2020 Volume 61 Issue 5 Pages 926-934
This work was motivated by the endeavour to experimentally determine the influence of crack position on the fatigue life of weldments. Plates were cut from a pipe of X52 pipeline steel – 830 mm in diameter and 10 mm in wall thickness – and their contact edges were then prepared for single-bevel butt welds. The plates were then welded by manual arc welding, and separate specimens – 10 mm in width and 5 mm in thickness – were cut from the weldment perpendicularly to the weld bead. The electro-spark method was then used to produce blunt crack discontinuities for the initiation of fatigue cracks. The cracked weldment specimens then underwent cyclic loading at reference force level Fmax = 5.5 kN and stress asymmetry ratio R = Fmin/Fmax = 0.1. The test results made it possible to quantify the effects of the size and position of crack-like discontinuities on weld fatigue life.
Fig. 5 Fatigue fracture surface of specimen (i) 3-2 with a face crack (A), (ii) 4-2 with a root crack (B), and (iii) 4-2 (detail) in position 1 (C).
At the fundamental level, welding consists of using heat, pressure, or a combination of both to bond two pieces of metal together. Welding requires knowledge of basic physics, chemistry, and metallurgy principles. There are a number of welding techniques and a science behind each one of them. The aim of the welding process is simply to produce joints which possess the mechanical properties required for their intended purpose of use. Many experiments were carried out to investigate various parameters in welding for obtaining required properties of the welded joints. For example, Sang-Woo Song et al.1) found that in friction stir welding of dissimilar Al joints the weld formation and mechanical properties of the joints depend on both the material arrangement and conventional welding parameters. Similarly, El-Labban and Mahmoud2) showed that mechanical properties of welds of Al alloy AA6028 and its nanocomposite (reinforced with 2 mass% Al2O3) can be varied by a filler material.
In some cases of welding, residual tensile stresses can be induced in welded joints as a result of shrinkage that is due to thermal contraction during solidification of the weld metal. These stresses can affect the strength and fatigue life of welded joints.3) Many studies have been done on fatigue properties of welded joints. They were aimed at (i) obtaining S-N curves for various combinations of weld geometry, welding conditions and residual stresses, (ii) estimation of fatigue behaviour of welded joints, and (iii) fatigue crack initiation from weld discontinuities and propagation of the cracks. For example, Berge4) investigated fatigue strength of transverse fillet welds in axial loading with the aim of determining the effect of the plate thickness on their fatigue strength. A power law decrease of the fatigue strength with the plate thickness was found for plates of thickness ranging from 12.5 mm to 80 mm. Wide background information on the fatigue lives of welded joints has been given by Maddox.5) He reviewed the behaviour of welded joints under fatigue loading, the role of significant features of welds under fatigue, factors which affect the fatigue process in welded joints, and fatigue failure. Papers concerned with fatigue analysis of welded joints are reviewed in the work of Fricke.6) Chapetti and Jaureguizahar7) attempted to predict the fatigue strength of welded joints on the basis of fracture mechanics, including the behaviour of short cracks. They used experimental results from literature for a comparison. Similarly, Zerbst et al.8) used fracture mechanics to determine the fatigue strength of weldments with fatigue cracks initiating at the weld toes. They also presented some validation examples which comprised different weldment types, two different types of steel, different weld geometries and different stress ratios. Another method for assessment of the fatigue life of welded joints was used by Mikkola et al.9) They used the equivalent crack length method to predict the crack propagation life of a welded joint from initial discontinuity size to the final crack length at fracture. The proposed method has been successfully applied to experimental data. However, owing to only fatigue crack propagation phase considered in fatigue life calculations, the method yields conservative predictions in high cycle fatigue.
The authors10) investigated the fatigue crack initiation life of butt-welded joints in relation to (i) weld geometry parameters like weld toe radius, plate thickness, preparation angle and weld bead flank angle, and (ii) residual welding stresses. The results of the study enabled the authors to develop a mathematical model for prediction of the effects of welding parameters on the fatigue life of welded joints. Similarly, Ohta et al.11) proposed a fatigue crack growth equation for welded structures on the basis of results of investigation into fatigue threshold and high crack growth rate region in several types of welded joints.
After a short excursion into the literature on fatigue life of welds it can be concluded that when dealing with welded structures exposed to cyclic loading, consideration of the effects of crack-like discontinuities potentially present in a weld is an indispensable aspect of evaluating safety of operation. The most reliable way of determining the impact of discontinuities in welded joints on their fatigue life would be to carry out fatigue tests on specimens with natural discontinuities. However, it should be taken into account that such tests cannot be carried out under equal damage conditions since the natural discontinuities in different specimens cannot be assumed to be mutually identical. A way to overcome this problem is to use specimens with simulated discontinuities for an assessment of the effect of weld defects on the fatigue life of welded joint specimens. We therefore carried out an experimental study in which weld defects were simulated by artificial discontinuities (slits) with pre-defined geometry, dimensions and position with respect to the weld seam.
From a longitudinally welded pipe DN 800 (ϕ 830/10 mm, steel X52 according to API) two plates were cut out from sections on both sides of the weld seam, the dimensions of the plates being ∼10 × 250 × 130 mm (thickness × length × width). The contact edges of the plates were prepared for a single bevel butt (a 1/2 V-weld). The plates were then welded up by manual arc welding (ISO 4063-111) with a coated electrode in three layers. A WTU 315.34 welding rectifier was used as the source for the welding current. The root layer was made by an ESAB Vamberk E-B-122 electrode (in accordance with CSN 055020 and CSN 055041) 2.5 mm in diameter. This is an electrode with a basic coating specified for welding root beads of pipelines. Chemical composition of the weld metal: C 0.08, Si 0.3, Mn 1.0; mechanical properties of the weld metal: Re = min 430 MPa, Rm = 500–650 MPa, A5 = min 20%, KCV = min 130 J/cm2 at a temperature of +20°C. An ESAB Vamberk E-B-241 electrode 3.2 mm in diameter (in accordance with CSN 055098 and CSN 055050) was used for welding the filling layer and the top layer. This is an electrode with a basic coating. Chemical composition of the weld metal: C 0.06, Si 0.3, Mn 1.0, Ni 1.0, Mo 0.3; and mechanical properties of the weld metal: Re = 550 MPa, Rm = 620 MPa, A5 = 24%, KV = 130 J at a temperature of +20°C and 40 J at a temperature of −50°C. All electrodes used here were hard dried at 300–350°C for 2 hours. The basic material to be welded was not pre-heated.
Separate specimens 5 mm in thickness and 10 mm in width were cut from the weldment in the direction perpendicular to the weld bead, as is shown in Fig. 1.
Geometry of single bevel butt-welded plates.
Slits for the initiation of fatigue cracks in the welds of these specimens were then produced in either the face side of the weld or the root side of the weld in the transition zone using the electro-spark method. For the relative ease of manufacturing a starting discontinuity and positioning it at the interface between the weld and the parent metal a single bevel butt was used instead of a single - V butt (V-weld). The slits were made on a VUMA VJ-4 cutting machine, using the following parameters: medium – kerosene, wire – Cu 0.3 mm in diameter, cutting rate - 0.5 mm2/min, speed of motion of the wire – 50 mm/s, peak voltage – 240 V, pulse width – 200 µs. The width of the electro-spark slits (blunt cracks) was ∼0.4 mm. Supposing a rounded root of the slit, the root radius was ρ ∼ 0.2 mm. According to Neuber12) we can arrive at the following theoretical stress concentration factors kt: 3.6 for crack depth a = 2 mm; 3.5 for crack depth a = 3 mm; and 3.3 for crack depth a = 4 mm. According to the position and the depth of the electro-sparked blunt crack, the specimens can be distributed into six groups characterized by the position and the depth of the blunt crack. The characteristics of the groups are shown in Table 1. Figure 2 shows a metallographic photograph of specimen 3-1 (Fig. 3) with a face discontinuity.
Metallographic photograph of specimen 3-1 with a face defect (a = 3 mm) and a fatigue crack.
Results of fatigue tests.
The purpose of the fatigue tests was to assess the impact of the depth of a sharp surface discontinuity (a blunt crack) on the residual life of welded joints, and the extent to which the position of the crack is decisive. The fatigue tests were carried out on a high frequency RUMUL vibrophore, working on the resonance principle with a maximum force capacity of 20 kN. Tests were performed in the uniaxial tensile loading regime at the reference force level Fmax = 5.5 kN with stress asymmetry ratio R = Fmin/Fmax = 0.1. Tensile stress corresponding to the force level 5.5 kN was σt = 110 MPa. The resonance frequency was monitored during cyclic loading; a decrease in the resonance frequency indicated the initiation and growth of a fatigue crack from the root of the starting discontinuity. Cyclic loading continued until the depth of the crack reached such a magnitude that further loading of the specimen in the resonance regime was not possible unless the amplitude was drastically reduced. This happened when the crack depth was approximately 70% of the width. The results of fatigue tests on the specimens in groups 1 through 6 are presented in Fig. 3. Specimen no. 5-3 was not taken into account when evaluating the results because the electro-spark slit was wrongly positioned a few millimeters away from the weld metal - parent metal interface, i.e. in the transition zone. Specimen no. 1-3 was also not taken into account because it was cycled at a maximum load level of Fmax = 7.0 kN due to a mistake made by the operating personnel.
The authors are aware of residual welding stresses which could affect the results of the fatigue tests. However, at this stage it is worth noting that the technology of manufacturing the fatigue specimens ensured that longitudinal residual stresses in the weldment were released by cutting thin specimens (5 mm in thickness) perpendicularly to the longitudinal weld bead. Secondly, eventual transverse residual stresses which could affect the results of the fatigue tests were reduced due to cutting the slits for the initiation of fatigue cracks. Owing to this the residual welding stresses in the specimens were neglected when analyzing the fatigue lives of specimens on the basis of fracture mechanics.
The specimens in group 1, with a blunt crack 2 mm in depth in the face side of the weld, exhibited a life in excess of 106 cycles at reference force level Fmax = 5.5 kN. No fatigue crack was initiated at the tip of the face blunt crack even after the application of more than one million cycles. However, a crack was initiated in the weld root where no starting blunt crack was present. It is interesting to note that fatigue damage took place at the tip of the face blunt crack in specimen 1-3 which was cyclically loaded at the level Fmax = 7.0 kN (by a mistake of the personnel). This shows that when cyclic loading is applied at the reference force level, the fatigue strength of a welded joint is not crucially influenced by a discontinuity 2 mm in depth artificially produced in the face part of the weld. Conversely, the critical location for the initiation of a fatigue crack is the weld root. In the specimens in group 2, all fatigue cracks were initiated at the tips of blunt cracks situated in the weld root. The average life of the specimens was ∼105 cycles.
4.2 Specimens in groups 3 and 4An average life of ∼500 000 cycles was found for the specimens in group 3 (see Fig. 3), and all fatigue cracks were initiated at the tip of face blunt cracks. Unlike for the specimens in group 1, a blunt crack 3 mm in depth is here the decisive discontinuity for the strength reliability of the weld for the given loading regime. The specimens in group 4 with blunt cracks of the same depth as for the specimens in group 3, but positioned in the weld root, had a life of only ∼25 000 cycles. In the following text the ratio of the fatigue life of a weld with a face blunt crack of a certain depth to the fatigue life of a weld with a root blunt crack of the same depth will be referred to as the life ratio. A comparison of the lives of the specimens in groups 3 and 4 shows that the life ratio is approximately 20. This means that the life of a weld with a weld root crack 3 mm in depth is only 5% of the average life of a weld with a discontinuity of the same depth positioned in the face part of the weld.
4.3 Specimens in groups 5 and 6The life of the specimens in groups 5 and 6 with blunt cracks 4 mm in depth is significantly less than in the case of the specimens in groups 1 and 2 and in groups 3 and 4. The specimens in group 5 with face cracks in the welds exhibit an average life of ∼90 000 cycles, while the specimens in group 6 with root cracks in the welds exhibit an average life of ∼9 000 cycles. The life ratio between them is therefore ∼10. A comparison between the life ratio for the specimens in groups 5 and 6 and the life ratio for the specimens in groups 3 and 4 shows that the relative danger (expressed by the life ratio) of a discontinuity 4 mm in depth in a weld root is lower than for a discontinuity 3 mm in depth, but that such a discontinuity in a weld root is approximately 10 times more dangerous than a similar discontinuity in the weld face. Thus, the life of a weld with a 4 mm deep crack in the weld root is only 10% of the life of a weld with a 4 mm deep crack in the weld face.
4.4 Some notes on the experimental resultsThe weld lives for cyclic loading with maximum force Fmax = 5.5 kN are demonstrated by the points in Fig. 4 in relation to the position and depth of the blunt crack. The probable courses of the average lives of specimens in groups 1 through 6 are represented by solid lines. Figure 4 shows that fatigue life decreases with increasing crack depth more rapidly for face cracks than for root cracks, so that the life ratio decreases with increasing crack depth. Even a small crack in the weld root considerably reduces the life of the weld, while a blunt crack 2 mm in depth in the weld face does not seem to be an initiatory discontinuity for the rise of a fatigue crack. Thus, in the case of a blunt crack 2 mm in depth, the specimen behaves as if there were no discontinuity in the weld face. A fractographic examination of fatigue fracture surfaces was carried out to provide more detailed insight into the significant differences in lives between specimens with a weld face discontinuity and specimens with a weld root discontinuity. The fracture surface of specimens 3-2 (A), 4-2 (B), and 4-2 in position 1 (C) is shown in Fig. 5.
The lives of welds with blunt cracks in cyclic loading with Fmax = 5.5 kN, R = 0.1.
Fatigue fracture surface of specimen (i) 3-2 with a face crack (A), (ii) 4-2 with a root crack (B), and (iii) 4-2 (detail) in position 1 (C).
Photo C represents the character of striations in position 1 of specimen 4-2. A similar photo of striations in specimen 3-2 was also taken and striation spacings from these photos were investigated. It was found that the average striation spacing is roughly 2 × 10−7 m, both for face cracks and for root cracks. Considering (i) the distance over which a fatigue crack has to grow in specimens 3-2 and 4-2 to reach the final fracture (4 mm), and (ii) the striation spacing 2 × 10−7 m, it can be calculated that a face crack grows by the length of the striation spacing approximately in each twenty second cycle, whilst a root crack grows by the same distance in almost each cycle. This point will be discussed shortly in paragraph 6.4.
Welded joints are neither homogeneous nor isotropic, hence fatigue crack growth is affected by the properties of the regions surrounding a weld as well as residual stresses. Reference is generally made to three basic regions. These are the base material, the weld’s heat affected zone (HAZ) and the weld metal. It is widely accepted that these regions may have differing mechanical properties. Nevertheless, for the sake of the argument we shall consider that a fatigue crack in a 1/2 V weld grows through the width (the thickness of the initial weldment) in the HAZ. As for the residual welding stresses, these can be neglected due to the arguments made in the previous text.
Now consider a fatigue specimen in the grips of a fatigue machine (upper part of Fig. 6). Because of the natural curvature of the specimen there will be bending stresses σb besides the tensile stress $\sigma _{t} = \frac{P}{Bw}$ acting on the specimen during application of the force P. This means that there is combined bending and tension of the specimen. The maximum tensile component of the bending stress will be at the internal surface of the specimen (as considering the pipe), and the maximum compressive component of the bending stress will be at the outside surface of the specimen. The bending moment is given by Pe where e – eccentricity is the distance of the specimen’s central cylindrical surface from the plane passing through intersections of the central cylindrical surface with the edges of the grips (force line). An equivalent to this model is a single edge notch specimen pin-loaded eccentrically by a tensile force with eccentricity e (lower part of Fig. 6). The length of specimens outside the grips (l) in tests was approximately 60 mm, and the mean pipe radius was R = (D − t)/2 = (830 − 10)/2 = 410 mm.
Schematic representation of a specimen in the grips of the fatigue machine (upper part of the figure) and substitution of the specimen by a single edge notch (SEN) specimen off-centre pin-loaded in tension (lower part of the figure).
Knowing this data and supposing the same curvature of the specimens as that of the pipe, the magnitude of the eccentricity e can be readily obtained:
| \begin{equation*} e = R - \sqrt{R^{2} - (l/2)^{2}} \end{equation*} |
The corresponding bending moment is then M = Pe = 5500 × 1.1 = 6050 Nmm. The section modulus is given by $W_{b} = \frac{Bw^{2}}{6}$. After substituting for B = 5 mm and w = 10 mm into this expression we can arrive at Wb = 83.3 mm3. The bending stress then will be $\sigma _{b} = \frac{M}{W_{b}} = 72.6$ MPa.
5.2 Determination of stress intensity factorsThe basic quantity which we will need to determine before calculating fatigue lives of the specimens is the stress intensity factor KI (opening mode). We shall proceed on the basis of the principle of superposition, i.e. we shall determine independently the KI factor for the tensile stress and then the KI factor for the bending stress. To distinguish between stresses acting on the specimens we shall suffix K by t for tension and by b for bending. Finally we shall sum the magnitudes of Kt and Kb to obtain the K factor for combined loading.
A schematic representation of tensile loading and bending loading of an SEN specimen is shown in Fig. 7.
Single edge crack tension specimen (A) and single edge crack bending specimen (B).
According to Tada and Paris13) the Kt factor for SEN specimens loaded over the width of the specimen (Fig. 7(A)) can be expressed by eq. (1)
| \begin{equation} K_{t} = \sqrt{w} \sqrt{\pi \frac{a}{w}}\sigma_{t}\,f_{t}(a/w) \end{equation} | (1) |
| \begin{equation} f_{t}(a/w) = g(a/w)\left[0.752 + 2.02\left(\frac{a}{w} \right) + 0.37\left(1 - \sin \frac{\pi a}{2w} \right)^{3} \right] \end{equation} | (2) |
| \begin{equation} g(a/w) = \cfrac{\sqrt{\cfrac{2w}{\pi a}tg\biggl(\cfrac{\pi a}{2w} \biggr)}}{\cos \biggl(\cfrac{\pi a}{2w} \biggr)} \end{equation} | (3) |
Again, according to Tada and Paris13) the Kb factor for SEN specimens (Fig. 7(B)) can be expressed by eq. (4)
| \begin{equation} K_{b} = \sqrt{w} \sqrt{\pi \frac{a}{w}}\sigma_{b}f_{b}(a/w) \end{equation} | (4) |
| \begin{equation} f_{b}(a/w) = g(a/w)\left[0.923 + 0.199\left(1 - \sin \frac{\pi a}{2w} \right)^{4} \right] \end{equation} | (5) |
The inaccuracy of eq. (4) is less than 0.5% when bending stress is linearly distributed across the thickness passing zero at the centre plane of the specimen, as shown in Fig. 7(B). The authors are aware of the use of Kb factor for a crack in the compressive stress field. This makes no sense while no tensile stress is acting. However, there is a tensile stress σt = 110 MPa which acts on the welded specimens, so that after adding this tensile stress to the bending stress (according to the principle of superposition) the total stress intensity factor can rise above the threshold value for the growth of fatigue cracks.
As a matter of interest we can compare the values of the stress intensity factor, as determined by the above equations, with those published by Gross and Srawley.14) The comparison is made in Table 2 for SEN specimens with width w = 10 mm, thickness B = 5 mm and force P = 5 500 N for the following ratios: e/w = −0.2; −0.1; 0.0; 0.1; 0.2 and a/w = 0.1; 0.2; 0.3; 0.4.
The authors14) used a boundary value collocation procedure in conjuction with the Williams stress function to determine the stress intensity factor Kb for single edge cracks of various depths in specimens subjected to pure bending and then they superposed the values of the stress intensity factor Kt for tension loaded SEN specimens, as determined from the results of authors.15) As follows from Table 2, our results compare quite well with the results of the work14) although they are consistently lower by several tenths of MPa$\sqrt{\text{m}} $.
Now we shall attempt to determine the fatigue lives of welded specimens with sharp slits according to Fig. 3 and will compare them with experimental results. In principle, the lives of all groups of specimens are given by the sum of the number of cycles needed to initiate a fatigue crack in the slit root, Ni, and the number of cycles needed to propagate the crack to the critical (final) depth, Np. If we denote the total number of stress cycles to fracture by Nf, it can be written:
| \begin{equation} N_{f} = N_{i} + N_{p} \end{equation} | (6) |
| \begin{equation} \log N_{i} = 8.760564 - 4.11438\log (\Delta K) \end{equation} | (7a) |
| \begin{equation} \log N_{i} = 8.591455 - 4.11438\log (\Delta K) \end{equation} | (7b) |
| \begin{equation} \log N_{i} = 9.75458 - 3.99568\log \frac{\Delta K}{\sqrt{\rho}} \end{equation} | (8a) |
| \begin{equation} \log N_{i} = 12.397011 - 3.99568\log \frac{\Delta K}{\sqrt{\rho}} \end{equation} | (8b) |
The results of Jack and Price’ investigation into the initiation of a crack at the tip of a sharp notch related to loading specimens in tension. However, in our analysis we also used the results for combined tension and bending by considering the total range of the stress intensity factor ΔK as a sum of the stress intensity factor range for tensile loading ΔKt and the stress intensity factor range for bending loading ΔKb. Taking into account that the radius ρ of the slits was ∼0.2 mm, we only used eq. (7a).
The number of cycles for crack propagation Np can be determined on the basis of the Paris law
| \begin{equation} \frac{da}{dN} = C(\Delta K_{\textit{ef}})^{m} \end{equation} | (9) |
| \begin{equation} \Delta K_{\textit{ef}} = \frac{\Delta K}{(1 - R)^{\gamma}} \end{equation} | (10) |
| \begin{equation*} \Delta K = K_{\text{max}} - K_{\text{min}} = (1 - R)K_{\text{max}} \end{equation*} |
| \begin{equation*} K_{\text{max}} = K_{t} + K_{b} = \sqrt{w} \sqrt{\pi\frac{a}{w}} (\sigma_{t}\,f_{t} + \sigma_{b}\,f_{b}) \end{equation*} |
| \begin{equation} \Delta K = (1 - R)\sqrt{w} \sqrt{\pi \frac{a}{w}} (\sigma_{t}\,f_{t} + \sigma_{b}\,f_{b}) \end{equation} | (11) |
| \begin{equation*} \Delta K = K_{\text{max}} - K_{\text{min}} = (1 - R)K_{\text{max}} \end{equation*} |
| \begin{equation*} K_{\text{max}} = K_{t} - K_{b} = \sqrt{w} \sqrt{\pi\frac{a}{w}} (\sigma_{t}\,f_{t} - \sigma_{b}\,f_{b}) \end{equation*} |
| \begin{equation} \Delta K = (1 - R)\sqrt{w} \sqrt{\pi\frac{a}{w}} (\sigma_{t}\,f_{t} - \sigma_{b}\,f_{b}) \end{equation} | (12) |
It is very likely that the fatigue cracks in the welded specimens under investigation propagated through the heat affected zone. To comply with this assumption we have used Paris law parameters for HAZ in X52 steel welds published by Zahiri et al.17) The magnitudes of these parameters were as follows: C = 1.13 × 10−9 and m = 3.25. Using these Paris law parameters we determined the number of stress cycles Np needed for a fatigue crack to propagate to a limit depth of 0.7 × wall thickness = 0.7 × 10 = 7 mm.
Calculation procedure:
| \begin{equation} N_{p} = \int\limits_{a_{o}}^{a_{\textit{cr}}}\frac{da}{C(\Delta K_{\textit{ef}})^{m}} \end{equation} | (13) |
| \begin{equation} N_{p} = \sum_{i = 1}^{n}\frac{\Delta a}{C(\Delta K_{\textit{ef},\,i})^{m}} \end{equation} | (14) |
| \begin{equation} \Delta a = \frac{a_{\textit{cr}} - a_{o}}{n} \end{equation} | (15) |
| \begin{equation*} a_{\textit{cr}} = 7\,\text{mm} \ \,C = 1.13 \times 10^{-9} \ \, a_{o} = 2, 3, 4\,\text{mm} \ \,m = 3.25 \end{equation*} |
Representation of lives Nf for face cracks.
Representation of lives Nf for root cracks.
For 2 mm deep slits at the face part of the weld the fatigue lives in Table 3 are denoted as >106 which is in keeping with both the experimental data and the calculated results. However, in Fig. 8 the results are plotted as 2 × 106 in order to assign them a concrete value. As follows from Fig. 8 and Fig. 9, the calculated results fall within the range of experimental points with the exception of the specimens with 4 mm deep root slits. In that case the calculated life fell beyond the lower bound of the extent of experimental results. The results represented in Fig. 8 and Fig. 9 show good agreement between predicted (calculated) fatigue lives of specimens and experimental lives.
6.4 A note to the relation between striation spacing and crack growth rateFirst it should be said how we arrived at the stating in paragraph 4.4 that a face crack grew by the length of the striation spacing s = 2 × 10−7 m approximately in each twenty second cycle whilst a root crack in almost each cycle. This was done on the basis of two assumptions: (i) striation spacing keeps constant over the whole distance from a0 = 3 mm to acr = 7 mm; (ii) the number of cycles Np for propagation of a crack from the length a0 = 3 mm to acr = 7 mm can be expressed as the difference between the experimental life Nf and the number of cycles for initiation of a crack Ni, calculated according to eq. (7a), i.e. Np = Nf − Ni. By dividing Np by the number of striations at the distance (acr − a0) we can obtain 22.8 cycles for the striation spacing s = 2 × 10−7 m for the specimen 3-2 and 1.3 cycle for the specimen 4-2.
An idea that a fatigue crack should grow cycle-by-cycle at low growth rates is not now a universal view for that an evidence has been presented which shows that in Al alloys and steels the growth of fatigue crack is intermittent in nature below a growth rate of 2 × 10−7 m/cycle. Among papers which support this view the paper of McEvily and Matsunaga18) and also the paper by Nedbal et al.19) can be cited. In the former publication the authors refer to the diagram in Fig. 10 which is based upon tests conducted by Roven and Nes.20)
Striation spacing vs. measured crack propagation rate for steel.
Striation markings can be observed here over the growth rate range of 10−10 to 10−7 m/cycle. An occurrence of idle cycles at low fatigue crack growth rate follows from the diagram. The latter paper19) provides an undoubtfull experimental evidence on idle cycles which have only a latent effect on the crack tip and they do not directly contribute to the crack growth.
This work investigated the effects of technological discontinuities in welds on the fatigue life of welded joints in structures. Weld discontinuities were simulated by blunt cracks produced by the electro-spark method. Due to the technology used in manufacturing the specimens from the weldment the residual welding stresses were largely reduced so that their effect on the fatigue life of the specimens was negligible. Because the specimens were made from a curved weldment they kept their natural curvature given by the mean radius of the pipe. This curvature caused additional bending of the specimens during tensile loading. A single edge notch (SEN) specimen pin-loaded eccentrically by a tensile force is equivalent to a curved specimen. The curvature of the specimens can account for (i) increased fatigue lives when initiation slits are situated in the compression part of a specimen and (ii) for reduced lives when initiation slits are situated in the tension part of a specimen. Because the weld was accomplished in such a way that the weld root appeared on the inside surface of the curved plates to be welded, the root was situated in the tension part of the specimen and the face of the weld was situated in the compression part of the specimen. Application of the fracture mechanics approach to the curved welded specimens subjected to cyclic loading made it possible to calculate the fatigue lives of specimens with initiation slits in either the face part of the weld or the root part of the weld. The calculated lives compared well with experimental results.
It was shown that application of fracture mechanics principles can predict reasonably well the fatigue life of welded joints subjected to cyclic loading providing there are no residual welding stresses in the welded joint and the crack propagates through a “single” structure of the weld (e.g. heat affected zone, weld metal) characterized by known Paris law constants. In engineering practice the cause for differences in experimentally observed fatigue lives of welded joints and lives calculated on the basis of fracture mechanics should be looked for in residual welding stresses.
The results of the paper can be generalized to some extent. The level of residual welding stress in the weldment can be determined by a simple method which requires only Paris law parameters to be determined experimentally on stress relieved specimens for the weld microstructure through which a fatigue crack is supposed to be propagated. First, a fatigue crack of a certain length a0 is initiated by stress cycling. After that a fatigue crack propagation test follows to increase the crack length a0 by a distance Δa applying the stress amplitude σa and the cyclic stress ratio R = σmin/σmax. The number of cycles needed to extend the crack length a0 by a distance Δa is denoted by Nexp. By substitution of Paris law parameters (C, m) to integral (13) with accounting ΔK relations with unknown residual welding stress σres it is possible to determine such value of σres that the integral (13) obtains the value Nexp.
The authors are grateful to the Technological Agency of the Czech Republic for supporting this work (Project No.: TE02000162).
