Showing papers on "Crack closure published in 1968"

Singular behaviour at the end of a tensile crack in a hardening material

Abstract: D istributions of stress occurring at the tip of a crack in a tension field are presented for both plane stress and plane strain. A total deformation theory of plasticity, in conjunction with two hardening stress-strain relations, is used. For applied stress sufficiently low such that the plastic zone is very small relative to the crack length, the dominant singularity can be completely determined with the aid of a path-independent line integral recently given by rice (1967). The amplitude of the tensile stress singularity ahead of the crack is found to be larger in plane strain than in plane stress.

Plastic stress and strain fields at a crack tip

Abstract: Further details of the stress and strain fields associated with the dominant singularity governing the plastic behaviour at a crack tip are presented for conditions of plane stress and plane strain for cracks in both far tensile and far shear fields. Results are obtained for a power hardening material. Limiting cases for non-hardening materials are shown to correspond to certain perfect plasticity solutions.

Fatigue crack propagation—an analysis

Abstract: A simple theory is developed to assess quantitatively the mechanism of fatigue crack propagation in metals. The basic laws governing fatigue are derived theoretically for failure in both the high and low stress regions, and the material parameters controlling crack propagation determined. The theory is compared with that developed in recent years using linear fracture mechanics.

Moisture assisted crack growth in ceramics

Abstract: A method is described to study subcritical crack growth in ceramic materials. Large, macroscopic size cracks were used and quantitative crack velocity measurements were made on glass and sapphire as a function of applied force, temperature and environment. The measured crack velocity was a complex function of stress and water vapor concentration in the environment and portions of the data could be adequately explained by the stress corrosion theory of Charles and Hillig.

Maximum Crack Width in Reinforced Concrete Flexural Members

Abstract: THE MAXIMUM CRACK WIDTH MEASUREMENTS FROM A NUMBER OF CRACK WIDTH INVESTIGATIONS WERE EXAMINED USING STATISTICAL METHODS. PREVIOUSLY PROPOSED EQUATIONS FOR MAXIMUM CRACK WIDTH WERE COMPARED AND NEW EQUATIONS WERE PROPOSED AS A RESULT OF THE ANALYSES. INTEREST IN CRACK WIDTHS IN FLEXURAL MEMBERS HAS BEEN STIMULATED BY THE TREND TO USE HIGH STRENGTH DEFORMED REINFORCING BARS. VARIOUS INVESTIGATIONS HAVE PRODUCED MUCH INFORMATION ABOUT THE WIDTH AND SPACING OF CRACKS. HOWEVER, DUE TO THE RELATIVELY LARGE SCATTER IN THE WIDTH OF THE LARGEST CRACKS, AND TO THE LARGE NUMBER OF INTERRELATED VARIABLES PRESENT IN REINFORCED CONCRETE BEAMS, AGREEMENT WAS LACKING AMONG THE INVESTIGATORS AS TO THE MOST PERTINENT VARIABLES INFLUENCING THE SIZE OF THE CRACKS. BY USING DATA FROM SIX DIFFERENT INVESTIGATIONS, THE SAMPLE WAS LARGE AND DIVERSE ENOUGH TO PERMIT RELIABLE STATISTICAL ANALYSES. THE MAXIMUM CRACK WIDTH MEASURED ON A BEAM AT A CERTAIN STEEL STRESS LEVEL REPRESENTED A STATISTICAL SAMPLE. IN THE COMPUTER INPUT, EACH SAMPLE WAS ACCOMPANIED BY ALL BEAM DETAILS THAT COULD INFLUENCE THE CRACK WIDTH. THE MAXIMUM CRACK WIDTH ON THE TENSION FACE OF THE BEAM AND THE MAXIMUM CRACK WIDTH ON THE SIDE OF THE BEAM AT THE LEVEL OF THE TENSILE REINFORCEMENT WERE ANALYZED SEPARATELY. THE FOLLOWING MAJOR CONCLUSIONS RESULTED FROM THE ANALYSIS OF THE MAXIMUM CRACK WIDTH: (1) THE STEEL STRESS IS THE MOST IMPORTANT VARIABLE, (2) THE DIAMETER OF THE REINFORCING BAR IS NOT A MAJOR VARIABLE, (3) THE THICKNESS OF THE CONCRETE COVER IS IMPORTANT, BUT IT IS NOT THE ONLY FACTOR REFLECTING GEOMETRY, (4) THE AREA OF THE CONCRETE SURROUNDING EACH REINFORCING BAR, A, ALSO INFLUENCES THE CRACK WIDTH, (5) THE SIZE OF THE SIDE CRACK WIDTH IS REDUCED BY THE PROXIMITY OF THE COMPRESSION ZONE (NEUTRAL AXIS) IN FLEXURAL MEMBERS, (6) THE BOTTOM CRACK WIDTH IS INFLUENCED BY THE STRAIN GRADIENT FROM THE LEVEL OF THE STEEL TO THE TENSION FACE OF THE BEAM. /ACIJP/

Diffraction of Antiplane Shear Waves by a Finite Crack

Abstract: The scattering of polarized harmonic shear waves by a sharp crack of finite length under antiplane strain is considered. Use is made of integral transforms, which reduce the problem to the evaluation of a system of coupled integral equations. Special emphasis is placed on obtaining the detailed structure of the crack‐front stress and displacement fields, which control the instability behavior of cracks in brittle materials. While the dynamic stresses around the singular crack point are found to be qualitatively the same as those encountered under statical loading, they differ quantitatively in that the intensity of the dynamical stress field, which may be regarded as a measure of the force tending to cause crack propagation, depends on the incident wavelength. At certain wavelengths, this intensification is shown to be larger than the static case. The method of solution in this paper applies equally well to boundary value problems in electromagnetic and acoustic theory.

The effect of a circular inclusion on the stresses around a line crack in a sheet under tension

Abstract: Based on the two-dimensional theory of elasticity and by the use of Muskhelishvili technique, the effect of a circular inclusion of different elastic material on the stress state around a line crack in an infinite plate subject to tension is discussed. Here, the circular inclusion is supposed to be on the line of prolongation of the crack. Numerical calculations were carried out and the variation of the crack-tip stress intensity factor due to the geometry and elastic properties of two media was clarified.

A dislocation model for fatigue crack growth in metals

Abstract: A model of fatigue crack growth is presented based on the analysis of plastic yield at a notch in terms of dislocations which has been given by Bilby et al. (1963). This analysis is extended to the case of relaxation of the applied stress, and the reverse plastic displacement at the crack tip is calculated. Reasons are given for equating this quantity with the amount of crack growth, and hence a growth law is obtained. The rate of growth for a specimen of finite width is similarly derived. In both cases, for low stresses, the growth per cycle is proportional to the square of the elastic stress intensity, while for higher stresses, terms involving the fourth and higher powers of stress enter. The model is expected to be applicable to the slip-band type of growth called stage I by Forsyth (1961) and to the ductile component of stage II growth. Although the model is developed only for shear cracks, there are indications that it may be at least approximately applicable to tension-compression fatigue,...

Fatigue-crack propagation in a high-strength aluminum alloy

Abstract: Fatigue-crack propagation experiments were carried out within the framework of linear-elastic fracture mechanics to examine the effect of water and its constituents on the rate of crack growth in a high-strength aluminum alloy over a range of test temperatures from 295 to 380° K. Dehumidified high-purity (99.9995 percent purity) argon was used as an inert reference environment. The results showed that water accelerated the rate of fatigue-crack propagation by about a factor of 10 in this temperature range, whereas dry oxygen and dry hydrogen had a negligible effect. They confirm the findings of Hartman, and Bradshaw and Wheeler that the cause for the large increase in the rate of crack growth is the formation of hydrogen gas at high pressure in the region ahead of the crack tip, driven in by the reaction of water with the-freshly created aluminum crack surfaces, as suggested by Broom and Nicholson. The results showed further that fatigue-crack propagation in water, as well as in the dry environments, is controlled by thermally activated processes, with apparent activation energies that depend strongly on the crack-tip stress-intensity parameter, ΔK. The rate controlling process appears to be that associated with the creation of new crack surfaces in the range of crack growth rates 10−6 to 10−5 inch per cycle. The strong dependence of the apparent activation energy on ΔK suggests that a careful study of the kinetics of fatigue-crack growth and of the crack growth laws is in order. Such a study should incorporate both the mechanical and chemical variables involved.

Local heating by plastic deformation at a crack tip.

Abstract: : This paper presents calculations of the temperature elevations accompanying rapid plastic deformation near a crack tip. Solutions for the stress and strain distribution in non-hardening materials are employed as a basis for the heating rate distribution. Results are approximate in that temperature independent mechanical and thermal properties are assumed and thermal stressing is neglected. Two cases are considered: a stationary crack under increasing load, and a running crack with locally constant speed and plastic zone size. Numerical results are presented as based on properties of 2024 aluminum alloy, 6Al-4V titanium alloy, and mild steel. Temperature rises predicted for test conditions on these metals seldom exceed 100C. This may, nevertheless, be large enough to influence fracture and to account for the observed rise in roughness at very fast rates. Consequences are examined for the assumption that the localized tip temperature elevation alone governs fracture toughness at very fast rates. (Author)

Stress Corrosion Cracking of Alpha Titanium Alloys at Room Temperature

Abstract: Transgranular stress corrosion cracks are formed in Ti-5Al-2.5Sn alloy immersed in a 3 percent NaCl aqueous solution when tensile specimens are dynamically strained over a narrow range of ...

Interaction between overlapping parallel cracks; a photoelastic study

Abstract: The interaction between two parallel cracks with a variable overlap distance in a tensile stress field was investigated. The principal stress trajectory patterns and the curves of constant shear stress for the interacting crack tips are presented. It was found that a) the stresses at the interacting crack tips are smaller than the noninteracting or outer crack tips and b) when there was a substantial overlap, the two cracks acted as one, i.e. the stresses at the outer tips were greater relative to those of either crack present by itself. Also, the propagation paths for the interacting crack tips are discussed for both conchoidal and cleavage fracture.

The fracture energy of glass

Abstract: The fracture energy of Float and Pyrex glass plates has been determined in various media using a simple double-cantilever cleavage technique. Although slow growth of the crack at constant displacement of the cantilever arms was observed in all environments, consistent values for the energy expended when the crack propagates rapidly were obtained. This ‘instantaneous fracture energy’ranged from ∼5000 erg/cm2 (Float glass) or 6000 erg/cm2 (Pyrex) in vacuum to 2500 erg/cm2 (for both glasses) in water. The results are discussed in terms of Marsh's hypothesis that localized plastic flow occurs at the crack tip.

Plastic energy dissipation due to a penny-shaped crack

Abstract: A penny-shaped crack in a material which is ideally elastic-plastic has been envisaged with the assumption that the plastic zone forms a very thin layer surrounding the crack. The Dugdale hypothesis has been adapted and thus the problem has been reduced to that of an elastic semi-space with properly modified boundary conditions. The entire energy absorbed in the process of creation of a new surface is associated with the work expanded in irreversible plastic deformation, the work of cohesive forces being neglected. The displacements of the crack surfaces are calculated as well as the plastic energy dissipation and the fracture criterion is discussed. The shape of the crack, obtained here, differs considerably from that predicted by the theory of elasticity, particularly at the crack tip. The differences in the values of the critical pressure calculated from the Griffith-Sack-Sneddon formula and those obtained by use of the equations derived here are also significant. It is shown that for macro-cracks when crack radius l is not too small the following formula holds $$P_{crit} = [\pi E\left( {dW_p /dA} \right)_{crit} /2\left( {1 - v^2 } \right)]^{{\raise0.5ex\hbox{$\scriptstyle 1$}\kern-0.1em/\kern-0.15em\lower0.25ex\hbox{$\scriptstyle 2$}}} $$ which agrees with the Orowan-Irwin modification of Griffith's theory; (dWp/dA)crit denotes the plastic work per unit area of new surface, dissipated in the course of loading before fracture. The results of this paper hold for the so called ‘quasi-brittle’ solids. Two schemes of loading are considered: 1. pressure applied on the crack surfaces and 2. applied at infinity. Attention is paid to a slightly different mechanism of fracture in both the cases.

An estimate of the limiting speed of a propagating ductile crack

Abstract: A steady state dynamic solution for a Dugdale crack propagating at a constant speed is obtained with the Sneddon-Radok formulation of the dynamic plane elasticity equations. The dynamic stress distribution and the Tresca yield condition are used to determine the limiting ductile crack propagation speed. It is shown that the limiting brittle crack speed criteria of Yoffe and of Craggs are satisfied as well. A simple relation between the flow stress and the crack speed based on observations of ductile crack propagation in steel foil is utilized in order to express the limiting speed in terms of the applied load and material properties. Calculated values of the limiting speed in steel and aluminium sheets are found to be not strongly dependent on the applied load and are about 0-1C 2 and 0-3C 2 , respectively.

Interaction between a crack front and cleavage steps

Abstract: Observations of the interaction of a crack front with cleavage steps on MgO fracture surfaces are presented and show that (a) steps exert a dragging force proportional to their height and (b) the crack front overlaps itself prior to the formation of the step. Based on these observations and on the hypothesis that a crack front possesses a line tension, a mechanism is proposed to explain the overlapping of one part of a crack front with the other, resulting in the formation of cleavage whiskers, steps undercut with cracks and foils of material that are associated with cleavage fracture. The energy absorbed during the parting of the steps is discussed.

Crack growth in notch fatigue

Abstract: A dislocation model which is appropriate for discussing the propagation of fatigue cracks from notches of elliptical or V-shaped profiles is presented. The principal conclusion is that the rate of crack growth is proportional to the fourth power of the stress intensity factor, deduced from the notch geometry. Detailed predictions are made about the variation of the rate of crack growth with the parameters governing the notch shape.

A theory of crack nucleation in high strain fatigue

Abstract: From previous observations of the surfaces of metals cycled in high strain fatigue, the mechanism of crack nucleation is considered a plastic instability phenomenon. A model for crack nucleation based on this conclusion is now developed quantitatively and a simple relationship between the number of cycles to nucleate a crack and the applied, plastic, strain range thus predicted. Since the model is valid for any material capable of plastic deformation, plasticine has been cycled in reversed bending to test its prediction. Cracks were observed to form in the plasticine by puckering of the surface at stress concentrations, in direct confirmation of the model. Moreover, the crack nucleation measurements on the plasticine and data on metals, taken from the literature, are considered to be in reasonable agreement with the prediction of the model.

Crack Branching in Strong Metals

Abstract: The phenomenon of crack branching in metals is discussed in terms of KB, the elastic stress intensity at the crack tip when crack branching occurs. It is shown that KB measurements may be useful in determining the fracture toughness of brittle metals.

The elastic-plastic mechanics of crack extension

Abstract: This paper briefly reviews progress in the elastic plastic analysis of crack extension. Analytical results for plane strain and plane stress deformation fields are noted, and elastic-plastic fracture instability as well as transitional behavior and combined rate and thermal effects are discussed.

Application of the method of finite element analysis to two-dimensional problems in fracture mechanics,

Abstract: : The method of direct stiffness is used to determine stress intensity factors for two-dimensional fracture mechanic problems of practical interest. For most problems, the crack opening displacement about three nodal positions away from the crack tip was used to determine the stress intensity factor within a projected accuracy of plus or minus 5%. The requirement of extremely small finite elements in the vicinity of the crack tip is circumvented and the amount of computational effort is reduced. Stress intensity factors obtained by this method include the double cantilever specimen, notched cylinder with internal pressure, edge-notched square plate with prescribed edge displacements, and the tension plate with slanted cracks. (Author)