Search Results for conservation equations

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.

This article illustrates the use of the American Petroleum Institute (API) 579-1/ASME FFS-1 fitness-for-service (FFS) code (2020) to assess the serviceability and remaining life of a corroded flare knockout drum from an oil refinery, two fractionator columns affected by corrosion under insulation in an organic sulfur environment, and an equalization tank with localized corrosion in the shell courses in a chemicals facility. In the first two cases, remaining life is assessed by determining the minimum thickness required to operate the corroded equipment. The first is based on a Level 2 FFS assessment, while the second involves a Level 3 assessment. The last case involves several FFS assessments to evaluate localized corrosion in which remaining life was assessed by determining the minimum required thickness using the concept of remaining strength factor for groove-like damage and evaluating crack-like flaws using the failure assessment diagram. Need for caution in predicting remaining life due to corrosion is also covered.

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.

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.

Failed ferrous components were analyzed from a crane that operated on an offshore platform. The crane failed during operation and fell into the sea. The brake spring on the boom hoist was found to have fractured in four places. The spring contained a line defect (seam) that was the source of each crack. The fracture of the oil quenched and tempered (HRC 50 ASTM A229) spring was by stress-corrosion cracking after the crane fell into the sea because fatigue cannot account for the fractures observed. The crane failure was caused by an overload created by the operator catching a free-falling load.

Thermomechanical fatigue (TMF) refers to the process of fatigue damage under simultaneous changes in temperature and mechanical strain. This article reviews the process of TMF with a practical example of life assessment. It describes TMF damages caused due to two possible types of loading: in-phase and out-of-phase cycling. The article illustrates the ways in which damage can interact at high and low temperatures and the development of microstructurally based models in parametric form. It presents a case study of the prediction of residual life in a turbine casing of a ship through stress analysis and fracture mechanics analyses of the casing.

This article offers an overview of fatigue fundamentals, common fatigue terminology, and examples of damage morphology. It presents a summary of relevant engineering mechanics, cyclic plasticity principles, and perspective on the modern design by analysis (DBA) techniques. The article reviews fatigue assessment methods incorporated in international design and post construction codes and standards, with special emphasis on evaluating welds. Specifically, the stress-life approach, the strain-life approach, and the fracture mechanics (crack growth) approach are described. An overview of high-cycle welded fatigue methods, cycle-counting techniques, and a discussion on ratcheting are also offered. A historical synopsis of fatigue technology advancements and commentary on component design and fabrication strategies to mitigate fatigue damage and improve damage tolerance are provided. Finally, the article presents practical fatigue assessment case studies of in-service equipment (pressure vessels) that employ DBA methods.

The lifetime assessment of polymeric products is complicated, and if the methodology utilized leads to inaccurate predictions, the mistakes could lead to financial loss as well as potential loss of life, depending on the service application of the product. This article provides information on the common aging mechanisms of polymeric materials and the common accelerated testing methods used to obtain relevant data that are used with the prediction models that enable service life assessment. Beginning with a discussion of what constitutes a product failure, this article then reviews four of the eight major aging mechanisms, namely environmental stress cracking, chemical degradation, creep, and fatigue, as well as the methods used in product service lifetime assessment for them. Later, several methods of service lifetime prediction that have gained industry-wide acceptance, namely the hydrostatic design basis approach, Miner's rule, the Arrhenius model, and the Paris Law for fatigue crack propagation, are discussed.

Thermomechanical fatigue (TMF) is the general term given to the material damage accumulation process that occurs with simultaneous changes in temperature and mechanical loading. TMF may couple cyclic inelastic deformation accumulation, temperature-assisted diffusion within the material, temperature-assisted grain-boundary evolution, and temperature-driven surface oxidation, among other things. This article discusses some of the major aspects and challenges of dealing with TMF life prediction. It describes the damage mechanisms of TMF and covers various experimental techniques to promote TMF damage mechanisms and elucidate mechanism coupling interactions. In addition, life modeling in TMF conditions and a practical application of TMF life prediction are presented.

This article provides an overview of the physics and math associated with moisture-related failures in plastic components. It develops key equations, showing how they are used to analyze the causes and effects of water uptake, diffusion, and moisture concentration in polymeric materials and resins. It explains how absorbed moisture affects a wide range of properties, including glass transition temperature, flexural and shear modulus,creep, stress relaxation, swelling, tensile and yield strength, and fatigue cracking. It provides relevant data on common polymers, resins, and fiber-resin composites.

Optimized modeling of fracture-critical structural components and connections requires the application of elastic-plastic fracture mechanics. Such applications, however, can require sophisticated analytical techniques such as crack tip opening displacement (CTOD), failure assessment diagram (FAD), and deformation plasticity failure assessment diagram (DPFAD). This article presents the origin and description of FAD and addresses R6 FAD using J-integral. It details the fracture criteria of BS 7910. The factors to be considered during the use of FAD and the applications of FAD are also reviewed.

This article describes the general aspects of creep, stress relaxation, and yielding for homogeneous polymers. It then presents creep failure mechanisms in polymers. The article discusses extrapolative methods for the prediction of long-term creep failure in polymer materials. Then, the widely used models to simulate the service life of polymers are highlighted. These include the Burgers power-law model, the Findley power-law model, the time-temperature superposition (or equivalence) principle (TTSP), and the time-stress superposition principle (TSSP). The Larson-Miller parametric method, one of the most common to describe the material deformation and rupture time, is also discussed.

Following a fracture mechanics “fitness-for-purpose” analysis of petroleum industry cold service pressure vessels, using the British Standard PD 6493, it was realized that an analogous approach could be used for the failure analysis of a similar pressure vessel dome which had failed in service some years previously. The failed pressure vessel, with a diam of 2.5 m and several meters tall, had been made of 12 mm thick IZETT steel plate of the same type and heat treatment as used in the earlier fitness-for-purpose already measured. Examination of the fracture surfaces suggested, from fatigue striations manifested by SEM, that the vessel was subject to significant fatigue cracking, which was probably corrosion assisted. From COD measurements at the operating temperature of -130 deg C (-202 deg F), and a finite stress analysis, a fracture mechanics evaluation using BS PD6493 yielded realistic critical flaw sizes (in the range 51 to 150 mm). These sizes were consistent with the limited fracture surface observations and such flaws could well have been present in the vessel dome prior to catastrophic failure. For similar pressure vessels, an inspection program based on a leak-before-break philosophy was consequently regarded as acceptable.

An API type 2 steel clamp located on the riser of a semisubmersible drilling rig between the lower ball joint and riser blowout preventer (BOP) conductor failed after 7 years of service. Failure analysis revealed the cause of failure to be the low toughness of the clamp material. Contributing factors included the presence of a hard, brittle, heat-affected zone and weld defects at the handling pad eye. It was recommended that the replacement clamp be made from a material with good toughness and that any installation of attachments by welding be done according to qualified procedures.

A 22 m (72 ft) diameter filled grain storage bin made from a 0.2% carbon steel collapsed at a temperature of −1 to 4 deg C (30 to 40 deg F). Failure analysis indicated that fracture occurred in a two-step process: first downward, by ductile failure of small ligament from a bolt hole near the bottom of the tank to create a crack 25 mm (1 in.) long, and then upward, by brittle fracture through successive 1.2 m (4ft) wide sheets of ASTM A446 material. Site investigation showed that the concrete base pad was not level. Chemical analysis indicated that the material had a high nitrogen content (0.020%). The allowable stress based on yield was estimated using four different design criteria. Correlation among those results was poor. The different criteria indicated that the material was loaded from the maximum allowable to approximately 30% less than allowable. Nevertheless, at this stress level, fracture mechanics indicated that the 25 mm (1 in.) starter crack exceeded or was very near the critical crack length for the material. Additional factors not taken into account in the design equations included cold work from a hole punching operation, thread imprinting in bolt holes, and an additional hoop stress created by forcing an incorrectly formed panel to fit the pad base radius. These factors increased the nominal design stress to a sufficiently large value to cause the critical crack length to be exceeded.

During a planned shut-down in 1990 it appeared that the bottom manifold parts made of wrought Incoloy 800H had undergone diametrical expansion of up to 2% due to creep. Further, cracking at the outer diam was found. It was decided to replace these parts. Microscopical investigations showed that the cracking could not be caused by creep. It was found that the cracking was confined to a 4-mm deep coarse-grained zone (ASTM 0-1) at the outer diameter. The cracking appeared to be caused by strain-induced intergranular oxidation. When the cracks reached the fine-grained material, the oxidation-cracks stopped. To determine the residual creep life of the sound (non-cracked) bottom manifold material, iso-stress creep tests were performed. It was found that tertiary creep started at 7% strain. The time-to-rupture was greater than 100,000 h. It was concluded that the bottom manifold (and thus the furnace) could be used safely during the foreseen production period.

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.

This article focuses on the life assessment methods for elevated-temperature failure mechanisms and metallurgical instabilities that reduce life or cause loss of function or operating time of high-temperature components, namely, gas turbine blade, and power plant piping and tubing. The article discusses metallurgical instabilities of steel-based alloys and nickel-base superalloys. It provides information on several life assessment methods, namely, the life fraction rule, parameter-based assessments, the thermal-mechanical fatigue, coating evaluations, hardness testing, microstructural evaluations, the creep cavitation damage assessment, the oxide-scale-based life prediction, and high-temperature crack growth methods.

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.

A commercial hybrid-iron golf club fractured during normal use. The club fractured through its cast aluminum alloy hosel. Optical analysis revealed casting pores through 20% of the hosel thickness. Mechanical properties were determined from characterization results, then used to construct a finite element model to analyze material performance under failure conditions. In addition, a full scale structural test was conducted to determine failure strength. It was concluded that the club failed not from ground impact but from a force reversal at the bottom of the downswing. Large moments generated during the downswing aggravated by manufacturing defects and stress concentration combined to create an overload condition.