Effect of electric current on migration of point defects near a crack tip

The effect of direct current on migration of point defects dissolved in a crystal near the tip of a crack in tension is estimated. Calculations are carried out with allowance for the plastic strain near the crack tip of a loaded specimen, caused by the motion of dislocations in the active slip planes of the crystal, the Joule heat released, and the effect of gas exchange on the crack edges on the evolution of distribution of interstitial impurity atoms. A numerical analysis is performed for an Fe crystal.     

Direct measurement of microscopic strain distribution near a crack tip

A dot map method was used for direct measurement of the microscopic strain field near a crack tip in a rubber-toughened epoxy. Results indicate that very large viscoelastic strains (37 percent) are present at the crack tip, though elongation in a tensile test is only 5.1 percent. Most of the strain is recovered immediately on unloading, and all of the remaining strain is recovered after annealing above the glass transition temperature.     

Large strain field near a crack tip in a rubber sheet

The distribution of stress-strain near a crack tip in a rubber sheet is investigated by employing the constitutive relation given by Gao (1997). It is shown that the crack tip field is composed of two shrinking sectors and one expanding sector. The stress state near the crack tip is in uniaxial tension. The analytical solutions are obtained for both expanding and shrinking sectors.     

On the asymptotics of the stress and strain fields near a crack tip

The problem is solved under the plane strain conditions for a crack of general form, which in general is neither a mode I nor a mode II crack. We assume that the strains are small and the material is nonlinearly elastic. The mathematical statement of the problem is reduced to the eigenvalue problem for a system of ordinary nonlinear differential equations. Its solution is obtained numerically. We show that, for an incompressible material with power-law relations between the stress and strain deviators, the solution (the well-known HRR-asymptotics [1, 2]) exists only for mode I and II cracks. In the general case, we can only speak of approximate solutions. A similar conclusion can be made for different-modulus materials. We analyze the results of the preceding papers [1–7], where specific cases of the problem were considered.     

Experimental study of the distribution of plastic strains near a crack tip during static loading

S. P. Timoshenko Institute of Mechanics, National Academy of Sciences of Ukraine, Kiev. Translated from Prikladnaya Mekhanika, Vol. 30, No. 11, pp. 69–75, November, 1994.     

Measurement of the strain field near a crack tip in polymethylmethacrylate by holographic interferometry

An experimental method has been developed for the detailed, real-time study of the strain field near a crack tip in any transparent material. This method combines holography and interferometry to measure the field of averaged transverse strain in a sheet specimen under inplane loading. It is shown that the solution for an edge crack in a semi-infinite sheet based on two-dimensional linear elastic theory can be applied to the finite-width polymethylmethacrylate specimen. This solution is observed to become less valid as the crack tip is approached due to the breakdown of the plane-stress assumption. This effect is evaluated for a range of thicknesses from much less to much more than the crack length.     

Calculation of the evolution of plastic yielding at the tip of a crack and related phenomena

Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, No. 3, pp. 154–160, May–June, 1993.     

Stress field of a damaged material near the crack tip

In this paper, a deformation theory of plasticity for damaged materials is proposed. An asymptotic expression forH near a crack tip is obtained. Finally, the stress and strain fields near the crack tip are presented.     

Intergranular strain evolution near fatigue crack tips in polycrystalline metals

The deformation field near a steady fatigue crack includes a plastic zone in front of the crack tip and a plastic wake behind it, and the magnitude, distribution, and history of the residual strain along the crack path depend on the stress multiaxiality, material properties, and history of stress intensity factor and crack growth rate. An in situ, full-field, non-destructive measurement of lattice strain (which relies on the intergranular interactions of the inhomogeneous deformation fields in neighboring grains) by neutron diffraction techniques has been performed for the fatigue test of a Ni-based superalloy compact tension specimen. These microscopic grain level measurements provided unprecedented information on the fatigue growth mechanisms. A two-scale model is developed to predict the lattice strain evolution near fatigue crack tips in polycrystalline materials. An irreversible, hysteretic cohesive interface model is adopted to simulate a steady fatigue crack, which allows us to generate the stress/strain distribution and history near the fatigue crack tip. The continuum deformation history is used as inputs for the micromechanical analysis of lattice strain evolution using the slip-based crystal plasticity model, thus making a mechanistic connection between macro- and micro-strains. Predictions from perfect grain-boundary simulations exhibit the same lattice strain distributions as in neutron diffraction measurements, except for discrepancies near the crack tip within about one-tenth of the plastic zone size. By considering the intergranular damage, which leads to vanishing intergranular strains as damage proceeds, we find a significantly improved agreement between predicted and measured lattice strains inside the fatigue process zone. Consequently, the intergranular damage near fatigue crack tip is concluded to be responsible for fatigue crack growth.     

The equilibrium field near the tip of a crack for finite plane strain of incompressible elastic materials

This investigation is concerned with the deformations and stresses in a slab of all-around infinite extent containing a traction-free plane crack, under conditions of plane strain. The analysis is carried out within the framework of the fully nonlinear equilibrium theory of homogeneous and isotropic incompressible elastic solids. For a fairly wide class of such materials and general loading conditions at infinity, assymptotic estimates appropriate to the various field quantities near the crack-tips are deduced. For a subclass of the materials considered, these results — in contrast to the analogous predictions of the linearized theory — lead to the conclusion that the crack opens up in the neighborhood of its tips even if the applied loading is antisymmetric about the plane of the crack, (e.g., Mode II loading). It is shown further that the non-linear global crack problem corresponding to such a loading in general cannot admit an antisymmetric solution.The results communicated in this paper were obtained in the course of an investigation supported in part by Contract N00014-75-C-0196 with the Office of Naval Research in Washington, D.C.     

Localized shear discontinuities near the tip of a mode I crack

In this paper we study the deformation and stress fields near the tip of a crack under plane strain mode I conditions. A fully nonlinear theory of finite deformations is used and the material, which is assumed to be homogeneous, isotropic, incompressible and elastic, is characterized by its stress-strain behavior in simple shear. For the class of materials considered the governing system of differential equations may lose ellipticity at sufficiently severe strains. The analysis is based on a direct asymptotic calculation. The results involve two curves, issuing from each crack-tip, across which the deformation gradient, the effective shear and the stresses are discontinuous.     

Finite element analysis of void growth near a blunting crack tip

Large deformation finite element analysis has been used to study the near crack tip growth of long cylindrical holes aligned parallel to the plane of a mode I plane strain crack. The near crack tip stress and deformation fields are analyzed. The results show that the holes are pulled towards the crack tip and change their shape to approximately elliptical with the major axis radial to the crack. They also grow faster directly ahead of the crack than at an angle to the crack plane. Several crack-hole coalescence criteria are discussed and estimates for the conditions for fracture initiation are given and compared with experimental results. The range of estimates now available from finite element calculations coincides quite well with the range of experimental data for materials containing inclusions which are only loosely bonded to the matrix.     

Stress and strain field near tip of mode III growing crack in materials with creep behavior

Using a proposed constitutive relation for materials with creep behavior, the stress and strain distribution near the tip of a Mode III growing crack is examined. Asymptotic equations of the crack tip field are derived and solved numerically. The stresses remain finite at the crack tip. Obtained qualitatively is the crack tip velocity and the local autonomy of the near tip field solution is discussed.     

An analysis on three-dimensional effects near the tip of a crack in an elastic plate

An infinite plate containing a finite through crack under tensile loading is analysed by Fourier transform based on the Kane-Mindlin kinematic assumptions for the quasi-three-dimensional deformation of plates in extension. The asymptotic expressions of stress and displacement fields near the crack tip, the variation of the stress intensity factor with the plate-thickness and the three-dimensional deformation zone near the crack tip are investigated. The results of the analysis show that, (a) the crack-tip stress and displacement fields accounting for the plate-thickness effects are different from the plane stress solutions and this is true even for extremely small parameter (=1–vh/6 a). In a very small region near the crack tip, plane strain solutions prevail; (b) the ratio of the stress intensity factor K_I to the corresponding plane stress one K_I, K_I/K _I ^o , approaches 1/(1–v²) as tends to zero; (c) plane stress solutions can give satisfactory results for points a distance from the crack tip greater than about three-fourths of the plate-thickness; (d) the linear elastic result for the zone of three-dimensional effects is approximately valid for an elasto-plastic material with linear strain-hardening when the plastic tangential mudulus E_t is not very small.The Project Supported by National Natural Science Foundation of China.     

An asymptotic finite-deformation analysis of the elastostatic field near the tip of a crack

Summary This paper contains an asymptotic treatment, consistent with the fully nonlinear equilibrium theory of compressible elastic solids, of the stresses and deformations near the tip of a traction-free crack in a slab of all-around infinite extent under conditions of plane strain. The loading applied at infinity is taken to be one of uniform uniaxial tension at right angles to the faces of the crack. For the particular class of elastic materials considered the tensile stress in large homogeneous uni-axial extension is asymptotic to a continuously adjustable power of the corresponding principal stretch. The asymptotic analysis of the foregoing crack problem is reduced to a nonlinear eigenvalue problem, the solution of which is established in closed form, in terms of elementary functions and a transcendental integral of such functions. This solution involves two arbitrary constants, one of which governs the amplitude of the ensuing elastostatic field near the tip of the crack. A precise estimate of the amplitude parameter, valid at sufficiently small load intensities, is deduced with the aid of a known conservation law. The remaining arbitrary constant, which is left indeterminate by the present lowest-order asymptotic analysis, does not affect the dominant behavior of the field quantities of primary physical interest. II-lustrative numerical results, appropriate to both hardening and softening materials, are presented.

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Zusammenfassung Diese Arbeit betrifft die asymptotische Ermittelung, im Rahmen der nichtlinearen Elastizitätstheorie ebener Verformungen, von den Spannungen und Verschiebungen am Ende eines Schlitzes in einer allseitig unendlich ausgedehnten Scheibe. Die Scheibe ist im Unendlichen durch einen gleichförmigen Zug senkrecht zur Schlitzachse belastet. Die asymptotische Behandlung dieses Problems wird auf ein Eigenwertproblem zurückgeführt, dessen Lösung in geschlossener Form durch elementare Funktionen dargestellt wird. Die gefundene Lösung enthält zwei unbestimmte Konstanten von welchen eine die Amplitude der lokalen Feldsingularitäten bestimmt. Diese Konstante wird für kleine Belastungen streng abgeschätzt auf Grund eines Erhaltungssatzes und mit Hilfe der bekannten Lösung des linearisierten Schlitzproblems.

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The results communicated in this paper were obtained in the course of an investigation supported under Contract N00014-67-A-0094-0020 of the California Institute of Technology with the Office of Naval Research in Washington, D.C.     

Study of the plastic zone near a crack in an anisotropic body

The plastic zone at a crack tip in a finite anisotropic body is studied. A boundary-value problem is formulated in terms of the components of the covariant displacement vector for small strains. Particular attention is given to the case of plain strain. In this case, a numerical solution is found for a long rectangular body with a central crack under tension. As a result, conditions for the occurrence and development of a plastic zone at the crack tip are established. A plastic zone on the lateral surface of the body is discovered. How both zones extend and coalesce is elucidated. The effect of anisotropy on the occurrence of a plastic zone is evaluated __________ Translated from Prikladnaya Mekhanika, Vol. 42, No. 7, pp. 29–44, July 2006.     

Modeling the fracture process zone near a crack tip in a nonlinear elastic body

The model of a fracture process zone near the tip of a mode I crack in a nonlinear elastic body is proposed. Using the numerical solution of an appropriate boundary-value problem, the effect of the fracture process zone on a crack opening displacement is examined     

Exponential stress and strain singularity at tip of mode I growing crack in power hardening plastic material

The stress-strain distribution near the tip of a Mode I growing crack in a power hardening plastic material is reconsidered. Two types of asymptotic equations are derived and solved numerically. It is shown that when the crack tip is approached, the stress is singular of the order r^−δ, while the strain is singular of the order r^−nδ, where r is the distance measured from the crack tip. The parameter δ is a constant; it depends on the hardening exponent n being greater than one.