Stochastic analysis on crack path of polycrystalline ceramics based on the difference between the released energies in crack propagation

The crack path of polycrystalline ceramics has been theoretically analysed with a stochastic model based on the difference between the released energies in intergranular and transgranular crack propagation. Assuming that the path with the lowest released energy should be realized as the actual crack path, the expected values of the fraction of transgranular fracture on fracture surface and the fracture toughness of polycrystalline ceramics were formulated as functions of grain size and the critical energy release rates of grain and grain boundary. By comparison between the theory and the experimental results it was shown that the stochastic model proposed here expressed the change of the crack path and the fracture toughness of polycrystalline Al₂O₃, relative to grain size. This revised version was published online in November 2006 with corrections to the Cover Date.     

The work of fracture in semiductile polymers

The work to fracture in tension double-notched samples of some semiductile polymeric materials (rigid PVC, Orgalloy and Ultranyl) has been measured as a function of the ligament length. It was established that the work of fracture was proportional to the extent of the plastic zone that developed in the ligament area during crack propagation. It is proposed that the total energy density is made up of two terms, one distributed all over the plastic zone and the other localized in the vicinity of the fracture path. It is then shown that a linear relationship exists between the specific work of fracture and the ligament size, provided the height of the plastic zone linearly depends on the ligament length. The linear extrapolation of the specific work of fracture to nil ligament, yields a value that coincides with J _IC and therefore can be treated as a critical parameter. It is also shown that, at large ligaments, the dependence of the specific work of fracture on the ligament length reflects the post-yield behaviour of the material and it is influenced by the tendency of the height of the plastic zone to level off. Consequently, no specific meaning can be given to quantities obtained, according to the essential work of fracture theory, in the large ligament region, e.g. ligaments larger than three to five times the sample thickness.     

Mode II fracture testing method for highly orthotropic materials like wood

In this paper a mode II fracture testing method has been developed for wood from analytical, experimental and numerical investigations. Analytical results obtained by other researchers showed that the specimen geometry and loading type used for the proposed mode II testing method results in only mode II stress intensity and no mode I stress intensity at the crack tip. Experiments have been carried out to determine mode II fracture toughness K _IIC and fracture energy G _IIF from the test data collected from both spruce (pice abies) and poplar (populus nigra) specimens. It was found that there existed a very good relation between fracture toughness K_IIC and fracture energy G _IIF when the influence of orthotropic stiffness E _II ^* in mode II was taken into account. It verified that for this mode II testing method the formula of LEFM can be employed for calculating mode II fracture toughness even for highly orthotropic materials like wood. In the numerical studies for the tested spruce specimen, the crack propagation process, stress and strain fields in front of crack tips and the stress distributions along the ligament have been investigated in detail. It can be seen that the simulated crack propagating process along the ligament is a typical shear cracking pattern and the development of cracks along the ligament is due to shear stress concentrations at the crack tips of the specimen. It has been shown that this mode II fracture testing method is suitable for measuring mode II fracture toughness K _IIC for highly orthotropic materials like wood.     

A numerical investigation on the geometry dependence of the crack growth resistance in CT specimens

The influence of the specimen thickness B and the ligament length b on the J _R -curves is numerically investigated for CT specimens. The thickness effect is taken into account with 2-D analyses by dividing a plain sided specimen into a plane stress part and a plane strain part. The fracture process is controlled by experimentally determined critical values of the crack tip opening displacement for crack growth initiation (CTOD_i) and the crack tip opening angle for stable crack growth (CTOA_C). It is shown that for the global behaviour of a plain sided specimen, the B/b ratio is essential. The difference between the geometry dependence of the initiation value of the J-integral and the geometry dependence of the slope of the J _R -curves is also shown.     

THE EFFECT OF MICROSTRUCTURE AND FRACTURE SURFACE ROUGHNESS ON FATIGUE CRACK PROPAGATION IN A Ti-6A1-4V ALLOY

Characteristics of fatigue crack propagation (FCP) have been studied on materials with three different microstructures of a Ti-6A1-4V alloy, prepared with different heat treatments. The effect of microstructure on the FCP behaviour was attributed to the development of crack tip shielding, primarily resulting from the role of crack path morphology in inducing crack closure and crack deflection. Roughness-induced crack closure played an important role on the near-threshold FCP behaviour at a stress ratio of 0.05, but the FCP data plotted in terms of the effective stress intensity factor range, δK_eff (allowing for crack closure), still exhibited the effect of microstructure. Fractographic examinations were performed, using a scanning electron microscope (SEM) with the aid of image processing, which enabled a three-dimensional reconstruction of the fracture surface using a stereo pair of SEM micrographs. Fracture surface roughness was evaluated quantitatively by the ratio of the real area of the reconstructed fracture surface to its projected area. As fracture surface roughness was taken into account in evaluating the FCP data in addition to crack closure, the effect of microstructure disappeared, indicating that the intrinsic FCP resistance was the same in all the materials. Thus, it was concluded that fracture surface roughness was a dominating parameter in controlling the FCP of the Ti-6A1-4V alloy.     

Size effects in concrete fracture – Part II: Analysis of test results

This paper presents an analysis of the extensive experimental program aimed at assessing the influence of maximum aggregate size and specimen size on the fracture properties of concrete. Concrete specimens used were prepared with varying aggregate sizes of 4.75, 9.5, 19, 38, and 76mm. Approximately 250 specimens varying in dimension and maximum aggregate size were tested to accomplish the objectives of the study. Every specimen was subjected to the quasi-static cyclic loading at a rate of 0.125mm/min (0.005in./min) leading to a controlled crack growth. The test results were presented in the form of load-crack mouth opening displacement curves, compliance data, surface measured crack length and crack trajectories as well as calculated crack length, critical energy release rate, and fracture toughness (G ₁). There is a well pronounced general trend observed: G ₁ increases with crack length (R-curve behavior). For geometrically similar specimens, where the shape and all dimensionless parameters are the same, the R-curve for the larger specimens is noticeably higher than that for the smaller ones. For a fixed specimen size, G ₁ increases with an increase in the aggregate size (fracture surface roughness). For the same maximum aggregate size specimens, the apparent toughness increases with specimen size. It was clear that the rate of increase in G ₁, with respect to an increase of the dimensionless crack length (the crack length normalized by the specimen width), increases with both specimen size and maximum aggregate size increase. The crack trajectory deviates from the rectilinear path more in the specimens with larger aggregate sizes. Fracture surfaces in concrete with larger aggregate size exhibit higher roughness than that for smaller aggregate sizes. For completely similar specimens, the crack tortuosity is greater for the larger size specimens. The crack path is random, i.e., there are no two identical specimens that exhibit the same fracture path, however, there are distinct and well reproducible statistical features of crack trajectories in similar specimens. Bridging and other forms of crack face interactions that are the most probable causes of high toughness, were more pronounced in the specimens with larger maximum size aggregates.     

Effects of pre-strain on plane stress ductile fracture in α-brass

The effects of pre-strain on plane stress ductile fracture in a 70/30 alpha brass Austral 207 have been studied using the deep-edge-notched tension (DENT) specimens. The amount of pre-strain varies between 5 and 35%. It is found that both the specific essential work of fracture (w _e) and the critical crack opening displacement (_c) decrease with increasing pre-strain. A simple theory for estimating the specific essential work of fracture in the presence of pre-strain is suggested and it gives good agreement with experimental results. Elongations to fracture in the DENT specimens are also predictable from a simple deformation analysis which considers the plastic elongations due to crack initiation, crack propagation and final stretch of a ligament that has reached a necking strain equal to that in a simple plain tension test. Micro-hardness measurements show that the strain localization is more intense near the fracture surface as the pre-strain level is increased and this is suggested to be an explanation for the low _c values obtained in pre-strained specimens.     

Fracture behaviour of polypropylene sheets filled with epoxidized natural rubber (ENR)-treated coal gangue powder

The morphology, deformation and fracture properties of polypropylene sheets filled with untreated and epoxidized natural rubber (ENR)-treated coal gangue powder (CGP) were investigated by scanning electron microscope (SEM) and the essential work of fracture (EWF) method. The results show that ENR obviously improves the dispersion of CGP particles in the PP matrix and the interfacial adhesion between CGP particles and PP matrix with the well-established interfacial layer. It is found that all composites fracture in a ductile manner as ligament yields completely and crack propagates steadily. The fracture toughness (w _e ) of the composites is significantly improved with the complete interfacial layer formed by ENR on the surface of CGP particles. With increasing ENR content, the specific plastic work (w _p ) per volume unit of plastic zone of the composites increases considerably in spite of the restricted plastic deformation of plastic zones. In Addition, the fracture parameters of different stages of tensile process demonstrate that the positive effect of ENR on the fracture performance of the composites is mainly achieved by notably reinforcing crack resistance at the stage of necking-tearing after yielding.     

A new constraint based fracture criterion for surface cracks

A new methodology for predicting the location of maximum crack extension along a surface crack front in ductile materials is presented. Three-dimensional elastic-plastic finite element analyses were used to determine the variations of a constraint parameter (α_h) based on the average opening stress in the crack tip plastic zone and the J-integral distributions along the crack front for many surface crack configurations. Monotonic tension and bending loads are considered. The crack front constraint parameter is combined with the J-integral to characterize fracture, the critical fracture location being the location for which the product Jα_h is a maximum. The criterion is verified with test results from surface cracked specimens.     

The essential work of fracture of polyamide 66 filled with TiO2 nanoparticles

The fracture property of 21-nm TiO₂-nanoparticle filled polyamide 66 was studied based on the essential work of fracture method. An energy-partitioned work of fracture approach was introduced, in which the resistance to crack initiation, w_ini, and the resistance to crack propagation, w_prop, were applied. Double-edge-notched-tension specimens with different original ligament lengths were tested at a constant cross-head speed. The results showed that the essential work term of composites filled with low nanoparticle concentration notably increased, while the plastic work fairly decreased compared to that of neat matrix at room temperature. Fractography analysis suggests a three-stage evolution of crack initiation. The individual nanoparticles acted as stress concentration points, which promoted cavitations and thus induced relatively large local deformation. Thereafter, the tiny cavitations coalesced into sub-micro ones and rapidly grow into micro-voids and crack initiation due to the high-level stress concentration. The plastic work of composites was decreased with increasing nanoparticle fractions, which was due to unavoidably aggregated nanoparticles leading to high level stress concentration that favouring the crack propagation.     

Experimental study of crack growth in thin sheet 2024-T3 aluminum under tension-torsion loading

To assess the viability of using a critical COD criterion for flaws in 2024-T3 aluminum experiencing tension stresses (S _P) and torsion stresses (S _T), the enclosed work presents (a) a complete set of measurements for critical COD during crack growth under nominal tension-torsion loading, (b) the evolution of crack path with crack growth and (c) crack surface shape as a function of loading. Data from this work will provide an important experimental database for use in assessing the predictive capability of advanced, three-dimensional, crack growth simulation tools. Results for COD during crack growth under tension-torsion loading indicates that the measured critical COD for tension-torsion loading is constant during crack growth. In addition, the value of COD measured using image correlation methods is approximately 8% larger than observed for in-plane tension-shear, with much of the increase apparently due to specimen deformations in the crack tip vicinity. In addition, crack path evolution data for the range of S _T/S _P considered in this work show that the crack experiences both tunneling and slant fracture during loading, with tunneling rapidly decreasing (a) as crack growth progresses for all S _T/S _P values or (b) as S _T/S _P increases. Furthermore, results indicate that tearing during tension-torsion loading always occurs in a manner so that the crack surfaces tend to interfere during growth. Finally, crack surface shape data indicates that, with the exception of a small secondary transition, the direction of crack growth remains stable along a straight line oriented along the initial fatigue crack direction for the range of S _T/S _P being considered.     

Fracture behavior of cracks in ductile plates under monotonic mixed-mode loading

An experimental study of the early stages of ductile fracture was undertaken by using scanning electromicroscopy (SEM). The variation of several parameters influencing this type of fracture was introduced during the study of the preliminary blunting phase followed by the creation of the damaged ligament in front of the crack which resulted in the initiation of the slow propagation phase. This was achieved by changing the angle of obliqueness, , of the edge cracks made in thin or thick plates of polycarbonate which exemplified cases where predominantly plane stress or plane strain conditions prevailed. The change of the angle influenced drastically the value of the mixed-mode factor = K ₁₁/K ₁. The parameters studied were the crack-tip opening angle (CTOA), the damaged ligament in front of the crack face, the direction and orientation of the subsequent crack initiation and propagation and finally the variation of crack propagation and velocity at the early stage of slow crack propagation. Important results were derived from this experimental study which clarified various aspects of ductile fracture during the initiation of a new step of propagation of the crack.     

CRACK TIP PARAMETERS FOR CREEP-BRITTLE CRACK GROWTH

Crack growth histories for creep-brittle aluminium alloy 2519-T87 are simulated by controlling the rate of release of finite element nodes along the crack growth path using a variable time-step, nodal release algorithm. While earlier experimental studies established little or no correlation between time-dependent fracture parameters and the crack growth rate, a˙, during creep-brittle fracture, the numerical results presented here indicate excellent correlation of the C_t parameter with a˙ during the quasi-steady state crack growth regime. Differences in the experimental and numerical determination of time-dependent fracture parameters are likely to be due to difficulties in experimental determination of the creep component of the load line deflection rate, V˙_c , during creep-brittle crack growth. A new quantity, K/rqc, is derived from time-dependent fracture parameters to predict crack growth for transient, quasi-steady state and steady state crack growth. However, C_t and K/rqc should only be employed as parameters for predicting creep-brittle crack growth with an understanding of the couplings which exist between these parameters and the crack growth rate.     

A local modulus analysis of rapid crack propagation in polymers

This work is concerned with the analysis of rapid crack propagation (RCP) in Polymethylmethacrylate (PMMA), Polycarbonate (PC) and two-layer PMMA/PC systems. Remarkably constant crack speeds were observed, and higher crack speeds corresponded to the higher preloads. Uniform fracture surfaces were associated with these constant speed RCPs. An indirect method was used to characterise dynamic fracture properties of the materials. The method relies on the recorded crack length histories and boundary conditions which are incorporated in a dynamic Finite Element (FE) code to generate the crack resistance (G _ID). The numerical simulation of the constant speed RCPs generated highly scattered G _ID data. Very large variations of the computed G _ID with the crack length did not correspond to fracture surface appearances. Geometry dependent and multivalued crack resistance results with respect to the crack speed cast doubt on the uniqueness of G _ID. In this work, attempts were made to overcome these difficulties by exploring the concept that the anomalies arise from large local strains around the rapidly moving crack tip, resulting in the crack seeing a low local modulus. It is demonstrated that the critical source of error on the analysis of RCP, is the improper linear elastic representation of the material behaviour around the propagating crack tip. Since the parameters describing the behaviour of the materials near the propagating crack tip were unknown, local non-linear effects were approximated by a local low modulus strip along the prospective crack path. The choice of the local modulus was justified by measurements of the strain histories along the crack path during RCP. The local strip low modulus model generated a larger amount of the kinetic energy in the sample and the crack resistance was reduced compared to results from the single constant modulus approach. Most importantly, G _ID data were nearly independent of the crack length, crack speed and the specimen size. This local modulus concept was also successfully applied to the analysis of RCP in the duplex specimen configuration.     

The mechanism of the failure of the dispersion-strengthened Cu–Al<Subscript>2</Subscript>O<Subscript>3</Subscript> nanosystem

The method of “in situ tensile testing in SEM” is suitable for investigations of fracture mechanisms because it enables to observe and document deformation processes directly, thank to which the initiation and development of plastic deformation and fracture can be reliably described. The deformation and fracture mechanisms of Cu–Al₂O₃ nanomaterials with 5 vol.% of Al₂O₃ phase has been analyzed using technique of the “in situ tensile testing in SEM.” It has been shown that the deformation process causes break-up of large Al₂O₃ particles and decohesion of smaller ones. The final fracture path is influenced also by boundaries of nanograins, through which the principal crack propagates towards the sample exterior surface. Based on the experimental observations, a model of damage and/or fracture mechanisms has been proposed.     

Prediction of ductile fracture initiation using micromechanical analysis

In the paper ductile fracture initiation analysis of low-alloyed ferritic steel has been made by application of two micromechanical models: the Rice–Tracey void growth model and the Gurson–Tvergaard–Needleman (GTN) model. The aim of the study was to analyse transferability of micromechanical parameters determined on specimens without initial crack to pre-cracked specimens. A significant part of the research has been carried out through participation in the round robin project organised by the European Structural Integrity Society (ESIS). Tensile tests have been performed on cylindrical smooth specimens and CT specimens. Critical values of micromechanical parameters determined on smooth specimen for both applied models, have been used for prediction of the crack growth initiation in CT specimen. Modelling of the first phase of ductile fracture––void nucleation––has been carried out using quantitative metallographic analysis of non-metallic inclusion content in tested steel. For determination of critical values of model parameters corresponding to ductile fracture initiation a simple procedure has been applied based on a combination of experimental and numerical results. Evaluated J-integral values corresponding to onset of crack growth, J_i, are in good agreement with experimental result and both models have proved to be suitable for determination of the ductile fracture initiation in tested steel. The effect of FE size at a crack tip on J_i-value has been particularly analysed: it has been established that the calculation with FE size corresponding to the mean free path λ between inclusions in steel gives results that are in accordance with the experimental ones.     

Shear ligament phenomena in Al–Si alloys

Abstract

Fracture problems in Al–Si alloys involve mixed mode (shear and opening) displacements in the aluminium matrix along the crack surface. Subject to such displacements, fracture must be influenced by the non-planarity of microcracks which depends on many factors including particle and slip orientation. Instead of producing brittle cracks along silicon particles clusters, a number of shear bands are formed in the aluminium matrix ligaments between microcracks. Shear ligaments, which are ligamentlike structures connected between microcracks, were observed on the tensile specimens. They undergo ductile fracture by shearing and enhance fracture toughness. This toughness was estimated by a micromechanical model. The amount of toughening depends on the ligament length, a ligament toughness parameter representing the work to fracture, the area fraction of the ligament, and the area fraction of frictional contact.     

A FINITE ELEMENT TECHNIQUE TO SIMULATE THE STABLE SHAPE EVOLUTION OF PLANAR CRACKS WITH AN APPLICATION TO A SEMI-ELLIPTICAL SURFACE CRACK IN A BIMATERIAL FINITE SOLID

This paper describes a numerical procedure to model the crack front evolution of initially arbitrary shaped planar cracks in a three-dimensional solid. The influence of a bimaterial interface on the fracture path of a semi-elliptical surface crack in a three-dimensional structure is examined. The analysis is based on the assumption that fracture is controlled by small-scale yielding and linear elastic fracture mechanics. The finite element method and the crack-tip contour J-integral in a volume domain representation are utilized to calculate the crack front energy release rate. The computed values of the energy release rate are used with a crack-tip velocity growth law to model crack growth increment. The progress of the crack growth evolution is brought forward by successive iterations. Examples of computed crack evolution are given for an embedded circular crack, a semi-elliptical surface crack in a finite plate, and a configuration that defines an isotropic homogeneous material layer with a surface crack located between two material layers. © 1997 by John Wiley & Sons, Ltd.     

Fracture behaviour of 8%Ni 980 MPa high strength steel at various temperatures Part 2 – COD tests

Abstract

The fracture behaviour of 8%Ni 980 MPa grade high strength steel is investigated by combining experimental results of crack opening displacement (COD) tests at various temperatures with detailed microscopic observations of fracture surfaces and crack configurations in unloaded specimens. The results reveal that this high strength steel possesses high toughness with a transition temperature around ?150°C. Even though at a very low temperature (?196°C), cleavage cracking dominates the fracture process and the crack does not propagate immediately through the entire ligament: a ‘pop-in’ extension is observed in macroscopic tests, and the microscopic fracture mode is quasi-cleavage. It is found that resistance to crack propagation is provided by three barriers: original austenite grain boundaries, bainite colony boundaries and interlayers between bainite laths. These barriers manifest themselves by tear ridges with dimples on the fracture surfaces. At higher temperatures, the fracture mechanism is dominated by fibrous rupture, associated with a ‘dimpled’ fracture surface and some individual quasi-cleavage facets.     

A STUDY OF FATIGUE FRACTURE SURFACES OF A CAST NICKEL-BASE SUPERALLOY

Morphological features of fatigue fracture surfaces of a cast nickel-base super-alloy were investigated over the range of crack growth rates, 10^-10 -10^-6m/cycle. The cleavage facet growth in stage I and the transition of crack propagation from state I to stage II were studied by a combined study of surface crack growth rate and fracture surface examinations. A correlation between fatigue crack growth and the fracture surface appearance plus microstructural aspects has been established. It is suggested that fatigue-induced vacancies might play a significant part in cleavage facet growth at lower crack growth rates.