An appraisal of the energy-size reduction relationships for mill scale-up design

In this paper, several well-known energy-size reduction relationships have been analyzed using Kapur’s similarity solution to the integro-differential equation of batch grinding. It has been shown that: (i) relationships proposed in terms of the energy actually utilized for breakage of particles, E, cannot be used to develop a practical energy-size reduction relationship as E is neither measurable nor it is found to be proportional to the measurable net energy input, E_n, (ii) the exponent of the characteristic particle size, $\overline{\mathrm{x}}$, in the relationship between E_n and $\overline{\mathrm{x}}$ is same as the exponent of particle size in the expression for the specific breakage rate function, α, which is not a function of $\overline{\mathrm{x}}$ in the case of ball mills, (iii) α values of 0, 0.5 and 1 cannot be associated with the laws of Kick, Bond and Rittinger, respectively. Based on the results of this analysis, the empirical scale-up models proposed by Bond and Morrell have been modified by replacing the exponents of 80% passing sizes by α. Further investigations have been recommended for resolution of large differences in the energy estimates obtained from these models for materials characterized by grindabilty values less than 1.0 and greater than 3.0?g/rev.     

Distributional and inferential properties of some new multivariate process capability indices for symmetric specification region

Statistical quality control is used to improve performance of processes. Since most of the processes are multivariate in nature, multivariate process capability indices (MPCIs) have been developed by many researchers depending on the context. However, it is generally difficult to understand and calculate MPCIs, compared to their univariate counterparts like $C_p$, $C_{pk}$, and so on. This paper discusses a relatively new development in MPCIs, namely, $C_G(u,v)$, which is a multivariate analogue of $C_p(u,v)$—the celebrated superstructure of univariate process capability indices . Some statistical properties of $C_G(u,v)$ are studied, particularly of $C_G(0,0)$, a member MPCI of the superstructure, which measures potential capability of a multivariate process. A threshold value of $C_G(0,0)$ is computed, and this can be considered as a logical cut-off for other member indices of $C_G(u,v)$ as well. The expression for the upper limit of the proportion of nonconformance is derived as a function of $C_G(0,0)$. Density plots of asymptotic distributions of four major member indices of $C_G(u,v)$, namely, $C_G(0,0)$, $C_G(1,0)$, $C_G(0,1)$, and $C_G(1,1)$, are made. Finally, a numerical example is discussed to supplement the theory developed in this paper.     

Efficient monitoring of coefficient of variation with an application to chemical reactor process

Control chart is a useful tool to monitor the performance of the industrial or production processes. Control charts are mostly adopted to detect unfavorable variations in process location (mean) and dispersion (standard deviation) parameters. In the literature, many control charts are designed for the monitoring of process variability under the assumption that the process mean is constant over time and the standard deviation is independent of the mean. However, for many real-life processes, the standard deviation may be proportional to mean, and hence it is more appropriate to monitor the process coefficient of variation (CV). In this study, we are proposing a design structure of the Shewhart type CV control chart under neoteric ranked set sampling with an aim to improve the detection ability of the usual CV chart. A comprehensive simulation study is conducted to evaluate the performance of the proposed $C{V}_{[\mathrm{NRSS}]}$ chart in terms of $ARL$, $MDRL,$ and $SDRL$ measures. Moreover, the comparison of $C{V}_{[\mathrm{NRSS}]}$ chart is made with the existing competitive charts, based on simple random sampling, ranked set sampling (RSS), median RSS, and extreme RSS schemes. The results revealed that the proposed chart has better detection ability as compared to all existing competitive charts. Finally, a real-life example is presented to illustrate the working of the newly proposed CV chart.     

Numerical investigation of natural convection of Al2O3-water nanofluid in a wavy cavity with conductive inner block using Buongiorno’s two-phase model

By employing the finite element method, thermophoresis and Brownian diffusion are studied numerically relating to the natural convection in a wavy cavity that is filled with an ${\text{Al}}_2{\text{O}}_3$-water nanofluid possessing a central heat-conducting solid block that is influenced by the local heater located on the bottom wall. An isothermal condition is established in the two wavy vertical walls, while adiabatic condition is for the top horizontal wall. Partial heating is applied to the bottom of the horizontal wall, while the remaining part remains in the adiabatic condition. Empirical correlations are employed for the thermal conductivity and dynamic viscosity of the nanofluid. The number of oscillations ($1?N\le 4$), Rayleigh number (${10}^3?\mathit{Ra}\le {10}^6$), nanoparticles volume fraction ($0??\le 0.04$) and dimensionless length of the bottom heater ($0.2?H?0.8$) govern the parameters in this study. The grid independency test, as well as experimental and numerical data from other published works, was employed to validate the developed computational code comprehensively. Based on the obtained results, it was found that the heat transfer inside the cavity is enhanced by introducing nanoparticles as well as a selection of optimal number of oscillations.     

Tensile strength of cohesive powders

Measurement and prediction of cohesive powder behaviour related to flowability, flooding or arching in silos is found to be very challenging. Previous round robin [52] attempts with ring shear testers did not furnish reliable data and have shown considerable degrees of scatter and uncertainty in key measurements. Thus studies to build a reliable experimental database using reference materials are needed in order to evaluate the repeatability and effectiveness of shear testers and the adopted procedures.In this paper, we study the effect of particle size on the yield locus for different grades of limestone (calcium carbonate). We use the nonlinear Warren Spring equation to obtain the values of cohesion C, tensile strength T, and the shear index n. We recover linear (n = 1) yield loci for $d_{50}>70$ μm with respectively small C and T, with consistent, finite macroscopic friction C/T = 0.7. With particle size decreasing below 70 μm the response becomes more and more cohesive and non-linear ($1<n<2$).Then we compare the values of the parameters $C,T$ and n obtained from two different shear testers (Schulze and Brookfield PFT). Both testers run at positive confining stresses (slightly different ranges) and give identical results for large fractions (weakly cohesive). For strongly cohesive samples, the PFT results are very similar to the ring shear tester, with slightly smaller values for T, C, and n. Further experiments with a variety of cohesive powders are needed to confirm or rebut this systematic difference the two testers display for cohesive powders.Finally, we compare the (extrapolated) values of T with a direct, transverse measurement running at negative stresses, using the Ajax tensile tester, and found a very good agreement, which validates the Warren Spring equation for negative stresses.     

Introducing C phase in additively manufactured Ti-6Al-4V: A new oxygen-stabilized face-centred cubic solid solution with improved mechanical properties

An oxygen-rich face-centred cubic (FCC) Ti phase was engineered in the microstructure of a Ti-6Al-4V alloy via additive manufacturing using laser powder bed fusion. Designated 'C', this oxygen-rich FCC phase has a lattice parameter of 0.406 nm and exhibits an orientation relationship with the parent α′ phase as follows: (0 0 0 1)_α′//{1 1 1}_C, and ${〈1\overline{2}10〉}_{\mathrm{\alpha }\prime }$ //${〈1\overline{1}0〉}_{\mathrm{C}}$. We propose that the formation of the C phase is facilitated by the combined effect of thermal gradients, deformation induced by the martensitic transformation, and local O enrichment. This enables an in-situ phase transformation from the hexagonal close-packed α′ phase to the C phase at elevated temperatures. Our density functional theory calculations indicate that oxygen occupancy in the octahedral interstices of the FCC structure is energetically preferred to corresponding sites in the α′ phase. The in-situ mechanical testing results indicate that the presence of the FCC phase significantly increases the local yield strength from 1.2 GPa for samples with only the α′ phase to 1.9 GPa for samples comprising approximately equal volume fractions of the α′ and FCC phases. No loss of ductility was reported, demonstrating great potential for strengthening and work hardening. We discuss the formation mechanism of the FCC phase and a pathway for future microstructural design of titanium alloys by additive manufacturing.