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.     

Measurement of mixed-mode crack profiles by holographic interferometry

Holographic interferometry was used to study the mixed-mode fracture characteristics of mortar. The nature of crack propagation in such quasibrittle materials and the theoretical model used to interpret the experimental results indicated that a highly sensitive measurement technique was required. The gradual curvature of the propagating crack at different sections of the specimen necessitated full-field observation capability. The nature of the problem made holographic interferometry the ideal technique for this application. To measure the in-plane components of the opening and sliding of the crack surfaces during propagation, a single holographic plate was placed very close to the specimen. This allowed four independent observations of any point on the specimen from the four corners of the plate without any need for additional optics of exposures. Double-exposure holograms were made at different crack-propagation stages. The developed plate was illuminated by an unexpanded reference beam to form a real image of the object and observe displacement fringes. Fringe data were interpreted by using computer software written for this research.     

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.     

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 deformation field near a crack tip in rubber-like material

This paper deals with strain field near a crack tip in a rubber-like material under plane strain condition. The constitutive relation adopted here is valid for both small and large strain. The asymptotic equations are derived for a shrinking sector and expanding sector. The closed mathematic solution is obtained for the latter while a numerical solution is found for the former. By connecting deformation of the two sectors, the crack tip field character is found.     

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.     

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.     

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 asymptotic elastic plastic analysis in plane strain deformation near a crack tip

In this paper, an asymptotic elasto-plastic analysis in plane strain deformation near a crack tip is established. In this article, special emphasis is laid on the well-known Irwin’s solution of elastic material. Thus, all the field quantity necessary for the elasto-plastic analysis of fracture mechanics can be obtained in this paper.     

Effect of electric current on the evolution of plastic strain near a crack tip

The effect of direct current on the evolution of plastic strain near the tip of a crack in a crystal in tension is studied. The plastic strain near the crack tip in the loaded specimen is the result of motion of dislocations in the active slip planes of the crystal under the action of shear stresses caused by external loading and electric current. The Joule heat, Thomson effect, and electron wind (electroplastic effect) are taken into account in calculations. The plastic strain and stress distributions near the crack tip are determined at different moments of time for a given magnitude ofelectric current. The effect of the plastic zone on the stressintensity factor of the crack is studied. It is found that the plastic strain is affected largely by the Joule heat released upon passage of the electric current. A numerical analysis is performed for an Fe crystal.     

Non-elliptic deformation field near the tip of a mixed-mode crack in a compressible hyperelastic material

This paper gives an asymptotic analysis of the deformation field near the tip of an arbitrary mixed-mode crack in a compressible hyperelastic harmonic material which loses ellipticity at sufficiently large deformations. It is found that the near-tip deformation field is characterized by a localized non-elliptic deformation band issuing from the crack-tip and bounded by two curves of discontinuous deformation gradient. Explicit expression for the near-tip deformation field is obtained both inside and outside the localized deformation band. In particular, a simple relation is derived that determines the orientation of the deformation band in terms of two complex governing parameters of the near-tip fields inside and outside the deformation band, respectively.     

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.     

Measurements of crack growth in a solid at elevated temperature by holographic interferometry

Real-time holographic interferometry was used to follow the crack-opening displacement (COD) of a compact tension specimen of zirconium 2.5-percent niobium subjected to a constant tensile load at 120°C for a period of 860 h. This was made possible by a dimensionally stable invar plate placed beside the specimen as the reference for the alignment of holograms. A finite-element elasto-plastic stress-analysis code and measurements on a duplicate specimen with a clip gage were used to correlate the measured COD and the corresponding crack growth.     

Mode I crack tip field with strain gradient effects

A plane strain mode I crack tip field with strain gradient effects is investigated. A new strain gradient theory is used. An elastic-power law hardening strain gradient material is considered and two hardening laws, i. e. a separation law and an integration law are used respectively. As for the material with the separation law hardening, the angular distributions of stresses are consistent with the HRR field, which differs from the stress results^[19]; the angular distributions of couple stresses are the same as the couple stress results^[19]. For the material with the integration law hardening, the stress field and the couple stress field can not exist simultaneously, which is the same as the conclusion^[19], but for the stress dominated field, the angular distributions of stresses are consistent with the HRR field; for the couple stress dominated field, the angular distributions of couple stresses are consistent with those in Ref. [19]. However, the increase in stresses is not observed in strain gradient plasticity because the present theory is based on the rotation gradient of the deformation only, while the crack tip field of mode I is dominated by the tension gradient, which will be shown in another paper. Supported by the National Science Foundation of China (No. 19704100), Science Foundation of Chinese Academy of Sciences (Project KJ951-1-20), CAS K. C. Wong Post-doctoral Research Award Fund and the Post Doctoral Science Fund of China.     

Stress field near interface crack tip of double dissimilar orthotropic composite materials

In this paper, double dissimilar orthotropic composite materials interfacial crack is studied by constructing new stress functions and employing the method of composite material complex. When the characteristic equations＇ discriminants △1 〉 0 and △2 〉0, the theoretical formula of the stress field and the displacement field near the mode I interface crack tip are derived, indicating that there is no oscillation and interembedding between the interfaces of the crack.     

The stress field near a blunting crack tip under mixed modes 1 and 2

The distribution of stress near a crack tip deforming in plane strain under mixed Modes 1 and 2 loads is calculated using slip-line field theory. Large geometry change effects are taken into account. The results are compared and contrasted both with known Mode 1 large-deformation solutions and with previous mixed-mode solutions for a sharp crack. The results are then combined with stress-based fracture criteria to discuss mixed-mode fracture on the lower shelf.     

A study of effective crack length using holographic interferometry

A technique using holographic interferometry and models of thin-sheet PMMA has been adapted to study the effective crack length for slots with rounded tips of various radii. The results suggest a rational means of applying sharp-crack fracture mechanics in certain nonideal situations and are compared with earlier studies.     

Finite-deformation analysis of the elastostatic field near the tip of a crack: Reconsideration and higher-order results

Summary In this paper we return to the asymptotic analysis, within the nonlinear equilibrium theory of compressible elastic solids, of the deformations and stresses near the tip of a traction-free crack in a slab of all-around infinite extent under conditions of plane strain. As before, the loading at infinity is taken to be one of uniform uni-axial tension at right angles to the faces of the crack. We show that once a restrictive assumption introduced at the start of our earlier asymptotic treatment of the problem is relinquished, certain perplexing anomalies encountered in the previous analysis no longer arise. The present reconsideration of the problem leads to modifications in the dominant-order results for the secondary deformations and stresses, while those pertaining to the physical quantities of primary interest remain unaffected. Furthermore, this investigation encompasses some higher-order considerations, which supply an essential clarification and improvement of the lowest-order asymptotic solution.

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Zusammenfassung In dieser Arbeit wird die asymptotische Ermittelung, im Rahmen der nichtlinearen Elastizitätstheorie ebener Verformungen, von dem elastostatischen Feld am Ende eines Risses in einer allseitig unendlichen Scheibe wieder aufgenommen und fortgesetzt. Wir zeigen hier, dass gewisse physikalisch unerklärbare Resultate in unserer früheren Behandlung des Problems beseitigt werden wenn man eine unserer ursprünglichen Annahmen über die asymptotische Struktur der Lösung verallgemeinert. Obwohl diese Verallgemeinerung keinen Einfluss auf die wichtigsten. vorher gefundenen Resultate hat, führt sie zu wesentlichen Änderungen in den sekundären Spannungen und in der sekundären Verschiebung. Die vorliegende Arbeit enthält überdies auch asymptotische Betrachtungen zweiter Ordnung die für das Verständnis der Lösung niedrigster Ordnung unentbehrlich sind.

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