The Fracture Characteristics of a Near Eutectic Al-Si Based Alloy Under Compression

The fracture of eutectic Si particles dictates the fracture characteristics of Al-Si based cast alloys. The morphology of these particles is found to play an important role in fracture initiation. In the current study, the effects of strain rate, temperature, strain, and heat treatment on Si particle fracture under compression were investigated. Strain rates ranging from 3 x 10(-4)/s to 10(2)/s and three temperatures RT, 373 K, and 473 K (100 A degrees C and 200 A degrees C) are considered in this study. It is found that the Si particle fracture shows a small increase with increase in strain rate and decreases with increase in temperature at 10 pct strain. The flow stress at 10 pct strain exhibits the trend similar to particle fracture with strain rate and temperature. Particle fracture also increases with increase in strain. Large and elongated particles show a greater tendency for cracking. Most fracture occurs on particles oriented nearly perpendicular to the loading axis, and the cracks are found to occur almost parallel to the loading axis. At any strain rate, temperature, and strain, the Si particle fracture is greater for the heat-treated condition than for the non-heat-treated condition because of higher flow stress in the heat-treated condition. In addition to Si particle fracture, elongated Fe-rich intermetallic particles are also seen to fracture. These particles have specific crystallographic orientations and fracture along their major axis with the cleavage planes for their fracture being (100). Fracture of these particles might also play a role in the overall fracture behavior of this alloy since these particles cleave along their major axis leading to cracks longer than 200 mu m.

Thermal vibration analysis of monolayer graphene embedded in elastic medium based on nonlocal continuum mechanics

This paper presents the thermal vibration analysis of single-layer graphene sheet embedded in polymer elastic medium, using the plate theory and nonlocal continuum mechanics for small scale effects. The graphene is modeled based on continuum plate theory and axial stress caused by the thermal effects is also considered. Nonlocal governing equation of motion for this graphene sheet system is derived from the principle of virtual displacements. The closed form solution for thermal-vibration frequencies of a simply supported rectangular nanoplate has been obtained by using the Navier's method of solution. Numerical results obtained by the present theory are compared with available solutions in the literature and the molecular dynamics results. The influences of the small scale coefficient, the room or low temperature, the high temperature, the half wave number and the aspect ratio of nanoplate on the natural frequencies are considered and discussed in detail. The thermal vibration analysis of single- and double-layer graphene sheets are considered for the analysis. The mode shapes of the respective graphene system are also captured in this work. The present analysis results can be used for the design of the next generation of nanodevices that make use of the thermal vibration properties of the graphene.

Determination of size-independent specific fracture energy of concrete mixes by two methods

The RILEM work-of-fracture method for measuring the specific fracture energy of concrete from notched three-point bend specimens is still the most common method used throughout the world, despite the fact that the specific fracture energy so measured is known to vary with the size and shape of the test specimen. The reasons for this variation have also been known for nearly two decades, and two methods have been proposed in the literature to correct the measured size-dependent specific fracture energy (G(f)) in order to obtain a size-independent value (G(F)). It has also been proved recently, on the basis of a limited set of results on a single concrete mix with a compressive strength of 37 MPa, that when the size-dependent G(f) measured by the RILEM method is corrected following either of these two methods, the resulting specific fracture energy G(F) is very nearly the same and independent of the size of the specimen. In this paper, we will provide further evidence in support of this important conclusion using extensive independent test results of three different concrete mixes ranging in compressive strength from 57 to 122 MPa. (c) 2013 Elsevier Ltd. All rights reserved.

Experimental Studies on the Mechanics of Cohesive Frictional Granular Media

The mechanical behaviour of cohesive-frictional granular materials is a combination of the strength pervading as intergranular friction (represented as an angle of internal friction - Phi), and the cohesion (C) between these particles. Most behavioral or constitutive models of this class of granular materials comprise of a cohesion and frictional component with no regard to the length scale i.e. from the micro structural models through the continuum models. An experimental study has been made on a model granular material, viz. angular sand with different weights of binding agents (varying degrees of cohesion) at multiple length scales to physically map this phenomenon. Cylindrical specimen of various diameters - 10, 20, 38, 100, 150 mm (and with an aspect ratio of 2) are reconstituted with 2, 4 and 8% by weight of a binding agent. The magnitude of this cohesion is analyzed using uniaxial compression tests and it is assumed to correspond to the peak in the normalized stress-strain plot. Increase in the cohesive strength of the material is seen with increasing size of the specimen. A possibility of ``entanglement'' occurring in larger specimens is proposed as a possible reason for deviation from a continuum framework.

Dynamics and fracture of ligaments from a droplet on a vibrating surface

A droplet residing on a vibrating surface and in the pressure antinode of an asymmetric standing wave can spread radially outward and atomize. In this work, proper orthogonal decomposition through high speed imaging is shown to predict the likelihood of atomization for various viscous fluids based on prior information in the droplet spreading phase. Capillary instabilities are seen to affect ligament rupture. Viscous dissipation plays an important role in determining the wavelength of the most unstable mode during the inception phase of the ligaments. However, the highest ligament capillary number achieved was less than 1, and the influence of viscosity in the ligament growth and breakup phases is quite minimal. It is inferred from the data that the growth of a typical ligament is governed by a balance between the inertial force obtained from the inception phase and capillary forces. By including the effect of acoustic pressure field around the droplet, the dynamics of the ligament growth phase is revealed and the ligament growth profiles for different fluids are shown to collapse on a straight line using a new characteristic time scale.

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.