一种镍基双晶材料疲劳裂纹扩展效应

对晶界平行裂纹和晶界垂直裂纹的双晶体进行三点弯曲疲劳实验，研究了双晶材料的疲劳裂纹扩展规律，测定了双晶的疲劳扩展速率，揭示了晶界对晶粒疲劳裂纹扩展的屏蔽效应：当裂纹距晶界某一特定长度时，裂纹扩展速率最快；而裂纹顶端交于晶界时，裂纹扩展速率最侵．进一步的晶体滑移有限元数值分析揭示了这种屏蔽效应的机理：晶界附近不协调的塑性变形，导致了裂纹尖端应力场的重新分布．     

The stress field near the front of an arbitrarily shaped crack in a three-dimensional elastic body

The problem stated in the title is investigated with special emphasis on the first three terms of the stress expansion, proportional to r ^-1/2, r ⁰=1 and r ^1/2 respectively, where r denotes the distance to the crack front. The particular case of a plane crack with a straight front and of stresses independent of the distance along the latter is studied first. It is shown that the classical plane strain and antiplane solutions must be supplemented by a few additional particular solutions to obtain the full stress expansion. The general case is then considered. The stress expansion is studied by writing the field equations (equilibrium, strain compatibility and boundary conditions) in a system of suitable curvilinear coordinates. It is shown that the number of independent constants in the stress expansion is the same as in the particular case considered previously but that the curvatures of the crack and its front and the non-uniformity of the stresses along the latter induce the appearance of corrective terms in this expansion.     

镍基双晶体晶界断裂特性研究

对单晶体以及晶界平行晶粒裂纹和晶界垂直晶粒裂纹的双晶体的断韧性进行了实验研究,设计了三种三点弯曲试件,得到了单晶体和晶界的断裂韧性值,在晶界垂直晶粒裂纹的双晶体试验中,揭示了晶界对晶粒断裂的屏蔽效应;当裂纹距晶界某一特定长度时,断裂韧性值最大,理论分析和晶体滑移有限元数值分析揭示了这种屏蔽效应的机理,双晶晶界处的变表相容性导致了理解纹尖端应国和场的重新分布,并由此产生了晶界屏蔽效应。     

Propagation of a cleavage crack front across a field of persistent grain boundaries

The nonuniform propagation of a cleavage front across a field of persistent grain boundaries is analyzed. When a cleavage crack advances in a field of grains, some of the grain boundaries cannot be directly broken through, which interrupts the crack growth process. When the crack front bypasses such persistent grain boundaries (PGB), the overall crack growth driving force must be increased so that the local stress intensity can overcome the local fracture resistance. A theoretical model is developed based on the R-curve analysis. A closed-form expression of the critical stress intensity factor is given as a function of the line content of PGB.     

Grain boundary oxidation and fatigue crack growth at elevated temperatures

Fatigue crack growth rate at elevated temperatures can be accelerated by grain boundary oxidation. Grain boundary oxidation kinetics and statistical distribution of grain boundary oxide penetration depth were studied.At a constant ΔK-level and at a constant test temperature, fatigue crack growth rate, da/dN, is a function of cyclic frequency, ν. A fatigue crack growth model of intermittent micro-ruptures of grain boundary oxide is constructed. The model is consustent with the experimental observations that, in the low frequency region, da/dN is inversely proportional to ν, and fatigue crack growth is intergranular.     

Variation of the stress intensity factor along the front of a 3-D rectangular crack subjected to mixed-mode load

Summary  The singular integral equation method is applied to the calculation of the stress intensity factor at the front of a rectangular crack subjected to mixed-mode load. The stress field induced by a body force doublet is used as a fundamental solution. The problem is formulated as a system of integral equations with r ⁻³-singularities. In solving the integral equations, unknown functions of body-force densities are approximated by the product of polynomial and fundamental densities. The fundamental densities are chosen to express two-dimensional cracks in an infinite body for the limiting cases of the aspect ratio of the rectangle. The present method yields rapidly converging numerical results and satisfies boundary conditions all over the crack boundary. A smooth distribution of the stress intensity factor along the crack front is presented for various crack shapes and different Poisson's ratio. Received 5 March 2002; accepted for publication 2 July 2002     

Damage analysis of tetragonal perovskite structure ceramics implicated by asymptotic field solutions and boundary conditions

Cracking of ceramics with tetragonal perovskite grain structure is known to appear at different sites and scale level. The multiscale character of damage depends on the combined effects of electromechanical coupling, prevailing physical parameters and boundary conditions. These detail features are exhibited by application of the energy density criterion with judicious use of the mode I asymptotic and full field solution in the range of r/a=10⁻⁴ to 10⁻² where r and a are, respectively, the distance to the crack tip and half crack length. Very close to the stationary crack tip, bifurcation is predicted resembling the dislocation emission behavior invoked in the molecular dynamics model. At the macroscopic scale, crack growth is predicted to occur straight ahead with two yield zones to the sides. A multiscale feature of crack tip damage is provided for the first time. Numerical values of the relative distances and bifurcation angles are reported for the PZT-4 ceramic subjected to different electric field to applied stress ratio and boundary conditions that consist of the specification of electric field/mechanical stress, electric displacement/mechanical strain, and mixed conditions. To be emphasized is that the multiscale character of damage in piezoceramics does not appear in general. It occurs only for specific combinations of the external and internal field parameters, elastic/piezoelectric/dielectric constants and specified boundary conditions.     

In-plane perturbation of a system of two coplanar slit-cracks – II: Case of close inner crack fronts or distant outer ones

The study of the in-plane perturbation of a system of two coplanar slit-cracks carried out in Part I is specialized to the case where the distance between the inner crack fronts is small, or equivalently that between the outer fronts large. The limit process involved is complex because of appearance of a “boundary layer” in the limiting case considered; this boundary layer occurs near the origin in the Fourier space used to determine the unknown components of the fundamental kernel looked for. A technique of matched asymptotic expansions is used to tackle this difficulty.The problem is thus reduced to determining two unknown functions only, which characterize the “interactions” between the two inner fronts. These functions obey a system of nonlinear differential equations in Fourier’s space, which are solved analytically near the origin and numerically in general. The results evidence a very slow decrease of long-range interactions between distinct points on the same front or distinct ones. This represents a striking difference with respect to the cases considered earlier of a single semi-infinite crack and a single slit-crack.     

Brittle versus ductile transition of nanocrystalline metals

The brittle versus ductile transition for conventional metals is dictated by the competition between dislocation emission and cleavage. For nanocrystalline metals with grain size below 25 nm, however, dislocation activities are suppressed and the classic theory fails to apply. In this paper, one of the competing mechanisms that control the brittle versus ductile transition of nanocrystalline metals is found to be the grain boundary dominated creep deformation versus the grain boundary decohesion. A model is proposed to quantify the crack propagation in nanocrystalline metals. The effects of material properties, initial configuration and applied loads on the property of crack propagation are addressed. It is concluded that either the increases in the initial crack length, the applied load and the grain boundary damage, or the deterrence in creep deformation, accelerate the crack propagation, and vice versa.     

A micromechanical basis for partitioning the evolution of grain bridging in brittle materials

A micromechanical model is developed for grain bridging in monolithic ceramics. Specifically, bridge formation of a single, non-equiaxed grain spanning adjacent grains is addressed. A cohesive zone framework enables crack initiation and propagation along grain boundaries. The evolution of the bridge is investigated through a variance in both grain angle and aspect ratio. We propose that the bridging process can be partitioned into five distinct regimes of resistance: propagate, kink, arrest, stall, and bridge. Although crack propagation and kinking are well understood, crack arrest and subsequent “stall” have been largely overlooked. Resistance during the stall regime exposes large volumes of microstructure to stresses well in excess of the grain boundary strength. Bridging can occur through continued propagation or reinitiation ahead of the stalled crack tip. The driving force required to reinitiate is substantially greater than the driving force required to kink. In addition, the critical driving force to reinitiate is sensitive to grain aspect ratio but relatively insensitive to grain angle. The marked increase in crack resistance occurs prior to bridge formation and provides an interpretation for the rapidly rising resistance curves which govern the strength of many brittle materials at realistically small flaw sizes.     

A centrally cracked thin circular disk, Part I: 3D Elastic–plastic finite element analysis

A full field solution, based on small deformation, three-dimensional elastic–plastic finite element analysis of the centrally cracked thin disk under mode I loading has been performed. The solution for the stresses under small-scale yielding and lo!cally fully plastic state has been compared with the HRR plane stress solution. At the outside of the 3D zone, within a distance of rσ_o/J=18, HRR dominance is maintained in the presence of a significant amount of compressive stress along the crack flanks. Ahead of this region, the HRR field overestimate the stresses. These results demonstrate a completely reversed state of stress in the near crack front compared to that in the plane strain case. The combined effect of geometry and finite thickness of the specimen on elastic–plastic crack tip stress field has been explored. To the best of our knowledge, such an attempt in the published literature has not been made yet. For the qualitative assessment of the results some of the field parameters have been compared to the available experimental results of K, gives a fair estimate of the crack opening stress near the crack front at a distance of order 10⁻² in. On the basis of this analysis, the Linear Elastic Fracture Mechanics approach has been adopted in analyzing the fatigue crack extension experiments performed in the disk (Part II).     

Fracture mechanics of plates and shells applied to fail-safe analysis of fuselage Part II: Computational results

In this paper, the problem of the fracture of a fuselage stiffened by longitudinal longerons and circumferential frames is analyzed by means of the finite element method. Our research is motivated by the fail-safety design concept of fuselage for civil aircraft. In this study, the total energy release rate are evaluated for five types of basic loading, namely, axial extension, pure bending, twisting, transverse shearing, and radial expansion due to internal pressure. The crack is located either at the mid-point or near the end of the fuselage. It extends in two bays with the stiffener at its center. The stiffener which bisects the crack is assumed to be broken at the location of the crack. Computational results indicate that the total energy release rate G_t increases with the increasing crack length. However, when the crack tip approaches the stiffener, the value of G_t decreases as a result of the reinforcement from the stiffener. For a crack near the end of the fuselage, as a result of boundary effect, the value of G_t is larger in comparison with the case of the crack at the mid-point of the fuselage. We also find that the effect of geometrical nonlinearity can reduce the value of G_t for the fuselage under axial tension or pure bending. For the fractured fuselage under pure bending, shell buckling can occur at the concave side of the fuselage prior to crack growth. The maximum tensile stress in the stiffener in front of the crack tip is also investigated.     

Effect of constraint induced by crack depth on creep crack-tip stress field in CT specimens

In this paper, the effect of constraint induced by the crack depth on creep crack-tip stress field in compact tension (CT) specimens is examined by finite element analysis, and the effect of creep deformation and damage on the Hutchinson–Rice–Rosengren (HRR) singularity stress field are discussed. The results show the constraint induced by crack depth causes the difference in crack-tip opening stress distributions between the specimens with different crack depth at the same C*. The maximum opening stress appears at a distance from crack tips, and the stress singularity near the crack tips does not exist due to the crack-tip blunting caused by the large creep deformation in the vicinity of the crack tips. The actual stress calculated by the finite element method (FEM) in front of crack tip is significantly lower than that predicted by the HRR field. Based on the reference stress field in the deep crack CT specimen with high constraint, a new constraint parameter R is defined and the constraint effect in the shallow crack specimen is examined at different distances ahead of the crack tip from transient to steady-state creep conditions. During the early stages of creep constraint increases with time, and then approaches a steady state value as time increases. With increasing the distance from crack tips and applied load, the negative R increases and the constraint decreases.     

Energy domain integral applied to solve center and double-edge crack problems in three-dimensions

A three-dimensional Boundary Element Method (BEM) implementation of the energy domain integral for the numerical computation of the crack energy release rate is presented in this paper. The domain expression of the energy release rate is naturally compatible with the BEM, since stresses, strains and derivatives of displacements at internal points can be evaluated using the appropriate boundary integral equations. The pointwise crack energy release rate is evaluated along the three-dimensional crack front over a cylindrical domains that surround a segment of the crack front. The accuracy of the implementation is demonstrated by solving several problems, which include geometries containing straight as well as curved crack fronts.     

Crack front pinning by design in planar heterogeneous interfaces

The propagation of an interfacial crack front along the weak plane of a thin film stack is considered. A simple patterning technique is used to create a toughness contrast within this perfectly two-dimensional weak interface. The transparency of the specimens allows us to directly observe the propagation of the purely planar crack obtained during a DCB (double cantilever beam) test. The effect on the crack front morphology of macroscopic unidimensional patterns in the direction of propagation is studied. In these weak pinning conditions, the geometry of the front quantitatively agrees with the first-order expansion proposed by Gao and Rice [1989. First-order perturbation analysis of crack trapping by arrays of obstacles. J. Appl. Mech. 56, 828-836] which accounts for the effect of the interfacial crack front geometry on the stress intensity factor.     

Microstructural modeling of crack nucleation and propagation in high strength martensitic steels

A dislocation-density based multiple-slip crystalline plasticity formulation, a dislocation-density grain boundary (GB) interaction scheme, and an overlapping fracture method were used to investigate crack nucleation and propagation in martensitic steel with retained austenite for both quasi-static and dynamic loading conditions. The formulation accounts for variant morphologies, orientation relationships, and retained austenite that are uniquely inherent to lath martensitic microstructures. The interrelated effects of dislocation-density evolution ahead of crack front and the variant distribution of martensitic blocks on crack nucleation and propagation are investigated. It is shown that dislocation-density generation ahead of crack front can induce dislocation-density accumulations and plastic deformation that can blunt crack propagation. These predictions indicate that variant distribution of martensitic blocks can be optimized to mitigate and potentially inhibit material failure.     

An elastic wave scattering problem relating to the rapid movement of a fracture in a plate

We consider the problem of a semiinfinite through crack in an elastic plate, which starts suddenly under the application of a step load (mode-I). As the crack propagates, microfractures grow rapidly at a small distance ahead of the tip, releasing pressure pulses. This process of microfracture nucleation, pulse emission and subsequent coalescence with the main fracture front continues to occur during crack motion. We crudely simulate this process by employing a single point dilatational source that is situated ahead of the crack tip and moves in unison with it, emitting pulses periodically. The total wavefield is then due to the effect of this point source, as well as the scattering of the pulses by the crack front. We model this elastodynamic problem under the plane stress assumption. A closed form solution is developed for the in-plane displacements of the crack faces due to the scattered field. The surface wave contribution can be pulled out separately and is expected to be significant. In particular, the results are cast into a form that is readily amenable to numerical analysis. We will be presenting the numerical results in Part II of this two part paper.     

On the effect of nano-particle clustering on toughening of nano-composite ceramics

In this paper, two and three-dimensional clustering models are developed to characterize the effect of nano-particle clustering on toughening of nanocomposite ceramics. It is found that crack pinning toughens the nano-composite ceramics because a higher stress intensity factor is needed for crack to propagate around or to pull-out the nano-particle. The nano-particle along the grain boundary steers the crack into the matrix grain due to the strong cohesion between the nanoparticle and the matrix. Since the fracture resistance of the grain boundary is lower than that of the grain lattice, the higher the probability of transgranular fracture induced by nano-particles, the tougher is the nano-composite. However, both crack pinning and transgranular fracture are affected by nano-particle clustering. Nanoparticle clustering, which increases with increasing volume fraction of nano-particles, leads to reduction of both the strength and toughness of the nano-composite ceramics. The larger the size of the clustered particle, and the more defects it contains, the easier it is for the crack to pass through the clustered particle, which means that the nano-particle clustering can reduce toughening induced by crack pinning and transgranular fracture. The theoretical prediction, based on the combination of the three mechanisms of nano-particles, is in agreement with the experimental data. The project supported by the National Natural Science Foundation of China (19891180) and the Research Grants Council of the HKSAR, China(HKU7081/00E)     

Controlling parameter of the stress intensity factors for a planar interfacial crack in three-dimensional bimaterials

Numerical solutions of singular integral equations are discussed in the analysis of a planar rectangular interfacial crack in three-dimensional bimaterials subjected to tension. The problem is formulated as a system of singular integral equations on the basis of the body force method. In the numerical analysis, unknown body force densities are approximated by the products of the fundamental density functions and power series, where the fundamental density functions are chosen to express singular behavior along the crack front of the interface crack exactly. The calculation shows that the present method gives smooth variations of stress intensity factors along the crack front for various aspect ratios. The present method gives rapidly converging numerical results and highly satisfied boundary conditions throughout the crack boundary. The stress intensity factors are given with varying the material combination and aspect ratio of the crack. It is found that the stress intensity factors K_I and K_II are determined by the bimaterial constant ε alone, independent of elastic modulus ratio and Poisson’s ratio.     

Initiation and growth characterization of corner cracks near circular hole

The finite element analysis of crack problems often incorporates the asymptotic character of the local solution into the formulation. Embedment of stress or strain singularities can impose serious restrictions on the outcome and inconsistencies in predicting crack and/or growth. These restrictions are discussed in connection with the problem of two diametrically opposite corner cracks near a circular hole subjected to remote uniform tension. Enforced in the numerical treatment is the 1/r character of the strain energy density function local to the corner crack border where r is the radial distance measured from the crack front. The tendency for the corner crack to become a through crack is predicted by assuming that each point of the crack border extends by an amount proportional to the strain energy density factor. The path would correspond to the loci of minimum strain energy density function. Numerical results are displayed graphically and discussed in connection with crack initiation and non-self-similar crack growth.