Fulun Yang

Equilibrium Based Curve Fitting Method for Test Data With Nonuniform Variance

A recently developed equilibrium based curve/surface fitting method is extended to linear function with heteroscedastic data (variable variance). The concept of equilibrium weighted ‘force’ and ‘moment’ is proposed to derive curve fitting formulae, which are exactly the same as that obtained with the traditional weighted least squares (LS) method for a linear function. Furthermore, a system of four equations, i.e., a “force” equilibrium equation, a “moment” equilibrium equation, a “equivalency” equation, and a “moment balance” equation have been established to solve both mean curve and the standard deviation simultaneously. Finally, the application of these methods to data of fatigue and creep lives is presented.Copyright

A New Linear Superposition Theory and its Application in Creep Fatigue-Oxidation Crack Growth Modeling

Fatigue, creep, oxidation or their combinations have long been recognized as the principal mechanisms in many high-temperature failures in power plant components, turbine engines, and exhaust systems in vehicles. Depending on the specific materials and loading conditions and temperature, the role of each damage mechanism may change significantly, ranging from independent development to competing and combined creep-fatigue, fatigue-oxidation, and creep-fatigue-oxidation. In this paper a new linear superposition theory is proposed to model the cycle-dependent and time-dependent creep-fatigue-oxidation crack growth phenomena. The model can be reduced to creep-fatigue and fatigue-oxidation crack growth models previously developed by the authors as well as, under some assumptions, the current widely used linear superposition theory. The limits of the current superposition theory and the advantages of the new theory are clearly demonstrated with several worked examples. A general probabilistic analysis procedure is also proposed by introducing the uncertainties of parameters in fatigue, creep, and oxidation crack growth laws with the help of the Monte Carlo simulation.Copyright

Hold-Time Effect on Thermo-Mechanical Fatigue Life and its Implications in Durability Analysis of Components and Systems

Thermo-mechanical fatigue (TMF) resistance of engineering materials is extremely important for the durability and reliability of components and systems subjected to combined thermal and mechanical loadings. However, TMF testing, modeling, simulation, validation, and the subsequent implementation of the findings into product design are challenging tasks because of the difficulties not only in testing but also in results interpretation and in the identification of the deformation and failure mechanisms. Under combined high-temperature and severe mechanical loading conditions, creep and oxidation mechanisms are activated and time-dependent failure mechanisms are superimposed to cycle-dependent fatigue, making the life assessment very complex. In this paper, the testing procedures and results for high-temperature fatigue testing using flat specimens and thermal-fatigue testing using V-shape specimens are reported; emphasis is given to hold-time effects and the possible underlying mechanisms. The uncertainty nature and the probabilistic characteristics of the V-shape specimen test data are also presented. Finally, the impact of hold-time effect on current product design and validation procedure is discussed in terms of virtual life assessment.

A Bayesian Statistics Based Design Curve Construction Method for Test Data With Extremely Small Sample Sizes

Fatigue design curve construction is commonly used for durability and reliability assessment of engineering components subjected to cyclic loading. A wide variety of design curve construction methods have been developed over the last decades. Some of the methods have been adopted by engineering codes and widely used in industry. However, the traditional design curve construction methods usually require significant amounts of test data in order for the constructed design curves to be consistently and reliably used in product design and validation. In order to reduce the test sample size and associated testing time and cost, several Bayesian statistics based design curve construction methods have been recently successfully developed by several research groups. Among all of these methods, an efficient Monte Carlo simulation based resampling method developed by the authors of this paper is of particular importance. The method is based on a large amount of reliable historical fatigue test data, the associated probabilistic distributions of the mean and standard deviation of the failure cycles, and an advanced acceptance-rejection resampling algorithm. However, finite element analysis (FEA) methods and a special stress recovery technique are required to process the test data, which is usually a time-consuming process. A more straightforward approach that does not require these intermediate processes is strongly preferred.This study presents such an approach, in which the only historical information needed is the distribution of the standard deviation of the cycles to failure. The distribution of the mean is directly calculated from the current tested data and the Central Limit Theorem. Neither FEA nor stress recovery technique is required for this approach, and the effort put into design curve construction can be significantly reduced. This method can be used to complement the previously developed Bayesian methods.Copyright

ACCELERATED DURABILITY TESTING AND DATA ANALYSIS FOR PRODUCTS WITH MULTIPLE FAILURE MECHANISMS

Durability and reliability performance is one of the most important concerns of ground vehicle systems, which usually experience cyclic fatigue loadings and eventually fail over time. Creep and oxidation caused damages at elevated temperature conditions further shorten the life of a system and make the life assessment even more complex. One of the key challenges posed to design engineers is to find a way to accelerate the durability tests for products with multiple failure modes and to validate designs within development cycle to satisfy customers and markets requirements. The accelerated testing procedures for products with single failure modes have been studied for several decades and essentially well established even though some fundamental issues are still unsolved. By contrast, much is needed to do for the accelerated testing procedure of products with multiple failure modes and their interactions. In this paper, a new accelerated testing and data analysis procedure suitable for products with linear homoscedastic data pattern is proposed. Examples related to durability life of high temperature components with single failure modes such as fatigue, creep, and oxidation are provided to demonstrate the procedure developed. Durability life assessment of components with multiple failure modes is also investigated and demonstrated with creep-fatigue and fatigue-oxidation damage analyses.

Nodal Force Based Finite Element Method and its Application in Durability Analysis

In the conventional finite element methods, the stresses are obtained from the computed nodal displacements and are thus a derived quantity, which is not accurate. Additionally, equilibrium of resulted element stresses is, in general, not satisfied at every point in the conventional finite element solutions, which is one of the major reasons for severe mesh-sensitivity in stress or strain results. However, the equilibrium of nodal force is always guaranteed in all finite element solutions regardless of mesh sizes. This equilibrium of nodal force provides a good way to recovering stress with improved accuracy, and various methods, including the currently widely used structural stress procedure for fatigue life assessment, have been proposed with varying degrees of complexity and success. In this paper, a new post-processing procedure is proposed to calculate surface traction stress for 3-D solid elements in terms of nodal forces from the conventional commercial finite element analysis software, such as Abaqus and Nastran. The applicability and limitation of the nodal force based method is demonstrated by applying it to two-dimensional and three-dimensional linear elastic continuum solid elements. Finally, its application in durability analysis such as fatigue and creep life assessments is discussed.© 2012 ASME

A Design Approach Based on Historical Test Data and Bayesian Statistics

Testing is still the final verification for a design even though there are substantial number of analytical and simulation methods available. Testing is seen to be also an indispensable part in the foreseeable future. Numerous test data have been generated in many testing institutions over the years and it is clear that future new tests will be conducted. Historical data with similar design and operating conditions can shed light on the current and future designs since they would share some common features when the changes are not dramatic. To effectively utilize the historical data for future design, two steps are necessary: (1) finding an approach to consistently correlate test data obtained from various conditions; (2) Use of Bayesian statistics which can provide a rational mathematical tool for extracting useful information from the historical data.In this paper, the basic Bayesian statistical procedure based on the historical data is outlined. With this information the reduction of sample size number or improving the accuracy and confidence with the same sample size are becoming possible. Examples of utilizing the historical data are also presented and the benefit of using the Bayesian statistics are highlighted.Copyright

Product Durability/Reliability Design and Validation Based on Test Data Analysis

Better quality leads to less waste, improved competitiveness, higher customer satisfaction, higher sales and revenues, and eventually higher profitability. Meeting the quality and performance goals requires that decisions be based on reliable tests and quantitative test data analysis. Statistical process control (SPC) is such a fundamental quantitative approach to quality control and improvement. Walter Shewhart in 1920s and 1930s pioneered the use of statistical methods as a tool to manage and control production.

Equilibrium and Equivalency (E2) Linear Surface Fitting Method for Data With Two Independent Variables

A recently developed equilibrium and equivalency (E2 ) mechanisms based curve fitting method is extended to surface fitting for linear function z = f (x, y) = a + bx + cy with two independent variables x and y. The concept of equilibrium of ‘force’ and ‘moment’ is adopted to derive surface fitting formulae, which are exactly the same as that obtained with traditional least squares (LS) method for the linear function. However, E2 method has obvious physical meaning and therefore is more intuitive in quickly and correctly identifying data pattern and subsequent data analysis. Furthermore, the formula based on perpendicular offsets method in terms of data variation along surface normal direction is derived and the results are compared with the traditional methods. Finally, the application of these methods to data of fatigue and creep lives is presented.Copyright