Showing papers on "Fracture mechanics published in 2007"

Progressive damage modeling in fiber-reinforced materials

Abstract: This paper presents an anisotropic damage model suitable for predicting failure and post-failure behavior in fiber-reinforced materials. In the model the plane stress formulation is used and the response of the undamaged material is assumed to be linearly elastic. The model is intended to predict behavior of elastic-brittle materials that show no significant plastic deformation before failure. Four different failure modes – fiber tension, fiber compression, matrix tension, and matrix compression – are considered and modeled separately. The onset of damage is predicted using Hashin’s initiation criteria [Hashin Z, Rotem A. A fatigue failure criterion for fiber-reinforced materials. J Compos Mater 1973;7:448; Hashin Z. Failure criteria for unidirectional fiber composites. J Appl Mech 1980;47:329–34] and the progression of damage is controlled by a new damage evolution law, which is easy to implement in a finite element code. The evolution law is based on fracture energy dissipation during the damage process and the increase in damage is controlled by equivalent displacements. The issues related to numerical implementation, such as mesh sensitivity and convergence in the softening regime, are also addressed.

On the Vickers Indentation Fracture Toughness Test

Abstract: The Vickers indentation fracture toughness test, or VIF, is addressed by considering its origins and the numerous equations that have been applied along with the technique to estimate the fracture resistance, or the KIc of ceramics. Initiation and propagation of cracks during the VIF test are described and contrasted with the pre-cracking and crack growth for internationally standardized fracture toughness tests. It is concluded that the VIF test technique is fundamentally different than standard fracture toughness tests. The VIF test has a complex three-dimensional crack system with substantial deformation residual stresses and damage around the cracks. The VIF test relates to an ill-defined crack arrest condition as opposed to the rapid crack propagation of the standardized fracture toughness tests. Previously published fracture toughness results employing the VIF technique are reviewed. These reveal serious discrepancies in reported VIF fracture toughness values. Finally, recent fracture resistance measurements by the VIF technique for the Standard Reference Material SRM 2100 are presented. These are compared with standardized test results for the same material. It is concluded that the VIF technique is not reliable as a fracture toughness test for ceramics or for other brittle materials. What the VIF actually measures in terms of fracture resistance cannot be readily defined. It is recommended that the VIF technique no longer be acceptable for the fracture toughness testing of ceramic materials.

Simulation of delamination in composites under high-cycle fatigue

Abstract: A damage model for the simulation of delamination propagation under high-cycle fatigue loading is proposed. The basis for the formulation is a cohesive law that links fracture and damage mechanics to establish the evolution of the damage variable in terms of the crack growth rate dA/dN. The damage state is obtained as a function of the loading conditions as well as the experimentally-determined coefficients of the Paris law crack propagation rates for the material. It is shown that by using the constitutive fatigue damage model in a structural analysis, experimental results can be reproduced without the need of additional model-specific curve-fitting parameters.

A three-dimensional meshfree method for continuous multiple-crack initiation, propagation and junction in statics and dynamics

Abstract: This paper proposes a three-dimensional meshfree method for arbitrary crack initiation and propagation that ensures crack path continuity for non-linear material models and cohesive laws. The method is based on a local partition of unity. An extrinsic enrichment of the meshfree shape functions is used with discontinuous and near-front branch functions to close the crack front and improve accuracy. The crack is hereby modeled as a jump in the displacement field. The initiation and propagation of a crack is determined by the loss of hyperbolicity or the loss of material stability criterion. The method is applied to several static, quasi-static and dynamic crack problems. The numerical results very precisely replicate available experimental and analytical results.

A meshfree method based on the local partition of unity for cohesive cracks

Abstract: We will present a meshfree method based on the local partition of unity for cohesive cracks. The cracks are described by a jump in the displacement field for particles whose domain of influence is cut by the crack. Particles with partially cut domain of influence are enriched with branch functions. Crack propagation is governed by the material stability condition. Due to the smoothness and higher order continuity, the method is very accurate which is demonstrated for several quasi static and dynamic crack propagation examples.

A Model of the Fracture of Double Network Gels

Abstract: I propose a very simple model accounting for the very high toughness of double network gels based on the assumption that the first, stiff network will break up forming multiple cracks when the stress is above a defined value. These cracks are held together by the second network. A multiply cracked damage zone will form around any macroscopic crack in the material, causing energy dissipation and shielding the second network. The toughness enhancement by this process is estimated to be about ×40. The effect of cross-linking of the second network is discussed and explained.

Breakage mechanics—Part II: Modelling granular materials

Abstract: The compression of granular materials has been traditionally modelled with the limitations of classical elasto-plasticity. The energy was implicitly assumed to dissipate from the frictional interaction of particles. However, the fact that brittle granular materials crush suggests that energy must also be dissipated from the fracturing of the grains, as in fracture mechanics. The concept of breakage as a thermomechanical internal variable was introduced in Part I [Einav, I., 2006. Breakage mechanics—Part I: theory. J. Mech. Phys. Solids 00,000–000] to describe the fracturing mechanisms. The theory allows to treat ideal theoretical materials that undergo dissipation purely from breakage with no other mechanism allowed for the energy consumption. However, as accounted for in elasto-plasticity, dissipation must also occur from the frictional rearrangement of grains. The combination of the two dissipative mechanisms of breakage and plasticity must therefore be investigated, as we do in this paper. Those two mechanisms are generally coupled, in the sense that one inevitably appears when the other develops. Plastic dissipation emerges as a by-product of breakage dissipation because after grains crush, local rearrangement must occur. This scenario may be termed an ‘active breakage mechanism’, and typifies compression deformations. In shear the plastic dissipation is dominant but breakage appears inevitably from grains abrasion. This scenario may be called a ‘passive breakage mechanism’. Based on the coupling assumption, models are developed for granular materials. In particular, we show that in compression isotropic hardening of sands may appear without involving plastic strains, i.e., independent of frictional dissipation. This interpretation of hardening is different from the one used in classical critical state soil mechanics. However, frictional dissipation leads to plastic straining that are necessary for the models to be predictive in unloading.

Hindered Crack Propagation in Materials with Periodically Varying Young's Modulus—Lessons from Biological Materials†

Abstract: Many biological materials, such as bone, nacre or biosilica, are known to be both stiff and tough. Their structure is hierarchical and appears to be optimized at all levels of hierarchy to combine the properties of its primary components, which are a tough protein and stiff mineral. Bone, for example, is a nanocomposite and the deformation pattern is clearly hierarchical. In lamellar cortical bone, fibrillar units aggregate into laminate sheets, in analogy to plywood. This lamellar structure has a dramatic effect on fracture toughness. Nacre and biosilica are also layered structures where thin organic layers separate sheets of aragonite mineral and biosilica, respectively. The high toughness of such layered biological structures is intriguing and may serve as a model for artificial layered composites. A possible origin for the toughness in layered structures is the deflection of racks at weak interfaces. However, we know from theoretical fracture mechanics that a variation of the material properties alone (even without inherently weak interfaces) may result in a shielding or anti-shielding effect to the crack tip, which leads to a change of the crack driving force and the energy consumed by the fracture process. In the current work, we therefore analyse the driving force onto cracks propagating inside a material where the Young’s modulus varies in a periodic way in a given direction (perpendicular to the lamellae). We derive a simple design criterion to obtain laminate structures without driving force for crack propagation perpendicular to the lamellae. We consider a crack in a plane configuration of unit thickness with the crack tip located at the point P, see Figure 1. Globally, the material is assumed to be elastic with a constant Young’s modulus Efar and a Poisson’s ratio m far away from the crack tip P. Inside a circular region with the radius R, however, the Young’s modulus E varies in space. We assume that this variation is periodic in x-direction with an average value E0. The specimen is loaded by a stress ∑ in y-direction on the upper and lower parts of the boundary Cfar (indicated as “o” and “u” in Fig. 1). The crack flanks are assumed to be stressfree. The stress field r near the crack tip T is described by the classical “near-tip field” expressed in polar coordinates r,h and the stress intensity factor KI, for details see the fracture mechanics literature, e.g., Gross et al., Ch. 4.2. The specific elastic strain energy density r e 2 can be calculated analytically for constant E and plane stress or strain conditions as

Cyclic Void Growth Model to Assess Ductile Fracture Initiation in Structural Steels due to Ultra Low Cycle Fatigue

Abstract: A new model is proposed to simulate ductile fracture initiation due to large amplitude cyclic straining in structural steels, which is often the governing limit state in steel structures subjected to earthquakes. Termed the cyclic void growth model (CVGM), the proposed technique is an extension to previously published models that simulate ductile fracture caused by void growth and coalescence under monotonic loading. The CVGM aims to capture ultra low cycle fatigue (ductile fracture) behavior, which is characterized by a few (generally, less than 20) reverse loading cycles to large inelastic strain amplitudes (several times the yield strain). The underlying mechanisms of low-cycle fracture involve cyclic void growth, collapse, and distortion, which are distinct from those associated with more conventional fatigue. The CVGM represents these underlying fracture mechanisms through plastic strain and stress triaxiality histories that can be modeled at the material continuum level by finite-element analyses. Development and validation of the CVGM is substantiated by about 100 notched bar tests, with accompanying finite-element analyses, metallurgical tests, and fractographic examinations of seven varieties of structural steels.

Fracture propagation as means of rapidly transferring surface meltwater to the base of glaciers

Abstract: [1] Propagation of water-filled crevasses through glaciers is investigated based on the linear elastic fracture mechanics approach. A crevasse will penetrate to the depth where the stress intensity factor at the crevasse tip equals the fracture toughness of glacier ice. A crevasse subjected to inflow of water will continue to propagate downward with the propagation speed controlled primarily by the rate of water injection. While the far-field tensile stress and fracture toughness determine where crevasses can form, once initiated, the rate of water-driven crevasse propagation is nearly independent of these two parameters. Thus, rapid transfer of surface meltwater to the bed of a cold glacier requires abundant ponding at the surface to initiate and sustain full thickness fracturing before refreezing occurs.

Concrete fracture prediction using bilinear softening

Abstract: A finite element-based cohesive zone model was developed using bilinear softening to predict the monotonic load versus crack mouth opening displacement curve of geometrically similar notched concrete specimens. The softening parameters for concrete material are based on concrete fracture tests, total fracture energy (GF), initial fracture energy (Gf), and tensile strength ( f t ′ ) , which are obtained from a three-point bending configuration. The features of the finite element model are that bulk material elements are used for the uncracked regions of the concrete, and an intrinsic-based traction-opening constitutive relationship for the cracked region. Size effect estimations were made based on the material dependent properties (Gf and f t ′ ) and the size dependent property (GF). Experiments using the three-point bending configuration were completed to verify that the model predicts the peak load and softening behavior of concrete for multiple specimen depths. The fracture parameters, based on the size effect method or the two-parameter fracture model, were found to adequately characterize the bilinear softening model.

A study of the representation of cracks with level sets

Abstract: The level set method has been used for a few years to represent cracks in fracture mechanics simulations instead of an explicit description of the cracks faces geometry. This paper studies in detail the shape of the level set functions around a crack in two dimensions that is propagating with a sharp kink, obtained both with level set update methods found in the literature and with several innovative update methods developed by the author. A criterion based on the computation of a J integral of a virtual displacement field obtained with the values of the level set functions is proposed in order to assess the quality of these update methods. With the help of this criterion, two optimal approaches are identified, which predict an accurate evolution of the crack with smooth and consistent level set functions. These methods are then applied in three dimensions to the case of an initially penny-shaped crack that propagates out of its plane. Copyright © 2006 John Wiley & Sons, Ltd.

Fatigue Crack Propagation in Metals and Alloys - Microstructural Aspects and Modelling Concepts

Abstract: Foreword. Preface. Symbols and Abbreviations. 1 Introduction. 2 Basic Concepts of Metal Fatigue and Fracture in the Engineering Design Process. 2.1 Historical Overview. 2.2 Metal Fatigue, Crack Propagation and Service-Life Prediction: A Brief Introduction. 2.2.1 Fundamental Terms in Fatigue of Materials. 2.2.2 Fatigue-Life Prediction: Total-Life and Safe-Life Approach. 2.2.3 Fatigue-Life Prediction: Damage-Tolerant Approach. 2.2.4 Methods of Fatigue-Life Prediction at a Glance. 2.3 Basic Concepts of Technical Fracture Mechanics. 2.3.1 The K Concept of LEFM. 2.3.2 Crack-Tip Plasticity: Concepts of Plastic-Zone Size. 2.3.3 Crack-Tip Plasticity: The J Integral. 3 Experimental Approaches to Crack Propagation. 3.1 Mechanical Testing. 3.1.1 Testing Systems. 3.1.2 Specimen Geometries. 3.1.3 Local Strain Measurement: The ISDG Technique. 3.2 Crack-Propagation Measurements. 3.2.1 Potential-Drop Concepts and Fracture Mechanics Experiments. 3.2.2 In Situ Observation of the Crack Length. 3.3 Methods of Microstructural Analysis and Quantitative Characterization of Grain and Phase Boundaries. 3.3.1 Analytical SEM: Topography Contrast to Study Fracture Surfaces. 3.3.2 SEM Imaging by Backscattered Electrons and EBSD. 3.3.3 Evaluation of Kikuchi Patterns: Automated EBSD. 3.3.4 Orientation Analysis Using TEM and X-Ray Diffraction. 3.3.5 Mathematical and Graphical Description of Crystallographic Orientation Relationships. 3.3.6 Microstructure Characterization by TEM. 3.3.7 Further Methods to Characterize Mechanical Damage Mechanisms in Materials. 3.4 Reproducibility of Experimentally Studying the Mechanical Behavior of Materials. 4 Physical Metallurgy of the Deformation Behavior of Metals and Alloys. 4.1 Elastic Deformation. 4.2 Plastic Deformation by Dislocation Motion. 4.3 Activation of Slip Planes in Single- and Polycrystalline Materials. 4.4 Special Features of the Cyclic Deformation of Metallic Materials. 5 Initiation of Microcracks. 5.1 Crack Initiation: Definition and Significance. 5.1.1 Influence of Notches, Surface Treatment and Residual Stresses. 5.2 Influence of Microstructual Factors on the Initiation of Fatigue Cracks. 5.2.1 Crack Initiation at the Surface: General Remarks. 5.2.2 Crack Initiation at Inclusions and Pores. 5.2.3 Crack Initiation at Persistent Slip Bands. 5.3 Crack Initiation by Elastic Anisotropy. 5.3.1 Definition and Significance of Elastic Anisotropy. 5.3.2 Determination of Elastic Constants and Estimation of the Elastic Anisotropy. 5.3.3 FE Calculations of Elastic Anisotropy Stresses to Predict Crack Initiation Sites. 5.3.4 Analytical Calculation of Elastic Anisotropy Stresses. 5.4 Intercrystalline and Transcrystalline Crack Initiation. 5.4.1 Influence Parameters for Intercrystalline Crack Initiation. 5.4.2 Crack Initiation at Elevated Temperature and Environmental Effects. 5.4.3 Transgranular Crack Initiation. 5.5 Microstructurally Short Cracks and the Fatigue Limit. 5.6 Crack Initiation in Inhomogeneous Materials: Cellular Metals. 6 Crack Propagation: Microstructural Aspects. 6.1 Special Features of the Propagation of Microstructurally Short Fatigue Cracks. 6.1.1 Definition of Short and Long Cracks. 6.2 Transgranular Crack Propagation. 6.2.1 Crystallographic Crack Propagation: Interactions with Grain Boundaries. 6.2.2 Mode I Crack Propagation Governed by Cyclic Crack-Tip Blunting. 6.2.3 Influence of Grain Size, Second Phases and Precipitates on the Propagation Behavior of Microstructurally Short Fatigue Cracks. 6.3 Significance of Crack-Closure Effects and Overloads. 6.3.1 General Idea of Crack Closure During Fatigue-Crack Propagation. 6.3.2 Plasticity-Induced Crack Closure. 6.3.3 Influence of Overloads in Plasticity-Induced Crack Closure. 6.3.4 Roughness-Induced Crack Closure. 6.3.5 Oxide- and Transformation-Induced Crack Closure. 6.3.6 &delta K/K max Thresholds: An Alternative to the Crack-Closure Concept. 6.3.7 Development of Crack Closure in the Short Crack Regime. 6.4 Short and Long Fatigue Cracks: The Transition from Mode II to Mode I Crack Propagation. 6.4.1 Development of the Crack Aspect Ratio a/c. 6.4.2 Coalescence of Short Cracks. 6.5 Intercrystalline Crack Propagation at Elevated Temperatures: The Mechanism of Dynamic Embrittlement. 6.5.1 Environmentally Assisted Intercrystalline Crack Propagation in Nickel-Based Superalloys: Possible Mechanisms. 6.5.2 Mechanism of Dynamic Embrittlement as a Generic Phenomenon: Examples. 6.5.3 Oxygen-Induced Intercrystalline Crack Propagation: Dynamic Embrittlement of Alloy 718. 6.5.4 Increasing the Resistance to Intercrystalline Crack Propagation by Dynamic Embrittlement: Grain-Boundary Engineering. 7 Modeling Crack Propagation Accounting for Microstructural Features. 7.1 General Strategies of Fatigue Life Assessment. 7.2 Modeling of Short-Crack Propagation. 7.2.1 Short-Crack Models: An Overview. 7.2.2 Model of Navarro and de los Rios. 7.3 Numerical Modeling of Short-Crack Propagation by Means of a Boundary Element Approach. 7.3.1 Basic Modeling Concept. 7.3.2 Slip Transmission in Polycrystalline Microstructures. 7.3.3 Simulation of Microcrack Propagation in Synthetic Polycrystalline Microstructures. 7.3.4 Transition from Mode II to Mode I Crack Propagation. 7.3.5 Future Aspects of Applying the Boundary Element Method to Short-Fatigue-Crack Propagation. 7.4 Modeling Dwell-Time Cracking: A Grain-Boundary Diffusion Approach. 8 Concluding Remarks. References. Subject Index.