Material Constitutive Behavior Research Articles

Numerical Modelling and Optimization of Dry Orthogonal Turning of Al6061 T6 Alloy

In this paper, the influence of machining parameters, Cutting Speed, Feed Rate, and Depth of cut, on surface finish during dry orthogonal turning of Al 6061 – T6 alloy, is studied using the response surface methodology (RSM). This paper proposes a unique way to predict the surface finish in turning, using the effective plastic strain (PEEQ) values obtained from the simulations. A comprehensive finite element model was proposed to predict the surface finish accurately, by correlating the variance of the PEEQ. The Johnson-Cook damage model is used to define the damage criteria and Johnson-Cook material model is used to explain the material constitutive behavior. A dynamic, explicit method is used along with the Adaptive Lagrangian-Eulerian (ALE) method to predict material flow accurately. The influence of machining parameters was studied by assuming Central Composite Design (CCD). The output response, PEEQ, was fitted into analytical quadratic polynomial models using regression analysis, which shows that feed rate was the most dominant factor for PEEQ than the other parameters considered in this study. Using the individual desirability function method, the objective, optimal setting of the machining parameters was obtained for better surface finish.

Investigation on initial grain size and laser power density effects in laser shock bulging of copper foil

Laser shock bulging process is a promising flexible microforming method in which the laser shock wave pressure is employed to cause plastic deformation and fabricate microfeatures on thin sheet metals. However, the influence of initial grain size and laser power density on the forming quality of bulged parts has not been well understood. In this paper, three various initial grain sizes as well as three levels of laser power densities were provided, and then, laser shock bulging experiments of T2 copper foil were conducted. The characteristics of bulging height, thickness distribution, microhardness, surface morphology, and microstructure were examined. It is revealed that the bulging height increases with the increase of grain size and the enhancement of laser power density. The exhibiting good formability of pure copper foil in laser shock bulging process is attributed to the inertial effect on necking stabilization and strain-rate effect on material constitutive behavior. The overall thickness of bulged parts decreases compared with its original thickness. Moreover, the microhardness in the laser-shocked region increases due to the strain hardening effect, but the microhardness distribution is nonuniform because of the inhomogeneous plastic deformation. The grain sizes of bulged parts are slightly refined with the increase of laser power density, especially for the coarse-grained part. The grain refinement in laser shock bulging forming process is attributed to the large plastic deformation at high strain rates under laser shock.

On Multi-Objective Based Constitutive Modelling Methodology and Numerical Validation in Small-Hole Drilling of Al6063/SiCp Composites.

Discrepancies in capturing material behavior of some materials, such as Particulate Reinforced Metal Matrix Composites, by using conventional ad hoc strategy make the applicability of Johnson-Cook constitutive model challenged. Despites applicable efforts, its extended formalism with more fitting parameters would increase the difficulty in identifying constitutive parameters. A weighted multi-objective strategy for identifying any constitutive formalism is developed to predict mechanical behavior in static and dynamic loading conditions equally well. These varying weighting is based on the Gaussian-distributed noise evaluation of experimentally obtained stress-strain data in quasi-static or dynamic mode. This universal method can be used to determine fast and directly whether the constitutive formalism is suitable to describe the material constitutive behavior by measuring goodness-of-fit. A quantitative comparison of different fitting strategies on identifying Al6063/SiCp’s material parameters is made in terms of performance evaluation including noise elimination, correlation, and reliability. Eventually, a three-dimensional (3D) FE model in small-hole drilling of Al6063/SiCp composites, using multi-objective identified constitutive formalism, is developed. Comparison with the experimental observations in thrust force, torque, and chip morphology provides valid evidence on the applicability of the developed multi-objective identification strategy in identifying constitutive parameters.

The influence of loading rates on hardening effects in elasto/viscoplastic strain-hardening materials

In this paper the influence of increasing loading rates on hardening effects is analyzed for rate-dependent elastoplastic materials. The effects of different loading rates on hardening rules are discussed with regard to the constitutive behavior of strain-hardening materials in elasto/viscoplasticity. A suitable procedure for the numerical simulation of rate-sensitive material behavior is illustrated. A comparative analysis is presented on constitutive relations in strain-hardening plasticity without rate effects and with rate effects in order to show the different role played by hardening rules in the rate-sensitivity analysis of elasto/viscoplastic strain-hardening materials. By reporting suitable numerical simulations for the adopted constitutive relations it is shown that when the rate of application of the loading is increased the influence of hardening has a different effect in the mechanical behavior of structures. Computational results and applications are finally illustrated in order to show numerically the different role played by hardening on the plastic strains when the loading rates are incremented for elasto/viscoplastic strain-hardening materials and structures.

Sensor calibration of polymeric Hopkinson bars for dynamic testing of soft materials

Split Hopkinson pressure bar (SHPB) testing is one of the most common techniques for the estimation of the constitutive behaviour of metallic materials. In this paper, the characterisation of soft rubber-like materials has been addressed by means of polymeric bars thanks to their reduced mechanical impedance. Due to their visco-elastic nature, polymeric bars are more sensitive to temperature changes than metallic bars, and due to their low conductance, the strain gauges used to measure the propagating wave in an SHPB may be exposed to significant heating. Consequently, a calibration procedure has been proposed to estimate quantitatively the temperature influence on strain gauge output. Furthermore, the calibration is used to determine the elastic modulus of the polymeric bars, which is an important parameter for the synchronisation of the propagation waves measured in the input and output bar strain gate stations, and for the correct determination of stress and strain evolution within the specimen. An example of the application has been reported in order to demonstrate the effectiveness of the technique. Different tests at different strain rates have been carried out on samples made of nytrile butadyene rubber (NBR) from the same injection moulding batch. Thanks to the correct synchronisation of the measured propagation waves measured by the strain gauges and applying the calibrated coefficients, the mechanical behaviour of the NBR material is obtained in terms of strain-rate–strain and stress–strain engineering curves.

Constitutive investigation based on the time-hardening model for AH36 material in continuous casting process

A detailed understanding of the constitutive behavior of AH36 material in continuous casting process was obtained through various high-temperature tensile testing at specific ranges of temperatures (1173–1673 K) and strain rates (10−4−10−2 s−1) using a Gleeble system. A significant variation in flow stress is evident over the entire range of temperatures under different strain rates. The constitutive equation of the AH36 material was suggested based on the time-hardening model. The results indicate that the accuracy of the model is relatively low at the temperatures of 1173, 1573, and 1673 K under the strain rates of 10−2 and 10−4 s−1. Therefore, a modification of the time-hardening model was carried out by including the compensation of strain rate in the Zener–Holloman parameter ( Z) to improve the accuracy. Furthermore, the deformation process was distributed into the regions of 1173, 1273–1473, and 1573–1673 K based on the exponent of strain rate at different ranges of temperature. The correlation coefficient between the computed and experimental flow stress data is 0.998. The average absolute relative error is within the range of allowable experimental conditions.

A condensed approach to model the constitutive behavior of multiphase ferroelectric and multiferroic materials

AbstractFerroelectric as well as ferromagnetic materials are widely used in smart structures and devices as actuators, sensors etc. Most of the developed models, describing the nonlinear behavior, are implemented within the framework of the Finite Element Method. Most investigations, however, are restricted to simple boundary value problems under uniaxial or biaxial loading and their goal is the calculation of hysteresis loops or to determine e.g. electromechanical coupling coefficients. Regarding these circumstances, the so‐called condensed method (CM) is introduced to investigate the macroscopic polycrystalline ferroelectric material behavior at a macroscopic material point without any kind of discretization scheme. In the presented paper, the CM is extended towards multiphase ferroelectric material behavior. Moreover, first numerical results of a multiphase ferroelectric material at the morphotropic phase boundary are presented. (© 2017 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Experimentally validated finite element analysis for evaluating subsurface damage depth in glass grinding using Johnson-Holmquist model

Subsurface damages (SSD) induced during grinding of brittle materials influence mechanical and physical properties of the machined specimen. Experimental evaluation of SSD is very expensive and time consuming due to need for performing various grinding testes in one hand and post-grinding processes such as angle polishing in another hand. Meanwhile, theoretical investigation lacks accuracy due to the various simplifications involved with theoretical models. Hence, a numerical study was performed to analyze SSD in optical glass grinding using finite element method. The constitutive material behavior of glass was defined based on the Johnson-Holmquist model. Performing FEM simulations, the SSD depth was obtained for various combinations of process parameters. Based on the statistical analysis of variance, feed velocity was found to be the most significant parameter followed by depth of cut and cutting velocity. The numerical results were then compared with experimental observations using angle polishing technique and Scanning Electron Microscopy. This comparison reveals good performance of FEM in prediction of SSD depth. Finally, an empirical/ mathematical model was developed to express SSD depth as a function of process parameters. The regression model revealed that by increasing feed velocity and cutting depth, SSD depth increases, while by increasing cutting velocity, SSD depth decreases.

A generalized statistical approach for modeling fiber-reinforced materials

We present a generalized statistical approach for the description of fully three-dimensional fiber-reinforced materials, resulting from the composition of two independent probability distribution functions of two spherical angles. We discuss the consequences of the proposed formulation on the constitutive behavior of fibrous materials. Upon suitable assumptions, the generalized formulation recovers existing alternative models, based on averaged structure tensors both at first- and second-order approximations. We demonstrate that the generalized formulation embeds standard behaviors of fiber-reinforced materials such as planar isotropy and transverse isotropy, while any intermediate behavior is easily obtained through the calibration of two material parameters. We illustrate the performance of the model by means of uniaxial and biaxial tests. For uniaxial loading, we introduce a preliminary discussion concerning the generalized tension–compression switch procedure.

Multiscale modeling of carbon nanotube reinforced concrete

The present paper proposes a hierarchical multiscale approach in order to evaluate the nonlinear constitutive behavior of concrete reinforced with carbon nanotubes (CNTs). To this purpose, representative volume elements, consistent to the microstructural topology of the material, are constructed and analyzed using finite elements. As the dimensions of the CNTs and those of a typical mesoscale concrete RVE differ by orders of magnitude, a hierarchical multiscale analysis strategy is implemented to pass information through scales with different RVEs assigned at each scale of separation. Both elastic and inelastic analyses are performed on all scales for various CNT weight fractions, defining a different nonlinear constitutive stress–strain behavior at each scale of separation. It is shown that the proposed computational approach can be used alternatively to corresponding costly experiments in order to accurately evaluate the nonlinear constitutive behavior of such complex materials.

Discrete particle translation gradient concept to expose strain localisation in sheared granular materials using 3D experimental kinematic measurements

It is well known that the constitutive behaviour of granular materials is influenced by strain localisation into zones of intensive shearing, known as shear bands. The failure mode of specimens tested under axisymmetric triaxial compression is commonly manifested through single or multiple shear bands, or diffuse bifurcation (bulging). The ability to monitor and detect the evolution of strain localisation has been enhanced by measuring particle kinematics using discrete-element methods or three-dimensional imaging techniques such as X-ray computed tomography. However, conventional particle kinematic techniques cannot expose intricate localised shearing during the hardening, before the peak principal stress ratio. This paper presents the concept of particle translation gradient to expose strain localisation in granular materials using experimental measurements of particle translation in three dimensions. Individual silica sand particles were identified and tracked through multiple strains and particles’ translations were calculated. Each particle's neighbouring particles were identified and translation fields for each of the neighbouring particles were calculated. The second-order norms between a particle translation vector and the neighbouring particles’ translation vectors were averaged, resulting in a relative translation value for each particle. The translation gradient concept is effective in uncovering the onset of strain localisation within sheared granular materials.

Experimental Investigation of the High Strain Rate Transverse Compression Behavior of Ballistic Single Fibers

This paper investigates the high strain rate transverse compression behavior of Kevlar® KM2 and ultra high molecular weight polyethylene Dyneema® SK76 single fibers widely used in protective components under ballistic and blast loading conditions. The micron scale fibers are compressed at strain rates in the range of 10,000–90,000 s−1 in a small (283 μm) diameter Kolsky bar with optical instrumentation. The nominal stress–strain response of single fibers exhibits nonlinear inelastic behavior under high rate transverse compression. The nonlinearity is due to both geometric and material behavior. The contact area growth at high rates is found to be smaller than at quasi-static loading leading to a stiffer material response at higher rates. The fiber material constitutive behavior is determined by removing the geometric nonlinearity due to the growing contact area. Atomic force microscopy analysis of the compressed fibers indicates less degree of fibrillation at high strain rates compared to quasi-static loading indicating that fibril properties and inter-fibrillar interactions could be strain rate dependent.

A Continuation method with combined restrictions for nonlinear structure analysis

In structural engineering, many problems present nonlinear behavior associated to a large number of sources, ranging from the presence of large displacements and large strains to the constitutive material behavior. The simulation of such complex structural systems with the finite element method often requires the use of analysis control schemes, called continuation methods. These schemes aim at depicting equilibrium paths, associated with system stiffness loss and to the occurrence of load and displacement limit points. Among them, the arc length and the strain control methods are very popular. However, under certain conditions, these methods either fail to provide the full system response or require a large number of iterations for convergence. In the present work, a continuation method with combined restrictions is proposed to provide the full system response in the presence of both geometric nonlinearities and material elasto-plastic softening. Two or more restrictions are combined resulting in a more robust scheme for the solution of the nonlinear system of equilibrium equations. Consistency of the extended system is reached through the least squares method. The efficiency of the combined control is compared to the application of the restrictions individually in a Newton-Raphson solution scheme. An automatic increment adaptation strategy for the control parameters is introduced which helps stabilize the incremental process with multiple restrictions. In the analysis of the highly non-linear problems studied in this paper, the proposed method with combined restrictions proves to be more robust than the standard procedure with single restrictions. In the cases where the single restrictions failed, the combined restriction was able to provide the full solution.

The incremental Virtual Fields Method and prestretching method applied to rubbers under uniaxial medium‐strain‐rate loading

AbstractConventional dynamic experiments on rubbers have several limitations including low signal‐to‐noise ratio and a long time period during which the specimen is not in static equilibrium, which causes difficulties separating constitutive material behaviour from specimen response. In order to overcome these limitations, we build on previous research in which the Virtual Fields Method (VFM) is applied to dynamic tensile experiments. A previous study has demonstrated that the VFM can be used to identify the material parameters of a hyperelastic model for a given rubber based on optical measurements of wave propagation in the rubber, eliminating the need for force measurements by instead using acceleration fields as a “virtual load cell.” In order for us to successfully characterise the strain hardening in the material, large deformations are required, and these were achieved by applying static preloads to the specimen before the dynamic loading. In order for us to then apply the VFM, measurements of the static force, or strain, or both, are required. This paper explores different methods for applying the VFM, in particular, comparing the use of a static force measurement, as in the previous research, to methods that only require strain fields in order to apply the incremental equation of motion. Finite element method simulations were conducted to compare the identification sensitivity to experimental error sources between the 2 VFM implementations; the experimental data used in the previous studies were then applied to the incremental VFM. A further experimental comparison is provided between constitutive parameters obtained in tensile experiments using the VFM and compressive measurements from a modified split Hopkinson bar technique equipped with a piezoelectric force transducer. Finally, there is a discussion of the effects of preloading and relaxation in the material.

Dynamic response of pre-loaded structures subjected to combined extreme environments

A series of experiments was performed on Hastelloy X plates which were subjected to a combination of extreme temperatures, in-plane tensile loading, and transverse shock loading. To achieve these conditions a shock tube apparatus was used in conjunction with a novel hydraulic pre-loading fixture and propane flame torches. In order to understand the effects of shock load magnitude on the deformation behavior of the plates, two series of experiments were carried out at peak shock pressures of 1.7MPa and 3.1MPa, respectively. Both series of experiments were conducted over a range of temperatures from room temperature to 900 °C. High speed photography and Digital Image Correlation (DIC) were used to obtain three-dimensional, full-field deformation information. Side view images were also captured to validate the DIC results. The addition of a tensile pre-load reduced the maximum deflection for all temperatures. However, a higher magnitude of the tensile pre-load did not further reduce the maximum out-of-plane deflection of the plate for temperatures higher than 400 °C. The specimen deformation increased with increasing temperature until 800 °C. However, at 900 °C, due to anomaly in material constitutive behavior, the specimen deflection was observed to be lower than at 800 °C. An indentation mode of deformation was observed in some instances of the 3.1MPa peak shock pressure experiments, particularly at higher temperatures.

Prediction of the critical stress to crack initiation associated to the investigation of fatigue small crack

ABSTRACT. Fatigue design is of vital importance to avoid fatigue small crack growth in engineering structures. This study shows that the critical fatigue design stress can be defined below the usual endurance limit, considered in rules and codes. The material constitutive behaviour is using linear isotropic elasticity. Lassere and Pallin-Luc [1-2] use the elastic energy and over-energy under uniaxial load (tension and rotating bending). The authors deduce the influencing critical stress value corresponding to ?*. It’s a linear approach. We propose an over-energy under dissymmetrical rotating bending and expressed in the ellipse axes. An asymptotic approach is transformed the over-energy in polynomial function of critical stress. Unknown depend on experimental service conditions, endurance limit of tension and rotating bending of specimen. The fatigue database of 30NCD16 steel studied by Froustey and Dubar [3-13] is used. Critical stresses are evaluated (Fig. 2). The research done by Manning and all [4] has shown the small crack effect to be as large as 0.3 mm. Small crack and critical stress are illustrated here in as resulting from pure bending approach expressed by Bazant law [7]. It’s reproduces well the Kitagawa diagram [6] (Fig. 3). When the short cracks are hidden in the material, we shows that the number cycles during small crack growth be significantly higher (Fig. 4) than the corresponding cycles of large cracks growth (ONI’s fatigue test) for the same physically crack size. Indeed its evolution can be blocked by a microstructural barrier (grain boundary, for example). Hence, the considerations of small crack growth are strongly influencing the fatigue life of a component or structure. KEYWORDS. Tensile; Dissymmetrical rotating bending; Over-energy; Critical stress; Small crack; Fatigue cycle.

Modeling the constitutive behavior of ferroelectric, ferromagnetic and multiferroic materials by using the condensed method (CM)

AbstractDue to the multifunctional applicability, smart materials are of particular interest in the field of material modeling. Most of the developed models, describing the nonlinear behavior, are implemented within the framework of the Finite Element Method (FEM). However, most investigations are restricted to simple boundary value problems (BVP) under uniaxial loading and their goal is the calculation of hysteresis loops. Regarding this circumstance, the so‐called condensed method (CM) is introduced to investigate the macroscopic polycrystalline ferroelectric material behavior at a global material point without any kind of discretization scheme. In the presented paper, the CM is extended towards ferromagnetic and multiferroic material behavior. Moreover, numerical results for a pure ferromagnetic behavior and a comparison between the magnetoelectric coupling coefficient calculated by the FEM and the CM are presented. (© 2016 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)

A coupled experimental/numerical approach for the characterization of material behaviour at high strain-rate using electromagnetic tube expansion testing

High speed forming processes such as magnetic pulse forming are gaining interest in the sheet metal industry. Their design and development require specific effort on numerical modelling as well as on the characterization of the high strain-rate mechanical behaviour of metals. Standard dynamic tests (SHPB, plate impact, simple tension…) are limited in their representativeness of the deformation modes encountered in high speed processes. The present study describes how the electromagnetic tube expansion test can be used as a high strain-rate test for the identification of material constitutive parameters. Through numerical analysis, the deformation mode and the sensitivity of radial expansion to material constitutive behaviour are depicted. Then, the material parameter identification methodology is applied to annealed 1050 aluminium tubes. It is shown that the test is capable of highlighting the strain-rate sensitivity of behaviour, in spite of relatively high sensitivity to measurement uncertainties.

Understanding the Interfacial Mechanical Response of Nanoscale Polymer Thin Films via Nanoindentation

Understanding the mechanical properties of interphase regions in supported polymer thin films is critical as it yields key insights into the constitutive behavior of nanostructured materials. While studies have consistently shown that polymer layers near the substrate exhibit a stiffened response, the size of this region has been reported to vary based on the measurement approach, ranging from hundreds of nanometers in atomic force microscopy (AFM) nanoindentation experiments to a few nanometers in molecular simulations and thin film wrinkling experiments. Here we employ nanoindentation simulations using a coarse-grained molecular dynamics approach to investigate the elastic moduli gradients near the substrate interface of a supported poly(methyl methacrylate) (PMMA) thin film. We find that indenter sizes commonly used in experiments give rise to observed interphase length scales that are larger than the regions in which polymer dynamics are significantly altered as quantified by the segmental molecular s...

Finite element modeling and analysis of piezo-integrated composite structures under large applied electric fields

In this article, we focus on static finite element (FE) simulation of piezoelectric laminated composite plates and shells, considering the nonlinear constitutive behavior of piezoelectric materials under large applied electric fields. Under the assumptions of small strains and large electric fields, the second-order nonlinear constitutive equations are used in the variational principle approach, to develop a nonlinear FE model. Numerical simulations are performed to study the effect of material nonlinearity for piezoelectric bimorph and laminated composite plates as well as cylindrical shells. In comparison to the experimental investigations existing in the literature, the results predicted by the present model agree very well. The importance of the present nonlinear model is highlighted especially in large applied electric fields, and it is shown that the difference between the results simulated by linear and nonlinear constitutive FE models cannot be omitted.