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upper-bound analysis
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in Models for Fracture during Deformation Processing
> Fundamentals of Modeling for Metals Processing
Published: 01 December 2009
Fig. 6 Upper-bound analysis of a double extrusion-forging process showing sound flow on the left and cavity formation at the centerline on the right. Source: Ref 13
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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...
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 in finite-element analyses of deformation processing. The article reviews the Cockcroft-Latham criterion of fracture and its reformulated extension for analysing the fracture locus for compression. It concludes with information on fundamental fracture models.
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Published: 01 January 2005
Fig. 27 Prediction for occurrence of center burst in wire drawing. Solid line is based on slip-line analysis of centerline tensile stress. Dashed lines are range of prediction based on upper-bound analysis.
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Published: 01 January 2005
Fig. 23 Prediction of central burst in wire drawing by the tensile stress criterion and slip-line field analysis of double indentation. The range of predictions by upper bound analysis ( Fig. 19 ) is shown by dashed lines.
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in Models for Fracture during Deformation Processing
> Fundamentals of Modeling for Metals Processing
Published: 01 December 2009
Fig. 12 Prediction of central burst in wire drawing by the tensile stress criterion and slip-line field analysis (solid line) of double indentation. The range of predictions by upper-bound analysis ( Fig. 8 ) is shown by dashed lines. Source: Ref 25
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Published: 01 January 2005
Fig. 14 Configuration of deformation zone in the application of numerical upper-bound analysis to the rolling of airfoil shapes. Source: Ref 21
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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
...), and the finite-element method (FEM). The slab method and upper bound method of analysis assume a known deformation field in the plastically deforming body and assume this field either satisfies the force equilibrium (SM) or power-conservation equations (UBM) to determine the stress field or the external load...
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
... deformation energy methods drawing finite-element analysis lower-bound analysis macroscopic process metal flow microscopic process upper-bound analysis METALLIC COMPONENTS consisting of two or more metals are often required by industry for reasons of economy or because the composites can achieve...
Abstract
Coextrusion is defined as the simultaneous extrusion of two or more metals to form an integral product that can be carried out using conventional extrusion or drawing equipment at a temperature appropriate to the metal system being formed. This article discusses the applications, 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 variables for which sound extrusions can be obtained. The article concludes with a discussion on the state-of-the-art of coextrusion that assists in developing process models, which accurately describe both the macroscopic and microscopic aspects of a 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
... The upper bound method of plasticity analysis requires the input of a flow field in mathematical function form. The external work required to produce this flow field is determined through extensive calculation. This value for external work is an upper bound on the actual work required. Through optimization...
Abstract
This article focuses on the effects of mechanical plasticity on workability; that is, process control of localized stress and strain conditions to enhance workability. It describes the nature of local stress and strain states in bulk forming processes, leading to a classification scheme, including testing procedures and specific process measurements, that facilitate the application of workability concepts. Using examples, the article applies these concepts to forging, rolling, and extrusion processes. The stress and strain environments described in the article suggest that a workability test should be capable of subjecting the material to a variety of surface strain combinations. By providing insights on fracture criteria, these tests can be used as tools for troubleshooting fracture problems in existing processes, as well as in the process development for new product designs.
Series: ASM Handbook
Volume: 14A
Publisher: ASM International
Published: 01 January 2005
DOI: 10.31399/asm.hb.v14a.a0009006
EISBN: 978-1-62708-185-6
... ). A novel approach to predicting centerbursts has been employed by Avitzur ( Ref 15 ). Using an upper-bound analysis, Avitzur has projected die angles and reductions for which the metal being worked will tend to flow apart at the centerline. As has been noted by Backofen ( Ref 19 ), this approach seeks...
Abstract
Workability is the ability of the workpiece metal to undergo extrusion or drawing without fracture or defect development. This article describes the limits of workability in extrusion and drawing in terms of fracture and flaw development and presents some comments on fracture mechanisms. It discusses the empirical projections of absolute workability from various mechanical tests. The article concludes with a discussion on extrusion and drawing process design implications.
Book Chapter
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...
Abstract
This article addresses the effects of damage to equipment and structures due to explosions (blast), fire, and heat as well as the methodologies that are used by investigating teams to assess the damage and remaining life of the equipment. It discusses the steps involved in preliminary data collection and preparation. Before discussing the identification, evaluation, and use of explosion damage indicators, the article describes some of the more common events that are considered in incident investigations. The range of scenarios that can occur during explosions and the characteristics of each are also covered. In addition, the article primarily discusses level 1 and level 2 of fire and heat damage assessment and provides information on level 3 assessment.
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
.... The measure of superior microstructure will be in the form of tensile strength measurements made from samples that have undergone different processing parameter combinations. A schedule of xperiments is set up in which the upper and lower bounds of the factors are chosen ( Table 2 ). These upper and lower...
Abstract
Thermomechanical are used to gain insight into the causes of problems that arise during a given thermomechanical process. This article provides examples to demonstrate how significant the parameters were selected for specific tests. It examines the types of problems that can occur during a thermomechanical process. The article provides information on the thermophysical properties, which include specific heat, coefficient of thermal expansion, thermal conductivity/diffusivity, and density. It concludes with examples that illustrate how the various considerations in testing are successfully used to solve practical thermomechanical processing problems.
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
... Abstract This article describes the historical background, uncertainties in structural parameters, classifications, and application areas of probabilistic analysis. It provides a discussion on the basic definition of random variables, some common distribution functions used in engineering...
Abstract
This article describes the historical background, uncertainties in structural parameters, classifications, and application areas of probabilistic analysis. It provides a discussion on the basic definition of random variables, some common distribution functions used in engineering, 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, the response surface method, and Monte Carlo sampling. A brief introduction to importance sampling, time-variant reliability, system reliability, and risk analysis and target reliabilities is also provided. The article examines the various application problems for which probabilistic analysis is an essential element. Examples of the use of probabilistic analysis are presented. The article concludes with an overview of some of the commercially available software programs for performing probabilistic analysis.
Book Chapter
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: 17
Publisher: ASM International
Published: 01 August 2018
DOI: 10.31399/asm.hb.v17.a0006463
EISBN: 978-1-62708-190-0
... the possible true states of nature that are consistent with the data analyzed. Statistical uncertainty bounds assume that the underlying mathematical model used in the analysis is the true model. There are two often-used methods that are followed to reflect the uncertainty about an estimate ( Ref 25...
Abstract
Probability of detection (POD) assesses the performance of a non-destructive evaluation (NDE)-based inspection, which is a method used to determine the capability of an inspection as a function of defect type and defect size. This article provides an overview of the concept of POD, why it is needed, the history behind the development of POD, how POD assessments are performed, and how modeling and simulation can be integrated into the execution of a POD assessment. It describes the methods by which POD is determined. This includes detail on the experimental process to acquire the needed data, the mathematical methods to obtain a POD curve, and techniques to assess uncertainty in the POD curve as it is obtained from a limited data set. The concept of model-assisted POD (MAPOD) is introduced, with additional details and representative examples of MAPOD.
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
... and 552 MPa (50 and 80 ksi). Crack-tip opening displacement toughness values δ m (upper shelf, Table 1 ) of 0.25 to 0.76 mm (0.01 to 0.03 in.) estimated from the fracture toughness tests were used in the analysis. Both the presence and absence of rolling residual stresses were considered. (Maximum...
Abstract
Optimized modeling of fracture-critical structural components and connections requires the application of elastic-plastic fracture mechanics. Such applications, however, can require sophisticated analytical techniques such as crack tip opening displacement (CTOD), failure assessment diagram (FAD), and deformation plasticity failure assessment diagram (DPFAD). This article presents the origin and description of FAD and addresses R6 FAD using J-integral. It details the fracture criteria of BS 7910. The factors to be considered during the use of FAD and the applications of FAD are also reviewed.
Series: ASM Handbook
Volume: 22A
Publisher: ASM International
Published: 01 December 2009
DOI: 10.31399/asm.hb.v22a.a0005400
EISBN: 978-1-62708-196-2
... + 3 c 1 − 5 c 2 + 2 c 3 + 5 d 1 − 3 d 2 − 2 d 3 ) These strain-slip equations are used subsequently. An upper bound to the yield locus for this same crystal is be found by: Imposing different ratios...
Abstract
This article presents the Schmid's law that describes the response of crystal structures to loading. It describes the Taylor model to calculate the uniaxial yield stress of an isotropic face-centered cubic aggregate in terms of critical resolved shear stress. The article discusses the stress-based approach of the Bishop and Hill procedure to directly find stress states that could simultaneously operate at least five independent slip systems. It presents ways to find isostress or lower-bound yield loci for sheets having single-crystal orientation.
Book: Composites
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
... inputs for braiding are displayed. Fig. 6 Braiding parameter input window in SEER-DFM software Note that various inputs can be “bounded” by a range of values. This allows a user to perform a risk analysis on one or more variables, in the event that exact inputs are not known or defined...
Abstract
Affordability is the key issue facing design engineers and manufacturers of composite components for current and next-generation aircraft, spacecraft, propulsion systems, and other advanced applications. This article describes the software tools available for modeling and analyzing costs associated with design and manufacturing options for advanced composites programs. It presents an example of a composite exhaust nozzle shroud where the design and manufacture options were analyzed and adjusted, based on the use of cost analysis tools. The article also lists some of the attributes found in various cost modeling software and the potential cost benefits.
Series: ASM Handbook
Volume: 14A
Publisher: ASM International
Published: 01 January 2005
DOI: 10.31399/asm.hb.v14a.a0009009
EISBN: 978-1-62708-185-6
... interface is described by the interface friction factor m = 3 τ i / σ 0 , both the slab method of plasticity analysis and the upper-bound analysis ( Ref 10 ) give the average axial flow stress as: (Eq 9) σ a = 4 P π D 2 = σ 0 ( 1 + m D 3 3...
Abstract
This article describes the use of compression tests, namely, cylindrical compression, ring compression, and plane-strain compression tests at elevated temperatures. It discusses the effects of the temperature, strain rate, and deformation heating on metals during the cylindrical compression test, with the help of flow curves. The article illustrates the testing apparatus used in the cylindrical compression test. It describes the issues regarding friction and temperature, and strain-rate control with proper test equipment and experimental planning during the ring compression test and plane-strain compression test. The article also reviews the testing conditions, procedures, and advantages of hot plane-strain compression test.
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...
Abstract
The primary objectives of the rolling process are to reduce the cross section of the incoming material while improving its properties and to obtain the desired section at the exit from the rolls. This article illustrates a rolling sequence for the fabrication of bars, shapes, and flat products from blooms, billets, and slabs. It describes two methods for shapes or sections: universal rolling and caliber rolling. The article provides information on two-high mills and three-high mills. Specialty mills for thin sheets, namely, the Sendzimir mill and planetary mill, are discussed. The article analyzes the components of a computer controlled system for high-speed mills. Steels and nonferrous materials are also discussed. The article concludes with information on the defects in flat, bar, or shaped products due to heating and rolling practices.
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