Showing papers on "Fracture mechanics published in 2003"

Numerical simulation of mixed-mode progressive delamination in composite materials

Abstract: A new decohesion element with the capability of dealing with crack propagation under mixed-mode loading is proposed and demonstrated. The element is used at the interface between solid finite elements to model the initiation and non-self-similar growth of delaminations in composite materials. A single relative displacement-based damage parameter is applied in a softening law to track the damage state of the interface and to prevent the restoration of the cohesive state during unloading. The softening law is applied in the three-parameter Benzeggagh-Kenane mode interaction criterion to predict mixed-mode delamination propagation. To demonstrate the accuracy of the predictions, steady-state delamination growth is simulated for quasi-static loading of various single mode and mixed-mode delamination test specimens and the results are compared with experimental data.

The Mechanical Properties of Human Dentin: a Critical Review and Re-evaluation of the Dental Literature:

Abstract: 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, approximately 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 (approximately 0.3-1.0 mm), it can grow to catastrophic proportion with cyclic loading at stresses below 30 MPa.

Dynamic crack propagation based on loss of hyperbolicity and a new discontinuous enrichment

Abstract: SUMMARY A methodology is developed for switching from a continuum to a discrete discontinuity where the governing partial dierential equation loses hyperbolicity. The approach is limited to rate-independent materials, so that the transition occurs on a set of measure zero. The discrete discontinuity is treated by the extendednite element method (XFEM) whereby arbitrary discontinuities can be incorporated in the model without remeshing. Loss of hyperbolicity is tracked by a hyperbolicity indicator that enables both the crack speed and crack direction to be determined for a given material model. A new method was developed for the case when the discontinuity ends within an element; it facilitates the modelling of crack tips that occur within an element in a dynamic setting. The method is applied to several dynamic crack growth problems including the branching of cracks. Copyright ? 2003 John Wiley & Sons, Ltd.

Microstructural Effects on the Tensile and Fracture Behavior of Aluminum Casting Alloys A356/357

Abstract: The tensile properties and fracture behavior of cast aluminum alloys A356 and A357 strongly depend on secondary dendrite arm spacing (SDAS), Mg content, and, in particular, the size and shape of eutectic silicon particles and Fe-rich intermetallics. In the unmodified alloys, increasing the cooling rate during solidification refines both the dendrites and eutectic particles and increases ductility. Strontium modification reduces the size and aspect ratio of the eutectic silicon particles, leading to a fairly constant particle size and aspect ratio over the range of SDAS studied. In comparison with the unmodified alloys, the Sr-modified alloys show higher ductility, particularly the A356 alloy, but slightly lower yield strength. In the microstructures with large SDAS (>50 µm), the ductility of the Sr-modified alloys does not continuously decrease with SDAS as it does in the unmodified alloy. Increasing Mg content increases both the matrix strength and eutectic particle size. This decreases ductility in both the Sr-modified and unmodified alloys. The A356/357 alloys with large and elongated particles show higher strain hardening and, thus, have a higher damage accumulation rate by particle cracking. Compared to A356, the increased volume fraction and size of the Fe-rich intermetallics (π phase) in the A357 alloy are responsible for the lower ductility, especially in the Sr-modified alloy. In alloys with large SDAS (>50 µm), final fracture occurs along the cell boundaries, and the fracture mode is transgranular. In the small SDAS (<30 µm) alloys, final fracture tends to concentrate along grain boundaries. The transition from transgranular to intergranular fracture mode is accompanied by an increase in the ductility of the alloys.

Fracture mechanisms in bulk metallic glassy materials.

Abstract: We find that the failure of bulk metallic glassy (BMG) materials follows three modes, i.e., shear fracture with a fracture plane significantly deviating from 45degrees to the loading direction, normal tensile fracture with a fracture plane perpendicular to the loading direction, or distensile fracture in a break or splitting mode with a fracture plane parallel to the loading direction. The actually occurring type of failure strongly depends on the applied loading mode and the microstructure of the material. Extensive evidence indicates that the Tresca fracture criterion is invalid, and for the first time, three fracture criteria are developed for isotropic materials with high strength, such as advanced BMGs or the newly developed bulk nanostructural materials.

Hyperelasticity governs dynamic fracture at a critical length scale.

Abstract: The elasticity of a solid can vary depending on its state of deformation. For example, metals will soften and polymers may stiffen as they are deformed to levels approaching failure. It is only when the deformation is infinitesimally small that elastic moduli can be considered constant, and hence the elasticity linear. Yet, many existing theories model fracture using linear elasticity, despite the fact that materials will experience extreme deformations at crack tips. Here we show by large-scale atomistic simulations that the elastic behaviour observed at large strains--hyperelasticity--can play a governing role in the dynamics of fracture, and that linear theory is incapable of fully capturing all fracture phenomena. We introduce the concept of a characteristic length scale for the energy flux near the crack tip, and demonstrate that the local hyperelastic wave speed governs the crack speed when the hyperelastic zone approaches this energy length scale.

Fatigue Strength of Steel Girders Strengthened with Carbon Fiber Reinforced Polymer Patch

Abstract: Fatigue sensitive details in aging steel girders is one of the common problems that structural engineers are facing today. The design characteristics of steel members can be enhanced significantly by epoxy bonding carbon fiber reinforced polymers~CFRP! laminates to the critically stressed tension areas. This paper presents the results of a study on the retrofitting of notched steel beams with CFRP patches for medium cycle fatigue loading (R50.1). A total of 21 specimens made of S12734.5 A36 steel beams were prepared and tested. Unretrofitted beams were also tested as control specimens. The steel beams were tested under four point bending with the loading rate of between 5 and 10 Hz. Different constant stress ranges between 69 and 379 MPa were considered. The length and thickness of the patch were kept the same for all the retrofitted specimens. In addition to the number of cycles to failure, changes in the stiffness and crack initiation and growth were monitored during each experiment. The results showed that the CFRP patch not only tends to extend the fatigue life of a detail more than three times, but also decreases the crack growth rate significantly.

Manuel Rocha Medal Recipient Rock Fracture and Collapse Under Low Confinement Conditions

Abstract: The primary objective of this work was an examination of the complimentary roles of tensile damage and confinement reduction (or stress relaxation) on excavation response of “hard” rockmasses. Tensile damage and relaxation are examined with respect to structurally controlled or gravity driven failure modes as well as to strength controlled or stress driven rockmass damage and yield. In conventional analysis of both structurally controlled and stress driven failure, the effects of tensile damage and tensile resistance as well as the elevated sensitivity to low confinement are typically neglected, leading to erroneous predictions of groundfall potential or rock yield. The important role of these two elements in underground excavation stability in hard rock environments is examined in detail through a review of testing data, case study examination and a number of analytical and numerical analogues including discrete element simulation, statistical theory and fracture mechanics. This rigorous theoretical treatment updates, validates and constrains the current use of semi-empirical design guidelines based on these mechanisms.

Fracture and fatigue in wood

Abstract: Introduction. Structure and Properties of Wood. Mechanical Behaviour of Wood: Concepts and Modelling. Principles of Fracture Mechanics. Fracture and Failure Phenomena in Wood. Fatigue in Wood. Fracture Modelling in Wood. Fatigue Modelling in Wood. Application of Information and Concepts. Index.

Crack growth resistance of hybrid fiber reinforced cement composites

Abstract: Crack propagation in cement-based matrices carrying hybrid fiber reinforcement was studied using contoured double cantilever beam (CDCB) specimens. Influence of fiber type and combination was quantified using crack growth resistance curves. It was demonstrated that a hybrid combination of steel and polypropylene fibers enhances the resistance to both nucleation and growth of cracks, and that such fundamental fracture tests are very useful in developing high performance hybrid fiber composites. The influence of number of variables which would otherwise have remained obscured in normal tests for engineering properties become apparent in the fracture tests. The paper emphasizes the desired durability characteristics of these composites and discusses their current and future applications.

Rupture Dynamics With Energy Loss Outside the Slip Zone

Abstract: [1] Energy loss in a fault damage zone, outside the slip zone, contributes to the fracture energy that determines rupture velocity of an earthquake. A nonelastic two-dimensional dynamic calculation is done in which the slip zone is modeled as a fault plane and material off the fault is subject to a Coulomb yield condition. In a mode 2 crack-like solution in which an abrupt uniform drop of shear traction on the fault spreads from a point, Coulomb yielding occurs on the extensional side of the fault. Plastic strain is distributed with uniform magnitude along the fault, and it has a thickness normal to the fault proportional to propagation distance. Energy loss off the fault is also proportional to propagation distance, and it can become much larger than energy loss on the fault specified by the fault constitutive relation. The slip velocity function could be produced in an equivalent elastic problem by a slip-weakening friction law with breakdown slip Dc increasing with distance. Fracture energy G and equivalent Dc will be different in ruptures with different initiation points and stress drops, so they are not constitutive properties; they are determined by the dynamic solution that arrives at a particular point. Peak slip velocity is, however, a property of a fault location. Nonelastic response can be mimicked by imposing a limit on slip velocity on a fault in an elastic medium.

On the relationship between microstructure, strength and toughness in AA7050 aluminum alloy

Abstract: The effect of process parameters such as quench rate and precipitation heat treatment on the compromise between the toughness and the yield strength of AA7050 aluminum alloy (AlZnMgCu) are investigated, as well as the anisotropy of this compromise in the rolling plane. Fracture toughness is experimentally approached by the Kahn tear test. The microstructure is studied quantitatively in detail by a combination of scanning electron microscopy, transmission electron microscopy and small-angle X-ray scattering, and the relative fractions of the various fracture modes as a function of microstructural state are quantitatively determined on scanning electron microscopy images. Toughness is confirmed to be minimum at peak strength, and lower for an overaged material than for an underaged material of the same yield strength. A lower quench rate is shown to result in an overall reduction of toughness, and in a reduced evolution of this toughness during the aging heat treatment. The overall toughness is also lowered when the main crack propagation direction is parallel to the preferential elongation direction of the coarse constituent particles (rolling direction). The competition between intergranular and transgranular fracture is explained in terms of the modifications of the work hardening rate, and of grain boundary precipitation. The evolution of fracture toughness is qualitatively explained in terms of evolution of yield stress, strain hardening rate, grain boundary precipitation and intragranular quench-induced precipitates.

The use of a cohesive zone model to study the fracture of fibre composites and adhesively-bonded joints

Abstract: Analytical solutions for beam specimens used in fracture-mechanics testing of composites and adhesively-bonded joints typically use a beam on an elastic foundation model which assumes that a non-infinite, linear-elastic stiffness exists for the beam on the elastic foundation in the region ahead of the crack tip. Such an approach therefore assumes an elastic-stiffness model but without the need to assume a critical, limiting value of the stress,σmax, for the crack tip region. Hence, they yield asingle fracture parameter, namely the fracture energy,Gc. However, the corresponding value ofσmax that results can, of course, be calculated from knowledge of the value ofGc. On the other hand, fracture models and criteria have been developed which are based on the approach thattwo parameters exist to describe the fracture process: namelyGcandσmax. Hereσmax is assumed to be a critical,limiting maximum value of the stress in the damage zone ahead of the crack and is often assumed to have some physical significance. A general representation of the two-parameter failure criteria approach is that of the cohesive zone model (CZM). In the present paper, the two-parameter CZM approach has been coupled mainly with finite-element analysis (FEA) methods. The main aims of the present work are to explore whether the value ofσmax has a unique value for a given problem and whether any physical significance can be ascribed to this parameter. In some instances, both FEA and analytical methods are used to provide a useful crosscheck of the two different approaches and the two different analysis methods.

Sublinear scaling of fracture aperture versus length: An exception or the rule?

Abstract: [1] Observations of natural fracture dimensions have sparked a continuing debate as to the nature of the fundamental relationship between fracture aperture (maximum opening) and length. On the basis of theoretical fracture mechanics, some have argued aperture-to-length scaling should be linear. This relationship implies that all fractures in a given population have the same driving stress regardless of fracture length, arguably a state that is difficult to reconcile with fracture propagation criteria. Also, some field observations indicate sublinear aperture-to-length scaling that is apparently inconsistent with the linear elastic fracture mechanics theory. In this work, a nonlinear aperture-to-length relationship is derived, still based on linear elastic fracture mechanics in a homogeneous body, but incorporating subcritical and critical (equilibrium law) fracture propagation criteria. The new hypothesis postulates that fractures of different lengths preserved in a body of rock are all in the same condition with respect to propagation (i.e., they all have the same stress intensity factor). This requires that fractures have driving stresses that vary inversely with the square root of fracture length, producing fracture apertures that scale with length to the 1/2 power. Under these conditions, fracture aspect ratio (aperture/length) decreases with increasing fracture length to the negative 1/2 power. Linear aperture-to-length scaling is still considered a possibility but is attributed to a relaxed, postpropagation mechanical state. Deviations in fracture aperture-to-length relationships from these idealized models can result from mechanical fracture interaction, fracture segmentation into en echelon arrays, and three dimensional effects in stratabound fractures.

Glass breaks like metal, but at the nanometer scale.

Abstract: We report in situ atomic force microscopy experiments which reveal the presence of nanoscale damage cavities ahead of a stress-corrosion crack tip in glass. Their presence might explain the departure from linear elasticity observed in the vicinity of a crack tip in glass. Such a ductile fracture mechanism, widely observed in the case of metallic materials at the micrometer scale, might be also at the origin of the striking similarity of the morphologies of fracture surfaces of glass and metallic alloys at different length scales.

Micro and macroscopic models of rock fracture

Abstract: SUMMARY The anelastic deformation of solids is often treated using continuum damage mechanics. An alternative approach to the brittle failure of a solid is provided by the discrete fiber-bundle model. Here we show that the continuum damage model can give exactly the same solution for material failure as the fiber-bundle model. We compare both models with laboratory experiments on the time dependent failure of chipboard and fiberglass. The power-law scaling obtained in both models and in the experiments is consistent with the power-law seismic activation observed prior to some earthquakes.

Application of fiber reinforced polymer overlays to extend steel fatigue life

Abstract: An experimental and analytical study was conducted to investigate the effectiveness of applying carbon fiber reinforced polymer (CFRP) overlays to steel fatigue tension coupons to prolong fatigue life. Specimens were either notched or center hole specimens and tested in uniaxial tension. Variables studied were CFRP system, bond length, bond area, one and two sided applications, and applications prior or subsequent to crack propagation. Two sided applications were very effective, prolonging fatigue life by as much as 115%. Similar application of CFRP materials subsequent to crack propagation extended the remaining fatigue life by approximately 170% without any other means of crack arrest. The method therefore showed promise as both a preventive technique and repair method. The epoxy performance was critical to the effectiveness of the system, with all failures initiated by debonding of the CFRP. Overlays were most effective when the system was applied directly to the potential crack trajectory. One-sided a...

Role of collagen and other organics in the mechanical properties of bone

Abstract: Relevant mechanical properties of bone The mechanical properties of bone material are determined by the relative amounts of its 3 major constituents: mineral, water, and organics (mainly type I collagen); by the quality of these components; and by how the resulting material is arranged in space. For our purposes, the mechanical properties of bone can be summed up as follows: modulus of elasticity, yield stress and yield strain, post-yield stress and post-yield strain, and the total area under the stress-strain curve. Also important are some fracture mechanics properties, but these are not discussed here. A typical tensile stress-strain curve for a bone specimen is shown in Fig. 1. The modulus of elasticity shows how stiff the bone material is. Indeed, stiffness is the prime property of bone, distinguishing it from tendon, which has much less tensile stiffness, almost no shear stiffness, but which is nearly as strong and is much tougher. Yield stress and strain determine how much energy can be absorbed before irreversible changes take place. Post-yield stress and strain determine mainly how much energy can be absorbed after yield but before fracture. Irreversible changes take place at yield, caused by microdamage. The total area under the stress-strain curve is equivalent to the work that must be done per unit volume on the specimen before it breaks. Fracture mechanics properties show the extent to which bone is resistant to crack initiation and to crack travel (which are different things and governed by somewhat different features). In fact, crack travel resistance is given rather well by post-yield stress and strain.

Effect of clustering on the mechanical properties of SiC particulate-reinforced aluminum alloy 2024 metal matrix composites

Abstract: Al 2024–SiC metal matrix composite (MMC) powders produced by centrifugal atomization were hot extruded to investigate the effect of clustering on their mechanical properties. Fracture toughness and tension tests were conducted on specimens reinforced with different volume fractions of SiC. A model was proposed to suggest that the strength of the MMCs could be estimated from the load transfer model approach that takes into consideration the extent of clustering. This model has been successful in predicting the experimentally observed strength and fracture toughness values of the Al 2024–SiC MMCs. On the basis of experimental observations, it is suggested that the strength of particulate-reinforced MMCs may be calculated from the relation: σ y = σ m V m + σ r ( V r − V c )− σ r V c , where σ and V represent the yield strength and volume fraction, respectively, and the subscripts m, r, and c represent the matrix, reinforcement, and clusters, respectively.

A fracture criterion for sharp V-notched samples

Abstract: The objective of this paper is to show the advantages of the cohesivecrack model for predicting fracture of V-notched components. Criticalvalues of the generalized stress intensity factor can be obtained fromthe knowledge of the material softening function and the elastic parameters,avoiding a cumbersome experimental work. The results were checked successfullyagainst experimental ones, from other authors, in different materials: steel,aluminium, PMMA and PVC. A non dimensional formulation of the fracturecriterion for sharp V-notched components was obtained and a simpleapproximate expression derived for easy appication.