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.

Multifunctional Properties of Multistage Spark Plasma Sintered HA-BaTiO3-Based Piezobiocomposites for Bone Replacement Applications

This work reports the processing-microstructure-property correlation of novel HA-BaTiO3-based piezobiocomposites, which demonstrated the bone-mimicking functional properties. A series of composites of hydroxyapatite (HA) with varying amounts of piezoelectric BaTiO3 (BT) were optimally processed using uniquely designed multistage spark plasma sintering (SPS) route. Transmission electron microscopy imaging during in situ heating provides complementary information on the real-time observation of sintering behavior. Ultrafine grains (0.50m) of HA and BT phases were predominantly retained in the SPSed samples. The experimental results revealed that dielectric constant, AC conductivity, piezoelectric strain coefficient, compressive strength, and modulus values of HA-40wt% BT closely resembles with that of the natural bone. The addition of 40wt% BT enhances the long-crack fracture toughness, compressive strength, and modulus by 132%, 200%, and 165%, respectively, with respect to HA. The above-mentioned exceptional combination of functional properties potentially establishes HA-40wt% BT piezocomposite as a new-generation composite for orthopedic implant applications.

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.

Size Control and Magnetic Property Trends in Cobalt Ferrite Nanoparticles Synthesized Using an Aqueous Chemical Route

Cobalt ferrite (CoFe2O4) is an engineering material which is used for applications such as magnetic cores, magnetic switches, hyperthermia based tumor treatment, and as contrast agents for magnetic resonance imaging. Utility of ferrites nanoparticles hinges on its size, dispersibility in solutions, and synthetic control over its coercivity. In this work, we establish correlations between room temperature co-precipitation conditions, and these crucial materials parameters. Furthermore, post-synthesis annealing conditions are correlated with morphology, changes in crystal structure and magnetic properties. We disclose the synthesis and process conditions helpful in obtaining easily sinterable CoFe2O4 nanoparticles with coercive magnetic flux density (H-c) in the range 5.5-31.9 kA/m and M-s in the range 47.9-84.9 A.m(2)Kg(-1). At a grain size of similar to 54 +/- 2 nm (corresponding to 1073 K sintering temperature), multi-domain behavior sets in, which is indicated by a decrease in H-c. In addition, we observe an increase in lattice constant with respect to grain size, which is the inverse of what is expected of in ferrites. Our results suggest that oxygen deficiency plays a crucial role in explaining this inverse trend. We expect the method disclosed here to be a viable and scalable alternative to thermal decomposition based CoFe2O4 synthesis. The magnetic trends reported will aid in the optimization of functional CoFe2O4 nanoparticles

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.

Microstructure Development, Nanomechanical, and Dynamic Compression Properties of Spark Plasma Sintered TiB2-Ti-Based Homogeneous and Bi-layered Composites

The growing threats due to increased use of small-caliber armor piercing projectiles demand the development of new light-weight body armor materials. In this context, TiB2 appears to be a promising ceramic material. However, poor sinterability and low fracture toughness remain two major issues for TiB2. In order to address these issues together, Ti as a sinter-aid is used to develop TiB2-(x wt pct Ti), (x = 10, 20) homogeneous composites and a bi-layered composite (BLC) with each layer having Ti content of 10 and 20 wt pct. The present study uniquely demonstrates the efficacy of two-stage spark plasma sintering route to develop dense TiB2-Ti composites with an excellent combination of nanoscale hardness (similar to 36 GPa) and indentation fracture toughness (similar to 12 MPa m(1/2)). In case of BLC, these properties are not compromised w.r.t. homogeneous composites, suggesting the retention of baseline material properties even in the bi-layer design due to optimal relief of residual stresses. The better indentation toughness of TiB2-(10 wt pct Ti) and TiB2-(20 wt pct Ti) composites can be attributed to the observed crack deflection/arrest, indicating better damage tolerance. Transmission electron microscope investigation reveals the presence of dense dislocation networks and deformation twins in alpha-Ti at the grain boundaries and triple pockets, surrounded by TiB2 grains. The dynamic strength of around 4 GPa has been measured using Split Hopkinson Pressure Bar tests in a reproducible manner at strain rates of the order of 600 s(-1). The damage progression under high strain rate has been investigated by acquiring real time images for the entire test duration using ultra-high speed imaging. An attempt has been made to establish microstructure-property correlation and a simple analysis based on Mohr-Coulomb theory is used to rationalize the measured strength properties.

Using heat treatment effects and EBSD analysis to tailor microstructure of hybrid Mg nanocomposite for enhanced overall mechanical response

In this study, a detailed investigation on the effect of heat treatment on the microstructural characteristics, texture evolution and mechanical properties of Mg-(5.6Ti+2.5B(4)C)(BM) hybrid nanocomposite is presented. Optimised heat treatment parameters, namely, heat treatment temperature and heat treatment time, were first identified through grain size and microhardness measurements. Initially, heat treatment of composites was conducted at temperature range between 100 and 300 degrees C for 1 h. Based on optical microscopic analysis and microhardness measurements, it was evident that significant grain growth and reduction in microhardness occurred for temperatures > 200 degrees C. The cutoff temperature that caused significant grain growth/matrix softening was thus identified. Second, at constant temperature (200 degrees C), the effect of variation of heat treatment time was carried out (ranging between 1 and 5 h) so as to identify the range wherein increase in average grain size and reduction in microhardness occurred. Furthering the study, the effect of optimised heat treatment parameters (200 degrees C, 5 h) on the microstructural texture evolution and hence, on the tensile and compressive properties of the Mg-(5.6Ti+2.5B(4)C)(BM) hybrid nanocomposite was carried out. From electron backscattered diffraction (EBSD) analysis, it was identified that the optimised heat treatment resulted in recrystallisation and residual stress relaxation, as evident from the presence of similar to 87% strain free grains, when compared to that observed in the non-heat treated/as extruded condition (i.e. 2.2 times greater than in the as extruded condition). For the heat treated composite, under both tensile and compressive loads, a significant improvement in fracture strain values (similar to 60% increase) was observed when compared to that of the non-heat treated counterpart, with similar to 20% reduction in yield strength. Based on structure-property correlation, the change in mechanical characteristics is identified to be due to: (1) the presence of less stressed matrix/reinforcement interface due to the relief of residual stresses and (2) texture weakening due to matrix recrystallisation effects, both arising due to heat treatment.

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.

Faster computation of the Karhunen-Loeve expansion using its domain independence property

The goal of this work is to reduce the cost of computing the coefficients in the Karhunen-Loeve (KL) expansion. The KL expansion serves as a useful and efficient tool for discretizing second-order stochastic processes with known covariance function. Its applications in engineering mechanics include discretizing random field models for elastic moduli, fluid properties, and structural response. The main computational cost of finding the coefficients of this expansion arises from numerically solving an integral eigenvalue problem with the covariance function as the integration kernel. Mathematically this is a homogeneous Fredholm equation of second type. One widely used method for solving this integral eigenvalue problem is to use finite element (FE) bases for discretizing the eigenfunctions, followed by a Galerkin projection. This method is computationally expensive. In the current work it is first shown that the shape of the physical domain in a random field does not affect the realizations of the field estimated using KL expansion, although the individual KL terms are affected. Based on this domain independence property, a numerical integration based scheme accompanied by a modification of the domain, is proposed. In addition to presenting mathematical arguments to establish the domain independence, numerical studies are also conducted to demonstrate and test the proposed method. Numerically it is demonstrated that compared to the Galerkin method the computational speed gain in the proposed method is of three to four orders of magnitude for a two dimensional example, and of one to two orders of magnitude for a three dimensional example, while retaining the same level of accuracy. It is also shown that for separable covariance kernels a further cost reduction of three to four orders of magnitude can be achieved. Both normal and lognormal fields are considered in the numerical studies. (c) 2014 Elsevier B.V. All rights reserved.