Cracking threshold of the welded joints subjected to high-cyclic loading/Suvirintuju jungciu pleisejimas veikiant daugiacikliam apkrovimui.

Stonkus, R. ; Leonavicius, M. ; Krenevicius, A. 等

1. Introduction

Parts of large-size mining-industry equipment, which exceeds 10 m in size, are produced for a particular purpose from welded elements. The longevity of such parts exceeds 25 years, and the number of loading cycles enters the giga-cyclic range (N >[10.sup.8] cycles) [1]. Welded joints are weak points in steel constructions, under the sway of cyclic load, corrosion and temperature fluctuation. Different defects in the welded joint and nearby determines the strength to cyclic loading. The durability of the equipment depends on the pattern of crack formation and propagation in these structural elements. Cracks may lead to the failure of the cracked elements or even to collapse of the structures. A large number of fatigue damage cases in welded elements and structures were reported. One of the main operational and technological requirements to welded joints is the compliance of their strength with basic metal.

Modern calculating methods used at initial stages of the crack formation are insufficiently reasoned. Supposedly, the fracturing changes its character. The time of the crack formation determines the longevity of the whole structure. The compatibility of strength, durability and resistance to dynamic loads in a particular material requires additional investigation. In many cases, the applicability of a material depends on such characteristic as impact ductility, brittleness, critical temperature and resistance to formation and propagation of cracks.

Cyclic strength of the welded joints was thoroughly analyzed in [2-6], where tensile deformations in various areas of the weld were considered. Well-known works [3-6] consider the impact of heat-treatment and non-uniformity of the microstructure of welded joints on their static and cyclic strength. Defects of various sizes and forms are found in the welded joints. Welding defects may be external (defects of the joint line) and internal structural defects and flaws of heterogeneous nature. External defects: deepened holes in the basic metal, craters, burned holes and pits in the line of the joint can be defected by visual inspection or by optical devices. Internal defects (inserts of slag, metal inserts, pores, nonwelding, cracks, nonfusion, etc.) can hardly be detected by nondestructive control methods because of their small size. Identified defects or operating cracks can be removed mechanically, i.e. by repairing the welded seam.

[FIGURE 1 OMITTED]

The principles of fracture mechanics [6-8] are applied to evaluate the strength of joints, depending on the nature of the load. The loading of structural elements of mineral mills and problems associated with the formation and propagation of cracks are discussed in [1-8].

2. The experiment

The paper presents the data on fracture toughness to cyclic loads of double-welded, heat-treated and rewelded joints. For experimental-analytical research, three 30 mm thick welded steel plates were chosen. (Fig. 1). Weld quality was checked by nondestructive (optic, ultrasonic and luminescent-magnetic) methods. The joints without defects in the weld were selected. One of the plates has double-V welded joint, the other one--heat-treated joint. In the weld of one of the plates, using nondestructive methods, defects of various forms were detected. The part of welded joints, where the defects were found, was removed by mechanical cutting and the joint was rewelded. No defects were found after repeated checking. Then, the surfaces of the plates were milled to the width of 26 mm. Chemical composition of the welded joints is:

--of the plate: C--0.05-0.06%, Mn--0.82-0.85%, Cr--0.10-0.12%, Ni--0.20-0.22%, Si--0.27-0.29%, Mo--0.05-0.54%, Cu--0.032-0.034%;

--of the weld: C--0.03-0.04%, Mn--1.20-1.25%, Cr--0.036-0.038%, Ni--0.078-0.084%, Si--0.300.32%, Mo--0.030-0.034%, Cu--0.18-0.21%.

Scheme of cutting specimens from all plates are shown in Fig. 2.

Microstructure of all the plates was studied at 6 points as indicated in Figs. 3-6. The microstructure: a) basic metal--pearlite, ferrite; b) transitional layers--ferrite, pearlite, carbide; c) weld--pearlite, ferrite, (nonhomogeneos material).

[FIGURE 2 OMITTED]

[FIGURE 3 OMITTED]

[FIGURE 4 OMITTED]

[FIGURE 5 OMITTED]

Cylinder samples (the initial diameter [d.sub.0] = 10mm, original gauge length [L.sub.0] = 40mm) made of the basic metal and weld seam were investigated to establish the mechanical properties (according LST EN 10002-1:2003 en). Table 1 presents the main properties of the basic and weld metals.

[FIGURE 6 OMITTED]

For determining the dependence of crack growth rate on the range of stress intensity factor, the methods of ASTM E 647-00 were applied and modified. Compact specimens (CT) were cut out of steel plates under the investigation with a slot orientated differently to the plate and weld axes. For producing diagrams, 2-6 compact samples of each plate and welded joint were tested.

The schemes of crack propagation of the samples are shown in Fig. 7.

[FIGURE 7 OMITTED]

3. Analysis of experimental results

The range of stress intensity factor was calculated according ASTM E 647-00 to the following formula

K = (F/[BW.sup.1/2])f([lambda]) (1)

[lambda] = a/W (2)

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.] (3)

where [DELTA]K = [K.sub.max] -[K.sub.min] is stress intensity factor range; r = [F.sub.min]/[F.sub.max] = [K.sub.min]/[K.sub.max] is stress ratio; [K.sub.min] and [K.sub.max] are minimum and maximum stress intensity factor in the cycle of loading.

Nominal stresses in the top of the crack

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.] (4)

or

[sigma] = (2F / BW)(2 + [lambda])/[(1 - [lambda]).sup.2] (5)

where F are axial force; M = F[a + (W - a)/ 2] is bending moment; A = (w -a)B is area of netto cross-section; Z = [[(W - a).sup.2]B]/6 is section modulus; a is crack length.

Experiments are performed using the regulation methodology, when the cycle asymmetry is r [approximately equal to] 0. On purpose to apply the experimental data for practical calculation, the variation of the cycle asymmetry coefficient must be estimated.

Cracking thresholds at different cycle asymmetry coefficients interrelate such dependence

[DELTA][K.sub.th] =[DELTA][K.sub.th0][(1 - r).sup.[gamma]] (6)

where [DELTA][K.sub.th] is threshold stress-intensity range, [DELTA][K.sub.th0] is limit interval of the stress-intensity factor, when r = 0, [gamma] - a coefficient, which depends on the material and fluctuates from 0.5 up to 1.

The cracking threshold, when r = 0, can be calculated by

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.] (7)

The cracking threshold stress-intensity range at any positive cycle asymmetry coefficient can be calculated as follows

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.] (8)

where r is current cycle asymmetry, [r.sub.th] is cycle asymmetry, at which the cracking threshold was established.

The stress range that is in accordance with the threshold stress-intensity factor range and estimate cycle asymmetry

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.] (9)

The formula is valid when r > 0.

The stress intensity threshold [DELTA][K.sub.th] was established in the case of stress ratio r [approximately equal to] 0.05. The diagrams of crack growth rate versus the range of stress intensity factor were compiled and the stress intensity threshold [DELTA][K.sub.th] was defined. The diagrams of the crack growth rate versus the range of stress intensity factor are shown in Figs. 8-15.

The dependences between the crack growth rate and stress intensity factor range for CT specimens of double welded joints, when fatigue crack growth is perpendicular to the weld, are: [DELTA][K.sub.th] = 14-20 MPa [square root of (m)] at v = [10.sup.-10] m/cycle and [DELTA][K.sub.th] = 13.6-20.2 MPa [square root of (m)] at v = [10.sup.-11] m/cycle (Fig. 9).

[FIGURE 8 OMITTED]

[FIGURE 9 OMITTED]

[FIGURE 10 OMITTED]

The dependences between the crack growth rate and stress intensity factor range for CT specimens of double welded joints, when crack growth is along the weld, are: [DELTA][K.sub.th] = 6.9-8.3 MPa [square root of (m)] at v = [10.sup.-10] m/cycle, [DELTA][K.sub.th] = 5.9-8.1 MPa [square root of (m)] at v = [10.sup.-11] m/cycle (Fig. 10).

The dependences between the crack growth rate and stress intensity factor range for CT specimens of heat treatment joints are: [DELTA][K.sub.th] = 7.6-8.2 MPa [square root of (m)] at v = [10.sup.-10] m/cycle and [DELTA][K.sub.th] = 6.4-8.0 MPa [square root of (m)] at v = [10.sup.-11] m/cycle (Fig. 12).

[FIGURE 11 OMITTED]

[FIGURE 12 OMITTED]

The dependences between the crack growth rate and stress intensity factor range for CT specimens of rewelded joints, when fatigue crack growth is perpendicular to the weld, are: AKA = 23-27 MPa [square root of (m)] at v = [10.sup.-10] m/cycle and [DELTA][K.sub.th] = 20-28 MPa [square root of (m)] at v = [10.sup.-11] m/cycle (Fig. 14).

[FIGURE 13 OMITTED]

The dependences between the crack growth rate and stress intensity factor range for CT specimens of rewelded joints, when crack growth is along the weld, are: [DELTA][K.sub.th] = 8.9-12.6 MPa [square root of (m)] at v = [10.sup.-10] m/cycle, [DELTA][K.sub.th] = 7.6-12 MPa [square root of (m)] at v = [10.sup.-11] m/cycle (Fig. 15).

[FIGURE 14 OMITTED]

[FIGURE 15 OMITTED]

Fig. 16 presents boundaries of the crack resistance of differently obtained welds, when crack growths are along or near the weld.

[FIGURE 16 OMITTED]

Fracture surface of CT specimens is shown in Fig. 17. It depends on the structure of the material and discontinuation of cracking. The mechanism of decomposition changes at the top of the crack. The crack front of the CT samples follows the main patterns of the fatigue crack. Fragile and tough zones are found in the static fracture area.

Since specimens are ductile (Z [approximately equal to] 70%), then, given the static loading (when specimens break) the stress state is two-dimensional. The fracture develops according to the plastic shear mechanism. Surfaces of fractures are oblique; however, some transitional process zone exists.

It is difficult for the crack to propagate in the CT samples with a slot made at the junction of the weld and the basic metal as the front of the crack runs into various structures. The crack passes through the joints and the basic metal, crossing their junction, i.e. the area of incomplete welding.

[FIGURE 17 OMITTED]

Each area has a different structure even after heat-treatment. The portion of the crack passing through the joint falls behind the crack portion passing through the basic metal, with the front of the crack acquiring the shape of a curve. Therefore, a conclusion can be drawn that both the joint and the area of the incomplete welding can withstand the cyclic load. A portion of the static fracture area has fragile and tough zones, and the impact is also made by the metal of the plate and joint.

The data obtained in the present work were used in the calculation of strength and durability of the welds, when the number of loading cycles exceeded [10.sup.8].

4. Conclusions

1. The dependences between the crack growth rate and limit stress intensity factor range for double-welded joints are as follows: fatigue crack grows perpendicular to the weld--[DELTA][K.sub.th] = 13.6-20.2 MPa [square root of (m)] at v = = [10.sup.-11] m/cycle; fatigue crack grows along or near the weld - [DELTA][K.sub.th] = 5.9-8.1 MPa [square root of (m)]at v = [10.sup.-11] m/cycle; for heat-treated welded joints (crack is along--near to the weld) are as follows--[DELTA][K.sub.th] = 6.4-8.0 MPa [square root of (m)] at v = [10.sup.-11] m/cycle; for rewelded joints (crack is along--near to the weld) are as follows--[DELTA][K.sub.th] = 7.6-12 MPa [square root of (m)] at v = [10.sup.-11] m/cycle; crack is perpendicular to the weld--[DELTA][K.sub.th] = 20-23 MPa [square root of (m)] at v = [10.sup.-11] m/cycle. The obtained results show that qualitatively rewelded seam is resistant enough.

2. The results show that cracking threshold perpendicular to the weld is 2-3 times as high as the cracking threshold along the weld. If the crack grows perpendicular to the welded joint, it impedes crack opening, thereby increasing stress intensity factor.

3. The obtained results are necessary to improve the welding technology to base calculation methods and insure strength of constructive elements.

Received January 21, 2009

Accepted March 31, 2009

References

[1.] Jones, S.M., Svalbonas, V. Large-size crushing mills. -Mining industry, 2003, p.2-7 (in Russian).

[2.] AWS D 1.1:2000. An American National Standard. Structural Welding Code--Steel. 1999.

[3.] Daunys, M., Stulpinaite, A. Statistical evaluation of low cycle durability for corrosion and heat-resistant steels welded joints materials at room and elevated temperature. -Mechanika. -Kaunas: Technologija, 2009, Nr.1(75), p.13-18.

[4.] Vishniakas, I. Special features of breaking the welded connections of the ferritic steels. -Mechanika. -Kaunas: Technologija, 2008, Nr.3(71), p.66-71.

[5.] Vaiciulis, D., Brazenas, A. Stress strain state of mechanically heterogeneous welded joint with mild square butt weld subjected to elastic pure bending.-Mechanika. -Kaunas: Technologija, 2007, Nr.1(63), p.5-10.

[6.] Panasiuk, V.V., Savruk, M.P., Jarema, S.J., Makhutov, O.N., Romaniv, O.N., Andreikiv, A.E. et al. Fracture Mechanics and Strength of Materials. -Kiev: Naukova dumka, 1988-1990. v.1-488p.; v.2-620p.; v.3-436p.; v.4-680p. (in Russian).

[7.] Ziliukas, A. Strength and Failure Criteria. -Kaunas: Technologija, 2006.-208p. (in Lithuanian).

[8.] Daunys, M. Cyclic Strength and Durability of Structures. -Kaunas, Technologija, 2005.-288p. (in Lithuanian).

R. Stonkus *, M. Leonavicius **, A. Krenevicius ***

* Vilnius Gediminas Technical University, Sauletekio al. 11, 10223 Vilnius, Lithuania, E-mail: [email protected]

** Vilnius Gediminas Technical University, Sauletekio al. 11, 10223 Vilnius, Lithuania, E-mail: [email protected]

*** Vilnius Gediminas Technical University, Sauletekio al. 11, 10223 Vilnius, Lithuania, E-mail: [email protected]

Table 1
Mechanical properties of the plate and the weld

Indexes                                Plate 1, 2, 3   Weld 1, 2, 3

Hardness (BHN)                            126-131        147-159
Lower yield strength [R.sub.eL], MPa      260-278        360-370
Upper yield strength [R.sub.eH], MPa      274-301        380-385
Tensile strength [R.sub.m], MPa           416-428        440-475
Modulus of elasticity E, GPa              210-215          211
Percentage reduction of area             66.6-74.5        75-78
at fracture Z, %
Percentage elongation at                 34.8-40.4       33.9-35
fracture [A.sub.t], %