The research on high-temperature pressure vessels is currently insufficient, while their application in industry has a history of several decades. Most of the high-temperature pressure vessels designed and put into operation in the past were conservative, so now the industrial interface faces a large number of "expired" high-temperature pressure vessels, whose service life far exceeds 105 hours. Whether these pressure vessels can continue to serve safely is a common concern in the industry. On the other hand, there are also some newer containers that, although their design life has not yet expired, have cracks found during regular inspections. In this case, how much residual life can be left and whether welding repair is needed are also concerns for engineers.

The residual life problem can be divided into two categories: the first category is how long the material can still be used after long-term use (under high temperature and stress) without discovering macroscopic cracks; The second type is the discovery of macroscopic cracks, what is the crack propagation rate, and how much time is left to reach the critical size.

（1） Materials without macroscopic cracks found

Non destructive testing is powerless for this material. Surface metallography may not necessarily represent the internal condition of the entire material, therefore, sampling analysis is often necessary.

After sampling, the most honest way is to redo the creep or endurance test. But this kind of experiment takes a long time and cannot solve the urgent decision-making problems in engineering, such as deciding whether to replace it in the next major overhaul. Accelerated testing method has been used in engineering for a long time, which involves increasing the test temperature and stress level, and then extrapolating to the working temperature and stress level. The earliest widely used parameter extrapolation formula was proposed by Larson Miller in the 1950s:

If experiments are conducted at higher temperatures and higher stresses to obtain the relationship curve between P (s) and s, it can be extrapolated to lower temperatures and lower stresses to calculate JR.

Due to the incomplete Larson Miller method, a considerable number of scholars have developed various parameter extrapolation methods in the past thirty years. The overall goal is to extrapolate the life data under actual working temperature and working stress that requires long-term testing through accelerated testing. For materials that have already been used, this is residual life estimation.

In addition to parameter extrapolation, there are other methods for estimating residual life, such as the "creep internal stress method".

（2） Discovery of macroscopic cracks

If macroscopic cracks are found in certain parts of the container or pipeline through non-destructive testing, the nature of the problem has changed and entered the realm of high-temperature fracture mechanics.

Firstly, it is necessary to understand the propagation rate of creep cracks and relate it to a suitable fracture mechanics parameter.

In the early 1970s, Britain conducted creep crack propagation tests using the same materials for accidents caused by creep crack propagation in power plants and the discovery of a large number of cracks. Siverns and Price proposed using the stress intensity factor K to summarize data, and the formula is:

Subsequent studies have shown that using K to summarize creep crack propagation data has a wide dispersion band.

The index (n ≈ 6, often greater than 6) is very high, which affects the accuracy of extrapolation.

In theory, under creep state, materials have high plasticity and toughness, and it is not reasonable to use the linear elastic fracture mechanics parameter K.

In 1976, Landes and Begley proposed a new parameter named C *, and the data induction formula is:

The proposal of C * has a certain theoretical background, and over the past decade, a considerable number of people have received good evaluations of C * through research. From the test results, there are two obvious advantages to using the C * parameter. Firstly, the data dispersion is significantly reduced, and secondly, the index φ (about 0.8) is lower, which is conducive to extrapolation.

However, a major problem encountered in the application of C * is how to calculate the C * value of cracks in actual structures, and research in this area is still in its infancy. In contrast, there are numerous references available for calculating the K value of structural cracks.

The current situation is that using K is unreasonable and incomplete, but it can address urgent issues in engineering; The use of C * is reasonable and the data induction is relatively regular, but it is quite difficult to apply in engineering. I believe there will be new progress in the next few years or a decade.