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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...
Abstract
This article focuses on the general methods and approaches from the perspective of a reconstruction analyst and includes discussions relevant to materials failure analysts at the incident scene. The elements of accident reconstruction are described. These have conceptual similarity with the principles for failure analysis of material incidents that are less complex than a large-scale accident. The article provides a brief review of some general concepts on the use of modeling which can be a very powerful tool for information pertaining to the reconstruction of an accident where the model can be a physical, mathematical, or logical representation of a physical system or process.
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...
Abstract
Failure analysis is generally defined as the investigation and analysis of parts or structures that have failed or appeared to have failed to perform their intended duty. Methods of field inspection and initial examination are also critical factors for both reconstruction analysts and materials failure analysts. This article focuses on the general methods and approaches from the perspective of a reconstruction analyst. It describes the elements of accident reconstruction, which have conceptual similarity with the principles for failure analysis of material incidents that are less complex than a large-scale accident. The approach presented is that the analysis and reconstruction is based on the physical evidence. The article provides a brief review of some general concepts on the use and limitations of advanced data acquisition tools and computer modeling. Legal implications of destructive testing are discussed in detail.
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...
Abstract
This article provides information on the development of finite element analysis (FEA) and describes the general-purpose applications of FEA software programs in structural and thermal, static and transient, and linear and nonlinear analyses. It discusses special-purpose finite element applications in piping and pressure vessel analysis, impact analysis, and microelectronics. The article describes the steps involved in the design process using the FEA. It concludes with two case histories that involve the use of FEA in failure analysis.
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...
Abstract
When complex designs, transient loadings, and nonlinear material behavior must be evaluated, computer-based techniques are used. This is where the finite-element analysis (FEA) is most applicable and provides considerable assistance in design analysis as well as failure analysis. This article provides a general view on the applicability of finite-element modeling in conducting analyses of failed components. It highlights the uses of finite-element modeling in the area of failure analysis and design, with emphasis on structural analysis. The discussion covers the general development and both general- and special-purpose applications of FEA. The special-purpose applications of FEA covered are piping and pressure vessel analysis, impact analysis, and microelectronic and microelectromechanical systems analysis. The article provides case histories that involved the use of FEA in failure analysis.
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...
Abstract
Shaft misalignment and rotor unbalance contribute to the premature failure of many machine components. To understand how these failures occur and quantify the effects, investigators developed a model of a rotating assembly, including a motor, flexible coupling, driveshaft, and bearings. Equations of motion accounting for misalignment and unbalance were then derived using finite elements. A spectral method for resolving these equations was also developed, making it possible to obtain and analyze dynamic system response and identify misalignment and unbalance conditions.
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...
Abstract
This article provides an outline of the issues to consider in performing a probabilistic life assessment. It begins with an historical background and introduces the most common methods. The article then describes those methods covering subjects such as the required random variable definitions, how uncertainty is quantified, and input for the associated random variables, as well as the characterization of the response uncertainty. Next, it focuses on specific and generic uncertainty propagation techniques: first- and second-order reliability methods, the response surface method, and the most frequently used simulation methods, standard Monte Carlo sampling, Latin hypercube sampling, and discrete probability distribution sampling. Further, the article discusses methods developed to analyze the results of probabilistic methods and covers the use of epistemic and aleatory sampling as well as several statistical techniques. Finally, it illustrates some of the techniques with application problems for which probabilistic analysis is an essential element.
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...
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.
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...
Abstract
This article provides some new developments in elevated-temperature and life assessments. It is aimed at providing an overview of the damage mechanisms of concern, with a focus on creep, and the methodologies for design and in-service assessment of components operating at elevated temperatures. The article describes the stages of the creep curve, discusses processes involved in the extrapolation of creep data, and summarizes notable creep constitutive models and continuum damage mechanics models. It demonstrates the effects of stress relaxation and redistribution on the remaining life and discusses the Monkman-Grant relationship and multiaxiality. The article further provides information on high-temperature metallurgical changes and high-temperature hydrogen attack and the steps involved in the remaining-life prediction of high-temperature components. It presents case studies on heater tube creep testing and remaining-life assessment, and pressure vessel time-dependent stress analysis showing the effect of stress relaxation at hot spots.
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...
Abstract
Statistical techniques provide the design engineer with a powerful tool for the analysis of failure data. By means of an actual case study, steps required to design a test yielding statistically meaningful data and procedures used in graphical analysis of results are presented. 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.
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...
Abstract
This article discusses the fundamental variables involved in fatigue-life assessment, which describe the effects and interaction of material behavior, geometry, and stress history on the life of a component. It compares the safe-life approach with the damage-tolerance approach, which employs the stress-life method of fatigue life assessment. The article examines the behavior of three different metallic materials used in the design and manufacture of structural components: steel, aluminum, and titanium. It also reviews the effects of retardation and spectrum load on component life. The article concludes with case studies of fatigue life assessment from the aerospace industry.
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...
Abstract
This article focuses primarily on what an analyst should know about applying X-ray diffraction (XRD) residual stress measurement techniques to failure analysis. Discussions are extended to the description of ways in which XRD can be applied to the characterization of residual stresses in a component or assembly. The article describes the steps required to calibrate instrumentation and to validate stress measurement results. It presents a practical approach to sample selection and specimen preparation, measurement location selection, and measurement depth selection, as well as an outline on measurement validation. The article also provides information on stress-corrosion cracking and corrosion fatigue. The importance of residual stress in fatigue is described with examples. The article explains the effects of heat treatment and manufacturing processes on residual stress. It concludes with a section on the XRD stress measurements in multiphase materials and composites and in locations of stress concentration.
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...
Abstract
This article reviews the abrasive and adhesive wear failure of several types of reinforced polymers, including particulate-reinforced polymers, short-fiber reinforced polymers (SFRP), continuous unidirectional fiber reinforced polymers (FRP), particulate-filled composites, mixed composites (SFRP and particulate-filled), unidirectional FRP composites, and fabric reinforced composites. Friction and wear performance of the composites, correlation of performance with various materials properties, and studies on wear-of failure mechanisms by scanning electron microscopy are discussed for each of these types.
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...
Abstract
A multi-million dollar, four-color printing press used to produce a major weekly magazine was breaking pinions (shouldered shafts) on rolls. The cause of fracture was cyclic fatigue. Steel quality and heat treatment met expected standards. The pinion fracture showed multiple origins indicating rotational vibration fatigue. Keeping bolts tight solved this problem. In another case, grinding machines were unable to produce surfaces of uniform quality and smoothness on steel bearing products. Measurements showed that self-excited vibrations were created when particular steels were ground. It was found that the natural frequency of the wheel truing device was the culprit. A tuned damped absorber was designed and built to modify the resonance. This eliminated the problem.
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...
Abstract
Cam crack failures are a common occurrence in cam-follower systems often caused by excessive loading or inappropriate operating conditions. An investigation into such a failure was conducted to assess the effect of cam crack damage on the dynamic behavior of cam-follower systems. It was shown both theoretically and experimentally that a cracked cam causes an overall reduction in stiffness. To further probe the effect, investigators derived an analytical formula expressing the time varying stiffness of a cam-follower system. They also succeeded in quantifying the relationship between crack size and stiffness, showing that cracks have an amplitude modulating effect.
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...
Abstract
X-ray diffraction (XRD) residual-stress analysis is an essential tool for failure analysis. This article focuses primarily on what the analyst should know about applying XRD residual-stress measurement techniques to failure analysis. Discussions are extended to the description of ways in which XRD can be applied to the characterization of residual stresses in a component or assembly and to the subsequent evaluation of corrective actions that alter the residual-stress state of a component for the purposes of preventing, minimizing, or eradicating the contribution of residual stress to premature failures. The article presents a practical approach to sample selection and specimen preparation, measurement location selection, and measurement depth selection; measurement validation is outlined as well. A number of case studies and examples are cited. The article also briefly summarizes the theory of XRD analysis and describes advances in equipment capability.
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...
Abstract
Several failed dies were analyzed and the results were used to evaluate fatigue damage models that have been developed to predict die life and aid in design and process optimization. The dies used in the investigation were made of H13 steels and fractured during the hot extrusion of Al-6063 billet material. They were examined to identify critical fatigue failure locations, determine corresponding stresses and strains, and uncover correlations with process parameters, design features, and life cycle data. The fatigue damage models are based on Morrow’s stress and strain-life models for flat extrusion die and account for bearing length, fillet radius, temperature, and strain rate. They were shown to provide useful information for the analysis and prevention of die failures.
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...
Abstract
This article describes concepts and tools that can be used by the failure analyst to understand and address deformation, cracking, or fracture after a stress-related failure has occurred. Issues related to the determination and use of stress are detailed. Stress is defined, and a procedure to deal with stress by determining maximum values through stress transformation is described. The article provides the stress analysis equations of typical component geometries and discusses some of the implications of the stress analysis relative to failure in components. It focuses on linear elastic fracture mechanics analysis, with some mention of elastic-plastic fracture mechanics analysis. The article describes the probabilistic aspects of fatigue and fracture. Information on crack-growth simulation of the material is also provided.
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...
Abstract
Due to the recent requirement of higher integration density, solder joints are getting smaller in electronic product assemblies, which makes the joints more vulnerable to failure. Thus, the root-cause failure analysis for the solder joints becomes important to prevent failure at the assembly level. This article covers the properties of solder alloys and the corresponding intermetallic compounds. It includes the dominant failure modes introduced during the solder joint manufacturing process and in field-use applications. The corresponding failure mechanism and root-cause analysis are also presented. The article introduces several frequently used methods for solder joint failure detection, prevention, and isolation (identification for the failed location).
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...
Abstract
This article describes the underlying fundamentals, applications, the relevance and necessity of performing proper stress analysis in conducting a failure analysis. It presents an introduction to the stress analysis of bodies containing crack-like imperfections and the topic of fracture mechanics. The fracture mechanics approach is an important part of stress analysis at the tips of sharp cracks or discontinuities. The article reviews fracture mechanics concepts, including linear elastic fracture mechanics, elastic-plastic fracture mechanics, and subcritical fracture mechanics. It also provides information on the applications of fracture mechanics in failure analysis.