Showing papers on "Fracture mechanics published in 2009"

Enhanced mechanical properties of nanocomposites at low graphene content.

Abstract: In this study, the mechanical properties of epoxy nanocomposites with graphene platelets, single-walled carbon nanotubes, and multi-walled carbon nanotube additives were compared at a nanofiller weight fraction of 0.1 ± 0.002%. The mechanical properties measured were the Young’s modulus, ultimate tensile strength, fracture toughness, fracture energy, and the material’s resistance to fatigue crack propagation. The results indicate that graphene platelets significantly out-perform carbon nanotube additives. The Young’s modulus of the graphene nanocomposite was ∼31% greater than the pristine epoxy as compared to ∼3% increase for single-walled carbon nanotubes. The tensile strength of the baseline epoxy was enhanced by ∼40% with graphene platelets compared to ∼14% improvement for multi-walled carbon nanotubes. The mode I fracture toughness of the nanocomposite with graphene platelets showed ∼53% increase over the epoxy compared to ∼20% improvement for multi-walled carbon nanotubes. The fatigue resistance resu...

Mechanical Behavior of Materials

Abstract: 1 Overview of Mechanical Behavior 2 Elastic Behavior 3 Dislocations 4 Plastic Deformation in Single and Polycrystalline Materials 5 Strengthening of Crystalline Materials 6 Composite Materials 7 High-Temperature Deformation of Crystalline Materials 8 Deformation of Noncrystalline Materials 9 Fracture Mechanics 10 Toughening Mechanisms and the Physics of Fracture 11 High-Temperature 12 Fatigue of Engineering Materials 13 Embrittlement 14 Cellular Solids

Regularized formulation of the variational brittle fracture with unilateral contact: Numerical experiments

Abstract: This paper presents a modified regularized formulation of the Ambrosio–Tortorelli type to introduce the crack non-interpenetration condition in the variational approach to fracture mechanics proposed by Francfort and Marigo [1998. Revisiting brittle fracture as an energy minimization problem. J. Mech. Phys. Solids 46 (8), 1319–1342]. We focus on the linear elastic case where the contact condition appears as a local unilateral constraint on the displacement jump at the crack surfaces. The regularized model is obtained by splitting the strain energy in a spherical and a deviatoric parts and accounting for the sign of the local volume change. The numerical implementation is based on a standard finite element discretization and on the adaptation of an alternate minimization algorithm used in previous works. The new regularization avoids crack interpenetration and predicts asymmetric results in traction and in compression. Even though we do not exhibit any gamma-convergence proof toward the desired limit behavior, we illustrate through several numerical case studies the pertinence of the new model in comparison to other approaches.

On the fracture toughness of advanced materials

Abstract: Few engineering materials are limited by their strength; rather they are limited by their resistance to fracture or fracture toughness. It is not by accident that most critical structures, such as bridges, ships, nuclear pressure vessels and so forth, are manufactured from materials that are comparatively low in strength but high in toughness. Indeed, in many classes of materials, strength and toughness are almost mutually exclusive. From a fracture-mechanics perspective, the ability of a microstructure to develop toughening mechanisms acting either ahead or behind the crack tip can result in resistance-curve (R-curve) behavior where the fracture resistance actually increases with crack extension; the implication here is that toughness is often developed primarily during crack growth and not for crack initiation. Biological materials are perfect examples of this; moreover, they offer microstructural design strategies for the development of new materials for structural applications demanding combinations of both strength and toughness.

A unified potential-based cohesive model of mixed-mode fracture

Abstract: 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 (eg 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

Mechanical and fracture stratigraphy

Abstract: Using examples from core studies, this article shows that separate identification of mechanical stratigraphy and fracture stratigraphy leads to a clearer understanding of fracture patterns and more accurate prediction of fracture attributes away from the wellbore. Mechanical stratigraphy subdivides stratified rock into discrete mechanical units defined by properties such as tensile strength, elastic stiffness, brittleness, and fracture mechanics properties. Fracture stratigraphy subdivides rock into fracture units according to extent, intensity, or some other observed fracture attribute. Mechanical stratigraphy is the by-product of depositional composition and structure, and chemical and mechanical changes superimposed on rock composition, texture, and interfaces after deposition. Fracture stratigraphy reflects a specific loading history and mechanical stratigraphy during failure. Because mechanical property changes reflect diagenesis and fractures evolve with loading history, mechanical stratigraphy and fracture stratigraphy need not coincide. In subsurface studies, current mechanical stratigraphy is generally measurable, but because of inherent limitations of sampling, fracture stratigraphy is commonly incompletely known. To accurately predict fractures in diagenetically and structurally complex settings, we need to use evidence of loading and mechanical property history as well as current mechanical states.

Laws of crack motion and phase-field models of fracture

Abstract: Recently proposed phase-field models offer self-consistent descriptions of brittle fracture. Here, we analyze these theories in the quasistatic regime of crack propagation. We show how to derive the laws of crack motion either by using solvability conditions in a perturbative treatment for slight departure from the Griffith threshold or by generalizing the Eshelby tensor to phase-field models. The analysis provides a simple physical interpretation of the second component of the classic Eshelby integral in the limit of vanishing crack propagation velocity: it gives the elastic torque on the crack tip that is needed to balance the Herring torque arising from the anisotropic surface energy. This force-balance condition can be interpreted physically based on energetic considerations in the traditional framework of continuum fracture mechanics, in support of its general validity for real systems beyond the scope of phase-field models. The obtained law of crack motion reduces in the quasistatic limit to the principle of local symmetry in isotropic media and to the principle of maximum energy-release-rate for smooth curvilinear cracks in anisotropic media. Analytical predictions of crack paths in anisotropic media are validated by numerical simulations. Interestingly, for kinked cracks in anisotropic media, force-balance gives significantly different predictions from the principle of maximum energy-release-rate and the difference between the two criteria can be numerically tested. Simulations also show that predictions obtained from force-balance hold even if the phase-field dynamics is modified to make the failure process irreversible. Finally, the role of dissipative forces on the process zone scale as well as the extension of the results to motion of planar cracks under pure antiplane shear are discussed.

Natural fracture characterization in tight gas sandstones: Integrating mechanics and diagenesis

Abstract: Accurate predictions of natural fracture flow attributes in sandstones require an understanding of the underlying mechanisms responsible for fracture growth and aperture preservation. Poroelastic stress calculations combined with fracture mechanics criteria show that it is possible to sustain opening-mode fracture growth with sublithostatic pore pressure without associated or preemptive shear failure. Crack-seal textures and fracture aperture to length ratios suggest that preserved fracture apertures reflect the loading state that caused propagation. This implies that, for quartz-rich sandstones, the synkinematic cement in the fractures and in the rock mass props fracture apertures open and reduces the possibility of aperture loss on unloading and relaxation. Fracture pattern development caused by subcritical fracture growth for a limited range of strain histories is demonstrated to result in widely disparate fracture pattern geometries. Substantial opening-mode growth can be generated by very small extensional strains (on the order of 104); consequently, fracture arrays are likely to form in the absence of larger scale structures. The effective permeabilities calculated for these low-strain fracture patterns are considerable. To replicate the lower permeabilities that typify tight gas sandstones requires the superimposition of systematic cement filling that preferentially plugs fracture tips and other narrower parts of the fracture pattern.

An extended finite element method for hydraulic fracture problems

Abstract: In this paper, the extended finite element method (X-FEM) is investigated for the solution of hydraulic fracture problems. The presence of an internal pressure inside the crack is taken into account. Special tip functions encapsulating tip asymptotics typically encountered in hydraulic fractures are introduced. We are especially interested in the two limiting tip behaviour for the impermeable case: the classical LEFM square root asymptote in fracture width for the toughness-dominated regime of propagation and the so-called ⅔ asymptote in fracture width for the viscosity-dominated regime. Different variants of the X-FEM are tested for the case of a plane-strain hydraulic fracture propagation in both the toughness and the viscosity dominated regimes. Fracture opening and fluid pressure are compared at each nodes with analytical solutions available in the literature. The results demonstrate the importance of correcting for the loss of partition of unity in the transition zone between the enriched part and the rest of the mesh. A point-wise matching scheme appears sufficient to obtain accurate results. Proper integration of the singular terms introduced by the enrichment functions is also critical for good performance. Copyright © 2008 John Wiley & Sons, Ltd.

Indentation techniques for evaluating the fracture toughness of biomaterials and hard tissues

Abstract: Indentation techniques for assessing fracture toughness are attractive due to the simplicity and expediency of experiments, and because they potentially allow the characterization of both local and bulk fracture properties. Unfortunately, rarely have such techniques been proven to give accurate fracture toughness values. This is a concern, as such techniques are seeing increasing usage in the study of biomaterials and biological hard tissues. Four available indentation techniques are considered in the present article: the Vickers indentation fracture (VIF) test, the cube corner indentation fracture (CCIF) test, the Vickers crack opening displacement (VCOD) test and the interface indentation fracture (IIF) test. Each technique is discussed in terms of its suitability for assessing the absolute and relative toughness of materials or material interfaces based on the published literature on the topic. In general, the VIF and CCIF techniques are found to be poor for quantitatively evaluating toughness of any brittle material, and the large errors involved (approximately +/-50%) make their applicability as comparative techniques limited. Indeed, indentation toughness values must differ by at least by a factor of three to conclude a significant difference in actual toughness. Additionally, new experimental results are presented on using the CCIF test to evaluate the fracture resistance of human cortical bone. Those new results indicate that inducing cracking is difficult, and that the cracks that do form are embedded in the plastic zone of the indent, invalidating the use of linear elastic fracture mechanics based techniques for evaluating the toughness associated with those cracks. The VCOD test appears to be a good quantitative method for some glasses, but initial results suggest there may be problems associated with applying this technique to other brittle materials. Finally, the IIF technique should only be considered a comparative or semi-quantitative technique for comparing material interfaces and/or the neighboring materials.

A procedure for superposing linear cohesive laws to represent multiple damage mechanisms in the fracture of composites

Abstract: The relationships between a resistance curve (R-curve), the corresponding fracture process zone length, the shape of the traction-displacement softening law, and the propagation of fracture are examined in the context of the through-the-thickness fracture of composite laminates. A procedure for superposing linear cohesive laws to approximate an experimentally-determined R-curve is proposed. Simple equations are developed for determining the separation of the critical energy release rates and the strengths that define the independent contributions of each linear softening law in the superposition. The proposed procedure is demonstrated for the longitudinal fracture of a fiber-reinforced polymer-matrix composite. It is shown that the R-curve measured with a Compact Tension Specimen test cannot be predicted using a linear softening law, but can be reproduced by superposing two linear softening laws.

Enhanced Fracture Properties of Carbon Reinforced Composites by the Addition of Multi-Wall Carbon Nanotubes

Abstract: In the present study, the fracture energy of hybrid carbon fiber reinforced polymers was investigated. The composites were modified by the addition of multi-walled carbon nanotubes into the matrix material. The interlaminar fracture properties under Mode I and Mode II remote loading were studied as a function of the carbon nanotube content in the matrix. With the addition of carbon nanotubes in the epoxy matrix, a significant increase in the load bearing ability as well as in the fracture energy was observed, for both Mode I and Mode II tests. It is speculated that carbon nanotubes due to their large aspect ratio have a significant toughening effect since extra energy is needed in order to pull them out from the matrix and start the crack propagation following a kinking out pattern at nanoscale.

Stress-corrosion mechanisms in silicate glasses

Abstract: The present review is intended to revisit the advances and debates in the comprehension of the mechanisms of subcritical crack propagation in silicate glasses almost a century after its initial developments. Glass has inspired the initial insights of Griffith into the origin of brittleness and the ensuing development of modern fracture mechanics. Yet, through the decades the real nature of the fundamental mechanisms of crack propagation in glass has escaped a clear comprehension which could gather general agreement on subtle problems such as the role of plasticity, the role of the glass composition, the environmental condition at the crack tip and its relation to the complex mechanisms of corrosion and leaching. The different processes are analysed here with a special focus on their relevant space and time scales in order to question their domain of action and their contribution in both the kinetic laws and the energetic aspects.

Prediction of crack paths in a quenched glass plate by using peridynamic theory

Abstract: The peridynamic theory is employed to predict crack growth patterns in quenched glass plates previously considered for an experimental investigation. The plates containing single and multiple pre-existing initial cracks are simulated to investigate the effects of peridynamic and experimental parameters on the crack paths. The critical stretch value in the peridynamic theory and the gap size between the heat reservoirs are determined to be the most significant parameters. The simulation results are in good agreement with the experimental observations published in the literature.

From criticality to final collapse: Evolution of the ''b-value" from 1.5 to 1.0

Abstract: Extensive research and studies on concrete fracture and failure by means of the acoustic emission (AE) technique have shown that fracture and damage growth can be characterized through a single synthetic parameter, namely the b-value, which changes systematically during the different stages of the failure process, as shown by several AE tests carried out from the specimen to the structural scale [Sammonds PR, Meredith PG, Murrel SAF, Main IG. Modelling the damage evolution in rock containing porefluid by acoustic emission. In: Proceedings of the Eurock’94; 1994; Colombo S, Main IG, Forde MC. Assessing damage of reinforced concrete beam using “b-value” analysis of acoustic emission signals. J Mater Civil Eng ASCE 2003;15:280–6; Carpinteri A, Lacidogna G, Niccolini G. Critical behaviour in concrete structures and damage localisation by Acoustic Emission. Key Eng Mater 2006;312:305–10]. This parameter can be linked to the value of the exponent α of the power-law distribution of the crack size in a damaged structure. In this paper, we propose a statistical interpretation for the variation of the b-value during the evolution of damage, based on a treatment originally proposed by [Carpinteri A. Mechanical damage and crack growth in concrete: plastic collapse to brittle fracture. Dordrecht: Martinus Nijhoff Publishers; 1986; Carpinteri A. Decrease of apparent tensile and bending strength with specimen size: two different explanations based on fracture mechanics. Int J Solid Struct 1989;25:407–29; Carpinteri A. Scaling laws and renormalization groups for strength and toughness of disordered materials. Int J Solid Struct 1994;31:291–302]. The proposed model captures the transition from the condition of criticality, in which α = 3, to that of imminent failure, characterized by α = 2, in terms of damage localisation.

A phantom node formulation with mixed mode cohesive law for splitting in laminates

Abstract: A phantom node method with mixed mode cohesive law is proposed for the simulation of splitting in laminates. With this method, a discontinuity in the displacement field can be modeled at arbitrary locations. The micromechanical phenomenon that splitting cracks grow parallel to the fiber, is incorporated on the mesolevel, i.e., in the homogenized ply, by setting the direction of the crack propagation equal to the fiber direction. A new mixed mode cohesive law is introduced for increased robustness of the incremental-iterative solution procedure. The model is validated with mixed mode bending tests, and its utility is illustrated with examples for a single ply and for a laminate.

Fracture and fatigue of natural fiber-reinforced cementitious composites

Abstract: This paper presents the results of an experimental study of resistance-curve behavior and fatigue crack growth in cementitious matrices reinforced with eco-friendly natural fibers obtained from agricultural by-products. The composites include: blast furnace slag cement reinforced with pulped fibers of sisal, banana and bleached eucalyptus pulp, and ordinary Portland cement composites reinforced with bleached eucalyptus pulp. Fracture resistance (R-curve) and fatigue crack growth behavior were studied using single-edge notched bend specimens. The observed stable crack growth behavior was then related to crack/microstructure interactions that were elucidated via scanning electron microscopy (SEM) and energy dispersive X-ray spectroscopy (EDS). Fracture mechanics models were used to quantify the observed crack-tip shielding due to crack-bridging. The implications of the results are also discussed for the design of natural fiber-reinforced composite materials for affordable housing.