Crack tip fields at a ductile single crystal-rigid material interface

Small-scale yielding around a stationary crack along a ductile single crystal–rigid material interface is analyzed. Plane strain conditions are assumed to prevail and geometry changes are neglected. The analyses are carried out using both continuum slip and discrete dislocation plasticity theory for model fcc and bcc crystal geometries having either two or three slip systems. Numerical and analytical asymptotic solutions are presented for continuum slip plasticity theory. Solutions exhibiting both slip bands and kink bands are obtained. The addition of a third slip system to ductile single crystals having two slip systems is found to have a significant effect on the interface crack-tip fields. The results illustrate the role that each of the formulations considered can play in elucidating crack tip fields in single crystals.     

Modelling of small fatigue crack growth interacting with grain boundary

The slip band at the tip of a small fatigue crack interacting with grain boundaries is modelled for four cases: a slip band not reaching the grain boundary, a slip band blocked by the grain boundary, a slip band propagated into an adjacent grain, and a slip band propagated through one and then blocked by a second grain boundary. The theory for continuously distributed dislocations is used to calculate the crack-tip sliding or opening displacement and the microscopic stress intensity factor under tensile and shear loading. Assuming that the range of the tip displacement directly determines the propagation rate of both Stage I and II cracks, prediction of the propagation behavior of a small crack is made as a function of the distance between the crack tip and the grain boundary, and of the difficulty to propagate slip into adjacent grains, as well as a function of crack length and stress level. The directions for further development of modelling are discussed.     

Numerical analysis of blunting of a crack tip in a ductile material under small-scale yielding and mixed mode loading

The blunting of the tip of a crack in a ductile material is analysed under the conditions of plane strain, small-scale yielding, and mixed mode loading of Modes I and II. The material is assumed to be an elastic-perfectly plastic solid with Poisson's ratio being 1/2. The stress and strain fields for a sharp crack under mixed mode loading are first determined by means of elastic-plastic finite element analysis. It is shown that only one elastic sector exists around the crack tip, in contrast with the possibility of existence of two elastic sectors as discussed by Gao. The results obtained for a sharp crack are used as the boundary conditions for the subsequent numerical analysis of crack tip blunting under mixed mode loading, based on slip line theory. The characteristic shapes of the blunted crack tip are obtained for a wide range of Mode I and Mode II combinations, and found to resemble the tip of Japanese sword. Also the stress field around the blunted crack tip is determined.     

Interface crack problems with strain gradient effects

In this paper, the strain gradient theory proposed by Chen and Wang (2001a, 2002b) is used to analyze an interface crack tip field at micron scales. Numerical results show that at a distance much larger than the dislocation spacing the classical continuum plasticity is applicable; but the stress level with the strain gradient effect is significantly higher than that in classical plasticity immediately ahead of the crack tip. The singularity of stresses in the strain gradient theory is higher than that in HRR field and it slightly exceeds or equals to the square root singularity and has no relation with the material hardening exponents. Several kinds of interface crack fields are calculated and compared. The interface crack tip field between an elastic-plastic material and a rigid substrate is different from that between two elastic-plastic solids. This study provides explanations for the crack growth in materials by decohesion at the atomic scale.     

Dislocation tri-material solution in the analysis of bridged crack in anisotropic bimaterial half-space

The problem of an edge-bridged crack terminating perpendicular to a bimaterial interface in a half-space is analyzed for a general case of elastic anisotropic bimaterials and specialized for the case of orthotropic bimaterials. The edge crack lies in the surface layer of thickness h bonded to semi-infinite substrate. It is assumed that long fibres bridge the crack. Bridging model follows from the assumption of “large” slip lengths adjacent to the crack faces and neglect of initial stresses. The crack is modelled by means of continuous distribution of dislocations, which is assumed to be singular at the crack tip. With respect to the bridged crack problems in finite dissimilar bodies, the reciprocal theorem (Ψ-integral) is demonstrated as to compute, in the present context, the generalized stress intensity factor through the remote stress and displacement field for a particular specimen geometry and boundary conditions using FEM. Also the application of the configurational force mechanics is discussed within the context of the investigated problem.     

Large strain field near an interface crack tip

In this paper the elastostatic field near the tip of an interface crack between two materials is analyzed with the fully nonlinear theory. By dividing the crack tip field into narrowing sectors and an expanding sector, the asymptotic equations for the crack tip field are derived and solved. The singular characters of stress and strain near the crack tip are revealed. The crack opening shape is discussed for various cases. It is shown that when large deformation is taken into account the oscillatory singularity does not occur.     

The range of applicability of the small-scale yielding approach in theoretical investigations of yield and fracture at a crack tip

Theoretical analysis of the processes of plastic deformation and fracture in the vicinity of a sharp crack tip becomes easier if plasticity is confined to the immediate vicinity of the crack tip, for linear elastic stress intensity factors can be used to give the surrounding elastic field, and it is possible to employ a boundary layer formulation to determine the elastic-plastic field in the immediate vicinity of the crack tip. Consideration is given to the range of applicability of the small-scale yielding approach using a simple model in which slip is confined to the crack plane. A range of stress-displacement laws is considered, the object being to assess the effect of a material's flow characteristics on the range of applicability. The conclusions are discussed with respect to plane strain crack propagation in mild steel.     

Crack tip fields in ductile crystals

Results on the asymptotic analysis of crack tip fields in elastic-plastic single crystals are presented and some preliminary results of finite element solutions for cracked solids of this type are summarized. In the cases studied, involving plane strain tensile and anti-plane shear cracks in ideally plastic f c c and b c c crystals, analyzed within conventional small displacement gradient assumptions, the asymptotic analyses reveal striking discontinuous fields at the crack tip.For the stationary crack the stress state is found to be locally uniform in each of a family of angular sectors at the crack tip, but to jump discontinuously at sector boundaries, which are also the surfaces of shear discontinuities in the displacement field. For the quasi-statically growing crack the stress state is fully continuous from one near-tip angular sector to the next, but now some of the sectors involve elastic unloading from, and reloading to, a yielded state, and shear discontinuities of the velocity field develop at sector boundaries. In an anti-plane case studied, inclusion of inertial terms for (dynamically) growing cracks restores a discontinuous stress field at the tip which moves through the material as an elastic-plastic shock wave. For high symmetry crack orientations relative to the crystal, the discontinuity surfaces are sometimes coincident with the active crystal slip planes, but as often lie perpendicular to the family of active slip planes so that the discontinuities correspond to a kinking mode of shear.The finite element studies so far attempted, simulating the ideally plastic material model in a small displacement gradient type program, appear to be consistent with the asymptotic analyses. Small scale yielding solutions confirm the expected discontinuities, within limits of mesh resolution, of displacement for a stationary crack and of velocity for quasi-static growth. Further, the discontinuities apparently extend well into the near-tip plastic zone. A finite element formulation suitable for arbitrary deformation has been used to solve for the plane strain tension of a Taylor-hardening crystal panel containing, a center crack with an initially rounded tip. This shows effects due to lattice rotation, which distinguishes the regular versus kinking shear modes of crack tip relaxation. and holds promise for exploring the mechanics of crack opening at the tip.     

Crack extension by alternating shear

A comparison of the slip line flow field at the tip of a sharp crack and of a blunted crack shows that a sharp crack can be extended by alternating shear until it becomes blunted. Crack tip blunting is associated with high strain concentration and fracture by hole growth and coalescence. Crack extension by alternating shear has been obtained in fully plastic, plane strain sharply notched, singly and doubly grooved tensile specimens. Electron fractography shows crack extension by alternating shear at the tip of cleavage and fatigue cracks. It is shown that fatigue crack propagation is the result of repeated cyclic crack extension by alternating shear.     

In situ study of martensitic transformation and nucleation and propagation of cracks in Cu-Ni-Al shape memory alloy

Abstract

The stress induced martensitic transformation and the relationship between it and the nucleation and propagation of cracks in the Cu-Ni-Al shape memory alloy were investigated through in situ tensile tests by SEM and TEM. The results indicated that the stress concentration ahead of the crack tip could induce formation of stacking faults and different types of martensites. Transmission electron microscope observations showed that the martensites could transform from one type to another type and even reversely to parent during loading. The microcracks nucleated along the martensite/parent interface and intersections between two martensites. When the crack propagated a certain distance, the stress concentration ahead of the crack tip was large enough to result in formation of slip bands, in this condition the microcrack nucleated along slip bands more easily.     

A computational model and experimental validation of shielding and amplifying effects at a crack tip near perpendicular strength-mismatched interfaces

The stress field around the crack tip near an elastically matched but strength-mismatched interface body in a bimetallic system is influenced when the crack tip yield or cohesive zone spreads to the interface body. The concept of crack tip stress intensity parameter, K _tip, is therefore employed in fracture analysis of the bimetallic body. A computational model to determine K _tip is reviewed in this paper. The model, based upon i) Westergaard??s complex potentials coupled with Kolosov?CMuskhelishvili??s relations between a crack tip stress field and complex potentials and ii) Dugdale??s representation of the cohesive zone clearly indicates shielding or amplifying effects of strength mismatch across the interface, depending upon the direction of the strength gradient, over the crack tip. The model is successfully validated by conducting series of high cycle fatigue tests over Mode I cracks advancing towards various strength-mismatched interfaces in bimetallic compact tension specimens prepared by electron beam welding of elastically identical weak ASTM 4340 alloy and strong MDN 250 maraging steels.     

On the influence of a bimaterial interface on dynamic stress intensity factors

Summary The method of dynamic Green's function and the integral transforms are applied to investigate the elasto-dynamic stress intensity factor of a crack straddling an interface of a bimaterial composite. The crack which extends to infinity on one side is assumed to extend an arbitrary distancea on the other side of the interface. Anti-plane line loads are suddenly applied at timet=0 on either side of the crack surface at arbitrary distancesl ₁ andl ₂ from the interface. The effect of the interface on the dynamic stress field near the crack tip is studied. It is found that the transmitted wave through the interface and reflected wave from the interface serve to increase or decrease the stress field in the vicinity of the crack tip depending on the elastic properties of the two materials.     

Characteristics of microcrack initiation in CuNiAl shape memory alloy

The mechanism of microcrack initiation in CuNiAl shape memory alloy was investigated through in situ tensile tests under optical microscopy, scanning electron microscopy and transmission electron microscopy. The results indicated that various martensite phases appeared first around a notch tip upon loading, and then microcracks initiated along the martensite/parent interface. The small martensite regions could transform back to the parent phase not only upon unloading but also upon loading or during crack propagation. There was no dislocation emission and motion before martensite formation. The slip bands formed after the crack had propagated a definite distance, and the microcracks nucleated and the cracks propagated either along the slip bands or the martensite/parent interface.     

Variable power singular interface elements for a crack normal to the bimaterial interface

Zero thickness crack tip interface elements for a crack normal to the interface between two materials are presented. The elements are shown to have the desired r^λ−1 (0 < λ < 1) singularity in the stress field at the crack tip and are compatible with other singular elements. The stiffness matrices of the quadratic and cubic interface element are derived. Numerical examples are given to demonstrate the applicability of the proposed interface elements for a crack perpendicular to the bimaterial interface.     

Constraint effect on the near tip stress fields due to difference in plastic work hardening for bi-material interface cracks in small scale yielding

The change in near-tip stress field in Small Scale Yielding (SSY) for cracks located at an interface between two materials with different plastic work hardening is investigated. The difference in hardening is termed hardening mismatch, and is quantified through the parameter n, which is the difference in hardening exponent between the two materials. For cracks in elastic-ideally plastic materials the stress level in front of the crack tip is mainly controlled by the angular extent of the part where the slip lines are curved, often referred to as a centered fan like slip line sector. It is shown that for an elastic-ideally plastic material coupled to a material with non-zero hardening, an increase in stress is observed due to an extension of this centered fan like slip line sector. The angular extension of the centered fan like sector is dependent on the radial distance from the crack tip. Further, the change in stress depends strongly on hardening mismatch, increasing as n increases. For the situation with coupling between two non-zero hardening materials it is shown that the full field stress solution develops in a self-similar manner, but differs from the homogeneous case due to a coupling between the radial and angular stress field dependence. The amplitude of the change in stress field is to a rather good approximation only controlled by the hardening mismatch, n, and is more or less independent of the absolute values of hardening exponent of the two materials.     

ELEVATED TEMPERATURE FATIGUE CRACK GROWTH IN ALLOY 718—PART II: EFFECTS OF ENVIRONMENTAL AND MATERIAL VARIABLES

Observations concerning the effects of the environment and material variables on the crack growth process in alloy 718 are reviewed and analyzed on the basis of deformation characteristics in the crack tip region. The review of the role of material variables has focused on the effects of chemical composition and microstructure parameters including precipitate size and morphology as well as grain size and morphology. These analyses have suggested that the governing mechanism at the crack tip is the degree of homogeneity of plastic deformation and associated slip density. For conditions promoting homogeneous plastic deformation, with a high degree of slip density, the environmental damage contribution is shown to be limited, thus permitting the dominance of cyclic damage effects which are characterized by a transgranular crack growth mode and a lower crack growth rate. Under conditions leading to inhomogeneous plastic deformation and lower slip density the crack tip damage is described in terms of grain boundary oxidation and related intergranular fracture mode. Considering that the crack growth damage mechanism in alloy 718 ranges from fully cycle dependent to fully environment dependent, conflicting experimental observations under different operating conditions are examined and a sensitizing approach is suggested to increase the alloy resistance to environmental effects.     

On the singularity of temperature gradient near an inclined crack terminating at bimaterial interface

This paper deals with the singularity of temperature gradient near an inclined crack terminating at a bimaterial interface. The temperature field is solved by considering the continuity of temperature and heat flux at the interface and appropriate thermal boundary conditions on crack surfaces. The singularity of temperature gradient around the crack tip is then studied for the cases for which the temperature on crack surfaces is prescribed or crack surfaces are insulated. It is found that, unlike the oscillatory singularity of the stress field, no oscillatory character near the crack tip is observed for these problems. The dependence of the singularity of temperature gradient on the inclined angle of crack and thermal conductivity ratio of two dissimilar media is also shown.     

Edge-Cracks in Single Crystals Under Monotonic and Cyclic Loads

Basic solutions are obtained for edge-cracks lying along the primary slip plane in a single crystal. The study is motivated by Stage I fatigue crack growth wherein crack orientation is controlled by the slip direction and continued growth is dependent on the crack overcoming barriers to slip. Plasticity is assumed to occur as slip along planes inclined at 45^ to the surface. Problems where slip is limited to persistent slip bands are considered side-by-side with the problem where slip is not confined. Results for both monotonic and cyclic loadings are presented, with emphasis on the crack tip opening and sliding displacements. Both small and large scale yielding are considered. Preliminary results are given for interaction with barriers to slip, such as a grain boundary. This revised version was published online in July 2006 with corrections to the Cover Date.     

Branch crack development from the flank of a fatigue crack propagating in mode II

The propagation of fatigue cracks in mode II often leads to the development of a branch starting from a crack flank, some distance behind the tip and not to the expected bifurcation at the crack tip. This type of branch is suggested to initiate by decohesion along a secondary slip plane and to grow in mode I due to the tensile component of the mode II stress field. Finite element calculations are performed to evaluate the stress intensity factors for the main crack and the branch as a function of the position of the latter. It is shown that the branch has a substantial shielding effect on the main crack and generates contact forces along its flanks. The simultaneous and competitive growth of the main crack and the branch in fatigue is simulated step by step using kinetic data for mode II and mode I obtained for a maraging steel.     

Slip initiation on frictional fractures

Direct shear tests and biaxial compression tests are conducted to investigate the onset of slip along a non-homogeneous frictional surface and to determine the effect of specimen thickness and confining stress on slip initiation and propagation. The specimens are made of two and three acrylic blocks with the contact surfaces between blocks having on their upper half a frictional strength smaller than on their lower half. This creates a “weak” surface on the upper half and a “strong” surface on the lower half. The specimens are then loaded in direct shear or biaxial compression with confining pressures ranging from 0.7 to 3.5 MPa. The onset of slip, slip propagation, and the stress field generated at the front and center of the blocks interfaces are monitored using a photoelastic technique where a thin photoelastic film is placed at the location where observations are made. The onset of slip at the weak-strong zone interface is treated as propagation of a frictional crack under Mode II loading. The critical stress intensity factor, K_IIC, at the onset of slip is obtained from photoelastic techniques. The results show a weak dependency of K_IIC on the normal stress applied and no influence of the specimen size for specimens thicker than 25.4 mm; for thinner specimens the K_IIC values are smaller because the boundaries of the specimen prevent the full development of the stress field ahead of the crack tip. The experiments show a linear increase of the critical energy release rate with normal stress which is explained with linear elastic fracture mechanics theories.