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log normal distribution
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Book: Casting
Series: ASM Handbook
Volume: 15
Publisher: ASM International
Published: 01 December 2008
DOI: 10.31399/asm.hb.v15.a0005225
EISBN: 978-1-62708-187-0
... process that always produces a wide range of droplet diameters. The article schematically illustrates typical log-normal droplet diameter probability density distribution on a mass or volume basis obtained by gas atomization. It also illustrates the changes in solid fraction during the spray casting...
Abstract
Spray casting, also known as spray forming, is a niche casting process for the manufacture of preforms. This article lists commercial examples of alloys manufactured by spray casting and provides sequential steps of the spray casting process. Gas atomization is a chaotic, stochastic process that always produces a wide range of droplet diameters. The article schematically illustrates typical log-normal droplet diameter probability density distribution on a mass or volume basis obtained by gas atomization. It also illustrates the changes in solid fraction during the spray casting process as a function of axial distance from the point of droplet atomization. The article concludes with a section on occurrence of macrosegregation and coarsening in spray cast preforms.
Book Chapter
Series: ASM Desk Editions
Publisher: ASM International
Published: 01 December 1998
DOI: 10.31399/asm.hb.mhde2.a0003196
EISBN: 978-1-62708-199-3
... 1340 666 1230 9260 743 1370 816 1500 749 1380 713 1315 The relief of residual stresses is a time-temperature related phenomenon ( Fig. 1 ), parametrically correlated by the Larson-Miller equation: Thermal effect = T ( log t + 20 ) ( 10 − 3...
Abstract
This article describes the heat treating (stress relieving, normalizing, annealing, quenching, tempering, martempering, austempering, and age hardening) of different types of steels, including ultrahigh-strength steels, maraging steels, and powder metallurgy steels. Tabulating the recommended temperatures for normalizing and austenitizing, it provides information on mechanism, cooling media, principal variables, process procedures, and applications of heat treating. In addition, the article gives a short note on the cold and cryogenic treatment of steel.
Series: ASM Handbook
Volume: 10
Publisher: ASM International
Published: 15 December 2019
DOI: 10.31399/asm.hb.v10.a0006667
EISBN: 978-1-62708-213-6
... neutron diffraction, powder diffraction, and pair distribution function analysis. The relationship between detector space and reciprocal space are presented. Various factors involved in sample preparation, calibration, and techniques used for analyzing diffraction data are described. The article also...
Abstract
This article provides a brief introduction to neutron diffraction as well as its state-of-the-art capabilities. The discussion covers the general principles of the neutron, neutron-scattering theory, generation of neutrons, types of incident radiation, and purposes of single-crystal neutron diffraction, powder diffraction, and pair distribution function analysis. The relationship between detector space and reciprocal space are presented. Various factors involved in sample preparation, calibration, and techniques used for analyzing diffraction data are described. The article also presents application examples and possible future developments in neutron diffraction.
Book Chapter
Series: ASM Desk Editions
Publisher: ASM International
Published: 01 November 1995
DOI: 10.31399/asm.hb.emde.a0003052
EISBN: 978-1-62708-200-6
... reactions, filtration and washing, and powder recovery techniques. It concludes with a discussion on characterization, centering on size distribution analysis, specific surface area, density, porosity chemical composition, phase, and surface composition. ceramic powders ceramic processing additives...
Abstract
This article explains how ceramic powders are made. It begins by briefly describing the raw materials used in structural clay products, whitewares, refractories, and advanced ceramics. It then examines various additives that promote uniformity at different stages of the process. After a description of the comminution process (wet and dry milling methods), it discusses batching and mixing operations and granulation methods. The article also deals with the effect of process variables and the steps involved in chemical synthesis, including preparation from solution and gas-phase reactions, filtration and washing, and powder recovery techniques. It concludes with a discussion on characterization, centering on size distribution analysis, specific surface area, density, porosity chemical composition, phase, and surface composition.
Series: ASM Handbook
Volume: 10
Publisher: ASM International
Published: 15 December 2019
DOI: 10.31399/asm.hb.v10.a0006634
EISBN: 978-1-62708-213-6
... dilution can be 1 M, 0.1 M, 0.01 M, 0.001 M, etc. A 10-fold dilution for each step is called a logarithmic dilution or log-dilution, a 3.16-fold (10 0.5 -fold) dilution is called a half-logarithmic dilution or half-log dilution, and a 1.78-fold (10 0.25 -fold) dilution is called a quarter-logarithmic...
Abstract
Most modern instrumental techniques produce an output or signal that is not absolute. To obtain quantitative information, the raw output from an instrument must be converted into a physical quantity. This is done by standardizing or calibrating the raw response from an instrument and subsequently analyzing the uncertainty from both the calibration process and the measurement process. This article briefly summarizes the most common calibration and uncertainty analysis methods, namely external standard methods, abbreviated external standard methods, internal normalization, internal standard, standard addition, and serial dilution methods. In addition, it includes information on the traceability of true value of a measured quantity.
Book Chapter
Series: ASM Handbook
Volume: 4B
Publisher: ASM International
Published: 30 September 2014
DOI: 10.31399/asm.hb.v04b.a0005968
EISBN: 978-1-62708-166-5
... are already available on many furnaces. For example, it may be desirable to measure and log the amount of time required to move a load from the hot zone to the quench operation. This result will vary over time and can warn of serious mechanical problems before they affect the process. Looking at...
Abstract
The heat treatment of steel involves a number of processes (such as stress relieving, normalizing, annealing etc) to condition the microstructure and obtain desired properties. This article discusses typical heat treating process control procedures for carbon and low-alloy steels, as well as the importance of time, and temperature control in heat treatment. Temperature Uniformity Survey, a testing procedure intended to map variations in temperature throughout the furnace work zone, helps in precise control of temperature. The article focuses on the measuring instruments used to determine gas pressure, vacuum level, gas flow, and gas composition. It focuses on their measuring quenchant characteristics, including bulk temperature, viscosity, composition, and cooling efficiency. The article describes the procedures for detecting variability in the incoming product. It presents, through an example, the general application of design of experiments techniques to locate and tune vital process parameters. The devices used in the control process of mechanical components are also reviewed.
Series: ASM Handbook
Volume: 4B
Publisher: ASM International
Published: 30 September 2014
DOI: 10.31399/asm.hb.v04b.a0005955
EISBN: 978-1-62708-166-5
... diffusion pump Hot zone control thermocouple signals are generally transmitted to a process temperature controller-programmer, often connected in parallel with temperature recorders, data logging instruments, or computers. The overtemperature thermocouple signal may be tracked accordingly, as a backup...
Abstract
Vacuum heat treating consists of thermally treating metals and alloys in cylindrical steel chambers that have been pumped down to less than normal atmospheric pressure. This article provides a detailed account of the operations and designs of vacuum furnaces, discussing their pressure levels, resistance heating elements, quenching systems, work load support, pumping systems, and temperature control systems. It describes the classification of instruments used for measuring and recording pressure inside a vacuum processing chamber. Common devices include hydrostatic measuring devices and devices for measuring thermal and electrical conductivity. The article also describes the applications of the vacuum heat treating process, namely, vacuum nitriding and vacuum carburizing. Finally, it reviews the heat treating process of tool steels, stainless steels, Inconel 718, and titanium and its alloys.
Book Chapter
Series: ASM Desk Editions
Publisher: ASM International
Published: 01 December 1998
DOI: 10.31399/asm.hb.mhde2.a0003088
EISBN: 978-1-62708-199-3
... used statistical distributions: normal, log normal, Weibull, and exponential, which are continuous in nature and binomial Poisson and hypergeometric, which are discrete functions. Each of these statistical distributions are briefly described below. References 34 , 35 , and 36 provide a...
Abstract
This article describes design factors for products used in engineering applications. The article groups these factors into three categories: functional requirements, analysis of total life cycle, and other major factors. These categories intersect and overlap, constituting a major challenge in engineering design. Performance specifications, risk and hazard analysis, design process, design for manufacture and assembly, design for quality, reliability in design, and redesign are considered for functional requirements. Life-cycle analysis considers raw-material extraction from the earth and product manufacture, use, recycling (including design for recycling), and disposal. The other major factors considered include evaluation of the current state of the art for a given design, designing to codes and standards, and human factors/ergonomics.
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
.... This allowed the collection of ET signal magnitudes and corresponding crack sizes (known as “ a -hat,” or â , versus a data). The review of the data collected by these systems showed that the data generally were linear on a log-log scale, with variance normally distributed around the mean...
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
Volume: 7
Publisher: ASM International
Published: 30 September 2015
DOI: 10.31399/asm.hb.v07.9781627081757
EISBN: 978-1-62708-175-7
Series: ASM Handbook
Volume: 14A
Publisher: ASM International
Published: 01 January 2005
DOI: 10.31399/asm.hb.v14a.a0009003
EISBN: 978-1-62708-185-6
... neck. Figure 6 shows that this gives close agreement for steel specimens but not for other metals with widely different necking strains. It has been shown that the Bridgman correction factor, B , can be estimated from ( Ref 3 ): (Eq 10) B = 0.83 − 0.186 log ε ( 0.15 ″ ε...
Abstract
This article provides the definitions of stress and strain, and describes the relationship between stress and strain by stress-strain curves and true-stress/true-strain curves. The emphasis is on understanding the factors that determine the extent of deformation a metal can withstand before cracking or fracture occurs. The article reviews the process variables that influence the degree of workability and summarizes the mathematical relationships that describe the occurrence of room-temperature ductile fracture under workability conditions. It discusses the most common situations encountered in multiaxial stress states. The construction of a processing map based on deformation mechanisms is also discussed.
Book Chapter
Book: Surface Engineering
Series: ASM Handbook
Volume: 5
Publisher: ASM International
Published: 01 January 1994
DOI: 10.31399/asm.hb.v05.a0005586
EISBN: 978-1-62708-170-2
... DIBS dual-ion-beam sputtering DIN Deutsche Industrie-Normen (German Industrial Standards) DLC diamondlike carbon dL / dX loading rate dpa displacements per incident atom DPH diamond pyramid hardness (Vickers hardness) e natural log base, 2.71828; charge of an...
Book: Fractography
Series: ASM Handbook
Volume: 12
Publisher: ASM International
Published: 01 January 1987
DOI: 10.31399/asm.hb.v12.a0001837
EISBN: 978-1-62708-181-8
... quantitative fractography is to express the characteristics of the features in the fracture surface in quantitative terms, such as the true area, length, size, spacing, orientation, and location, as well as distributions of these, as required. As will be discussed in this article, the more prominent techniques...
Abstract
The principal objective of quantitative fractography is to express the characteristics of features in the fracture surface in quantitative terms, such as the true area, length, size, spacing, orientation, and location. This article provides a detailed account of the development of more quantitative geometrical methods for characterizing nonplanar fracture surfaces. Prominent techniques for studying fracture surfaces are based on the projected images, stereoscopic viewing, and sectioning. The article provides information on various roughness and materials-related parameters for profiles and surfaces. The applications of quantitative fractography for striation spacings, precision matching, and crack path tortuosity are also discussed.
Series: ASM Handbook
Volume: 14A
Publisher: ASM International
Published: 01 January 2005
DOI: 10.31399/asm.hb.v14a.a0004017
EISBN: 978-1-62708-185-6
... express the flow curve of many metals in the region of uniform plastic deformation, that is, from yielding up to maximum load: (Eq 17) σ = K ε n where n is the strain-hardening exponent and K is the strength coefficient. A log-log plot of true stress and true strain up to maximum load...
Abstract
This article focuses on the factors that determine the extent of deformation a metal can withstand before cracking or fracture occurs. It informs that workability depends on the local conditions of stress, strain, strain rate, and temperature in combination with material factors. The article discusses the common testing techniques and process variables for workability prediction. It illustrates the simple and most widely used fracture criterion proposed by Cockcroft and Latham and provides a workability analysis using the fracture limit line. The article describes various workability tests, such as the tension test, ring compression test, plane-strain compression test, bend test, indentation test, and forgeability test. It concludes with information on the role of the finite-element modeling software used in workability analysis.
Series: ASM Handbook
Volume: 22A
Publisher: ASM International
Published: 01 December 2009
DOI: 10.31399/asm.hb.v22a.a0005433
EISBN: 978-1-62708-196-2
...) σ = σ o + B ε where log σ o = a o + a 1 log ε ˙ + a 2 log 2 ε ˙ + a 3 log 3 ε ˙ + a 4 log 4 ε ˙ . The polynomial models developed through linear regression methods tend to provide...
Abstract
This article presents a mechanical description of superplasticity and discusses constitutive equations that are essential for simulating superplastic forming processes, applicable to structural superplasticity. It presents the phenomenological constitutive equations of superplasticity and classical physical constitutive equations. The article also reviews the accommodation mechanisms that are divided into two major groups, namely, diffusional accommodation and accommodation by dislocations.
Series: ASM Handbook
Volume: 22A
Publisher: ASM International
Published: 01 December 2009
DOI: 10.31399/asm.hb.v22a.a0005405
EISBN: 978-1-62708-196-2
... mean grain size (40 μm) as a function of applied loading cycles (lower right) for multiple statistical realizations of equiaxed polycrystalline IN 100 tructures with log normal grain size distribution. Fig. 13 Estimated distribution for fraction of grains with cracks that reach a length three...
Abstract
The purposes and methods of fatigue modeling and simulation in high-cycle fatigue (HCF) regime are to design either failsafe components or components with a finite life and to quantify remaining life of components with pre-existing cracks using fracture mechanics, with the intent of monitoring via an inspection scheme. This article begins with a discussion on the stages of the fatigue damage process. It describes hierarchical multistage fatigue modeling and several key points regarding the physics of crack nucleation and microstructurally small crack propagation in the HCF regime. The article provides a description of the microstructure-sensitive modeling to model fatigue of several classes of advanced engineering alloys. It describes the various modeling and design processes designed against fatigue crack initiation. The article concludes with a discussion on the challenges in microstructure-sensitive fatigue modeling.
Series: ASM Handbook
Volume: 6
Publisher: ASM International
Published: 01 January 1993
DOI: 10.31399/asm.hb.v06.9781627081733
EISBN: 978-1-62708-173-3
Book: Casting
Series: ASM Handbook
Volume: 15
Publisher: ASM International
Published: 01 December 2008
DOI: 10.31399/asm.hb.v15.a0005207
EISBN: 978-1-62708-187-0
... solidification free growth model carbide-boride model grain refinement model constitutional undercooling model thermodynamics NUCLEATION PROCESSES play a key role in the solidification of castings by controlling to a large extent the initial structure type, size scale, and spatial distribution of the...
Abstract
This article discusses selected highlights of thermodynamic relationships during solidification and nucleation kinetics behavior in connection with the basis of nucleation treatments, such as grain refinement and inoculation, to provide a summary of nucleation phenomena during casting. Nucleation during solidification is a thermally activated process involving a fluctuational growth in the sizes of clusters of solids. The article describes nucleation phenomenon such as homogeneous nucleation and heterogeneous nucleation. It discusses various grain refinement models, such as carbide-boride model, free growth model, and constitutional undercooling model. The article concludes with a section on thermal analysis techniques for assessing grain-refining characteristics during master alloy processing.
Series: ASM Handbook
Volume: 22A
Publisher: ASM International
Published: 01 December 2009
DOI: 10.31399/asm.hb.v22a.a0005403
EISBN: 978-1-62708-196-2
... considered in some detail later. If the value of n is known, the aforementioned relation can be used to evaluate the ratio t 95 / t 5 , for example, for different materials. For plotting purposes, it is useful to take the double log of 1 / ( 1 − X ) so that the progress...
Abstract
Recrystallization is to a large extent responsible for their final mechanical properties. This article commences with a discussion on static recrystallization (SRX) and dynamic recrystallization (DRX). The DRX includes continuous dynamic recrystallization (CDRX) and discontinuous dynamic recrystallization (DDRX). The article discusses the assumptions and simplifications for the Avrami analysis. It describes the effects of nucleation and growth rates on recrystallization kinetics and recrystallized grain size based on the Johnson-Mehl-Avrami-Kolmogorov model for static recrystallization. The article reviews the kinetics of DRX with the aid of the Avrami relations. It considers the basic framework of the mesoscale approach for DDRX, including the three basic equations for grain size changes, strain hardening and dynamic recovery, and nucleation. The article explains the mesoscale approach for CDRX to predict microstructural evolutions occurring during hot deformation, along with an illustration of the main features of the CDRX mesoscale model.
Book: Casting
Series: ASM Handbook
Volume: 15
Publisher: ASM International
Published: 01 December 2008
DOI: 10.31399/asm.hb.v15.a0005192
EISBN: 978-1-62708-187-0
... ) + 3 H 2 ( in Al ) The standard free energy change, Δ G o , for this reaction is extremely high: (Eq 14) Δ G o = − 979 , 100 − 719 T log 10 T + 413 T where T is the temperature in K. Inserting this value of free energy change into the van't...
Abstract
This article reviews the solubilities of the common gases present in ferrous metals, such as cast irons, and nonferrous metals, such as aluminum, copper, magnesium, and their alloys. The kinetics of the relevant reactions, reactions during solidification, and possible methods of control or removal of the dissolved gases are discussed. The most common method for removing hydrogen from aluminum, copper, and magnesium is inert gas flushing. The article concludes with a discussion on overcoming gas porosity in ferrous and nonferrous metals.