Foil Bending Research Articles

Application of combined process of holding pressure and ultrasonic vibration to control the springback behavior of pure titanium foils

Foil bending is one of the promising approaches to fabricating micro-bending parts. However, it is difficult to bend pure titanium foils with high precision due to the double effect of size effects and close-packed hexagonal crystal structure. To control the springback behavior of pure titanium foils, an ultrasonic vibration-assisted bending platform was developed, and the mechanism by which ultrasonic vibration affects the springback behavior was investigated. The results indicate that the compressive stress induced by ultrasonic vibration has a plastic penetration effect, which forces the hard-oriented grains to deform and eventually changes the stress distribution state of the bending region. Therefore, both the amount and the scatter of springback decrease with increasing ultrasonic amplitude. The surface roughness of foils with a t/d value of 5.4 decreases by 42.4% under ultrasonic vibration. However, ultrasonic vibration is effective in controlling the spring-back behavior only at the initial stage (0–5 s), so there is no need to extend the ultrasonic vibration time substantially. The plastic penetration capacity of compressive stress can be greatly enhanced by applying holding pressure, so the combined use of holding pressure and ultrasonic vibration is a useful process to control the bending springback behavior of foils. This work provides a basis for the efficient and precise fabrication of micro-bending parts.

Numerical study on debris cloud and channeling effect of honeycomb sandwich shields under hypervelocity impact

In this study, the finite element and smoothed-particle hydrodynamics adaptive method was used to reproduce experiments on honeycomb sandwich shields impacted by spherical projectiles at hypervelocities, which can provide phenomena that are difficult to observe experimentally. The simulation results clearly reproduced the formation, development, and stabilization processes of the debris cloud as well as the damage and response processes of the honeycomb sandwich shield. The petal-shaped multicellular internal structure of the debris cloud was proposed by combining the formation and development of the debris cloud with its experimentally observed morphology. The damage and response processes of the honeycomb sandwich shield can be divided into two stages, namely, the crushing and inertial motion stages, to elaborate the varying failure modes of the honeycomb sandwich shield in different stages. The crushing stage represents the response of the material, whose failure modes include penetration, bending, buckling, tensile fracture, and compression failure. The inertial motion stage represents the structural response (bending and buckling of foils), which, at different positions, leads to folding and compaction of the honeycomb core layer by layer along the radial direction. The factors influencing the channeling effect were investigated, and the influences of the projectile diameter and impact position on the channeling effect and protection performance of the honeycomb sandwich shield were analyzed. The envelope analysis method for damage areas, which can predict the damage to the honeycomb core and rear plate at any impact position using an envelope diagram, was proposed. It was shown that the foil at different positions works by blocking or partitioning, which seriously affects the channeling effect. This study provides new ideas for optimizing the design of Whipple shields.

Estimating the dimensional change behavior of nuclear graphite with heavy-ion irradiation-induced bending

Two promising reactor Generation IV designs employ nuclear graphite as their moderator and reflector. To this end, new graphite grades are being developed, which will require their suitability for reactor design to be established. Understanding graphite irradiation behavior, especially dimensional change, is critical when selecting a particular nuclear graphite grade. This is usually established by fast neutron irradiation experiments in a material test reactor (MTR). However, due to the limited accessibility to the MTR irradiation facility, cost, and the time required for such experiments to be carried out, the development of new nuclear graphite grades is restrictive. Here, a novel approach is proposed to enable suitable grades to be selected from a number of candidates before an MTR program is implemented by estimating the irradiation-induced dimensional change behaviors of several nuclear graphite grades based on the bending of graphite foils under ion irradiation. The method is capable of efficiently distinguishing the most dimensionally stable graphite grades in the laboratory without the need to irradiate many samples in an MTR program.

Modeling of Cyclic Bending of Thin Foils Using Higher-Order Strain Gradient Plasticity

Modeling of Cyclic Bending of Thin Foils Using Higher-Order Strain Gradient Plasticity

On energetic and dissipative gradient effects within higher-order strain gradient plasticity: Size effect, passivation effect, and Bauschinger effect

The size effect, the passivation effect, and the plastic behavior under non-proportional loading in the context of bending and tension of thin foils, and a combination of compression and shear of constrained layers, are studied using Gudmundson's higher-order strain gradient visco-plasticity theory. Bending experiments on thin nickel foils with and without passivation are performed with a load-unload technique. The passivated layer increases the flow stress significantly. Finite element simulations are carried out on elasto-viscoplastic foils under bending and tension, and on constrained layers under combined compression and shear. The simulation results are generally in agreement with the experimental observations. Implications for higher-order boundary conditions and the roles of energetic and dissipative gradient terms are highlighted. The dissipative gradient terms contribute to the increased yield strength, whereas the energetic gradient terms lead to increased strain hardening and an anomalous Bauschinger effect. The modeling of the deformation of constrained layers suggests that compressive stress has a significant influence on the shear flow stress, reducing it compared with the shear flow stress under pure shear.

On the role of higher-order conditions in distortion gradient plasticity

We focus on Gurtin’s gradient plasticity (GP) theory adopting Nye’s tensor as primal higher-order (HO) kinematic variable, contributing to the free energy. In the absence of other HO kinematic variables, this framework is characterised by kinematic HO boundary conditions (BCs) which admit discontinuity in some components of the plastic distortion. This implies that the finite element (FE) implementation of this theory requires a “non-standard” approach. To address this issue, here, we develop a specific H(curl) FE. A “standard” FE implementation, in which the nodal degrees of freedom are all the displacement and plastic distortion components, is successful if the above theory is extended by including a dissipative HO stress, proportional to a material length L, conjugated to the gradient of the plastic distortion rate, such that the HO BCs must be imposed on each plastic distortion component. The foregoing switch in the kinematic HO BCs makes it difficult to obtain reliable FE solutions for the first theory by particularising the “standard” FE code for the enriched theory with the choice of a suitably small L. Beside showing this, in this work, we aim at shedding light on the distortion GP based on Nye’s tensor only, in which also the use of an appropriately small rate-sensitivity parameter to obtain rate-independent solutions within a viscoplastic framework reveals interesting aspects. To this purpose, we consider three plane strain benchmarks, with focus on limit load capacity: the bending of thin foils, relevant to validate our novel implementation by comparison with literature results; the simple shear of a strip constrained between bodies impenetrable to dislocations, that we discuss on the basis of a new analytical solution for the rate-independent case; a composite problem approximating a polycrystal, whose main feature consists of internal grain boundaries in which we impose homogeneous kinematic HO conditions. This last benchmark shows that the computational model involving HO dissipation cannot predict a collapse mechanism predicted by the novel H(curl) FE model.

On the analysis of pure bending of rigid-plastic beams in strain-gradient plasticity

Abstract The complete stress field, including the microstress, the moment-stress, and the line forces are derived for the pure bending of a rigid-plastic beam of rectangular cross-section in the model of strain-gradient plasticity. The workless spherical parts of the microstress and the moment-stress tensors are incorporated in the analysis. Their determination is shown to be of importance for the fulfilment of the higher-order traction boundary conditions, the physical interpretation of line forces, and their contributions to bending moments. Three equivalent methods are used to derive the moment-curvature relationship for any of the gradient-enhanced effective plastic strain measures from the considered broad class of these measures. Specific results are given for the selected choice of the stress-strain relationship describing the uniaxial tension test. Closed-form analytical expressions are obtained in the case of linear hardening, and in some cases of nonlinear hardening. The analysis of the plane-strain bending of thin foils is also presented. In this case there are two sets of line forces along the edges of the beam. The relationships between the applied bending moment and the curvature, and between the lateral bending moment and the curvature are derived and discussed. The lateral bending moment along the lateral sides of the beam, needed to keep the plane-strain mode of deformation, is one-half of the applied bending moment.

On the Finite Element implementation of higher-order gradient plasticity, with focus on theories based on plastic distortion incompatibility

We consider work-conjugate Gradient Plasticity (GP) theories involving both energetic and dissipative higher-order contributions. We show that the conceptually most straightforward Finite Element (FE) implementation, in which the displacement components and the relevant plastic distortion contributions are employed as nodal degrees of freedom, leads to a very efficient Backward-Euler FE algorithm if a proper viscoplastic potential is adopted, the latter in general involving dissipative higher-order terms. We also show that the proposed viscoplastic constitutive law can accurately represent rate-independent behaviour, without losing computational efficiency. To draw our conclusions we consider many benchmarks (simple shear of a constrained strip, bending of thin foils, micro-indentation) and both phenomenological and crystal GP theories whose distinctive feature is a contribution to the free energy, called the defect energy, written in terms of Nye’s dislocation density tensor.

Strain gradient elasto-plasticity with a new Taylor-based yield function

For micron-scale elasto-plastic deformations, a theory of strain gradient elasto-plasticity (SGEP) has been established to explain some phenomena that have recently attracted intensive investigations, which include size effects around the elastic limit and in plastic hardening, the anomalous Bauschinger effect, plastic softening, and the unconventional load–unload hysteresis loops. Based on the fact that for most materials the elastic length scale is far smaller than the plastic length scale, our dimensional analysis reveals that the elastic strain gradient is generally dominant over the plastic strain gradient, which indicates the significant role of elasticity. Therefore, a more rigorous consideration of the elastic deformation is implemented within the proposed SGEP framework, featured by a new Taylor plasticity-based yield function and the elasto-plastic decompositions of both strain and strain gradient. The proposed yield function emphasizes the reversibility of elastic deformation-related dislocations, which has been frequently observed experimentally. This proposed SGEP not only does satisfy the principle of nonnegative plastic dissipation for material hardening, but also allows for the existence of material softening which has been observed in recent experiments. The wire torsion and foil bending problems are used as examples, to validate the SGEP’s capability in interpreting the above-mentioned phenomena by comparison with experimental data in the literature.

A finite element framework for distortion gradient plasticity with applications to bending of thin foils

A novel general purpose Finite Element framework is presented to study small-scale metal plasticity. A distinct feature of the adopted distortion gradient plasticity formulation, with respect to strain gradient plasticity theories, is the constitutive inclusion of the plastic spin, as proposed by Gurtin (2004) through the prescription of a free energy dependent on Nye’s dislocation density tensor. The proposed numerical scheme is developed by following and extending the mathematical principles established by Fleck and Willis (2009). The modeling of thin metallic foils under bending reveals a significant influence of the plastic shear strain and spin due to a mechanism associated with the higher-order boundary conditions allowing dislocations to exit the body. This mechanism leads to an unexpected mechanical response in terms of bending moment versus curvature, dependent on the foil length, if either viscoplasticity or isotropic hardening are included in the model. In order to study the effect of dissipative higher-order stresses, the mechanical response under non-proportional loading is also investigated.

Second order stress gradient plasticity with an application to thin foil bending

The continuum theory of dislocations is applied to formulate the problem of a double ended dislocation pileup under quadratic applied stress. Accordingly, a second order stress gradient plasticity model is presented to address the contribution of the first and the second stress gradients in the effect interpretation. The model is employed to predict the initial strengthening and subsequent hardening in curved and straight thin foils under pure bending within the continuum framework. It is shown that the so-called stress gradient plasticity model that ignores the second stress gradient may not give sound interpretations of the size effects. The plastic response of thin foils is affected by both the first and second stress gradients, yet their interaction strongly depends upon the length scale parameter. The larger the length scale parameter, the quadratic term contribution would be important and the predictions of the first and second order models deviate significantly from each other.

Grain size effect on springback behavior in bending of Ti-2.5Al-1.5Mn foils

The precise bend forming of metal foils is difficult, mainly because that the springback behavior cannot be easily controlled. In order to investigate the springback behavior in bending of metal foils, roll bending and pressure sizing tests were conducted on Ti-2.5Al-1.5Mn foils in this study. It has been observed that the springback behavior has a close correlation with the thickness to grain diameter (T/D) ratio and crystallographic texture. A certain critical T/D ratio value is observed, which divides the variation trend of the springback behavior into two different parts. Stress distribution is disturbed in specimens with small T/D ratio, which leads to large scatter of springback angle after unloading. Pressure sizing process can change the state of stress distribution of deformation region and it is a useful process to reduce the amount of springback angle and the scatter in bending of metal foils by controlling the sizing repetitions, sizing force, holding time and punch speed. Based on these findings, a micro scale honeycomb structure is successfully manufactured.

Towards a Uniform Model for Lattice Defect Image Simulations

For more than seven decades, diffraction contrast in the TEM has been used for the study of both linear and planar lattice defects, such as dislocations, stacking faults, anti-phase boundaries, and so on. In recent years, several alternative approaches for defect imaging have become available: using a standard annular dark field detector, the STEM diffraction contrast image (DCI) mode produces medium angle annular dark field (MAADF) images which display strong defect contrast, even for relatively thick foils [1], while suppressing contrast due to foil bending and such. Both systematic row and zone axis orientations can be used in the STEM-DCI technique, in contrast with conventional TEM bright field/dark field imaging, where the zone axis orientation is mostly avoided. The arsenal of scanning electron microscopy (SEM) modalities has been extended with the electron channeling contrast imaging (ECCI) approach, which allows for the imaging of low density surface penetrating lattice defects over large sample areas. It is to be noted that in all of these techniques, the diffraction contrast is caused by the same dynamical scattering mechanisms; the only differences are the instrument accelerating voltage, the illumination mode (parallel or conical, stationary or scanning), and the shape and position of the detector (CCD, annular detector). The common underlying physics principles suggest that a single computational approach to defect image simulations might be possible, covering all the above mentioned observations modes.

Finite Element Analysis of the Effect of Flexible Pad on the Deformation of Metal Foils in Flexible Pad Laser Shock Microforming

Flexible Pad Laser Shock Forming (FPLSF) is a new microforming process using laser-induced shock pressure and a flexible pad. This process involves high strain-rate (~105 s-1) plastic deformation of metallic foils along with the hyperelastic deformation of the flexible elastomer pad over which the foil is positioned. This paper studies the influence of flexible pad on the shockwave propagation behavior and the plastic deformation of metal foil in FPLSF using finite element analysis. The effect of flexible pad materials such as silicone rubber, polyurethane rubber and natural rubber on the deformation of copper foils has been analysed in detail. An increase in crater depth is observed with the reduction in flexible pad hardness. However, it is found that there exists an optimum hardness of the flexible pad to achieve perfect hemispherical craters on metal foils, as bending of foils at non-deformed region is observed with softer pads whereas flattening of crater surface occurs with harder pads. The effect of flexible pad thickness on the foil deformation was analyzed at six different thickness levels: 300 μm, 600 μm, 900 μm, 1200 μm, 1500 μm, and 2000 μm. Similarly, there exists an optimum flexible pad thickness to maximize the crater depth and achieve the hemispherical shapes. Analysis of flexible pad thickness indicates that the pad thickness influences the elastic recovery of the flexible-pad and hence the plastic deformation of the metallic foils.

Towards a further understanding of dislocation pileups in the presence of stress gradients

This study is an essential complement and extension to the stress-gradient concept recently proposed by Hirth. An analytic method is presented for studying the behaviour of double-ended dislocation pileup in the presence of various stress gradients by solving a singular integral equation based on the continuous approximation of dislocations. Four special cases of double-ended pileup in the presence of stress gradients are discussed in detail. The corresponding dislocation distribution, the length of pileup, the total number of dislocations within the pileup and the force on the leading dislocations at the pileup ends are derived, respectively. It is shown that both the number of dislocations and the force on the leading dislocation in a pileup are sensitive to the relative magnitude of stress near the dislocation source and both are less than that in constant stress case. Of particular importance, it is indicated that the small-scaled materials subjected to a stress involving a gradient would be stronger than that under a constant stress. Applied to wire torsion and foil bending, the stress gradient model predicts an increase in the initial yielding, which is in reasonable agreement with the recent experimental data. The proposed stress gradient concept may provide a new physical insight into the size-dependent plasticity phenomena at small length scale.

Flow control by means of a traveling curvature wave in fishlike escape responses

Fish usually bend their bodies into a ''C'' shape and then beat their tails one or more times to escape from predators (in nature) or stimuli (in experiments). The maneuvering behavior, i.e., the C-shape bending and the return flapping, is called C-start. In this paper, the escaping performance of fishlike C-start motions has been numerically investigated for a flow physics study by the use of a two-dimensional deformable foil bending and stretching quickly. The C-start motions, performed in the quiescent water and based on prescribed deforming modes, are predicted by a numerical method coupling the two-dimensional incompressible Navier-Stokes equations and the deforming body dynamic equations. It has been found earlier that a typical C-start motion consists of (1) a main C-shape bending and (2) a rearward travelling curvature wave which was seldom mentioned in previous studies. In order to reveal the flow control mechanism of the traveling curvature wave in a fish's C-start motion, two kinds of C-start flows with different deforming modes, namely the integrated mode (IM, a C-shape bending plus a travelling curvature wave) and the basic mode (BM, a C-shape bending only) are analyzed and compared in detail. According to the numerical results, it shows that if proper values of the travelling curvature wave parameters are chosen, the foil's escaping maneuverability presented in the IM is much better than that in the BM, i.e. the turn angle and the speed of the center of mass at the end of a C-start in the IM is almost twice as large as those in the BM. Further study shows that the travelling curvature wave not only can enhance the thrust and the centripetal force but also increase the propulsive efficiency. These results suggest that an efficient travelling curvature wave is of great significance in the flow control of a C-start motion. Finally, a parametric study finds that the phase difference between the C-shape bending and the travelling curvature wave (i.e., the initial phase angle in the travelling curvature wave of the deforming model) is a key parameter in the flow control. To achieve the desirable turn angle, escaping speed, and propulsive efficiency in the C-start motions, the initial phase angles must be ranged within specific magnitudes. It is found that for optimum values of the initial phase angle, the foil's flexible deforming process is qualitatively consistent with that of a fish body in nature. The results obtained in this study provide a new physical insight into the understanding of swimming mechanisms of fish's C-start maneuvers.

J161042 箔材の超音波援用曲げ加工における変形特性評価([J16104]マイクロナノメカト口ニクス(4))

J161042 箔材の超音波援用曲げ加工における変形特性評価([J16104]マイクロナノメカト口ニクス(4))

Slide-Bend Forming of Very Thin Metal Sheet Using Slide-Ironing Tool

Characteristics of slide-bend forming were investigated. In this process, foil specimens can be bent to various shaped products by indenting and sliding a tool. The effects of the tool indentation load, the foil thickness and the number of slide repetition on the bending angle were examined experimentally for three kinds of foil materials. In addition, the deformation of bent region was examined using a rigid-plastic finite element analysis. Bending angle increased with increasing the indentation load or decreasing the foil thickness. When the number of slide repetition increased, the bending angle increased slightly. The slide repetition can be effective for adjusting bending angle slightly. By sliding a thin edge-shaped tool relative to the foil specimen, bending angle and radius of curvature of specimens can be controlled freely.

Nano-scale quasi-melting of alkali-borosilicate glasses under electron irradiation

Quasi-melting of micro- and nano-samples during transmission electron microscope irradiation of glassy materials is analysed. Overheating and true melting by the electron beam is shown not to be an explanation due to the ultra-sharp boundary between transformed and intact material. We propose that the observed fluidisation (quasi-melting) of glasses can be caused by effective bond breaking processes induced by the energetic electrons in the electron beam. The bond breaking processes modify the effective viscosity of glasses to a low activation energy regime. The higher the electron flux density the lower is the viscosity. Quasi-melting of glasses at high enough electron flux densities can result in shape modification of nano-sized particles including formation of perfect beads due to surface tension. Accompanying effects, such as bubble formation and foil bending are revisited in the light of the new interpretation.

Micro-deformation of flexible substrate for electronic devices during handling prior to lithography patterning

The dimensional stability of poly(ethylene naphthalene-2,6-dicarboxylate) (PEN) foils during the handling and production process, is crucial for the quality of the final multilayer flexible electronic devices. The foil-on-carrier (FOC) – foil/adhesive/Si-wafer sandwich – is a handling method, which is currently used to temporary attach the foil to a Si-wafer carrier during the lithography processing. This handling method ensures good surface flatness of the foils during the processing. However this technique has two drawbacks: (1) it creates an in-plane micro-deformation of the PEN foil and (2) bending of FOC due to the lamination procedure and lithography processing. In this article the temperature dependence of in-plane foil deformation and bending of FOC was reported and the final curing step of lamination procedure was identified as the main source of in-plane deformation and bending. Finally the resultant stresses introduced to FOC by the curing step derived from the experimental measurements were compared to stress values calculated from the Stoney’s and Ohring’s equations.