Showing papers on "Fracture mechanics published in 2004"

Virtual crack closure technique: History, approach, and applications

Abstract: : An overview of the virtual crack closure technique is presented. The approach used is discussed, the history summarized, and insight into its applications provided. Equations for two-dimensional quadrilateral elements with linear and quadratic shape functions are given. Formula for applying the technique in conjuction with three-dimensional solid elements as well as plate/shell elements are also provided. Necessary modifications for the use of the method with geometrically nonlinear finite element analysis and corrections required for elements at the crack tip with different lengths and widths are discussed. The problems associated with cracks or delaminations propagating between different materials are mentioned briefly, as well as a strategy to minimize these problems. Due to an increased interest in using a fracture mechanics based approach to assess the damage tolerance of composite structures in the design phase and during certification, the engineering problems selected as examples and given as references focus on the application of the technique to components made of composite materials.

Modeling elastic and plastic deformations in nonequilibrium processing using phase field crystals.

Abstract: A continuum field theory approach is presented for modeling elastic and plastic deformation, free surfaces, and multiple crystal orientations in nonequilibrium processing phenomena. Many basic properties of the model are calculated analytically, and numerical simulations are presented for a number of important applications including, epitaxial growth, material hardness, grain growth, reconstructive phase transitions, and crack propagation.

Propagation Regimes of Fluid-Driven Fractures in Impermeable Rocks

Abstract: This paper reviews recent results of a research program aimed at developing a theoretical framework to understand and predict the different modes of propagation of a fluid-driven fracture. The research effort involves constructing detailed solutions of the crack tip region, developing global models of hydraulic fractures for plane strain and radial geometry, and identifying the parameters controlling the fracture growth. The paper focuses on the propagation of hydraulic fractures in impermeable rocks. The controlling parameters are identified from scaling laws that recognize the existence of two dissipative processes: fracturing of the rock (toughness) and dissipation in the fracturing fluid (viscosity). It is shown that the two limit solutions (corresponding to zero toughness and zero viscosity) are characterized by a power law dependence on time and that the transition between these two asymptotic solutions depends on a single number, which can be chosen to be either a dimensionless toughness or a dimen...

Mechanical Behavior of Materials

Abstract: 1. Stress and strain 2. Elasticity 3. Mechanical tensile testing 4. Strain hardening of metals 5. Plasticity 6. Strain-rate and temperature dependence of flow stress 7. Slip 8. Dislocation geometry and energy 9. Dislocation mechanics 10. Mechanical twinning 11. Hardening mechanisms 12. Discontinuous and inhomogeneous deformation 13. Ductility and fracture 14. Fracture mechanics 15. Viscoelasticity 16. Creep and stress rupture 17. Fatigue 18. Residual stresses 19. Ceramics 20. Polymers 21. Composites 22. Mechanical working Appendix I. Miller indices Appendix II. Stereographic projection.

A Comparative Study on Various Ductile Crack Formation Criteria

Abstract: Various fracture criteria, based on different assumptions and different mechanical models, have been proposed in the past to predict ductile fracture. The objective of this study is to assess their effectiveness and accuracy in a wide range of process parameters. A series of tests on 2024-T351 aluminum alloy, including upsetting tests and tensile tests is carried out. It is found that none of the existing fracture criteria give consistent results. Two totally different fracture mechanisms are clearly observed from microfractographs of upsetting and tensile specimens. This observation confirms that it is impossible to capture all features of ductile crack formation in different stress states with a single criterion. It is shown that different functions are necessary to predict crack formation for different ranges of stress triaxiality. Weighting functions in a wide range of stress states can be obtained by determining the fracture locus in the space of equivalent strain to fracture and stress triaxiality.

Micromechanical Model for Simulating the Fracture Process of Rock

Abstract: A micromechanical model is proposed to study the deformation and failure process of rock based on knowledge of heterogeneity of rock at the mesoscopic level. In this numerical model, the heterogeneity of rock at the mesoscopic level is considered by assuming the material properties in rock conform to the Weibull distribution. Elastic damage mechanics is used to describe the constitutive law of meso-level elements, the finite element method is employed as the basic stress analysis tool and the maximum tensile strain criterion as well as the Mohr-Coulomb criterion is utilized as the damage threshold. A simple method, similar to a smeared crack model, is used for tracing the crack propagation process and interaction of multiple cracks. Based on this model, a numerical simulation program named Rock Failure Process Analysis Code (RFPA) is developed. The influence of parameters that include the Weibull distribution parameters, constitutive parameters of meso-level elements and number of elements in the numerical model, are discussed in detail. It is shown that the homogeneity index is the most important factor to simulate material failure with this model. This model is able to capture the complete mechanical responses of rock, which includes the crack patterns associated with different loading stages and loading conditions, localization of deformation, stress redistribution and failure process. The numerical simulation of rock specimens under a variety of static loading conditions is presented, and the results compare well with experimental results.

Quantized fracture mechanics

Abstract: A new energy-based theory, quantized fracture mechanics (QFM), is presented that modifies continuum-based fracture mechanics; stress- and strain-based QFM analogs are also proposed. The differentials in Griffith's criterion are substituted with finite differences; the implications are remarkable. Fracture of tiny systems with a given geometry and type of loading occurs at ‘quantized’ stresses that are well predicted by QFM: strengths predicted by QFM are compared with experimental results on carbon nanotubes, β-SiC nanorods, α-Si3N4 whiskers, and polysilicon thin films; and also with molecular mechanics/dynamics simulation of fracture of carbon nanotubes and graphene with cracks and holes, and statistical mechanics-based simulations on fracture of two-dimensional spring networks. QFM is self-consistent, agreeing to first-order with linear elastic fracture mechanics (LEFM), and to second-order with non-linear fracture mechanics (NLFM). For vanishing crack length QFM predicts a finite ideal strength in agre...

Hybrid fracture and the transition from extension fracture to shear fracture

Abstract: Fracture is a fundamental mechanism of material failure. Two basic types of brittle fractures are commonly observed in rock deformation experiments--extension (opening mode) fractures and shear fractures. For nearly half a century it has been hypothesized that extension and shear fractures represent end-members of a continuous spectrum of brittle fracture types. However, observations of transitional fractures that display both opening and shear modes (hybrids) in naturally deformed rock have often remained ambiguous, and a clear demonstration of hybrid fracture formation has not been provided by experiments. Here we present the results of triaxial extension experiments on Carrara marble that show a continuous transition from extension fracture to shear fracture with an increase in compressive stress. Hybrid fractures form under mixed tensile and compressive stress states at acute angles to the maximum principal compressive stress. Fracture angles are greater than those observed for extension fractures and less than those observed for shear fractures. Fracture surfaces also display a progressive change from an extension to shear fracture morphology.

Intermediate-depth earthquake faulting by dehydration embrittlement with negative volume change.

Abstract: Earthquakes are observed to occur in subduction zones to depths of approximately 680 km, even though unassisted brittle failure is inhibited at depths greater than about 50 km, owing to the high pressures and temperatures. It is thought that such earthquakes (particularly those at intermediate depths of 50-300 km) may instead be triggered by embrittlement accompanying dehydration of hydrous minerals, principally serpentine. A problem with failure by serpentine dehydration is that the volume change accompanying dehydration becomes negative at pressures of 2-4 GPa (60-120 km depth), above which brittle fracture mechanics predicts that the instability should be quenched. Here we show that dehydration of antigorite serpentinite under stress results in faults delineated by ultrafine-grained solid reaction products formed during dehydration. This phenomenon was observed under all conditions tested (pressures of 1-6 GPa; temperatures of 650-820 degrees C), independent of the sign of the volume change of reaction. Although this result contradicts expectations from fracture mechanics, it can be explained by separation of fluid from solid residue before and during faulting, a hypothesis supported by our observations. These observations confirm that dehydration embrittlement is a viable mechanism for nucleating earthquakes independent of depth, as long as there are hydrous minerals breaking down under a differential stress.

Mechanisms and modeling of cleavage fracture in simulated heat-affected zone microstructures of a high-strength low alloy steel

Abstract: The effect of the welding cycle on the fracture toughness properties of high-strength low alloy (HSLA) steels is examined by means of thermal simulation of heat-affected zone (HAZ) microstructures. Tensile tests on notched bars and fracture toughness tests at various temperatures are performed together with fracture surface observations and cross-sectional analyses. The influence of martensite-austenite (M-A) constituents and of “crystallographic” bainite packets on cleavage fracture micromechanisms is, thus, evidenced as a function of temperature. Three weakest-link probabilistic models (the “Master-curve” (MC) approach, the Beremin model, and a “double-barrier” (DB) model) are applied to account for the ductile-to-brittle transition (DBT) fracture toughness curve. Some analogy, but also differences, are found between the MC approach and the Beremin model. The DB model, having nonfitted, physically based scatter parameters, is applied to the martensite-containing HAZ microstructures and gives promising results.

Failure criteria for brittle elastic materials

Abstract: The successful use of linear elastic fracture mechanics theory in predicting brittle fracture in isotropic domains with cracks is attributed to the successful correlation of a single parameter, namely the stress intensity factor, with experimental observations for the determination of failure initiation or crack propagation.

Discrete vs smeared crack models for concrete fracture: bridging the gap

Abstract: Discrete and smeared crack models for concrete fracture are discussed in a historical perspective. It is argued that these two computational approaches, originally conceived as very different, can be brought together by exploiting the partition-of-unity property of finite element shape functions. The cohesive segments method, which exploits this partition-of-unity property, exhibits advantages of both the discrete and smeared crack approaches, and is capable of describing the transition from distributed micro-cracking to a dominant crack. The versatility of the cohesive methodology is shown by incorporating water diffusion and ion transport into the formulation.

Dynamic crack propagation with cohesive elements: a methodology to address mesh dependency

Abstract: In this paper, two brittle fracture problems are numerically simulated: the failure of a ceramic ring under centrifugal loading and crack branching in a PMMA strip. A three-dimensional finite element package in which cohesive elements are dynamically inserted has been developed. The cohesive elements' strength is chosen to follow a modified weakest link Weibull distribution. The probability of introducing a weak cohesive element is set to increase with the cohesive element size. This reflects the physically based effect according to which larger elements are more likely to contain defects. The calculations illustrate how the area dependence of the Weibull model can be used to effectively address mesh dependency. On the other hand, regular Weibull distributions have failed to reduce mesh dependency for the examples shown in this paper. The ceramic ring calculations revealed that two distinct phenomena appear depending on the magnitude of the Weibull modulus. For low Weibull modulus, the fragmentation of the ring is dominated by heterogeneities. Whereas many cracks were generated, few of them could propagate to the outer surface. Monte Carlo simulations revealed that for highly heterogeneous rings, the number of small fragments was large and that few large fragments were generated. For high Weibull modulus, signifying that the ring is close to being homogeneous, the fragmentation process was very different. Monte Carlo simulations highlighted that a larger number of large fragments are generated due to crack branching. Copyright (C) 2003 John Wiley Sons, Ltd.

Detection and monitoring of hidden fatigue crack growth using a built-in piezoelectric sensor/actuator network: II. Validation using riveted joints and repair patches

Abstract: A built-in diagnostic technique for monitoring hidden fatigue crack growth in aircraft structures has been developed in part I of the study. The technique uses diagnostics signals, generated from nearby piezoelectric actuators built into the structures, to detect crack growth. In this second part of the study, the proposed diagnostic technique was applied to monitor fatigue crack growth in riveted fuselage joints and a cracked metallic plate repaired with a bonded composite patch. A complete built-in diagnostic system for the tests was developed, including a sensor network, hardware and the diagnostic software. Predictions were correlated quite well with measurements from the eddy current test and the ultrasonic scan methods as well as visual inspection. The damage index successfully detected both crack growth and debond damage for the structures considered.

Optimisation of steel fibre reinforced concretes by means of statistical response surface method

Abstract: The objective of this research is to optimise the fracture parameters of steel fibre reinforced concretes to obtain a more ductile behaviour than that of plain concrete. The effects of the aspect ratio (L/d) and volume fraction of steel fibre (Vf) on fracture properties of concrete in bending were investigated by measuring the fracture energy (GF) and characteristic length (lch). For optimisation, three-level full factorial experimental design and response surface method were used. The results show that the effects of fibre volume fraction and aspect ratio on fracture energy and characteristic length are very significant.