Crystal Plasticity Modelling of Large Strain Deformation in Single Crystals of Magnesium

Magnesium, with a Hexagonal Close-Packed (HCP) structure, is the eighth most abundant element in the earth’s crust and the third most plentiful element dissolved in the seawater. Magnesium alloys exhibit the attractive characteristics of low densities and high strength-to-weight ratios along with good castability, recyclability, and machinability. Replacing the steel and/or aluminum sheet parts with magnesium sheet parts in vehicles is a great way of reducing the vehicles weight, which results in great savings on fuel consumption. The lack of magnesium sheet components in vehicle assemblies is due to magnesium’s poor room-temperature formability. In order to successfully form the sheets of magnesium at room temperature, it is necessary to understand the formability of magnesium at room temperature controlled by various plastic deformation mechanisms. The plastic deformation mechanisms in pure magnesium and some of its alloys at room temperature are crystallographic slip and deformation twinning. The slip systems in magnesium at room temperature are classified into primary (first generation), secondary (second generation), and tertiary (third generation) slip systems. The twinning systems in magnesium at room temperature are classified into primary (first generation) and secondary (second generation, or double) twinning systems. A new comprehensive rate-dependent elastic-viscoplastic Crystal Plasticity Constitutive Model (CPCM) that accounts for all these plastic deformation mechanisms in magnesium was proposed. The proposed model individually simulates slip-induced shear in the parent as well as in the primary and secondary twinned regions, and twinning-induced shear in the primary and secondary twinned regions. The model also tracks the texture evolution in the parent, primary and secondary twinned regions. Separate resistance evolution functions for the primary, secondary, and tertiary slip systems, as well as primary and secondary twinning systems were considered in the formulation. In the resistance evolution functions, the interactions between various slip and twinning systems were accounted for. The CPCM was calibrated using the experimental data reported in the literature for pure magnesium single crystals at room temperature, but needs further experimental data for full calibration. The partially calibrated model was used to assess the contributions of various plastic deformation mechanisms in the material stress-strain response. The results showed that neglecting secondary slip and secondary twinning while simulating plastic deformation of magnesium alloys by crystal plasticity approach can lead to erroneous results. This indicates that all the plastic deformation mechanisms have to be accounted for when modelling the plastic deformation in magnesium alloys. Also, the CPCM in conjunction with the Marciniak–Kuczynski (M–K) framework were used to assess the formability of a magnesium single crystal sheet at room temperature by predicting the Forming Limit Diagrams (FLDs). Sheet necking was initiated from an initial imperfection in terms of a narrow band. A homogeneous deformation field was assumed inside and outside the band, and conditions of compatibility and equilibrium were enforced across the band interfaces. Thus, the CPCM only needs to be applied to two regions, one inside and one outside the band. The FLDs were simulated under two conditions: a) the plastic deformation mechanisms are primary slip systems alone, and b) the plastic deformation mechanisms are primary slip and primary twinning systems. The FLDs were computed for two grain orientations. In the first orientation, primary extension twinning systems had favourable orientation for activation. In the second orientation, primary contraction twinning systems had favourable orientation for activation. The effects of shear strain outside the necking band, rate sensitivity, and c/a ratio on the simulated FLDs in the two grain orientations were individually explored

A Likelihood Ratio Test Approach to Profile Monitoring in Tourism Industry

A new statistical profile monitoring technique to monitor and detect changes in logistic profiles with an application in the tourism industry is presented in this paper. In the statistical process control literature, profile is usually referred to as a relationship between a response variable and one or more explanatory variables. In the tourism case study presented in this paper, time is considered as the explanatory variable and tourism satisfaction as the response variable. The Likelihood ratio test is used as a vehicle to detect any changes in the satisfaction profile in phase II of profile monitoring. The performance of the proposed method is evaluated using the average run length criterion. The numerical data indicate satisfactory results for the proposed approach

Dynamics and Control of a Piano Action Mechanism

The piano action is the mechanism that transforms the finger force applied to a key into the motion of a hammer that strikes a piano string. This thesis focuses on improving the fidelity of the dynamic model of a grand piano action which has been already developed by Hirschkorn et al. at the University of Waterloo. This model is the state-of-the-art dynamic model of the piano in the literature and is based on the real components of the piano action mechanism (key, whippen, jack, repetition lever, and hammer). Two main areas for improving the fidelity of the dynamic model are the hammer shank and the connection point between the key and the ground. The hammer shank is a long narrow wooden rod and, by observation with a high-speed video camera, the flexibility of this part has been confirmed. In previous work, the piano hammer had been modelled as a rigid body. In this work, a Rayleigh beam model is used to model the flexible behaviour of the hammer shank. By comparing the experimental and analytical results, it turns out that the flexibility of the hammer shank does not significantly affect the rotation of the other parts of the piano mechanism, compared with the case that the hammer shank has been modelled as a rigid part. However, the flexibility of the hammer shank changes the impact velocity of the hammer head, and also causes a greater scuffing motion for the hammer head during the contact with the string. The connection of the piano key to the ground had been simply modelled with a revolute joint, but the physical form of the connection at that point suggests that a revoluteprismatic joint with a contact force underneath better represents this connection. By comparing the experimental and analytical results, it is concluded that incorporating this new model significantly increases the fidelity of the model for the blows. In order to test the accuracy of the dynamic model, an experimental setup, including a servo motor, a load cell, a strain gauge, and three optical encoders, is built. The servo motor is used to actuate the piano key. Since the purpose of the motor is to consistently mimic the finger force of the pianist, the output torque of the motor is controlled. To overcome the problem associated with the motor torque control method used in previous work, a new torque control method is implemented on a real-time PC and a better control of the motor torque output is established. Adding a more realistic model of the piano string to the current piano action model and finding a better contact model for the contacts that happen between the surfaces that are made of felt (or leather), are two main areas that can be worked on in the future research. These two areas will help to further increase the fidelity of the present piano action model

Dynamics and Control of a Piano Action Mechanism

The piano action is the mechanism that transforms the finger force applied to a key into the motion of a hammer that strikes a piano string. This thesis focuses on improving the fidelity of the dynamic model of a grand piano action which has been already developed by Hirschkorn et al. at the University of Waterloo. This model is the state-of-the-art dynamic model of the piano in the literature and is based on the real components of the piano action mechanism (key, whippen, jack, repetition lever, and hammer). Two main areas for improving the fidelity of the dynamic model are the hammer shank and the connection point between the key and the ground. The hammer shank is a long narrow wooden rod and, by observation with a high-speed video camera, the flexibility of this part has been confirmed. In previous work, the piano hammer had been modelled as a rigid body. In this work, a Rayleigh beam model is used to model the flexible behaviour of the hammer shank. By comparing the experimental and analytical results, it turns out that the flexibility of the hammer shank does not significantly affect the rotation of the other parts of the piano mechanism, compared with the case that the hammer shank has been modelled as a rigid part. However, the flexibility of the hammer shank changes the impact velocity of the hammer head, and also causes a greater scuffing motion for the hammer head during the contact with the string. The connection of the piano key to the ground had been simply modelled with a revolute joint, but the physical form of the connection at that point suggests that a revoluteprismatic joint with a contact force underneath better represents this connection. By comparing the experimental and analytical results, it is concluded that incorporating this new model significantly increases the fidelity of the model for the blows. In order to test the accuracy of the dynamic model, an experimental setup, including a servo motor, a load cell, a strain gauge, and three optical encoders, is built. The servo motor is used to actuate the piano key. Since the purpose of the motor is to consistently mimic the finger force of the pianist, the output torque of the motor is controlled. To overcome the problem associated with the motor torque control method used in previous work, a new torque control method is implemented on a real-time PC and a better control of the motor torque output is established. Adding a more realistic model of the piano string to the current piano action model and finding a better contact model for the contacts that happen between the surfaces that are made of felt (or leather), are two main areas that can be worked on in the future research. These two areas will help to further increase the fidelity of the present piano action model

Dynamic modeling and Experimental Testing of a Piano Action Mechanism”,

ABSTRACT The piano action is the mechanism that transforms the finger force applied to a key into a motion of a hammer that strikes a piano string. This paper presents a state-of-the-art model of a grand piano action, which is based on the five main components of the action mechanism (key, whippen, jack, repetition lever, and hammer). Even though Askenfelt and Jansson [1] detected some flexibility for the hammer shank in their experiments, all previous piano models have assumed the hammers to be rigid bodies. In this paper, we have accounted for the hammer shank flexibility using a Rayleigh beam model. It turns out that the flexibility of the hammer shank does not significantly affect the rotation of the other parts of the piano mechanism, compared with the case that the hammer shank has been modeled as a rigid part. However, the flexibility of the hammer shank changes the impact velocity of the hammer head, and also causes a greater scuffing motion for the hammer head during the contact with the string. To validate the theoretical results, experimental measurements were taken by two strain gauges mounted on the hammer shank, and by optical encoders at three of the joints

Developing an integrated blood supply chain network in crisis conditions considering the concentration of sites in facilities and blood types substitution

In the management of the blood supply chain network, the existence of a coherent and accurate program can help increase the efficiency and effectiveness of the network. This research presents an integrated mathematical model to minimize network costs and blood delivery time, especially in crisis conditions. The model incorporates various factors such as the concentration of blood collection, processing, and distribution sites in facilities, emergency transportation, pollution, route traffic (which can cause delivery delays), blood type substitution, and supporter facilities to ensure timely and sufficient blood supply. Additionally, the model considers decisions related to the location of permanent and temporary facilities at three blood collection, processing, and distribution sites, as well as addressing blood shortages. The proposed model was solved for several problems using the Augmented epsilon-constraint method. The results demonstrate that deploying advanced processing equipment in field hospitals, concentrating sites in facilities, and implementing blood type substitution significantly improve network efficiency. Therefore, managers and decision-makers can utilize these proposed approaches to optimize the blood supply chain network, resulting in minimized network costs and blood delivery time.IntroductionOne of the most important aspects of human life is health, which has a significant impact on other aspects of life. In this study, a two-objective mathematical programming model is proposed to integrate the blood supply chain network for both normal and crisis conditions at three levels: blood collection, processing and storage, and blood distribution. The proposed two-objective mathematical model simultaneously minimizes network costs and response time. The model is solved using the augmented epsilon-constraint method. To enhance the responsiveness to patient demand in healthcare facilities and address shortages, the model considers the concentration of levels (collection, processing and storage, and distribution of blood to patients) in facilities, blood type substitution, and supporter facilities. In blood type substitution, not every blood type can be used for every patient. Among several compatible blood groups, there is a prioritization for blood type substitution, allowing for an optimal allocation of blood groups based on the specific needs.Materials and MethodsIn this research, a two-objective mathematical programming model is proposed to design an integrated blood supply chain network at three levels: collection, processing, and distribution of blood in crisis conditions. The proposed model determines decisions related to the number and location of all permanent and temporary facilities at the three levels of blood collection, processing, and distribution, the quantity of blood collection, processing, and distribution, inventory levels and allocation, amount of blood substitution, and transportation method considering traffic conditions. Achieving an optimal solution for the developed two-objective model, which minimizes both objective functions simultaneously while considering the trade-off between the objective functions, is not feasible. Therefore, multi-objective solution methods can be used to solve problems considering the trade-off between objectives. In this research, the augmented epsilon-constraint method is employed to solve the proposed two-objective mathematical model. In this method, all objective functions, except one, are transformed into constraints and assigned weights. By defining an upper bound for the transformed objective functions, they are transformed into constraints and solved.Discussion and ResultsAlthough the two-objective mathematical model is transformed into a single-objective model using the augmented epsilon-constraint method, this approach can still yield Pareto optimal points. Therefore, managers and decision-makers can create a balanced blood supply chain network considering the importance of costs and blood delivery time. Sensitivity analysis was conducted to examine the effect of changes in the weights of the objective functions and the blood referral rate (RD parameter) on the values of the objective functions for three numerical examples. With changes in the weights of the objective functions relative to each other, the trend of changes in the values of the first and second objective functions for all three solved problems is similar. Specifically, when reducing the weight of the first objective function from 0.9 to 0.1, the values of the first objective function increase, while the values of the second objective function decrease when the weight of the second objective function increases from 0.1 to 0.9. The total amount of processed blood in field hospitals and main blood centers was compared for equal weights and time periods for the three problems. Additionally, the amount of processed blood in field hospitals is significantly higher than in main blood centers. This indicates that eliminating the cost and time of blood transfer in field hospitals (due to the concentration of blood collection, processing, and distribution levels) results in an increased amount of processed blood compared to main blood centers (single-level facilities), ultimately leading to a reduction in network costs.ConclusionThis study presents a two-objective mathematical model for the blood supply chain network, integrating pre- and post-crisis conditions. Decisions are proposed for the deployment of four types of facilities, including temporary blood collection centers, field hospitals, main blood centers, and treatment centers, at three levels of blood collection, processing, and distribution. Additionally, inventory, allocation, blood group substitution, blood shortage, transportation mode, and route traffic (delivery delays) are considered for four 24-hour periods in the model. For the first time in this field, knowledge of concentration levels in facilities is utilized, with simultaneous existence of the three levels of blood collection, processing, and distribution in field hospitals. This problem is formulated in a mixed-integer linear programming model with two objective functions aiming to minimize system costs and blood delivery time. The proposed model is solved using the augmented epsilon-constraint evolution method. Sensitivity analysis is conducted for the weights of the objective functions, and additional experiments (RD parameter) are performed. The sensitivity analysis on the weights of the objective functions reveals that reducing the weight of the first objective function leads to a decrease in blood delivery time, while increasing the weight of the second objective function results in an increase in network costs. The investigation of the impact of reducing the amount of additional testing (RD parameter) on the values of the objective functions confirms that advanced equipment at the processing sites of field hospitals reduces network costs and blood delivery time

A comparative study of the viscoelastic constitutive models for frictionless contact interfaces in solids

The nature of the constitutive contact force law utilized to describe contact-impact events in solid contact interfaces plays a key role in predicting the response of multibody mechanical systems and in the simulation of engineering applications. The goal of this work is to present a comparative study on the most relevant existing viscoelastic contact force models. In the sequel of this process, their fundamental characteristics are examined and their performances evaluated. Models developed based on the Hertz contact theory and augmented with a damping term to accommodate the dissipation of energy during the impact process, which typically is a function of the coefficient of restitution between the contacting solids, are considered in this study. In particular, the identified contact force models are compared in the present study for simple solid impact problems with the sole purpose of comparing the performance of the various models and examining the corresponding system behavior. The outcomes indicate that the prediction of the dynamic behavior of contacting solids strongly depends on the selection of the contact force model.Fundação para a Ciência e a Tecnologia (FCT

A Multi-Variate/Multi-Attribute Approach for Plant Layout Design

This paper presents an integrated multivariate and multi attribute analysis approach for solving plant layout design problems. The integrated approach discussed in this paper is based Principal Component Analysis (PCA) and Analytic Hierarchy Process (AHP). The validity of the model is verified and validated by Numerical Taxonomy (NT) approach. Furthermore, a non-parametric correlation method, namely, Spearman correlation experiment is used to show the correlation between the findings of PCA and NT. The integrated PCA AHP approach of this study presents exact whereas previous DEA AHP studies presents incomplete and non exact plant layout alternatives. Furthermore, the superiority and effectiveness of PCA AHP approach is compared with previous DEA AHP study through a case study. The integrated PCA AHP would help policy makers and top managers to have precise understanding and improve existing systems with respect to facility layout performance. Furthermore, it provides complete and exact rankings of the plant layout alternatives. Moreover, Numerical Taxonomy is used to verify and validate the findings of PCA whereas previous DEA AHP does not have verification and validation feature

The Study of the Effect of the Sill Slope on the Discharge Coefficient of the Labyrinth Weir

The discharge coefficient of the labyrinth weirs is influenced by geometric factors and flow characteristics. In this study, the effect of the sill slope that is a geometric factor on the discharge coefficient of the labyrinth weirs has been studied. The physical model is used for this purpose. In this regard, nine weir models were made with two cycles, and wall thickness of 3 cm, a quadrant shape crest, the heights of 10, 15, 20 centimeters and with sill slopes of 0%, 13%, 25%, 37%, and experimented in a laboratory flume with length of 9 meters, a bed width of 60 cm, and a wall height of 70 cm. Experiments were performed in a wide range of flow and discharge between 1 to 150 lps. The results indicated that the sill slope has a significant effect on the discharge coefficient of the labyrinth weir. In general, the weir performance will increase as the sill slope increases. So the sill slope of 25% appeared to be the optimum slope