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Novel methods to probe and evaluate the mechanical properties of High entropy alloy are gaining popularity to accelerate the development of new material for structural application and for establishing the physics-based mechanical property models. Nanoindentation techniques are predominantly suitable for evaluating the properties of materials in which deformation volumes can be cautiously controlled, and indentation can be applied to probe the properties of specific phases or features present within the microstructure. The current investigation is based on the plastic deformation response of Eutectic High Entropy Alloy, AlCoCrFeNi2.1, using experimental and computational approaches. In this paper, the plastic deformation of eutectic high entropy alloy AlCoCrFeNi2.1 is investigated using nanoindentation over a broad range of strain rates at room temperature to probe the mechanical properties of Eutectic High Entropy Alloy, AlCoCrFeNi2.1 and also to understand its elasto-plastic behaviour of BCC and FCC phase present in the alloy. In order to capture the deformation mechanism of material under the tip of the nano-indenter as well as to predict the load variation with depth, molecular dynamic simulation is performed. A characteristic load-depth curve has also been generated from the developed model, which is in good agreement with the experimental one. These findings will lead to understanding the phase-specific contribution to bulk mechanical response of multicomponent alloys and aid in designing structural materials with high fracture toughness. [ABSTRACT FROM AUTHOR]

An in-depth understanding of the role of non-metallic inclusions (NMIs) in the hydrogen-induced failure of structural materials is important in the manufacture and application of steels. In this paper we investigated the type, the amount and the distribution of NMIs in pipeline steels and their relation to the susceptibility to hydrogen-induced cracking (HIC). Scanning Electron Microscope (SEM) observation confirmed the interlinking of the microcracks formed at the inclusion-matrix interfaces. By combining with the nondestructive three-dimensional (3D) mapping of crack propagation paths, based on the synchrotron tomography technique, we obtained direct evidence that the cracking initiation at the NMIs and then interlinking on the (nearly) same plane are the main mechanism of HIC failure in X70 steels. We built an elastic-energy-based model, which can be applied to quantitatively predict the HIC-induced dependence of the fracture toughness on NMIs, based on statistical information of the NMIs. The theoretical results show a good agreement with the experimental observation. We proposed a criterion to determine the susceptibility to HIC by the observation of NMIs. We also developed a thermodynamics-based model to analyze the hydrogen trapping at the inclusion-matrix interface and its dependence on the strength of the steel matrix. For the first time, the direct relationship between NMIs and HIC-induced degradation of fracture toughness is obtained. [ABSTRACT FROM AUTHOR]

Previous models of a single erosion impact, for a rigid axisymmetric indenter defined by the shape function, have shown that a critical shape parameterexists which determines the behaviour of the threshold fracture energy. However, repeated investigations into this parameter have found no physical explanation for its value. Again utilising the notion of incubation time prior to fracture, this paper attempts to provide a physical explanation of this phenomena by introducing a supersonic stage into the model. The final scheme allows for the effect of waves along the indenters contact area to be taken into account. The effect of this physical characteristic of the impact on the threshold fracture energy and critical shape parameterare investigated and discussed. [ABSTRACT FROM PUBLISHER]

Models classically used to describe the probability of brittle fracture in nuclear power plants are written on a macroscale. Physical phenomena are not naturally captured by this type of approach, so that application of these models far from their identification domain (such as temperature history, loading path) may become questionable. To improve the quality of the prediction of resistance and life time, microstructural information describing the heterogeneous character of the material and its deformation mechanisms has to be taken into consideration. The objective of this work is to propose a model able to describe local stress and strain fields in an A508 Cl3 bainitic steel. This information will then be used to introduce critical variables for multiscale failure models. The microstructure of A508 Cl3 steel is made of bainitic packets (coming from former austenitic grains), which are not randomly oriented. An accurate model must take the actual microstructure into account, in order to provide realistic local stress and strain fields. Starting from experimental observations of the bainitic microstructure (texture measurements, morphological analysis), the paper first proposes a numerical model able to produce quantitatively representative numerical aggregates, then discusses the results obtained by a finite element treatment of the aggregates involving crystal plasticity. [ABSTRACT FROM AUTHOR]

This paper investigates the debris generation mechanism for polymers due to the actions of the micro-asperities of a hard counterface. Nanoscratching tests were conducted on the surface of five commercially available polymers using a diamond conical tip indenter with three different scratching sequences namely unidirectional multipass, orthogonal multipass and orthogonal omnipass. The scratch damage surface was analysed using an atomic force microscope and a scanning electron microscope to investigate the material removal phenomenon for the selected polymers. The results show that debris generation in polymers is largely a phenomenon of low-cycle fatigue when asperities contribute to the localized plastic deformation of the surface. Hence the rate of material removal is reduced for a polymer which has higher toughness and a higher percentage of elongation before failure. The hardness of the polymer has a counter effect on wear as higher hardness tends to reduce the toughness property in polymers which leads to microcracking and further wear debris generation. [ABSTRACT FROM AUTHOR]

A new adaptive multiscale method for the non-linear fracture simulation of heterogeneous materials is proposed. The two major sources of errors in the finite element simulation are discretization and modelling errors. In the failure problems, the discretization error increases due to the strain localization which is also a source for the error in the homogenization of the underlying microstructure. In this paper, the discretization error is controlled by an adaptive mesh refinement procedure following the Zienkiewicz–Zhu technique, and the modelling error, which is the resultant of homogenization of microstructure, is controlled by replacing the macroscopic model with the underlying heterogeneous microstructure. The scale adaptation criterion which is based on an error indicator for homogenization is employed for our non-linear fracture problem. The control of both discretization and homogenization errors is the main feature of the proposed multiscale method. [ABSTRACT FROM PUBLISHER]

In the field of crystal plasticity, the two decades 1950–1969 were a time of great activity, in which the foundations were laid for our present understanding of the work-hardening of face-centred cubic metals in terms of dislocation mechanisms. Decisive developments were the ‘invention’ of the Frank–Read source, the recognition of the importance of the specific energy of stacking faults, and the (at least partial) resolution of the controversy between macroscopic stress–strain measurements, X-ray results, ferromagnetism and the study of slip lines and slip bands on the one hand, and the observation of dislocations by transmission electron microscopy of thin foils prepared from plastically deformed macroscopic specimens on the other hand. The understanding of the dislocation mechanisms dominant at very large plastic strains was and still is limited, however. It is argued that here a holistic approach based on concepts such as energy dissipation and self-organization is more promising than the mechanistic approach based on concepts successfully developed in the two decades covered in the paper. [ABSTRACT FROM PUBLISHER]

The paper starts from concerns expressed by Sir Alan Cottrell, in the early 1970s, related to the safety of the pressurized water reactor (PWR) proposed at that time for the next phase of electrical power generation. It proceeds to describe the design and operation of nuclear generation plant and gives details of the manufacture of PWR reactor pressure vessels (RPVs). Attention is paid to stress-relief cracking and under-clad cracking, experienced with early RPVs, explaining the mechanisms for these forms of cracking and the means taken to avoid them. Particular note is made of the contribution of non-destructive inspection to structural integrity. Factors affecting brittle fracture in RPV steels are described: in particular, effects of neutron irradiation. The use of fracture mechanics to assess defect tolerance is explained, together with the failure assessment diagram embodied in the R6 procedure. There is discussion of the Master Curve and how it incorporates effects of irradiation on fracture toughness. Dangers associated with extrapolation of data to low probabilities are illustrated. The treatment of fatigue-crack growth is described, in the context of transients that may be experienced in the operation of PWR plant. Detailed attention is paid to the thermal shock associated with a large loss-of-coolant accident. The final section reviews the arguments advanced to justify ‘Incredibility of Failure’ and how these are incorporated in assessments of the integrity of existing plant and proposed ‘new build’ PWR pressure vessels. [ABSTRACT FROM PUBLISHER]

Among Alan Cottrell’s many extraordinary talents was that of an inspirational teacher. He had a masterful ability to explain the underlying physics of the Science of Materials and at the same time to simplify and to present the big picture. His teaching-texts live on, still among the clearest and most insightful expositions of the subject. This paper surveys part of one of the fields to which he contributed so much – Fracture – with education and the big picture in mind. [ABSTRACT FROM PUBLISHER]

The commercial aluminium alloy 5083 was processed via cryomilling to produce nanocrystalline (NC) powders with an average grain size of ∼25–50 nm. The powders were subsequently degassed at 723 K (450°C), pre-heated and immediately quasi-isostatic (QI)-forged to produce a thermally stable bulk ultrafine grain (UFG) material having average grain size values ranging from 190 to 350 nm, depending on the processing conditions used. In this paper, the tensile properties and fracture behaviour of the bulk UFG material are presented and compared with the tensile properties of its conventionally processed counterpart. The specific influence of preheat temperature on strength and ductility of the alloy is briefly discussed. Three different pre-heat temperatures of 523, 623 and 723 K (250, 350 and 450°C) were chosen and used with the primary objective of controlling grain growth during forging. The influence of preheat temperature on tensile deformation and final fracture behaviour is highlighted. The macroscopic fracture modes of the bulk nanostructured material (BNM) prepared following three pre-heat temperatures are investigated. The microscopic mechanisms controlling tensile deformation and final fracture behaviour are discussed with regards to the intrinsic microstructural effects in the UFG alloy, nature of loading, and the kinetics and mechanisms of deformation. [ABSTRACT FROM AUTHOR]

This paper deals with the three-dimensional problem of a spheroidal quasicrystalline inclusion, which is embedded in an infinite matrix consisting of a two-dimensional quasicrystal subject to uniform loadings at infinity. Based on the general solution of quasicrystals in cylindrical coordinates, a series of displacement functions is adopted to obtain the explicit real-form results for the coupled fields both inside the inclusion and matrix, when three different types of loadings are studied: axisymmetric, in-plane shear and out-of-plane shear. Furthermore, the present results are reduced to the limiting cases involving inhomogeneities including rigid inclusions, cavities and penny-shaped cracks. [ABSTRACT FROM AUTHOR]

Following Gurtin and many others, the critical energy release rate is commonly identified as an ill-defined surface energy. The primary objectives of this paper are to clarify the definition of this surface energy and the role of the entropy inequality in the discussion of critical conditions. In view of an increasing emphasis on ab initio computations, a secondary objective is to show how the critical energy release rate and the compatibility constraint 1 can be used to solve a problem for which we have experimental data, using only ab initio estimates of surface tension and bond potential, both of which are increasingly available. [ABSTRACT FROM PUBLISHER]

The explosive increase in computational power and the paradigm of computer-based engineering practice have prompted analyses that claim to carry knowledge of material physics at small scales to the performance observed at the structural level. This hierarchical multi-scale approach has logical appeal and some mathematical formulation to support it for heterogeneous solids. However, when such solids suffer damage in the form of multiple cracks, the length scale hierarchy is no longer fixed or simple. Connecting multiple scales is then a challenge that needs addressing for given material systems, such as composite laminates, accounting for the pertinent damage. This paper describes damage in fiber-reinforced composites, illustrating the characteristic length scales of damage and their relationship with the fixed scales of heterogeneities. Hierarchical versus top-down approaches are discussed and a case is made for the so-called synergistic approach that combines continuum damage mechanics and micro-damage mechanics. [ABSTRACT FROM AUTHOR]

Three-point bend tests carried out by Folk [R.H. Folk, The brittle to ductile transition in silicon: evidence of a criticaly yield event. PhD thesis, University of Pennsylvania (2000).] on initially dislocation-free specimens of semiconductor-grade single crystals of Si showed that, for a given strain rate, above a critical temperature, Tc, and at a certain stress, a large load drop occurs upon yielding and the sample deforms plastically. Below Tc specimens fail by brittle fracture after a small load drop, or at even lower temperatures without apparent prior plastic flow. This paper describes a simple dislocation model and computer simulation to explain the occurrence of a yield drop, the strain-rate dependence of Tc and Folk's etch pit observations of the plastic zone. Good agreement is obtained between the temperature dependence of the upper yield stress and the strain-rate dependence of Tc with the predictions of the model. These parameters are controlled by dislocation velocity. [ABSTRACT FROM AUTHOR]

The migration kinetics of point defects near a slowly moving brittle crack are studied under the condition of pure drift. In the pure-drift approximation it is assumed that the point-defect flow in the vicinity of a crack tip is dominated by the elastic interaction between the stress field of the crack and a point defect and that concentration gradient effects can be neglected. While such a pure-drift approach has been shown to be useful to calculate the short-time diffusion kinetics of impurity-induced subcritical crack growth, previous applications are based on the drift solutions for a stationary crack. In the present paper, the first-order drift diffusion equation for a slowly moving crack at uniform velocity is solved. This yields the flow lines of the point defects and the impurity segregation rate directly in terms of the crack growth rate. The flow line patterns reveal important insights with respect to the point-defect migration kinetics near a steadily advancing crack. Although the calculation is entirely elastic, it is shown that the present drift model maintains some relevance also in the presence of a plastic zone ahead of the crack tip. [ABSTRACT FROM AUTHOR]

This paper examines the thermoelectric behaviour of a thermoelectric thin film bonded to an elastic substrate. A calculation model for thermoelectric thin films is developed based on the singular integral equation method. The interface shear stress is found to exhibit singular behaviour at the ends of the films. Numerical results for the thermal stress distribution in the film and the film/substrate interface are obtained. Effects of film thickness and the substrate to film stiffness ratio on the stress of the film and the stress intensity factor of the interface are identified. The effects of interface electricity conductivity and the elastic–plastic deformation of the film are discussed. [ABSTRACT FROM AUTHOR]

Stage-II fatigue crack propagation in FCC metals is investigated using 3D discrete dislocation dynamics (DD) simulations. The calculations show that dislocation/grain–boundary interaction affects slip dispersion everywhere in the grain, including in the crack tip region. The results are analysed and drawn in the form of simple, quantitative mathematical expressions, depending on a set of physical variables. This approach helps in developing a comprehensive crack propagation model, where the crack growth rate da/dN depends on both the crack tip opening displacements and the tip-related nucleation of nano-cavities. It is shown that the modelled crack response is compatible with the well-known Paris expression, which we further interpreted as a ratio between the energy stored in the tip region over the energy spent extending the crack surfaces. The model validity is finally evaluated by a comparison with relevant experimental evidence. [ABSTRACT FROM AUTHOR]

Alan Cottrell was among the first to recognize the potential of field ion microscopy for the atomic-scale study of crystal defects. The study of atomic configurations at the core of dislocations by this method proved to be unexpectedly difficult, because of the mechanical stresses imposed on the specimen by the high electric field. The development of atom probe tomography revitalized such studies. In particular, the atom probe technique permitted the first direct observations of solute atom distributions in the region of dislocations and confirmed the existence of so-called ‘Cottrell Atmospheres’ which are of great importance in the understanding of phenomena such as strain ageing. Atom probe studies of dislocation–solute interactions in a diverse range of alloy systems are outlined. [ABSTRACT FROM PUBLISHER]

Cottrell’s account of persistent slip poses a puzzle which has challenged all subsequent research. Persistent slip bands (PSB) endure repeated plastic shear which constantly produces narrower and narrower dipoles, as observed by Veyssière. At the same time, because narrow interstitial dipoles have a larger elastic energy than otherwise identical vacancy ones, shear will eject larger interstitial dipoles to the surface, whilst retaining smaller vacancy ones in the interior, thereby producing excess vacancy loops. This causes a longitudinal tensile stress (the ‘fibre stress’) inside the band. The ejection process lowers the energy by a term linear in the fibre stress, but increases it by a term quadratic in the fibre stress, giving rise to an equilibrium value of the fibre stress, tensile, in order-of-magnitude agreement with observations of extrusions at low temperatures, where only plasticity can occur. The fibre stress produces logarithmic infinities in the surface stress at the edges of the PSB, and thus can be responsible for sharp stage I fatigue cracks. At higher temperatures which allow pipe diffusion and/or volume diffusion, interstitial loops are drawn by the tensile fibre stress into the PSB. Then, as cyclic plasticity attempts to maintain equilibrium, the loops are ejected where the band meets the surface, producing growing extrusions. Such extrusions can grow almost without limit. At low temperatures, the rate of extrusion formation is maximal at one Burgers vector per cycle, but it will be slower than this if it is diffusion limited. [ABSTRACT FROM PUBLISHER]

In this work, we study invariant properties of defect potentials that are capable of describing defect motions in a continuum. By formulating two canonical defect theories, a generalized Nye theory and the Kroner-de Wit theory, we have found three defect potentials that are variational, i.e. their associated Euler-Lagrange equations are differential compatibility conditions of the continuum and defects. Consequently, symmetry properties of these variational functionals render several classes of new conservation laws and invariant integrals that are related with continuum compatibility conditions, which are independent of the constitutive relations of the continuum. The contour integral of the corresponding conserved quantity is path-independent, if the domain encompassed by such an integral is specifically defect-free. The invariant integral is applied to study macroscopically brittle fracture, and a multiscale Griffith criterion is proposed, which leads to a rigorous justification of the well-known Griffith-Irwin theory. [ABSTRACT FROM AUTHOR]

Experimental results for cracked piezoelectric materials demonstrate that applied electric fields can enhance or inhibit crack growth, which cannot be explained via stress intensity factor K σ and energy release rate G , but may be predicted according to the fracture criterion of mechanical strain energy release rate G m . However, the G m criterion fails to predict the experimental observation that purely electric fields can drive crack growth in a poled ferroelectric ceramic. In this paper, using electric boundary conditions dependent on the crack-opening displacement, the nonlinear relation between the electric displacement at the crack faces and applied loading is given explicitly. The Fourier transform technique is employed to reduce the problem to dual-integral equations. Solving the resulting equations, expressions for the electroelastic field in the entire plane are obtained for a piezoelectric material weakened by a Griffith crack perpendicular to the poling axis. The distribution of asymptotic field and the intensity factors of electroelastic field as well as the elastic T-stress are determined. In particular, the strain intensity factor K s is suggested as a fracture criterion for piezoelectric materials, which can explain successfully relevant experimental results. Results reveal that an applied electric field tends to cause crack to open or close, depending on its positive or negative direction. A comparison of numerical results for -5H indicates that the K s criterion is superior to other fracture criteria. [ABSTRACT FROM AUTHOR]

Most models in the literature that are used to understand and predict ductile failure, ductility or fracture toughness implicitly consider that the plastic response of the material is homogeneous at the level of the microstructure. However, in a number of situations, plasticity is intrinsically localized, because the microstructure is spatially heterogeneous, or because the loading leads to strain localization on the microscale, such as in fatigue loading, or because the dynamics of plastic flow are unstable, such as in Portevin-Le Chatelier instabilities. This paper presents, from analysing various examples, the influence of these strain localization phenomena on the ductile fracture behaviour of metallic alloys. Examples to illustrate these effects will be chosen from, firstly, internal necking between cavities growing to ductile fracture, secondly, damage mechanisms from fatigue persistent slip bands, thirdly, the effect of Portevin-Le Chatelier bands on toughness and, fourthly, damage mechanisms in alloys with precipitate-free zones at grain boundaries. [ABSTRACT FROM AUTHOR]

Understanding the evolution of dislocations and twinning at the crack front is critical for designing micro-mechanical systems with improved performance. In this work, the dislocation evolution at the crack front in thin pre-cracked FCC single crystals is correlated with the associated fracture toughness, which is shown to be dependent on material specific properties such as stable stacking fault energy (γ s s f) and crystal orientation using atomistic simulations. For materials with high γ s s f value, sessile dislocations form at the crack front causing increased localised plastic flow stress that leads to low fracture toughness. Whereas the fracture process in materials with low γ s s f value is governed by the motion of glissile dislocations and stress-induced twinning leads to high fracture toughness. For this case, twinning occurs at high stress levels followed by un-twinning due to stress relaxation at crack front by twinning. The crystal orientation influences the type of dislocations emitted (screw/edge) from the crack front which governs the mode of crack propagation. The Mode-III crack propagation by the emission of screw type dislocations causes significant decrease in the fracture toughness compared to Mode I crack propagation which is caused by simultaneous emission of edge type dislocations on the two symmetrically inclined slip planes at the crack front. For certain pre-cracked crystal orientations, twinning is seen during the early stages of plastic deformation in materials with high γ s s f value. However, un-twinning is not observed in crystal orientation-based twinning at the crack front. [ABSTRACT FROM AUTHOR]

Material failure by white-etching-cracks (WECs) can cause enormous economic costs. The formation of WECs emerges from the decomposition of the original, usually cementite-containing, microstructure. As small amounts of electric current can trigger this failure mechanism, we investigate the contribution of electric current to cementite decomposition. We applied ∼700 A/cm2 for two weeks at 60°C to a pearlitic Fe-0.74C (wt%) specimen. The comparison of the microstructure before and after showed no differences. Theoretical considerations support the conclusion that at this low temperature such electric current densities cannot directly cause cementite decomposition. Electric current could play an indirect role in the formation of WECs, however, by generating hydrogen from the lubricant which is known to accelerate WECs formation. [ABSTRACT FROM AUTHOR]

The indentation of a metal specimen by a narrow-angle wedge produces extreme plastic deformation, with an effect akin to cutting into the metal. Simulation of such processes is challenging, and complicated by the need to model material separation along the indentation symmetry axis. Here we use an Arbitrary Lagrangian Eulerian (ALE) framework to enforce the symmetry boundary conditions (bcs) in their original, 'strong' form, as well as conventional Lagrangian FE to impose the bcs in a complementary, 'weak' form. Taken together these two cases, representing perfectly strong and perfectly weak interfaces, produce accurate bounds on the mechanical response for indentation by wedges with semi-apical angles as small as 15 degrees, and encompass intermediate cases that would require complicated models of ductile failure. The method accurately predicts the transition from the cutting pattern to the non-cutting (radially compressive) pattern as the apical angle is increased. In combination with Lagrangian particle tracking, the simulations reveal the deformation pattern as well as strain, strain-rate, and velocity fields in narrow angle indentation at high resolution. Interestingly, the strong form predicts a thin (tens of microns), near-wall layer of intense plastic strain, which has been observed recently in indentation experiments. With the exception of this feature, the strong and weak bc solutions are quite similar. The present approach reveals insights about plastic flow past narrow obstacles in a range of related problems including cone penetration and machining, and suggests using narrow-angle indentation as a way to probe material failure. [ABSTRACT FROM AUTHOR]

A unified theory captures both brittle and ductile fracture. The fracture toughness is proportional to the applied stress squared and the length of the crack. For purely brittle solids, this criterion is equivalent to Griffith's theory. In other cases, it provides a theoretical basis for the Irwin-Orowan formula. For purely ductile solids, the theory makes direct contact with the Bilby-Cottrell-Swinden model. The toughness is highest in ductile materials because the shielding dislocations in the plastic zone provide additional resistance to crack growth. This resistance is the force opposing dislocation motion, and the Peach-Koehler force overcomes it. A dislocation-free zone separates the plastic zone from and the tip of the crack. The dislocation-free zone is finite because molecular forces responsible for the cohesion of the surfaces near the crack tip are not negligible. At the point of crack growth, the length of the dislocation-free zone is constant and the shielding dislocations advance in concert. As in Griffith's theory, the crack is in unstable equilibrium. The theory shows that a dimensionless variable controls the elastoplastic behaviour. A relationship for the size of the dislocation-free zone is derived in terms of the macroscopic and microscopic parameters that govern the fracture. [ABSTRACT FROM AUTHOR]

To comprehensively understand the quantitative mechanical-thermal properties and fracture mechanisms of Zr-based bulk metallic glass (BMG), by using self-made miniature tensile/compressive device and motor-piezoelectric coupling driven fatigue device, a series of static and dynamic mechanical tests at elevated temperatures of bulk Zr55Cu30Al10Ni5 BMG with glass transition temperature Tg of 411°C were carried out. Uniaxial tensile and compressive behaviours at temperatures with range from RT to 400°C were experimentally obtained by means of digital speckle correlation analysis, the estimation of Young's modulus and fracture strengths as a function of the applied temperatures were investigated. The static and cyclic fracture morphologies at various temperatures were obtained to describe the mechanical-thermal fracture mechanisms in detail. The coupling effect of loading types, stress-induced temperature rise and applied temperature on the evolution of cleavage features, dimples, vein patterns and shear softening behaviours were investigated. [ABSTRACT FROM AUTHOR]

Grain boundary-engineered materials are of immense interest for their corrosion resistance, fracture resistance and microstructural stability. This work contributes to a larger goal of understanding both the structure and thermodynamic properties of grain boundaries vicinal (within) to the(coherent twin) boundary which is found in grain boundary-engineered materials. The misoriented boundaries vicinal to the twin show structural changes at elevated temperatures. In the case of nickel, this transition temperature is substantially below the melting point and at temperatures commonly reached during processing, making the existence of such boundaries very likely in applications. Thus, the thermodynamic stability of such features is thoroughly investigated in order to predict and fully understand the structure of boundaries vicinal to twins. Low misorientation angle grain boundaries () show distinctdisconnections which accommodate misorientation in opposite senses. The two types of disconnection have differing low-temperature structures which show different temperature-dependent behaviours with one type undergoing a structural transition at approximately 600 K. At misorientation angles greater than approximately, the discrete disconnection nature is lost as the disconnections merge into one another. Free energy calculations demonstrate that these high-angle boundaries, which exhibit a transition from a planar to a faceted structure, are thermodynamically more stable in the faceted configuration. [ABSTRACT FROM AUTHOR]

Age-hardened aluminium alloys have various degrees of precipitate-free zones (PFZs) along grain boundaries (GBs). The PFZs are weak zones and their existence promotes combined transgranular and intergranular fracture, thus reducing the ductility of the alloy. In this study, transmission electron microscopy (TEM) is used to display the geometrical properties and the chemical composition of the PFZs in the AA7075-T651 aluminium alloy. PFZs are found along grain and sub-GBs and their widths are about 40 and 20 nm, respectively. The PFZs are depleted of alloying elements compared with the nominal composition due to GB precipitation, but still they contain a certain amount of such elements in solid solution which will contribute to increase the yield strength and the work hardening compared to pure aluminium. Based on the results from the TEM study, a micromechanical finite element model of an idealized microstructure including grains and soft zones along the GBs is established. The Gurson model was used to represent the behaviour of the material in the grains and in the soft zones, using different initial void volume fractions to account for GB precipitation. Several loading conditions were applied to the micromechanical model in order to evaluate the localization of strains inside the soft zones and thus to get a better understanding of the role of the PFZs in ductile fracture of age-hardened aluminium alloys. It was found that the global failure strain varies non-monotonically with the global stress triaxiality due to the heterogeneity of the idealized microstructure. [ABSTRACT FROM PUBLISHER]

We consider rotational mechanism of macrocrack propagation based on breakage of the bonds between mutually rotating grains. The mechanism is multiscale with the macroscopic scale corresponding to the macrocrack, the next, smaller scale corresponding to the grain rotations and the smallest scale corresponding to the microcracks formed in the bonds whose propagation causes the bond breakage. The bond breakage is initiated by their bending or twisting caused by the corresponding moments. The sign of the moments only affects the side of the bond where the microfracturing starts. The independence of the microfracturing of the sign of the moment stresses provides a unified way of describing such apparently different types of fractures as tensile (Mode I) cracks, compaction bands (Mode I anticracks) and shear bands (Mode II and III). Modelling of this mechanism is based on the Cosserat theory. The bending/twisting moments are controlled by the corresponding components of moment stress. In the cases, when the Cosserat characteristic lengths are comparable with the grain sizes, the Cosserat theory is reduced to the couple-stress theory. It is found that the stress exhibits the square root singularity that coincides with the conventional ones, while the moment stress has singularity of the power −3/2. TheJ-integral, however, reflects only stress singularities, while the moment stress singularities do not contribute to the energy release rate. Subsequently, the energy criterion of macrofracture propagation can be based on the conventionalJ-integral and is not affected by the strong moment stress singularity. [ABSTRACT FROM PUBLISHER]

A phase field theory for coupled twinning and fracture in single crystal domains is developed. Distinct order parameters denote twinned and fractured domains, finite strains are addressed and elastic nonlinearity is included via a neo-Hookean strain energy potential. The governing equations and boundary conditions are derived; an incremental energy minimization approach is advocated for prediction of equilibrium microstructural morphologies under quasi-static loading protocols. Aspects of the theory are analysed in detail for a material element undergoing simple shear deformation. Exact analytical and/or one-dimensional numerical solutions are obtained in dimensionless form for stress states, stability criteria and order parameter profiles at localized fractures or twinning zones. For sufficient applied strain, the relative likelihood of localized twinning vs. localized fracture is found to depend only on the ratio of twin boundary surface energy to fracture surface energy. Predicted criteria for shear stress-driven fracture or twinning are often found to be in closer agreement with test data for several types of real crystals than those based on the concept of theoretical strength. [ABSTRACT FROM AUTHOR]

In microelectronic devices, the interface between barrier metal and dielectric is of particular interest for a reliable electronic functionality. However, it is frequently observed that this interface is prone to failure. In this work, the strength of interfaces between an as-deposited borophosphosilicate dielectric glass (BPSG) layer and a W(Ti) metallization with and without Ti interlayer was the centre of interest. Four-point-bending tests were used for the mechanical characterization combined with a topological and chemical analysis of the fracture surfaces. In addition, the interface chemistry was studied locally prior to the testing to search for a possible Ti enrichment at the interface. The fracture results will be discussed taking the chemical and topological information into account. [ABSTRACT FROM PUBLISHER]

The role that grain boundary (GB) structure plays on the directional asymmetry of an intergranular crack (i.e. cleavage behaviour is favoured along one direction, while ductile behaviour along the other direction of the interface) was investigated using atomistic simulations for aluminium 〈1 1 0〉 symmetric tilt GBs. Middle-tension (M(T)) and Mode-I crack propagation specimens were used to evaluate the predictive capability of the Rice criterion. The stress–strain response of the GBs for the M(T) specimens highlighted the importance of the GB structure. The observed crack tip behaviour for certain GBs (Σ9 (2 2 1), Σ11 (3 3 2) and Σ33 (4 4 1)) with the M(T) specimen displayed an absence of directional asymmetry which is in disagreement with the Rice criterion. Moreover, in these GBs with the M(T) specimen, the dislocation emission from a GB source at a finite distance ahead of the crack tip was observed rather than from the crack tip, as suggested by the Rice criterion. In an attempt to understand discrepancy between the theoretical predictions and atomistic observations, the effect of boundary conditions (M(T), Mode-I and the edge crack) on the crack tip events was examined and it was concluded that the incipient plastic events observed were strongly influenced by the boundary conditions (i.e. activation of dislocation sources along the GB, in contrast to dislocation nucleation directly from the crack tip). In summary, these findings provide new insights into crack growth behaviour along GB interfaces and provide a physical basis for examining the role of the GB character on incipient event ahead of a crack tip and interface properties, as an input to higher scale models. [ABSTRACT FROM AUTHOR]

We analytically present the characteristic dimensional limit below which the thermal shock failure of ceramics never occurs. This limit, together with the critical temperature difference, separates the state space of the ceramics under thermal shock into two parts – the cracked and the uncracked. Based on the water-quench tests of ceramics, we experimentally proved that when the states of ceramics are in the uncracked region, the ceramics do not produce any cracks during thermal shock. The results provide a guide to prevent thermal shock failure in ceramic. [ABSTRACT FROM AUTHOR]

In order to analytically solve crack problems regarding functionally graded materials (FGMs), some ideal assumptions are often made. They are: (1) the properties of FGMs are usually assumed to be described by very particular functions; (2) the crack is assumed to be vertical to (or parallel to) the gradient of FGMs. However, these assumptions may not be practical for actual FGMs. Since the controlling differential equations with general mechanical properties are very difficult to solve and the arbitrarily oriented crack causes great trouble in the analytical procedure, a general piecewise-exponential model (GPE model) is proposed to investigate the fracture behaviour of FGMs with general mechanical properties and an arbitrarily oriented crack. “General mechanical properties” means that the mechanical properties in the GPE model are not required to be very particularly pre-defined functions but arbitrary functions determined by fitting the experimental results of FGMs. The studied FGMs are divided into some sub-layers with each layer’s properties varying exponentially so that the general mechanical properties can be approximated by a series of exponential functions and hence the stresses and displacements of each layer which may contain a mixed-mode crack can be solved analytically. By use of integral transform methods, principle of superposition, residual theorem and theory of singular integral equations, the mixed-mode crack problem can be turned into solving a group of singular integral equations from which mixed-mode stress intensity factors (SIFs) can be obtained. Finally, the influences of the nonhomogeneous and geometric parameters on the mixed-mode SIFs are analysed. [ABSTRACT FROM AUTHOR]

Powder of a nickel-based superalloy, RR1000, has been hot isostatically pressed (HIPped) at a supersolvus temperature and post-HIP heat treated to produce different microstructures. Microstructures were investigated using a scanning electron microscope together with an energy dispersive X-ray spectrometer and a wave-length dispersive X-ray spectrometer. High cycle four-point bending fatigue and tension–tension fatigue tests have been performed on the fabricated samples. It was found that HIPped and aged samples showed the best four-point bending fatigue limit while HIPped and solution-treated and aged samples had the lowest fatigue limit. The four-point bending fatigue crack initiations all occurred from the sample surfaces either at the sites of inclusion clusters or by cleavage through large grains on the surfaces. The tension–tension fatigue crack initiation occurred mainly due to large hafnia inclusion clusters, with lower fatigue lives for samples where inclusions were closer to the surface. Crack initiation at the compact Al2O3inclusion cluster led to a much higher fatigue life than found when cracks were initiated by large hafnia inclusion clusters. The tension–tension fatigue limits were shown to decrease with increased testing temperature (from room temperature to 700 °C). [ABSTRACT FROM AUTHOR]

The effects of Al addition on the precipitation and fracture behaviour of Fe–Mn–Ni alloys were investigated. With the increasing of Al concentration, the matrix and grain boundary precipitates changed from L10θ-MnNi to B2 Ni2MnAl phase, which is coherent and in cube-to-cube orientation relationship with theα′-matrix. Due to the suppression of theθ-MnNi precipitates at prior austenite grain boundaries (PAGBs), the fracture mode changed from intergranular to transgranular cleavage fracture. Further addition of Al resulted in the discontinuous growth of Ni2MnAl precipitates in the alloy containing 4.2 wt.% Al and fracture occurred by void growth and coalescence, i.e. by ductile dimple rupture. The transition of the fracture behaviour of the Fe–Mn–Ni–Al alloys is discussed in relation to the conversion of the precipitates and their discontinuous precipitation behaviour at PAGBs. [ABSTRACT FROM AUTHOR]

Twenty-six (Pb0.95Sn0.05Te)0.92(PbS)0.08–0.055% PbI2–SiC nanoparticle (SiCnp) composite thermoelectric specimens were either hot pressed or pulsed electric current sintered (PECS). Bloating (a thermally induced increase in porosity,P, for as-densified specimens) was observed during annealing at temperatures >603 K for hot-pressed specimens and PECS-processed specimens from wet milled powders, but in contrast seven out of seven specimens densified by PECS from dry milled powders showed no observable bloating following annealing at temperatures up to 936 K. In this study, bloating in the specimens was accessed via thermal annealing induced changes in (i) porosity measured by scanning electron microscopy on fractured specimen surfaces, (ii) specimen volume and (iii) elastic moduli. The moduli were measured by resonant ultrasound spectroscopy. SiCnpadditions (1–3.5 vol.%) changed the fracture mode from intergranular to transgranular, inhibited grain growth, and limited bloating in the wet milled PECS specimens. Inhibition of bloating likely occurs due to cleaning of contamination from powder particle surfaces via PECS processing which has been reported previously in the literature. [ABSTRACT FROM AUTHOR]

Alan Cottrell had a unique ability to impact the metallurgical/materials research community via his fundamental approaches at various length scales and by providing micromechanistic approaches to fracture in crystalline materials, culminating in the macro-mechanics of large-scale engineering structures. His concepts/techniques/analyses have been successfully applied to a range of structural materials and are being applied to an ever-increasing range of more complicated materials systems, ranging from ferrous-based crystalline systems to amorphous metals and biological systems. The field of Modern Fracture Mechanics requires an increasingly complex set of experimental and computational tools to capture material deformation, damage accumulation and failure across multiple size and time scales and builds directly from some of the earliest works and desires of Sir Alan, as reviewed herein. [ABSTRACT FROM PUBLISHER]

Temperature dependence of intrinsic stacking-fault energies (SFE) and anti-phase boundary energies (APBE) of AlSc is investigated in first-principles calculations using the axial Ising model and supercell approach. The temperature effect has been taken into consideration by including the one-electron thermal excitations in the electronic structure calculations, and vibrational free energy in the harmonic approximation as well as by using temperature dependent lattice constant. The latter has been determined within the Debye–Grüneisen model, which reproduces well the experimental data. The APBE and SFE are found to be reduced by about 10% in the temperature interval from 0 to 1000 K. It is shown that the inclusion of the free energy of lattice vibrations in the harmonic approximation increases the SFE further by about 4%. We also find a substantial contribution from local lattice relaxations in the case of APBE for the (1 1 1) plane and SFE leading to their reduction by about 30%. [ABSTRACT FROM PUBLISHER]

Propagation of 3-D fatigue cracks is analyzed using a discrete dislocation representation of the crack opening displacement. Three dimensional cracks are represented with Volterra dislocation loops in equilibrium with the applied external load. The stress intensity factor (SIF) is calculated using the Peach–Koehler (PK) force acting on the crack tip dislocation loop. Loading mode decomposition of the SIF is achieved by selection of Burgers vector components to correspond to each fracture mode in the PK force calculations. The interaction between 3-D cracks and free surfaces is taken into account through application of the superposition principle. A boundary integral solution of an elasticity problem in a finite domain is superposed onto the elastic field solution of the discrete dislocation method in an infinite medium. The numerical accuracy of the SIF is ascertained by comparison with known analytical solution of a 3-D crack problem in pure mode I, and for mixed-mode loading. Finally, fatigue crack growth simulations are performed with the Paris law, showing that 3-D cracks do not propagate in a self-similar shape, but they re-configure as a result of their interaction with external boundaries. A specific numerical example of fatigue crack growth is presented to demonstrate the utility of the developed method for studies of 3-D crack growth during fatigue. [ABSTRACT FROM AUTHOR]

The effect of geometrical shape of eroding absolutely rigid particles on the threshold rate of failure has been studied. The Shtaerman–Kilchevsky theory of quasi-static blunt impact, which generalizes the Hertzs classical impact theory, is used for modelling the frictionless contact interaction of an axially-symmetric particle with an elastic half-space. The incubation time fracture criterion is applied for predicting surface fracture. It is shown that there exists a critical value of the particle shape parameter such that for all its lower values, the fracture energy possesses a non-zero minimal value. [ABSTRACT FROM AUTHOR]

The foundations of theIntegrity Factor Modelare laid down and the model is discussed. The calculation of the internal stresses in microcracked materials (as a function of temperature) is done on the basis of both the macroscopic dilation and the lattice expansion measured by diffraction. The derivation is made starting from first principles for a single crystal, and then extending the approach to polycrystals, including complex microstructures, such as those containing porosity, microcracks, and multiple phases. Focus is cast on the fundamentals of the relationship between material properties and microstructure of anisotropic crystals, and on the resulting macroscopic behavior. The model is validated against experimental data, with the examples of the microcracked β-eucryptite and porous microcracked aluminum titanate composite. [ABSTRACT FROM AUTHOR]

We study the evolution of structure inside a deforming, cohesionless granular material undergoing failure in the absence of strain localisation – so-called diffuse failure. The spatio-temporal evolution of the basic building blocks for self-organisation (i.e. force chains and minimal contact cycles) reveals direct insights into the structural origins of failure. Irrespective of failure mode, self-organisation is governed by the cooperative behaviour of truss-like 3-cycles providing lateral support to column-like force chains. The 3-cycles, which are initially in scarce supply, form a minority subset of the minimal contact cycle bases. At large length-scales (i.e. sample size), these structures are randomly dispersed, and remain as such while their population progressively falls as loading proceeds. Bereft of redundant constraints from the 3-cycles, the force chains are initially just above the isostatic state, a condition that progressively worsens as the sample dilates. This diminishing capacity for redistribution of forces without incurring physical rearrangements of member particles renders the force chains highly prone to buckling. A multiscale analysis of the spatial patterns of force chain buckling reveals no clustering or localisation with respect to the macroscopic scale. Temporal patterns of birth-and-death of 3-cycles and 3-force chains provide unambiguous evidence that significant structural reorganisations among these building blocks drive rheological behaviour at all stages of the loading history. The near-total collapse of all structural building blocks and the spatially random distribution of force chain buckling and 3-cycles hint at a possible signature of diffuse failure. [ABSTRACT FROM PUBLISHER]

The creep deformation behaviour of single crystals of Co–Al–W-based alloys with γ + γ′ two-phase microstructures has been investigated in tension under a constant stress of 137 MPa in air at 1000°C as a function of the γ′ solvus temperature and the volume fraction of the γ′ phase. When described by the creep strain rate versus time curve, the creep deformation of Co–Al–W-based alloys consists of transition and accelerating regions without a steady-state region, as observed in many modern nickel-based alloys. However, the creep strength of the present Co–Al–W-based alloys is comparable with nickel-based superalloys of the first generation but is much weaker than those of the second and higher generations. Unlike in nickel-based superalloys, the so-called p (parallel)-type raft structure, in which the γ′ phase is elongated along the tensile axis direction, is formed during creep in Co–Al–W-based alloys, being consistent with what is expected from the positive values of lattice misfit between the γ and γ′ phases. As a result, of the alloys investigated, the best creep properties are obtained with the alloy possessing the highest volume fraction (85%) of the γ′ phase, which is far larger than usual for nickel-based superalloys (55–60%). [ABSTRACT FROM AUTHOR]

The major objective of this work was to model within a continuum framework the dynamic nucleation and evolution of failure surfaces in aluminum alloys with complex microstructures, using a recently developed compatibility-based fracture criterion for large deformations. Computational analyses were conducted to understand how Mn-bearing dispersoids, Ω and θ′ precipitates affect dynamic fracture processes in an Al–Cu–Mg–Ag alloys (2139-Al). High strain-rate simulations were based on a rate-dependent dislocation-density-based crystalline plasticity formulation and a nonlinear explicit dynamic finite-element approach. Results indicate that the fracture criterion elucidated how dispersoids and precipitates have a dominant role in dynamic crack blunting, branching and arrest. Rationally orientated precipitates result in overall dynamic microstructural strengthening and enhanced uniformity of deformation. These precipitates, however, accelerated unstable crack propagation, and this is amplified in the presence of a pre-crack. In contrast, dispersoids decreased microstructural toughness and ductility, but greatly improved dynamic damage tolerance, especially in the presence of a pre-crack. It can also be predicted that low angle boundaries can change the propagation direction of ductile cracks, and contribute to damage tolerance without crack initiation. Collectively, rationally oriented precipitates and dispersoids can significantly improve the combined dynamic strength, toughness and damage tolerance of crystalline aluminum alloys. [ABSTRACT FROM AUTHOR]

Using the derived relation for point defect generation according to a new constitutive relation, the notion of nano-void formation at grown-in nano-particles is examined and its consequences deduced as the nano-voids grow in size with continued deformation. Assuming that void growth is due only to point defect accumulation, the analysis of fracture strains in tension of natural-aged AA6111 suggests that coalescence by micro-plastic activity occurs when the void diameter becomes about one third of the evolving inter-void spacing. Hence, the derived limit strain to incipient void-coalescence is inversely proportional to the square root of point defect generation as determined from the stress–strain data. Using this criterion, failure prediction maps can be constructed for strain modes of plane-strain and balanced bi-axial to result in the outer bounds of the forming limit diagram. Trial examinations with AA5754 and AA3003 show great promise. [ABSTRACT FROM PUBLISHER]

Fracture experiments using micrometer-sized notched cantilevers were conducted to investigate the possibility of determining fracture mechanical parameters for the semi-brittle material tungsten. The experiments were also used to improve the understanding of semi-brittle fracture processes for which single crystalline tungsten serves as a model material. Due to the large plastic zone in relation to the micrometer sample size, linear elastic fracture mechanics is inapplicable and elastic-plastic fracture mechanics has to be applied. Conditional fracture toughness values J Q were calculated from corrected force vs. displacement diagrams. Crack growth was accessible by direct observation of in-situ experiments as well as with the help of unloading compliances. As a further tool, fracture toughness can be determined via crack tip opening displacement. The micro samples behave more ductile and exhibit higher fracture toughness values compared to macro-sized single crystals and fail by stable crack propagation. [ABSTRACT FROM PUBLISHER]

The dislocation emission surface in (k I, k II, k III) space is calculated by means of atomistic simulations for the {111}⟨110⟩ crack in Al. For each relevant combination of loading mode, the precise nature of the dislocations and of the emission process are determined. When appropriate, the analytic formulas proposed by Rice are used by calculating the unstable stacking energy including the effect of the mixed mode loading. Quantitative agreement with the full atomistic calculation is found in the case where dislocations glide in the crack plane. This clearly identifies when and how ab initio data can be introduced in the calculation. [ABSTRACT FROM AUTHOR]