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The design curves, such as fatigue design S-N curves, required in engineering designs, are usually constructed by analyzing test data, which often exhibit large scatter. There are many methods available to construct a design curve and many of these methods, with varying degrees of conservativeness, accuracy, and simplicity, have been adopted by engineering standards, codes and guidelines, such as the ASME and ASTM codes and standards. However, to meet the increasing engineering demands, a simplified, user friendly engineering method with rigorous mathematical and physical basis is still urgently needed to accurately manage the margin of safety on one hand and decrease the cost on the other hand. In this paper the current engineering practices for constructing a design curve is reviewed. It is followed by the tolerance limit concept for general regression cases, because of its capability to relate the design curve to sample size, probability, and confidence level. A simple approximate solution is derived for Owen’s tolerance limit approach, which previously could be solved only with a very complex procedure. Finally, recognizing the physical unsoundness of the hyperbolic shape of the design curves constructed with the Owen’s tolerance limit approach, a new simple design curve construction method is proposed based on the “equal partition principle”. The predicted results from the new method are compared with that of other methods and the advantage of the proposed procedure over other methods is demonstrated with several worked examples. Linear design curve construction with heteroscedastic characteristics (variable variance) and nonlinear design curve are also discussed.

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 B S T R A C T Thermal fatigue resistance of materials is an extremely important criterion for the longterm durability and reliability performance of very high-temperature components and systems, such as advanced auto engine and exhaust systems. There is a broad range of material choices for thermal fatigue resistance applications. The final selection of the materials depends on the balance of engineering performance of the materials and the cost. To optimize the thermal fatigue resistance and cost of those materials, a reliable testing procedure for material thermal fatigue characterization and a material evaluation/selection matrix must be established. In this paper, the V-shape specimen testing method in evaluating thermal fatigue resistance performance is introduced first. The influence of several factors, such as the thickness of specimens, operating temperature and hold time, on the thermal fatigue resistance is experimentally investigated. Subsequently, the statistical and probabilistic characteristics of the thermal fatigue failure data are analysed to reveal the possible failure mechanisms. Finally, a general rational approach for thermal fatigue resistance characterization and ranking is demonstrated, and a simple parameter λ = kσ f /Eα, which combines the material strength, thermal conductivity and thermal expansion, is found to be the new breakthrough parameter, correlating to V-shape thermal fatigue test results. Results on four currently used stainless steels verify the correlations and indicate the validity of this approach. , C 3 = coefficients in fatigue life models c = specific heat E = elastic modulus F(x) = cumulative distribution function (CDF) f(x) = probability density function (PDF) g() = function related to hold time H = thickness of the V-shape specimen k = thermal conductivity N f = cycles to failure n = sample size or test number s = sample standard deviation T = temperature T m = melting temperature ΔT = temperature range Δt = hold time W = fixture distance x = a variable λ = thermal fatigue (thermal shock) resistance parameter α = thermal expansion coefficient ρ = density Correspondence: Z. Wei.

V-shape specimen testing is a relatively new, simple and useful technique to characterize the thermal-fatigue resistance of materials subjected to combined thermal/mechanical loadings, and to rank and select materials. However, the V-shape specimen test data, similar to many other life test data, always contain an inherent scatter not only because of material non-uniformity but also of the difficulties in operating control, such as loading, boundary conditions, and environment. Therefore, statistical and probabilistic approaches have to be used to interpret the test data in order to implement the observations into new product designs. In this paper, the V-shape specimen test data are selected, analyzed and the scatter properties of the test data are fitted using several continuous probability distribution functions. The results are compared, and the root failure mechanisms of the V-specimens are also discussed. Finally, the main observations are summarized, and a recommendation is provided.