Dahl Friction Model for Driving Characteristics of V-Shape Linear Ultrasonic Motors.

The contact process of stator and slider described by the Coulomb friction model is basically in a pure sliding friction state, and a mechanical model based on the Dahl friction theory was proposed to describe the contact process between stator and slider of V-shape linear ultrasonic motor. With consideration for the tangential compliance of stator and slider, the dynamic contact and friction processes of stator and slider were addressed in stages. The simulation results show that the ratio of the friction positive work decreases with the increase of the preload, and the vibration amplitude of the stator increases the proportion of positive work of the friction force. Improving the contact stiffness of the stator and slider is conducive to improving the output performance of the ultrasonic motor. The asymmetry of the left and right performance of the V-shaped vibrator will cause a difference in the left and right running speeds of the ultrasonic motor. The improved Dahl friction-driving model makes up for the discontinuity of tangential contact force calculated by the Coulomb friction model. This study demonstrates that the friction-driving model based on the Dahl theory is reliable and reasonable for linear ultrasonic motors according to the experimental results.

A New Semi-Analytical Solution for an Arbitrary Hardening Law and Its Application to Tube Hydroforming.

The present study consists of two parts. The first part supplies an exact semi-analytical solution for a general model of rigid plastic strain hardening material at large strains. The second part applies this solution to tube hydroforming design. The solution provides stress and velocity fields in a hollow cylinder subject to simultaneous expansion and elongation/contraction. No restriction is imposed on the hardening law. A numerical method is only required to evaluate ordinary integrals. The solution is facilitated using Lagrangian coordinates. The second part of the paper is regarded as an alternative to the finite element design of tube hydroforming processes, restricted to rather simple final shapes. An advantage of this approach is that the hardening law is not required for calculating many process parameters. Therefore, the corresponding design is universally valid for all strain hardening materials if these parameters are of concern. In particular, the prediction of fracture initiation at the outer surface is independent of the hardening law for widely used ductile fracture criteria. The inner pressure is the only essential process parameter whose value is controlled by the hardening law.

Spring Back Behavior of Large Multi-Feature Thin-Walled Part in Rigid-Flexible Sequential Loading Forming Process.

The spring back behavior of large complex multi-feature parts in the rigid-flexible sequential forming process has certain special characteristics. The hydraulic pressure loading locus has a significant influence on the spring back of small features of the part, and the applicability of the spring back prediction model to the process needs further research. Therefore, this paper takes the large aluminum alloy inner panel of an automobile as the research object, and the spring back model and the influence laws of the hydraulic pressure loading locus are revealed by combining the theoretical analysis and numerical simulation with the process tests. Meanwhile, based on the theoretical prediction and experimental results, the spring back compensation of the complex inner panel is carried out. Results show that the hardening model has a greater impact on the accuracy of spring back prediction than the yield criterion does, and the prediction accuracy of Barlat'89 + Yoshida-Uemori mixed hardening model is the highest. Finally, the optimized loading locus of hydraulic pressure is obtained, and the accuracy results of the compensated parts verify the accuracy of the analysis model.

An Upper Bound Solution for the Compression of an Orthotropic Cylinder.

The upper bound theorem is used in conjunction with Hill's quadratic yield criterion for determining the force required to upset a solid cylinder. The kinematically admissible velocity field accounts for the singular behavior of the real velocity field in the vicinity of the friction surface if the maximum friction law is adopted. The regime of sticking is also taken into consideration. The effect of this regime on the upper bound limit load is revealed. In particular, the kinematically admissible velocity field that includes the regime of sticking may result in a lower upper bound than that with no sticking. The boundary value problem is classified by a great number of geometric and material parameters. Therefore, a systematic parametric analysis of the effect of these parameters on the compression force is practically impossible. An advantage of the solution found is that it provides a quick estimate of this force for any given set of parameters.

Finite Plane Strain Bending under Tension of Isotropic and Kinematic Hardening Sheets.

The present paper provides a semianalytic solution for finite plane strain bending under tension of an incompressible elastic/plastic sheet using a material model that combines isotropic and kinematic hardening. A numerical treatment is only necessary to solve transcendental equations and evaluate ordinary integrals. An arbitrary function of the equivalent plastic strain controls isotropic hardening, and Prager's law describes kinematic hardening. In general, the sheet consists of one elastic and two plastic regions. The solution is valid if the size of each plastic region increases. Parameters involved in the constitutive equations determine which of the plastic regions reaches its maximum size. The thickness of the elastic region is quite narrow when the present solution breaks down. Elastic unloading is also considered. A numerical example illustrates the general solution assuming that the tensile force is given, including pure bending as a particular case. This numerical solution demonstrates a significant effect of the parameter involved in Prager's law on the bending moment and the distribution of stresses at loading, but a small effect on the distribution of residual stresses after unloading. This parameter also affects the range of validity of the solution that predicts purely elastic unloading.

Effect of Rotation of the Principal Stress Axes Relative to the Material on the Evolution of Material Properties in Severe Plastic Deformation Processes.

Severe plastic deformation (SPD) processes are widely used for improving material properties. A distinguishing feature of many SPD processes is that the principal axes of the stress tensor intensively rotate relative to the material. Nevertheless, no measure of this rotation is involved in the constitutive equations that predict the evolution of material properties. In particular, a typical way of describing the effect of SPD processes on material properties is to show the dependence of various parameters that characterize these properties on the equivalent strain. However, the same level of the equivalent strain can be achieved in a process in which the principal axes of the stress tensor do not rotate relative to the material. It is, therefore, vital to understand which properties are dependent and which properties are independent of the rotation of the principal axes of the stress tensor relative to the material. In the present paper, a new multistage SPD process is designed such that the principal stress axes do not rotate relative to the material during each stage of the process but the directions of the major and minor principal stresses interchange between two subsequent stages. The process is practically plane strain, and it may be named the process of upsetting by V-shape dies. In addition, axisymmetric compression by Rastegaev's method is conducted. In this case, the principal stress axes are fixed in the material throughout the entire process of deformation. Material properties and microstructure generated in the two processes above are compared to reveal the effect of the rotation of the principal stress axes relative to the material on the evolution of these properties.

A Novel Approach to Predict Wrinkling of Aluminum Alloy During Warm/Hot Sheet Hydroforming Based on an Improved Yoshida Buckling Test.

In order to predict the wrinkling of sheet metal under the influence of fluid pressure and temperature during warm/hot hydroforming, a numerical simulation model for sheet wrinkling prediction was established, taking into account through-thickness normal stress induced by fluid pressure. From simulations using linear and quadratic elements, respectively, it was found that the latter gave results that were much closer to experimental data. A novel experimental method based on an improved Yoshida Buckling Test (YBT) was proposed for testing the wrinkling properties of sheets under the through-thickness normal stress. A wrinkling coefficient suitable for predicting wrinkling was also presented. Based on the numerical simulations, an experimental validation of wrinkling performance was conducted. Ridge-height curves measured along the main diagonal tensile direction of the sheet were presented and showed that the wrinkling prediction criterion provided good discrimination. Furthermore, the wrinkling properties of several different materials were simulated to evaluate the accuracy of the prediction method, and the results revealed that the improved YBT gave good predictions for wrinkling in the conventional sheet metal forming process, while the prediction results for wrinkling in warm/hot sheet hydroforming were also accurate with the fluid pressure of zero.

Solution Behavior near Envelopes of Characteristics for Certain Constitutive Equations Used in the Mechanics of Polymers.

The present paper deals with plane strain deformation of incompressible polymers that obey quite a general pressure-dependent yield criterion. In general, the system of equations can be hyperbolic, parabolic, or elliptic. However, attention is concentrated on the hyperbolic regime and on the behavior of solutions near frictional interfaces, assuming that the regime of sliding occurs only if the friction surface coincides with an envelope of stress characteristics. The main reason for studying the behavior of solutions in the vicinity of envelopes of characteristics is that the solution cannot be extended beyond the envelope. This research is also motivated by available results in metal plasticity that the velocity field is singular near envelopes of characteristics (some space derivatives of velocity components approach infinity). In contrast to metal plasticity, it is shown that in the case of the material models adopted, all derivatives of velocity components are bounded but some derivatives of stress components approach infinity near the envelopes of stress characteristics. The exact asymptotic expansion of stress components is found. It is believed that this result is useful for developing numerical codes that should account for the singular behavior of the stress field.

Description of Residual Stress and Strain Fields in FGM Hollow Disc Subject to External Pressure.

Elastic/plastic stress and strain fields are obtained in a functionally graded annular disc of constant thickness subject to external pressure, followed by unloading. The elastic modulus and tensile yield stress of the disc are assumed to vary along the radius whereas the Poisson's ratio is kept constant. The flow theory of plasticity is employed. However, it is shown that the equations of the associated flow rule, which are originally written in terms of plastic strain rate, can be integrated with respect to the time giving the corresponding equations in terms of plastic strain. This feature of the solution significantly facilitates the solution. The general solution is given for arbitrary variations of the elastic modulus and tensile yield stress along the radial coordinate. However, it is assumed that plastic yielding is initiated at the inner radius of the disc and that no other plastic region appears in the course of deformation. The solution in the plastic region at loading reduces to two ordinary differential equations. These equations are solved one by one. Unloading is assumed to be purely elastic. This assumption should be verified a posteriori. An illustrative example demonstrates the effect of the variation of the elastic modulus and tensile yield stress along the radius on the distribution of stresses and strains at the end of loading and after unloading. In this case, it is assumed that the material properties vary according to power-law functions.

A Theory of Elastic/Plastic Plane Strain Pure Bending of FGM Sheets at Large Strain.

An efficient analytical/numerical method has been developed and programmed to predict the distribution of residual stresses and springback in plane strain pure bending of functionally graded sheets at large strain, followed by unloading. The solution is facilitated by using a Lagrangian coordinate system. The study is concentrated on a power law through thickness distribution of material properties. However, the general method can be used in conjunction with any other through thickness distributions assuming that plastic yielding initiates at one of the surfaces of the sheet. Effects of material properties on the distribution of residual stresses are investigated.