A 3-D finite element method for non-isothermal sheet-forming processes

The deformation behaviour of dual phase titanium alloys has been investigated using experimental and modelling methods. The motivation for conducting this investigation was to improve understanding of the deformation behaviour of dual phase titanium alloys in order to contribute to the long term goal of reducing manufacturing cost and improving production efficiency. Dual phase titanium alloys have been studied under two deformation conditions: high speed machining and uniaxial compression, which represent respectively high rate and low rate deformation. The microstructure and texture of the serrated chips obtained during high speed cutting of the dual phase Ti-6Al-4V alloy have been studied. The cutting speed, depth of cut and the orientation of the sample were found to have a significant influence on the deformation of serrated chips. Adiabatic shear bands were found in the serrated chips due to non-uniform deformation of Ti-6Al-4V alloy and deformation heating. In addition, there is reasonable agreement between the predicted texture using the visco-plastic self-consistent (VPSC) model and the measured texture using the electron backscatter diffraction (EBSD) technique indicating that the deformation in an adiabatic shear band is due to shear. The deformation behaviour of dual phase Ti-Mn alloys has been characterised with uniaxial compression at different temperatures and strain rates. The flow stress plateau phenomenon was observed in all the Ti-Mn alloys in the low to medium temperature range (27~500°C), which is attributed to the occurrence of dynamic strain aging (DSA). The flow softening behaviour was observed in dual phase Ti-Mn alloys in the high to sub-transus temperature range (600~800°C), which is attributed to the change in volume fraction of β phase during deformation due to the rise in temperature caused by deformation heating. The yield point phenomenon was observed when the Ti-Mn alloys are above their β transus temperatures. This phenomenon has been attributed to the multiplication of dislocations at the beginning of plastic deformation and dynamic recovery in the following plastic deformation. The strain rate sensitivity of Ti-Mn alloys was low in the low to medium temperature range and thus the effect of strain rate on deformation is not obvious. However, it was high in the high to sub-transus temperature range and thus the effect of strain rate on the deformation is significant. The 0.2% proof stress was found to increase with the volume fraction of β phase. The strain rate sensitivity was found to decrease with the volume fraction of β phase in the low to medium temperature range because the strain rate sensitivity of the α phase is higher than the β phase. However, the strain rate sensitivity was found to increase with the volume fraction of β phase at high temperatures because the strain rate sensitivity of the β phase becomes larger than the α phase. A considerable temperature rise was observed during compression of the Ti-Mn alloys and this indicates that the effect of deformation heating on deformation is not negligible. A composite model has been constructed to predict the plastic stress-strain curves of the dual phase Ti-Mn alloys using the in-situ behaviour of the component phases. The partition of stress and strain between the component phases has been accounted for by using three partitioning assumptions: iso-strain, iso-stress and iso-work. There was good agreement between the predicted curves and the experimental curves. It was found that the in-situ behaviour of the α phase is different in different dual phase Ti-Mn alloys and it exhibits a linear relationship with the volume fraction of β phase when the dominant matrix is the same. The modelling results in the low to medium temperature range indicate that most of the plastic deformation occurs in the localised shear band, which is consistent with the experimental observation that the dual phase Ti-Mn alloys were more susceptible to the formation of localised shear bands. In addition, it was found that a change in the dominant matrix in dual phase Ti-Mn alloys significantly influences the in-situ behaviour of the α phase. The modelling results in the high to sub-transus temperature range indicate that the flow softening behaviour observed in dual phase Ti-Mn alloys is related to the change in volume fraction of the β phase and the diffusion of Mn during the deformation.

Three phenomenological yield criteria are adopted to describe the plastic behaviour of sheet metals with normal plastic anisotropy. The sheet metals are assumed to be elastic-plastic, rate-sensitive and incompressible. A rate-sensitive thin shell nite element formulation based on the virtual work principle is derived for the three yield criteria. The eects of the yield surface shapes based on the three yield criteria with the same value of the plastic anisotropy parameter R on the strain distribution and localization are investigated under a hemispherical punch stretching operation and a plane strain drawing operation. The results of the simulations show that the yield surface shape, in addition to the plastic anisotropy parameter R, controls the punch force, strain distribution and strain localization for the punch stretching operation. However, the yield surface shape does not aect the punch force and the strain distribution signicantly for the plane strain drawing operation. ? 1998 John Wiley & Sons, Ltd. Int. J. Numer. Meth. Engng., 41, 559{584 (1998)

A framework for quantifying the thermomechanical response of polymer bonded explosives (PBX) at the microstructural level is developed using a cohesive finite element method (CFEM). This framework allows the contributions of individual constituents, fracture and frictional contact along failed crack surfaces to heating to be analyzed and tracked. Digitized micrographs of actual PBX materials and idealized microstructures with various distributions of grain sizes are used in the analysis. The analysis concerns impact loading of HMX/Estane with strain rates on the order of 104 – 105 s-1. Issues studied include large deformation, thermomechanical coupling, failure in the forms of microcracks in both bulk constituents and along grain/matrix interfaces, and frictional heating. The Estane matrix is described by a thermo-elasto-viscoelastic constitutive formulation, accounting for temperature dependence, strain rate sensitivity and strain hardening. The HMX crystals are assumed to be elastic under the conditions analyzed. Energy localization leading to formation of local hot spots as potential ignition sites is primarily due to the viscoelastic dissipation in the matrix in early stages of deformation and frictional heating along crack surfaces in later stages of deformation. Microstructure-response relations that can be used in the design of soft energetic composites are established.

Atomic simulations on the deformation mechanisms in nano-crystalline Ni–Al series Ni-based superalloy based on grain size, strain rate and temperature

Probing the micro-mechanism of precipitate-strengthened alloys with precipitate free zone: An experimental and theoretical study

Innovative mass timber panels, known as composite laminated panels (CLP), have been developed using lumber and laminated strand lumber (LSL) laminates. In this study, strain distributions of various 5‐layer CLP and cross‐laminated timber (CLT) were investigated by experimental and two modelling methods. Seven (7) different panel types were tested in third‐point bending and short‐span shear tests. During the tests, the digital imaging correlation (DIC) technique was used to measure the normal and shear strain in areas of interest. Evaluated component properties were used to determine strain distributions based on the shear analogy method and finite element (FE) modelling. The calculated theoretical strain distributions were compared with the DIC test results to evaluate the validity of strain distributions predicted by the analytical model (shear analogy) and numerical model (FE analysis). In addition, the influence of the test setup on the shear strain distribution was investigated. Results showed that the DIC strain distributions agreed well with the ones calculated by the shear analogy method and FE analysis. Both theoretical methods agree well with the test results in terms of strain distribution shape and magnitude. While the shear analogy method shows limitations when it comes to local strain close to the supports or gaps, the FE analysis reflects these strain shifts well. The findings support that the shear analogy is generally applicable for the stress and strain determination of CLP and CLT for structural design, while an FE analysis can be beneficial when it comes to the evaluation of localized stresses and strains. Due to the influence of compression at a support, the shear strain distribution near the support location is not symmetric. This is confirmed by the FE method.

Functionally graded material (FGM) concept has been applied successfully in order to improve/design heat transfer, electric and electronic conductivity, static and dynamic strengths of adhesive joints by reliving stress distributions in both adhesive and adherend materials. This new approach relies on tailoring material composition of adhesive and adherends along one or more coordinate directions. Thermal residual stresses in adhesive joints are a vital issue in terms of the joint strength. FGM concept also allows to relieve/control thermal residual stresses encountered in adhesive joints due to mismatches between coefficients of thermal expansion of adhesive and adherend materials. Mathematical models and solutions on the thermal residual stress analysis have been continuously improved. This paper reviews the current status of mathematical models, and offers an improved mathematical model and numerical solution method by considering two-dimensional thermal stress and deformation states of adhesively bonded bi-directional functionally graded clamped plates subjected to an in-plane heat flux along one of the ceramic edges. This mathematical model assumes the material properties of the functionally graded plates to vary with a power law along two in-plane directions and not through the plate thickness direction, in particular, considers the spatial derivatives of thermal and mechanical properties of the material, and enables the investigation of the effects of the bi-directional composition variations and spatial derivative terms on the displacement, strain and stress distributions. The heat conduction and Navier equations describing the twodimensional thermo-elastic problem are discretized using finite-difference method, and the set of linear equations are solved using the pseudo singular value method. The functionally graded plates relieve both stress and strain distributions and levels in the adhesive layer and in the plates even though the adhesive layer is still ungraded. The spatial derivatives of mechanical and thermal properties of the local material become more effective on the strain and stress distributions of the plates and adhesive layer. The model, disregarding these derivative terms, exhibits sensitivity to small changes in the compositional gradients (n, m) by adjusting the variations of ceramic volume fraction along the x - and y-directions, respectively, and instability in the calculation of stress and strain distributions and levels. However, the improved model with material derivatives, which considers the effects of these derivative terms, predicts stress and strain distributions and levels complying with changes in the compositional gradient exponents.

The heat transfer characteristics for condensation onto three plates (flat, taper fin, and flat fin) of water-ethanol vapor have been systematically investigated. A comparison of the three condensation heat transfer characteristics was made, and the effect of temperature gradients on the Marangoni condensation heat transfer was investigated. The results showed that the condensation modes on the surfaces with temperature gradients were usually a mixture of several different modes, while a single mode usually occurred on the condensing surface of the plat plate. The change of condensation modes on plates with fins was less marked and frequent than that on the flat plate. The mean heat transfer coefficients for the flat-fin plate, which had larger temperature gradients on the condensing surface, were greater than those on the surfaces with smaller temperature gradients. However, the degree of promotion of heat transfer by the temperature gradients depended on their values. Temperature gradients on the condensing surface made the vapor-to-surface temperature difference region, responsible for enhancing heat transfer, move to the lower region, and larger temperature gradients produced more significant movement. Moreover, the positive effect of both vapor velocity and pressure on the heat transfer was weakened by temperature gradients. The enhancement effect of vapor velocity and pressure on heat transfer was weaker when the temperature gradients on the condensing surface were larger.

Non-linear finite element model for dynamic analysis of high-speed valve train and coil collisions

Adsorption of a two-component gas mixture of acetone and methylbenzene was tested in a fixed-bed apparatus, and a coupled model of heat and mass transfer was developed according to the theory of Soret and Dufour effects. The numerical simulation results agreed well with the experimental results. Using this mathematical model, the coupled effects of heat and mass transfer were studied in a fixed-bed adsorption simulation, and numerical analysis results were used to discuss the influences of heat transfer coefficients, mass transfer coefficients, and the coupled effect of heat and mass transfer on the fixed-bed process. These results show that heat transfer coefficients have little effect on mass transfer. In contrast, mass transfer coefficients have some impact on heat transfer. The mass transfer effect caused by the temperature gradient is more obvious than the heat transfer effect caused by the concentration gradient.

The frictional heat transfer regularity in the mechanical seal system consisting of the rotating ring, the stationary ring, the fluid film in the end faces and the sealed medium was investigated. The primary factors affecting the frictional heat transfer regularity, such as the heat transfer coefficients from the rings to the sealed medium, the frictional heat flux, the frictional heat distribution ratio and so on, were discussed. The equations for calculating the temperature field both in the sealing members and in the fluid film were derived. The coupling analysis of the frictional heat of the fluid film and the thermal deformation of the two end faces of the rings was carried out to obtain the separation angle of the two deformed end faces in consideration of the viscosity change of the fluid film. The results indicate that the frictional heat of the fluid film heavily affects its characteristic and the sealing performance of mechanical seals. The frictional heat changes not only the shape of the gap between the end faces but also the viscosity of the fluid film, and thereupon leads to the increase of the leakage rate. The maximum temperature of the system is at the inner radius of the fluid film, and most of the frictional heat is conducted by the rotating ring. Based on the heat transfer analysis method put forward in this paper, the parameterized design of mechanical seals can be realized to determine the best geometrical parameters and to select the appropriate material of the sealing members.

The paper reports the results of the study of highly effective relaxation mechanisms of plastic deformation in Cu-Al single crystals and their effect on mechanical properties and tendency toward strain localization. The experiments concern a wide range of aluminium content (0–16 at. % Al) in copper based single crystals, tested in tension. These were oriented in the centre of stereographic triangle. Slip markings, changes of crystal shape, strain hardening rate and strain rate sensitivity provided independent information permitting to identify the mechanism of relaxation and to determine its kinetic features. It was found that selfinduced entry of critical slip system causes sudden decrease of hardening rate, changes the strain rate sensitivity and leads to strain localization. The effect occurs regardless the crystal composition but its extent is dependent on Al content. The model of the relaxation mechanism has been proposed.

We discuss the statistical properties of interacting dislocations in plastically deformed crystals. Due to their long-range mutual interactions, dislocations arrange into jammed configurations, that can be set into motion under the action of an external stress. Disorder provides an additional source of pinning which we study by scaling theories, considering the case of parallel arrays of dislocations in a pileup or a low angle grain boundaries. As an application of these ideas, we discuss the plastic yielding of a vortex lattice in the Corbino disk and the growth of a vortex polycrystal in a field cooling experiment. 1I ntroduction Plastic deformation is a multi-scale problem of immense complexity. Relevant processes range from the atomistic scale where the atomic arrangement and defect properties of a material are of crucial importance for its deformation properties, up to the geological scale where deformation instabilities manifest themselves in the form of earthquakes, avalanches and so on. In the past, the problem of plastic deformation has been addressed by two quite distinct communities, using di! erent methods and distinct conceptual frameworks. The mechanics community has developed the powerful mathematical framework of continuum mechanics into a tool for handling complex deformation processes. Finite element modeling has become a standard method for describing deformation processes in engineering applications. Due to the very nature of the continuum framework, in the absence of ’pathological’ cases (plastic instabilities) it is assumed that the state of the material can be characterized by smooth and di! erentiable displacement fields, and plastic deformation is envisaged as a smooth, quasi laminar flow process. The microscopic properties of materials are reflected by constitutive laws which serve as an input to the mathematical formalism. The plasticity view of the

Anisotropy influence on flow behaviour and plastic instability of Ti6Al4V sheets deformed in a wide range of temperatures and strain rates

To accurately obtain the flow and temperature field in mechanical seals and investigate the key influencing factors, a numerical analysis of flow and heat transfer in a contact mechanical seal with high-sealing pressure, high-operating temperature, and high-rotational speed is presented. A three-dimensional (3D) computational model consisting of seal rings, surrounding flushing fluid, and other seal components is constructed. fluent, a commercial computational fluid dynamics (CFD) software, is used to solve the 3D fluid–solid coupling model. Frictional heat, stirred heat, and convection coefficients are focused on in this study to ensure the reliability of the numerical results. The flow field and temperature distributions of the mechanical seal are presented, and the influence of different flushing fluid temperatures, flushing flow rates, and thermal conductivities of the seal rings on heat transfer is discussed. The results show that the stirred heat (accounting for about 10% of the frictional heat in the present mechanical seal) cannot be ignored for high-parameter mechanical seals. The flushing parameters can only influence temperature magnitudes on the seal rings but have minimal effects on the temperature gradients, which, however, can be well improved by adjusting the thermal conductivities of the seal rings.