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mathematical modeling

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Series: ASM Handbook Archive
Volume: 11
Publisher: ASM International
Published: 01 January 2002
DOI: 10.31399/asm.hb.v11.a0003523
EISBN: 978-1-62708-180-1
... where the model can be a physical, mathematical, or logical representation of a physical system or process. accident reconstruction failure analysis modeling FAILURE ANALYSIS is generally defined as the investigation and analysis of parts or structures that have failed or appeared to have...
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
... of this Volume. Investigators are now capable of deploying various tools (laser scanning, photogrammetry, drones, etc.) to acquire high-quality, highly accurate data to successfully document accident scenes while preserving evidence for future examination. A model is a physical, mathematical, or logical...
Series: ASM Handbook Archive
Volume: 11
Publisher: ASM International
Published: 01 January 2002
DOI: 10.31399/asm.hb.v11.a0003526
EISBN: 978-1-62708-180-1
... technique that allows numerical solutions to be obtained for complex mathematical and engineering problems. It is a technique that relies on creating a geometric mathematical model of the structure out of discrete or finite numbers of individual nodes and elements. Displacement functions are assumed...
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
... numerical solutions to be obtained for complex mathematical and engineering problems. It is a technique that relies on creating a geometric mathematical model of the structure out of discrete or finite numbers of individual nodes and elements. Displacement functions are assumed that allow displacements...
Series: ASM Failure Analysis Case Histories
Volume: 3
Publisher: ASM International
Published: 01 December 2019
DOI: 10.31399/asm.fach.v03.c9001851
EISBN: 978-1-62708-241-9
... ] is the elasticity matrix due to the bending motion. [ 4 ] Bearing Modeling The mathematical model for a bearing is a massless spring-damper system ( Fig. 7 ). Its characteristics (stiffness and damping) in horizontal and vertical directions are different. The cross-coupled [ 13 ] characteristics...
Series: ASM Handbook
Volume: 11A
Publisher: ASM International
Published: 30 August 2021
DOI: 10.31399/asm.hb.v11A.a0006803
EISBN: 978-1-62708-329-4
... of the basic events, which is covered in a detailed overview. How the methods are applied is demonstrated by two examples in the section “Case Studies” in this article. Any probabilistic model relies on a physical and mathematical model, which is deterministic in the case of sampling-based methods...
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
.... The coefficient of variation is defined as: C X = σ X μ X Described in the following section are statistical models (standard mathematical forms) that are used to describe the PDF and CDF. Common Engineering Distributions There are a large number of probability distributions...
Series: ASM Handbook
Volume: 11A
Publisher: ASM International
Published: 30 August 2021
DOI: 10.31399/asm.hb.v11A.a0006807
EISBN: 978-1-62708-329-4
... of the information and in the search for better information when the need arises ( Ref 2 ). Various mathematical models have been developed over the years to express the data generated from uniaxial creep tests in suitable forms for the design of components operating in the creep regime. The slope of the creep...
Series: ASM Handbook
Volume: 11
Publisher: ASM International
Published: 15 January 2021
DOI: 10.31399/asm.hb.v11.9781627082952
EISBN: 978-1-62708-295-2
Series: ASM Failure Analysis Case Histories
Publisher: ASM International
Published: 01 June 2019
DOI: 10.31399/asm.fach.auto.c9001732
EISBN: 978-1-62708-218-1
.... The Weibull distribution is the statistical model used as a basis for these techniques. This method of failure analysis provides the engineer with clear, positive design direction. Door lock assembly Fatigue (materials) Statistical analysis Weibull distribution Metal (Other, miscellaneous...
Series: ASM Handbook Archive
Volume: 11
Publisher: ASM International
Published: 01 January 2002
DOI: 10.31399/asm.hb.v11.a0003516
EISBN: 978-1-62708-180-1
..., the initial flaw is grown mathematically through iterative calculations that take into account the expected stress history and the material crack growth properties and geometry of the component. The resulting life estimate is then divided by a safety factor (usually two or three) to obtain the inspection...
Series: ASM Handbook Archive
Volume: 11
Publisher: ASM International
Published: 01 January 2002
DOI: 10.31399/asm.hb.v11.a0003528
EISBN: 978-1-62708-180-1
... straightforward and is normally carried out by plotting the measured d -spacing versus sin 2 ψ, with careful selection of the measurement directions, ψ and ϕ. A variety of mathematical models and measurement approaches have been proposed to evaluate the stress-tensor components of interest ( Ref 1 , 2 , 3 , 4...
Series: ASM Handbook Archive
Volume: 11
Publisher: ASM International
Published: 01 January 2002
DOI: 10.31399/asm.hb.v11.a0003572
EISBN: 978-1-62708-180-1
... aspects of composite tribology. This topic is briefly discussed with some emphasis on various mathematical models starting with the simple rule of mixtures. More complex methods developed for describing the wear performance of each type of composite are also available, but such models, along with the data...
Series: ASM Failure Analysis Case Histories
Publisher: ASM International
Published: 01 June 2019
DOI: 10.31399/asm.fach.design.c9001551
EISBN: 978-1-62708-233-4
.... Expressed mathematically in its simplest form, vibration is characterized by the equation x = A sin wt, where x is the instantaneous position of the object at time t, A is the maximum amplitude of the vibration, and ω is the frequency of oscillation of the vibration. Simple vibrations are frequently...
Series: ASM Failure Analysis Case Histories
Volume: 3
Publisher: ASM International
Published: 01 December 2019
DOI: 10.31399/asm.fach.v03.c9001797
EISBN: 978-1-62708-241-9
... the relationship between crack size and stiffness, showing that cracks have an amplitude modulating effect. cam fracture rolling-contact fatigue steel crack numerical simulation stiffness steel (steel, general) Introduction Dynamic Modeling of the Cam–Follower Mechanism Modeling of Cam...
Series: ASM Handbook
Volume: 11
Publisher: ASM International
Published: 15 January 2021
DOI: 10.31399/asm.hb.v11.a0006768
EISBN: 978-1-62708-295-2
... residual-stress analysis Evaluation of the stress-tensor components, σ ij , is generally straightforward and is normally carried out by plotting the measured d -spacing versus sin 2 ψ, with careful selection of the measurement directions, ψ and φ. A variety of mathematical models and measurement...
Series: ASM Failure Analysis Case Histories
Volume: 3
Publisher: ASM International
Published: 01 December 2019
DOI: 10.31399/asm.fach.v03.c9001788
EISBN: 978-1-62708-241-9
... ductility coefficient, b the fatigue strength exponent, c the fatigue ductility exponent, and E the modulus of elasticity. Both these models are based on the use of damage parameters (i.e. σ a and ε a ), which describe a mathematical relationship between maximum stress–strain conditions...
Series: ASM Handbook
Volume: 11
Publisher: ASM International
Published: 15 January 2021
DOI: 10.31399/asm.hb.v11.a0006767
EISBN: 978-1-62708-295-2
... normal stress reaches the yield strength of the material. Tresca’s theory states that yield at a point begins when the maximum shear stress equals the shear stress in a tension specimen when it begins to yield. Another common failure model is the von Mises criterion, which is based on a determination...
Series: ASM Handbook
Volume: 11A
Publisher: ASM International
Published: 30 August 2021
DOI: 10.31399/asm.hb.v11A.a0006827
EISBN: 978-1-62708-329-4
... (No. 5 ), 2010 , p 428 – 475 10.1016/j.pmatsci.2010.01.001 8. Syed A. , Accumulated Creep Strain and Energy Density Based Thermal Fatigue Life Prediction Models for SnAgCu Solder Joints , Proc. 54th Electronic Components and Technology Conference , 2004 , p 737 – 746 9. Long...
Series: ASM Handbook Archive
Volume: 11
Publisher: ASM International
Published: 01 January 2002
DOI: 10.31399/asm.hb.v11.a0003530
EISBN: 978-1-62708-180-1
... the maximum shear stress equals the shear stress in a tension specimen when it begins to yield. Another common failure model is the von Mises criterion, which is based on a determination of distortion energy at yield and recognizes that in a constant-volume isotropic material, hydrostatic stresses cannot...