Design and analysis of novel compression fracture specimen with constant form factor: Edge cracked semicircular disk (ECSD)

Inspired by the Brazilian disk geometry we examine the utility of an edge cracked semicircular disk (ECSD) specimen for rapid assessment of fracture toughness of brittle materials using compressive loading. It is desirable to optimize the geometry towards a constant form factor F for evaluating K-I. In this investigation photoelastic and finite element results for K-I evaluation highlight the effect of loading modeled using a Hertzian. A Hertzian loading subtending 4 degrees at the center leads to a surprisingly constant form factor of 1.36. This special case is further analyzed by applying uniform pressure over a chord for facilitating testing.

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.

Microcracking and fracture process in cement mortar and concrete: a comparative study using acoustic emission technique

This article reports the acoustic emission (AE) study of precursory micro-cracking activity and fracture behaviour of quasi-brittle materials such as concrete and cement mortar. In the present study, notched three-point bend specimens (TPB) were tested under crack mouth opening displacement (CMOD) control at a rate of 0.0004 mm/sec and the accompanying AE were recorded using a 8 channel AE monitoring system. The various AE statistical parameters including AE event rate , AE energy release rate , amplitude distribution for computing the AE based b-value, cumulative energy (I E) pound and ring down count (RDC) were used for the analysis. The results show that the micro-cracks initiated and grew at an early stage in mortar in the pre peak regime. While in the case of concrete, the micro-crack growth occurred during the peak load regime. However, both concrete and mortar showed three distinct stages of micro-cracking activity, namely initiation, stable growth and nucleation prior to the final failure. The AE statistical behavior of each individual stage is dependent on the number and size distribution of micro-cracks. The results obtained in the laboratory are useful to understand the various stages of micro-cracking activity during the fracture process in quasi-brittle materials such as concrete & mortar and extend them for field applications.

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.

Estimation of fracture properties for high strength and ultra high strength concrete beams and size effect

This article presents the details of estimation of fracture parameters for high strength concrete (HSC, HSC1) and ultra high strength concrete (UHSC). Brief details about characterization of ingredients of HSC, HSC1 and UHSC have been provided. Experiments have been carried out on beams made up of HSC, HSC1 and UHSC considering various sizes and notch depths. Fracture characteristics such as size independent fracture energy (G(f)), size of fracture process zone (C-f), fracture toughness (K-IC) and crack tip opening displacement (CTODc) have been estimated based on the experimental observations. From the studies, it is observed that (i) UHSC has high fracture energy and ductility inspite of having a very low value of C-f; (ii) relatively much more homogeneous than other concretes, because of absence of coarse aggregates and well-graded smaller size particles; (iii) the critical SIF (K-IC) values are increasing with increase of beam depth and decreasing with increase of notch depth. Generally, it can be noted that there is significant increase in fracture toughness and CTODc. They are about 7 times in HSC1 and about 10 times in UHSC compared to those in HSC; (iv) for notch-to-depth ratio 0.1, Bazant's size effect model slightly overestimates the maximum failure loads compared to experimental observations and Karihaloo's model slightly underestimates the maximum failure loads. For the notch-to-depth ratio ranging from 0.2 to 0.4 for the case of UHSC, it can be observed that, both the size effect models predict more or less similar maximum failure loads compared to corresponding experimental values.

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.

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.

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.

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 general methodology for calculating mixed mode stress intensity factors and fracture toughness of solder joints with interfacial cracks

Solder joints in electronic packages undergo thermo-mechanical cycling, resulting in nucleation of micro-cracks, especially at the solder/bond-pad interface, which may lead to fracture of the joints. The fracture toughness of a solder joint depends on material properties, process conditions and service history, as well as strain rate and mode-mixity. This paper reports on a methodology for determining the mixed-mode fracture toughness of solder joints with an interfacial starter-crack, using a modified compact mixed mode (CMM) specimen containing an adhesive joint. Expressions for stress intensity factor (K) and strain energy release rate (G) are developed, using a combination of experiments and finite element (FE) analysis. In this methodology, crack length dependent geometry factors to convert for the modified CMM sample are first obtained via the crack-tip opening displacement (CTOD)-based linear extrapolation method to calculate the under far-field mode I and II conditions (f(1a) and f(2a)), (ii) generation of a master-plot to determine a(c), and (iii) computation of K and G to analyze the fracture behavior of joints. The developed methodology was verified using J-integral calculations, and was also used to calculate experimental fracture toughness values of a few lead-free solder-Cu joints. (C) 2014 Elsevier Ltd. All rights reserved.

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.