Search Results for stress analysis equations

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.

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.

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.

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.

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.

Several torsion bars had failed in a projectile weaving machine and were analyzed to determine the cause. Specimens prepared from the damaged components were subjected to visual inspection, hardness testing, chemical analysis, and metallurgical evaluations. The failed torsion bars had been fabricated from spring steel which, according to stress calculations, did not have sufficient torsional strength. Examination of the damaged parts confirmed the finding, revealing that all fractures started at a shoulder radius in an area of high stress concentration. Based on the investigation, the shoulder radius should be increased to alleviate stress and the working torsion angle of the bar should be decreased to improve safety factors.

A wire hoisting rope on a drilling rig failed during a lift, after a few cycles of operation, causing extensive damage to support structures. The failure investigation that followed included mechanical property testing and chemical, metallurgical, and finite element analysis. The rope was made from multiple strands of 1095 steel wire. Its chemical composition, ferrite-pearlite structure, and high hardness indicate that the wire is a type of extra improved plow steel (EEIPS grade). The morphologies of the fracture surfaces suggest that the wires were subjected to tensile overloading. This was confirmed by finite element analysis, which also revealed compressive contact stresses between the wires and between the rope and sheave surface. Based on the results, it was concluded that a tensile overload, due to the combined effect of a sudden load and undersized sheave, is what ultimately caused the rope to fail.

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.

Failures of 10Cr-Mo9-10 and X 20Cr-Mo-V12-1 superheated pipes during service in steam power generation plants are described. Through micrographic and fractographic analysis, creep and overheating were identified as the cause of failure. The Larson-Miller parameter is computed, as a function of oxidation thickness, temperature and time, confirming the creep failure diagnostic.

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.

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.

Several newly developed liquid propane gas (LPG) cylinders made from Fe-0.13C-0.42Mn steel failed, each fracturing in the longitudinal direction. One of the cylinders was thoroughly analyzed to determine the cause. Deep-drawing flaws were observed on the inner wall of the cylinder, oriented in the direction of the fracture and roughly equal in length. Flaws about 1.3 mm deep, steps, and a chevron pattern were observed on the fractured surface as were cleavage facets, revealed by SEM. Hardness was relatively high and the microstructure near the fracture surface appeared elongated. In addition, the stress intensity factor KI calculated from the value of the internal pressure was lower than that estimated by the fracture toughness test. All of this suggests that the tanks were not sufficiently annealed and prone to brittle fracture. The analysis thus proves that cracks initiated by deep-drawing flaws were the primary cause of failure.

Several pressurized air containers (i.e., diving tanks) made of non-heat-treatable Al-5Mg aluminum alloy failed catastrophically. Catastrophic failure occurred when a subcritical stress corrosion crack reached a critical size. Critical crack size for unstable propagation was reached prior to wall penetration, which could have led to subsequent loss of pressure, resulting in explosion of the cylinder. It was recommended that more stress corrosion resistant alloys be used for sea diving applications. Furthermore, cylinders should have a reduced wall thickness that can be determined employing the “leak-before-break” design philosophy, developed using fracture mechanics, to eliminate the possibility of catastrophic ruptures.

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.

Failure of structural polymeric materials under cyclic application of stress or strain is a subject of industrial importance. The understanding of fatigue mechanisms (damage) and the development of constitutive equations for damage evolution, leading to crack initiation and propagation as a function of loading or displacement history, represent a fundamental problem for scientists and engineers. This article describes the approaches to predict fatigue life and discusses the difference between thermal and mechanical fatigue failure of polymers.

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.

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.

Arms bolted to powerline towers were falling off two weeks after installation. Metallurgical and chemical analysis performed on the base metal, weld zone, and heat-affected zone showed acceptable quality material. Residual stress appeared to be responsible for the high failure rate. The sources of residual stress included welding, environment, and assembly operation.

This article reviews the impact response of plastic components and the various methods used to evaluate it.. It describes the effects of loading rate on polymer deformation and the influence of temperature and strain rate on failure mode. It discusses the advantages and limitations of standard impact tests, the use of puncture tests for assessing material behavior under extreme strain, and the application of fracture mechanics for analyzing impact failures. It also develops and demonstrates the theory involved in the design and analysis of thin-walled, injection-molded plastic components.