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.

Applying general techniques of failure analysis, the authors deduced that an in-flight explosion brought down a passenger plane. Other evidence pinpointed the location of the explosive, an important factor in establishing responsibility.

A 150 mm (6 in.) schedule 80S type 304 stainless steel pipe (11 mm, or 0.432 in., wall thickness), which had served as an equalizer line in the primary loop of a pressurized-water reactor, was found to contain several circumferential cracks 50 to 100 mm (2 to 4 in.) long. Two of these cracks, which had penetrated the pipe wall, were responsible for leaks detected in a hydrostatic test performed during a general inspection after seven years of service. Investigation (visual inspection, visual and ultrasonic weld examination, water analysis, and chemical analysis) supported the conclusion that the failure was caused by SCC due to stress, sensitization, and environment. Recommendations included replacing all pipe sections and installing them using low-heat-input, multiple-pass welding procedures.

A portable propane container with a name-plate soldered onto it exploded in service. When the vessel was inspected afterwards, it was found to have developed a crack in the top end plate. A portion of the end plate cut out to include the midlength and one termination of the crack was examined microscopically. This revealed that the crack was associated with intergranular penetration by molten metal. The microstructure in general was indicative of a good-quality mild steel. It was evident from that solder that was responsible for the penetration and that fused brass from the hand wheel had not played any part. Tensile stress was present at the time of the failure sufficiently high to enable solder penetration to take place. The use of soft solder as a medium for attaching name-plates directly on to stressed steel parts is not recommended. It would be preferable to use a welded-on patch plate or to employ one of the high-strength, non-metallic adhesives.

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.

This article describes the viscoelastic behavior of plastics in their solid state only, from the standpoint of the material deforming without fracturing. The consequences of viscoelasticity on the mechanical properties of plastics are described, especially in terms of time-dependencies, as well as the dependence of the viscoelastic character of a plastic on chemical, physical, and compositional variables. By examining the viscoelastic behavior of plastics, the information obtained are then applied in situations in which it may be important to anticipate the long-term properties of a material. This includes assessing the extent of stress decay in materials that are pre-stressed, the noise and vibration transmission characteristics of a material, the amount of heat build-up in a material subjected to cyclic deformation, and the extent a material can recover from any prior deformation. Several qualitative graphs are presented, which highlights the possible differences in the viscoelastic behavior that can exist among plastics.

An experimental high-temperature rotary valve was found stuck due to growth and distortion after approximately 100 h. Gas temperatures were suspected to have been high due to overfueled conditions. Both the rotor and housing in which it was stuck were annealed ferritic ductile iron similar to ASTM A395. Visual examination of the rotor revealed unusually heavy oxidation and thermal fatigue cracking along the edge of the gas passage. Material properties, including microstructure, composition, and hardness, of both the rotor and housing were evaluated to determine the cause of failure. The microstructure of the rotor was examined in three regions. The shaft material, the heavy section next to the gas passage and the thin edge of the rotor adjacent to the gas passage. The excessive gas temperatures were responsible for the expansion and distortion that prevented rotation of the rotor. Actual operating temperatures exceeded those intended for this application. The presence of transformation products in the brake-rotor edge indicated that the lower critical temperature had been exceeded during operation.

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.

Following the discovery numerous cracks at many of the welded seams of a mild steel CO2 absorber vessel, a sample for examination was removed from the worst affected area where repairs had been effected. A 12 in. long circumferential crack was visible. Specimens were taken to cover the several locations of cracking which, in all cases, were found to be similar and of the intergranular type filled with oxide or corrosion product. The association of the cracks with the weld seams indicated that contraction stresses from welding were primarily responsible. Failure of the absorber vessel was found to be due to stress corrosion. Although the active agent present was not positively identified, the aqueous solution of monoethanolamine was thought to be the most probable. The origin of the stresses was not elucidated but the association of the cracks with the welded seams indicated inherent residual stresses as being primarily responsible. Tests carried out tend to suggest that stress relief was not carried out. For the replacement plant, consideration of stress relieving or the use of an alternative material was advised.

Mower blades manufactured from grade 1566 high-manganese carbon steel failed a standard 90 deg test. The blades had been austempered and reportedly fractured in a brittle manner during testing. The austempering treatment was intended to produce a bainitic microstructure, but investigation (visual inspection, 2% nital etched 8.9x/196x images) showed that the typical core microstructure contained alternating bands of martensite and bainite. The conclusion was that the nonuniform microstructure was likely responsible for the atypical brittle behavior of the blades, and the observed structure suggests that the austempering heat treatment was performed too close to the nominal martensite start temperature. Recommendations included raising the austempering salt-bath temperature 56 deg C (100 deg F) to account for localized compositional variation.

One of the coils in the radiant section of a primary reformer furnace used in an ammonia plant was found leaking. The bottom of one of seven outlet headers (made of ASME SA-452, grade TP316H, stainless steel) was revealed during examination to be ruptured. It was revealed by metallurgical examination that it had failed as a result of intergranular fissuring and oxidation (creep rupture). The ruptured area revealed that the header had failed by conventional long-time creep rupture as a result of exposure to operating temperatures probably between 900 and 955 deg C. Three samples from different sections (ruptured area, slightly bulged but nonruptured area and visually sound metal) were inspected. The presence of pinhead-size intergranular fissures throughout the cross sections of the latter two samples was observed. An ultrasonic attenuation method was employed to investigate the remaining headers. All headers were revealed by ultrasonic readings to be in an advanced stage of creep rupture and no areas were found to be fissured to a degree that they needed immediate replacement. As a conclusion, the furnace was deemed serviceable and it was established that in the absence of local hot spots, the headers would survive for a reasonable period of time.

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.

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.

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.

Vibration analysis can be used in solving both rotating and nonrotating equipment problems. This paper presents case histories that, over a span of approximately 25 years, used vibration analysis to troubleshoot a wide range of problems.

The broken end of a shaft from a centrifugal pump had a smooth fracture surface characteristic of failure from fatigue. Failure occurred in the plane of the keyway end and followed a slightly helical path, indicating that combined bending and torsional stresses were responsible. The material was a Cr-Mo-Ni alloy steel of the En 19 type in the hardened and tempered condition and of satisfactory quality. The assembly also included a copper sleeve attached by a circumferential braze behind the plane of fracture. The cracks were examined for the presence of copper, thinking that penetration by molten copper may have played a role, but no evidence was seen. An absence of chromium plating at the region of the heat-affected zone was also observed but could not be explained. Unfortunately, the end portion of the shaft was not available for examination.

After about four years of service, cracks appeared on the internal or process-side surfaces of four evaporator pans in a sugar concentrator. The pans consisted of a Mo stabilized austenitic stainless steel inner vessel surrounded by a mild steel steam jacket. Corrosion of the external surface had taken place in the form of confluent pitting over a band adjacent to the fillet weld which attached the pan to the blocking ring. Numerous cracks were present in this corroded zone. Microscopical examination of several specimens cut from the sample revealed that the internal cracks in the pan itself originated from the external side of the plate, i.e. from the region covered by the shrouding ring. They were predominantly of the transgranular type. Because the cracks were not of the intergranular type as usually found with weld decay, they were considered to be indicative of stress-corrosion cracking. Stresses responsible for the cracking resulted from weld contraction. The pans had been hosed down periodically with water from local boreholes to remove sugar from the external surfaces, which introduced the corrosive medium.

A heavily worked 304 stainless steel wire basket recrystallized and distorted while in service at 650 deg C (1200 deg F). This case study demonstrates that heavily cold worked austenitic stainless steel components can experience large losses in creep strength, and potentially structural collapse, under elevated temperature service, even at temperatures more than 300 deg C (540 deg F) below the normal solution annealing temperature. The creep strength of the recrystallized 304/304L steel was more than 1000 times less than that achievable with solution annealed 304H. These observations are consistent with limitations (2000 Addendum to ASME Boiler and Pressure Vessel Code) on the use of cold worked austenitic stainless steels for elevated temperature service.

The purpose of this investigation was to determine the cause of the ultrasonic signal attenuation noted during an inspection of a composite aircraft component. Although ultrasonics was able to identify the location of the defective areas, destructive analysis had to be utilized to determine the exact nature of the defect. The investigation describes how cross-sectioning, fractography, and chemical analysis were utilized to determine the type of defect responsible for the signal attenuation.

This article considers two mechanisms of cavitation failure: those for ductile materials and those for brittle materials. It examines the different stages of cavitation erosion. The article explains various cavitation failures including cavitation in bearings, centrifugal pumps, and gearboxes. It provides information on the cavitation resistance of materials and other prevention parameters. The article describes two American Society for Testing and Materials (ASTM) standards for the evaluation of erosion and cavitation, namely, ASTM Standard G 32 and ASTM Standard G 73. It concludes with a discussion on correlations between laboratory results and service.