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Evaluation of Metal failure Criteria in the Conditions of Complex LoadingE.Kossyh, N.Babich
Research laboratory for Problem of Strength and Resourcesavings
Fracture behaviour of structural alloys under cyclic mode III, mode III + mode I, mode III + mode II, mode I + mode II+ mode III loading has been studied insufficiently. Therefore, it seems urgent to investigate the influence of mode III and mode III + mode I loading upon fracture toughness characteristics of structural alloys (fatigue crack propagation laws, threshold and critical values of stress intensity factors).
The aim of the present work is to study the laws of fatigue crack propagation threshold (KIIIth KIth, KIeqth) ahd critical (KIfc, KIc, KIIIfc, KIIIc, Keqfc) stress intensity factor for a number of structural streels and cast iron under static and cylclic loading.
The aim of the presehts work is to study the laws of fatigue crack propagation threshold (KIIIth, KIth, KIeqth) ahd critical (KIfc, KIc, KIIIfc, KIIIc, Keqfc) stress factors for a number of structural steels and cast iron under static and cylclic loding.
In propagation of fatigue cracks from the initiation to final fracture distinguished are a few stages:
|Fig 1: Fatigue crack growth rate as a fuction of Kmax for different mode kink growth: ×18KhGT; ×25KhGT; x 40Kh; +15Kh2MFA(II); Δ SCh20|
Influence of the mode of loading on fracture toughness characteristics. The results of the investigation into the influence of the loading mode on the laws of fatigue crack growth (FCG) and the resistance of the materials studied to FCG are given in Table 1 and in Fig.1 (a,b).
|Material||Steel||Cast Iron SCh20|
|KI c, MpaÖm;||208,4||151,6||123,7||55-60||91,6|
|KI th, MpaÖm;||12,5||15,9||14,1||10||8,1|
|KI fc, MpaÖm;||112,4||87,4||80,1||28||51,6|
|KIII c, MpaÖm;||20,6||10,2||29,9||12,8||10,5|
|KIII th, MpaÖm;||3,1||1,15||2,2||2,1||-|
|KIII fc, MpaÖm;||11,4||7,3||14,7||6,3||8,1|
|Keq c, MpaÖm;||80,3||79,6||69,9||68,5||132,4|
|Keq th, MpaÖm;||8,2||6,9||7,8||7,2||13,8|
|Kqe fc, MpaÖm;||46,2||45,1||36,2||24,8||75,1|
|Table 1: Characterictics of material crack resistance|
The analysis of the results presented shows that under mode III loading the resistance to FCG decreases as well as the values of both Kth, and Kfc, (Table 1). At the same time for 18KhGT and 25KhGT steels under mode III loading and for 40Kh steel under mode I + mode III loading, the resistance to FCG on the first portion of the FCG diagram increases (Fig.1 (a,b)).
FCG diagrams for mode I + mode III loading take an intermediate position between FCG diagrams for mode I and mode III loading. It should be noted that for SCh20 cast iron, is contrast to the group of steels, an increase in the resistance to FCG under mixed mode (mode I + mode III) loading (Fig.l(a,b)) was found experimentally.
Fracture criteria. In ref., construction of diagrams on coordinates KII/KIic - KI/KIic is proposed.
These diagrams show the combination of KI and KII necessary for the initiation of mode I or mode II fracture.
Figures 2 and 3 present experimental dependencies on coordinate KIII/KIc - KI/KIc and KIII/KIIIc - KI/KIIIc (static loading) and KIIImax/KIfc - KImax/KIfc and KIIImax/KIIIfc - KImax/KIIIfc (cyclic loading) which, according to , show the combinations of KI and KIII, as well as KImax and KIIImax necessary for the initiation of mode I or mode III fracture.
|Fig 2: Experimentaly found values of KIII/KIc ahd KI/KIc also KIII/KIIIc ahd KI/KIIIc at fracture (marks according to Fig.1).|
|Fig 3: Experimentally found values of KIIImax/KIfc ahd KInax/KIfc also KIIImax/KIIIfc ahd KImax/KIIIfc at fracture (marks according to Fig.1).|
For each of the materials studied there exists its own combination of KI and KIII which determines the crack growth onset in mode I or mode III, e.g. mode III crack propagation in 40Kh steel is possible only with KIII/KIc » 0.18...0.24 or mode I crack propagation is possible only when KIII<KIc / 4,2 ≈ 0.24 KIc.
|Fig 6: To the Forecast of changing the properties of steel 08X18H12T in the process of long operation.|
The construction of two-parametrical diagram of the failure in the coordinates KIII/KIIIc - KI/KIc proves the conclusions, made by A.Chizhik in his works on the dimorphism of failure at status failure and shows the legitimacy of applying the theory of dimorphism of failure for the cases of cyclic loading (Fig.6.) and the foundary surfaces of failure at the cuclic loading can be approximate with planes having the equation:
It allows to formulate the conditions of failure at the cyclic loading subject to the mechanism of crack propagation and values KIc, KIIIc, KIfc, KIIIfc:
the failure by breaking away
In Fig.5. two-criteria diagrams are given. They show the tendencies of changing the rellationship of threshold KIth and KIIIth, and the critical KIfc and KIIIfc SIF at the transition from loading according, to the scheme of the mode I towards loading according to the scheme of the mode III through loading according to the scheme of the mode III.
|Fig 4:Experimental dependence KIIIfc/KIIIc from KIfc/KIc||Fig 5: Experimental dependence KIIIfh/KIIIfc from KIth/KIfc|
From the diagram in Fig.5 one can see, that for the cases investigated the following inteshold and critical SIF are typical
It permitted to formulate the conditions of failure at the cyclic loading subject to the mechanism of crack propagation and values KIth, KIIIth, KIfc and KIIIfc.
failure by breakind away
and the foundary planes of failure can be appoximated by means of the equation
All the given experimental results prove that the presence of the shift component in the external loading increases the dander of failure and the role the influtnce the shift component to the characteristocs of the cyclic crack resistance should njt be neglected in the strength analysis.
Let's consider the kinetics of changing the properties of stainless steel 08X18H12T in connection with the operation in the conditions of the first coolant loop of water reactor of the atomic power station.
|Characterization||Unit measurement||Mean speed changes|
|Fatigue limit, s-1||MPa/year||+ 2,5|
|Stress intensity factor Ktth||MPaÖm/year||- 2,57 . 10-1|
|Limitary compression||mm/year||- 1,85 . 10-2|
|Stamp size||mm/5 year|
|HB||- 2,1 . 10-2|
|HV||- 3,45 . 10-2|
|Table 2: The average speeds of charging the characteristics of the mechanicaj properties|
In the table 2 the average speeds of charging the characteristics of the mechanicaj properties are given. They are calculated in the supposition that the process of accumulating the fatigue damages is linear according to the given data the first four characteristics can be controlled annually. At least every year of operation is changing them to a such extent that this change can be registered with the help of modern nethods of control, measurement and test/ hardness is the exception: its significant change can be registered only in fave years. It is necessary to note that from the practical point of view hardness has more important value: it can be measured without destructing the object.
Among two investigated numbers of hardess the ball mark becomes more preferable, because the introduction of the ball in the surface gives unmeasuredle less damage than the introduction of the pyramid.
In this connection the figure 6 dives the nomographfor predicted estimation of steel state 08X18H12T in the process of operation. If at the moment of time t* to determine (statically) the sige of the diameter of the ball mark, then jne can set up the suggested values Ktth, s t-1, obtained by the indicated moment of time, which is of great practical interest. At the moment it is not clear whether it is possible to extrapolate this nomograph into the field of operating time, excessing 100000 hours, but theoretically there are no reasons why the given extrapolation is impossible. That is why such an anticipated prediction is made in the Fig.6. It turned out that after 150000 hours of operation the fatigue limit of material at the symmrtrical cycle would reach the value s -1 ≈ 280 Mpa, and the threshhold SIF would be approximately equat to zero (the chart dives the change of Kth for the specimens with the crack propagation from in the circle directon).
We do not give absolute significfnce to this prediction, but we would like to note its usefulness: the operating staff must understand what they have to prepare for, if the pipes from stell 08X18H12T will be still operated in the first loop for some long time.
We note, that from the practical point of view considerale difficulties appear when the material damage is the method of the ball probe. Firstly, one can expect that in time the hardness of the surface layers chandes non-linearly. Secondly, there is an essential scattering of the diameter of the ball mark, and its average value, which is defined in 5 years, still lies in the field of variation d in the former 5 years. Consequently, relativery reliable forecast can be made only according to the static results of measuremehts, byt it is difficult to carry out such measurements in the operations.
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