Fracture Mechanic

Carbon nanotube science is a new exciting subject for all the carbon community. We now have in hand 1D graphite prototypes opening a new field for basic research and increasing the technological potential of traditional carbon fibers. In addition to many open fundamental questions, one of the main difficulties resides on the technological side, since large scale synthesis, high purity samples, and manipulation at the nanoscale are not yet fully developed. In this paper, we present recent development on different nanotube aspects: preparation and purification, electronic transport properties, electron spin resonance, mechanical behaviour of individual nanotubes, and field-emission.

The paper gives a bibliographical review of finite element methods(FEMs) applied for the analysis of pressure vessel structures/components and piping from the theoretical as well as practical points of view. This bibliography is a new addendum to the Finite elements in the analysis of pressure vessels and piping-a bibliography [1][2][3]. The listings at the end of the paper contain 856 references to papers and conference proceedings on the subject that were published in 2001-2004. These are classified in the following categories: linear and nonlinear, static and dynamic, stress and deflection analyses; stability problems; thermal problems; fracture mechanics problems; contact problems; fluid-structure interaction problems; manufacturing of pipes and tubes; welded pipes and pressure vessel components; development of special finite elements for pressure vessels and pipes; finite element software; and other topics. q † linear and nonlinear, static and dynamic, stress and deflection analyses (STR) † stability problems (STA) † thermal problems (THE) † fracture mechanics problems (FRA) † contact problems (CON) † fluid-structure interaction problems (FLU) † manufacturing of pipes and tubes (MAN) † welded pipes and pressure vessel components (WEL) † development of special finite elements for pressure vessels and pipes (ELE) † finite element software (SOF) † other topics (OTH)

Indentation fracture of a series of well-characterized WC-Co cermets was studied with a Vickers diamond pyramid indenter. The resulting crack length-indentation load data were analysed in terms of relations characteristic of radial (Palmqvist) and fully developed radial/median (half-penny) crack geometries. The radial crack model gave a better fit to the data on all the alloys studied. Crack shapes determined by repeated surface polishing confirmed the radial nature of the cracks. An indentation fracture mechanics analysis based on the assumption of a wedge-loaded crack is shown to be consistent with the observed linear relation between the radial crack length and the indentation load. The analysis also predicts a simple relation among the fracture toughness (Kic), the Palmqvist toughness (W) and the hardness (H) of the WC-Co alloys.

The compressive and tensile deformation, as well as the fracture behavior of a Zr 59 Cu 20 Al 10 Ni 8 Ti 3 bulk metallic glass were investigated. It was found that under compressive loading, the metallic glass displays some plasticity before fracture. The fracture is mainly localized on one major shear band and the compressive fracture angle, q C , between the stress axis and the fracture plane is 43°. Under tensile loading, the material always displays brittle fracture without yielding. The tensile fracture stress, s T F , is about 1.58 GPa, which is lower than the compressive fracture stress, s C F ( ϭ 1.69 GPa). The tensile fracture angle, q T , between the stress axis and the fracture plane is equal to 54°. Therefore, both q C and q T deviate from the maximum shear stress plane (45°), indicating that the fracture behavior of the metallic glass under compressive and tensile load does not follow the von Mises criterion. Scanning electron microscope observations reveal that the compressive fracture surfaces of the metallic glass mainly consist of a vein-like structure. A combined feature of veins and some radiate cores was observed on the tensile fracture surfaces. Based on these results, the fracture mechanisms of metallic glass are discussed by taking the effect of normal stress on the fracture process into account. It is proposed that tensile fracture first originates from the radiate cores induced by the normal stress, then propagates mainly driven by shear stress, leading to the formation of the combined fracture feature. In contrast, the compressive fracture of metallic glass is mainly controlled by the shear stress. It is suggested that the deviation of q C and q T from 45°can be attributed to a combined effect of the normal and shear stresses on the fracture plane.

In this chapter we consider reduced basis (RB) approximation and a posteriori error estimation for linear functional outputs of affinely parametrized linear parabolic partial differential equations. The essential ingredients are Galerkin projection onto a low-dimensional space associated with a smooth parametrically induced manifolddimension reduction; efficient and effective POD-Greedy RB sampling methods for identification of optimal and numerically stable approximations spaces -rapid convergence; rigorous and sharp a posteriori error bounds for the linear-functional outputs of interest -certainty; and Offline-Online computational decomposition strategies -minimum marginal cost. The RB approach is effective in the real-time context in which the expensive Offline stage is deemed unimportant -for example parameter estimation and control; the RB approach is also effective in the many-query context in which the expensive Offline stage is asymptotically negligible -for example design

A study is made of the mechanics of two basic types of indentation fracture, cone cracks ("blunt" indenters) and median cracks ("sharp" indenters). The common feature which forms the central theme in this work is that both crack types, in their well-developed stages of growth, may be regarded as essentially "pennylike". On this basis a universal similauity relation is derived for equilibrium crack dimension as a function of indentation load. Experimental measurements ccnfirm the general form of this relation. A more detailed fracture mechanics analysis is then given, to account for additional, contact variable evident in the data.

A continuum damage model for the prediction of the onset and evolution of intralaminar failure mechanisms and the collapse of structures manufactured in fiber-reinforced plastic laminates is proposed. The failure mechanisms occurring in the longitudinal and transverse directions of a ply are represented by a set of scalar damage variables. Crack closure effects under load reversal are taken into account by using damage variables that are established as a function of the sign of the components of the stress tensor. Damage activation functions based on the LaRC04 failure criteria are used to predict the different failure mechanisms occurring at the ply level.

The detailed cross-sectional shape of stress induced well bore breakouts has been studied using specially processed ultrasonic borehole televiewer data. We show breakout shapes for a variety of rock types and introduce a simple elastic failure model which explains many features of the observations. Both the observations and calculations indicate that the breakouts define relatively broad and flat curvilinear surfaces which enlarge the borehole in the direction of minimum horizontal compression. This work supports the hypothesis that breakouts result from shear failure of the rock where the compressive stress concentration around the well bore is greatest and that breakouts can be used to determine the orientation of the horizontal principal stresses in situ.

The past 50 years of research on the mechanical properties of human dentin are reviewed. Since the body of work in this field is highly inconsistent, it was often necessary to re-analyze prior studies, when possible, and to re-assess them within the framework of composite mechanics and dentin structure. A critical re-evaluation of the literature indicates that the magnitudes of the elastic constants of dentin must be revised considerably upward. The Young's and shear moduli lie between 20-25 GPa and 7-10 GPa, respectively. Viscoelastic behavior (time-dependent stress relaxation) measurably reduces these values at strain rates of physiological relevance; the reduced modulus (infinite relaxation time) is about 12 GPa. Furthermore, it appears as if the elastic properties are anisotropic (not the same in all directions); sonic methods detect hexagonal anisotropy, although its magnitude appears to be small. Strength data are re-interpreted within the framework of the Weibull distribution function. The large coefficients of variation cited in all strength studies can then be understood in terms of a distribution of flaws within the dentin specimens. The apparent size-effect in the tensile and shear strength data has its origins in this flaw distribution, and can be quantified by the Weibull analysis. Finally, the relatively few fracture mechanics and fatigue studies are discussed. Dentin has a fatigue limit. For stresses smaller than the normal stresses of mastication, ~ 30 MPa, a flaw-free dentin specimen apparently will not fail. However, a more conservative approach based on fatigue crack growth rates indicates that if there is a pre-existing flaw of sufficient size (~ 0.3-1.0 mm), it can grow to catastrophic proportion with cyclic loading at stresses below 30 MPa.

Abstraet--A plane strain model for a fault is presented that takes into account the inelastic deformation involved in fault growth. The model requires that the stresses at the tip of the fault never exceed the shear strength of the surrounding rock. This is achieved by taking into account a zone, around the perimeter of the fault surface, where the fault is not well developed, and in which sliding involves frictional work in excess of that required for sliding on the fully developed fault. The displacement profiles predicted by the fault model taper out gradually towards the tip of the fault and compare well with observed displacement profiles on faults. Using this model it is found that both (1) the shape of the displacement profile, and (2) the ratio of maximum displacement to fault length are a function of the shear strength of the rock in which the fault forms. For the case of a fault loaded by a constant remote stress, the displacement is linearly related to the length of the fault and the constant of proportionality depends on the shear strength of the surrounding rock normalized by its shear modulus. Using data from faults in different tectonic regions and rock types, the in situ strength of intact rock surrounding a fault is calculated to be on the order of 100 MPa (or a few kilobars). These estimates exceed, by perhaps a factor of 10, the strength of a well developed fault and thus provide an upper bound for the shear strength of the crust. It is also shown that the work required to propagate a fault scales with fault length. This result can explain the observation that the fracture energy calculated for earthquake ruptures and natural faults are several orders of magnitude greater than that for fractures in laboratory experiments.

There are more than 200 different methods for measuring adhesion, suggesting it to be material, geometry and even industry specific. This availability has exploded at least partly due to the arrival of dissimilar material interfaces and thin films and the ease with which microfabrication techniques apply to silicon technology. Having an eye toward those tests utilized for thin films, this paper reviews only a few of these techniques. The emphasis is on measuring thin film adhesion from the standpoint of fracture mechanics, when the film is mechanically or by other means removed from the substrate, and the amount of energy necessary for this process is calculated per unit area of the removed film. This tends to give values approaching the true work of adhesion at small thickness and greater values of the practical work of adhesion at larger thickness, all being in the 30-30,000 nm range. The resulting large range of toughnesses is shown to be dependent on the scale of plasticity achieved as controlled by film thickness, microstructure, chemistry and test temperature.

Epoxy/clay nanocomposites with a better exfoliated morphology have been successfully prepared using a so-called "slurry-compounding" process. The microstructures of the nanocomposites (epoxy/S-clays) were characterized by means of optical microscopy and transmission electron microscopy (TEM). It was found that clay was highly exfoliated and uniformly dispersed in the resulting nanocomposite. Characterizations of mechanical and fracture behaviors revealed that Young's modulus increases monotonically with increasing the clay concentration while the fracture toughness shows a maximum at 2.5 wt % of clay. No R-curve behavior was observed in these nanocomposites. The microdeformation and fracture mechanisms were investigated by studying the microstructure of arrested crack tips and the damage zone using TEM and scanning electron microscopy (SEM). The initiation and development of microcracks are the dominant microdeformation and fracture mechanisms in the epoxy/ S-clay nanocomposites. Most of the microcracks initiate between clay layers. The formation of a large number of microcracks and the increase in the fracture surface area due to crack deflection are the major toughening mechanisms.

A continuous cracked beam vibration theory is developed for the lateral vibration of cracked Euler-Bernoulli beams with single-edge or double-edge open cracks. The Hu-Washizu-Barr variational formulation was used to develop the differential equation and the boundary conditions of the cracked beam as a one-dimensional continuum. The displacement field about the crack was used to modify the stress and displacement field throughout the bar. The crack was modelled as a continuous flexibility using the displacement field in the vicinity of the crack, found with fracture mechanics methods. The results of two independent evaluations of the lowest natural frequency of lateral vibrations for beams with a single-edge crack are presented: the continuous cracked beam vibration theory developed here, and a lumped cracked beam vibration analysis. Experimental results from aluminum beams with fatigue cracks are very close to the values predicted. A steel beam with a double-edge crack was also investigated with the above mentioned methods, and results compared well with existing experimental data.

A new set of six phenomenological failure criteria for fiber-reinforced polymer laminates denoted LaRC03 is described. These criteria can predict matrix and fiber failure accurately, without the curve-fitting parameters. For matrix failure under transverse compression, the angle of the fracture plane is solved by maximizing the Mohr-Coulomb effective stresses. A criterion for fiber kinking is obtained by calculating the fiber misalignment under load and applying the matrix failure criterion in the coordinate frame of the misalignment. Fracture mechanics models of matrix cracks are used to develop a criterion for matrix failure in tension and to calculate the associated in situ strengths. The LaRC03 criteria are applied to a few examples to predict failure load envelopes and to predict the failure mode for each region of the envelope. The analysis results are compared to the predictions using other available failure criteria and with experimental results.

The successful applications of magnesium-based alloys as degradable orthopaedic implants are mainly inhibited due to their high degradation rates in physiological environment and consequent loss in the mechanical integrity. This study examines the degradation behaviour and the mechanical integrity of calcium-containing magnesium alloys using electrochemical techniques and slow strain rate test (SSRT) method, respectively, in modified-simulated body fluid (m-SBF). Potentiodynamic polarisation and electrochemical impedance spectroscopy (EIS) results showed that calcium addition enhances the general and pitting corrosion resistances of magnesium alloys significantly. The corrosion current was significantly lower in AZ91Ca alloy than that in AZ91 alloy. Furthermore, AZ91Ca alloy exhibited a five-fold increase in the surface film resistance than AZ91 alloy. The SSRT results showed that the ultimate tensile strength and elongation to fracture of AZ91Ca alloy in m-SBF decreased only marginally (w15% and 20%, respectively) in comparison with these properties in air. The fracture morphologies of the failed samples are discussed in the paper. The in vitro study suggests that calcium-containing magnesium alloys to be a promising candidate for their applications in degradable orthopaedic implants, and it is worthwhile to further investigate the in vivo corrosion behaviour of these alloys.

The mechanical integrity of tin-doped indium oxide (ITO) thin films sputtered onto a high temperature aromatic polyester developed for flexible display applications was investigated by means of tensile experiments equipped with electrical measurement, and carried out in-situ in an optical microscope. Attention was paid to the influence of ITO thickness, composition and crystalline microstructure, internal stress, annealing, and polymer substrate. It was observed that process-induced internal stresses were systematically compressive, and that tensile cracks in the ITO always initiated at pin-hole defect sites. A transition from stable to unstable crack growth was detected when crack length was several 100 times coating thickness. The occurrence of such a transition, which corresponded to an increase in electrical resistance equal to approximately 10%, indicated that crack propagation controlled the loss of functional performance of the device. It was moreover found that an improved surface quality of the polymer substrate, such as that obtained with planarization hard coats, was a major factor to increase the cohesive properties of ITO thin films. It was also observed that the intrinsic crack onset strain followed classic fracture mechanics scaling, in inverse proportion to the square root of ITO thickness. ᮊ

This paper examines the use of a continuum damage model to predict strength and size effects in notched carbon-epoxy laminates. The effects of size and the development of a fracture process zone before final failure are identified in an experimental program. The continuum damage model is described and the resulting predictions of size effects are compared with alternative approaches: the point stress and the inherent flaw models, the Linear-Elastic Fracture Mechanics approach, and the strength of materials approach. The results indicate that the continuum damage model is the most accurate technique to predict size effects in composites. Furthermore, the continuum damage model does not require any calibration and it is applicable to general geometries and boundary conditions.

Plate tectonics has provided a method of visualizing the geometry of the deformation of the Earth’s lithosphere on a large scale. The description is so concise that for many purposes it provides an explanation of geological processes that overshadows the need to understand the driving processes. The mechanics of the zones between the plates are less well understood, particularly in continental regions where large areas are subject to deformation. Both continuous and discontinuous models have been tried but both have obvious drawbacks. In this paper concepts of geometrical self-similarity are adapted to provide a description of the multiscale faulting that must occur in such environments. The fractal geometry of Mandelbrot is applied to the problem of continental triple junctions and it is shown that certain arrays of faults can “stabilize” a junction where three faults meet. The conditions required to do this indicate that earthquakes of different sizes must occur in certain proportions. For simple assumptions and conditions of triaxial deformation the proportion is that which is observed globally for earthquakes. Thus, the b-value of unity found empirically by Gutenberg and Richter and others can be regarded as a consequence of three-dimensional self-similar fault geometry. The geometric description can be used to understand the way in which fault systems evolve. Earthquakes initiate and terminate in regions where fault systems bend, because the bends become zones subject to multiscale faulting. Movement on many faults in these regions distributes the stress concentration of a propagating rupture front and terminates motion. The multiple faults create offsets in the next fault to move. These offsets are the asperities that must break before a new earthquake occurs. The self-similar fault geometry requires that a substantial proportion of the deformation in a fault system occur on minor faults and not on the main faults. The proportion of the deformation taken up off the main fault depends on the form of the slip function on the main fault. The off-fault deformation produces aftershock sequences and forms background seismicity and foreshocks. The geometric relation of aftershocks and foreshocks to the main faults suggests that the former will tend to have b-values greater than unity and the latter b-values less than unity. The geometric description can be compared to the ideas of fracture mechanics, and it is shown that for earthquake faulting and brittle deformation of the lithosphere in general, fracture toughness, critical stress intensity factor and the Griffith Fracture Energy are not material properties but properties of the geometry of fault systems. Examined in terms of self-similar behaviour, concepts such as ductility can become ill defined. What may be treated as ductile behaviour viewed at a large enough scale is seen to be brittle when examined more closely. Clear-cut boundaries between the two phenomena do not necessarily exist. At very large scales and very small scales self-similar behaviour breaks down. Intermediate scales occur but are not discussed at length. The upper scale limit is the Plate Tectonic scale, which provides a very wide range of deformational boundary conditions, and the lower limit is the scale of opening fissures. The latter process can be microscopic or macroscopic. At whatever scale it occurs it is responsible for the confining pressure dependence of shear failure that is responsible for frictional or dilatant behaviour of rocks. Although we do not discuss the relations between fault motion and rotation, the large strains that can be accommodated by the mechanisms we describe will, in general, be accompanied by rotations of similar magnitude. This paper is concerned with the deformation of the brittle upper part of the Earth. Many aspects of the descriptions, however, are also appropriate to the brittle deformation of any solid.

Disorder and long-range interactions are two of the key components that make material failure an interesting playfield for the application of statistical mechanics. The cornerstone in this respect has been lattice models of the fracture in which a network of elastic beams, bonds or electrical fuses with random failure thresholds are subject to an increasing external load. These models describe on a qualitative level the failure processes of real, brittle or quasi-brittle materials. This has been particularly important in solving the classical engineering problems of material strength: the size dependence of maximum stress and its sample to sample statistical fluctuations. At the same time, lattice models pose many new fundamental questions in statistical physics, such as the relation between fracture and phase transitions. Experimental results point out to the existence of an intriguing crackling noise in the acoustic emission and of self-affine fractals in the crack surface morphology. Recent advances in computer power have enabled considerable progress in the understanding of such models. Among these partly still controversial issues, are the scaling and size effects in material strength and accumulated damage, the statistics of avalanches or bursts of microfailures, and the morphology of the crack surface. Here we present an overview of the results obtained with lattice models for fracture, highlighting the relations with statistical physics theories and more conventional fracture mechanics approaches.

Given a general balance statement we derive an expression for the associated crack tip flux integral. The conditions under which the integral is physically meaningful and yields a non-trivial result are outlined. To illustrate the approach a number of well known integrals in use in fracture mechanics are derived. It is demonstrated that complementary analogues to these integrals can be derived in a similar fashion and a result indicating the equality of dual integrals under quite general conditions is presented. We discuss the domain integral method as an alternative means of representing crack tip integrals and we show that the method may be interpreted as a particular form of Signorini's theorem of stress means. A discussion of some associated integral identities is presented. Une expression pour l'intégrale de flux á l'extrémité d'une fissure est obtenue sur base d'un état général d'équilibre. On souligne les conditions pour lesquelles l'intégrale a un sens physique et ne mène pas á des résultats triviaux. L'approche adoptée est illustrée par 1'établissement d'une série d'intégrales bien connues, utilisées en mécanique de rupture. On démontre que l'on peut tirer d'une manière similaire des contreparties compl'ementaires à ces intégrales et on présente un résultat indiquant que les intégrales doubles ainsi établies sont égales dans des conditions très générales. On discute de la méthode d'intégration sur un domaine comme variante de représentation des intégrales à l'extrémité d'une fissure et on montre que cette méthode peut être interprêtée comme une forme particulière du théorème de Signorini des contraintes médianes. On présente enfin une discussion sur diverses formes d'intégrales associées.

Attractive elevated-temperature properties and low density make the titanium aluminides very interesting for both engine and airframe applications, particularly in the aerospace industry. The challenge to the materials scientist is to maintain these characteristics while building-in "forgiveness". The basic phase diagram and crystal structure of both the Ti3AI and TiAI phases are reviewed, followed by a consideration of chemistry-processing-microstructuredeformation/fracture-mechanical property relationships in monolithic material. Conventional and innovative synthesis methods are presented, including use of hydrogen as a temporary alloying element. Composite concepts as a method to enhance not only "forgiveness" but also elevated-temperature behaviour are discussed. Environmental effects are evaluated prior to consideration of present and projected applications of both monolithic and composite material. It is concluded that while the titanium aluminides in monolithic form can be used now in non-demanding applications, much further research and development is required before this material class can be used in critical applications, especially in composite concepts.

Nanoparticles of metal oxides have applications as additives in thin nanocomposite films. For optical applications that include transparent films and coatings, nanoparticles should be uniformly dispersed in the polymer film. Most commercially available nanoparticles are large agglomerates about 1 Am in maximum dimensions composed of primary particles with sizes ranging from 5 to 50 nm. The large agglomerates scatter light and are not directly suitable for optical systems. Ultrasonication of liquid suspensions was used to prepare stable dispersions from commercial titania nanopowders. The mean diameter of sonicated titania nanopowders was correlated inversely to the specific energy. After a rapid initial size reduction, continued ultrasonication lead to insignificant reduction and even reagglomeration of the particles. Both erosion and fracture mechanisms were observed. None of the commercial nanopowders were successfully broken to their primary particle sizes. Reagglomeration of the dispersion could be prevented by electrostatic stabilization with nitric acid or ammonium hydroxide when its zeta potential value was less than À 30 mV or greater than + 30 mV. D (N. Mandzy). Powder Technology 160 (2005) 121 -126 www.elsevier.com/locate/powtec Fig. 4. Intensity analysis results for TiO 2 nanopowders before and after ultrasonication: (a) intensity distribution for anatase aggregates from N&A; (b) intensity distribution for rutile agglomerates from N&A; (c) intensity distribution for anatase agglomerates from Degussa; (d) intensity distribution for agglomerates from TAL. N. Mandzy et al. / Powder Technology 160 (2005) 121 -126 125

For some twenty years the marine coatings industry has been intrigued by polymer surfaces with low adhesion to other materials, especially to the biological glues used by marine organisms. Polymers with fouling release surfaces have been made from sundry materials, and their resistance to marine fouling in both static and dynamic tests has been evaluated in the world's oceans. Although the polymer surface property most frequently correlated with bioadhesion is its critical surface tension (), resistance to fouling is also influenced by other bulk and surface properties of the polymer. This paper reviews the types of bonding associated with polymeric materials used in fouling resistant coatings, describes the removal process in terms of fracture mechanics, and discusses the importance of surface energy, elastic modulus and coating thickness in the release of biofoulants.

A generalized potential-based constitutive model for mixed-mode cohesive fracture is presented in conjunction with physical parameters such as fracture energy, cohesive strength and shape of cohesive interactions. It characterizes different fracture energies in each fracture mode, and can be applied to various material failure behavior (e.g. quasi-brittle). The unified potential leads to both intrinsic (with initial slope indicators to control elastic behavior) and extrinsic cohesive zone models. Path dependence of work-of-separation is investigated with respect to proportional and non-proportional paths-this investigation demonstrates consistency of the cohesive constitutive model. The potential-based model is verified by simulating a mixed-mode bending test. The actual potential is named PPR (Park-Paulino-Roesler), after the first initials of the authors' last names.

The microstructure and compressive properties of Alx(TiVCrMnFeCoNiCu)100−x (x = 0, 11.1, 20 and 40 at.%) high-entropy alloys were studied. With the increase of Al content, the number of phases in the alloys gradually decreases. When Al content is 20 at.%, only bcc solid-solution structure is found in the alloy. The effect of high mixing entropy does facilitate the formation of simple solid solutions, making the total number of phases well below the maximum equilibrium number allowed by the Gibbs phase rule. The solid-solution strengthening mechanism and the structure transformation from fcc to bcc make the alloys have fairly high compressive strength; among them the compressive strength of Al11.1(TiVCrMnFeCoNiCu)88.9 alloy reaches 2.431 GPa.

The structure and mechanical properties of the exoskeleton (cuticle) of the sheep crab (Loxorhynchus grandis) were investigated. The crab exoskeleton is a natural composite consisting of highly mineralized chitin-protein fibers arranged in a twisted plywood or Bouligand pattern. There is a high density of pore canal tubules in the direction normal to the surface. These tubules have a dual function: to transport ions and nutrition and to stitch the structure together. Tensile tests in the longitudinal and normal to the surface directions were carried out on wet and dry specimens. Samples tested in the longitudinal direction showed a convex shape and no evidence of permanent deformation prior to failure, whereas samples tested in the normal orientation exhibited a concave shape. The results show that the composite is anisotropic in mechanical properties. Microindentation was performed to measure the hardness through the thickness. It was found that the exocuticle (outer layer) is two times harder than the endocuticle (inner layer). Fracture surfaces after testing were observed using scanning electron microscopy; the fracture mechanism is discussed.

Fracture-mechanism maps are diagrams with tensile stress as one axis and temperature as the other, showing the fields of dominance of a given micromechanism of fracture: cleavage, ductile fracture, rupture, intergranular creep fracture, and so on. Superimposed on the fields are ...

Root tensile strength is an important factor to consider when choosing suitable species for reinforcing soil on unstable slopes. Tensile strength has been found to increase with decreasing root diameter, however, it is not known how this phenomenon occurs. We carried out tensile tests on roots 0.2-12.0 mm in diameter of three conifer and two broadleaf species, in order to determine the relationship between tensile strength and diameter. Two species, Pinus pinaster Ait. and Castanea sativa Mill., were then chosen for a quantitative analysis of root cellulose content. Cellulose is responsible for tensile strength in wood due to its microfibrillar structure. Results showed that in all species, a significant power relationship existed between tensile strength and root diameter, with a sharp increase of tensile strength in roots with a diameter <0.9 mm. In roots >1.0 mm, Fagus sylvatica L. was the most resistant to failure, followed by Picea abies L. and C. sativa., P. pinaster and Pinus nigra Arnold roots were the least resistant in tension for the same diameter class. Extremely high values of strength (132-201 MPa) were found in P. abies, C. sativa and P. pinaster, for the smallest roots (0.4 mm in diameter). The power relationship between tensile strength and root diameter cannot only be explained by a scaling effect typical of that found in fracture mechanics. Therefore, this relationship could be due to changes in cellulose content as the percentage of cellulose was also observed to increase with decreasing root diameter and increasing tensile strength in both P. pinaster and C. sativa.

Rock fracture mechanics has been widely applied to blasting, hydraulic fracturing, mechanical fragmentation, rock slope analysis, geophysics, earthquake mechanics, hot dry rock geothermal energy extraction and many other practical problems. But a standard method to accurately determine fracture toughness of rocks, one of the most important parameters in fracture mechanics as an intrinsic property of rock, has not been yet well established. To obtain rock fracture toughness, disc-type specimens were used in this study. Rock fracture toughness under mixed-mode conditions was measured by using the straightthrough crack assumption (STCA) applied to the cracked chevron-notched Brazilian disc (CCNBD) specimen and the semicircular bend (SCB) specimen. Size effects, in terms of specimen thickness, diameter and notch length on fracture toughness, were investigated. From the mixed-mode test results, fracture envelopes were obtained by applying various regression curves. The mixed-mode test results were also compared with the three well-known mixed-mode failure criteria.

The paper deals with the strong discontinuity approach and shows the links with the decohesive fracture mechanics provided by that approach. On the basis of 1D continuum damage models it is shown that, by introducing some few ingredients like the strong discontinuity kinematics, discrete constitutive models (traction vs. displacement jumps) are automatically induced. For the general 2D±3D cases it is shown that the weak discontinuity concept is an additional ingredient, necessary in order to ful®ll the strong discontinuity conditions, which allows to establish additional links with the fracture process zone concept. Also classical fracture mechanics properties as the fracture energy are related to the continuum model properties in a straightforward manner. Ó

Elastic and elastic-plastic fracture mechanics solutions are modified to predict the behaviour of short cracks. An effective crack length, ~e0 is introduced into the solutions for both the linear elastic stress intensity factor and the J integral. Crack growth results for short cracks, in both elastic and plastic strain fields of unnotched specimens, when interpreted in terms of the modified solutions, show excellent agreement with elastic long crack data. The modified J integral solutions are extended to plastically strained notches, and the solutions obtained are tested in the correlation of data for growth of sort cracks near notches of varying severity with data for long crack under elastic loading. Although constant stress amplitude tests of these notches gave crack growth rate versus crack length curves which varied from monotonically increasing for blunt notches, to an initial decrease followed by an increase of sharp notches, all the data fell within the long crack data when correlated by the J integral solutions. Conversely, these solutions can be used to predict elastic and inelastic short crack growth curves for notches of various severities.

The structural integrity of multi-component structures is usually determined by the strength and durability of their unions. Adhesive bonding is often chosen over welding, riveting and bolting, due to the reduction of stress concentrations, reduced weight penalty and easy manufacturing, amongst other issues. In the past decades, the Finite Element Method (FEM) has been used for the simulation and strength prediction of bonded structures, by strength of materials or fracture mechanics-based criteria. Cohesive-zone models (CZMs) have already proved to be an effective tool in modelling damage growth, surpassing a few limitations of the aforementioned techniques. Despite this fact, they still suffer from the restriction of damage growth only at predefined growth paths. The eXtended Finite Element Method (XFEM) is a recent improvement of the FEM, developed to allow the growth of discontinuities within bulk solids along an arbitrary path, by enriching degrees of freedom with special displacement functions, thus overcoming the main restriction of CZMs. These two techniques were tested to simulate adhesively bonded single-and double-lap joints. The comparative evaluation of the two methods showed their capabilities and/or limitations for this specific purpose.

Signiÿcant progress has been recently made in modelling the onset of void coalescence by internal necking in ductile materials. The aim of this paper is to develop a micro-mechanical framework for the whole coalescence regime, suitable for ÿnite-element implementation. The model is deÿned by a set of constitutive equations including a closed form of the yield surface along with appropriate evolution laws for void shape and ligament size. Normality is still obeyed during coalescence. The derivation of the evolution laws is carefully guided by coalescence phenomenology inferred from micromechanical unit-cell calculations. The major implication of the model is that the stress carrying capacity of the elementary volume vanishes as a natural outcome of ligament size reduction. Moreover, the drop in the macroscopic stress accompanying coalescence can be quantiÿed for many initial microstructures provided that the microstructure state is known at incipient coalescence. The second part of the paper addresses a more practical issue, that is the prediction of the acceleration rate in the Tvergaard-Needleman phenomenological approach to coalescence. For that purpose, a Gurson-like model including void shape e ects is used. Results are presented and discussed in the limiting case of a non-hardening material for di erent initial microstructures and various stress states. Predicted values of are extremely sensitive to stress triaxiality and initial spacing ratio. The e ect of initial porosity is signiÿcant at low triaxiality whereas the e ect of initial void shape is emphasized at high triaxiality. ?

Two current theories [11, of interfacial debonding and fibre pull-out, which have been developed on the basis of fracture mechanics and shear strength criteria, respectively, are critically compared with experimental results of several composite systems. From the plots of partial debond stress, c~, as a function of debond length, three different cases of the interfacial debond process can be identified, i.e. totally unstable, partially stable and totally stable. The stability of the debond process is governed not only by elastic constants, relative volume of fibre and matrix but more importantly by the nature of bonding at the interface and embedded fibre length, L. It is found that for the epoxy-based matrix composite systems, Gao et al. 's model [17] predicts the trend of maximum debond stress, cy*, very welt for long L, but it always overestimates cy* for very short L. In contrast, Hsueh's model [11] has the capability to predict cy* for short L, but it often needs significant adjustment to the bond shear strength for a better fit of the experimental results for long L. For a ceramic-based matrix composite, o* predicted by the two models agree exceptionally well with experiment over almost the whole range of L, a reflection that the assumed stable debond process in theory is actually achieved in practice. With respect to the initial frictional pull-out stress, cyf, the agreement between the two theories and experiments is excellent for all range of L and all composite systems, suggesting that the solutions for cyf proposed by the two models are essentially identical. Although Gao et aL's model has the advantage to determine accurately the important interfacial properties such as residual clamping stress, qo, and coefficient of friction, IEt, it needs some modifications if accurate predictions of ~* are sought for very short L. These include varying interfacial fracture toughness, G~c with debond crack growth, unstable debonding for very short L and inclusion of shear deformation in the matrix for the evaluation of G~c and fibre stress distribution. Hsueh's model may also be improved to obtain a better solution by including the effect of matrix axial stress existing at the debonded region on the frictionless debond stress, (Yo.

216A PROPERTIESTIME DEPENDENCE Model laws have been derived that relate experimental parameters of a physical model of hydraulic fracture propagation to the prototype parameters. Correct representation of elastic deformation, fluid friction, crack propagation, and fluid leakoff forms the basis of the scaling laws. For tests at in-situ stress, high fluid viscosity and low fracture toughness are required. Tests on cement blocks agreed with the scale laws based on elastic behavior. (Authors)

An approach to quantify the grinding behaviour of different materials is presented. Based on a dimensional analysis and on fracture mechanical considerations, two material parameters, f Mat. and W m,min , are derived theoretically. f Mat. characterises the resistance of particulate material against fracture in impact comminution. f Mat. comprises the effect of particle size on fracture and the resistance against the external load which is quantified by the specific impact energy. W m,min characterises the specific energy which a particle can take up without fracture. Values for f Mat. and W m,min which determine the grindability of different materials are given. Both the dimensional analysis and the fracture mechanical considerations lead to the same influence of initial particle size, mass-specific impact energy and newly derived material parameters on the comminution result. Experimentally, the material parameters are determined by single-particle impact tests. Together with the initial particle size and the impact energy, they allow for a quantitative description of the breakage probability of different materials in the form of a mastercurve and can also be applied for the qualitative description of the breakage function. The results for five polymers, limestone and glass spheres of different sizes are shown. D

Abstracl-Fracture mechanics and damage mechanics are two correlated theories. In some instances, e.g., for large specimens, crack propagation may be viewed equivalently as a sudden localization of damage. Relationships based on thermodynamic considerations between the two theories are presented in this paper. They lead to the definition of the equivalent crack concept, in passing from a damage zone to a fracture problem and, conversely, a damage zone is determined which is equivalent to a crack. Different possible applications are presented showing that, for the same problem, the two concepts can be used depending on the situation. Furthermore a solution to calculate fracture energy for large specimens, when damage parameters deduced from classical tests are known, is proposed to illustrate the capability of these equivalences. Copyright 0 1996 Elsevier Science Ltd.

A coupled theory of continuum damage mechanics and finite strain plasticity (with small elastic strains) is formulated in the Eulerian reference system. The yield function used is of the von Mises type and incorporates both isotropic and kinematic hardening. An explicit matrix representation is derived for the damage effect tensor for a general state of deformation and damage. Although the theory is applicable to anisotropic d.-unage, the matrix representation is restricted to isotropy.

We describe a novel implicit level set algorithm to locate the free boundary for a propagating hydraulic fracture. A number of characteristics of the governing equations for hydraulic fractures and their coupling present considerable challenges for numerical modeling, namely: the degenerate lubrication equation; the hypersingular elastic integral equation; the indeterminate form of the velocity of the unknown fracture front, which precludes the implementation of established front evolution strategies that require an explicit velocity field; and the computationally prohibitive cost of resolving all the length scales. An implicit algorithm is also necessary for the efficient solution of the stiff evolution equations that involve fully populated matrices associated with the coupled non-local elasticity and degenerate lubrication equations. The implicit level set algorithm that we propose exploits the local tip asymptotic behavior, applicable at the computational length scale, in order to locate the free boundary. Local inversion of this tip asymptotic relation yields the boundary values for the Eikonal equation, whose solution gives the fracture front location as well as the front velocity field. The efficacy of the algorithm is tested by comparing the level set solution to analytic solutions for hydraulic fractures propagating in a number of distinct regimes. The level set algorithm is shown to resolve the free boundary problem with first order accuracy. Further it captures the field variables, such as the fracture width, with the first order accuracy that is consistent with the piecewise constant discretization that is used.

Measurements in PMMA of both the energy flux into the tip of a moving crack and the total surface area created via the microbranching instability indicate that the instability is the main mechanism for energy dissipation by a moving crack in brittle, amorphous material. Beyond the instability onset, the rate of fracture surface creation is proportional to the energy flux into the crack. At high velocities microbranches create nearly an order of magnitude larger fracture surface than smooth cracks. This mechanism provides an explanation for why the theoretical limiting velocity of a crack is never realized.

Electron microscopy, diffraction and microanalysis, X-ray diffraction, and auger spectroscopy have been used to study quenched and quenched and tempered 0.3 pct carbon low alloy steels. Some in situ fracture studies were also carried out in a high voltage electron microscope. Tempered martensite embrittlement (TME) is shown to arise primarily as a microstructural constraint associated with decomposition of interlath retained austenite into M3C films upon tempering in the range of 250 °C to 400 °C. In addition, intralath Widmanstätten Fe3C forms from epsilon carbide. The fracture is transgranular with respect to prior austenite. The situation is analogous to that in upper bainite. This TME failure is different from temper embrittlement (TE) which occurs at higher tempering temperatures (approximately 500 °C), and is not a microstructural effect but rather due to impurity segregation (principally sulfur in the present work) to prior austenite grain boundaries leading to intergranular fracture along those boundaries. Both failures can occur in the same steels, depending on the tempering conditions.

To design against premature mechanical failure, most implant devices such as coronary and endovascular stents are assessed on the basis of survival, i.e., if a fatigue life of 10 8 cycles is required, testing is performed to ascertain whether the device will survive 10 8 cycles under accelerated in vitro loading conditions. This is a far from satisfactory approach as the safety factors, which essentially tell you how close you are to failure, remain unknown; rather, the probability of fatigue failure should instead be assessed on the basis of testing to failure. In this work, a new damage-tolerant analysis of a cardiovascular stent is presented, where the design life is conservatively evaluated using a fracture mechanics methodology. In addition to enabling estimates of safe in vivo lifetimes to be made, this approach serves to quantify the effect of flaws in terms of their potential effect on device failure, and as such provides a rational basis for quality control. r

We develop continuum field model for crack propagation in brittle amorphous solids. The model is represented by equations for elastic displacements combined with the order parameter equation which accounts for the dynamics of defects. This model captures all important phenomenology of crack propagation: crack initiation, propagation, dynamic fracture instability, sound emission, crack branching, and fragmentation.

Fracture toughness of natural fibers/castor oil polyurethane composites was investigated. The main interest in studying these biomass composites arises from the fact that both fibers and matrix are derived from renewable resources and the formed composite constitute an attempt towards environmental preservation. Sisal and coconut short fibers and woven sisal fabric were used Ôin naturaÕ and sodium hydroxide treated. The best fracture toughness performance was displayed by the sisal fabric composite. The alkaline treatment showed to be harmful for fracture toughness of the sisal fiber composites since the improved interfacial adhesion impaired the main energy absorption mechanisms. On the other hand, an enhancement on the fracture toughness of coconut fiber composites was observed, which has been credited to the fibrillation process occurring under the severest condition of the alkaline treatment, which creates additional fracture mechanisms.