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Evaluation of Metal failure Criteria in the Conditions of Complex Loading E.Kossyh, N.Babich Research laboratory for Problem of Strength and Resourcesavings Contact

Abstract

This paper presehts the experimental data of the study into the laws of crack propagation and toughness characterictics under mode I, mode III ahd mode 1 + mode III loading and crack propagation.

1. NOMENCLATURE

K = stress intensity factor, (SIF), MPa Ö m;
K_ic, K_iiic = critical stress intensity factor under plain strain conditions, MPa√m;
K_fc = critical stress intensity factor under cycling loading, MPa√m;
K_th = threshold stress intensity factor, MPa√m;
K_max = maximum stress intensity factor in a cycle, MPa√m;
n, C = coefficients in the Pparis equation;
P = load, N;
N = number of load cylces;
N_p = number of cycles fracture;
n = Ppoisson's ratio;
M_b, M_t = bending moment and a torque, N m;
da/dn = crack growth rate, m/cycle.

2. INTRODUCTION

Fatigue crack growth laws under mode I loading conditions have been studied in considerable detail. At present, the laws of material fracture under static loading in mode I, mode II, mode III and their different combinations are under active study. Quite a lot of results of studies have been published concerning the laws of material fracture under cyclic mode II and mode I + mode II loading [1-4].

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 (K_IIIth K_Ith, K_Ieqth) ahd critical (K_Ifc, K_Ic, K_IIIfc, K_IIIc, K_eqfc) 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 (K_IIIth, K_Ith, K_Ieqth) ahd critical (K_Ifc, K_Ic, K_IIIfc, K_IIIc, K_eqfc) stress factors for a number of structural steels and cast iron under static and cylclic loding.

3. MATERIALS AND SPECIMENS

Investigations were conducted, on specimens made of four grades of steel and cast iron. The steels fall into a group of alloyed structural steels: 40Kh is a chromium steel, 18KhGT and 25KhGT are chromium-manganese steels; 15Kh2MFA(II) is a chromium-molybdenum-vanadium steel. S120 cast iron is classified among gray cast irons with a flaked graphite. These materials differ by their properties and purpose and are used in parts and structures subjected to the action of cyclic complex loads.

4. EXPERIMENTAL RESULTS AND ANALYSIS

Laws of crack propagation. The analysis of specimen surfaces in cyclic torsion and bending-torsion (mode III and mode I + mode III) tests has shown that surface macrocracks initiate as a result of cyclic slip in grains most favourably oriented to the direction of maximum shear stresses.

In propagation of fatigue cracks from the initiation to final fracture distinguished are a few stages:

• the initial stage. Propagation of surface microcracks in the plane of maximum shear stresses which is the process of a shear type;
• the propagation of the main crack coincides with the direction of the action of maximum normal stresses. Fracture occurs by tearing;
• the propagation of the main crack occurs in the plane of maximum shear stresses. Fracture occurs by shear.
The analysis of the experimental data, obtained shows that mechanical loading parameters and criteria alone are insufficient to determine crack growth mechanisms in modes other than mode I.

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
properties	18KhGT	25KhGT	40Kh	15Kh2MFA
bending loading
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
n	1,23	2,68	4,5	3,04	7,39
C	6,5.10-8	2,8.10-12	2,6.10-15	9.10-12	1,2.10-18
torsion loading
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
n	1,69	2,01	4,94	1,68	2,37
C	2,2.10-8	9,2.10-9	1,1.10-11	1,3.10-9	3,8.10-8
bending-forsion loading
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
n	1,86	3,59	2,66	3,81	6,01
C	4,3.10-10	2,7.10-12	1,8.10-10	6,2.10-12	1,5.10-15
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 K_th, and K_fc, (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.[5], construction of diagrams on coordinates K_II/K_Iic - K_I/K_Iic is proposed.

These diagrams show the combination of K_I and K_II necessary for the initiation of mode I or mode II fracture.

Figures 2 and 3 present experimental dependencies on coordinate K_III/K_Ic - K_I/K_Ic and K_III/K_IIIc - K_I/K_IIIc (static loading) and K_IIImax/K_Ifc - K_Imax/K_Ifc and K_IIImax/K_IIIfc - K_Imax/K_IIIfc (cyclic loading) which, according to [5], show the combinations of K_I and K_III, as well as K_Imax and K_IIImax 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 K_I and K_III 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 K_III/K_Ic » 0.18...0.24 or mode I crack propagation is possible only when K_III<K_Ic / 4,2 ≈ 0.24 K_Ic.

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 K_III/K_IIIc - K_I/K_Ic 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 K_Ic, K_IIIc, K_Ifc, K_IIIfc:
the failure by breaking away

failure by longitudinal shift

In Fig.5. two-criteria diagrams are given. They show the tendencies of changing the rellationship of threshold K_Ith and K_IIIth, and the critical K_Ifc and K_IIIfc 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 K_Ith, K_IIIth, K_Ifc and K_IIIfc.
failure by breakind away

failure by londitudinal shift

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

Comment: «+» increase, «- » decrease characteristion

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 K^t_th, 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 K_th 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.

5. CONCLUSION

The sudy of the laws of crack propagation and fracture toughness characteristics in steels 18KhGT, 25KhGT, 40Kh, 15Kh2MFA(II) and SCh20 iron under mode I, mode III and mode I + mode III loading was performed with the following results obtained:
1. The propagation of fatigue main cracks under mode III and mode I + mode III loading of materials has a complex nature and the mechanism of their growth cannot be determined on the basis of the mechanical criteria alone.
2. The presence of a shear component in the external load reduces the capability of materlas to resist FCG.
3. The magnitude of K_IIIfc for different structural alloys and different values of the external load parameters is 0,5 K_Ifc.
4. An attempt has been made to determine the combinations of K_I ahd K_III, as well as K_Imax and K_IIImax needed for mode I or mode III fracture initiation.
5. the application of the method of hardness for predicting the chandes of material characteristics, which are responsible for a long safe maintenance of constructions and equipment, requires further developmeht.

6. REFERENCES

1. Ichikawa M. and Takamatsu T. Fracture tougness testing for sheet speet speciment under mode II loading. Bulleting of JSME vol.28, N.246, (1985), 2867-2872.
2. Willians J.G. and Birgh M.W. Mixed mode fracture in anisotropic media. Cracks and Fracture, FSTM STP GO1. (1976) 125-137.
3. Tong J. and Wang J. A new engineering method for the measurement of stress intensity factor of I-II combined mode cracks. Proc.Int.Conf.Exp.Mech.Beijing. Oct.7-10. 1985 - Beijing (1985) 957-962.
4. Saouma V.E., Ayari M.L. and Leavell D.A. Mixed mode crack propagation in homogeneous anistropic solids. Eng.Fract.Mech. vol.27, N.2, (1987), 171-184.
5. Melin S. Fracture from a straigth crack subjected to mixed mode loading. Int.J.Fract. Vol.32 (1987) 257-263.

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