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mathematical modeling

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Published: 01 July 2000
Fig. 4.2 Array of anodic and cathodic reaction surfaces for mathematical modeling of potentials and currents in an electrolyte More
Series: ASM Technical Books
Publisher: ASM International
Published: 01 November 2010
DOI: 10.31399/asm.tb.scm.t52870201
EISBN: 978-1-62708-314-0
..., flow, voids, and residual stress. It then discusses each variable in detail, explaining how it affects the cure process, how it is measured, and how it can be expressed mathematically in the form of a simple model. The discussions throughout the chapter are supported by numerous images, diagrams...
Series: ASM Technical Books
Publisher: ASM International
Published: 01 February 2005
DOI: 10.31399/asm.tb.chffa.t51040247
EISBN: 978-1-62708-300-3
... model for microstructure development in Waspaloy forging Table 19.1 Mathematical model for microstructure development in Waspaloy forging Dynamic recrystallization Z = ε ¯ ˙  exp ( 468000 / RT ) ε ¯ c = 0.8 ε ¯ p...
Book Chapter

Series: ASM Technical Books
Publisher: ASM International
Published: 01 April 2013
DOI: 10.31399/asm.tb.imub.t53720063
EISBN: 978-1-62708-305-8
... is presented, until the machine is familiar with the part. Then, the actual production parts are studied by comparison with this stored model of a standard part. Mathematical Modeling Although model building, or programming, is generally accomplished by presenting a known sample object to the machine...
Series: ASM Technical Books
Publisher: ASM International
Published: 01 February 2005
DOI: 10.31399/asm.tb.chffa.t51040091
EISBN: 978-1-62708-300-3
... to a mathematical one involves certain assumptions that lead to the differential equation governing the mathematical model. As illustrated in Fig. 9.5 , refinement of the mesh size, alteration of the boundary conditions, etc., may be needed to increase the accuracy of the solution. Fig. 9.5 The process...
Series: ASM Technical Books
Publisher: ASM International
Published: 01 August 2012
DOI: 10.31399/asm.tb.smfpa.t53500019
EISBN: 978-1-62708-317-1
..., punch stroke position, etc.). These are summarized in a recent publication that also discusses the development of a computer program, BEND, which predicts bending variables ( Ref 2.13 ). Mathematical Model for Air Bending In designing air bending operations (tool design, control of punch stroke...
Book Chapter

Series: ASM Technical Books
Publisher: ASM International
Published: 01 December 1995
DOI: 10.31399/asm.tb.sch6.t68200133
EISBN: 978-1-62708-354-6
... part. This capability should not be confused with Solid Modeling which will be discussed next. Solid Modeling Solid modelers are highly sophisticated computer tools that allow the “creation” on a screen, of mathematically defined solids and surfaces. Although these programs have the capability...
Series: ASM Technical Books
Publisher: ASM International
Published: 01 December 2008
DOI: 10.31399/asm.tb.ssde.t52310281
EISBN: 978-1-62708-286-0
... ), which describes mathematically the thermodynamics of a system through a representation of the Gibbs energies of the different crystalline phases relevant to that system and defined by the chemical composition of the system. Thermo-Calc minimizes the total Gibbs energy of the system with respect...
Series: ASM Technical Books
Publisher: ASM International
Published: 01 March 2012
DOI: 10.31399/asm.tb.pdub.t53420263
EISBN: 978-1-62708-310-2
... to crystalline phases, but the model can also be extended to consider ionic liquids, where mixing on ionic sublattices is considered. The model is phenomenological in nature and does not define any crystal structure within its general mathematical formulation. It is possible to define internal parameter...
Book Chapter

Series: ASM Technical Books
Publisher: ASM International
Published: 01 August 2005
DOI: 10.31399/asm.tb.mmfi.t69540391
EISBN: 978-1-62708-309-6
... in its mathematical expression. Other supplemental factors are added, depending on the situation. Thus, K SSF is often used in fatigue analysis to replace the geometrical stress concentration factor K t . This approach is equally applicable to both stress-based and strain-based analysis methods...
Series: ASM Technical Books
Publisher: ASM International
Published: 01 December 2003
DOI: 10.31399/asm.tb.cfap.t69780089
EISBN: 978-1-62708-281-5
... is evolving through the use of mathematical models. These models predict the extent of conversion and the viscosity behavior as a function of time and temperature and offer almost unlimited potential for cure-cycle development and real-time process control of thermosets. In addition, mathematical modeling...
Series: ASM Technical Books
Publisher: ASM International
Published: 01 December 2009
DOI: 10.31399/asm.tb.sfa.t52780157
EISBN: 978-1-62708-268-6
... of the preceding chapter on design analysis. Statistics is a branch of mathematics dealing with the collection, analysis, and interpretation of data from a sample population of objects or measurements. Statistics refers to gathering numerical data to present information about a subject. Probability is another...
Series: ASM Technical Books
Publisher: ASM International
Published: 01 June 2016
DOI: 10.31399/asm.tb.hpcspa.t54460067
EISBN: 978-1-62708-285-3
... or illustrated through mathematical modeling or numerical simulation. These physical phenomena and the corresponding models are discussed subsequently. Deformation and Materials Models The process of deformation plays the key role in accommodation of particles in a cold-sprayed deposit. Therefore, almost...
Series: ASM Technical Books
Publisher: ASM International
Published: 01 February 2005
DOI: 10.31399/asm.tb.chffa.t51040185
EISBN: 978-1-62708-300-3
... as the FEM because of the assumptions made in developing the mathematical approach, it is still attractive because it does not require considerable computation time and does not require training for the user. In addition, the slab method can show the trend in the calculation of forging load while the FEM...
Series: ASM Technical Books
Publisher: ASM International
Published: 30 April 2021
DOI: 10.31399/asm.tb.tpsfwea.t59300047
EISBN: 978-1-62708-323-2
... strength of an asperity junction, and h is bulk hardness of the softer member. The famous Russian tribologist, Kragel’skii, developed a mathematical model for each component of the friction coefficient. His formula for the composite coefficient of friction is: (Eq 3.2) µ = 2 . 4 T o...
Series: ASM Technical Books
Publisher: ASM International
Published: 01 November 2019
DOI: 10.31399/asm.tb.mfadr7.t91110666
EISBN: 978-1-62708-247-1
... in Probability and Statistics, ( 1990 ) 10.1002/9780470316795 [7] Lawless J. , Statistical Models and Methods for Lifetime Data , Wiley Series in Probability and Mathematical Statistics ( 1982 ) [8] McPherson J. , Reliability Physics and Engineering – Time-To-Failure Modeling , Springer...
Series: ASM Technical Books
Publisher: ASM International
Published: 01 March 2000
DOI: 10.31399/asm.tb.aet.t68260029
EISBN: 978-1-62708-336-2
... spray quenching by water. This chapter will discuss the thermodynamics in extrusion, including a simplified mathematical model, influence of extrusion variables on temperature rise, temperature measurements, and isothermal extrusion. Extrusion Thermodynamics Heat Balance in Direct Extrusion...
Series: ASM Technical Books
Publisher: ASM International
Published: 01 January 1998
DOI: 10.31399/asm.tb.ts5.t65900325
EISBN: 978-1-62708-358-4
... transformations by which hardening is accomplished, can minimize or compensate for dimensional changes, there is a great need to be able to precisely predict dimensional changes caused by hardening, especially in parts of complex shapes. As a result, characterizing the quenching process and mathematical modeling...
Book Chapter

Series: ASM Technical Books
Publisher: ASM International
Published: 01 July 1997
DOI: 10.31399/asm.tb.wip.t65930003
EISBN: 978-1-62708-359-1
... by the concept of constitutional supercooling criterion ( Ref 6 ), which can be mathematically stated as: (Eq 1) G L / R > Δ T 0 D L   f o r   p l a n e   f r o n t   s o l i d i f i c a t i o n or (Eq 2) G L / R...
Book Chapter

Series: ASM Technical Books
Publisher: ASM International
Published: 01 August 2018
DOI: 10.31399/asm.tb.msisep.t59220583
EISBN: 978-1-62708-259-4
... for one nucleation condition. With this model, Ref 29 started developing mathematical modeling of cast iron solidification and opened the way for using thermal analysis as a valuable tool in the control of microstructure of these castings. Further studies have confirmed that the effect of nucleants may...