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Series: ASM Handbook
Volume: 22A
Publisher: ASM International
Published: 01 December 2009
DOI: 10.31399/asm.hb.v22a.a0005436
EISBN: 978-1-62708-196-2
... analytical method empirical method cooling curve computational fluid dynamics thermal modeling inverse conduction HEAT TREATING AND QUENCHING are a complex business. The configuration of parts is endless, as is the types of furnaces available for heat treating. Numerous variables in the quenching...
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...
Book: Casting
Series: ASM Handbook
Volume: 15
Publisher: ASM International
Published: 01 December 2008
DOI: 10.31399/asm.hb.v15.a0005237
EISBN: 978-1-62708-187-0
... example of the utility of the analytical model, calculated values of C S as a function of f S after complete solidification can be generated in a multicomponent alloy and compared to empirically measured microsegregation profiles. Equations 3 and 4 cannot be used for this purpose because C S...
Series: ASM Handbook
Volume: 22A
Publisher: ASM International
Published: 01 December 2009
DOI: 10.31399/asm.hb.v22a.a0005419
EISBN: 978-1-62708-196-2
... incorporating the constraint loss is important in this case. Fig. 7 Schematic of analytical crack-closure model under cyclic loading. (a) Maximum stress. (b) Minimum stress. Source: Ref 22 Fig. 8 Crack growth in 7075-T7351 aluminum alloy subject to spectrum loading. (a) Crack-growth comparison...
Series: ASM Handbook
Volume: 22A
Publisher: ASM International
Published: 01 December 2009
DOI: 10.31399/asm.hb.v22a.a0005411
EISBN: 978-1-62708-196-2
... environmental conditions. The need to accurately predict component life at elevated temperatures in a creep-fatigue-environment operating regime will continually motivate future work in this critical research area. To push the analytical models for predicting creep-fatigue-environment interactions to the next...
Series: ASM Handbook
Volume: 22A
Publisher: ASM International
Published: 01 December 2009
DOI: 10.31399/asm.hb.v22a.a0005431
EISBN: 978-1-62708-196-2
... MODELS are often used to determine the response of structure, component, process, or system to a set of conditions. The models may be based on closed-form equations, which allow analytical solutions to the response of behavior of a system. In many cases, however, analytical (closed-form) solutions are...
Series: ASM Handbook
Volume: 11
Publisher: ASM International
Published: 15 January 2021
DOI: 10.31399/asm.hb.v11.a0006773
EISBN: 978-1-62708-295-2
... correct and applicable Development of any necessary analytical models (including FEA) that can be used to simulate all possible loading conditions the failed structure may have experienced (i.e., thermal, structural, vibration, or impact conditions) Performance of analyses to determine the loading...
Series: ASM Handbook
Volume: 11
Publisher: ASM International
Published: 15 January 2021
DOI: 10.31399/asm.hb.v11.a0006772
EISBN: 978-1-62708-295-2
... accuracy or comparison with experimental data. A model can be defined as a representation of a physical system or process. Engineers and scientists commonly use models for both illustrative and analytical purposes. General types of models are illustrative or analytical. The cost of...
Book: Casting
Series: ASM Handbook
Volume: 15
Publisher: ASM International
Published: 01 December 2008
DOI: 10.31399/asm.hb.v15.a0005236
EISBN: 978-1-62708-187-0
... PF simulation or from analytical models (see below). For a PF simulation, a typical domain would be the CA REV cell (highlighted area in Fig. 2 shown expanded in Fig. 2 ), fully paved with PF REV (small squares shown within Fig. 2 ). For a CA simulation, CA REV cells are overlaid onto the domain...
Series: ASM Handbook
Volume: 22A
Publisher: ASM International
Published: 01 December 2009
DOI: 10.31399/asm.hb.v22a.a0005406
EISBN: 978-1-62708-196-2
... quantities. The rules come from microscopic descriptions developed for the evolution of a mushy zone (e.g., microsegregation) and can be taken either from a PF simulation or from analytical models (see below). For a PF simulation, a typical domain would be the CA REV cell (highlighted area in Fig. 2a shown...
Series: ASM Handbook
Volume: 22A
Publisher: ASM International
Published: 01 December 2009
DOI: 10.31399/asm.hb.v22a.a0005420
EISBN: 978-1-62708-196-2
... = 0.02821 ε ˙ 0.3131 Δ T B 0.8638 where ε ˙ is the strain rate (s −1 ) and Δ T B is the brittle temperature range (°C) defined between the temperatures corresponding to solid fractions of 0.9 and 0.99. An elegant analytical-criterion model has been derived to...
Book: Casting
Series: ASM Handbook
Volume: 15
Publisher: ASM International
Published: 01 December 2008
DOI: 10.31399/asm.hb.v15.a0005238
EISBN: 978-1-62708-187-0
.... Model validation with both analytical solutions and experiments is a crucial step in any computational analysis, and thermomechanical modeling is no exception. Weiner and Boley ( Ref 59 ) derived an analytical solution for unidirectional solidification of an unconstrained plate with a unique...
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
... and friction). The equations describing the physical phenomena in material behavior models and/or their coupling with process models are often too complex for solution by analytical means, except under somewhat restrictive (albeit often insightful) conditions. This is usually the case for real-world...
Series: ASM Handbook
Volume: 14A
Publisher: ASM International
Published: 01 January 2005
DOI: 10.31399/asm.hb.v14a.a0004028
EISBN: 978-1-62708-185-6
... technological applications. The article defines the basic kinematic tensors, reports their relations, and presents expressions for calculating the change in crystallographic orientation associated with plastic deformation. It surveys some of the polycrystal models in terms of the relative strength of the...
Series: ASM Handbook
Volume: 22A
Publisher: ASM International
Published: 01 December 2009
DOI: 10.31399/asm.hb.v22a.a0005434
EISBN: 978-1-62708-196-2
... Abstract This article focuses on transport phenomena and modeling approaches that are specific to vapor-phase processes (VPP). It discusses the VPP for the synthesis of materials. The article reviews the basic notions of molecular collisions and gas flows, and presents transport equations. It...
Series: ASM Handbook
Volume: 22A
Publisher: ASM International
Published: 01 December 2009
DOI: 10.31399/asm.hb.v22a.a0005413
EISBN: 978-1-62708-196-2
... as cell size, volume fraction of cell boundaries, and the partition of the total dislocation content in cell and boundary dislocations, the model arrives at a relationship for the hardening coefficient in stage III of quite the same analytical form as follows from Eq. 8 . In a recent publication...
Series: ASM Handbook
Volume: 22A
Publisher: ASM International
Published: 01 December 2009
DOI: 10.31399/asm.hb.v22a.a0005401
EISBN: 978-1-62708-196-2
... Abstract The modeling and simulation of texture evolution for titanium alloys is often tightly coupled to microstructure evolution. This article focuses on a number of problems for titanium alloys in which such coupling is critical in the development of quantitative models. It discusses the...
Series: ASM Handbook
Volume: 22A
Publisher: ASM International
Published: 01 December 2009
DOI: 10.31399/asm.hb.v22a.a0005439
EISBN: 978-1-62708-196-2
... Abstract This article presents various equations that are essential for the modeling of both single-phase and multiphase profiles. It includes the fundamental laws of diffusion, along with its equations and solutions. The article provides information on the series of applications that...
Series: ASM Handbook
Volume: 4B
Publisher: ASM International
Published: 30 September 2014
DOI: 10.31399/asm.hb.v04b.a0005950
EISBN: 978-1-62708-166-5
... transformations, and stress evolution. Because of the complexity and the coupled, nonlinear nature of the problem, there is no analytical solution for it. The rigorous treatment of the problem requires a coupled total thermo-mechano-metallurgical theory. Several models have been proposed for “staggered numerical...
Series: ASM Handbook
Volume: 4E
Publisher: ASM International
Published: 01 June 2016
DOI: 10.31399/asm.hb.v04e.a0006277
EISBN: 978-1-62708-169-6
... Abstract This article describes the integration of thermodynamic modeling, mobility database, and phase-transformation crystallography into phase-field modeling and its combination with transformation texture modeling to predict phase equilibrium, phase transformation, microstructure evolution...