Showing papers on "Fracture mechanics published in 1998"

Plastic-Damage Model for Cyclic Loading of Concrete Structures

Abstract: A new plastic-damage model for concrete subjected to cyclic loading is developed using the concepts of fracture-energy-based damage and stiffness degradation in continuum damage mechanics. Two damage variables, one for tensile damage and the other for compressive damage, and a yield function with multiple-hardening variables are introduced to account for different damage states. The uniaxial strength functions are factored into two parts, corresponding to the effective stress and the degradation of elastic stiffness. The constitutive relations for elastoplastic responses are decoupled from the degradation damage response, which provides advantages in the numerical implementation. In the present model, the strength function for the effective stress is used to control the evolution of the yield surface, so that calibration with experimental results is convenient. A simple and thermodynamically consistent scalar degradation model is introduced to simulate the effect of damage on elastic stiffness and its recovery during crack opening and closing. The performance of the plastic-damage model is demonstrated with several numerical examples of simulating monotonically and cyclically loaded concrete specimens.

Dynamic Fracture Mechanics

Abstract: Preface List of symbols 1. Background and overview 2. Basic elastodynamic solutions for a stationary crack 3. Further results for a stationary crack 4. Asymptotic fields near a moving crack tip 5. Energy concepts in dynamic fracture 6. Elastic crack growth at constant speed 7. Elastic crack growth at nonuniform speed 8. Plasticity and rate effects during crack growth Bibliography Index.

Introduction to Composite Materials Design

Abstract: Introduction Basic Concepts The Design Process Composites Design Methods Design for Reliability Fracture Mechanics Materials Fiber Reinforcements Fiber-Matrix Compatibility Fiber Forms Matrix Materials Thermoset Matrices Thermoplastic Matrices Creep, Temperature, and Moisture Corrosion Resistance Flammability Manufacturing Processes Hand Lay-up Pre-preg Lay-up Bag Molding Autoclave Processing Compression Molding Resin Transfer Molding Vacuum Assisted Resin Transfer Molding Pultrusion Filament Winding Micro-mechanics Basic Concepts Stiffness Moisture and Thermal Expansion Strength Ply Mechanics Coordinate Systems Stress and Strain Stress-Strain Equations Off-axis Stiffness Macro-mechanics Plate Stiffness and Compliance Computation of Stresses Common Laminate Types Laminate Moduli Design Using Carpet Plots Hygro-thermal Stresses (*) Strength Lamina Failure Criteria Laminate First Ply Failure Laminate Strength Strength Design Using Carpet Plots Stress Concentrations (*) Damage Continuum Damage Mechanics Longitudinal Tensile Damage Longitudinal Compression Damage Transverse Tension and In-plane Shear Fabric-reinforced Composites Weave Pattern Description Analysis Tow Properties Element Stiffness and Constitutive Relationship Laminate Properties Failure Analysis Woven Fabrics with Gap Twill and Satin Randomly Oriented Reinforcement Beams Preliminary Design Thin Walled Beams Plates and Stiffened Panels Plate Bending Plate Buckling Stiffened Panels Shells Shells of Revolution Cylindrical Shells with General Loading Strengthening of Reinforced Concrete Strengthening Design Materials Flexural Strengthening of RC Beams Shear Strengthening Beam-column Appendices Bibliography

Fatigue Assessment of Welded Joints by Local Approaches

Abstract: Introduction Nominal stress approach for welded joints Structural stress or strain approach for seam-welded joints Notch stress approach for seam-welded joints Notch strain approach for seam-welded joints Crack propagation approach for seam-welded joints Notch stress intensity approach for seam-welded joints Local approaches applied to a seam-welded tubular joint Structural stress or strain approach for spot-welded and similar lap joints Stress intensity approach for spot-welded and similar lap joints Notch stress, notch strain and crack propagation approach for spot-welded and similar lap joints Significance, limitations and potential of local approaches.

Progressive Delamination Using Interface Elements

Abstract: The paper describes a method for modelling progressive mixed-mode delamination in fibre composites. The procedure, which is incorporated within the non-linear finite element method, is based on the use of interface elements in conjunction with softening relationships between the stresses and the relative displacements. Fracture mechanics is indirectly introduced by relating the areas under the stress/displacement curves to the critical fracture energies.

Impact-induced delamination of composites: A 2D simulation

Abstract: The delamination process in thin composite plates subjected to low-velocity impact is simulated using a specially developed 2D cohesive/volumetric finite element scheme. Cohesive elements are introduced along the boundaries of the inner layers and inside the transverse plies to simulate the spontaneous initiation and propagation of transverse matrix cracks and delamination fronts. The analysis is performed within the framework of the finite deformation theory of elasticity to account for the nonlinear stiffening of the thin composite plate and the large rotations which accompany the fracture process. The simulation is dynamic and uses an explicit time stepping scheme. Comparison with existing experiments performed on graphite/epoxy laminates indicates that the cohesive/volumetric finite element scheme is able to capture the complex mechanisms leading to the delamination, including the initial micro-cracking of the matrix, the appearance of critical transverse matrix cracks and the rapid propagation of delamination cracks initiated at the intersections between the critical matrix cracks and the adjacent plies.

Indentation Damage and Mechanical Properties of Human Enamel and Dentin

Abstract: Understanding the mechanical properties of human teeth is important to clinical tooth preparation and to the development of "tooth-like" restorative materials. Previous studies have focused on the macroscopic fracture behavior of enamel and dentin. In the present study, we performed indentation studies to understand the microfracture and deformation and the microcrackmicrostructure interactions of teeth. It was hypothesized that crack propagation would be influenced by enamel rods and the dentino-enamel junction (DEJ), and the mechanical properties would be influenced by enamel rod orientation and tooth-to-tooth variation. Twenty-eight human third molars were used for the measurement of hardness, fracture toughness, elastic modulus, and energy absorbed during indentation. We examined the effect of enamel rod orientation by propagating cracks in the occlusal surface, and in the axial section in directions parallel and perpendicular to the occlusal surface. The results showed that the cracks in the enamel a...

Solution of Crack Problems: The Distributed Dislocation Technique

Abstract: Preface. 1. Introduction to Fracture Mechanics. 2. Distributed Dislocation Fundamentals. 3. Further Topics in Plane Crack Problems. 4. Interface Cracks. 5. Solution of Axi-Symmetric Crack Problems. 6. Three-Dimensional Cracks: An Introduction. 7. Three-Dimensional Cracks: Further Concepts. 8. Concluding Remarks. A: Dislocation Influence Functions. B: Numerical Solution of SIEs with Cauchy Kernel. C: Plane and Ring Dipole Influence Functions. D: Contour Integral and Kernel Function. References. Index.

Numerical simulation of crack growth in an isotropic solid with randomized internal cohesive bonds

Abstract: A virtual internal bond (VIB) model with randomized cohesive interactions between material particles is proposed as an integration of continuum models with cohesive surfaces and atomistic models with interatomic bonding. This approach differs from an atomistic model in that a phenomenological “cohesive force law” is assumed to act between “material particles” which are not necessarily atoms; it also differs from a cohesive surface model in that, rather than imposing a cohesive law along a prescribed set of discrete surfaces, a randomized network of cohesive bonds is statistically incorporated into the constitutive law of the material via the Cauchy-Born rule, i.e., by equating the strain energy function on the continuum level to the potential energy stored in the cohesive bonds due to an imposed deformation. This work is motivated by the notion that materials exhibit multiscale cohesive behaviors ranging from interatomic bonding to macroscopic ductile failure. It is shown that the linear elastic behavior of the VIB model is isotropic and obeys the Cauchy relation; the instantaneous elastic properties under equibiaxial stretching are transversely isotropic, with all the in-plane components of the material tangent moduli vanishing at the cohesive stress limit; the instantaneous properties under equitriaxial stretching are isotropic with a finite strain modulus. We demonstrate through two preliminary numerical examples that the VIB model can be applied in direct simulation of crack growth without a presumed fracture criterion. The prospect of this type of approach in numerical simulations of fracture seems to be highly promising.

Cell model for nonlinear fracture analysis – I. Micromechanics calibration

Abstract: A computational approach based on a cell model of material offers real promise as a predictive tool for nonlinear fracture analysis A key feature of the computational model is the modeling of the material in front of the crack by a layer of similarly-sized cubic cells Each cell of size D contains a spherical void of initial volume fraction f 0 The microseparation characteristics of the material in a cell, a result of void growth and coalescence, is described by the Gurson–Tvergaard constitutive relation; the material outside the layer of cells can be modelled as an elastic- plastic continuum The success of this computational model hinges on developing a robust calibration scheme of the model parameters Such a scheme is proposed in this study The material-specific parameters are calibrated by a two-step micromechanics/fracture-process scheme This article describes the micromechanics calibration of void growth taking into account both the strain hardening and the strength of the material The fracture-process calibration is addressed in a companion paper

Quasicontinuum simulation of fracture at the atomic scale

Abstract: We study the problem of atomic scale fracture using the recently developed quasicontinuum method in which there is a systematic thinning of the atomic-level degrees of freedom in regions where they are not needed. Fracture is considered in two distinct settings. First, a study is made of cracks in single crystals, and second, we consider a crack advancing towards a grain boundary (GB) in its path. In the investigation of single crystal fracture, we evaluate the competition between simple cleavage and crack-tip dislocation emission. In addition, we examine the ability of analytic models to correctly predict fracture behaviour, and find that the existing analytical treatments are too restrictive in their treatment of nonlinearity near the crack tip. In the study of GB-crack interactions, we have found a number of interesting deformation mechanisms which attend the advance of the crack. These include the migration of the GB, the emission of dislocations from the GB, and deflection of the crack front along the GB itself. In each case, these mechanisms are rationalized on the basis of continuum mechanics arguments.

Experimental analysis of desiccation crack propagation in clay liners

Abstract: A laboratory investigation on a scaled model of a landfill liner was conducted to provide data regarding the occurrence and extent of desiccation cracking of prototype liners. The crack intensity factor, CIF, was introduced as a descriptor of the extent of surficial cracking. CIF is defined as the ratio of the surface crack area A, to the total surface area of the clay liner, At. A computer aided image analysis program was used to determine CII’ values from scanned photographs of the desiccation process. The variation of the CII’ was related to duration of drying and measured soil moisture suctions. The soil of this investigation experienced significant cracking, with crack widths approaching 10 mm in the first drying cycle and penetration through the entire 16 cm thickness. Crack propagation was limited to a very intense period of the desiccation process. Nearly 90 percent of the crack development occurred during a 19-hour time period, although the total duration of the desiccation cycle was approximately 170 hours. The soil moisture suction changed by only 2 bars during the period of rapid crack growth, although it changed by more than 40 bars during the period of reduced growth.

Load interaction effects during fatigue crack growth under variable amplitude loading : A literature review. Part I : Empirical trends

Abstract: A summary is given of reported trends in fatigue crack growth observed in variable amplitude fatigue tests on metallic materials, specifically on steels, under both simple and complex load histories. The effects of load variables, specimen geometry, material properties, microstructure and environment are considered. Attention is given to the threshold behaviour and small crack effects. The reviewed data suggest that, depending on a particular combination of load parameters, material, geometry and environment, variable amplitude load sequences of the same type can produce either retardation or acceleration in fatigue crack growth.

Mixed Mode Fracture of Concrete under Proportional and Nonproportional Loading

Abstract: A novel testing procedure for mixed mode crack propagation in concrete is presented: four point bend of notched beams under the action of two independent force actuators. In contrast to classical procedures, this method allows nonproportional loading and crack trajectory modifications by changing the action of one actuator. Different experimental crack trajectories, under mixed mode and nonproportional loading, are presented together with the corresponding curves of load-CMOD and load-displacement. The tests were performed for three homotetic specimen sizes and two mixed mode loading conditions. The results are useful for checking the accuracy of mixed mode fracture analytical and numerical models. The models should predict the crack trajectory and a complete group of experimental records of load and displacements on several control points in the specimen.

Axisymmetric adhesion tests of soft materials

Abstract: We describe a general, linearized fracture mechanics analysis for studying the adhesive properties of elastic, low modulus materials Several adhesion tests are described, but all involve an elastic material which is brought into contact with a rigid surface along an axis of radial symmetry Relationships between the load, displacement, and radius of the circular contact area between the two materials are described These relationships involve the elastic modulus of the compliant material, the energy release rate (or adhesion energy) and various parameters which characterize the geometry of interest The ratio of the contact radius to the thickness of the elastic material is shown to be a particularly important parameter After reviewing some general concepts relevant to the adhesion of soft polymeric materials, we describe the fracture mechanics analysis, and provide examples from our own work on the adhesion of elastomers, thermoreversible gels and pressure sensitive adhesives

Nonlinear Fracture Mechanics for Engineers

Abstract: Overview Introduction Classification of Fracture Mechanics Regimes History of Developments in Fracture Mechanics Review of Solid Mechanics Stress Strain Elasticity Plasticity Consideration of Creep Component Analysis in the Plastic Regime Fully Plastic/Limit Loads Review of Linear Elastic Fracture Mechanics Basic Concepts Crack Tip Plasticity Compliance Relationships Fracture Toughness and Predictive Fracture in Components Subcritical Crack Growth Limitations of LEFM Analysis of Cracks under Elastic-Plastic Conditions Introduction Rice's J-Integral J-Integral, Crack Tip Stress Fields, and Crack Tip Opening Displacement J-Integral as a Fracture Parameter and Its Limitations Methods of Estimating J-Integral Analytical Solutions J-Integral for Test Specimens J for Growing Cracks Numerically Obtained Solutions Tables of J-Solutions Crack Growth Resistance Curves Fracture Parameters under Elastic-Plastic Loading Experimental Methods for Determining Stable Crack Growth and Fracture Special Considerations for Weldments Instability, Dynamic Fracture, and Crack Arrest Fracture Instability Fracture under Dynamic Conditions Crack Arrest Test Methods for Dynamic Fracture and Crack Arrest Constraint Effects and Microscopic Aspects of Fracture Higher Order Terms of Asymptotic Series Cleavage Fracture Ductile Fracture Ductile-Brittle Transition Fatigue Crack Growth under Large-Scale Plasticity Crack Tip Cyclic Plasticity, Damage, and Crack Closure ?J-Integral Test Methods for Characterizing FCGR under Large Plasticity Conditions Behavior of Small Cracks Analysis of Cracks in Creeping Materials Stress Analysis of Cracks Under Steady-State Creep Analysis of Cracks under Small-Scale and Transition Creep Consideration of Primary Creep Effects of Crack Growth on the Crack Tip Stress Fields Crack Growth in Creep-Brittle Materials Creep Crack Growth Test Methods for Characterizing Creep Crack Growth Microscopic Aspects of Creep Crack Growth Creep Crack Growth in Weldments Creep-Fatigue Crack Growth Early Approaches for Characterizing Creep-Fatigue Crack Growth Behavior Time-Dependent Fracture Mechanics Parameters for Creep-Fatigue Crack Growth Methods of Determining (Ct)avg Experimental Methods for Characterizing Creep Crack Growth Creep-Fatigue Crack Growth Correlations Case Studies Applications of Fracture Mechanics Fracture Mechanics Analysis Methodology Case Studies Appendices Index

Numerical modeling of fracture coalescence in a model rock material

Abstract: The crack pattern, as well as crack initiation, -propagation and -coalescence observed in experiments on gypsum specimens with pre-existing fractures in uniaxial, biaxial, and tensile loading are satisfactorily predicted with the numerical model presented in this paper. This was achieved with a new stress-based crack initiation criterion which is incorporated in FROCK, a Hybridized Indirect Boundary Element method first developed by Chan et al. (1990). The basic formulation of FROCK is described, and the code verified for both open and closed pre-existing fractures either with only friction or with friction and cohesion. The new initiation criterion requires only three material properties: σcrit, the critical strength of the material in tension; τcrit, the critical strength of the material in shear; r0, the size of the plastic zone. The three parameters can be determined with the results from only one test. Predictions using this model are compared with experiments on gypsum specimens with pre-existing fractures loaded in uniaxial and biaxial compression performed by the authors. Specifically, wing crack and shear crack initiation, crack propagation, coalescence stress and -type as well as the crack pattern up to coalescence can be modeled. The model can also duplicate experimental results in compression and tension obtained by other researchers. These results show that stress-based criteria can be effectively used in modeling crack initiation and crack coalescence.

Dynamic Fracture of Nominally Brittle Materials

Abstract: Current understanding of dynamic fracture mechanisms and the methods of modeling are reviewed critically. Experimental methods used in dynamic fracture investigations and key experimental observations are reviewed. This is followed by a critical review of the dynamic fracture models. Mechanistic and phenomenological models as well as discrete and continuum models and their ability to reproduce experimental results are discussed.