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The present work deals with the strength scaling to characterize size effect of the cylindrical ceramic specimen for bimodular materials. The analysis is based on Weibull statistical theory. The derived semi-analytical expressions for effective volume and effective surface area for characterizing volume and surface flaws, respectively, have been validated with the experimental based numerical model. The flexural testing on cylindrical specimens has been done. The characteristic unimodular and bimodular strength has been estimated with different estimators like linear regression and maximum likelihood estimators for two different sized flexural specimens. The strength distribution analysis is controlled by 90% of the confidence interval, and coefficient of determination has been tabulated for goodness of the fit of Weibull distribution curve. The numerical based unimodular and bimodular models have been developed and also its post-processing code has been developed to evaluate the effective volume and surface area numerically. The comparison has been made for different fracture criteria such as principal of independent action (PIA) and normal stress averaging (NSA). © 2020, Springer Nature Singapore Pte Ltd.

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Lecture Notes in Mechanical Engineering

Size Effect in Bimodular Flexural Cylindrical Specimens

The present study addresses the issues of shifting of elastic axis and elastic surface for strength scaling of bimodular C-ring specimens using a Weibull statistical model. A semianalytical weakest link theory approach has been followed to evaluate the effective volume and effective area with presumed surface and volume distributed scattered flaws in the specimen. Experimentation, semianalytic, and finite element-based numerical procedures have been pursued to iteratively evaluate the Weibull characteristic parameters for typical loading configurations. Significant asymptotic variation in these two parameters has been observed at a low Weibull modulus for a set of change in elastic modulus ratio of tension and compression in contrast to unimodular assumptions. This variation can be ascribed to the significant shifting of neutral surface from the centroidal surface, thereby exhibiting the low level of confidence in designing bimodular structures. Also, the gradients of the curve are very steep, reflecting the uncertainty in strength characteristics as compared to the unimodular case, thus causing changes in the Weibull effective volume and effective surface area. The variation in Weibull effective surface area is less in comparison to the effective volume for unimodular and bimodular thick and thin C-ring specimens. The tabulated results can be used to substitute for a large number of expensive experiments for the design and analysis of bimodular structural components. Copyright © 2019 by ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959

Journal of Testing and Evaluation

Semianalytic Weibull model to assess the influence of strength controlling flaws for bimodular C-ring specimen

In this work, a universal path independent integral Ju that represents the energy release rate or flux during crack extension in a homogeneous and isotropic material, has been derived for straight crack subjected to multiple loads. This version of integral includes the effect of elastic strain, Eigen strain, thermal strain, body forces and magnetic strain. Particularly focus is made on thermo-mechanical and magnetic strains. The 3D J-integral expression represents the energy release rate in the combined thermoelastic field with magnetostriction characteristics. This integral is applicable to the real field problems concerning medium in an electric field where the multiphysics of heat generation and magnetic field are involved. 3D finite element analysis of edge cracked magnetostrictive specimen has been carried out to demonstrate the efficacy of the integral expressions. © 2018 Elsevier Ltd

Mechanics Research Communications

3D Path independent integral for thermoelastic and magnetostriction problem

The influence of bimodularity (different stress ∼ strain behaviour in tension and compression) on fracture behaviour of graphite specimens has been studied with fracture toughness (KIc), critical J-integral (JIc) and critical strain energy release rate (GIc) as the characterizing parameter. Bimodularity index (ratio of tensile Young's modulus to compression Young's modulus) of graphite specimens has been obtained from the normalized test data of tensile and compression experimentation. Single edge notch bend (SENB) testing of pre-cracked specimens from the same lot have been carried out as per ASTM standard D7779-11 to determine the peak load and critical fracture parameters KIc, GIc and JIc using digital image correlation technology of crack opening displacements. Weibull weakest link theory has been used to evaluate the mean peak load, Weibull modulus and goodness of fit employing two parameter least square method (LIN2), biased (MLE2-B) and unbiased (MLE2-U) maximum likelihood estimator. The stress dependent elasticity problem of three-dimensional crack progression behaviour for the bimodular graphite components has been solved as an iterative finite element procedure. The crack characterizing parameters critical stress intensity factor and critical strain energy release rate have been estimated with the help of Weibull distribution plot between peak loads versus cumulative probability of failure. Experimental and Computational fracture parameters have been compared qualitatively to describe the significance of bimodularity. The bimodular influence on fracture behaviour of SENB graphite has been reflected on the experimental evaluation of GIc values only, which has been found to be different from the calculated JIc values. Numerical evaluation of bimodular 3D J-integral value is found to be close to the GIc value whereas the unimodular 3D J-value is nearer to the JIc value. The significant difference between the unimodular JIc and bimodular GIc indicates that GIc should be considered as the standard fracture parameter for bimodular brittle specimens. © 2018 Elsevier B.V.

Journal of Nuclear Materials

Experimental and computational correlation of fracture parameters KIc, JIc, and GIc for unimodular and bimodular graphite components

Reduced graphene oxide (rGO) modified transition metal oxide based composites were successfully synthesized via a sol-gel assisted Hummers' method. The present study includes the synthesis of CuCr2O4·0.7TiO2, the synthesis of rGO and the synthesis of rGO modified CuCr2O4·0.7TiO2. In order to synthesize the desired catalyst, rGO and Cu-Cr-O-0.7TiO2 were synthesized individually. The CuCr2O4·0.7TiO2 composite was synthesized via a sol-gel method. Reduced graphene oxide (rGO) used as a modifier in the catalyst, was also synthesized in the laboratory and was calcined at high temperature (1050 °C) to improve its activity. Finally, Cu-Cr-O-0.7TiO2 was modified with 10 wt% rGO. The post synthesis characterizations were performed using various instrumental techniques including X-ray diffraction (XRD) for phase analysis, Fourier transform infrared (FTIR) and Raman spectroscopy for molecular interactions, scanning electron microscopy (SEM) for surface morphology, energy dispersive X-ray analysis (EDX), elemental analysis and X-ray photoelectron spectroscopy (XPS) for binding energy. The catalytic efficiency of the synthesized composite catalyst samples based thermal decomposition of the host material (i.e. AP) was determined by differential thermal analysis (DTA) and thermogravimetric analysis (TGA). The rGO modification into the Cu-Cr-O-0.7TiO2 tri-metallic composition made it the most promising catalyst for the thermal decomposition of AP, due to the tremendously high electrical and thermal conductivity of rGO. Different amounts (2.5, 5.0, 7.5 and 10 wt%) of Cu-Cr-O-0.7TiO2-rGO were added to ammonium perchlorate (AP) to investigate its effect on the thermal decomposition of AP, which is a well known oxidizer used worldwide in the solid composite propellant (SCP) in modern rocketry. The 5 wt% of catalyst (Cu-Cr-O-0.7TiO2-rGO) addition into AP exhibited the remarkably enhanced thermal decomposition of AP. Finally, the burn rate of SCP was examined with 5 wt% catalyst modified AP. The 5 wt% of catalyst modified AP exhibited 175.31% higher burn rate of SCP, compared to the burn rate of pure AP added SCP. Furthermore, when it was compared with an industrial catalyst, i.e. activated copper chromite (ACR), it showed 133.61% higher burn rate of SCP. The SCP exhibited excellent ballistic performance with 0.6% of catalyst in AP, which enhanced the burn rate from 4.866 mm s-1 (for SCP having pure AP) to 8.531 mm s-1 (for SCP having catalyst added AP) and 6.385 mm s-1 (for SCP having industrial catalyst added AP) at 33 bar. © 2017 The Royal Society of Chemistry.

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RSC Advances

The effect of reduced graphene oxide on the catalytic activity of Cu-Cr-O-TiO2 to enhance the thermal decomposition rate of ammonium perchlorate: An efficient fuel oxidizer for solid rocket motors and missiles

The objective of this present work was to predict the strength distribution of bi-modular cylindrical ceramic specimen from that of another based on Weibull statistical theory. In order to do so, initially, semi-analytical expression for effective volume and effective surface for the cylindrical bar loaded in flexure were derived. In addition, strength scaling ratio from one flexural loading configuration to another with various Weibull modulus was made available. Elaborate experimentation and numerical simulations was carried out to verify the analytical model. Generally, strength scaling for specimen size is dependent on whether the flaws are volume or surface distributed; however, in this study, it was observed that the ratio of strengths from any two configurations, such as three-point flexural to four-point, is independent of whether the flaws are volume or surface distributed when the crosssectional sizes are the same. Copyright © 2015 by ASTM International.

Weibull effective volumes, surfaces, and strength scaling for cylindrical flexure specimens having bi-modularity http://compass.astm.org/download/JTE20150301.39445.pdf

In the present work, the integral, originally developed for a 2D stationary circular arc crack in a homogeneous and isotropic material subjected to multiple loads, has been implemented into a finite element postprocessing program for examining the path-independence behavior under elastic deformation while employing rapidly varying mechanical load. Under different loading rates, the integral has been computed on several contours in order to describe the invariant property of the integral. Numerical results reveal that, within the limits of computational accuracy, the path-invariant property is well preserved over the integration contours for the present loading rates. The variation of the integral with respect to time has also been studied for both plane strain and plane stress conditions. The numerical investigations confirm that the performance of the integral is sufficiently impressive and therefore suggest applicability in fracture-related studies. © 2013 Taylor & Francis Group, LLC.

Mechanics Based Design of Structures and Machines

Assessment of structural integrity under dynamic loading using path-independent integral

It has been a great challenge for many scientists and engineers to compute elastic-plastic solutions for dynamically loaded cracked structures due to the fact that the solutions are much more complicated and computationally time consuming than corresponding static problems. The path independent integral J^F, originally developed for a two-dimensional dynamically loaded stationary circular arc crack in a homogeneous and isotropic material, is evaluated in the present study by taking elastic-plastic material properties to quantify the crack problem. All the numerical results presented in this study were evaluated using general purpose finite element commercial software ANSYS together with the post-processing program (using FORTRAN) developed by the authors. Numerical results thus obtained are compared with good agreement within the limits of computational accuracy and the path invariant property of J^ F is well preserved over the integration contours. © 2013 Elsevier B.V.