Don R. Metzger

Reliability Analysis of the Tube Hydroforming Process Based on Forming Limit Diagram

Tube hydroforming is an attractive manufacturing process in the automotive industry because it has several advantages over alternative methods. In order to determine the reliability of the process, a new method to assess the probability of failure is proposed in this paper. The method is based on the reliability theory and the forming limit diagram, which has been extensively used in metal forming as the criteria of formability. From the forming limit band in the forming limit diagram, the reliability of the forming process can be evaluated. A tube hydroforming process of free bulging is then introduced as an example to illustrate the approach. The results show this technique to be an innovative approach to avoid failure during tube hydroforming.

Improving the Reliability of the Tube-Hydroforming Process by the Taguchi Method

The tube-hydroforming process has undergone extremely rapid development. To ensure a reliable hydroforming process at the design stage, applying robust design methodologies becomes crucial to the success of the resulting process. The reliability of the tube-hydroforming process based on the tube wall thickness thinning ratio is studied in this paper. In order to improve the reliability of the process, the Taguchi method, which is capable of evaluating the effects of process variables on both the mean and variance of process output, is used to determine the optimal forming parameters for minimizing the variation and average value of the thinning ratio. Finite element simulation is used to analyze the virtual experiments according to the experimental arrays. A cross-extrusion hydroformed tube is employed as an example to illustrate the effectiveness of this approach.

A Unified Finite Element Approach for the Study of Postyielding Deformation Behavior of Formable Sheet Materials

Deformation and fracture behavior of several formable automotive aluminum alloys and steels have been assessed experimentally at room temperature through standard uniaxial tension, plane strain tension, and hemispherical dome tests. These materials exhibit the same deformation sequence: normally uniform elongation followed by diffuse necking, then localized necking in the form of crossed intense-shear bands, and finally fracture. The difference among these alloys lies primarily with respect to the point at which damage (i.e., voiding) starts. Damage develops earlier in the steel samples, although in all cases very little damage is observed prior to the onset of shear instability. A unified finite element model has been developed to reproduce this characteristic deformation sequence. Instability is triggered by the introduction of microstructural inhomogeneities rather than through the commonly utilized Gurson-Tvergaard-Needleman damage model. The predicted specimen shape change, shear band characteristics, distribution of strain, and the fracture modes for steels and aluminum alloys are all in good agreement with the experimental observations.

A Finite Element Study of Capstan Friction Test

In this paper the capstan friction test, which is also called as SMFS (sheet metal forming simulator) test, was simulated by the explicit finite element method. By using 3D finite element models and local axis system, pressure distributions on the frictional contact surfaces were investigated. The simulation showed non‐uniform pressure distributions both in longitudinal and transverse directions of a contact surface. It was also observed that the real pin/strip contact angle is less than the wrap angle. Finally, friction coefficients were calculated using the tension forces obtained from the simulations by the commonly used equation that originated from the rope/pulley analogy. In spite of the observed phenomena, which deviate from the expectation of rope/pulley analogy, the equations well predicted the friction coefficients.

Non‐uniform Pressure Distribution in Draw‐Bend Friction Test and its Influence on Friction Measurement

From various draw‐bend friction tests with sheet metals at lubricated conditions, it has been unanimously reported that the friction coefficient increases as the pin diameter decreases. However, a proper explanation for this phenomenon has not been given yet. In those experiments, tests were performed for different pin diameters while keeping the same average contact pressure by adjusting applied tension forces. In this paper, pressure profiles at pin/strip contacts and the changes in the pressure profiles depending on pin diameters are investigated using finite element simulations. To study the effect of the pressure profile changes on friction measurements, a non‐constant friction model (Stribeck friction model), which is more realistic for the lubricated sheet metal contacts, is implemented into the finite element code and applied to the simulations. The study shows that the non‐uniformity of the pressure profile increases and the pin/strip contact angle decreases as the pin diameter decreases, and the...

A Finite Element Study of Friction Effect in Four-Point Bending Creep Test

Creep tests are often performed in four-point bending and the stress distribution in the bending specimen is nonlinear, so creep properties are estimated from bend creep test data. However, getting creep properties from bending creep tests is often doubted because of uncertainties from contact point shift and frictional effect between loading pin and specimen in four-point bending creep tests. Finite element simulations of the four-point bending creep tests were performed with geometric models which include contact conditions. It was found from simulation studies that friction in the bend tests can cause error in the estimation of creep properties, but when no friction was applied in simulations the creep properties were well predicted from bend test data.Copyright

The Meshless Dynamic Relaxation Techniques for Simulating Atomic Structures of Materials

Traditionally, Molecular Dynamics combined with pair potential functions or the Embedded Atom Method (EAM) is applied to simulate the motion of atoms. When a defect is generated in the crystalline lattice, the equilibrium of atoms around it is destroyed. The atoms move to find a new place where the potential energy in the system is minimum, which could result in a change of the local atomic structure. The present paper introduces new Dynamic Relaxation algorithm, which is based on explicit Finite Element Analysis, and pair or EAM potential function, to find equilibrium positions of the block of atoms containing different structural defects. The internal force and stiffness at the atoms (nodes) are obtained by the first and second derivatives of the potential energy functions. The convergence criterion is based on the Euclidean norm of internal force being close to zero when the potential energy is minimum. The damping ratio affects the solution path so that different damping ratios could lead to different minimum potential energy and equilibrium shapes. The numerical responses and results by applying free boundary conditions and certain periodic boundary conditions are presented. The choice of scaled mass of atoms, proper time step and damping appropriate for the efficient and stable simulation is studied.Copyright

Reliability Analysis of the Tube Hydroforming Process Using Fuzzy Sets Theory

Tube hydroforming currently enjoys increasingly widespread application in industry, especially in the automotive industries, because of several advantages over traditional methods. Reliability analysis as a probabilistic method to deal with the probability of the failure of the structure or the system has been widely used in industry. A new reliability analysis approach for the tube hydroforming process using the fuzzy sets theory is presented in this paper. The stress of the hydroformed tube is related to several parameters, such as geometry, material properties, and process parameters. In most cases, it is difficult to express in a mathematical formula, and its relative parameters are not random variables, but the uncertain variables that have not only randomness but also fuzziness. In this paper, the finite element method is applied as a numerical experiment tool to find the statistical property of the stress directly by a fuzzy linear regression method. Based on the fuzzy stress-random strength interference model, the fuzzy reliability of the tube hydroforming process can be evaluated. A tube hydroforming process for cross-extrusion is then introduced as an example to illustrate the approach. The result shows that this approach can be extended to a wide range of practical tube hydroforming process.© 2004 ASME

Effect of Hydrogen Concentration on the Threshold Stress Intensity Factor for Delayed Hydride Cracking in Zr-2.5Nb Pressure Tubes

The Zr-2.5Nb pressure tubes of CANDU reactors are susceptible to a crack initiation and growth mechanism known as Delayed Hydride Cracking (DHC), which is a repetitive process that involves hydrogen diffusion, hydride precipitation, hydrided region formation and fracture at a flaw or crack tip. The threshold stress intensity for DHC initiation from a crack, KIH , is an important material parameter for assessing DHC initiation from flaws in pressure tubes. KIH is used to determine whether DHC initiation may occur from flaws which are postulated as crack-like. It is also an input parameter in the engineering process-zone methodology to assess DHC initiation from blunt flaws. Tests were performed to determine the effect of hydrogen concentration in solution on KIH in unirradiated Zr-2.5 Nb material, subjected to different thermo-mechanical treatments to obtain different yield strength or hardness. Hydrogen concentration in solution represents the diffusible hydrogen available for the DHC process, and is different than the total hydrogen concentration which includes the immobile hydrogen in the zirconium hydride phase. For all material conditions, the KIH values at 250°C are significantly higher when the hydrogen concentration in solution is low. Post test metallographic examination indicates that the crack-tip hydride is large and has a taper shape when the hydrogen concentration in solution is high. This suggests that KIH is reached due to insufficient stress to crack the hydrides. When the hydrogen concentration in solution is low, the crack-tip hydride is small and KIH is reached due to limited hydride growth. Finite element diffusion analysis was performed to determine the crack tip hydride accumulation as a function of KI and hydrogen in solution. For high hydrogen concentration in solution, the model predicts a taper hydride shape and hydride lengths which are consistent with the trend observed in the experiments. Another set of KIH tests was performed at 200°C on unirradiated pressure tube material hydrided to 60 and 100 ppm hydrogen. The test results indicated that KIH is controlled by the hydrogen in solution and is not affected by the amount of hydrogen in bulk hydrides.Copyright

A Finite Element Study on Contact Pressure Distribution in Draw-Bend Friction Test and Its Effect on Friction Measurement

Various experimental and numerical works have shown the existence of pressure peaks at the contact interface of draw-bend tests. From this observation, a need has been raised for the re-examination of the methodology to calculate the friction coefficient from the draw-bend friction test. In this paper, the draw-bend friction tests have been simulated by the explicit finite element method. By using 3D finite element models and local axis system, the existence of pressure peaks was confirmed. A non-constant friction model (Stribeck friction model), which is more realistic for sheet metal forming than a constant friction model (Coulomb friction model), was implemented into the finite element code. Simulations were performed with constant and non-constant friction models. From the comparisons, the effect of existence of pressure peaks on the friction measurement was evaluated.Copyright