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.

Fracture Testing at Small-Length Scales: From Plasticity in Si to Brittleness in Pt

The field of micro-/nano-mechanics of materials has been driven, on the one hand by the development of ever smaller structures in devices, and, on the other, by the need to map property variations in large systems that are microstructurally graded. Observations of `smaller is stronger' have also brought in questions of accompanying fracture property changes in the materials. In the wake of scattered articles on micro-scale fracture testing of various material classes, this review attempts to provide a holistic picture of the current state of the art. In the process, various reliable micro-scale geometries are shown, challenges with respect to instrumentation to probe ever smaller length scales are discussed and examples from recent literature are put together to exhibit the expanse of unusual fracture response of materials, from ductility in Si to brittleness in Pt. Outstanding issues related to fracture mechanics of small structures are critically examined for plausible solutions.

Study of fracture behaviour of bond coats on nickel superalloy by three-point bending of microbeams

A microbeam testing geometry is designed to study the variation in fracture toughness across a compositionally graded NiAl coating on a superalloy substrate. A bi-material analytical model of fracture is used to evaluate toughness by deconvoluting load-displacement data generated in a three-point bending test. It is shown that the surface layers of a diffusion bond coat can be much more brittle than the interior despite the fact that elastic modulus and hardness do not display significant variations. Such a gradient in toughness allows stable crack propagation in a test that would normally lead to unstable fracture in a homogeneous, brittle material. As the crack approaches the interface, plasticity due to the presence of Ni3Al leads to gross bending and crack bifurcation.

Verification of the applicability of lattice model to concrete fracture by AE study

Notched three-point bend specimens (TPB) were tested under crack mouth opening displacement (CMOD) control at a rate of 0.0004 mm/s and the entire fracture process was simulated using a regular triangular two-dimensional lattice network only over the expected fracture proces zone width. The rest of the beam specimen was discretised by a coarse triangular finite element mesh. The discrete grain structure of the concrete was generated assuming the grains to be spherical. The load versus CMOD plots thus simulated agreed reasonably well with the experimental results. Moreover, acoustic emission (AE) hits were recorded during the test and compared with the number of fractured lattice elements. It was found that the cumulative AE hits correlated well with the cumulative fractured lattice elements at all load levels thus providing a useful means for predicting when the micro-cracks form during the fracturing process, both in the pre-peak and in the post-peak regimes.

Evaluation of ductile-brittle transition temperature (DBTT) of aluminide bond coats by micro-tensile test method

A method has been suggested to accurately determine the DBTT of diffusion aluminide bond coats. Micro-tensile testing of free-standing coating samples has been carried out. The DBTT was determined based on the variation of plastic strain-to-fracture with temperature. The positive features of this method over the previously reported techniques are highlighted. (C) 2010 Elsevier B.V. All rights reserved.

Flow Instabilities and fracture in Ti-6Al-4V deformed in compression at 298 K to 673 K

Uniaxial compression tests were conducted on Ti-6Al-4V specimens in the strain-rate range df 0.001 to 1 s(-1) and temperature range of 298 to 673 K. The stress-strain curves exhibited a peak flow stress followed by flow softening. Up to 523 K, the specimens cracked catastrophically after the flow softening started. Adiabatic shear banding was observed in this regime. The fracture surface exhibited both mode I and II fracture features. The state of stress existing in a compression test specimen when bulging occurs is responsible for this fracture. The instabilities observed in the present tests are classified as ''geometric'' in nature and are state-of-stress dependant, unlike the ''intrinsic'' instabilities, which are dependant on the dynamic constitutive behavior of the material.

ADC Static Nonlinearity Estimation Using Linearity Property of Sinewave

Prohibitive test time, nonuniformity of excitation, and signal nonlinearity are major concerns associated with employing dc, sine, and triangular/ramp signals, respectively, while determining static nonlinearity of analog-to-digital converters (ADCs) with high resolution (i.e., ten or more bits). Attempts to overcome these issues have been examined with some degree of success. This paper describes a novel method of estimating the ``true'' static nonlinearity of an ADC using a low-frequency sine signal (for example, less than 10 Hz) by employing the histogram-based approach. It is based on the well-known fact that the variation of a sine signal is ``reasonably linear'' when the angle is small, for example, in the range of +/- 5 degrees to +/- 7 degrees. In the proposed method, the ADC under test has to be ``fed'' with this ``linear'' portion of the sinewave. The presence of any harmonics and offset in input excitation makes this linear part of the sine signal marginally different compared with that of an ideal ramp signal of equal amplitude. However, since it is a sinusoid, this difference can be accurately determined and later compensated from the measured ADC output. Thus, the corrected ADC output will correspond to the true ADC static nonlinearity. The implementation of the proposed method is discussed along with experimental results for two 8-b ADCs and one 10-b ADC which are then compared with the static characteristics estimated by the conventional DC method.

Graphical method to determine the parameters of the two-parameter fracture model for concrete

To evaluate the parameters in the two-parameter fracture model, i.e. the critical stress intensity factor and critical crack tip opening displacement for the fracture of plain concrete in Mode 1 for the given test configuration and geometry, considerable computational effort is necessary. A simple graphical method has been proposed using normalized fracture parameters for the three-point bend (3PB) notched specimen and the double-edged notched (DEN) specimen. A similar graphical method is proposed to compute the maximum load carrying capacity of a specimen, using the critical fracture parameters both for 3PB and DEN configurations.

Studies on indentation fracture toughness on ceramic and ceramic composite using acoustic emission technique

This paper is aimed at investigating the acoustic emission activities during indentation toughness tests on an alumina based wear resistant ceramic and 25 wt% silicon carbide whisker (SIC,) reinforced alumina composite. It has been shown that the emitted acoustic emission signals characterize the crack growth during loading. and unloading cycles in an indentation test. The acoustic emission results indicate that in the case of the composite the amount of crack growth during unloading is higher than that of loading, while the reverse is true in case of the wear resistant ceramics. Acoustic emission activity observed in wear resistant ceramic is less than that in the case of composite. An attempt has been made to correlate the acoustic emission signals with crack growth during indentation test.

Evaluation of Fracture Parameters by Double-G, Double-K Models and Crack Extension Resistance for High Strength and Ultra High Strength Concrete Beams

This paper presents the advanced analytical methodologies such as Double- G and Double - K models for fracture analysis of concrete specimens made up of high strength concrete (HSC, HSC1) and ultra high strength concrete. Brief details about characterization and experimentation of HSC, HSC1 and UHSC have been provided. Double-G model is based on energy concept and couples the Griffith's brittle fracture theory with the bridging softening property of concrete. The double-K fracture model is based on stress intensity factor approach. Various fracture parameters such as cohesive fracture toughness (4), unstable fracture toughness (K-Ic(c)), unstable fracture toughness (K-Ic(un)) and initiation fracture toughness (K-Ic(ini)) have been evaluated based on linear elastic fracture mechanics and nonlinear fracture mechanics principles. Double-G and double-K method uses the secant compliance at the peak point of measured P-CMOD curves for determining the effective crack length. Bi-linear tension softening model has been employed to account for cohesive stresses ahead of the crack tip. From the studies, it is observed that the fracture parameters obtained by using double - G and double - K models are in good agreement with each other. Crack extension resistance has been estimated by using the fracture parameters obtained through double - K model. It is observed that the values of the crack extension resistance at the critical unstable point are almost equal to the values of the unstable fracture toughness K-Ic(un) of the materials. The computed fracture parameters will be useful for crack growth study, remaining life and residual strength evaluation of concrete structural components.

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.

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.

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.

Biocompatibility property of 100% strontium-substituted SiO2-Al2O3-P2O5-CaO-CaF2 glass ceramics over 26 weeks implantation in rabbit model: Histology and micro-Computed Tomography analysis

One of the desired properties for any new biomaterial composition is its long-term stability in a suitable animal model and such property cannot be appropriately assessed by performing short-term implantation studies. While hydroxyapatite (HA) or bioglass coated metallic biomaterials are being investigated for in vivo biocompatibility properties, such study is not extensively being pursued for bulk glass ceramics. In view of their inherent brittle nature, the implant stability as well as impact of long-term release of metallic ions on bone regeneration have been a major concern. In this perspective, the present article reports the results of the in vivo implantation experiments carried out using 100% strontium (Sr)-substituted glass ceramics with the nominal composition of 4.5 SiO2-3Al(2)O(3)-1.5P(2)O(5)-3SrO-2SrF(2) for 26 weeks in cylindrical bone defects in rabbit model. The combination of histological and micro-computed tomography analysis provided a qualitative and quantitative understanding of the bone regeneration around the glass ceramic implants in comparison to the highly bioactive HA bioglass implants (control). The sequential polychrome labeling of bone during in vivo osseointegration using three fluorochromes followed by fluorescence microscopy observation confirmed homogeneous bone formation around the test implants. The results of the present study unequivocally confirm the long-term implant stability as well as osteoconductive property of 100% Sr-substituted glass ceramics, which is comparable to that of a known bioactive implant, that is, HA-based bioglass. (c) 2014 Wiley Periodicals, Inc. J Biomed Mater Res Part B: Appl Biomater, 103B: 1168-1179, 2015.