Analysis of an Orthotropic Deck Stiffened with a Cement-Based Overlay

Over the past years, with increasing traffic volumes and higher wheel loads, fatigue damage in steel parts of typical orthotropic steel bridge decks has been experienced on heavily trafficked routes. A demand exists to find a durable system to increase the fatigue safety of orthotropic steel bridge decks. A solution might be to enhance the stiffness of the traditional orthotropic bridge deck by using a cement-based overlay. In this paper, an orthotropic steel bridge deck stiffened with a cement-based overlay is analyzed. The analysis is based on nonlinear fracture mechanics, and utilizes the finite-element method. The stiffness of the steel deck reinforced with an overlay depends highly on the composite action. The composite action is closely related to cracking of the overlay and interfacial cracking between the overlay and underlying steel plate (debonding). As an example, a real size structure, the Far? bridges located in Denmark, are analyzed. The steel box girders of the Far? bridges spans 80?m, and have a depth of 3.5?m, and a width of 19.5?m. The focus of the present study is the top part of the steel box girders, which is constructed as an orthotropic deck plate. Numerous factors can influence the cracking behavior of the cement-based overlay system. Both mechanical and environmental loading have to be considered, and effects such as shrinkage, temperature gradients, and traffic loading are taken into account. The performance of four overlay materials are investigated in terms of crack widths. Furthermore, the analysis shows that debonding is initiated for a certain crack width in the overlay. The load level where cracking and debonding is initiated depends on the stress-crack opening relationship of the material.     

The role of metal plasticity and interfacial strength in the cracking of metal/ceramic laminates

Two models based on elastic-plastic fracture mechanics and fiber bridging are developed to study the role of plastic yielding in metals and the interfacial strength of metal/ceramic laminates. There are two types of damage observed in metal/ceramic laminates: multiple cracking and macroscopic crack propagation. The former occurs around the macroscopic crack tip and thus distributes the damage and enhances the composite's toughness. The present models establish that there exists a critical metal/ceramic layer thickness ratio above which multiple cracking dominates and that this ratio decreases (hence increasing the possibility of multiple cracking) as the ratios of metal yield stress over ceramic strength, metal modulus over ceramic modulus, and metal/ceramic interfacial strength over ceramic strength increase. Good agreement between the present models and experimental results is observed for both damage modes, i.e. multiple cracking vs macroscopic crack propagation, and for critical stress intensity factors. The elastic-plastic fracture mechanics and fiber-bridging models predict that multiple cracking is ensured if the metal layer thickness is 2.5 times larger than the ceramic layer thickness, regardless of the metal/ceramic properties.     

Fracture Toughness to Understand Stretch-Flangeability and Edge Cracking Resistance in AHSS

The edge fracture is considered as a high risk for automotive parts, especially for parts made of advanced high strength steels (AHSS). The limited ductility of AHSS makes them more sensitive to the edge damage. The traditional approaches, such as those based on ductility measurements or forming limit diagrams, are unable to predict this type of fractures. Thus, stretch-flangeability has become an important formability parameter in addition to tensile and formability properties. The damage induced in sheared edges in AHSS parts affects stretch-flangeability, because the generated microcracks propagate from the edge. Accordingly, a fracture mechanics approach may be followed to characterize the crack propagation resistance. With this aim, this work addresses the applicability of fracture toughness as a tool to understand crack-related problems, as stretch-flangeability and edge cracking, in different AHSS grades. Fracture toughness was determined by following the essential work of fracture methodology and stretch-flangeability was characterized by means of hole expansions tests. Results show a good correlation between stretch-flangeability and fracture toughness. It allows postulating fracture toughness, measured by the essential work of fracture methodology, as a key material property to rationalize crack propagation phenomena in AHSS.     

冲击荷载下岩石裂纹扩展研究进展

为了给深部资源开采和大型地下空间工程中围岩体的变形机理及稳定性控制提供理论基础,通过查阅大量关于表征岩石裂纹扩展的裂纹扩展模型、应力强度因子和断裂韧性的国内外文献,总结了前人的研究成果。依据现有研究,提出了动荷载作用下岩石裂纹扩展的几点建议：（1）综合考虑弹性力学、断裂力学和损伤力学建立岩石材料从微观断裂到宏观破坏这一演变过程的理论模型,使理论模型更加适应岩石材料的非线性特征;（2）采用分形、自组织和混沌等非线性理论表征动荷载作用下岩石内部以及表面裂纹的扩展演化特征;（3）采用颗粒离散元和有限差分模拟岩石材料裂纹扩展演化特征。     

Crack deflection processes—I. Theory

A fracture mechanics approach has been used to predict fracture toughness increases due to crack deflection around second phase particles. The analysis is based on a determination of the initial tilt and the maximum twist of the crack front between particles, which provides the basis for evaluating the deflection-induced reduction in crack driving force. Features found to be important in determining the toughness increase include the volume fraction of second phase, the particle morphology and aspect ratio, and the distribution of interparticle spacing. Predictions are compared with expected surface area increases.     

Effects of microstructure on the strength and fatigue behavior of a silicon carbide fiber-reinforced titanium matrix composite and its constituents

The results of a systematic study of the effects of microstructure on the strength and fatigue behavior of a symmetric [0/90]_2s Ti-15Al-3Cr-3Al-3Sn/SiC (SCS-6) composite are presented along with relevant information on failnure mechanisms in the composite constituents, i.e., the interface, fiber, and matrix materials. Damage micromechanisms are elucidated via optical microscopy, scanning electron microscopy (SEM), and nondestructive acoustic emission (AE) and ultrasonic techniques. Composite damage is shown to initiate early under cyclic loading conditions and is dominated by longitudinal and transverse interfacial cracking. Subsequent fatigue damage occurs by matrix slip band formation, matrix and fiber cracking, and crack coalescence, prior to the onset of catastrophic failure. However, the sequence of the damage is different in material annealed above or below the β solvus of the Ti-15-3 matrix material. Mechanistically based micromechanics models are applied to the prediction of the changes in modulus induced by fatigue damage. Idealized fracture mechanics models are also employed in the prediction of the fatigue lives of smooth specimens deformed to failure at room temperature. The article highlights the potential to develop mechanistically based predictive models based on simplified mechanics idealizations of experimental observations.     

Crack branching in carbon steel. Fracture mechanisms

The fracture surfaces of pressure vessels made of carbon steel that form during crack branching propagation are examined by fractography. Crack branching is found to occur at a crack velocity higher than a certain critical value V > V _c . In this case, the material volume that is involved in fracture and depends on the elastoplastic properties of the material and the sample width has no time to dissipate the energy released upon crack motion via the damage mechanisms intrinsic in the material under given deformation conditions (in our case, via cracking according to intragranular cleavage).     

Distributed Thermal Cracking of AC Pavement with Frictional Constraint

This paper develops a model to simulate the distributed thermal cracking of concrete structures with frictional constraint. This model is developed primarily for the thermal cracking asphalt-concrete (AC) pavement structures; however, with some modifications, it is also applicable to similar problems such as shrinkage cracking of concrete and cracking of reinforced concrete in uniaxial tension. This model reflects the multiscale nature of these problems: microcracking or damage on the mesoscale and localization or redistribution on the macroscale. Randomly distributed fictitious cracks are introduced to represent the inhomogeneities and damage in the material at the mesoscale. Friction is recognized as the mechanism leading to stress redistribution and, therefore, damage localization on the macroscale. When the problem is assumed to be 1D and Coulomb friction is used, a semianalytical numerical scheme is developed. The formation of stress-free open cracks is due to the combination of continuous crack growth and unstable jumps, which involve a nonlinear stability analysis. Equilibrium solutions and stability conditions are given in the paper. Displacement controlled analysis is used to follow the unstable equilibrium path after the structure has lost stability. Numerical simulations clearly show that, with slight mesoscale inhomogeneities and in the presence of a constraining frictional force, microcracking or damage on the mesoscale localizes and finally leads to open cracks distributed at a spacing on the order of the macroscale.     

Mechanisms of hydrogen induced delayed cracking in hydride forming materials

Mechanisms which have been formulated to describe delayed hydrogen cracking in hydride-forming metals are reviewed and discussed. Particular emphasis is placed on the commercial alloy Zr-2.5 pct Nb (Cb) which is extensively used in nuclear reactor core components. A quantitative model for hydrogen cracking in this material is presented and compared with available experimental data. The kinetics of crack propagation are controlled by the growth of hydrides at the stressed crack tip by the diffusive ingress of hydrogen into this region. The driving force for the diffusion flux is provided by the local stress gradient which interacts with both hydrogen atoms in solution and hydrogen atoms being dissolved and reprecipitated at the crack tip. The model is developed using concepts of elastoplastic fracture mechanics. Stage I crack growth is controlled by hydrides growing in the elastic stress gradient, while Stage II is controlled by hydride growth in the plastic zone at the crack tip. Recent experimental observations are presented which indicate that the process occurs in an intermittent fashion; hydride clusters accumulate at the crack tip followed by unstable crack advance and subsequent crack arrest in repeated cycles.     

Thermal stress fracture of refractory lining components: Part III. Analysis of Fracture

The fracture behavior of refractory components heated from one end is simulated using a twodimensional constant heating rate thermoelastic model and the maximum principal tensile stress fracture criterion. Dimensionless graphical relationships that can be used to predict location of fracture and orientation of cracking are presented. Dimensional analysis and the finite element numerical method are used to develop a general solution for the total strain energy. Based on the premise that extent of crack propagation is directly related to available strain energy at fracture and inversely related to the surface energy per unit area, the solution for total strain energy is used to derive a damage resistance parameter useful for the design and selection of refractory components that accounts for material properties, geometry, and heating and cooling rate. Model predictions of location of fracture, orientation of cracking, and extent of crack propagation are in general agreement with experimental results previously reported in the literature. Limitations of the two-dimensional thermoelastic model are discussed.     

Computational Constitutive Model for Predicting Nonlinear Viscoelastic Damage and Fracture Failure of Asphalt Concrete Mixtures

A computational constitutive model was developed to predict damage and fracture failure of asphalt concrete mixtures. Complex heterogeneity and inelastic mechanical behavior are addressed by the model by using finite-element methods and elastic–viscoelastic constitutive relations. Damage evolution due to progressive cracking is represented by randomly oriented interface fracture, which is governed by a newly developed nonlinear viscoelastic cohesive zone model. Computational simulations demonstrate that damage evolution and failure of asphalt concrete mixtures is dependent on the mechanical properties of the mixture. This approach is suitable for the relative evaluation of asphalt concrete mixtures by simply employing material properties and fracture properties of mixture components rather than by performing expensive laboratory tests recursively, which are typically required for continuum damage mechanics modeling.     

A strain-based fracture model for stress corrosion cracking of low-alloy steels

The stress corrosion cracking (SCC) behavior of 4135 steel under different heat treatments is analyzed in an attempt to relate microstructural characteristics with macroscopic measurements of SCC resis-tance, especially the very impressive improvements associated with changes from intergranular (IG) to transgranular (TG) fracture paths. Considering that local hydrogen embrittlement at the crack tip causes SCC processes, a local cracking criterion, based on a critical strain depending on hydrogen concentration, is assumed to control the process. Stress corrosion cracking is viewed as a discontin-uous series of unstable crack extensions through the locally embrittled regions. The model developed on this basis explains the macroscopic behavior observed at the threshold situation and partially at stage II propagation and clarifies the role of the metallurgical variables in each of the types of fracture detected.     

Multiple-cracking phenomenon of the galvannealed coating layer on steels under thermal and tensile stresses

The multiple-cracking phenomenon of the Fe-Zn intermetallic coating layer on the hot-dip galvannealed (GA) steels under thermal and tensile stresses was studied experimentally by tensile tests and analytically by means of the finite-element analysis. The multiple cracking of the coating layer had occurred in the as-supplied samples, and it progressed with increasing applied strain. Based on the calculated dependence of the stress of the coating layer on the crack spacing and applied strain, the multiple cracking in the as-supplied samples was accounted for by the thermally induced residual stress, and the further multiple cracking with increasing applied strain was accounted for by the increased stress of the coating layer. The experimentally observed decrease of the average crack spacing with increasing applied strain was described well, and the tensile strength of the coating layer was estimated to be 260 MPa, by application of the calculated relation between the increased stress of the coating layer and applied strain. The influences of the thickness of the coating layer and the substrate material on the multiple cracking were discussed based the stress analysis. It was revealed that the thinner the coating layer and the higher the flow stress of the substrate, the higher the stress of the coating layer becomes and, therefore, the smaller the crack spacing becomes.     

Use of Material Interfaces in DEM to Simulate Soil Fracture Propagation in Mode I Cracking

Mode I fracture is common in geomechanics in desiccation cracking, hydraulic fracture, and pressuremeter testing. The cohesive crack model has been used extensively and successfully in numerical modeling of such fracture in concrete and steel but has not been applied in modeling of soil fracture to the same extent. It is argued that the cohesive crack model may be more appropriate than linear elastic fracture mechanics (LEFM) for soils because it takes into account finite tensile strength and any likely plasticity during fracture. With special reference to the Universal Distinct Element Code (UDEC) computer program, a methodology of using interfaces in the distinct element method (DEM) of analysis to model fracture has been validated herein, and this approach is considered to be useful in geomechanical modeling applications. The methodology is based on the cohesive crack approach and shows how softening laws could be back-calculated from load-displacement curves of test specimens. It has been validated using three geometries: a tension test with a rectangular cross section, a notched three-point bend beam, and a compact tension test. Approximate softening laws for St. Albans clay from Canada are proposed.     

Toward a Physical Damage Variable for Concrete

Continuum damage mechanics models, while elegant and useful, suffer from what are typically highly idealized relationships between model and material. In this technical note, using three-dimensional (3D) measurements of internal cracking, direct, albeit simple relationships were made between the quantity of cracking and a corresponding scalar damage variable. Geometric properties of internal cracks were measured through 3D image analysis of in situ microtomographic scans of small concrete specimens subject to compression. A scalar damage variable was determined from the changes in stiffness measured in successive loading cycles. Results showed a nearly linear relationship between the damage variable and the volume of new cracks formed. In contrast, results showed a nonlinear relationship between the damage variable and the crack surface area. Such relationships can potentially lead to a more physical basis for continuum damage formulations.     

Numerical Simulation of Ductile Fracture Based on Local Approach Concept

In this paper a finite-element analysis on ductile fracture in two-dimensional quasi-static state is performed by using the local approach concept in continuum damage mechanics. An isotropic damage model based on the generalized concept of effective stress is proposed. Crack propagation is achieved by removing critically damaged elements. The finite-element approximation of a largely deforming body based on the incremental total Lagrangian concept is carried out. As numerical examples, the mesh size sensitivity analysis and the simulation of the shearing mode failure in plane strain state are carried out to verify the present formulation qualitatively. For an edge cracked plate under plane stress state, load-displacement curves and successively fractured shapes are shown. It can be concluded that the proposed model may be stated as a reasonable tool to explain ductile fracture initiation and crack propagation.     

The interaction between deformation,fracture initiation and fracture propagation in two phase Co-CoAl alloys

Fracture initiation and propagation in two phase alloys containing fairly large volume fractions of nonplastically deforming inclusions have been analyzed. The Argon, Im and Safoglu treatment of fracture initiation of elastic inclusions as a result of back stresses resulting from strain accommodation of the phases has been extended to relatively large volume fractions of second phase. This allows calculation of the distribution of fractured particles as a function of alloy strain provided the fracture stress of the elastically deforming phase is known. The analysis has been applied to the Co-CoAl two phase alloy for volume fractions of CoAl ranging from about two to twenty-five pct. Quantitative metallographic analysis of fractured specimens indicates very good agreement between the measured fraction of fractured particles and those predicted from the theory without recourse to any adjustable parameters. Critical crack propagation in alloys of this type can also be analyzed on the basis of a fracture mechanics approach of Rice which was modified to consider that the crack spacing decreases with increasing strain due to cumulative hard phase cracking. The tensile strengths of the alloys can then be predicted with recourse to one adjustable parameter which varies with hard phase volume fraction. The deduced variation of this parameter with hard phase volume fraction, however, is as expected. Formerly graduate student, Michigan Technological University, Houghton, MI. Formerly Postdoctoral Research Associate, Michigan Technological University.     

N80套管射孔性能的断裂韧性判据及验证

射孔性能是油层套管很重要的一项指标,它代表着油层套管抵抗裂纹脆性扩展的能力。文章利用射孔开裂分析的断裂力学模型,对模拟射孔后的油层套管进行了分析,建立了能满足射孔性能要求的断裂韧性判据,并通过试验进行了验证。     

Fracture behaviours of fracture toughness testing specimens with metallurgical heterogeneity along crack front

Safe use of welded structures is dependent on fracture mechanics properties of welded joints. In present research, high strength low alloyed HSLA steel in a quenched and tempered condition, corresponding to the grade HT 80, was used. The fluxo cored arc welding process (FCAW), with CO₂ as shielding gas, was used and two different tubular wires were selected. The aim of this paper is to analyse fracture behaviour of undermatched welded joints, and also to determine relevant parameters which contribute to higher critical values of fracture toughness. Towards this end three differently undermatched welded joints were analysed using results of testing the composite notched specimens with through thickness crack front positioned partly in the weld metal, partly in heat affected zone (HAZ) and partly in base material (BM).The presence of different microstructures along the pre‐crack fatigue front has an important effect on the critical crack tip opening displacement (CTOD). This value is the relevant parameter for safe service of welded structure. In the case of specimens with through thickness notch partly in the weld metal, partly in the heat affected zone and partly in the base material, i.e. using the composite notched specimen, fracture behaviour strongly depends on a partition of ductile base material, size and distribution of mismatching factor along vicinity of crack front. If local brittle zones occur in the process zone, ductile base metal can not prevent pop‐in instability, but it can reduce it to an insignificant level while the fracture toughness parameter is higher and the weakest link concept can not be applied.     

Peridynamic Analysis of Impact Damage in Composite Laminates

The traditional methods for analyzing deformation in structures attempt to solve the partial differential equations of the classical theory of continuum mechanics. Yet these equations, because they require the partial derivatives of displacement to be known throughout the region modeled, are in some ways unsuitable for the modeling of discontinuities caused by damage, in which these derivatives fail to exist. As a means of avoiding this limitation, the peridynamic model of solid mechanics has been developed for applications involving discontinuities. The objective of this method is to treat crack and fracture as just another type of deformation, rather than as pathology that requires special mathematical treatment. The peridynamic theory is based on integral equations so there is no problem in applying the equations across discontinuities. The peridynamic method has been applied successfully to damage and failure analysis in composites. It predicts in detail the delamination and matrix damage process in composite laminates due to low velocity impact, and the simulation results of damage area correlates very well with the experimental data.