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upper-bound method

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Published: 01 December 2009
Fig. 7 Computational algorithm for the incremental upper bound method. The discrete elements are chosen to represent workpiece geometry—plane strain, axisymmetric, or three-dimensional (blocks)—and the calculation updated as the die compresses the workpiece incrementally. Source: Ref 34 More
Series: ASM Handbook
Volume: 22A
Publisher: ASM International
Published: 01 December 2009
DOI: 10.31399/asm.hb.v22a.a0005456
EISBN: 978-1-62708-196-2
... Abstract This article focuses on approximate closed-form analytical methods, such as slab and upper bound methods, used for forward and inverse design of metal forming problems. Selected examples of application of these methods to metal forming processes are also discussed. slab method...
Series: ASM Handbook
Volume: 22A
Publisher: ASM International
Published: 01 December 2009
DOI: 10.31399/asm.hb.v22a.a0005461
EISBN: 978-1-62708-196-2
... Abstract This article discusses physical analysis, including slab method and upper-bound method and slip-line field analysis, for calculating stress states in plastic deformation processes. It presents various validation standards and models for evaluating the criterion of fracture for use...
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Published: 01 December 2009
Fig. 8 Velocity fields for the extrusion of a T-shaped profile using the upper bound method, and the predicted results for the relative stress and relative die length between the various segments for the various area ratios of the profile. Source: Ref 36 More
Series: ASM Handbook
Volume: 14A
Publisher: ASM International
Published: 01 January 2005
DOI: 10.31399/asm.hb.v14a.a0004013
EISBN: 978-1-62708-185-6
..., billet configurations, and metal flow modes of coextrusion. It presents the analytical studies of coextrusion: deformation energy methods, lower-bound (slab) analyses, upper-bound analyses, and finite-element analyses. These studies are used to identify the regime of material properties and process...
Series: ASM Handbook
Volume: 14A
Publisher: ASM International
Published: 01 January 2005
DOI: 10.31399/asm.hb.v14a.a0009004
EISBN: 978-1-62708-185-6
... to models of fracture, criteria have been developed from macroscopic concepts of fracture. The Cockcroft criterion is based on the observation that both tensile stress and plastic deformation are necessary ingredients, which lead to a tensile deformation energy condition for fracture. The upper bound method...
Series: ASM Handbook
Volume: 14B
Publisher: ASM International
Published: 01 January 2006
DOI: 10.31399/asm.hb.v14b.a0005169
EISBN: 978-1-62708-186-3
... generation due microinch to strain hardening; elastic strain energy micron (micrometer) upper bound upper-bound element technique microsecond upper-bound method ultrahigh carbon Poisson s ratio Uni ed Numbering System ultimate tensile strength pi (3.14159. . .) density of a material; dislocation density...
Series: ASM Handbook
Volume: 14A
Publisher: ASM International
Published: 01 January 2005
DOI: 10.31399/asm.hb.v14a.a0009013
EISBN: 978-1-62708-185-6
... leading to 2 n tests ( n = number of factors). Following this method, the factors, and more importantly the combination of factors, having the greatest influence on the quality of the product (i.e., tensile strength) are known. Example of lower and upper bounds selected for three factors considered...
Series: ASM Handbook
Volume: 11A
Publisher: ASM International
Published: 30 August 2021
DOI: 10.31399/asm.hb.v11A.a0006804
EISBN: 978-1-62708-329-4
... as failed components where the load may have been higher than the failure load. Upper bound: The object had to receive less than a certain load. While it is certainly possible to have other options, cases where the object did not deform or where the supports remained intact may provide upper bounds...
Series: ASM Handbook Archive
Volume: 11
Publisher: ASM International
Published: 01 January 2002
DOI: 10.31399/asm.hb.v11.a0003514
EISBN: 978-1-62708-180-1
..., selection of a probability distribution, the failure model definition, and a definition of the probability of failure. The article also explains the solution techniques for special cases and general solution techniques, such as first-second-order reliability methods, the advanced mean value method...
Series: ASM Handbook
Volume: 14A
Publisher: ASM International
Published: 01 January 2005
DOI: 10.31399/asm.hb.v14a.a0009002
EISBN: 978-1-62708-185-6
.... By contrast, the upper-bound method, introduced by Taylor and Bishop and Hill ( Ref 47 , Ref 48 ), assumes that each grain undergoes the same strain as that imposed on the aggregate and that the strain is uniform within the grains. The accommodation of an arbitrary imposed strain state (with five arbitrary...
Series: ASM Handbook
Volume: 17
Publisher: ASM International
Published: 01 August 2018
DOI: 10.31399/asm.hb.v17.a0006463
EISBN: 978-1-62708-190-0
... in standard documents to date, despite its demonstrated success in fitting data from large POD experiments. Confidence bounds have been calculated on POD estimates since the early damage-tolerance standards were written. The POD curves calculated by the methods of the aerospace, nuclear, and petrochemical...
Series: ASM Handbook
Volume: 7
Publisher: ASM International
Published: 30 September 2015
DOI: 10.31399/asm.hb.v07.a0006085
EISBN: 978-1-62708-175-7
... , 13 , 14 ). A typical deformation zone geometry, as defined by the upper-bound method, and the accompanying hodograph are shown in Fig. 9 . This analytical technique is reviewed thoroughly by Sheppard et al. ( Ref 9 , 11 , 12 ) and Avitzur ( Ref 16 ). Fig. 9 Typical deformation zone...
Series: ASM Handbook
Volume: 14A
Publisher: ASM International
Published: 01 January 2005
DOI: 10.31399/asm.hb.v14a.a0004009
EISBN: 978-1-62708-185-6
... 13 , 17 ). The roll-separating force and the roll torque can be estimated with various levels of approximations by such mathematical techniques as the slab method, the upper bound method ( Ref 14 ), or the slip line method of analysis ( Ref 2 , 4 ). Computerized numerical techniques are also being...
Series: ASM Handbook Archive
Volume: 11
Publisher: ASM International
Published: 01 January 2002
DOI: 10.31399/asm.hb.v11.a0003513
EISBN: 978-1-62708-180-1
...). The critical combination of S and a for each aspect ratio a / c is estimated from the intersection of the FAP surface with the FAC ( Fig. 11 ). The results of this process are shown in Fig. 12 for one aspect ratio, a / c = 0.5, and the lower bound to the test-estimated upper-shelf CTOD toughness, δ m...
Series: ASM Handbook
Volume: 22A
Publisher: ASM International
Published: 01 December 2009
DOI: 10.31399/asm.hb.v22a.a0005425
EISBN: 978-1-62708-196-2
... was made possible by the advent of inexpensive computers and ever-increasing computing power beginning in the 1990s. Modern process models have evolved from relatively simple analytical and numerical techniques. These include the slab, upper-bound, and slip-line field methods (for predicting loads...
Series: ASM Handbook
Volume: 14A
Publisher: ASM International
Published: 01 January 2005
DOI: 10.31399/asm.hb.v14a.a0004022
EISBN: 978-1-62708-185-6
..., such as upper-bound elemental technique ( Ref 6 ) and shape transformation method ( Ref 7 ) are used to obtain a quick, but not as accurate, evolution of the billet shape and state variables such as strain. The finite-element method is well suited for optimization if the anticipated number of simulation...
Series: ASM Handbook
Volume: 22A
Publisher: ASM International
Published: 01 December 2009
DOI: 10.31399/asm.hb.v22a.a0005416
EISBN: 978-1-62708-196-2
... uncertainty does not necessarily imply that the estimate is incorrect. Figure 7 shows that, in spite of the calculated uncertainties (the upper and lower bounds indicated by the two broken lines), novel data are accurately predicted because of the robust design of the neural network, based on meaningful...
Series: ASM Handbook
Volume: 21
Publisher: ASM International
Published: 01 January 2001
DOI: 10.31399/asm.hb.v21.a0003396
EISBN: 978-1-62708-195-5
..., as shown in the upper right corner. Outputs, reports, and charts are provided in the lower half of the screen. The parameter window in Fig. 6 corresponds to the shell work element highlighted in Fig. 5 . In this example, braiding is selected as the material placement method, and all of the required...
Book Chapter

Series: ASM Handbook
Volume: 22A
Publisher: ASM International
Published: 01 December 2009
DOI: 10.31399/asm.hb.v22a.a0005452
EISBN: 978-1-62708-196-2
... 1 + | y 2 ′ | 2 ) d x L where y 1 = f 1 ( x ) and y 2 = f 2 ( x ) are the equations of the upper and lower part of the bounding curve, and L is the length of the entire curve. For a homogeneous curvilinear trapezoid, as shown in Fig. 12(c...