Showing papers on "Fracture mechanics published in 2008"

Analysis of crack formation and crack growth in concrete by means of fracture mechanics and finite elements

Abstract: A method is presented in which fracture mechanics is introduced into finite element analysis by means of a model where stresses are assumed to act across a crack as long as it is narrowly opened. This assumption may be regarded as a way of expressing the energy adsorption GC in the energy balance approach, but it is also in agreement with results of tension tests. As a demonstration the method has been applied to the bending of an unreinforced beam, which has led to an explanation of the difference between bending strength and tensile strength, and of the variation in bending strength with beam depth.

Designing metallic glass matrix composites with high toughness and tensile ductility

Abstract: Metallic glasses have been the subject of intense scientific study since the 1960s, owing to their unique properties such as high strength, large elastic limit, high hardness, and amorphous microstructure. However, bulk metallic glasses have not been used in the high strength structural applications for which they have so much potential, owing to a highly localized failure mechanism that results in catastrophic failure during unconfined loading. In this thesis, bulk metallic glass matrix composites are designed with the combined benefits of high yield strengths and tensile ductility. This milestone is achieved by first investigating the length scale of the highly localized deformation, known as shear bands, that governs fracture in all metallic glasses. Under unconfined loading, a shear band grows to a certain length that is dependent on the fracture toughness of the glass before a crack nucleates and fracture occurs. Increasing the fracture toughness and ductility involves adding microstructural stabilization techniques that prevent shear bands from lengthening and promotes formation of multiple shear bands. To accomplish this, we develop in-situ formed bulk metallic glass matrix-composites with soft crystalline dendrites whose size and distribution are controlled through a novel semi-solid processing technique. The new alloys have a dramatically increased room-temperature ductility and a fracture toughness that appears to be similar to the toughest steels. Owing to their low modulus, the composites are therefore among the toughest known materials, a claim that has recently been confirmed independently by a fracture mechanics group. We extend our toughening strategy to a titanium-vanadium-based glass-dendrite composite system with density as low as 4.97 g/cm3. The new low-density composites rival the mechanical properties of the best structural crystalline Ti alloys. We demonstrate new processing techniques available in the highly toughened composites: room temperature cold rolling, work hardening, and thermoplastic forming. This thesis is a proven road map for developing metallic glass composites into real structural engineering materials.

The true toughness of human cortical bone measured with realistically short cracks

Abstract: Bone is more difficult to break than to split. Although this is well known, and many studies exist on the behaviour of long cracks in bone, there is a need for data on the orientation-dependent crack-growth resistance behaviour of human cortical bone that accurately assesses its toughness at appropriate size scales. Here, we use in situ mechanical testing to examine how physiologically pertinent short (<600 microm) cracks propagate in both the transverse and longitudinal orientations in cortical bone, using both crack-deflection/twist mechanics and nonlinear-elastic fracture mechanics to determine crack-resistance curves. We find that after only 500 microm of cracking, the driving force for crack propagation was more than five times higher in the transverse (breaking) direction than in the longitudinal (splitting) direction owing to major crack deflections/twists, principally at cement sheaths. Indeed, our results show that the true transverse toughness of cortical bone is far higher than previously reported. However, the toughness in the longitudinal orientation, where cracks tend to follow the cement lines, is quite low at these small crack sizes; it is only when cracks become several millimetres in length that bridging mechanisms can fully develop leading to the (larger-crack) toughnesses generally quoted for bone.

Mechanical, Fracture, and Microstructural Investigations of Rubber Concrete

Abstract: Waste tire rubber constitute a serious worldwide problem due to the lack of landfills and the health hazards associated with these landfills. In addition to the environmental motivation for providing a means of recycling large quantities of waste tire rubbers, the use of tire rubber particles provides a new type of concrete that has unique mechanical and fracture criteria. This paper presents the results of recent experimental investigations on rubber concrete. Chipped and crumbed tire rubber particles were used to replace coarse and fine aggregate with different volume replacement levels. The mechanical and fracture properties of rubber concrete were examined. Quasi-brittle fracture mechanics models are used to determine the effect of incorporating tire rubber particles on the fracture performance of rubber concrete. Finally, some microstructural features of rubber concrete are also reported. It is concluded that the choice of the optimal replacement ratio of the tire rubber particles can yield concretes with desirable strength and fracture toughness criteria for different applications.

Extended finite element method for fracture analysis of structures

Abstract: Dedication. Preface . Nomenclature . Chapter 1 Introduction. 1.1 ANALYSIS OF STRUCTURES. 1.2 ANALYSIS OF DISCONTINUITIES. 1.3 FRACTURE MECHANICS. 1.4 CRACK MODELLING. 1.4.1 Local and non-local models. 1.4.2 Smeared crack model. 1.4.3 Discrete inter-element crack. 1.4.4 Discrete cracked element. 1.4.5 Singular elements. 1.4.6 Enriched elements. 1.5 ALTERNATIVE TECHNIQUES. 1.6 A REVIEW OF XFEM APPLICATIONS. 1.6.1 General aspects of XFEM. 1.6.2 Localisation and fracture. 1.6.3 Composites. 1.6.4 Contact. 1.6.5 Dynamics. 1.6.6 Large deformation/shells. 1.6.7 Multiscale. 1.6.8 Multiphase/solidification. 1.7 SCOPE OF THE BOOK. Chapter 2 Fracture Mechanics, a Review. 2.1 INTRODUCTION. 2.2 BASICS OF ELASTICITY. 2.2.1 Stress-strain relations. 2.2.2 Airy stress function. 2.2.3 Complex stress functions. 2.3 BASICS OF LEFM. 2.3.1 Fracture mechanics. 2.3.2 Circular hole. 2.3.3 Elliptical hole. 2.3.4 Westergaard analysis of a sharp crack. 2.4 STRESS INTENSITY FACTOR, K . 2.4.1 Definition of the stress intensity factor. 2.4.2 Examples of stress intensity factors for LEFM. 2.4.3 Griffith theories of strength and energy. 2.4.4 Brittle material. 2.4.5 Quasi-brittle material. 2.4.6 Crack stability. 2.4.7 Fixed grip versus fixed load. 2.4.8 Mixed mode crack propagation. 2.5 SOLUTION PROCEDURES FOR K AND G . 2.5.1 Displacement extrapolation/correlation method. 2.5.2 Mode I energy release rate. 2.5.3 Mode I stiffness derivative/virtual crack model. 2.5.4 Two virtual crack extensions for mixed mode cases. 2.5.5 Single virtual crack extension based on displacement decomposition. 2.5.6 Quarter point singular elements. 2.6 ELASTOPLASTIC FRACTURE MECHANICS (EPFM). 2.6.1 Plastic zone. 2.6.2 Crack tip opening displacements (CTOD). 2.6.3 J integral. 2.6.4 Plastic crack tip fields. 2.6.5 Generalisation of J . 2.7 NUMERICAL METHODS BASED ON THE J INTEGRAL. 2.7.1 Nodal solution. 2.7.2 General finite element solution. 2.7.3 Equivalent domain integral (EDI) method. 2.7.4 Interaction integral method. Chapter 3 Extended Finite Element Method for Isotropic Problems. 3.1 INTRODUCTION. 3.2 A REVIEW OF XFEM DEVELOPMENT. 3.3 BASICS OF FEM. 3.3.1 Isoparametric finite elements, a short review. 3.3.2 Finite element solutions for fracture mechanics. 3.4 PARTITION OF UNITY. 3.5 ENRICHMENT. 3.5.1 Intrinsic enrichment. 3.5.2 Extrinsic enrichment. 3.5.3 Partition of unity finite element method. 3.5.4 Generalised finite element method. 3.5.5 Extended finite element method. 3.5.6 Hp-clouds enrichment. 3.5.7 Generalisation of the PU enrichment. 3.5.8 Transition from standard to enriched approximation. 3.6 ISOTROPIC XFEM. 3.6.1 Basic XFEM approximation. 3.6.2 Signed distance function. 3.6.3 Modelling strong discontinuous fields. 3.6.4 Modelling weak discontinuous fields. 3.6.5 Plastic enrichment. 3.6.6 Selection of nodes for discontinuity enrichment. 3.6.7 Modelling the crack. 3.7 DISCRETIZATION AND INTEGRATION. 3.7.1 Governing equation. 3.7.2 XFEM discretization. 3.7.3 Element partitioning and numerical integration. 3.7.4 Crack intersection. 3.8 TRACKING MOVING BOUNDARIES. 3.8.1 Level set method. 3.8.2 Fast marching method. 3.8.3 Ordered upwind method. 3.9 NUMERICAL SIMULATIONS. 3.9.1 A tensile plate with a central crack. 3.9.2 Double edge cracks. 3.9.3 Double internal collinear cracks. 3.9.4 A central crack in an infinite plate. 3.9.5 An edge crack in a finite plate. Chapter 4 XFEM for Orthotropic Problems. 4.1 INTRODUCTION. 4.2 ANISOTROPIC ELASTICITY. 4.2.1 Elasticity solution. 4.2.2 Anisotropic stress functions. 4.2.3 Orthotropic mixed mode problems. 4.2.4 Energy release rate and stress intensity factor for anisotropic. materials. 4.2.5 Anisotropic singular elements. 4.3 ANALYTICAL SOLUTIONS FOR NEAR CRACK TIP. 4.3.1 Near crack tip displacement field (class I). 4.3.2 Near crack tip displacement field (class II). 4.3.3 Unified near crack tip displacement field (both classes). 4.4 ANISOTROPIC XFEM. 4.4.1 Governing equation. 4.4.2 XFEM discretization. 4.4.3 SIF calculations. 4.5 NUMERICAL SIMULATIONS. 4.5.1 Plate with a crack parallel to material axis of orthotropy. 4.5.2 Edge crack with several orientations of the axes of orthotropy. 4.5.3 Single edge notched tensile specimen with crack inclination. 4.5.4 Central slanted crack. 4.5.5 An inclined centre crack in a disk subjected to point loads. 4.5.6 A crack between orthotropic and isotropic materials subjected to. tensile tractions. Chapter 5 XFEM for Cohesive Cracks. 5.1 INTRODUCTION. 5.2 COHESIVE CRACKS. 5.2.1 Cohesive crack models. 5.2.2 Numerical models for cohesive cracks. 5.2.3 Crack propagation criteria. 5.2.4 Snap-back behaviour. 5.2.5 Griffith criterion for cohesive crack. 5.2.6 Cohesive crack model. 5.3 XFEM FOR COHESIVE CRACKS. 5.3.1 Enrichment functions. 5.3.2 Governing equations. 5.3.3 XFEM discretization. 5.4 NUMERICAL SIMULATIONS. 5.4.1 Mixed mode bending beam. 5.4.2 Four point bending beam. 5.4.3 Double cantilever beam. Chapter 6 New Frontiers. 6.1 INTRODUCTION. 6.2 INTERFACE CRACKS. 6.2.1 Elasticity solution for isotropic bimaterial interface. 6.2.2 Stability of interface cracks. 6.2.3 XFEM approximation for interface cracks. 6.3 CONTACT. 6.3.1 Numerical models for a contact problem. 6.3.2 XFEM modelling of a contact problem. 6.4 DYNAMIC FRACTURE. 6.4.1 Dynamic crack propagation by XFEM. 6.4.2 Dynamic LEFM. 6.4.3 Dynamic orthotropic LEFM. 6.4.4 Basic formulation of dynamic XFEM. 6.4.5 XFEM discretization. 6.4.6 Time integration. 6.4.7 Time finite element method. 6.4.8 Time extended finite element method. 6.5 MULTISCALE XFEM. 6.5.1 Basic formulation. 6.5.2 The zoom technique. 6.5.3 Homogenisation based techniques. 6.5.4 XFEM discretization. 6.6 MULTIPHASE XFEM. 6.6.1 Basic formulation. 6.6.2 XFEM approximation. 6.6.3 Two-phase fluid flow. 6.6.4 XFEM approximation. Chapter 7 XFEM Flow. 7.1 INTRODUCTION. 7.2 AVAILABLE OPEN-SOURCE XFEM. 7.3. FINITE ELEMENT ANALYSIS. 7.3.1 Defining the model. 7.3.2 Creating the finite element mesh. 7.3.3 Linear elastic analysis. 7.3.4 Large deformation. 7.3.5 Nonlinear (elastoplastic) analysis. 7.3.6 Material constitutive matrix. 7.4 XFEM. 7.4.1 Front tracking. 7.4.2 Enrichment detection. 7.4.3 Enrichment functions. 7.4.4 Ramp (transition) functions. 7.4.5 Evaluation of the B matrix. 7.5 NUMERICAL INTEGRATION. 7.5.1 Sub-quads. 7.5.2 Sub-triangles. 7.6 SOLVER. 7.6.1 XFEM degrees of freedom. 7.6.2 Time integration. 7.6.3 Simultaneous equations solver. 7.6.4 Crack length control. 7.7 POST-PROCESSING. 7.7.1 Stress intensity factor. 7.7.2 Crack growth. 7.7.3 Other applications. 7.8 CONFIGURATION UPDATE. References . Index

Fracture of Ceramics

Abstract: The paper reviews the current state of art of the fracture of brittle ceramic materials. Typical loading situations (thermal shock, contact damage) are analysed and the resulting fracture modes are discussed. In focus of the paper are the brittle fracture and the resulting probabilistic aspects. The delayed failure of brittle materials (sub critical crack growth and cyclic fatigue) is also discussed.

Constitutive relationships and physical basis of fault strength due to flash heating

Abstract: [1] We develop a model of fault strength loss resulting from phase change at asperity contacts due to flash heating that considers a distribution of contact sizes and nonsteady state evolution of fault strength with displacement. Laboratory faulting experiments conducted at high sliding velocities, which show dramatic strength reduction below the threshold for bulk melting, are well fit by the model. The predicted slip speed for the onset of weakening is in the range of 0.05 to 2 m/s, qualitatively consistent with the limited published observations. For this model, earthquake stress drops and effective shear fracture energy should be linearly pressure-dependent, whereas the onset speed may be pressure-independent or weakly pressure-dependent. On the basis of the theory, flash weakening is expected to produce large dynamic stress drops, small effective shear fracture energy, and undershoot. Estimates of the threshold slip speed, stress drop, and fracture energy are uncertain due to poor knowledge of the average contact dimension, shear zone thickness and gouge particle size at seismogenic depths.

A new crack tip element for the phantom-node method with arbitrary cohesive cracks

Abstract: We have developed a new crack tip element for the phantom node method. In this method, a crack tip can be placed inside an element. Therefore cracks can propagate almost independent of the finite element mesh. We developed two different formulations for the three-node triangular element and four-node quadrilateral element, respectively. Although this method is well suited for the one-point quadrature scheme, it can be used with other general quadrature schemes. We provide some numerical examples for some static and dynamic problems.

The simulation of dynamic crack propagation using the cohesive segments method

Abstract: The cohesive segments method is a finite element framework that allows for the simulation of the nucleation, growth and coalescence of multiple cracks in solids. In this framework, cracks are introduced as jumps in the displacement field by employing the partition of unity property of finite element shape functions. The magnitude of these jumps are governed by cohesive constitutive relations. In this paper, the cohesive segments method is extended for the simulation of fast crack propagation in brittle solids. The performance of the method is demonstrated in several examples involving crack growth in linear elastic solids under plane stress conditions: tensile loading of a block; shear loading of a block and crack growth along and near a bi-material interface.

High‐velocity frictional properties of a clay‐bearing fault gouge and implications for earthquake mechanics

Abstract: [1] Frictional properties of natural kaolinite-bearing gouge samples from the Median Tectonic Line (SW Japan) have been studied using a high-velocity rotary shear apparatus, and deformed samples have been observed with optical and electron (scanning and transmission) microscopy. For a slip velocity of 1 m s−1 and normal stresses from 0.3 to 1.3 MPa, a dramatic slip-weakening behavior was observed. X-ray diffraction analysis of deformed samples and additional high-velocity friction experiments on pure kaolinite indicate kaolinite dehydration during slip. The critical slip-weakening distance Dc is of the order of 1 to 10 m. These values are extrapolated to higher normal stresses, assuming that Dc is rather a thermal parameter than a parameter related to a true characteristic length. The calculation shows that dimensionally, Dc ∝ 1/σn2, where σn is the normal stress applied on the fault. The inferred Dc values range from a few centimeters at 10 MPa normal stress to a few hundreds of microns at 100 MPa normal stress. Microscopic observations show partial amorphization and dramatic grain size reduction (down to the nanometer scale) localized in a narrow zone of about 1 to 10 μm thickness. Fracture energy Gc is calculated from the mechanical curves and compared to surface energy due to grain size reduction, and energies of mineralogic transformations. We show that most of the fracture energy is either converted into heat or radiated energy. The geophysical consequences of thermal dehydration of bonded water during seismic slip are then commented in the light of mineralogical and poromechanical data of several fault zones, which tend to show that this phenomenon has to be taken into account in most of subsurface faults and in hydrous rocks of subducted oceanic crust.

Low-speed fracture instabilities in a brittle crystal

Abstract: Multiscale models predict detailed features of surfaces left by crack propagation and rationalize the occurrence of fracture instabilities in a technologically important material, silicon. As a crack propagates along the most stable cleavage plane in silicon at relatively low speeds (800 metres per second), an instability suddenly appears. The authors find that beyond the very tip of the crack, when fracture speed is slow enough, bonds are broken one atomic layer below the fracture plane leading to a systematic downward deflection of the crack. Conversely, deflecting of fracture on another cleavage plane of silicon occur when the fracture speed is very high. Preliminary simulations reveal that similar instabilities could occur in diamond and silicon carbide. When a brittle material is loaded to the limit of its strength, it fails by the nucleation and propagation of a crack1. The conditions for crack propagation are created by stress concentration in the region of the crack tip and depend on macroscopic parameters such as the geometry and dimensions of the specimen2. The way the crack propagates, however, is entirely determined by atomic-scale phenomena, because brittle crack tips are atomically sharp and propagate by breaking the variously oriented interatomic bonds, one at a time, at each point of the moving crack front1,3. The physical interplay of multiple length scales makes brittle fracture a complex ‘multi-scale’ phenomenon. Several intermediate scales may arise in more complex situations, for example in the presence of microdefects or grain boundaries. The occurrence of various instabilities in crack propagation at very high speeds is well known1, and significant advances have been made recently in understanding their origin4,5. Here we investigate low-speed propagation instabilities in silicon using quantum-mechanical hybrid, multi-scale modelling and single-crystal fracture experiments. Our simulations predict a crack-tip reconstruction that makes low-speed crack propagation unstable on the (111) cleavage plane, which is conventionally thought of as the most stable cleavage plane. We perform experiments in which this instability is observed at a range of low speeds, using an experimental technique designed for the investigation of fracture under low tensile loads. Further simulations explain why, conversely, at moderately high speeds crack propagation on the (110) cleavage plane becomes unstable and deflects onto (111) planes, as previously observed experimentally6,7.

Atomistic Modeling of Materials Failure

Abstract: Basics of Atomistic, Continuum and Multiscale Methods.- Basic Atomistic Modeling.- Basic Continuum Mechanics.- Atomistic Elasticity: Linking Atoms and Continuum.- Multiscale Modeling and Simulation Methods.- Material Deformation and Failure.- Deformation and Dynamical Failure of Brittle Materials.- Deformation and Fracture of Ductile Materials.- Deformation and Fracture Mechanics of Geometrically Confined Materials.

Meso-structural study of concrete fracture using interface elements. I: numerical model and tensile behavior

Abstract: A recently developed FE-based mesostructural model for the mechanical behavior of heterogeneous quasi-brittle materials is used systematically to analyze concrete specimens in 2D. The numerical model is based on the use of zero-thickness interface elements equipped with a normal-shear traction-separation constitutive law representing non-linear fracture, which may be considered a mixed-mode generalization of Hillerborg’s “Fictitious Crack Model.” Specimens with 4 × 4 and 6 × 6 arrays of aggregates are discretized into finite elements. Interface elements are inserted along the main lines in the mesh, representing potential crack lines. The calculations presented in this paper consist of uniaxial tension loading, and the continuum elements themselves are assumed to behave as linear elastic. In this way, the influence of various aspects of the heterogeneous geometry and interface parameters on the overall specimen response has been investigated. These aspects are aggregate volume fraction, type of arrangement and geometry, interface layout, and values of the crack model parameters chosen for both the aggregate-aggregate and matrix-aggregate interfaces. The results show a good qualitative agreement with experimental observations and illustrate the capabilities of the model. In the companion second part of the paper, the model is used to represent other loading states such as uniaxial compression, Brazilian test, or biaxial loading.

Energy dissipation in fracture of bulk metallic glasses via inherent competition between local softening and quasi-cleavage

Abstract: Compression, tension and high-velocity plate impact experiments were performed on a typical tough Zr41.2Ti13.8Cu10Ni12.5Be22.5 (Vit 1) bulk metallic glass (BMG) over a wide range of strain rates from similar to 10(-4) to 10(6) s(-1). Surprisingly, fine dimples and periodic corrugations on a nanoscale were also observed on dynamic mode I fracture surfaces of this tough Vit 1. Taking a broad overview of the fracture patterning of specimens, we proposed a criterion to assess whether the fracture of BMGs is essentially brittle or plastic. If the curvature radius of the crack tip is greater than the critical wavelength of meniscus instability [F. Spaepen, Acta Metall. 23 615 (1975); A.S. Argon and M. Salama, Mater. Sci. Eng. 23 219 (1976)], microscale vein patterns and nanoscale dimples appear on crack surfaces. However, in the opposite case, the local quasi-cleavage/separation through local atomic clusters with local softening in the background ahead of the crack tip dominates, producing nanoscale periodic corrugations. At the atomic cluster level, energy dissipation in fracture of BMGs is, therefore, determined by two competing elementary processes, viz. conventional shear transformation zones (STZs) and envisioned tension transformation zones (TTZs) ahead of the crack tip. Finally, the mechanism for the formation of nanoscale periodic corrugation is quantitatively discussed by applying the present energy dissipation mechanism.

Super-tough silicon nitride with R-curve behavior

Abstract: Silicon nitride with a fracture toughness of 10.6 + or - 0.5 MPa sq rt m has been developed. This tough, nontransforming ceramic exhibits pronounced R-curve behavior. Double cantilever-beam and indentation/strength measurements were used to characterize the R-curve, and good agreement between the two methods was obtained. The high toughness and R-curve behavior of this silicon nitride material is attributed to extensive crack deflection and crack bridging phenomena arising from its unique microstructure. As a result of R-curve behavior, the material exhibits flaw tolerance and is, therefore, characterized by a high Weibull modulus. Furthermore, this ceramic is more damage-tolerant than silicon nitrides with flat crack growth resistance. 19 refs.

Strength, plasticity and brittleness of bulk metallic glasses under compression: statistical and geometric effects

Abstract: To investigate the flaw sensitivity and reliability of bulk metallic glasses (BMGs), compressive testing was performed on a statistically significant number of specimens. Despite the fact that BMGs exhibit little or no macroscopic plasticity before failure (similar to other brittle materials), we observe surprisingly high uniformity in compressive strength. Weibull analysis was employed to study the statistical dispersion in strength, giving very high Weibull moduli of about 25 for an intrinsically brittle glass, and near 75 for an intrinsically malleable one. This high uniformity is encouraging for the use of BMGs in structural applications. Furthermore, we illustrate that subtle imperfections in the test geometry (i.e. miscut or deviations from orthogonality) dramatically affect the compression response. In brittle glasses these act as failure-critical flaws, whereas in malleable glasses they constrain shear bands, lead to tilting and bending during testing, and give rise to misleading macroscopic measu...

Damage mechanisms and lifetime behavior of plasma-sprayed thermal barrier coating systems for gas turbines — Part II: Modeling

Abstract: Detailed damage analyses of a plasma sprayed ZrO 2 /8 wt–% Y 2 O 3 –MCrAlY–CMSX-4 TBC system during isothermal and cyclic oxidation tests with different dwell times at high temperature have been performed The resulting failure mode, ie the particular delamination crack path, is strongly dependent on the temperature cycle applied Isothermal exposure promotes crack propagation within the TGO, whereas thermal cycling shifts the crack path towards the TBC Thermal cycling with dwell time at high temperature leads to a mixed delamination crack path (partly within TBC and TGO) The respective correlation between TBC lifetimes and duration of high temperature dwell time per cycle (cycle frequency) is shown and discussed