Prediction of the Cyclic Life of Pieces with Macrocracks by Thermographic Method

To improve the accuracy for prediction of cyclic life of pieces with macrocracks we propose to use a new thermographic method. Traditionally this question is solved on the basis Paris formula which connects the speed of crack growth (SCG) with Stress intensity factor K. However parameter K is not identical to the SCG because K doesn’t consider non-linear processes at the top of crack (TC). That is why the using K gives the considerable error. For overcoming this problem we proposed instead of K to connect SCG with another diagnostic parameter, such as ( ) 1 —increment of specific entropy for cycle (ISE) at the TC, which can be calculated with sufficient accuracy through passive temperature field on the surface of tested object. Parameter ISE can be obtained both simultaneously with building of a kinetic fatigue diagram and on the basis of measuring of temperature under exploitation of piece. In both cases the prediction of cyclic lifetime is much higher than with the help parameter K. Besides parameter ISE allows to follow the crack development inside tested object. This means that suggested parameter ISE is more universal and convenient than traditional parameter K.


Introduction
Under cyclic deforming of pieces with macrocrack and certain conditions some plastic domain in top of crack is appeared. As a result the crack begins its movement. As it is known, under plastic deforming of metals the most part of mechanical energy is transformed in the heat energy. Therefore, a heat source DOI: 10.4236/opj.2018. 86015 166 Optics and Photonics Journal arises at the top of a growing crack. Because of high heat conductivity of metals these heat sources form a passive thermal field on the surface of testing object, which characterizes the irreversible changing in the material and has a lot of information about damaging processes. This information can be received without contact with investigated object by using up-to-date infrared equipment allows to fix the kinetics of temperature distributions near top of crack with high precision. Thermographic method, based on that phenomenon, has some advantages in comparison with traditional approaches. These advantages consist in a higher accuracy and universality, because thermographic method sufficiently enlarged range of tested pieces [1]- [7]. Note also, that Stress intensity factor K is attribute

Objectives and Method of Research
The main problem in the thermographic method is correct choice of damage parameter. Such natural parameter is temperature. But there is essential moment.
It is necessary to calculate not itself temperature in the domain of damage, but its change for sufficiently small interval of time, let us say, for one cycle of oscillation. In that case influence of background's temperature is practically excepted.
As direct damage's parameter we use gives dependence n(l) allowing to calculate the lifetime of the piece n − n 0 , which corresponds to the crack growth at a critical length l c .
It must be noticed that using SIF as criterion of crack growth is often criticized at last years. SIF is attribute of linear elastic medium and using it as parameter of destruction not takes into account of many factors which have influence on the events near top of crack. It leads to essential, often unpredicted errors in cyclic life calculation.
Besides we notify the some limitations on using formula (3). These limitations connect with necessity of receipt function K max (l). It leads to using of standard details for which function K max (l) is certain. In case of cyclic life prediction for non standard pieces, that function can be received by experiment. Bun in that case it is necessary overcomes essential difficulties, connected with measuring length of growing crack especially if the crack grows inside detail.
These difficulties to some extent are softened and overcame under using as damage parameter ( ) 1c S ∆ -increment that part of specific entropy, produced in damage domain, which caused it's direct heating [13] [14]: here c v -specific heat capacity of material, Т 1 and Т 2 -temperatures of domain at the beginning and end of given cycle.
Our investigations show that under using thermographic method it is conveniently to keep structure of (2). Corresponding formula lead to For prediction of cyclic life Formula (5) must be integrated and after that critical growth of crack c l ∆ , corresponding cyclic life c n , is determined: We tested some samples, produced from various materials under different loads and built kinetic fatigue diagrams (Figure 1) on the basis Formula (5).
These diagrams have qualitatively the same form as corresponding diagrams built by Paris Formula (2), but our diagrams allowed to define the parameters of materials not only tested samples.
On the Figure 1 where β and α-empirical coefficients.
Dependence (7) under constant oscillation's amplitude can be received by two methods: • direct from diagram ( Figure 1); in that case function must be considered as characteristic of material and prediction of cyclic life will be probable; • by testing givens ample under some small cycles of loading (so keep the cyclic life), or by observing for detail under its exploitation; in that case ( ) ( ) 1c n S ∆ will be characteristic of given sample and prediction of cyclic life will be individual.

Results of Experiments
All tested samples are brought to destruction, and as result its actual cyclic life n f is defined. Cyclic life, calculated from experiment, is defined by first method ( 1 e n ) and by second one (n e ). After that it is counted divergence δ between 1 e n , n e and n f .
The results both experiment and calculation for one sample are showed in Table 1.  With multistage loading, it is possible to consider various tasks for determining a cyclic resource. In particular, the task can be put as: the numbers of cycles n i and crack increment on the previous stages of loading are known; it is necessary to calculate the number of cycles to destruction n e on the last stage.
Peculiarity of calculation by Formula (8) consists in necessity to count over again the actual number of cycles from previous stage of loading on equivalent ones on the next stage, proceeding from the same increment of crack.
Let us examine that peculiarity at the example of cyclic life calculation for one sample on the second stage of loading (Table 2).
Second stage: f = 3 mm, n f2 = 1.1 × 10 5 cycles (destruction), ∆l i = 2.31 mm. Let us calculate cyclic life at second stage n e2 and compare it with n f2 . Using Formula (7)  Similar calculation under two-stages loading fulfils for samples № 6-9 and one-stage loading for samples № 1-5, 10 ( Table 2). As it follows from Table 2, error of cyclic life prediction practically not changes.

Analysis of the Results and Conclusions
Elaborated thermographic method for prediction cyclic life of pieces with ma- 3) Considerably widen the range of objects for control, in particular, for pieces, having some difficulties for observation at crack development.