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The prediction of nominal strength is very important in the design and evaluation of materials especially polymer matrix composites. Various cohesive laws forms are successfully used in predicting the nominal strength of laminated composite structures. For composite structures, fracture toughness is dominated parameter when using cohesive laws to predict their nominal strength. In spite of complex reported models, this study propose an easy simple model to predict the fracture toughness of multidirectional composite laminates using the fracture toughness of the 0 ply ones. This model is mainly based on the geometry of fiber orientation and linear elastic fracture mechanics and uses the fracture toughness of the 0 ply obtained from compact tension test specimens. A good prediction is obtained by comparing the model results with experimental data which are obtained from center-cracked specimens manufactured using different lay-ups orientations and materials. POLYM. ENG. SCI., 54:234-238, 2014. [C] 2013 Society of Plastics Engineers, INTRODUCTION The prediction of nominal strength of composites structure take care a lot of investigations because of its importance in design of aerospace and automobile (1-3). Some analytical models have [...]

Untreated multiwalled carbon nanotubes (MWCNTs) were incorporated into a brittle epoxy matrix at 1 wt% by solvent evaporation and showed significant gains in tensile strength, strain at break, and electrical conductivity. However, only fractional improvement in fracture toughness was observed. To improve fracture toughness, 10 pm polyamide-12 (PA) preformed particles were added at 20 wt% loading. The PA particles were observed to aid in the dispersion of MWCNTs, reducing most of the large MWCNT clusters to submicron sizes. The epoxy/PA/MWCNT ternary composite exhibits an increased electrical percolation threshold, but nearly identical electrical scaling behavior as the epoxy/ MWCNT composite. The similarity in percolation parameters suggest conduction occurs by efficient electron transport through MWCNT clusters, rather than pathways composed of individual tubes. The ternary composite also shows significant improvements in strain at break and fracture toughness due to synergistic interaction between filler phases. The usefulness of this ternary composite approach in vacuum-assisted resin transfer molding for advanced composite applications is discussed. POLYM. ENG. SCI., 51:2245-2253, 2011. © 2011 Society of Plastics Engineers, INTRODUCTION Epoxy resins have been used as high performance polymers because of their excellent mechanical properties, chemical resistance, and thermal stability, but require a second phase conductive filler material in [...]

Statistical analysis based on two-parameter Weibull distribution was applied to poly(acrylonitrile-butadiene-styrene) to characterize involvement of two damage types in tensile test specimens, which appear as tiny strips and uniform whitening, respectively. Analysis using Weibull distribution suggests that the probability density functions (PDF) for extension at break and total energy consumption (named toughness) give distinctively different characteristics between the two damage types. PDF curve for the tiny strips consists of a sharp peak, whereas that for the uniform whitening a broad hump. Using two-group mixed Weibull distribution, effect of pre-existing damage on the fracture process was examined. The PDF curves show that presence of one damage type (e.g., uniform whitening) tends to suppress generation of the other damage type (e.g., tiny strips) even in a test condition that would have favored the latter in virgin specimens. Involvement of the two damage types was quantified using portion for each subpopulation from the Weibull distribution analysis. POLYM. ENG. SCI., 51:573-584, 2011. [C]2011 Society of Plastics Engineers, INTRODUCTION Fracture resistance of polymers, often referred to as toughness, is an area of great interest to many research groups. Nature of 'ductile' or 'brittle' fracture is not absolute for [...]

Splitting failure modes of perpendicular to grain bolted connections have received little attention when compared to splitting modes in parallel to grain connections. Previous research by the authors tested a series of single bolt, double shear perpendicular to grain connections of machine stress rated (MSR) lumber, laminated veneer lumber (LVL), and parallel strand lumber (PSL). Many of the experimental tests resulted in failure by splitting. Two fracture mechanics based models for connections proposed elsewhere were applied. Input parameters for the models were generated by testing matched sections to the connection strength samples. Input properties for the Van der Put model included shear modulus and Mode I fracture energy. Inputs for the Jensen model included shear modulus, modulus of elasticity, Mode I fracture energy, and tension perpendicular to grain strength. Mode I fracture energy of PSL was markedly greater than the energy associated with MSR Lumber and LVL. The Van der Put model overpredicted the experimental connection strength by at least 77%. The Jensen model was found to most accurately predict the connection strength over the entire range of configurations tested. Comparing the Van der Put and Jensen models to the previous work using the national design specification, the Jensen model performed the best in terms of accuracy. The tension perpendicular to grain strength and the method of fracture energy calculation may be important parameters for the capacity of perpendicular to grain loaded wood members. DOI: 10.1061/(ASCE)MT.1943-5533.0000141 CE Database subject headings: Wood; Cracking; Connections; Composite beams; Dowels. Author keywords: Wood beams.

High Cr ferritic heat resisting steels have been widely used for boiler components in ultrasupercritical thermal power plants operated at about 600[degrees]C. In the welded joint of these steels, type-IV crack initates in the fine-grained heat affected zone during long-term use at high temperatures and their creep strength decreases. In this paper, creep properties and creep crack growth (CCG) properties of P92 welds are presented. The CCG tests are carried out using cross-welded compact tension C(T) specimens at several temperatures. The crack front was located within the fine-grained HAZ region to simulate type-IV cracking. Finite element analysis was conducted to simulate multiaxiality in welded joints and to compare experimental results. The constitutive behavior for these materials is described by a power-law creep model [C.sup.*] and [Q.sup.*] parameters are used to evaluate CCG rate of P92 welds for comparison. [C.sup.*] parameters can characterize approximately 20% of the total life of CCG in P92 welds, and [Q.sup.*] parameters can characterize approximately 80% of the total life. [Q.sup.*] parameter is one of the useful parameters to predict CCG life in P92 welds. [DOI: 10.1115/1.4001522]

Whereas considerable interest exists in self-assembly of well-ordered, porous 'inverse opal' structures for optical, electronic, and (bio)chemical applications, uncontrolled defect formation has limited the scale-up and practicality of such approaches. Here we demonstrate a new method for assembling highly ordered, crack-free inverse opal films over a centimeter scale. Multilayered composite colloidal crystal films have been generated via evaporative deposition of polymeric colloidal spheres suspended within a hydrolyzed silicate sol-gel precursor solution. The coassembly of a sacrificial colloidal template with a matrix material avoids the need for liquid infiltration into the preassembled colloidal crystal and minimizes the associated cracking and inhomogeneities of the resulting inverse opal films. We discuss the underlying mechanisms that may account for the formation of large-area defect-free films, their unique preferential growth along the (110) direction and unusual fracture behavior. We demonstrate that this coassembly approach allows the fabrication of hierarchical structures not achievable by conventional methods, such as multilayered films and deposition onto patterned or curved surfaces. These robust Si[O.sub.2] inverse opals can be transformed into various materials that retain the morphology and order of the original films, as exemplified by the reactive conversion into Si or Ti[O.sub.2] replicas. We show that colloidal coassembly is available for a range of organometallic sol-gel and polymer matrix precursors, and represents a simple, low-cost, scalable method for generating high-quality, chemically tailorable inverse opal films for a variety of applications. coassembly | colloidal assembly | crack-free films | inverse opals | nanoporous doi/ 10.1073/pnas.1000954107

The results of research initiated in the early 1980s led to the replacement of plasticity-based design guidelines for the load-carrying capacity of headed anchors embedded in concrete with those developed using fracture mechanics. While provisions are available in the design codes that account for the presence of tensile fields causing concrete cracking, no provisions are available for anchors embedded in prestressed concrete. This paper presents the results of linear elastic fracture mechanics (LEFM) analyses and of a preliminary experimental investigation of the progressive failure of headed anchors embedded in a concrete matrix under compressive or tensile prestress. The model predicts an increase (decrease) in load-carrying capacity and ductility with increasing compressive (tensile) prestress. It is shown that despite neglecting the dependence on size of concrete fracture toughness, LEFM predicts with remarkable accuracy the functional dependence of the ultimate capacity on prestress. DOI: 10.1061/(ASCE)EM.1943-7889.0000120 CE Database subject headings: Anchors; Axisymmetry; Finite element method; Prestressed concrete; Cracking; Tensile strength. Author keywords: Headed anchors.

[1] Transform motion along oceanic transforms generally occurs along narrow faults zones. Another class of oceanic transforms exists where the plate boundary is quite large (~100 km) and includes several subparallel faults. Using a 2-D numerical modeling, we simulate the slip distribution and the crustal stress field geometry within such broad oceanic transforms (BOTs). We examine the possible configurations and evolution of such BOTs, where the plate boundary includes one, two, or three faults. Our experiments show that at any time during the development of the plate boundary, the plate motion is not distributed along each of the plate boundary faults but mainly occurs along a single master fault. The finite width of a BOT results from slip transfer through time with locking of early faults, not from a permanent distribution of deformation over a wide area. Because of fault interaction, the stress field geometry within the BOTs is more complex than that along classical oceanic transforms and includes stress deflections close to but also away from the major faults. Application of this modeling to the 100 km wide Tjornes Fracture Zone (TFZ) in North Iceland, a major BOT of the Mid-Atlantic Ridge that includes three main faults, suggests that the Dalvik Fault and the Husavik-Flatey Fault developed first, the Grismsey Fault being the latest active structure. Since initiation of the TFZ, the Husavik-Flatey Fault accommodated most of the plate motion and probably persists until now as the main plate structure. Citation: Homberg, C., F. Bergerat, J. Angelier, and S. Garcia (2010), Fault interaction and stresses along broad oceanic transform zone: Tjornes Fracture Zone, north Iceland, Tectonics, 29, TC 1002, doi: 10.1029/2008TC002415.

If multiple discrete flaws are detected that are in close proximity to one another, alignment rules are used to determine whether the flaws should be treated as nonaligned or as coplanar. Alignment rules are defined in many fitness-for-service codes and standards in the world. However, the criteria of the alignment rules are different in these codes and standards. This paper introduces the current alignment rules and, in addition, interaction of stress intensity factors for nonaligned through-wall flaws was calculated by finite element analysis. Also, brittle fracture experiments were performed on carbon steel plates with two nonaligned flaws. From these calculations and experiments, authors studied the effect of stress intensity factor interaction on fracture behavior and proposed a new alignment rule ,for linear elastic fracture mechanics evaluation. [DOI: 10.1115/1.3152229]

Problem statement: The use of fracture mechanics techniques in the assessment of performance and reliability of structure is on increase and the prediction of crack propagation in structure play important part. The finite element method is widely used for the evaluation of SIF for various types of crack configurations. Source code program of two-dimensional finite element model had been developed, to demonstrate the capability and its limitations, in predicting the crack propagation trajectory and the SIF values under linear elastic fracture analysis. Approach: Two different geometries were used on this finite element model in order, to analyze the reliability of this program on the crack propagation in linear and nonlinear elastic fracture mechanics. These geometries were namely; a rectangular plate with crack emanating from square-hole and Double Edge Notched Plate (DENT). Where, both geometries are in tensile loading and under mode I conditions. In addition, the source code program of this model was written by FORTRAN language. Therefore, a Displacement Extrapolation Technique (DET) was employed particularly, to predict the crack propagations directions and to, calculate the Stress Intensity Factors (SIFs). Furthermore, the mesh for the finite elements was the unstructured type; generated using the advancing front method. And, the global h-type adaptive mesh was adopted based on the norm stress error estimator. While, the quarter-point singular elements were uniformly generated around the crack tip in the form of a rosette. Moreover, make a comparison between this current study with other relevant and published research study. Results: The application of the source code program of 2-D finite element model showed a significant result on linear elastic fracture mechanics. Based on the findings of the two different geometries from the current study, the result showed a good agreement. And, it seems like very close compare to the other published results. Conclusion: A developed a source program of finite element model showed that is capable of demonstrating the SIF evaluation and the crack path direction satisfactorily. Therefore, the numerical finite element analysis with displacement extrapolation method, had been successfully employed for linear-elastic fracture mechanics problems. Key words: Finite element, linear elastic fracture mechanics, adaptive refinement, stress intensity factors, finite element, INTRODUCTION The use of fracture mechanics techniques in the assessment of performance and reliability of structure is on increase and the prediction of crack propagation in structure play important part. [...]

Gluing of fiber reinforced polymer (FRP) strips by a structural adhesive into thin slits cut in the cover of reinforced concrete (RC) beams' lateral faces is a shear strengthening technique that is gaining increasing attention of the FRP community. Nonetheless, certain aspects related to the failure modes affecting the behavior at ultimate of such near surface mounted (NSM) strips need to be clarified. Recent findings have spotlighted that besides debonding and tensile rupture of the strips, another possible failure mode should be considered, which involves the fracture of concrete in the shape of semicones along the strips. Thus, a comprehensive analytical model accounting for all of those failure modes was recently developed for predicting the NSM contribution to RC beams shear capacity. Despite its consistency with experimental recordings, that model still needs improvement since some aspects related to the interaction between the force transferred by bond to the surrounding concrete and its tensile fracture still need to be clarified. The need to improve that analytical model led us to further address the issues regarding the debonding failure mode affecting the behavior, at ultimate, of a NSM FRP strip. A new local bond stress-slip relationship is proposed and closed-form equations to be implemented in that analytical model are derived and appraised on the basis of some of the most recent experimental results available in the literature. DOI: 10.1061/(ASCE)0733-9445(2009)135:6(619) CE Database subject headings: Shear strength; Bonding; Concrete beams; Cracking.

During the last two decades, several research efforts have focused on the thermal cracking behavior of asphalt binders. Recently, important low-temperature cracking models have been introduced to include the failure properties and thermovolumetric properties at low temperatures. The main objective of this study is to evaluate selected modified asphalt binders in terms of low-temperature failure and related thermovolumetric properties. The effect of modification on fracture failure properties and related thermovolumetric properties of asphalt binder was determined by laboratory testing. The low-temperature cracking temperatures using the collected laboratory testing data were predicted. The focus of this study is on how commonly used asphalt modifiers affect the failure and thermovolumetric properties for a wide temperature range, in particular at low temperatures. Efforts were also made in this study to put more emphasis on the consideration of strain criterion, the effect of cooling rate, and nonlinearity of the coefficient of thermal contraction of asphalt binders into the prediction of low temperature cracking. The results indicate that modification of asphalt binders can have significant effects on their properties and predicted thermal cracking temperatures. The findings also suggest that in order to have a better understanding of binder behavior, the use of both failure and thermovolumetric properties is necessary. DOI: 10.1061/(ASCE)0899-1561(2009)21:5(198) CE Database subject headings: Asphalts; Binders, materials; Cracking; Temperature effects; Failures.

Solar silicon wafers are mainly produced through multiwire-sawing. This sawing implies microcracks on the wafer surface, which are responsible for brittle fracture. In order to reduce the sawing-induced cracks, the wafers are damage etched after sawing. This paper develops a model for the impact of crack length manipulation on fracture stress distribution. It investigates the effect of damage-etching on the mechanical properties of solar silicon wafers. The main idea is to transform the fracture stress distribution into a crack length intensity function and to model the effect of etching in terms of crack lengths. The fracture stress distribution is determined statistically by fracture tests of wire-sawn and sawn and etched wafers. The Griffith criterion then enables the transition to crack lengths and crack length intensity functions. Two numerical parameters, called truncation parameter and scaling parameter, determine this relationship and enable a quantitative description of the effect of etching. They turn out to be dependent on etchant and geometry of load and thus tested crack population. [DOI: 10.1115/1.3028048] Keywords: fracture theory, fracture stress, etching, silicon wafer, strength, Weibull distribution

Diffusive mass transfer between fracture and matrix accompanied with sorption significantly influences the efficiency of natural attenuation in hard rocks. While these processes have extensively been studied in a fractured formation, limited information exists on the sorption nonlinearity. For this purpose, a numerical model is developed that couples matrix diffusion and nonlinear sorption at the scale of a single fracture using the dual-porosity concept. The study is limited to a constant continuous solute source boundary condition. The influence of both favorable and unfavorable sorption intensities on solute mobility is investigated using the method of spatial moments. The differing capacities of available sorption sites between fracture surfaces at the fracture-matrix interface and the solid grain surfaces within the rock matrix result in a slower migration of solutes along the fracture, and a larger amount of diffusive mass transfer away from the high permeability fracture. DOI: 10.1061/(ASCE)0733-9372(2009) 135:1 (1) CE Database subject headings: Mass transfer; Sorption; Numerical models; Spatial analysis; Rocks.

This paper presents the results of a numerical study undertaken to assess the influence of residual stresses on the ductile tearing behavior of a high strength low toughness aluminum alloy. The Gurson-Tvergaard model was calibrated against conventional fracture toughness data using parameters relating to void nucleation, growth, and coalescence. The calibrated model was used to predict the load versus ductile tearing behavior of a series of full-scale and quarter-scale wide-plate tests. These center-cracked tension tests included specimens that contained a self-balancing residual stress field that was tensile in the region of the through-wall crack. Analyses of the full-scale wide-plate tests indicated that the model provides a good prediction of the load versus the ductile tearing behavior up to approximately 3 mm of stable tearing. The influence of residual stress on the load versus the crack growth behavior was accurately simulated. Predictions of the load versus the crack growth behavior of full-scale wide-plate tests for crack extensions greater than 3 mm and of the quarter-scale tests were low in terms of predicted load at a given amount of tearing. This was considered to result from (i) the 'valid' calibration range in terms of specimen thickness and crack extension, (ii) the development of shear lips, and (iii) the differences in the micromechanism of ductile void formation under plane strain and under plane stress conditions. [DOI: 10.111511.2967876] Keywords: ductile fracture, residual stresses, fracture mechanics, damage mechanics, Gurson-Tvergaard model

The bulge test is successfully extended to the determination of the fracture properties of silicon nitride and oxide thin films. This is achieved by using long diaphragms made of silicon nitride single layers and oxide/nitride bilayers, and applying a comprehensive mechanical model that describes the mechanical response of the diaphragms under uniform differential pressure. The model is valid for thin films with arbitrary z-dependent plane-strain modulus and prestress, where z denotes the coordinate perpendicular to the diaphragm. It takes into account the bending rigidity and stretching stiffness of the layered materials and the compliance of the supporting edges. This enables the accurate computation of the load-deflection response and stress distribution throughout the composite diaphragm as a function of the load, in particular at the critical pressure leading to the fracture of the diaphragms. The method is applied to diaphragms made of single layers of 300-nm-thick silicon nitride deposited by low-pressure chemical vapor deposition and composite diaphragms of silicon nitride grown on top of thermal silicon oxide films produced by wet thermal oxidation at 950 [degrees]C and 1050 [degrees]C with target thicknesses of 500, 750, and 1000 nm. All films characterized have an amorphous structure. Plane-strain moduli [E.sub.ps] and prestress levels [[sigma].sub.o] of 304.8 [+ or -] 12.2 GPa and 1132.3 [+ or -] 34.4 MPa, respectively, are extracted for [Si.sub.3][N.sub.4], whereas [E.sub.ps] = 49.1 [+ or -] 7.4 GPa and [[sigma].sub.o] = -258.6 [+ or -] 23.1 MPa are obtained for Si[O.sub.2] films. The fracture data are analyzed using the standardized form of the Weibull distribution. The [Si.sub.3][N.sub.4] films present relatively high values of maximum stress at fracture and Weibull moduli, i.e., [[sigma].sub.max] = 7.89 [+ or -] 0.23 GPa and m = 50.0 [+ or -] 3.6, respectively, when compared to the thermal oxides ([[sigma].sub.max] 0.89 [+ or -] 0.07 GPa and m = 12.1 [+ or -] 0.5 for 507-nm-thick 950 [degrees]C layers). A marginal decrease of [[sigma].sub.max] with thickness is observed for Si[O.sub.2], with no significant differences between the films grown at 950 [degrees]C and 1050 [degrees]C. Weibull moduli of oxide thin films are found to lie between 4.5 [+ or -] 1.2 and 19.8 [+ or -] 4.2, depending on the oxidation temperature and film thickness. [2007-0269] Index Terms--Bulge test, fracture, pooled Weibull analysis, silicon nitride ([Si.sub.3][N.sub.4]), silicon oxide (Si[O.sub.2]).

Research applications involving design tool development for multi phase material design are at an early stage of development. The computational requirements of advanced numerical tools for simulating material behavior such as the finite element method (FEM) and the molecular dynamics (MD) method can prohibit direct integration of these tools in a design optimization procedure where multiple iterations are required. One, therefore, requires a design approach that can incorporate multiple simulations (multiphysics) of varying fidelity such as FEM and MD in an iterative model management framework that can significantly reduce design cycle times. In this research a material design tool based on a variable fidelity model management framework is presented. In the variable fidelity material design tool, complex 'high-fidelity' FEM analyses are performed only to guide the analytic 'low-fidelity' model toward the optimal material design. The tool is applied to obtain the optimal distribution of a second phase, consisting of silicon carbide (SIC) fibers, in a silicon-nitride ([Si.sub.3][N.sub.4]) matrix to obtain continuous fiber SiC-[Si.sub.3][N.sub.4] ceramic composites with optimal fracture toughness. Using the variable fidelity material design tool in application to two test problems, a reduction in design cycle times of between 40% and 80% is achieved as compared to using a conventional design optimization approach that exclusively calls the high-fidelity FEM. The optimal design obtained using the variable fidelity approach is the same as that obtained using the conventional procedure. The variable fidelity material design tool is extensible to multiscale multiphase material design by using MD based material performance analyses as the high-fidelity analyses in order to guide low-fidelity continuum level numerical tools such as the FEM or finitedifference method with significant savings in the computational time. [DOI: 10.1115/1.2965361] Keywords: CFCC, FEM, fidelity, fracture toughness, optimal, scaling, stress intensity

Tests and finite-element analyses of blunt notch and dogbone specimens are presented to demonstrate the application and validation of the cyclic void growth model (CVGM) to evaluate the initiation of ductile fracture under cyclic loading in steel structures. Modeling concepts and procedures for characterizing the CVGM material parameters using notched bar tests are described. Accuracy of the model is validated through a series of cyclic tests of 14 blunt notch compact fracture specimens and four dogbone specimens. Four types of moderate to high strength structural steels are investigated (two types of A572-Grade 50, A514-Grade 110, HPS70W). The test specimens reflect stress and strain conditions encountered in structural steel components and provide sufficiently strong stress and strain gradients to validate the characteristic length assumptions in the model. Detailed finite-element analyses that employ the CVGM criterion are shown to predict fracture with good accuracy across the specimen geometries, steel types, and loading histories. DOI: 10.1061/(ASCE)0733-9445(2008)134:9(1528) CE Database subject headings: Validation; Voids; Cracking; Steel; Finite element method.

A numerical study on the fracture behavior of steel fiber-reinforced concrete (SFRC) slabs on grade for industrial pavements is presented. Finite element analyses have been carried out by using a commercial finite element code where user subroutines based on nonlinear fracture mechanics have been implemented to describe the progressive cracking behavior of SFRC. The model is capable of simulating both primary and secondary cracks when they occur in concrete and it has been validated by comparing numerical predictions with experimental observations of full-scale tests on slabs on elastic subgrade under point loads in different positions. A real pavement with contraction or construction joints has been numerically simulated to investigate the stress and the strain fields for the most significant positions of point loads. DOI: 10.1061/(ASCE)0899-1561(2008)20:9(599) CE Database subject headings: Pavements; Slabs; Joints; Reinforced concrete; Fiber reinforced materials; Concrete structures; Fracture; Nonlinear analysis.

To increase the crack bridging capacity of concretes and mortars, fibers are often added to cement-based matrices. As a result, the fracture energy of a fiber-reinforced concrete (FRC) is the sum of the cohesive forces of the matrix and of the pullout resistance given by the fibers crossing the crack. In the case of fibers randomly inclined with respect to crack surfaces, the so-called frictional snubbing effect must be added to the previous contributions, if the energy released during crack growth has to be computed. Of course, snubbing forces are not present when fibers are perfectly orthogonal to crack surfaces. As the classical formulas are not always effective in the evaluation of snubbing phenomenon, a cohesive interface model is here proposed for a more precise definition of the frictional snubbing forces. The model is able to predict adequately the experimental results obtained by pulling out steel fibers at different inclinations angles from cement-based matrices. By analyzing fibers with different bond properties, the proposed model can be also used to define the crack bridging capacity of both bonded and unbonded steel fibers. Moreover, it seems to suggest a more simplified approach for the definition of the postcracking response of FRC. DOI: 10.1061/(ASCE)0899-1561(2008)20:9(588) CE Database subject headings: Fiber reinforced materials; Bonding; Friction; Cracking; Cements.

Byline: Andrzej Dzielinski (Warsaw University of Technology, Faculty of Electrical Engineering, Institute of Control and Industrial Electronics, Koszykowa 75, 00-662 Warszawa, Poland); Dominik Sierociuk (Warsaw University of Technology, Faculty of [...]

With increasing traffic loads and changes in crude petroleum refining techniques, cracking in asphalt pavements continues to be a major cause of structural and functional deterioration of these systems, particularly in cold climates. Although modern design tools such as the AASHTO Mechanistic Empirical Pavement Design Guide have recognized the need to predict pavement cracking in pavement life cycle cost analyses, the development of true fracture tests and associated models is hampered by a lack of fundamental knowledge of the physical nature of cracking in asphalt concrete materials. A clustered discrete element method (DEM) was employed as a means to investigate fracture mechanisms in asphalt concrete at low temperatures. The DEM approach was first verified by comparing elastic continuum theory and the discontinuum approach using uniform axial compression and cantilever beam models. A bilinear cohesive zone model was implemented into the DEM framework to enable simulation of crack initiation and propagation in asphalt concrete. Verification of the cohesive zone fracture model was carried out using a double cantilever beam. The main advantage of the DEM approach was that a mesoscale representation of the morphology of the material could be easily incorporated into the model using high-resolution imaging, image analysis software, and by developing a relatively simple mesh generation code. The simulation results were shown to compare favorably with experimental results, and moreover, the simulations provide new insight into the mechanisms of fracture in asphalt concrete. The modeling technique can provide more details of the fracture process in laboratory fracture tests, the influence of heterogeneity on crack path, and the effects of local material strength and fracture energy on global fracture test response. DOI: 10.1061/(ASCE)0899-1561 (2008)20:8(552) CE Database subject headings: Discrete elements; Cracking; Asphalts; Concrete; Simulation.

This paper presents very recent results of an experimental program aimed at disclosing size and strain rate effects on the fracture behavior of reinforced concrete beams. Thirty-six reinforced beams made from two microconcretes with different Hillerborg's characteristic length [one is 66 mm (material A), the other is 105 mm (material B)], of three sizes (75, 150, and 300 mm in depth), were tested under four strain rates (1.05 X [10.sup.-5], 1.25 x [10.sup.-3], 1.25 x [10.sup.-2], and 3.75 x [10.sup.-2] [s.sup.-1]). The results show that the peak loads increase with an increase in the strain rate; the rate dependence of the peak load is stronger for larger specimens than for smaller ones. Moreover, size effect is only shown under the nominal strain rate 1.05 x [10.sup.-5] [s.sup.-1]; under the higher strain rates, it is inconspicuous. These results seem to reveal an apparent physical inconsistency, since there is no obvious reason that the size effect disappears when the strain rate increases. The explanation to this is sought numerically using an explicit cohesive model. DOI: 10.1061/(ASCE)0899-1561 (2008)20:8(544) CE Database subject headings: Cracking; Concrete, reinforced; Strain rate; Size effects; Experimentation.

This paper presents a numerical study of the failure response of an aircraft engine containment panel obliquely impacted by a titanium turbine fragment. A three-branch Bao-Wierzbicki fracture criterion is first calibrated for the target material (2219-T851 aluminum alloy) by performing tensile tests on round bars and upsetting tests on short cylinders. With this fracture model, the finite-element simulation of the impact test successfully captures the formation of an indentation/gouging channel on the proximal surface of the panel and the growth of a crack on the distal surface. An extensive parametric study is conducted on the effect of fracture criteria, mesh size, projectile pitch angles, and finite-element codes. Deficiencies of the Johnson-Cook and the constant critical strain fracture model are identified. It is found that the numerically predicted residual thickness and mass loss of the panel are sensitive to the magnitude of the pitch angle of the projectile. A large difference in calculated energy dissipation between ABAQUS and LS-DYNA is observed. CE Database subject headings: Cracking; Size effect; Containment; Engines.

Predicting the fatigue life of solder interconnections is a challenge due to the complex nonlinear behavior of solder alloys and the importance of the load history. Long experience with Sn-Pb solder alloys together with empirical fatigue life models such as the Coffin-Manson rule have helped us identify reliable choices among package design alternatives. However, for the currently popular Pb-free choice of SnAgCu solder joints, designing accelerated thermal cycling tests and estimating the fatigue life are challenged by the significantly different creep behavior relative to Sn-Pb alloys. In this paper, a hybrid fatigue modeling approach inspired by nonlinear fracture mechanics is developed to predict the crack trajectory, and fatigue life of a solder interconnection. The model is shown to be similar to well accepted cohesive zone models in its theoretical development and application and is anticipated to be computationally more efficient compared to cohesive zone models in a finite element setting. The approach goes beyond empirical modeling in accurately predicting crack trajectories and is validated against experiments performed on lead-free as well as Sn-Pb solder joint containing microelectronic packages. Material parameters relevant to the model are estimated via a coupled experimental and numerical technique. [DOI: 10.1115/l.2840057] Keywords: lead-free solder, acceleration factors, cohesive zone modeling

A two-stage experimental program was conducted, which was aimed at examining the process of initiation/propagation of fracture in human radii under the conditions simulating a fall onto an outstretched hand. It involved a number of destructive tests on dried cadaver bones. The bones were first subjected to DXA as well as spiral CT measurements to establish the density properties and the details of geometry. Subsequently, the specimens were tested under controlled boundary conditions, to induce Colles' type of fracture. Following these tests, samples of cortical bone tissue were extracted at different orientations with respect to the direction of osteons and tested in axial tension. The results of material tests were used to verify the performance of an anisotropic fracture criterion for the cortical tissue. It has been demonstrated that the proposed criterion can reproduce the basic trends in the directional dependence of the tensile strength characteristics. For the structural tests, a correlation was established between the geometric characteristics of the cortex, the strength properties and the fracture load for individual radii that were tested. It was shown that the morphological traits and/or the strength properties alone are not adequate predictors of the fracture load of intact radii. A rational assessment of the fracture load requires a mechanical analysis that incorporates the key elements of the experimental program outlined here, i.e., the information on bone geometry, material properties of the bone tissue, and the static/kinematic boundary conditions. A preliminary example of a finite element analysis, for one of the radii bones tested, has been provided.

A comprehensive fracture-mechanics-based life prediction methodology is presented for fcc single crystal components based on the computation of stress intensity factors (SIFs), and the modeling of the crystallographic fatigue crack growth (FCG) process under mixed-mode loading conditions. The 3D finite element numerical procedure presented for computing SIFs for anisotropic materials under mixed-mode loading is very general and not just specific to fcc single crystals. SIFs for a Brazilian disk specimen are presented for the crack on the {111}) plane in the and directions, which represent the primary and secondary, slip directions. Variation of SIFs as a function of thickness is also presented. Modeling of the crystallographic FCG behavior is performed by using the resolved shear stress intensity coefficient, [K.sub.rss]. This parameter is sensitive to the grain orientation and is based on the resolved shear stresses on the slip planes at the crack tip, which is useful in identifying the active crack plane as well as in predicting the crack growth direction. A multiaxial fatigue crack driving force parameter, [DELTA][K.sub.rss], was quantified, which can be used to predict the FCG rate and, hence, life in single crystal components subject to mixed-mode fatigue loading.

This study presents experimental procedures conducted to characterize the bond between concrete and fiber reinforced polymeric laminates. The experimental characterization was aimed at obtaining the softening of the concrete-epoxy interface (CEI) formed during the installation of these laminates. In particular, splitting tensile and three-point bending tests were used to determine the tensile strength ([f.sub.t]), the size-effect fracture energy ([G.sub.f]), and the cohesive fracture energy ([G.sub.F]) of two concrete-epoxy interfaces. The sensitivity of these properties to the type of epoxy, specimen geometry, and surface conditions was also investigated experimentally. From this study, it was found that the tensile strength ([f.sub.1]) and the cohesive fracture energy ([G.sub.F]) of plain concrete and the two concrete-epoxy interfaces under consideration are similar in magnitude. Conversely, the size-effect fracture energies ([G.sub.f]) of plain concrete and a CEI are up to 64% different. Experimental results indicate that the condition of the concrete surface is the principal factor affecting the size-effect fracture energy ([G.sub.f]) of a concrete-epoxy interface. Results also indicate that the size-effect fracture energy ([G.sub.f]) can be used to characterize and compare concrete-epoxy interfaces. DOI: 10.1061/(ASCE)0899-1561(2008)20:4(303) CE Database subject headings: Composite materials; Concrete; Cracking; Damage; Bonding; Interfaces.

This technical note presents the behavior of dam and sieved concretes in uniaxial tension and compression together with the effects of curing age on large size specimens of 450 mm x 450 mm x 900 mm (prism shape) and 450 mm X 450 mmx 450 mm (cube shape) and small size specimens of 150 mm x 150 mm X 350 mm and 150 mm X 150 mm X 150 mm, respectively. The complete stress-strain curves both in tension and compression were acquired through a systematic experimental program. The specimen ages varied from 7 to 180 days. Models with hyperbolic form are proposed to estimate the tensile and compressive strengths, the elastic modulus, and the fracture parameters of the concretes with effects of specimen ages. On top of that, the maximum crack width, fracture energy, and brittleness of dam concretes were also obtained based on the stress-deformation curves. It was found that the strengths, modulus of elasticity, and fracture energy increase with specimen age, and that the specimen size and maximum aggregate diameter significantly affect the fracture energy, peak strain, and crack width of concretes in uniaxial tension. DOI: 10.1061/(ASCE)0899-1561(2008)20:4(321) CE Database subject headings: Dams, concrete; Mechanical properties; Cracking; Stress strain relations; Brittleness; Aging.

In many concrete structural applications, such as concrete pavements, joints or cracks are relied upon to transfer load between adjacent slabs in order to better distribute the stresses in the material. This study has developed a new method to characterize the shear transfer ability of preexisting concrete cracks and joints. The measured concrete surface roughness and fracture energy ([G.sub.F]) were related to a concrete mixtures ability to transfer shear load across a preexisting cracked surface. The wedge splitting test (WST) was used to obtain the concrete's fracture energy. A modified method for determining [G.sub.F] based on WST is presented. A novel laser profilometer was implemented for quantifying the three-dimensional cracked concrete surface characteristics. The fracture energy was found to characterize both the physical and mechanical properties of the concrete crack face better than previously used surface parameters. In addition, the surface roughness of the concrete crack was related to the fracture energy at the time of cracking, whereas its ability to transfer shear load or shear stiffness was more related to the fracture energy at 28-day age. DOI: 10.1061/(ASCE)0899-1561 (2008)20:4(275) CE Database subject headings: Concrete; Cracking; Energy; Surface roughness; Stiffness.

Moving surface loads cause crack extension at a constant subcritical speed between perfectly bonded materials. The materials differ only in thermal properties and are governed by coupled thermoelastic equations that admit as special cases Fourier heat conduction and thermal relaxation with one or two relaxation times. Convection from the crack surfaces is allowed and for the latter two models is itself influenced by thermal relaxation. A dynamic steady state of plane strain is assumed. Fourier heat conduction is shown to dominate away from the crack edge at low speeds; solution behavior at the crack edge at high speeds depends upon the particular thermal model Thermal mismatch is seen to cause solution behavior similar to that for the isothermal bimaterial, and so insight into the case of general material mismatch is provided. [DOI: 10.1115/1.2793802] Keywords: thermal mismatch, dynamic interface crack, thermal relaxation, Fourier heat conduction, convection, Biot number, singular integral equations

The spectral stiffness microplane (SSM) model developed in the preceding Part I of this study is verified by comparisons with experimental data for uniaxial and biaxial tests of unidirectional and multidirectional laminates. The model is calibrated by simulating the experimental data on failure stress envelopes analyzed in the recent so-called 'World Wide Failure Exercise,' in which various existing theories were compared. The present theory fits the experiments as well as the theories that were best in the exercise. In addition, it can simulate the post-peak softening behavior and fracture, which is important for evaluating the energy-dissipation capability of composite laminate structures. The post-peak softening behavior and fracture are simulated by means of the crack band approach which involves a material characteristic length. [DOI: 10.1115/1.2744037] Keywords: fiber composites, laminates, spectral methods, microplane model, fracture energy, crack band model, damage, failure criteria

The paper presents the spectral stiffness microplane model, which is a general constitutive model for unidirectional composite laminates, able to simulate the orthotropic stiffness, prepeak nonlinearity, failure envelopes, and, in tandem with the material characteristic length, also the post-peak softening and fracture. The framework of the microplane model is adopted. The model exploits the spectral decomposition of the transversely isotropic stiffness matrix of the material to define orthogonal strain modes at the microplane level. This decomposition is a generalization of the volumetric-deviatoric split already used by Bazant and co-workers in microplane models for concrete, steel, rocks, soils, and stiff foams. Linear strain-dependent yield limits (boundaries) are used to provide bounds for the normal and tangential microplane stresses, separately for each mode. A simple version, with an independent boundary for each mode, can capture the salient aspects of the response of a unidirectional laminate, although a version with limited mode coupling can fit the test data slightly better. The calibration of model parameters, verification by test data, and analysis of multidirectional laminates are postponed for the subsequent companion paper. [DOI: 10.1115/1.2744036] Keywords: fiber composites, laminates, spectral methods, microplane model fracture energy, crack band model, damage, failure criteria, finite elements

In this paper, we present a new model to predict the fracture in brittle materials from a geometrical weakness presenting an arbitrary stress concentration. The main idea is to combine the strain gradient elasticity with a cohesive model that includes both the displacement and the rotation jumps between the cohesive surfaces in the separation law. Three material parameters were used in the establishment of the fracture criterion. The first two parameters are the commonly used [[sigma].sub.c], the ultimate stress, and [G.sub.c], the critical energy release rate. The third parameter is the characteristic length l as in most of the strain gradient models. The proposed three-parameter model enables to take the different stress concentration levels into account, thus providing a criterion to predict fractures for any stress concentration, whether it is singular or not. Experimental results were selected to verify the accuracy and efficiency of the criterion. It was shown that the proposed model is physically reasonable, highly accurate, and easy to apply. It can be used in crack initiation prediction of engineering structures made of brittle materials. [DOI: 10.1115/1.2775498] Keywords: Fracture criterion, strain gradient, cohesive model PMMA, brittle or quasibrittle materials, size effect, stress concentration

This paper considers a piezoelectric ceramic layer with a surface electrode. It focuses on the effect of the layer thickness on the electrode tip fields. A closed-form solution for the electromechanical fields at the electrode tip is obtained and is expressed in terms of the applied electric field intensity factor, which can be obtained exactly for infinite layer thickness and numerically for finite layer thickness. The stress, electric displacement, and electric field are plotted to show the effect of layer thickness. It is found that the stresses and field intensities at the electrode tip can be reduced considerably by decreasing the thickness of the piezoelectric layer, confirming the previous finding. The paper also gives a solution for two identical and collinear surface electrodes. The relative distance between the electrodes is observed to have significant influence on the electromechanical field in the piezoelectric layer. [DOI: 10.1115/1.2775504] Keywords: piezoelectric materials, electrode, fracture mechanics

The deformation, ultimate load capacity, and fracture behavior of full-scale welded K-joints fabricated from cold-formed rectangular hollow sections have been studied both numerically and experimentally. An extensive experimental program of welded K-joints tested to failure at temperatures between 23 and -60[degrees]C revealed that the primary failure mode was ductile tearing of the chord flange at the toe of the tension brace-to-chord weld. For some joints tested at -40 and -60[degrees] C, initial ductile tearing led to brittle fracture. Finite-element based J-integral assessment of an advancing crack for one K-joint geometry was combined with J-[DELTA]a material curves measured at -40[degrees] C. Assessment revealed that crack advance, once initiated, would be expected to continue at a nearly constant load. The assumed shape and size of the initial crack in the finite-element model were considered to be conservative and the estimated maximum load capacity and joint ductility were conservatively predicted with respect to the experimental results. This procedure was found to be promising for assessing the ultimate ductility of tubular joints at low temperatures. DOI: 10.1061/(ASCE)0733-9445(2008)134:2(181) CE Database subject headings: Assessments; Cracking; Welds; Joints; Deformation; Hollow sections.

By conducting curved wide plate tensile tests for girth welded joints of X80 line pipe containing a surface notch in the weld metal the effects of strength matching on fracture performance were evaluated. Parametric studies were also conducted using a finite element method simulating the experiments to clarify the effects of strain hardening capacity of the base metal, softening in the heat affected zone, and groove configuration on fracture performance. A strain at failure significantly decreased with the decreasing strength matching. This was expected to be due to a difference in local straining behavior at the notch tip caused by the shielding effect. The analytical studies revealed that the strain hardening capacity of the base metal the softening in the heat affected zone, and the groove configuration affected the allowable strain for a given toughness level in the case of overmatching. However, these factors hardly affected the allowable strain in the case of undermatching. [DOI: 10. I 115/1.2746402]

Four-point-bending V-notched specimens of lead zirconate titanate (PZT) poled parallel to the long axis are fractured under conditions of controlled crack growth in a custom-made device. In addition to the mechanical loading electric fields, up to 500 V/mm are applied parallel and anti-parallel to the poling direction, i.e., perpendicular to the crack surface. To determine the different contributions to the total energy release rate, the mechanical and the piezoelectric compliance, as well as the electrical capacitance of the sample, are recorded continuously using small signal modulation/demodulation techniques. This allows for the calculation of the mechanical, the piezoelectric, and the electrical part of the total energy release rate clue to linear processes. The sum of these linear contributions during controlled crack growth is attributed to the intrinsic toughness of the material. The nonlinear part of the total energy release rate is mostly associated to domain switching leading to a switching zone around the crack tip. The measured force-displacement curve, together with the modulation technique, enables us to determine this mechanical nonlinear contribution to the overall toughness of PZT. The intrinsic material toughness is only slightly dependent on the applied electric field (10% effect), which can be explained by screening charges or electrical breakdown in the crack interior. The part of the toughness due to inelastic processes increases from negative to positive electric fields by up to 100%. For the corresponding nonlinear electric energy change during crack growth, only a rough estimate is performed. [DOI: 10.1115/1.2744027] Keywords: PZT, piezoelectric, fracture criterion, compliance, energy release rate

Because the observed size effect follows neither the strength theory nor the linear elastic fracture mechanics, the delamination fracture of laminate-foam sandwiches under uniform bending moment is treated by the cohesive crack model. Both two-dimensional geometrically nonlinear finite element analysis and one-dimensional representation of skin (or facesheet) as a beam on elastic-softening foundation are used. The use of the latter is made possible by realizing that the effective elastic foundation stiffness depends on the ratio of the critical wavelength of periodic skin wrinkles to the foam core thickness, and a simple description of the transition from shortwave to longwave wrinkling is obtained by asymptotic matching. Good agreement between both approaches is achieved. Skin imperfections (considered proportional to the the first eigenmode of wrinkling), are shown to lead to strong size dependence of the nominal strength. For large imperfections, the strength reduction due to size effect can reach 50%. Dents from impact, though not the same as imperfections, might be expected to cause as a similar size effect. Using proper dimensionless variables, numerical simulations of cohesive delamination fracture covering the entire practical range are performed. Their fitting, heeding the shortwave and longwave asymptotics, leads to an approximate imperfection-dependent size effect law of asymptotic matching type. Strong size effect on postpeak energy absorption, important for impact analysis, is also demonstrated. Finally, discrepancies among various existing formulas for critical stress at periodic elastic wrinkling are explained by their applicability to different special cases in the shortwave-longwave transition. [DOI: 10.1115/1.2722778]

Deformation and fracture behavior of several formable automotive aluminum alloys and steels have been assessed experimentally at room temperature through standard uniaxial tension, plane strain tension, and hemispherical dome tests. These materials exhibit the same deformation sequence: normally uniform elongation followed by diffuse necking, then localized necking in the form of crossed intense-shear bands, and finally fracture. The difference among these alloys lies primarily with respect to the point at which damage (i.e., voiding) starts. Damage develops earlier in the steel samples, although in all cases very little damage is observed prior to the onset of shear instability. A unified finite element model has been developed to reproduce this characteristic deformation sequence. Instability is triggered by the introduction of microstructural inhomogeneities rather than through the commonly utilized Gurson-Tvergaard-Needleman damage model. The predicted specimen shape change, shear band characteristics, distribution of strain, and the fracture modes for steels and aluminum alloys are all in good agreement with the experimental observations. [DOI: 10.1115/1.2767360] Keywords: localization, damage, FEM, fracture, formability

High power beam welds, such as electron beam welds or laser welds, sometimes provide fracture path deviation (FPD) in standardized Charpy V-notch fracture toughness testing due to narrow bead profile together with higher overmatching in strength between weld metal and base metal. Moreover, it should be noted that these typical features of beam welds might result in a plastic constraint loss around both the notch and crack tip in fracture toughness test specimens. Even in the temperature range where FPD would not occur, the fracture toughness test results could not necessarily be an intrinsic value of such beam welds. These fracture properties make it difficult to evaluate fracture performance of girth welded pipe joints. In this paper, the estimation method of intrinsic fracture toughness of beam weld metal itself using standard toughness test specimens is proposed on the basis of 'Weibull stress criterion.' The predicted intrinsic fracture toughness was found to be lower than the test results both in standard Charpy specimen and in three-point bend specimen with fatigue precrack. The assessment of brittle fracture performance of girth welded pipeline was conducted from the estimated intrinsic fracture toughness of girth welds by means of Weibull stress criterion. It was demonstrated that the low intrinsic fracture toughness of beam welds could not directly lead to the low fracture performance of a pipe joint under tensile loading. This is because of a lower plastic constraint compared to a three-point bend specimen due to difference in loading mode together with constraint loss in pipe joints and shielding effect of straining in weld metal due to highly overmatched narrow welds. [DOI: 10.1115/1.2767652] Keywords: beam welds, linepipe, Charpy impact testing, three-point bend testing, fracture toughness, FPD (fracture path deviation), toughness transition curve, Weibull stress, plastic constraint, fracture performance

The fundamental fracture mechanisms of biological protein materials remain largely unknown, in part, because of a lack of understanding of how individual protein building blocks respond to mechanical load. For instance, it remains controversial whether the free energy landscape of the unfolding behavior of proteins consists of multiple, discrete transition states or the location of the transition state changes continuously with the pulling velocity. This lack in understanding has thus far prevented us from developing predictive strength models of protein materials. Here, we report direct atomistic simulation that over four orders of magnitude in time scales of the unfolding behavior of [alpha]-helical (AH) and [beta]-sheet (BS) domains, the key building blocks of hair, hoof, and wool as well as spider silk, amyloids, and titin. We find that two discrete transition states corresponding to two fracture mechanisms exist. Whereas the unfolding mechanism at fast pulling rates is sequential rupture of individual hydrogen bonds (HBs), unfolding at slow pulling rates proceeds by simultaneous rupture of several HBs. We derive the hierarchical Bell model, a theory that explicitly considers the hierarchical architecture of proteins, providing a rigorous structure-property relationship. We exemplify our model in a study of AHs, and show that 3-4 parallel HBs per turn are favorable in light of the protein's mechanical and thermodynamical stability, in agreement with experimental findings that AHs feature 3.6 HBs per turn. Our results provide evidence that the molecular structure of AHs maximizes its robustness at minimal use of building materials. [alpha]-helix | deformation | intermediate filaments | rupture | structure

Abstract: Spalling and strain bursting has long been recognized as a mechanism of failure in deep underground mines in hard rock and in deep infrastructure tunnels. The latter is a [...]

Microcantilever beams are frequently utilized as sensor platforms in microelectromechanical system devices. These highly compliant surface-micromachined structures generally fail by adhering to the underlying substrate during processing or subsequent operation. Such failures, which are commonly known as 'stiction' failures, can be prevented or repaired in a number of ways, including low adhesion coatings, rinsing with low surface energy agents, and active approaches such as laser irradiation. Gupta et al. [J. Microelectromech. Syst. vol. 13, pp. 696-700, 2004] recently demonstrated that stress waves could be used to repair stiction-failed structures. This paper extends the work of Gupta et al. by developing a fracture mechanics theory of the repair process and compares that theory with corresponding experiments. We show that: 1) incremental crack growth is associated with each laser pulse, the extent of which is directly related to the laser fluence; 2) repeated pulsing fully repairs all of the microcantilevers; and 3) a fracture mechanics model accurately predicts the observed experimental results. [1664] Index Terms--Fracture mechanics, laser, stiction, stress waves.

The lifetime distribution of a component subjected to fatigue loading is calculated using a micromechanics model for crack initiation and a fracture mechanics model for crack growth. These models are implemented in a computer code which uses the local stress field obtained in a finite-element analysis as input data. Elemental failure probabilities are defined which allow us to identify critical regions and are independent of mesh refinement. An example is given to illustrate the capabilities of the code. Special emphasis is put on the effect of the initiation phase on the lifetime distribution. [DOI: 10.1115/1.2436569]

Numerical simulation of fatigue crack propagation based on fracture mechanics and the conventional finite element method requires a huge amount of computational resources when the cracked structure shows a complicated condition such as the multiple site damage or thermal fatigue. The objective of the present study is to develop a simulation technique for fatigue crack propagation that can be applied to complex situations by employing the continuum damage mechanics (CDM). An anisotropic damage tensor is defined to model a macroscopic fatigue crack. The validity of the present theory is examined by comparing the elastic stress distributions around the crack tip with those obtained by a conventional method. Combined with a nonlinear elasto-plastic constitutive equation, numerical simulations are conducted for low cycle fatigue crack propagation in a plate with one or two cracks. The results short, good agreement with the experiments. Finally, propagations of multiply distributed cracks under low cycle fatigue loading are simulated to demonstrate the potential application of the present method. [DOI: 10.1115/1.2388993]

Size effect is studied here with reference to the bonding of short, deformed bars, embedded in normal-strength concrete (NSC) and high-performance concrete (HPC). Tests on 48 cylindrical specimens reinforced with a single bar and subjected to a pull-out or push-in force show that bond exhibits a strong size effect, which is well described by Bazant's general-type size-effect law. Four diameters are considered ([d.sub.b]=5, 12, 18, and 26 mm), with bonded length-to-bar diameter ratios equal to 3.5 (HPC) and 5 (NSC). All specimens are highly confined by means of a steel jacket to prevent or control cover splitting and to investigate bond behavior in highly confined conditions. Test results on short, anchored bars were instrumental in working out the local bond stress-slip law, taking into account size effect, which appears in the formulation of the maximum bond stress through the bar diameter. Short embedments also prevented bar yielding. The proposed local bond stress-slip law (1) is formulated as an extension of the law suggested in European Model Code MC90, also including some later proposals; (2) fits quite well with the available test data on short, well-confined anchored bars; (3) introduces the favorable effects that the confining reinforcement (generally consisting of stirrups and longitudinal bars) has on bond strength; and (4) may be easily introduced into a design code. CE Database subject headings: Anchorages; Bonding strength; Confinement; Cracking; Fracture mechanics; High strength concretes; Slip; Size effect.