studied. The theory allows designing for a maximum crack width if the crack spacing is known. The previously proposed slip-free concept yields limit loads which are found to correspond to the states just before the start of a rapid increase in crack opening, while the classical frictional approach yields limit loads that are achieved only after very wide cracks develop.

Near-Threshold Fatigue Crack Growth in 2 1/4 Cr-1Mo Pressure Vessel Steel in Air and Hydrogen

Abstract: As part of an ongoing program to examine subcritical flaw growth in candidate steels for proposed coal gasifier pressure vessels, an initial study is made of characteristics of ultralow growth rate fatigue crack propagation in thick-section, normalized 2 1/4 Cr-1Mo pressure vessel steel (ASTM A387, Class 2 Grade 22). Crack propagation data are generated over a wide range of growth rates, from 10−8 to 10−2 mm/cycle, for load ratios between 0.05 and 0.80 at ambient temperatures in low pressure environments of moist air, dry hydrogen gas and dry argon gas. Particular emphasis is placed on behavior at near-threshold growth rates, below 10−6 mm/cycle, approaching the so-called threshold stress intensity for fatigue crack growth, ΔK0 . Near-threshold growth rates, in addition to showing a marked sensitivity to load ratio, are found to be significantly enhanced in gaseous hydrogen compared to air. Similar environmentally-enhanced growth is observed in argon gas. To account for such results, previous models of threshold behavior based on environmental factors (e.g., hydrogen embrittlement) are questioned, and a new approach is presented in terms of the role of oxide debris from moist environments in promoting crack closure. This oxide-induced closure model is found to be consistent with most experimental observations of near-threshold fatigue crack propagation behavior and is proposed as a mechanism for environmental effects at ultra-low growth rates.

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...

Microcrack closure in rocks under stress: Direct observation

Abstract: Direct observations of the closure of microcracks in rocks under increasing stress are reported. Uniaxial stresses up to 300 bars were applied to untreated and previously heated samples of Westerly granite and Frederick diabase by a small hydraulic press which fit entirely within a scanning electron microscope. Crack closure characteristics are found to depend on crack orientation, with cracks perpendicular to the applied stress closing and those parallel tending to open, as well as crack aspect ratio, crack intersection properties, stress concentrations and surface roughness. Uniaxial and hydrostatic stress measurements are found to be strongly dependent on fracture content as observed by SEM, and the observed hysteresis in strain measurements in the first stress cycles is also related to microscopic processes

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.

Stress intensity factors and COD in an orthotropic strip

Abstract: The elasticity problem for an orthotropic strip or a beam with an internal or an edge crack under general loading conditions is considered. The numerical results are given for four basic loading conditions, namely, uniform tension, pure bending, three point bending, and concentrated surface shear loading. For the strip with an edge crack additional results regarding the crack opening displacements are obtained by using the plastic strip model. A critical quantity which is tabulated is the maximum compressive stress in the plane of the crack. It is shown that this stress may easily exceed the yield limit in compression and hence may severely limit the range of application of the plasticity results.

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.

Quasi-Static Steady Crack Growth in Small-Scale Yielding

Abstract: A numerical analysis of quasi-static, steady-state crack growth under small-scale yielding conditions has been carried out for antiplane shear (Mode III) and plane strain, Mode I. In addition to results for an elastic-perfectly plastic solid, the study includes results relating to the influence of strain hardening on stable crack growth. Limited results based on a corner theory of plasticity give some indication of the extent to which stable crack growth predictions are sensitive to the type of plasticity theory used.

In situ fracture experiments in b.c.c. metals

Abstract: Crack propagation and the structure of the plastic zone formed ahead of a crack have been investigated during in situ electron microscope fracture experiments of the b.c.c. metals molybdenum and tungsten. Most frequently, the cracks in polycrystalline specimens propagated along the grain boundaries. In some cases, the cracks were preceded by thin twins. When the cracks propagated transgranularly, the plastic zone ahead of the cracks consisted of an inverse pile-up of dislocations. In these cases, the relationship between the plastic zone size and the crack tip displacement was compared with the predictions of the theory of Bilby, Cottrell and Swinden (BCS). It is concluded that the plastic zone size agrees with the predictions of the BCS theory if the theory is modified to include the surface effects in thin foils.

Stress analysis of a semi-infinite plate with an oblique edge crack

Abstract: A semi-infinite plate with an oblique edge crack is analyzed as a thin plate bending problem and a plane elastic problem. The rational mapping function of the sum of fractional expressions and the complex variable method are used. Closed solutions are obtained for these respective problems. Stress distributions, stress intensity factors are investigated for loads causing transverse bending, twisting and uniform tension. The relations between the stress intensity factors and the angle of the oblique edge crack are also investigated.

A simple theory for low cycle multiaxial fatigue

Abstract: — A theoretical development based on a simple physical model is proposed to help the designer predict high strain multi-axial fatigue behaviour. This approach hypothesises that the maximum shear strain γ*, on planes driving the crack through the thickness, controls the fatigue crack propagation rate and hence the life. The direct strain δ*n acting normal to the plane of γ* can exert a secondary modifying influence. Experimental results from several research laboratories have been analysed in this manner with some success.

The noncontinuum crack tip deformation behavior of surface microcracks

Abstract: The crack tip opening displacement (CTOD) of small surface fatigue cracks (lengths of the grain size) in Al 2219-T851 depends upon the location of a crack relative to the grain boundaries. Both CTOD and crack tip closure stress are greatest when the crack tip is a large distance from the next grain boundary in the direction of crack propagation. Contrary to behavioral trends predicted by continuum fracture mechanics, crack length has no detectable effect on the contribution of plastic deformation to CTOD. It is apparent from these observations that the region of significant plastic deformation is confined by the grain boundaries, resulting in a plastic zone size that is insensitive to crack length and to external load.

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.

High-temperature fracture and diffusional deformation mechanisms in Si-Al-O-N ceramics

Abstract: A comparison has been made of hot-pressed Si-Al-O-N ceramics, with different impurity sintering aids (MgO and Mn3O4), in relation to microstructure, high-temperature creep and fracture. The Mn-containing ceramic exhibits a mechanism for creep of grainboundary sliding accompanied by cavitation at triple junctions, nucleated within an impurity silicate residue. The measured non-integral stress exponent (n∼1.5) and activation energyQ in the creep equation $$\dot \varepsilon $$ = const. σ n exp (-Q/kT) are typical of commercial silicon nitrides. A similar cavity-interlinkage is the principal mechanism for sub-critical crack growth, characterized by a low value for the stress-intensity exponent (n) in the relationV (crack velocity)=const.K 1 determined on double-torsion test specimens. Triple-junction silicate, and hence cavitation, is absent in the Mg-containing ceramic, which exhibits a Coble diffusional creep mechanism (stress exponentn=1). Sub-critical crack growth occurs only over a narrow range of stress intensity, near toK lC withn∼13 in theV-K 1 relation. A grain-boundary de-segregation caused mainly by extraction of impurities into an oxide film results in further improvement in creep and resistance to sub-critical crack growth.

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.