Modelling the Flow Behaviour of Al Alloy Sheets at Elevated Temperatures Using a Modified Zerilli-Armstrong Model and Phenomenological-Based Constitutive Models.

The flow behaviour of AA2060 Al alloy under warm/hot deformation conditions is complicated because of its dependency on strain rates (ε˙), strain (ε), and deformation modes. Thus, it is crucial to reveal and predict the flow behaviours of this alloy at a wide range of temperatures (T) and ε˙ using different constitutive models. Firstly, the isothermal tensile tests were carried out via a Gleeble-3800 thermomechanical simulator at a T range of 100, 200, 300, 400, and 500 °C and ε˙ range of 0.01, 0.1, 1, and 10 s-1 to reveal the warm/hot flow behaviours of AA2060 alloy sheet. Consequently, three phenomenological-based constitutive models (L-MJC, S1-MJC, S2-MJC) and a modified Zerilli-Armstrong (MZA) model representing physically based constitutive models were developed to precisely predict the flow behaviour of AA2060 alloy sheet under a wide range of T and ε˙. The predictability of the developed constitutive models was assessed and compared using various statistical parameters, including the correlation coefficient (R), average absolute relative error (AARE), and root mean square error (RMSE). By comparing the results determined from these models and those obtained from experimentations, and confirmed by R, AARE, and RMSE values, it is concluded that the predicted stresses determined from the S2-MJC model align closely with the experimental stresses, demonstrating a remarkable fit compared to the S1-MJC, L-MJC, and MZA models. This is because of the linking impact between softening, the strain rate, and strain hardening in the S2-MJC model. It is widely known that the dislocation process is affected by softening and strain rates. This is attributed to the interactions that occurred between ε and ε˙ from one side and between ε, ε˙, and T from the other side using an extensive set of constants correlating the constitutive components of dynamic recovery and softening mechanisms.

Modified Fields-Backofen and Zerilli-Armstrong constitutive models to predict the hot deformation behavior in titanium-based alloys.

This work presents modifications for two constitutive models for the prediction of the flow behavior of titanium-based alloys during hot deformation. The modified models are the phenomenological-based Fields-Backofen and the physical-based Zerilli-Armstrong. The modifications are derived and suggested by studying the hot deformation of titanium-based alloy Ti55531. The predictability of the modified models along with the original Fields-Backofen and another modified Zerilli-Armstong models is assessed and evaluated using the well-known statistical parameters correlation coefficient (R), Average Absolute Relative Error (AARE), and Root Mean Square Error (RMSE), for the Ti55531 alloy, and validated with other two different titanium-based alloys SP700 and TC4. The results show that the modified Fields-Backofen gives the best performance with R value of 0.996, AARE value of 3.34%, and RMSE value of 5.64 MPa, and the improved version of the modified Zerilli-Armstrong model comes in the second-best place with R value of 0.992, AARE value of 3.52%, and RMSE value of 9.15 MPa for the Ti55531 alloy.

On the Prediction of the Flow Behavior of Metals and Alloys at a Wide Range of Temperatures and Strain Rates Using Johnson-Cook and Modified Johnson-Cook-Based Models: A Review.

This paper reviews the flow behavior and mathematical modeling of various metals and alloys at a wide range of temperatures and strain rates. Furthermore, it discusses the effects of strain rate and temperature on flow behavior. Johnson-Cook is a strong phenomenological model that has been used extensively for predictions of the flow behaviors of metals and alloys. It has been implemented in finite element software packages to optimize strain, strain rate, and temperature as well as to simulate real behaviors in severe conditions. Thus, this work will discuss and critically review the well-proven Johnson-Cook and modified Johnson-Cook-based models. The latest model modifications, along with their strengths and limitations, are introduced and compared. The coupling effect between flow parameters is also presented and discussed. The various methods and techniques used for the determination of model constants are highlighted and discussed. Finally, future research directions for the mathematical modeling of flow behavior are provided.

A Logarithmic Formulation for Anisotropic Behavior Characterization of Bovine Cortical Bone Tissue in Long Bones Undergoing Uniaxial Compression at Different Speeds.

The mechanical properties of bone tissues change significantly within the bone body, since it is considered as a heterogeneous material. The characterization of bone mechanical properties is necessary for many studies, such as in prosthesis design. An experimental uniaxial compression study is carried out in this work on bovine cortical bone tissue in long bones (femur and tibia) at several speeds to characterize its anisotropic behavior. Several samples from different regions are taken, and the result selection is carried out considering the worst situations and failure modes. When considering different displacement rates (from 0.5 to 5 mm/min), three findings are reported: The first finding is that the behavior of bone tissues in radial and tangential directions are almost similar, which allows us to consider the transversal isotropic behavior under static loads as well as under dynamic loads. The second finding is that the failure stress values of the longitudinal direction is much higher than those of the radial and tangential directions at low displacement rates, while there is no big difference at the high displacement rates. The third finding is a new mathematical model that relates the dynamic failure stress with the static one, considering the displacement rates. This model is validated by experimental results. The model can be effectively used in reliability and optimization analysis in prosthesis design, such as hip prosthesis.

Improvement of structural efficiency in metals by the control of topological arrangements in ultrafine and coarse grains.

Improvement of structural efficiency in various materials is critically important for sustainable society development and the efficient use of natural resources. Recently, a lot of attention in science and engineering has been attracted to heterogeneous-structure materials because of high structural efficiency. However, strategies for the efficient design of heterogenous structures are still in their infancy therefore demanding extensive exploration. In this work, two-dimensional finite-element models for pure nickel with bimodal distributions of grain sizes having 'harmonic' and 'random' spatial topological arrangements of coarse and ultrafine-grain areas are developed. The bimodal random-structure material shows heterogeneities in stress-strain distributions at all scale levels developing immediately upon loading, which leads to developing concentrations of strain and premature global plastic instability. The bimodal harmonic-structure material demonstrates strength and ductility significantly exceeding those in the bimodal random-structure as well as expectations from a rule of mixtures. The strain hardening rates also significantly exceed those in homogeneous materials while being primarily controlled by coarse-grain phase at the early, by ultrafine-grain at the later and by their compatible straining at the intermediate stages of loading. The study emphasises the importance of topological ultrafine-/coarse-grain distributions, and the continuity of the ultrafine-grain skeleton in particular.

Efficient System Reliability-Based Design Optimization Study for Replaced Hip Prosthesis Using New Optimized Anisotropic Bone Formulations.

An efficient reliability algorithm is developed to transfer the system reliability problem to a single-component reliability problem, considering the uncertainty of loading cases and the material properties. The main difficulty is that femoral bone densities change after hip arthroplasty and, thus, the mechanical properties of the distinctive bone tissues and, therefore, the corresponding elasticity modulus and yield stress values change. Therefore, taking these changes into account during the hip prosthesis design process is strongly needed. As the bone possesses anisotropic behaviors, as the material properties in both radial and tangential directions in long bone (femur, tibia) are almost similar, the bone anisotropy is represented in this study by transversal isotropy. Two optimized formulations for yield stress against the elasticity modulus relationship are first developed and then integrated into an efficient reliability algorithm. Thus, a coupling between reliability and optimization, so-called reliability-based design optimization (RBDO), is introduced in order to control the reliability level. The proposed RBDO algorithm using optimum safety factors (OSF) takes into account the material uncertainties and leads to new stem dimensions. An in-depth numerical analysis on a cementless hip prosthesis is implemented to demonstrate the appropriateness of the proposed algorithm with the consideration of many different loading cases. The results show that the studied model can be effectively used when compared to previous works, which concerns the changes in both geometry and material properties.

Constitutive Models for the Prediction of the Hot Deformation Behavior of the 10%Cr Steel Alloy.

The aim of this paper is to establish a reliable model that provides the best fit to the specific behavior of the flow stresses of the 10%Cr steel alloy at the time of hot deformation. Modified Johnson-Cook and strain-compensated Arrhenius-type (phenomenological models), in addition to two Artificial Neural Network (ANN) models were established with the view toward investigating their stress prediction performances. The ANN models were trained using Scaled Conjugate Gradient (SCG) and Levenberg-Marquardt (LM) algorithms. The prediction accuracy of the established models was evaluated using the following well-known statistical parameters: (a) correlation coefficient (R), (b) Average Absolute Relative Error (AARE), (c) Root Mean Squared Error (RMSE), and Relative Error (RE). The results showed that both of the modified Johnson-Cook and strain-compensated Arrhenius models could not competently predict the flow behavior. On the contrary, the results indicated that the two proposed ANN models precisely predicted the flow stress values and that the LM-trained ANN provided a superior performance over the SCG-trained model, as it yielded an RMSE of as low as 0.441 MPa.

Integration of reliability analysis into mini-plate fixation strategy used in human mandible fractures: Convalescence and healing periods.

PURPOSE: The objective was to assess the reliability level of mini-plate fixation used in fracture mandibles in order to evaluate the structure stability in both convalescence and healing periods. METHODS: In the convalescence period, the failure scenario is measured by the relative displacement between two fracture surfaces which should not exceed an acceptable value in order to obtain a good stability for rapid bone healing and to limit any trauma. However, in the healing period, it is the objective to obtain an acceptable rigidity. Hereby, the failure scenario is measured by the von Mises stresses being as indicator of mandible fractures. RESULTS: During the surgery operation, some muscles can be cut or harmed and cannot operate at its maximum capability. Thus, there is a strong motivation to introduce the loading uncertainties in order to obtain reliable designs. A 3-dimensional finite element model was developed in order to study the negative effect caused by stabilization of the fracture. The different results were obtained when considering a clinical case of a 35-year-old male patient. The results show the importance of fixation of symphysis fracture by two I-plates with four holes. The structural reliability level was estimated when considering a single failure mode and multiple failure modes. CONCLUSIONS: The integration of reliability concepts into mini-plate fixation strategy is considered a novel aspect. The reliability evaluation seams to be a reasonable asset in both convalescence and healing periods.

Determination of spatially dependent diffusion parameters in bovine bone using Kalman filter.

Although many studies have been made for homogenous constant diffusion, bone is an inhomogeneous material. It has been suggested that bone porosity decreases from the inner boundaries to the outer boundaries of the long bones. The diffusivity of substances in the bone matrix is believed to increase as the bone porosity increases. In this study, an experimental set up is used where bovine bone samples, saturated with potassium chloride (KCl), were put into distilled water and the conductivity of the water was followed. Chloride ions in the bone samples escaped out in the water through diffusion and the increase of the conductivity was measured. A one-dimensional, spatially dependent mathematical model describing the diffusion process is used. The diffusion parameters in the model are determined using a Kalman filter technique. The parameters for spatially dependent at endosteal and periosteal surfaces are found to be (12.8 ± 4.7) × 10(-11) and (5 ± 3.5) × 10(-11)m(2)/s respectively. The mathematical model function using the obtained diffusion parameters fits very well with the experimental data with mean square error varies from 0.06 × 10(-6) to 0.183 × 10(-6) (µS/m)(2).