The study of crack tip stress and strain field in elasto-plastic materials

Making use of the elastic-plastic finite element program and the small scale yielding crack tip solution, three point bend and compact tension specimens are analysed at various levels of work hardening. Special attention is given to the singular stress distribution at a crack tip, to the fracture behaviour characterized by path independent integral and by crack tip opening displacement. Comparison is made between experimental and theoretical results for a structural low alloy steel. Correlation between the two is satisfactory, the experimental data are bounded by plane strain and plane stress solutions. It is indicated that the uncertainty in the true stress-strain curve in the region of initial yield may strongly influence the theoretical calculations.The authors would like to thank Professor Dr. H.Bethge, director of the Institute of Solid State Physics and Electron Microscopy in Halle (GDR) and Professor Dr. P.Ry, director of the Institute of Physical Metallurgy, Czechoslovak Academy of Sciences in Brno for their support of this cooperative research project.     

On the plastic zone size and crack tip opening displacement of a sub-interface crack in an infinite bi-material plate

Elastic–plastic stress analysis has been carried out for the plastic zone size and crack tip opening displacement of a sub-interface crack with small scale yielding. In our study, the shape of plastic zone is assumed as a long, slim strip at both crack tips. In the plastic zone, both normal stress and shear stress exist and are considered due to the bi-material interface. The values of the plastic zone size, normal stress and shear stress are determined by satisfying the conditions where both Modes I and II stress intensity factors vanish and Von Mises yield criterion is met. In the present paper, the sub-interface crack is simulated by continuously distributed dislocations which will result in singular integral equations. Those singular integral equations can be solved by reducing them to a set of linear equations. The values of the plastic zone size and crack tip opening displacement are obtained through an iterative procedure. Finally, the effect of normalized loading, normalized crack depth (distance to the interface) and Dundurs’ parameters on the normalized plastic zone size and the normalized crack tip opening displacement is discussed.     

Fracture behaviors induced by thermal stress in an anisotropic half plane superconductor

This Letter presents a theoretical analysis to the fracture behavior of a large single domain YBCO superconductor under thermal stress based on the two-dimensional theory of anisotropic thermoelasticity, the coupled finite element and infinite element numerical method. The thermal stress intensity factors are obtained due to a uniform heat flux by a line crack in a generally half plane superconductor. It is found that the thermal stress intensity factors decrease with the decrease of temperature, and while the longer the crack length is, the larger the stress intensity factors. Additionally, the J-integral at the crack tip is also investigated, a similar behavior to the thermal stress intensity factors is found. These results are benefit for us to understand the fracture mechanism of superconductor both in theory and application.     

Selective role of bainitic lath boundary in influencing slip systems and consequent deformation mechanisms and delamination in high-strength low-alloy steel

We elucidate here the deformation behaviour and delamination phenomenon in a high-strength low-alloy bainitic steel, in terms of microstructure, texture and stress evolution during deformation via in situ electron back-scattered diffraction and electron microscopy. Furthermore, the selective role of bainitic lath boundary on slip systems was studied in terms of dislocation pile-up and grain boundary energy models. During tensile deformation, the texture evolution was concentrated at {1 1 0}<1 1 1> and the laths were turn parallel to loading direction. The determining role of lath on the deformation behaviour is governed by length/thickness (l/t) ratio. When l/t > 28, the strain accommodates along the bainite lath rather than along the normal direction. The delamination crack initiated normal to (0 1 1) plane, and become inclined to (0 1 1) plane with continued strain along (0 1 1) plane and lath plane. This indicated that the delamination is not brittle process but plastic process. The lack of dimples at the delaminated surface is because of lack of strain normal to the direction of lath. The delaminated (0 1 1) planes were associated with cleavage along the (1 0 0) plane.     

A model of a belt chamber cracking based on crack profiles calculations

Abstract

The problem of a Belt chamber matrix cracking is presented. The influence of crack surface quality on the effective values of near crack tip stress is discussed. It is shown that under working conditions of the vessel, the existing shear friction between upper and lower crack surfaces caused by crack surface roughness can prevent the crack surface sliding displacement. Therefore, the control variable for matrix cracking is the value of stress intensity factor K_I corresponding to normal node of loading only. The calculations are performed by finite element method within the range of linear elastic fracture mechanics.     

A Modified Free Volume Model for Characterizing of Rate Effect in Bulk Metallic Glasses

We investigate the plastic deformation and constitutive behaviour of bulk metallic glasses （BMGs）. A dimensionless Deborah number DeiD = tr/ti is proposed to characterize the rate effect in BMGs, where tr is the structural relaxing characteristic time of BMGs under shear load, ti is the macroscopic imposed characteristic time of applied stress or the characteristic time of macroscopic deformation. The results demonstrate that the modified free volume model can characterize the strain rate effect in BMGs effectively.     

Force distribution in an inhomogeneous sandpile

The force perturbation field in a two-dimensional pile of frictionless gravity-loaded discs or spheres arising from lattice distortions is derived to first order. The starting point is the model proposed by Liffman et al. (Powder Technology (1992) pp. 255-267) and Hong (Phys. Rev. E 47, 760-762 (1993)) in which discs of uniform size are arranged on a regular lattice: this predicts a uniform normal stress distribution at the base of the pile. The analysis is applied to two problems: (i) deformable (rather than rigid) grains that undergo Hertzian deformation at the points of contact; (ii) a pile containing a gradient in particle size from the centre to the free surfaces. The former results in the classical pressure dip at the centre; the latter also produces a dip if the larger particles are at the centre. Received 29 January 1998 and Received in final form 7 September 1998     

Effect of plastic deformation at the crack tip in a crystal on the direction of the tip growth under a mixed load

Evolution of plastic deformation at the tip of a wedge-shaped crack in a crystal under planar strain (modes I and II) was calculated for different cleavage planes, easy-slip systems, angles at the wedge tip, and ratios of the external extension and shear loads. Time distributions are obtained for the plastic deformation, the effective shear stress, the stress intensity factor, and the crack growth direction under monotonic load of the crystal up to a specified limit and further relaxation to establishment of equilibrium distributions under a constant external load. Numerical calculations were performed for an α-Fe crystal.     

A convective instability mechanism for quasistatic crack branching in a hydrogel

Experiments on quasistatic crack propagation in gelatin hydrogels reveal a new branching instability triggered by wetting the tip opening with a drop of aqueous solvent less viscous than the bulk one. We show that the emergence of unstable branches results from a balance between the rate of secondary crack growth and the rate of advection away from a non-linear elastic region of size G/E , where G is the fracture energy and E the small strain Young modulus. We build a minimal, predictive model that combines mechanical characteristics of this mesoscopic region and physical features of the process zone. It accounts for the details of the stability diagram and lends support to the idea that non-linear elasticity plays a critical role in crack front instabilities.     

Influence of low temperatures on the fracture micromechanism of materials with bcc and fcc lattice structures under single loading conditions

General regularities of the influence of the local stress state of a material on the plastic zone formation at the crack tip and the fracture micromechanism of materials with bcc and fcc lattice structures under single loading (static, impact, high-speed pulsed) conditions have been established. Schemes of plastic zone formation under plane strain, plane stress, and in the transient region from plane strain to plane stress are proposed.     

Dislocation Plasticity Effects on Interfacial Fracture

Analyses are reviewed where plastic flow in the vicinity of an interfacial crack is represented in terms of the nucleation and glide of discrete dislocations. Attention is confined to cracks along a metal-ceramic interface, with the ceramic idealized as being rigid. Both monotonic and fatigue loading are considered. The main focus is on the stress and deformation fields near the crack tip predicted by discrete dislocation plasticity, in comparison with those obtained from conventional continuum plasticity theory. The role that discrete dislocation plasticity can play in interpreting interface fracture properties in the presence of plastic flow is discussed.     

The optical method of caustics

An overview of the basic principles of the optical method of caustics for the determination of stress intensity factors in crack problems is presented. The method is based on the assumption that the state of stress in the neighborhood of the crack tip is plane stress. However, the state of stress changes from plane strain very close to the tip to plane stress at a critical distance from the tip through an intermediate region where the stress field is three-dimensional. The caustic is the image of the so-called initial curve on the specimen and, therefore, depends on the state of stress along the initial curve. For the determination of stress intensity factors the values of the stress-optical constants are needed. These values depend strongly on the state of stress being plane stress, plane strain or three-dimensional. This complicated the experimental determination of stress intensity factors. For the characterization of the state of affairs near the crack tip a phenomenological triaxiality factor is introduced. A methodology based on the use of optically birefringent materials is developed for the determination of stress intensity factors without paying attention to the location of the initial curve in the plane stress, plane strain or three-dimensional region. Finally, a comparison of the methods of photoelasticity and caustics takes place, and the potentialities and limitations of both methods for the solution of crack problems are explored.     

First-Principles Calculations of Elastic Properties of LaNi4.75Sn0.25 Alloys under Pressure

The equilibrium lattice constants, bulk modulus, shear modulus, elastic constants and Debye temperature of LaNi4.75 Sn0.25 under pressure are calculated using the full-potential linearized augmented plane wave （FP-LAPW） method as well as the quasi-harmonic Debye model. The results at zero pressure are in excellent agreement with the experimental data. The Sn atom is found to occupy the equivalent 3g site （0.5a, 0.75b, 0.5c） in the quadruple cell. The Debye temperature of LaNi4.75Sn0.25 is lower than that of LaNi5. The dependences of bulk modulus on finite temperature and on finite pressure are also investigated. The results show that the bulk modulus B increases monotonously as pressure increases.     

Compact solution for a multizone BCS and TTN crack model

This paper evaluates a compact formula incorporating both the Bilby-Cottrell-Swinden (BCS) and the Taira-Tanaka-Nakai (TTN) by considering a rectilinear crack traversing an arbitrary number of zones with different friction stresses. Symmetry is not required. The expressions for the dislocation density and the plastic displacement as well as the stress distribution in the plane of the crack are obtained.     

Combined mode-I and mode-II fracture of ceramics with crack-face grain and/or whisker bridging

Crack-face grain and/or whisker bridging in ceramics was investigated under combined mode-I and mode-II loading. A novel technique for analysing the stress shielding at the crack tip caused by the bridging was proposed, in which the critical values of the local mode-I and mode-II stress intensity factors were numerically derived from an azimuthal angle at the onset of noncoplanar crack extension using the mixed-mode failure criteria. The wedging effect, which induced local mode-I crack opening at the tip, was identified under the combined-mode loading on polycrystalline alumina as well as an alumina matrix composite reinforced with silicon carbide whiskers. The effect was accelerated with the increase in the mode-II component of nominally applied loading and the decrease in the bridging zone length. It was also found that the stress shielding due to the whisker bridging was not only effective for mode-I but also for mode-II crack opening.     

Why is nacre strong? II. Remaining mechanical weakness for cracks propagating along the sheets

In our previous paper (Eur. Phys. J. E 4, 121 (2001)) we proposed a coarse-grained elastic energy for nacre, or stratified structure of hard and soft layers found in certain seashells . We then analyzed a crack running perpendicular to the layers and suggested one possible reason for the enhanced toughness of this substance. In the present paper, we consider a crack running parallel to the layers. We propose a new term added to the previous elastic energy, which is associated with the bending of layers. We show that there are two regimes for the parallel-fracture solution of this elastic energy; near the fracture tip the deformation field is governed by a parabolic differential equation while the field away from the tip follows the usual elliptic equation. Analytical results show that the fracture tip is lenticular, as suggested in a paper on a smectic liquid crystal (P.G. de Gennes, Europhys. Lett. 13, 709 (1990)). On the contrary, away from the tip, the stress and deformation distribution recover the usual singular behaviors ( and 1/, respectively, where x is the distance from the tip). This indicates there is no enhancement in toughness in the case of parallel fracture. Received 16 November 2001     

Evolution of the concentration of point defects at the tip of a crack

The evolution of the distribution of interstitial impurity atoms in the plastic zone around the tip of a tension crack is analyzed. The transport of point defects is determined by: 1) the hydrostatic component of the elastic stress at the crack tip, created by the superposition of the elastic fields of the crack and dislocations; 2) the elastic field of moving dislocations (“sweeping out” of interstitial impurity atoms); 3) the dislocation-driven transport of point defects present in the dislocation cores. The contributions of each mechanism of transport of point defects to the crack tip are calculated over the entire time from the start of loading of a sample containing a crack until an equilibrium distribution of plastic deformation is established after the cessation of loading. Numerical calculations are carried out for interstitial hydrogen atoms dissolved in an α-Fe crystal. Fiz. Tverd. Tela (St. Petersburg) 39, 1580–1585 (September 1997)     

Plastic analysis of crack problems in three-dimensional icosahedral quasicrystalline material

Due to their complexity, the basic plastic properties of all quasicrystalline materials are essentially unknown [M. Feuerbacher, C. Thomas, K. Urban, Plastic behaviour of quasicrystalline materials, in Quasicrystals: Structure and Physical Properties, H.R. Trebin, ed., Wiley/VCH, Berlin, 2003]. Plastic deformation of cracks in icosahedral quasicrystals have been analyzed in a strict and systematic form and the crack tip opening displacement (CTOD) and size of the plastic zone around the crack tip was determined exactly. CTOD is suggested as a parameter of plastic fracture for quasicrystalline materials. The present work may also provide a novel methodology for plastic analysis of quasicrystals.     

Emission of stress waves during fracture

Emission of both longitudinal and surface (Rayleigh) waves during fracture of plates under conditions of plane stress and plane strain were studied experimentally. The non-equilibrated tensile stress in the fractured section of the plate creates an elastic wave, which travels radially along the plate at the sound speed. Moreover, the high surface deformation around the crack tip, due to the high stress concentration there, propagates as a surface wave following fracture of this zone, at the respective Rayleigh wave speed with a circular wavefront. The influence of the thickness of the plate and the type of fracture (brittle or ductile) was examined and interesting results were derived, by utilizing a high speed photography technique.