Theoretical and Experimental Analysis of Failure for the Hemisphere Punch Hydroforming Processes

1996 ◽  
Vol 118 (3) ◽  
pp. 434-438 ◽  
Author(s):  
Tze-Chi Hsu ◽  
Shian-Jiann Hsieh
Keyword(s):  
Experimental Data ◽  
Limit Theorem ◽  
Sheet Metal ◽  
Lower Bounds ◽  
Yield Criterion ◽  
Fluid Pressure ◽  
Upper And Lower Bounds ◽  
Premature Failure ◽  
Hydroforming Process ◽  
Theoretical Results

A limit theorem of plasticity has been developed to investigate the hemisphere punch hydroforming process. The limit theorem of plasticity is used to predict the upper and lower bounds of the permissible fluid pressure. Loci representing the critical fluid pressures which result in the rupture and wrinkling are presented. The property of the sheet metal is governed by Hill’s quadratic yield criterion with a power-law hardening for anisotropic material. The premature failure is avoidable if the fluid pressure path is restricted to travel only within the suggested bounds. The theoretical results which include the failure prediction and wrinkling distribution are verified by conducting a serial of hydroforming experiments. The experimental data agrees well with the computed results and demonstrates the technological usefulness of the results.

A Critical Review of Tube and Sheet Metal Hydroforming Technology

1996 ◽  
Author(s):  
Jian An ◽  
A. H. Soni
Keyword(s):  
Sheet Metal ◽  
Thickness Distribution ◽  
Fluid Pressure ◽  
Point Of View ◽  
Parameter Design ◽  
Back Side ◽  
Part Quality ◽  
Element Simulation ◽  
Part Surface ◽  
Hydroforming Process

Abstract The hydroforming technology, which is rapidly gaining popularity in the sheet metal and tube forming industry is reviewed. The features and the characteristics of the hydroforming process are described. The uniformly distributed fluid pressure covers the back side of the sheet as a die generates many advantages in the technical point of view as improving the part surface quality, reducing the forming severity and smoothing the thickness distribution. The benefits of using hydroforming technology are examined and analyzed in a technical level. The better part quality, less cost of tooling, materials saving and part weight reduction can be achieved using the hydroforming technology. The design methodologies for the hydroforming process parameters are reviewed and discussed in a certain detail. Computer-aided-engineering such as finite element simulation is suggested for such process parameter design.

Calculated R.R.K.M. unimolecular dissociation rate constants for hydrazine

1969 ◽  
Vol 47 (14) ◽  
pp. 2593-2599 ◽  
Author(s):  
D. W. Setser ◽  
W. C. Richardson
Keyword(s):  
Experimental Data ◽  
Lower Bounds ◽  
Rate Constants ◽  
Chemical Activation ◽  
Dissociation Rate ◽  
Upper And Lower Bounds ◽  
Unimolecular Dissociation ◽  
Complex Models ◽  
Dissociation Rate Constants ◽  
Activated Complex

Unimolecular rate constants for hydrazine dissociation by thermal and chemical activation have been calculated according to the R.R.K.M. theory. The two activated complex models used in the calculations represent plausible upper and lower bounds to the rate constants. The calculations are mainly directed toward establishing expected decomposition to stablilization ratios of N2H4 produced by combination of NH2 radicals; however, a general comparison to available experimental data for hydrazine dissociation is made.

scholarly journals On non-uniform and global descriptions of the rate of convergence of Asymptotic expansions in the central limit theorem

1986 ◽  
Vol 41 (3) ◽  
pp. 326-335 ◽  
Author(s):  
Peter Hall ◽  
T. Nakata
Keyword(s):  
Central Limit Theorem ◽  
Limit Theorem ◽  
Rate Of Convergence ◽  
Central Limit ◽  
Lower Bounds ◽  
Rates Of Convergence ◽  
Upper And Lower Bounds ◽  
The Central Limit Theorem ◽  
Order Of Magnitude ◽  
Leading Term

AbstractThe leading term approach to rates of convergence is employed to derive non-uniform and global descriptions of the rate of convergence in the central limit theorem. Both upper and lower bounds are obtained, being of the same order of magnitude, modulo terms of order n-r. We are able to derive general results by considering only those expansions with an odd number of terms.

Some Exact and Approximate Solutions for the Modified von Mises Yield Criterion

1988 ◽  
Vol 55 (2) ◽  
pp. 260-266 ◽  
Author(s):  
J. H. Lee
Keyword(s):  
Lower Bounds ◽  
Yield Criterion ◽  
Approximate Solutions ◽  
Upper And Lower Bounds ◽  
Plasticity Model ◽  
Plastic Deformations ◽  
Volume Increase ◽  
Strength Differential ◽  
Von Mises Yield Criterion ◽  
Von Mises

The effects of Strength Differential (SD) and plastic compressibility for materials obeying the modified von Mises yield criterion were exemplified by solving two boundary-value problems. The assumptions of associated plasticity (leading to maximum plastic volume increase) and nonassociated plasticity (leading to zero plastic volume increase) were used for comparative studies on the effects of plastic compressibility. The solutions for compression processes showed that SD effects increased the pressure at initial yielding and at failure, as well as increased the capacity of the materials to withstand plastic deformations. The opposite was true for tension processes. For associated and nonassociated plasticity, upper and lower bounds for stresses and strains for load and stroke-controlled situations were indicated. The results also showed unrealistic restrictions on the Poisson’s ratio and C/T for nonassociated plasticity under certain conditions. Hence, plastic volume increase, although small, should be incorporated into a more realistic plasticity model.

Punch Radius Influence on “Large Size” Hydroformed Components

2012 ◽  
Vol 504-506 ◽  
pp. 937-942
Author(s):  
Gabriele Papadia ◽  
Antonio del Prete ◽  
Alessandro Spagnolo
Keyword(s):  
Sheet Metal ◽  
Process Parameters ◽  
Process Design ◽  
Numerical Study ◽  
Fluid Pressure ◽  
Large Size ◽  
Blank Sheet ◽  
Punch Radius ◽  
Hydroforming Process ◽  
Compressed Fluid

Sheet metal hydroforming has gained increasing interest during last years, especially as application in the manufacturing of some components for: automotive, aerospace and electrical appliances for niche productions. Different studies have been also done to determine the optimal forming parameters making an extensive use of FEA. In the hydroforming process a blank sheet metal is formed through the action of a fluid and a punch. It forces the sheet into a die, which contains a compressed fluid. Many studies have been focused on the analysis of process and geometric parameters influence about the hydroforming process of a single product with main dimensions till to 100 mm. In this paper the authors describe the results of an experimental activity developed on two different large sized products obtained through sheet metal hydroforming. Different geometric and process parameters have been taken into account during the testing phase to study, in particular, the punch radius influence on the process feasibility. An ANOVA analysis has been implemented to study the influence of geometrical and process parameters on the maximum hydroforming depth. Through this work it has been possible to verify that in the hydroforming process of large size products geometry and, in particular, punch radius, are some of the main factors that influences the feasibility of the products. Different considerations can be made about the effects of the blankholder force and the fluid pressure on the maximum hydroforming depth. As further developments, the authors would perform a numerical study in order to enlarge the knowledge of the process design space to other possible values of the punch radius.

scholarly journals The Asymptotic Behavior of the Average $L^p-$Discrepancies and a Randomized Discrepancy

10.37236/378 ◽  
2010 ◽  
Vol 17 (1) ◽  
Author(s):  
Stefan Steinerberger
Keyword(s):  
Asymptotic Behavior ◽  
Limit Theorem ◽  
Lower Bounds ◽  
Probabilistic Approach ◽  
Upper Bounds ◽  
Upper And Lower Bounds

This paper gives the limit of the average $L^p-$star and the average $L^p-$extreme discrepancy for $[0,1]^d$ and $0 < p < \infty$. This complements earlier results by Heinrich, Novak, Wasilkowski & Woźnia-kowski, Hinrichs & Novak and Gnewuch and proves that the hitherto best known upper bounds are optimal up to constants.We furthermore introduce a new discrepancy $D_{N}^{\mathbb{P}}$ by taking a probabilistic approach towards the extreme discrepancy $D_{N}$. We show that it can be interpreted as a centralized $L^1-$discrepancy $D_{N}^{(1)}$, provide upper and lower bounds and prove a limit theorem.

Characterizing the rate of convergence in the central limit theorem. II

1981 ◽  
Vol 89 (3) ◽  
pp. 511-523 ◽  
Author(s):  
Peter Hall
Keyword(s):  
Central Limit Theorem ◽  
Limit Theorem ◽  
Rate Of Convergence ◽  
Central Limit ◽  
Lower Bounds ◽  
Normal Approximation ◽  
Random Variables ◽  
Upper And Lower Bounds ◽  
The Central Limit Theorem ◽  
Order Of Magnitude

AbstractWe obtain upper and lower bounds of the same order of magnitude for the error between the distribution of a sum of independent and identically distributed random variables, and a normal approximation by a portion of a Chebychev-Cramér series. Our results are sufficiently general to contain the familiar characterizations by Ibragimov(4), Heyde and Leslie (3) and Lifshits(5), and complement some of those obtained earlier by the author (2).

Physical modeling of friction conditions on the wall thickness variation during sheet hydroforming

2015 ◽  
Vol 29 (13) ◽  
pp. 1550058
Author(s):  
Feng Li ◽  
Peng Xu ◽  
Xinlong Zhang ◽  
Qiang Liu
Keyword(s):  
Theoretical Model ◽  
Friction Coefficient ◽  
Sheet Metal ◽  
Wall Thickness ◽  
Yield Criterion ◽  
Fluid Pressure ◽  
Sheet Thickness ◽  
Quantitative Variation ◽  
304 Stainless Steel ◽  
Thickness Variation

In order to research the influence of friction conditions on the sheet metal deformation behavior under the fluid pressure, the experimental method that can test the relationship between fluid pressure and wall thickness was proposed in this paper. The theoretical model about the quantitative variation relationship between fluid pressure and wall thickness together with the theoretical model about the quantitative variation relationship between friction coefficient and wall thickness, was obtained by theoretical derivation. At the same time, it could be concluded that friction contact region close to the tensile end was easier to satisfy the plastic yield criterion. Therefore, the plastic deformation initially occurred at this area and fracture emerged on account of excessive reduction of the sheet thickness. Simulation analysis with 304 stainless steel was carried out. The result indicated that the capacity of sheet uniform deformation decreased with the increasing of the friction coefficient. When the friction coefficient increased from 0.08 to 0.20, the uniform elongation decreased by 32%. But when other conditions were kept unchanged, the greater the fluid pressure was, the thinner the sheet would be. Experiments indicated that the necking and fracture appeared in the gauge length near the tensile end with different lubricants. And these provided a theoretical basis for the process and device design of sheet metal hydroforming.

scholarly journals On the Generalized Distance Energy of Graphs

Mathematics ◽  
2019 ◽  
Vol 8 (1) ◽  
pp. 17 ◽  
Author(s):  
Abdollah Alhevaz ◽  
Maryam Baghipur ◽  
Hilal A. Ganie ◽  
Yilun Shang
Keyword(s):  
Lower Bounds ◽  
Complete Graph ◽  
Connected Graph ◽  
Distance Matrix ◽  
Wiener Index ◽  
Diagonal Matrix ◽  
Upper And Lower Bounds ◽  
Star Graph ◽  
Extremal Graphs ◽  
Generalized Distance

The generalized distance matrix D α ( G ) of a connected graph G is defined as D α ( G ) = α T r ( G ) + ( 1 − α ) D ( G ) , where 0 ≤ α ≤ 1 , D ( G ) is the distance matrix and T r ( G ) is the diagonal matrix of the node transmissions. In this paper, we extend the concept of energy to the generalized distance matrix and define the generalized distance energy E D α ( G ) . Some new upper and lower bounds for the generalized distance energy E D α ( G ) of G are established based on parameters including the Wiener index W ( G ) and the transmission degrees. Extremal graphs attaining these bounds are identified. It is found that the complete graph has the minimum generalized distance energy among all connected graphs, while the minimum is attained by the star graph among trees of order n.

scholarly journals Hadamard k-fractional inequalities of Fejér type for GA-s-convex mappings and applications

2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
Hui Lei ◽  
Gou Hu ◽  
Zhi-Jie Cao ◽  
Ting-Song Du
Keyword(s):  
Lower Bounds ◽  
Hypergeometric Functions ◽  
Upper And Lower Bounds ◽  
Weighted Inequalities ◽  
Convex Mappings ◽  
Special Means

Abstract The main aim of this paper is to establish some Fejér-type inequalities involving hypergeometric functions in terms of GA-s-convexity. For this purpose, we construct a Hadamard k-fractional identity related to geometrically symmetric mappings. Moreover, we give the upper and lower bounds for the weighted inequalities via products of two different mappings. Some applications of the presented results to special means are also provided.

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