Bilinear tension softening diagrams of concrete mixes corresponding to their size-independent specific fracture energy

The study of the fracture behaviour of concrete structures using the fictitious crack model requires two fracture properties of the concrete mix, namely, the size-independent specific fracture energy G(F). and the corresponding tension softening relation sigma(w) between the residual stress carrying capacity sigma and the crack opening w in the fracture process zone ahead of a real crack. In this paper, bi-linear tension softening diagrams of three different concrete mixes, ranging in compressive strength from 57 to 122 MPa whose size-independent specific fracture energy has been previously determined, have been constructed in an inverse manner based on the concept of a non-linear hinge from the load-crack mouth opening plots of notched three-point bend beams. (C) 2013 Elsevier Ltd. All rights reserved.

A systematic investigation of fracture mechanisms in Al-Si based eutectic alloy-Effect of Si modification

The fracture characteristics of Al-Si based eutectic alloy are investigated in the unmodified and modified conditions under compression. The investigations are carried out at different strain rates and temperatures. Fracture of the alloy starts with eutectic Si particle fracture and modification plays an important role in particle fracture. The fraction of fractured particles is found to be always lesser in the modified condition than in the unmodified condition. Particle fracture increases with increase in strain. It is found that the Si particle fracture shows an increase with increase in strain rate and decreases with increase in temperature at 10% strain. Large and elongated particles show a greater tendency for fracture in the unmodified and modified conditions. Particle orientation plays an important role on fracture and the cracks are found to occur almost in a direction normal to the tensile strain imposed upon the particles by the deforming matrix in the unmodified alloy. The modified alloy shows a random distribution of fractured particles and crack orientation. The criteria of fracture based on dislocation pile-up mechanism and fiber loading explain the observed difference in particle fracture characteristics due to modification. The particle fracture for the modified alloy is also discussed in terms of Weibull statistics and the existing models of dispersion hardening. Particle/matrix interface decohesion is observed at higher strain rates and temperatures in the modified alloy. Dendritic rotation of 10 degrees is also observed at higher strain rates, which can increase the amount of particle fracture. (C) 2013 Elsevier B.V. All rights reserved.

Incorporation of Interfacial Intermetallic Morphology in Fracture Mechanism Map for Sn-Ag-Cu Solder Joints

A fracture mechanism map (FMM) is a powerful tool which correlates the fracture behavior of a material to its microstructural characteristics in an explicit and convenient way. In the FMM for solder joints, an effective thickness of the interfacial intermetallic compound (IMC) layer (t (eff)) and the solder yield strength (sigma (ys,eff)) are used as abscissa and ordinate axes, respectively, as these two predominantly affect the fracture behavior of solder joints. Earlier, a definition of t (eff), based on the uniform thickness of IMC (t (u)) and the average height of the IMC scallops (t (s)), was proposed and shown to aptly explain the fracture behavior of solder joints on Cu. This paper presents a more general definition of t (eff) that is more widely applicable to a range of metallizations, including Cu and electroless nickel immersion gold (ENIG). Using this new definition of t (eff), mode I FMM for SAC387/Cu joints has been updated and its validity was confirmed. A preliminary FMM for SAC387/Cu joints with ENIG metallization is also presented.

Experimental study of fracture behavior of magnesium single crystals

In this work, the fracture behavior of magnesium single crystals is studied by conducting experiments with notched three point bend specimens of three crystallographic orientations. In the first and second orientations, the c-axis is along the normal to the flat surface of the notch, while in the third it is aligned with the notch front. For all the orientations, in situ electron back scattered diffraction observations made around the notch root show profuse tensile twinning of {10 (1) over bar2} type. Further, in the first two orientations basal and prismatic slip traces are identified from optical metallography. The width of the most prominent twin saturates at around 120-150 mu m, while twins continue to nucleate farther away to accommodate plastic deformation. In all the orientations, crack initiation occurs before the attainment of peak load and the crack grows stably along twin-matrix interface before deflecting at twin-twin intersections. Results show that profuse tensile twinning is an important energy dissipating mechanism that enhances the fracture toughness. (C) 2013 Elsevier B.V. All rights reserved.

Closed-form nonlinear sectional analysis of pretwisted anisotropic beam with multiple delaminations

Fiber reinforced laminated composite open-section beams are widely used as bearingless rotor flex beams because of their high specific strength and stiffness as well as fatigue life. These laminated composite structures exhibit a number of different failure modes, including fiber-matrix debonding within individual layers, delamination or separation of the layers, transverse cracks through one or more layers and fiber fracture. Delamination is a predominant failure mode in continuous fiber reinforced laminated composites and often initiate near the free edges of the structure. The appearance of delaminations in the composite rotorcraft flexbeams can lead to deterioration of the mechanical properties and, in turn, the helicopter performance as well as safety. Understanding and predicting the influence of free-edge delamination on the overall behavior of the laminates will provide quantitative measures of the extent of the damage and help ensure their damage tolerance.

Free turbulent shear layer in a point vortex gas as a problem in nonequilibrium statistical mechanics

This paper attempts to unravel any relations that may exist between turbulent shear flows and statistical mechanics through a detailed numerical investigation in the simplest case where both can be well defined. The flow considered for the purpose is the two-dimensional (2D) temporal free shear layer with a velocity difference Delta U across it, statistically homogeneous in the streamwise direction (x) and evolving from a plane vortex sheet in the direction normal to it (y) in a periodic-in-x domain L x +/-infinity. Extensive computer simulations of the flow are carried out through appropriate initial-value problems for a ``vortex gas'' comprising N point vortices of the same strength (gamma = L Delta U/N) and sign. Such a vortex gas is known to provide weak solutions of the Euler equation. More than ten different initial-condition classes are investigated using simulations involving up to 32 000 vortices, with ensemble averages evaluated over up to 10(3) realizations and integration over 10(4)L/Delta U. The temporal evolution of such a system is found to exhibit three distinct regimes. In Regime I the evolution is strongly influenced by the initial condition, sometimes lasting a significant fraction of L/Delta U. Regime III is a long-time domain-dependent evolution towards a statistically stationary state, via ``violent'' and ``slow'' relaxations P.-H. Chavanis, Physica A 391, 3657 (2012)], over flow time scales of order 10(2) and 10(4)L/Delta U, respectively (for N = 400). The final state involves a single structure that stochastically samples the domain, possibly constituting a ``relative equilibrium.'' The vortex distribution within the structure follows a nonisotropic truncated form of the Lundgren-Pointin (L-P) equilibrium distribution (with negatively high temperatures; L-P parameter lambda close to -1). The central finding is that, in the intermediate Regime II, the spreading rate of the layer is universal over the wide range of cases considered here. The value (in terms of momentum thickness) is 0.0166 +/- 0.0002 times Delta U. Regime II, extensively studied in the turbulent shear flow literature as a self-similar ``equilibrium'' state, is, however, a part of the rapid nonequilibrium evolution of the vortex-gas system, which we term ``explosive'' as it lasts less than one L/Delta U. Regime II also exhibits significant values of N-independent two-vortex correlations, indicating that current kinetic theories that neglect correlations or consider them as O(1/N) cannot describe this regime. The evolution of the layer thickness in present simulations in Regimes I and II agree with the experimental observations of spatially evolving (3D Navier-Stokes) shear layers. Further, the vorticity-stream-function relations in Regime III are close to those computed in 2D Navier-Stokes temporal shear layers J. Sommeria, C. Staquet, and R. Robert, J. Fluid Mech. 233, 661 (1991)]. These findings suggest the dominance of what may be called the Kelvin-Biot-Savart mechanism in determining the growth of the free shear layer through large-scale momentum and vorticity dispersal.

Micromechanisms of fracture and strengthening in free-standing Pt-aluminide bond coats under tensile loading

Free-standing Pt-aluminide (PtAl) bond coats exhibit a linear stress strain response under tensile loading and undergo brittle cleavage fracture at temperatures below the brittle-to-ductile transition temperature (BDTT). Above the BDTT, these coatings show yielding and fail in a ductile manner. In this paper, the various micromechanisms affecting the tensile fracture stress (FS) below the BDTT and yield strength (YS) above the BDTT in a PtAl bond coat have been ascertained and quantified at various temperatures. The micromechanisms have been identified by carrying out microtensile testing of stand-alone PtAl coating specimens containing different levels of Pt at temperatures between room temperature and 1100 degrees C and correlation of the corresponding fracture mechanisms with the deformation substructure in the coating. An important aspect of the influence of Pt on the tensile behavior, slip characteristics, FS/YS and BDTT in the PtAl coating has also been examined. The addition of Pt enhances the FS of the coating by Pt solid solution strengthening and imparts a concomitant increase in fracture toughness and yet causes a significant increase in the BDTT of the coating. Published by Elsevier Ltd. on behalf of Acta Materialia Inc.

Role of Crosslinking and Entanglements in the Mechanics of Silicone Networks

The goal of this study is to investigate the applicability of different constitutive models for silicone networks using comprehensive multiaxial experimental tests, including non-equibiaxial mechanical tests which introduce differential constraints on the networks in the two orthogonal directions, on samples prepared using various crosslinking densities. Uniaxial stress-strain experiments show that a decrease in crosslinker amounts used in the preparation of silicone networks lead to more compliant material response as compared to that obtained using higher amounts of crosslinker. Biaxial data were used to obtain fits to the neo- Hookean, Mooney-Rivlin, Arruda-Boyce and the Edward-Vilgis slip-link constitutive models. Our results show that the slip-link model, based on separation of the individual contributions of chemical crosslinks and physical entanglements, is better at describing the stress-strain response of highly crosslinked networks at low stretches as compared to other constitutive models. Modulus obtained using the slip-link model for highly crosslinked networks agrees with experimentally determined values obtained using uniaxial tension experiments. In contrast, moduli obtained using coefficients to the other constitutive models underpredict experimentally determined moduli by over 40 %. However, the slip-link model did not predict the experimentally observed stiffening response at higher stretches which was better captured using the Arruda-Boyce model.

An experimental study on loading rate effect on acoustic emission based b-values related to reinforced concrete fracture

This article reports on analysis of fracture processes in reinforced concrete (RC) beams with acoustic emission (AE) technique. An emphasis was given to study the effect of loading rate on variation in AE based b-values with the development of cracks in RC structures. RC beams of length 3.2 m were tested under load control at a rate of 4 kN/s, 5 kN/s and 6 kN/s and the b-value analysis available in seismology was used to study the fracture process in RC structures. Moreover, the b-value is related to the strain in steel to assess the damage state. It is observed that when the loading rate is higher, quick cracking development lead to rapid fluctuations and drops in the b-values. Also it is observed that concrete behaves relatively more brittle at higher loading rates (or at higher strain rates). The average b-values are lower as a few but larger amplitudes of AE events occur in contrast to more number of low amplitude AE events occur at low loading rates (or at low strain rates). (C) 2014 Elsevier Ltd. All rights reserved.

Finite element simulations of notch tip fields in magnesium single crystals

Recent experiments using three point bend specimens of Mg single crystals have revealed that tensile twins of {10 (1) over bar2}-type form profusely near a notch tip and enhance the fracture toughness through large plastic dissipation. In this work, 3D finite element simulations of these experiments are carried out using a crystal plasticity framework which includes slip and twinning to gain insights on the mechanics of fracture. The predicted load-displacement curves, slip and tensile twinning activities from finite element analysis corroborate well with the experimental observations. The numerical results are used to explore the 3D nature of the crack tip stress, plastic slip and twin volume fraction distributions near the notch root. The occurrence of tensile twinning is rationalized from the variation of normal stress ahead of the notch tip. Further, deflection of the crack path at twin-twin intersections observed in the experiments is examined from an energy standpoint by modeling discrete twins close to the notch root.

Effects of Microstructure and Loading on Fracture of Sn-3.8Ag-0.7Cu Joints on Cu Substrates with ENIG Surface Finish

When dropped, electronic packages often undergo failure by propagation of an interfacial crack in solder joints under a combination of tensile and shear loading. Hence, it is crucial to understand and predict the fracture behavior of solder joints under mixed-mode high-rate loading conditions. In this work, the effects of the loading conditions (strain rate and loading angle) and microstructure interfacial intermetallic compound (IMC) morphology and solder yield strength] on the mixed-mode fracture toughness of Sn-3.8 wt.%Ag-0.7 wt.%Cu solder joints sandwiched between two Cu substrates with electroless nickel immersion gold (ENIG) metallization have been studied, and compared with the fracture behavior of joints attached to bare Cu. Irrespective of the surface finish, the fracture toughness of the solder joints decreased monotonically with strain rate and mode-mixity, both resulting in increased fracture proportion through the interfacial IMC layer. Furthermore, the proportion of crack propagation through the interfacial IMC layer increased with increase in the thickness and the roughness of the interfacial IMC layer and the yield strength of the solder, resulting in a decrease in the fracture toughness of the joint. However, under most conditions, solder joints with ENIG finish showed higher resistance to fracture than joints attached directly to Cu substrates without ENIG metallization. Based on the experimental observations, a fracture mechanism map is constructed correlating the yield strength of the solder, the morphology and thickness of the interfacial IMC, and the fracture mechanisms as well as the fracture toughness values for different solder joints under mode I loading.

A meshless adaptive multiscale method for fracture

The paper presents a multiscale method for crack propagation. The coarse region is modelled by the differential reproducing kernel particle method. Fracture in the coarse scale region is modelled with the Phantom node method. A molecular statics approach is employed in the fine scale where crack propagation is modelled naturally by breaking of bonds. The triangular lattice corresponds to the lattice structure of the (111) plane of an FCC crystal in the fine scale region. The Lennard-Jones potential is used to model the atom-atom interactions. The coupling between the coarse scale and fine scale is realized through ghost atoms. The ghost atom positions are interpolated from the coarse scale solution and enforced as boundary conditions on the fine scale. The fine scale region is adaptively refined and coarsened as the crack propagates. The centro symmetry parameter is used to detect the crack tip location. The method is implemented in two dimensions. The results are compared to pure atomistic simulations and show excellent agreement. (C) 2014 Elsevier B. V. All rights reserved.

On the variability in fracture toughness of `ductile' bulk metallic glasses

The mode I fracture toughness, K-Ic, of ductile bulk metallic glasses (BMGs) exhibits a high degree of specimen-to-specimen variability. By conducting fracture experiments in modes I and II, we demonstrate that the observed high variability in mode I, vis-a-vis mode II, is a result of highly variable propensity for the conversion of shear bands into cracks in mode I whereas in mode II, crack growth direction is fixed. Thus, the measured variability in K-Ic is intrinsic to the nature of BMGs. (C) 2015 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.

Optimization of clamped beam geometry for fracture toughness testing of micron-scale samples

Fracture toughness measurements at the small scale have gained prominence over the years due to the continuing miniaturization of structural systems. Measurements carried out on bulk materials cannot be extrapolated to smaller length scales either due to the complexity of the microstructure or due to the size and geometric effect. Many new geometries have been proposed for fracture property measurements at small-length scales depending on the material behaviour and the type of device used in service. In situ testing provides the necessary environment to observe fracture at these length scales so as to determine the actual failure mechanism in these systems. In this paper, several improvements are incorporated to a previously proposed geometry of bending a doubly clamped beam for fracture toughness measurements. Both monotonic and cyclic loading conditions have been imposed on the beam to study R-curve and fatigue effects. In addition to the advantages that in situ SEM-based testing offers in such tests, FEM has been used as a simulation tool to replace cumbersome and expensive experiments to optimize the geometry. A description of all the improvements made to this specific geometry of clamped beam bending to make a variety of fracture property measurements is given in this paper.