TEM observations of dislocation emission at crack tips in aluminium

Direct observations were made of the propagation of ductile cracks and associated dislocation behaviour at crack tips in aluminium during tensile deformation in an electron microscope. In the electropolished area, the cracks propagated as a Mode III shear-type by emitting screw dislocations on a plane coplanar to the crack plane. A zone free of dislocations was observed between the crack tip and the plastic zone. As the cracks propagated into thicker areas, the fracture mode changed from Mode III to predominantly Mode I. The crack top of the Mode I cracks was blunted by emitting edge dislocations on planes inclined to the crack plane. The blunted cracks did not propagate until the area ahead of the crack tip was sufficiently thinned by plastic deformation. The cracks then propagated abruptly, apparently without emitting dislocations. The stress intensity factor was measured from the crack tip geometry of Mode III cracks and it was found to be in good agreement with the critical value of the stress intensity factor required for dislocation generation.     

A finite element analysis of fracture initiation in ductile/brittle periodically layered composites

A near-tip plane strain finite element analysis of a crack terminating at and normal to the interface in a laminate consisting of alternate brittle and ductile layers is conducted under mode-I loading. The studies are carried out for a system representing steel/alumina composite laminate. The Gurson constitutive model, which accounts for the ductile failure mechanisms of microvoid nucleation, growth and coalescence, is employed within the framework of small deformation plasticity theory. Evolution of plastic zone and damage in the ductile layer is monitored with increasing load. High plastic strain localization and microvoid damage accumulation are found to occur along the brittle/ductile interface at the crack-tip. Fracture initiation in the ductile phase is predicted and the conditions for crack renucleation in the brittle layer ahead of the crack are established for the system under consideration. Ductile fracture initiation has been found to occur before plasticity spreads in multiple ductile layers. Effects of material mismatch and yield strength on the plastic zone evolution are briefly discussed. This revised version was published online in August 2006 with corrections to the Cover Date.     

A model of brittle fracture propagation part I—continuum aspects

The micromechanism of crack propagation in steel is described and analyzed in continuum terms and related to the macroscopic fracture behavior. It is proposed that propagation of cleavage microcracks through favorably oriented grains ahead of the main crack tip is the principal weakening mode in brittle fracture. This easy cleavage process proceeds in the Griffith manner and follows a continuous, multiply connected, nearly planar path with a very irregular front which spreads both forward and laterally and leaves behind disconnected links which span the prospective fracture surface. A discrete crack zone which extends over many grains thus exists at the tip of a running brittle crack. Final separation of the links is preceeded by plastic straining within the crack zone and occurs gradually with the increasing crack opening displacement. It is suggested that in low stress fracture, straining of the links is the only deformation mode. However, it is recognized that under certain conditions plastic enclaves may adjoin the crack zone. This deformation mode is associated with high stress fracture, energy transition and eventually with crack arrest.

Energy dissipation resulting from the two deformation mechanisms is related to crack velocity, applied load and temperature and the crack velocity in a given material is expressed as a function of the external conditions. Fracture initiation and crack arrest are then discussed in terms of the conditions which are necessary to maintain the propagation process. Finally, the dimensions of a small scale crack tip zone for a steady state, plane strain crack are evaluated as functions of material properties and the elastic stress intensity factor.

The microstructural aspects of brittle fracture will be discussed in a separate Part 2 [1].     

Inclined pileup of screw dislocations at the crack tip with a dislocation-free zone

A single pileup of screw dislocations extending from the crack tip along an inclined direction has been observed in experiments. It is often associated with dislocation emission mechanisms at the crack tip. This linear pileup is a microplastic slipline emanating from the crack tip. A region near the crack tip is often free from dislocations because of a finite resistance value for the crack tip to emit dislocations. The mathematical problem is solved in this paper by applying the extended Wiener-Hopf method. The condition of finite stress at the end of the plastic zone, the crack opening displacement, and the stress distribution along the slipline are obtained in analytical expressions. Numerical values are calculated and the results can be used to discuss brittle versus ductile fracture for metals as treated in previous studies. A method to approximately calculate the corresponding results for edge dislocations is suggested.     

Fracture of notched polycarbonate under hydrostatic pressure

The brittle fracture behaviour and plastic deformation of round-notched polycarbonate bars subjected to three-point bending under hydrostatic pressure have been studied. Below a certain critical pressure, the brittle fracture initiated from an internal craze nucleated at the tip of the local plastic zone ahead of the notch rooT. The position of the nucleation of the craze receded from the tip of the notch with increasing applied pressure. When the pressure was increased over a critical value, general yielding occurred by passage of the plastic zone across the notched cross-section, that is, the brittle to ductile transition took place. A qualitative analysis of the stress distribution within the plastic zone explains that the brittle to ductile transition under hydrostatic pressure occurs when the general yield takes place before a critical stress for brittle crack propagation is reached.     

Modeling the brittle–ductile transition in ferritic steels: dislocation simulations

We present a model for the brittle–ductile transition in ferritic steels based on two dimensional discrete dislocation simulations of crack-tip plasticity. The sum of elastic fields of the crack and the emitted dislocations defines an elasto–plastic crack field. Effects of crack-tip blunting of the macrocrack are included in the simulations. The plastic zone characteristics are found to be in agreement with continuum models, with the added advantage that the hardening behavior comes out naturally in our model. The present model is composed of a macrocrack with microcracks ahead of it in its crack-plane. These microcracks represent potential fracture sites at internal inhomogeneities, such as brittle precipitates. Dislocations that are emitted from the crack-tip account for plasticity. When the tensile stress along the crack plane attains a critical value σ _F over a distance fracture is assumed to take place. The brittle–ductile transition curve is obtained by determining the fracture toughness at various temperatures. Factors that contribute to the sharp upturn in fracture toughness with increasing temperature are found to be: the increase in dislocations mobility, and the decrease in tensile stress ahead of the macrocrack tip due to increase in blunting, and the slight increase in fracture stress of microcracks due to increase in plasticity at the microcrack. The model not only predicts the sharp increase in fracture toughness near the brittle–ductile transition temperature but also predicts the limiting temperature above which valid fracture toughness values cannot be estimated; which should correspond to the ductile regime. The obtained results are in reasonable agreement when compared with the existing experimental data.     

Change of fracture mode in Charpy toughness transition temperature range

Abstract

A transition layer of width 5 - 10 μm was found on the boundary between ductile and brittle fracture for Charpy V notch specimens in the transition temperature range of a structural steel having a microstructure of polygonal ferrite -pearlite. The fracture mode in the transition layer was shearing with occasional submicrometre dimples. From tensile tests on notched specimens, the cleavage fracture stress and flow stress by ductile decohesion were determined. Based on the experimental data and the assumption that the volume of metal involved in the plastic deformation during fracture was related to the volume of the dimples, it was deduced that the transition layer width represents the size of the plastic zone immediately before cleavage initiation. The crack opening displacement and the crack tip radius for the change of fracture mode were calculated.     

The cohesive zone model in a problem of delayed hydride cracking of zirconium alloys

The crack tip model with the cohesive zone ahead of a finite crack tip has been presented. The estimation of the length of the cohesive zone and the crack tip opening displacement is based on the comparison of the local stress concentration, according to Westergaard's theory, with the cohesive stress. To calculate the cohesive stress, von Mises yield condition at the boundary of the cohesive zone is employed for plane strain and plane stress. The model of the stress distribution with the maximum stress within the cohesive zone is discussed. Local criterion of brittle fracture and modelling of the fracture process zone by cohesive zone were used to describe fracture initiation at the hydride platelet in the process zone ahead of the crack tip. It was shown that the theoretical K _IH-estimation applied to the case of mixed plane condition within the process zone is qualitatively consistent with experimental data for unirradiated Zr-2.5Nb alloy. In the framework of the proposed model, the theoretical value of K ^H _IC for a single hydride platelet at the crack tip has been also estimated.     

In situ TEM observations of fracture in nanolaminated metallic thin films

Fracture of single crystal nanolaminated thin films has been investigated through in situ straining of cross-sectional samples of Cu/Ni nanolaminates grown on Cu (001) single crystal substrates. The earlest stages of deformation exhibits a confined layer slip mechanism. With continued straining, unstable fracture occurs creating a mixed-mode crack that propagates across the nanolaminate, roughly perpendicular to the interfaces. Eventually, stable crack growth with intense plastic deformation ahead of the crack tip occurs over many bilayers in the direction of crack growth. Simultaneously, plasticity was seen to spread only 1 or 2 bilayer distances normal to the crack, creating an extremely localized plastic zone. Transmission electron microscopic (TEM) examination after the test did not reveal the presence of dislocations in the crack wake, except where severe crack deflection was observed. By comparison, the plastic zone size in the substrate was greater by several of orders of magnitude.     

The cohesive zone model in a problem of delayed hydride cracking of zirconium alloys

The crack tip model with the cohesive zone ahead of a finite crack tip has been presented. The estimation of the length of the cohesive zone and the crack tip opening displacement is based on the comparison of the local stress concentration, according to Westergaard's theory, with the cohesive stress. To calculate the cohesive stress, von Mises yield condition at the boundary of the cohesive zone is employed for plane strain and plane stress. The model of the stress distribution with the maximum stress within the cohesive zone is discussed. Local criterion of brittle fracture and modelling of the fracture process zone by cohesive zone were used to describe fracture initiation at the hydride platelet in the process zone ahead of the crack tip. It was shown that the theoretical K _IH-estimation applied to the case of mixed plane condition within the process zone is qualitatively consistent with experimental data for unirradiated Zr-2.5Nb alloy. In the framework of the proposed model, the theoretical value of K ^H _IC for a single hydride platelet at the crack tip has been also estimated.     

A critical shear displacement criterion for ductile–brittle transition under mixed mode I and II loading

Abstract

Micromechanisms producing ductile and brittle damage operate in parallel at a crack tip. The dominant mode of failure depends upon which of the two (ductile or brittle) damage parameters first reaches its critical value. This has been shown by a study of ductile–brittle transition behaviour in HY100 steel under mixed mode I and II loading. The transition from ductile to brittle behaviour in HY100 steel was found to be affected by mixed mode I and II ratio (ratio of imposed tensile and shear loading) in a manner such that with increasing shear the transition temperature decreased. In the present paper, a criterion is proposed based on the shear strain ahead of a notch tip, to predict the fracture behaviour at any given temperature and mixed mode ratio.     

Fracture toughness of layered structures: Embrittlement due to confinement of plasticity

The fracture toughness of a layered composite material is analyzed employing a combined two dimensional dislocation dynamics (DD)-cohesive zone (CZ) model. The fracture mechanism of an elastic-plastic (ductile) material sandwiched within purely elastic layers approaches ideally brittle behaviour with decreasing layer thickness. We investigate the influence of different constitutive parameters concerning dislocation plasticity as well as the effect of cohesive strength of the ductile material on the scaling of fracture toughness with layer thickness. For a constant layer thickness, the results of the numerical model are consistent with the expectation that fracture toughness decreases with increasing yield strength, but increases with the cohesive strength of the material. The scaling behaviour of the fracture toughness with layer thickness depends on these material parameters, but also on the dislocation microstructure in the vicinity of the crack tip. Strain localization due to easy dislocation generation right at the crack tip improves toughness in thin layers and leads to a jump-like increase of fracture toughness with layer thickness. However, the fracture toughness for films that are thick enough to exhibit bulk behaviour proves to be higher when the distribution of dislocations is more homogeneous, because in this case the crack grows in a stable fashion over some distance.     

Nature of Microcracks in Ferritic Steels Occurred during Fracture under Conditions of Ductile-Brittle Transition Temperature Region

It has been shown by means of EBSD techique that fracture of ferritic steel in ductile-brittle transition temperature region, along with the formation of previously discribed cleavage microcracks, results in the formation of ductile microcracks. It has also been shown that microstructure of plastic zones under brittle and ductile fracture components produced by the main crack propagation differ significantly. Better developed plastic zone under ductile fracture component protects steel from overstress. The plastic zone under brittle fracture surface, apparently, has a reduced local plasticity. Consequently, the cleavage microcracks formation precedes the fracture process. During the main crack formation such microcracks occur in steel microvolumes located both in front of its tip and in adjacent to its edges microvolumes. Further propagation of the main crack is realized in steel which already contains scattered cavities and reduces to ductile fracture of the connections between them.     

A unified model for dislocation nucleation, dislocation emission and dislocation free zone

In this paper, a unified model for dislocation nucleation, emission and dislocation free zone is proposed based on the Peierls framework. Three regions are identified ahead of the crack tip. The emitted dislocations, located away from the crack tip in the form of an inverse pileup, define the plastic zone. Between that zone and the cohesive zone immediately ahead of the crack tip, there is a dislocation free zone. With the stress field and the dislocation density field in the cohesive zone and plastic zone being, respectively, expressed in the first and second Chebyshev polynomial series, and the opening and slip displacements in trigonometric series, a set of nonlinear algebraic equations can be obtained and solved with the Newton-Raphson Method. The results of calculations for pure shearing and combined tension and shear loading after dislocation emission are given in detail. An approximate treatment of the dynamic effects of the dislocation emission is also developed in this paper, and the calculation results are in good agreement with those of molecular dynamics simulations.Presented at the Far East Fracture Group (FEFG) International Symposium on Fracture and Strength of Solids, 4–7 July 1994 in Xi'an, China.     

Microscale characterization of granular deformation near a crack tip

This paper presents a study of microscale plastic deformation at the crack tip and the effect of microstructure feature on the local deformation of aluminum specimen during fracture test. Three-point bending test of aluminum specimen was conducted inside a scanning electron microscopy (SEM) imaging system. The crack tip deformation was measured in situ utilizing SEM imaging capabilities and the digital image correlation (DIC) full-field deformation measurement technique. The microstructure feature at the crack tip was examined to understand its effect on the local deformation fields. Microscale pattern that was suitable for the DIC technique was generated on the specimen surface using sputter coating through a copper mesh before the fracture test. A series of SEM images of the specimen surface were acquired using in situ backscattered electronic imaging (BEI) mode during the test. The DIC technique was then applied to these SEM images to calculate the full-field deformation around the crack tip. The grain orientation map at the same location was obtained from electron backscattered diffraction (EBSD), which was superimposed on a DIC strain map to study the relationship between the microstructure feature and the evolution of plastic deformation at the crack tip. This approach enables to track the initiation and evolution of plastic deformation in grains adjacent to the crack tip. Furthermore, bifurcation of the crack due to intragranular and intergranular crack growth was observed. There was also localization of strain along a grain boundary ahead of and parallel to the crack after the maximum load was reached, which was a characteristic of Dugdale–Barenblatt strip-yield zone. Thus, it appears that there is a mixture of effects in the fracture process zone at the crack tip where the weaker aspects of the grain boundary controls the growth of the crack and the more ductile aspects of the grains themselves dissipate the energy and the corresponding strain level available for these processes through plastic work.     

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.     

The mechanism of brittle fracture in notched impact tests on polycarbonate

The impact testing of notched polycarbonate bars that are thick enough to yield in plane strain has been investigated. Shear bands occur in the plastic zone that resemble the slip line field for yielding from a circular notch. Eventually, an internal craze nucleates at the tip of the plastic zone, where the stresses are highest, and a crack forms in the thickest part of the craze. Above –15 C the stress for the craze to nucleate is a nearly constant multiple of the yield stress. It is shown that previous observations that annealing polycarbonate causes a ductile to brittle transition is a consequence of testing bars of thickness less than 5 mm.     

Molecular dynamics simulation of crack tip blunting in opposing directions along a symmetrical tilt grain boundary of copper bicrystal

Mode I crack growth along some grain boundaries of copper embrittled by solute segregation shows strong anisotropy. For instance, growth along the direction on the symmetrical tilt boundary has been reported to occur by intergranular brittle fracture, whereas growth along the opposite sense occurs in a ductile manner. In this paper, we simulate such crack configurations using molecular dynamics (embedded atom method [EAM]) in 3-dimensional perfect bicrystalline samples of pure copper of the aforementioned orientation at room temperature. In both cases the response is ductile, crack opening taking place by dislocation emission from the crack tip. The critical stress intensity factors (SIFs) for dislocation emission have been calculated by matching the displacement fields of the atoms in the tip neighbourhood with the continuum elastic fields. They are of the same order of magnitude for both growth senses despite the different morphology of their respective blunted crack tips and of the patterns of dislocations constituting their plastic zones. Thus, it seems that, in agreement with published results of continuum crystalline plasticity for the same problem, the plastic anisotropy associated with the different orientation of the slip systems with respect to the crack cannot in this case explain the experimental behaviour observed with solute embrittled bicrystals.     

Constraint effects on ductile fracture processes near a notch tip under mixed-mode loading

In this work, the effect of constraint on ductile fracture process of microvoid growth and coalescence near a notch tip in a ductile material under mode I and mixed mode loading (involving modes I and II) is investigated. To this end, two sets of finite element simulations are carried out under two-dimensional plane strain conditions. In the first set, a modified boundary layer formulation is employed in which the mixed mode elastic K–T field is prescribed as remote boundary conditions. Several analyses are carried out corresponding to different values of T-stress and remote elastic mode-mixity. Next, ductile four point bend specimens subjected to mode I and mixed mode loading are considered. In both sets of simulations, the interaction between a notch tip and a pre-nucleated hole ahead of it is modelled. The background material is represented by the Gurson constitutive model and micro-void nucleation at uniformly distributed small scale particles is also taken into account. The accumulation of matrix plastic strain and porosity in the ligament between the notch tip and the hole as well as the growth of the hole are studied. Finally, the effect of crack tip constraint on the relationship between the fracture toughness and mode mixity is examined.