Fatigue life prediction for toe ground welded joints
Yan-Hui Zhang and Stephen J Maddox
Structural Integrity Technology Group
CB1 6AL, UK
Paper published in International Journal of Fatigue, Vol. 31, Issue 7, July 2009, 1124-1136.
The paper presents the results of an investigation of the effect of weld toe burr grinding on the fatigue performance of non-load-carrying transverse fillet welded joints. Crack initiation and propagation were monitored by a modified replica method. It was found that, although the average life increase due to toe grinding was in agreement with published data, the majority of the fatigue cracks in specimens that gave fatigue lives <~106 cycles initiated at flaws just beneath the ground surface. Both the experiments and calculations based on fracture mechanics suggested that the fatigue lives of the toe ground joints in this life regime were dominated by the crack propagation process. However, in the long life regime (>106 cycles), crack initiation became significant. Reasonable estimates of the crack initiation period were made using the local stress approach proposed by Lawrance et al. The investigation suggested that more benefit from weld toe grinding could be claimed in the long (N > 106 cycles) than the short life regime.
Welds, toe grinding, LCF, crack initiation, crack growth.
Nomenclature and definitions
Bottom welds: The two welds below the attachments in the present specimens that were held vertically for fatigue testing (welds toe ground and then needle peened)
Crack aspect ratio: Ratio of crack depth to crack length, a/2c
Equivalent (constant amplitude) stress range ΔS eq : For a particular number of cycles to failure, ΔSeq is the constant amplitude stress range which, according to Miner's linear cumulative damage rule, is equivalent in terms of fatigue damage to a stress range spectrum
LCF: Low cycle fatigue
Life increase factor (LIF): The ratio of the fatigue endurance of ground welds to that of the as welded joints
Stress ratio R: The ratio of minimum to maximum applied stress in a cycle, Smin/Smax
Top welds: The two welds above the attachments in the present specimens that were held vertically for fatigue testing (welds toe ground only)
a: Crack depth
2c: Crack length
q: notch sensitivity factor, defined as (K f - 1)/(K t )
Kf: Fatigue notch factor
Kt: Stress concentration factor (SCF)
Mk: The stress intensity magnification factor
Mka: The stress intensity magnification factor at the deepest point on the semi-elliptical crack front (depth 'a')
Mkc: The stress intensity magnification factor at the ends of the major axis of a semi-elliptical crack, on the plate surface
T: plate thickness
Symbols used for low cycle fatigue analysis:
|K' ||cyclic strength coefficient |
|n' ||cyclic strain hardening exponent |
|Δεe ||elastic strain range |
|Δεp ||plastic strain range |
|σf ' ||fatigue strength coefficient |
|σ m ||mean stress, a combination of applied and residual stresses |
|εf ' ||fatigue ductility coefficient |
|b ||fatigue strength exponent |
|c ||fatigue ductility exponent |
|σ re ||residual stress |
|σ UTS ||ultimate tensile strength |
|S and ΔS ||nominal stress and nominal stress range |
|σ and Δσ ||local stress and local stress range |
|e and Δe ||nominal strain and nominal strain range |
|ε and Δε ||local strain and local strain range |
With respect to the process(es) leading to fatigue failure of welded joints, there are two different opinions. One view is that, because small, sharp, slag intrusions are unavoidably present at the weld toe and act as crack initiation sites, the fatigue life of a welded joint is predominantly controlled by the crack propagation process. Indeed, metallurgical examinations showed that the average depth of these flaws is 0.15mm and typically the maximum depth is approximately 0.4mm.[2,3] A review by Grover suggested that even high-quality welds contain flaws up to a depth of about 0.1mm. One approach then available for calculating the fatigue life is to integrate the fracture mechanics-based fatigue crack growth law for the material concerned between the limits of flaw size and critical crack size corresponding to failure.[5,6]
A different view is that fatigue endurance of welded joints is composed of both crack initiation and crack propagation processes. Lawrence et al applied a local approach developed by Morrow to estimate the fatigue crack initiation period as part of the evaluation of the fatigue strength of welded joints. This was defined as the number of cycles required to produce a crack of a certain size. It was estimated using a low-cycle fatigue (LCF) approach which utilised a Coffin-Manson type equation. The LCF properties of the heat affected zone (HAZ), where crack initiation occurred, were estimated by applying the empirical relation between hardness and tensile strength of steels. A significant crack initiation period, about 40-50% of the total life, for endurances between 105 to 106 cycles was reported. [7,9] The percentage of the total life spent initiating a crack was predicted to increase with increasing fatigue endurance. A weakness in the approach is that the transition crack size, at which the fatigue damage process is assumed to change from crack initiation to crack growth, has been defined arbitrarily, ranging from 0.1mm, to 0.15mm to 0.25mm. It will also be noted that the assumption that part of the fatigue life of a welded joint is governed by the tensile strength of the material is in direct contradiction of the well established finding that the fatigue lives of welded joints are independent of the material's tensile strength. Consequently, the approach is not generally used to assess as-welded joints.
Weld toe grinding is a well-established technique for improving the fatigue strength of welded joints. The main aims of the operation are to reduce the local stress concentration and to remove crack-like flaws at the weld toe. To obtain significant improvement in fatigue life, it is recommended to grind to at least 0.5mm below any visible undercut to ensure that the intrusions and crack-like flaws are removed. Such treatment justifies an increase in fatigue design endurance of at least 2.2 times according to.
Since all flaws are expected to have been removed after grinding, the proportion of the fatigue endurance spent initiating a crack is expected to be significant. Consequently, the local approach for evaluating fatigue crack initiation in welded joints mentioned earlier may be suitable for application to toe ground joints. Although many attempts have been made to calculate the fatigue endurance of welded joints by considering crack initiation and propagation, work on ground joints is limited. Furthermore, there is little convincing data in the literature to verify any model for calculating the fatigue crack initiation period. The work described in this paper addressed this lack of data and analysis. On the basis of experimental results and fatigue life calculations for welds in steel plate, the aim was to develop a method for predicting the fatigue lives of toe ground welded joints allowing for both the fatigue crack initiation and propagation processes.
2 Experimental details
2.1 Test specimens
Specimens of the design shown in Figure 1 were manufactured from steel plate complying with EN 10025 S355JR. The chemical composition of the material is given in Table 1. The yield and tensile strengths of the material were determined by tensile testing to be 406 and 539MPa, respectively. The transverse non-load-carrying joints with nominally 10mm leg length fillet welds were made in two passes using 3.25 and 5.0mm diameter electrodes complying with AWS 5.1:E6013. All the weld toes were dressed by burr grinding following the standard TWI practice, which is in accordance with the recommendations given in BS 7608. The radius of the burr was 5.0mm and the maximum depth of grinding was limited to ~0.8mm. After grinding, each weld was carefully examined visually to ensure that no flaws were present on the ground surface. As seen in Figure 1, in each test specimen there were four fillet welds, two above the attachments (termed 'top welds') and two below (termed 'bottom welds'). As will be described later, crack initiation and growth in welds were determined by a replica method. Since it was difficult to make a replica on the bottom welds when the specimens were installed in the fatigue testing machine, it was decided to confine attention to the top welds. There is evidence that peening after weld toe burr grinding can increase fatigue performance further by introducing compressive residual stresses. Therefore, the bottom welds were also needle peened after being burr ground to delay crack initiation there.
Fig.1. Fatigue test specimen design (dimensions in mm).
Table 1 Chemical composition of the parent materials
|Element ||C ||Mn ||Si ||S ||P ||Cr ||Ni ||Al ||Cu ||Nb ||Ti |
|Wt% ||0.17 ||1.36 ||0.26 ||0.002 ||0.031 ||0.017 ||0.016 ||0.029 ||0.011 ||<0.002 ||0.004 |
2.2 Fatigue tests
A total of six specimens were fatigue tested axially at a stress ratio of R=0.1 in a servo-hydraulic fatigue test machine under load control in air, using a sinusoidal waveform with a frequency between 3 to 7Hz. To produce beach marks on the fracture surfaces, in some specimens the applied stress range was periodically reduced while keeping the same maximum stress to avoid crack growth retardation. Over 90% of the fatigue damage (as measured by the product of ΔS3x N, where ΔS is stress range and N is number of cycles) occurred under the higher stress range. After failure, each specimen was broken open to use the beach marks to estimate the crack depth at a given number of cycles, in conjunction with the surface crack length measurements made by the replica method, and to examine the crack shape evolution.
2.3 Crack initiation monitoring and crack growth measurements
To detect crack initiation reliably and to measure crack size accurately for the ground welds, the replica method was adopted. This is usually applied to polished surfaces of plain materials but it was thought that it should also be suitable for application to ground weld toes. The fatigue tests were periodically interrupted at specified numbers of cycles, depending on the applied stress range, to take the replicas. Confining attention to the two 'top welds', a strip of cellulose acetate replicating tape, wetted with acetone, was laid over each groove produced by toe grinding. When the replica was dry, the tape was peeled off and stuck to a piece of double-sided sticky tape to prevent curling. From initial trials, it proved to be difficult to observe very small cracks due to poor contrast in the replica. This was significantly improved by combining the conventional replica method with the application of a dye penetrant. Dye penetrant was first sprayed to the weld surface to be replicated and then washed out with acetone. The dye penetrated any crack or flaw that was present in the weld and created a high contrast in the subsequent replica. This allowed cracks as little as 0.1mm in length to be detected readily. During the tests, each replica was examined in an optical microscope to check crack initiation, or, if it had occurred, to measure the surface crack length. To determine the size of small cracks more accurately, some replicas were examined in a scanning electron microscope (SEM).
In spite of the practical difficulty of applying replicas to the bottom welds, this was attempted on one specimen (number 06). The attempt was successful and crack initiation and growth data were recorded.
2.4 Post-test examinations
After fatigue testing, the fracture surfaces of those specimens tested under two stress ranges were examined in an optical microscope to determine the variation of crack aspect ratio (crack depth/crack length) with crack growth from the beach marks on the fracture surfaces.
To establish whether fatigue cracks initiated from the parent metal, weld metal or HAZ, two fatigue cracks, one from specimen 01 and the other from specimen 06, were sectioned at their centres and metallurgical samples were prepared. Micro-hardness measurements (5kg load) were also made in different microstructures around the groove produced by grinding to estimate the tensile strength and the LCF properties in order to calculate the number of cycles for crack initiation.
3 Presentation and analysis of experimental results
3.1 Fatigue endurance test results
The fatigue endurance of the burr ground welds is given in Table 2. The results are plotted in Figure 2 for comparison with the mean S-N curve reported by Booth for burr ground joints. As-welded specimens from the same batch as the present ones were fatigue tested at R=0.1 in a separate project and the results obtained are included in Figure 2. They proved to be in good agreement with the BS 7608. Class F mean curve, the appropriate class for as-welded joints of this type, is also shown.
Table 2 Fatigue endurance of the ground joints
|Specimen No. ||Loading history ||Total number of |
cycles to failure, N f
|Equivalent stress |
|Life increase factor compared |
to Class F mean curve
|Failure location 1 |
|01 ||5.40x105 cycles at ΔS=240MPa |
2.16x105 cycles at ΔS=143MPa
|7.56x10 5 ||220.4 ||4.7 ||Top weld |
|02 ||1.06x106 cycles at ΔS=210MPa |
1.0x105 cycles at ΔS=140MPa
|1.16x10 6 ||205.7 ||5.8 ||Bottom weld |
|03 ||7.79x105 cycles at ΔS=210MPa |
2.45x105 cycles at ΔS=140MPa
|1.02x10 6 ||197.5 ||4.6 ||Top weld |
|04 ||1.12x106 cycles at ΔS=210MPa ||1.12x10 6 ||210 ||6.0 ||Bottom weld |
|05-a ||5.45x106 cycles at ΔS=180MPa ||5.45x10 6 ||180 ||>18.4 ||Run out |
|05-b ||8.03x105 cycles at ΔS=220MPa ||8.03x10 5 ||220 ||5.0 ||Bottom weld (retest) |
|06 ||7.46x105 cycles at ΔS=220MPa ||7.46x10 5 ||220 ||4.6 ||Bottom weld |
1. The toes of the two top welds (above the attachments) in each specimen were burr ground, while the toes of the two bottom welds (below the attachments) were burr ground and needle peened.
Fig.2. Comparison of the fatigue lives of the ground welds with those of as-welded joints. The average S-N curve for burr ground joints and the Class F mean curve  are also included for comparison.
The fatigue performance of the specimens tested at two stress ranges, to produce beach marks on the fracture surfaces, were evaluated using the equivalent constant amplitude stress range. This is the constant amplitude stress range which, according to Miner's linear cumulative damage rule, is equivalent in terms of fatigue damage to a stress range spectrum. It relates to the constant amplitude S-N curve for the detail as follows:
where m is the slope of the constant amplitude S-N curve, that is 3.0 in the present case, and n i is the number of cycles applied at stress range ΔSi.
It will be seen from Table 2 and Figure 2 that the fatigue lives of all six ground joints agreed well with those of burr ground joints reported in the literature, except for one specimen tested at a relatively low stress range. The fatigue performance of all the ground joints was significantly better than that of the as-welded joints. The life increase factor (LIF), defined as the ratio of the fatigue endurance of ground welds to that of the as-welded joints (assumed to correspond to the Class F mean curve), ranged from 4.6 to >18.4, with an average value of ≥7.4. In other words, the LIFs of all the specimens were at least double the design factor of 2.2 recommended in BS 7608 for ground welds (corresponding to a 30% increase in the allowed stress range). They were also higher than the LIF of 3.0 reported by Haagensen, but in closer agreement with the LIF of 4.6 from Booth's review of data for burr ground joints.
Specimen 05 was initially tested at a stress range of 180MPa. After 5.46 x 106 cycles, which exceeded 18 times the fatigue life for the Class F mean curve, there was still no indication of fatigue crack initiation, and the result was treated as a run-out. The specimen was then retested at the higher stress range of 220MPa. It failed after 803,000 cycles, still exceeding 5 times the fatigue life given by the Class F mean curve at this stress range. It appeared that the previous loading history at the lower stress range did not produce sufficient fatigue damage to affect the subsequent test result.
From Table 2, it will be seen that four out of six specimens failed from the bottom joints, which had been both burr ground and needle peened, suggesting that the needle peening did not improve the fatigue endurance of the burr ground welds.
3.2 Detection of fatigue crack initiation
Table 3 summarises the experimental results related to the detection of crack initiation. It will be seen that initiation of several cracks was recorded and most of the cracks initiated from pre-existing flaws. Examples of crack initiation from flaws are shown in Figure 3. Figure 4 shows an example where crack initiation was not obviously associated with a flaw. The following describes in detail the test result for each specimen:
- Specimen 01 failed from one of the two top welds where crack initiation and growth were monitored by the replica method. A 1.4mm long crack was observed in the first replica made at 100,000 cycles at a stress range of 240MPa, which corresponded to ~21% of the total life of the specimen. The crack initiated from a flaw, see Figure 3a. The growth of this crack led to final failure of the specimen. According to the crack aspect ratio determined, which will be described later, the crack depth for a crack length of 1.4mm was estimated to be about 0.6mm. Two further cracks initiated later, neither of which was obviously linked with any flaw.
- Specimen 02 failed from one of the two bottom welds where no replicas had been applied. For the two top welds, however, replicas were made regularly and no crack initiation was observed even in the last replica made shortly before the specimen failed from a bottom weld.
- Specimen 03 failed from one of the two top welds. The first replica was made after 510,000 cycles. However, three cracks were found, all of which initiated from flaws. Two of them were already 2.8mm and 3.1mm long, as shown in Figures 3b and d respectively. The growth of crack TA-1 (Figure 3c and 3d) led to the final failure of the specimen.
- Specimen 04 failed from one of the two bottom welds where replicas had not been applied. For the two top welds, replicas were made regularly and the very small, 0.11mm long, crack shown in Figure 4 was observed in the replica made shortly before the specimen failed from a bottom weld.
- Specimen 05 was initially tested at a stress range of 180MPa. No cracking was observed in either of the two top welds up to a fatigue endurance of 5.45 x 106 cycles. It was declared as a run-out. The specimen was subsequently re-tested at the higher stress range of 220MPa. It failed from one of the bottom welds. Although replicas were made periodically on the two top welds, there was still no indication of crack initiation from these welds in the last replica, which was made shortly before the failure of the specimen.
- In specimen 06, a 0.5mm long crack was observed in one of the top welds in the first replica made at 2 x 105 cycles. It initiated from a flaw. After the specimen had been tested to 5 x 105 cycles, replicas were also made, with great difficulty, on the two bottom welds. Three cracks were observed, all initiating from flaws. The growth of two of these cracks (BB-1 and BB-2), which finally coalesced, led to failure of the specimen.
Table 3 Crack initiation lives of the ground joints
|Specimen No. ||Crack ID (1) ||Crack initiation ||Crack initiation from pre-existing flaw? ||Estimated life to a=0.15mm (3) |
|Length of crack first detected by replica, mm ||Corresponding number of cycles (2) |
|01 ||TA-1 * ||1.4 ||1.0x105 at Δσ=240MPa ||Yes || |
|TB-1 ||0.5 ||4.4x105 at Δσ=240MPa ||Not obvious ||3.3x10 5 |
|TB-2 ||0.5 ||2.3x105 at Δσ=240MPa ||Not obvious ||2.2x10 5 |
|02 || ||no crack found ||1.0x106 at Δσ=210MPa || ||Run out |
|03 ||TA-1 * ||2.8 ||5.1 x105 at Δσ=210MPa ||Yes || |
|TA-2 ||3.1 ||5.1 x105 at Δσ=210MPa ||Yes || |
|TA-3 ||0.3 ||5.1 x105 at Δσ=210MPa ||Yes || |
|04 ||TB-1 ||0.11 ||1.1 x106 at Δσ=210MPa ||Not obvious ||1.1x106 (actual) |
|05-a || ||no crack found ||5.5x106 at Δσ=180MPa || ||Run out |
|05-b || ||no crack found in top weld; failed from bottom welds ||7.0x105 at Δσ=220MPa || ||Run out |
|06 ||TA-1 ||0.5 ||2.0 x105 at Δσ=220MPa ||Yes || |
|BB-1 * ||1.8 ||5.0 x105 at Δσ=220MPa ||Yes || |
|BB-2 * ||2.0 ||5.0 x105 at Δσ=220MPa ||Yes || |
|BB-3 ||1.2 ||5.0 x105 at Δσ=220MPa ||Yes || |
1. The first letter T or B represents top or bottom weld; the second letter A or B represents side A or side B; the * indicates crack(s) that grew to failure.
2.The number of cycles at the main (higher) stress range is given for those specimens tested under two stress ranges.
3. Estimated using the mean crack growth rates (A=1.3x10-13) experimentally determined from the ground welds.
Fig.3. Examples of crack initiation from flaws a) SEM micrograph of replica, showing crack TA-1 in Specimen 01 (at N=238,000 cycles, 2c=1.4mm). The area where the crack initiated from is circled;
b) SEM micrograph of replica, showing crack TA-3 in Specimen 03 (at N=529,230 cycles, 2c=0.33mm). The area where the crack initiated from is circled;
c) Optical micrograph taken directly from specimen 03 just before it failed, showing the initiation site for crack TA-1.
d) Optical micrograph of replica, same crack as (c) but taken at N=509,230 cycles, 2c=2.8mm.
Fig.4. SEM micrograph of replica showing crack initiation not obviously related to surface flaws, Specimen 04, crack TB-1, 2c= 0.11mm, N=1,100,000 cycles at 210MPa.
Table 3 summarises the number of cycles at which a crack was first observed, the corresponding crack size and its location. The numbers of cycles at the lower stress range used for some specimens were excluded from the Table since their fatigue damage contribution was small compared to that at the higher stress range. The last column of the Table shows the calculated number of cycles to initiation for some cracks, which did not seem to have initiated from a flaw, related to the achievement of a fatigue crack depth of 0.15mm (crack length of 0.36mm) on the basis of the average crack growth rates for ground joints. Details of the method used to do this calculation and the determination of the crack growth rates will be described later.
3.3 Crack initiation site
In order to model the fatigue crack initiation process in the toe ground welded joints relevant properties are required for the material where crack initiation took place. Therefore, etched macro-sections of the two specimens from which metallurgical sections transverse to the weld had been prepared, specimens 03 (Figure 5) and 06 (Figure 6), were examined in detail. It was found that both cracks initiated in weld metal, at a similar location within the toe ground groove. The crack lengths were 1.3 and 1.5mm, respectively. From Figure 5a), it will be seen that some porosity was present in the weld metal (arrowed in the figure). The profile of the burr grinding can be appreciated in the two figures (specimen 03 and specimen 06).
Fig.5. Cross-section view of a crack initiated at the ground weld toe of specimen 03. The crack initiated in weld metal and its final surface length was about 1.3mm, crack No. TA-3:
a) At a lower magnification, showing the profile of the ground joint and the embedded flaws,
b) At a higher magnification, showing the initiation of the crack in weld metal
Fig.6. Cross-section view of crack initiation (crack No. TA-1) in the ground weld toe of specimen 06. The crack initiated in weld metal and its final surface length was about 1.5mm:
a) Optical micrograph taken at a lower magnification;
b) SEM micrograph, showing the initiation of the crack in weld metal;
c) SEM micrograph taken at a higher magnification, before micro-hardness measurements were carried out
As both cracks initiated in weld metal and all other cracks that originated from flaws also initiated at a similar location in the grooves, it was tentatively concluded that all cracks associated with flaws initiated in the weld metal. It should be noted that this location did not correspond to the deepest point (mid-section) of the groove (see Figure 5) where there is a greater reduction in the plate thickness and hence where the stress concentration factor (SCF) is highest.[10,16]
The results of the micro-hardness measurements on two cross-sections are given in Table 4. The average hardness (HV) values from the measurements for parent metal, weld metal and HAZ were 177, 210 and 309, respectively. These values were used to estimate the corresponding ultimate tensile strengths of the materials, one of the material properties needed to perform the fatigue crack initiation analysis.
Table 4 Results of micro-hardness measurements
|Indent No. ||Cross-section 1, specimen 03 ||Cross-section 2, specimen 06 ||Average hardness |
|Material ||Hardness, HV5 ||Material ||Hardness, HV5 ||Material ||HV5 |
|1 ||Parent metal ||167 ||Parent metal ||171 ||parent metal ||177 |
|2 ||Parent metal ||181 ||Parent metal ||172 ||HAZ ||309 |
|3 ||Parent metal ||172 ||Parent metal ||184 ||weld metal ||210 |
|4 ||Fine grained HAZ ||238 ||Parent metal ||183 || || |
|5 ||Coarse grained HAZ ||374 ||Parent metal ||182 || || |
|6 ||Weld metal ||209 ||Fine grained HAZ ||218 || || |
|7 ||Weld metal ||208 ||Fine grained HAZ ||246 || || |
|8 ||Weld metal ||218 ||Coarse grained HAZ ||386 || || |
|9 ||Weld metal ||215 ||Coarse grained HAZ ||391 || || |
|10 || || ||Weld metal ||198 || || |
|11 || || ||Weld metal ||208 || || |
|12 || || ||Weld metal ||212 || || |
|13 || || ||Weld metal ||208 || || |
3.4 Input parameters for fatigue crack growth model
The observations of fatigue cracking in the present specimens were used to develop a fracture mechanics-based model for predicting the fatigue crack propagation period of their lives. This involved identification of the shape of the fatigue crack as it grew, calculation of the stress intensity factor, K, for a crack at the ground weld toe and the fatigue crack growth law for the steel concerned.
3.4.1 Determination of crack aspect ratio
By applying blocks of small stress cycles following blocks of the major stress cycles, beach marks were successfully produced on the fracture surfaces. One example is shown in Figure 7a. The evolution of the crack aspect ratio (a/2c, where 'a' is crack depth and '2c' is the surface crack length) with increasing crack size was determined from the beach marks on two fracture surfaces, see Figure 8. When the crack was small (2c ≤3mm), the crack aspect ratio was relatively large, ~0.42. The shape of a crack changed with increasing crack size and reached an aspect ratio of between 0.32 and 0.35 as the crack approached through-thickness. This information was used to: i) estimate the length of a crack at the end of the crack initiation phase, defined here as the achievement of a 0.15mm deep crack; ii) estimate the stress intensity magnification factor on the surface, Mkc, that would be consistent with the crack shape actually observed. The relevant concepts will be introduced in the next section.
Fig.7. Comparison of the crack shapes seen on the fracture surfaces from a ground joint and an as-welded joint:
a) Ground joint, specimen 01. The beach marks can be clearly seen on the fracture surface;
b) As-welded joint. The scales in both images are in mm.
Fig.8. Evolution of a fatigue crack shape determined from beach marks in ground joints
The crack shape in as-welded specimens differed from that in ground joints. A typical fracture surface from an as-welded specimen is shown in Figure 7b for comparison. The comparatively larger a/2c value associated with the ground weld was one of the reasons why crack growth was slower, as will be discussed later.
3.4.2 Stress intensity factor
The stress intensity factor for a semi-elliptical shaped weld toe crack can be expressed as:
K = YM k ΔS√Πa 
where Y is a function of the crack front shape (a/2c), crack depth (a), section size and loading mode while Mk is a magnification factor that reflects the stress concentration effect of the welded joint geometry and depends on the crack size, section thickness and loading mode. BS 7910 provides a suitable solution for Y but not for Mk if the weld toe is ground.
Mk is defined as :
Mk =Kin plate with weld/Kin plate without weld 
Mk quantifies the change in stress intensity factor K as a result of the surface discontinuity at the weld toe. For ground fillet welds, a 2-dimensional (2D) Mk solution was established by Pang using finite element analyses for several different weld toe radii, including 5mm adopted in the present investigation. In his model, the fillet weld toe angle was 45° and the depth of grinding beneath the weld toe surface was 1.0mm, slightly greater than 0.8mm taken in this investigation. It is assumed that this difference will not have significant effect on Mk. Therefore, the Mk solution derived by Pang for a ground toe radius of 5mm, re-produced in Figure 9 was used in the fracture mechanics analysis below. It should be noted that the crack growth in depth depends on the crack aspect ratio assumed. The 2D Mk solution determined by Pang was directly applicable to an edge crack so that it referred to crack growth in depth from the plate surface for an aspect ratio of a/2c=0. Therefore, the crack shape measurement results shown in Figure 8 were first used to estimate the crack depth for each initial crack length measured from the replicas. During crack growth, a constant value was assigned to the stress intensity magnification factor on the surface, Mkc. It was determined in such a way that the aspect ratio of the final crack just before breaking through-thickness, was in agreement with that observed experimentally (Figure 8).
Fig.9. Mk distributions through plate thickness, weld angle=45°, ground weld toe radius=5mm, depth of grinding beneath the weld toe surface=1.0mm, T: plate thickness.
3.4.3 Determination of crack growth rate relationship
The simple Paris power law fatigue crack growth relationship was assumed to describe fatigue crack growth in the test specimens:
where da/dN is crack growth rate (in mm/cycle), ΔK is stress intensity factor range (in N/mm3/2), m and A are constants. The exponent m was assigned the value of 3.0, as recommended for steels in BS 7910 and consistent with the slope of the S-N curve for the as-welded joint (see Figure 2).
The crack growth parameter A in Eq.4 was estimated using the following information:
- The initial crack length (when the crack was first observed).
- The final crack length (when the last replica was made).
- The correlation between the crack aspect ratio and crack length.
- The loading history applied during growth between the initial and final crack lengths.
- The Mk solution for the ground weld.
The crack growth rate parameter A for a total of ten cracks was thus determined and the results are summarised in Table 5. The parameter A exhibited scatter, ranging from 8.0 x 10-14 to 2.2 x 10-13, with an average value of 1.3 x 10-13. This is significantly lower than the published mean value of 2.5x10-13 for a stress ratio R>0.5,[17,18] but only slightly less than 1.5 x 10-13 for R~0.1. In another investigation where stress ratio R was 0.3, parameter A was determined to be 1.67 x 10-13 in as-welded joints with similar joint geometry to the current one, slightly greater than the value obtained in this investigation for the ground joints tested at R=0.1.
Table 5 Estimated fatigue crack growth parameter A (exponent m was assumed to be 3.0)
|Specimen no ||Crack ID ||Experimental crack growth data ||Estimated crack growth rate parameter A |
|Initial crack size1, mm ||Stress range and the accumulated number of cycles 2 ||Final crack length3, mm |
|01 ||TA-1 ||1.4 ||240MPa for 4.2x105 cycles |
143MPa for 2.1x105 cycles
|28.0 ||9.1x10 -14 |
|TB-1 ||0.5 ||240MPa for 8.2x104 cycles |
143MPa for 6.0x104 cycles
|0.7 ||1.5x10 -13 |
|TB-2 ||0.5 ||240MPa for 2.9x105 cycles |
143MPa for 2.0x105 cycles
|2.8 ||1.4x10 -13 |
|03 ||TA-1 ||2.8 ||210MPa for 2.7x105 cycles |
140MPa for 2.5x105 cycles
|18.0 ||1.1x10 -13 |
|TA-2 ||3.1 ||16.8 ||1.0x10 -13 |
|TA-3 ||0.3 ||1.3 ||2.2x10 -13 |
|06 ||TA-1 ||0.5 ||220MPa for 5.5x105 cycles ||1.5 ||8.0x10 -14 |
|BB-1 ||1.8 ||220MPa for 2.0x105 cycles ||5.0 ||1.3x10 -13 |
|BB-2 ||2.0 ||220MPa for 2.0x105 cycles ||5.0 ||1.2x10 -13 |
|BB-3 ||1.2 ||220MPa for 2.0x105 cycles ||3.3 ||1.5x10 -13 |
1. The surface length 2c of the crack first detected by the replica method.
2. The number of cycles from the initial to the final crack sizes.
3. The size measured in the last replica before the specimen failed.
4 Fatigue life prediction based on crack growth
4.1 Initial crack size and stress intensity factor solution
The flaw lengths observed in the replicas for the ground joints varied between 0.1 and ~0.5mm. Therefore, two initial flaw sizes were assumed in the life prediction: one was 0.15mm deep and 0.36mm long (flaw aspect ratio=0.42) and the other was 0.2mm deep and 0.8mm long, a slightly lower aspect. The former and the latter were the sizes assumed to represent respectively the average and the upper limit for any pre-existing flaws in the toe ground joints. These flaws were assumed to be on or just below the surface of the groove, in weld metal.
The Y solution for semi-elliptical surface cracks under axial loading recommended in BS 7910 (based on the original work by Newman-Raju) was used. In addition, the Mk solution determined by Pang for ground joints with a radius of 5mm, Figure 9, was adopted to account for the increase of stress intensity factor due to the weld toe stress concentration.
4.2 Calculation of fatigue endurance
The simplified Paris power law expression, Eq.2, was used. By assuming the exponent m=3.0, the average value of parameter A was determined to be 1.3 x 10-13 as described before. With the above input, the fatigue endurance for ground joints was estimated by integration of Eq.2. The results are shown in Figure 10. It will be seen that the estimated fatigue endurance, based on fatigue crack growth only, agreed well with the experimental data, which, except for the test results from specimens failing beyond 106 cycles, fall between the two estimates for the different initial flaw sizes assumed. The calculations suggest that, for fatigue endurances less than ~106 cycles, the fatigue endurance of ground welds can be predicted well by crack growth alone. The actual lives are greater than the estimated for longer endurances, suggesting that there is now a significant fatigue crack initiation phase in the fatigue life and ignoring it underestimates the fatigue endurance of ground joints.
Fig.10. Comparison of fracture mechanics (FM) predicted lives for two different initial flaw sizes with the experimental results of the ground joints (arrow indicates run-out).
Table 6 compares the average LIFs obtained experimentally with those calculated. The latter were divided into two parts by two separate calculations: one was related to the reduced stress intensity magnification factor Mk and the other was attributed to the reduced crack growth rates associated with the ground joints. For this comparison, the crack growth parameter A for the as-welded joints was needed and estimated to be ~2.5x10-13, the mean value for R>0.5. This was justified on the basis that the fatigue performance of the as welded joints could be predicted by adopting this crack growth rate, assuming an initial flaw depth of 0.15mm and using the 3D Mk solution for as-welded joints. For example, at a stress range of 220MPa, the fatigue life of an as-welded joint containing an initial flaw of 0.15 x 0.4mm was predicted to be 168,000 cycles as compared to 162,000 cycles given by the Class F mean curve. Possible reasons for the reduced crack growth rates are discussed in Section 6.
Table 6 Life increase factors predicted on the basis of fatigue crack growth process only
|Stress range, MPa ||Experimentally determined average life increase factor ||Predicted life increase factor (LIF) |
|LIF due to geometry only 1 ||LIF due to growth rate only 2 ||Total LIF |
|220 ||5.2 ||2.62 ||1.93 ||5.06 |
|180 ||>18 ||2.64 ||1.96 ||5.16 |
1. The LIF due to the reduced stress intensity magnification factor Mk for ground joints when compared to the as-welded joints at the same growth rates (assuming A=2.5x10-13, the mean value for R>0.5 (17)).
2. The LIF due to reduced growth rate parameter A associated with the ground joints (A=1.3x10-13), when compared to A=2.5x10-13 for the as welded joints.
It will be seen from Table 6 that the LIF was attributed more to the effect of improved weld geometry for ground joints than the differences in crack growth rates between the two cases. At a stress range of 220MPa, the total LIF predicted was comparable with the average value obtained experimentally. However, at a lower stress range (eg 180MPa), the calculation based on crack growth alone underestimated the endurance for the ground joints, suggesting that a significant proportion of the life was actually spent initiating a crack. Hence, under certain circumstances, the crack initiation process must be considered, as described below.
5 Calculation of crack initiation period
Although most cracks initiated from pre-existing flaws, and the fatigue endurance of ground joints at fatigue endurance ≤106 cycles was predicted well by the crack growth process alone, some cracks initiated without obvious connection with a flaw and it appeared that a significant proportion of the total endurance was spent initiating fatigue cracks. In addition, the top welds of some specimens were monitored regularly and there was still no indication of crack initiation just before these specimens failed from the bottom welds. The crack initiation lives of these top welds were therefore equal to or greater than the endurance of these specimens. Furthermore, at a comparatively low stress range of 180MPa, the fatigue life of the ground joint (specimen 05) was more than 18 times longer than that of the as-welded joint and could not be predicted on the basis of the fatigue crack growth process only. It is believed that if flaws were totally removed from the weld toe, crack initiation would play an important part and the fatigue performance of ground joints could be increased further, especially in the low stress regime. For this reason, estimation of the crack initiation period was attempted below, using the procedures described by Lawrence for welded joints.
The prediction of crack initiation life involves the following few steps.
5.2 Local stress and strain range determination
The relation between the local stress and strain must satisfy both Neuber's equation and the local stress-strain curve. Neuber's equation, which was modified for fatigue by Topper et al, was used to relate the remote (nominal) stress range to the product of local stress and strain ranges, and can be described by:
where Δσ and Δε are local true stress and true strain ranges, ΔS is nominal stress range and E is Young's modulus. Kf is the fatigue notch factor and was assumed to be equal to the SCF, Kt. This is so because the notch-sensitivity factor, q, defined in Eq.6, for a notch with a radius of 5mm, as for the present ground joints, approaches unity:
The cyclic stress-strain response of the material at the notch root was assumed to follow the Ramberg-Osgood stabilised cyclic strain curve:
where K' is the cyclic strength coefficient and n' is the cyclic strain hardening exponent. The local stress and strain were determined by solving Equations (5) and (7) simultaneously.
5.3 Estimation of fatigue crack initiation life
For a smooth specimen, the fatigue crack initiation period, Ni, can be estimated by the Coffin Manson equation modified by Morrow to take into account the local mean stress:
Δεe is elastic strain range
Δεp is plastic strain range
σf' is fatigue strength coefficient
σm is mean stress
εf' is fatigue ductility coefficient
b is fatigue strength exponent
c is fatigue ductility exponent.
For the present transverse welds, residual stresses were assumed to be equal to the yield strength of the parent material as a conservative estimate. This represents one of the uncertainties in the analysis as residual stress will vary from one joint to another. For a given stress range, the maximum local stress was first determined from the intersection of the monotonic tensile stress-strain curve with Neuber's curve. The effective mean stress, σm, was estimated from the applied stress ratio, stress range and assumed residual stress.
5.4 Estimation of the relevant low cycle fatigue parameters
The pertinent LCF properties for the material in which fatigue cracks initiated were estimated from the tensile strength, which was calculated from the hardness measured in the relevant material. For cracks initiating from flaws, as shown above, initiation was in weld metal. For those cracks not obviously associated with flaws during initiation, no crack sectioning was made to reveal which material they initiated in. It is reasonably expected that, if cracking from flaws could be avoided in the ground joints, fatigue cracks would initiate in the parent metal where the SCF due to the ground groove was expected to be the greatest. Because of uncertainty in which material the 'natural' cracks initiated, two calculations were carried out: one assuming crack initiation in the parent metal and the other assuming weld metal. The hardness values of both the parent and weld metals were used to estimate the tensile strengths, which were then used to estimate the LCF properties of the parent and weld metals on the basis of the empirical relations suggested by Lawrence et al, which is described below.
The relation between hardness and tensile strength was taken as:
The average hardness values for the parent and weld metal were measured to be 177HV5 (168HB) and 210HV5 (200HB), respectively. The corresponding tensile strengths were estimated to be 580 and 690MPa, respectively.
Other parameters were estimated as follows:
σf'=0.95σuts +370 (MPa)
The estimated values of these parameters are summarised in Table 7.
Table 7 Estimated low cycle fatigue properties for the parent and weld metals
|Material ||σuts, MPa ||E, MPa ||σy', MPa ||K', MPa ||n' ||σf', MPa ||εf' ||b ||c |
|Parent ||580 ||207000 ||352 ||937 ||0.157 ||921 ||0.90 ||-0.094 ||-0.60 |
|Weld ||690 ||207000 ||420 ||1057 ||0.149 ||1026 ||0.82 ||-0.089 ||-0.60 |
The maximum Kt value was determined to be 1.64 and was used in these calculations. This value was similar to but slightly less than the value of 1.73 calculated for ground joints with a slightly smaller radius of 3.7mm.
Based on the above procedures, crack initiation periods for both the parent and weld metals were estimated. To evaluate the effect of residual stresses, two different σre values were assumed in a sensitivity study, equal to the yield strength of the material, in accordance with the conservative recommendation given in BS 7910, or about half of the yield strength (200MPa). The resulting estimates of the crack initiation endurances are shown in Figure 11 for the parent metal and Figure 12 for the weld metal. The limited experimental data are also included for comparison. These data include the following:
- The initiation endurances of those cracks which did not obviously initiate from flaws.
- The fatigue lives of those top welds, which did not show any fatigue cracking when the specimens failed from the bottom welds. They are shown as run-outs in the two figures.
- The fatigue endurance of Specimen 05, which was a run-out at a stress range of 180MPa.
Fig.11. Comparison of the experimentally obtained crack initiation lives (in the absence of flaws) with those predicted for the parent metal.
Fig.12. Comparison of the experimentally obtained crack initiation lives (in the absence of flaws) with those predicted for the weld metal.
The crack initiation endurance was defined as the number of cycles to reach a crack depth of 0.15mm, the average flaw depth observed in as-welded joints. By assuming a crack aspect ratio of 0.42 for small cracks (refer to Figure 8), the crack length corresponding to a crack depth of 0.15mm was estimated to be 0.36mm. For those cracks, whose initial crack lengths were slightly longer than 0.36mm, their initiation endurances were estimated by subtracting the number of cycles required to grow the crack from 2c=0.36mm to the observed length using the average crack growth rate for the ground welds (i.e, m=3.0, A=1.3x10-13). The resulting values are included in Table 3. No attempt was made to estimate the initiation period for those cracks with sizes significantly greater than 0.36mm when they were first detected. This was based on the consideration that the accuracy of the estimate for the crack initiation period might be compromised by extrapolation over a large crack growth period. The fatigue endurance of the test specimens is also shown in Figures 11 and 12 for comparison.
By comparing Figures 11 and 12, it will be seen that, if crack initiation was not associated with any flaws, the initiation endurance was estimated reasonably well when crack initiation was assumed to be in the parent metal while it tended to be overestimated when crack initiation was assumed to be in the weld metal. This difference between the two predicted endurances may, of course, be a reflection of inaccuracies in the assumptions made in the analysis. In particular, that difference was due mainly to the difference in tensile strengths. Since these were estimated from the approximate correlation between tensile strength and hardness they could have been incorrect, but in any case it would be surprising to find that such a small difference was as significant as indicated. Alternatively, if the estimated crack initiation endurances are correct, they could indicate that crack initiation is more likely to take place in the parent metal. This would be consistent with the fact that the maximum SCF at the ground weld toe was located in the parent metal. The assumed residual stresses did not have a significant effect on the predicted crack initiation lives for the conditions adopted. This was largely due to the greater stress relaxation for welds with the higher assumed residual stress. Although the difference in the assumed residual stresses was about 200MPa, the difference in mean stress was only 40 50MPa depending on the applied stress level. It will also be seen from Figures 11 and 12 that the predicted curves were significantly shallower than expected for as-welded joints, consistent with the expectation that the crack initiation phase will become increasingly significant with decreasing applied stress range.
Although it may be arguable whether crack initiation life is significant or not for as welded joints, it is generally believed that one of the main benefits of toe grinding is to remove welding-induced flaws, which should significantly increase the crack initiation endurance and hence the total fatigue life. However, the present work suggested that, despite the standard grinding procedures having been followed and the life increase exceeding those reported in the literature, crack initiation quickly took place from flaws on or just below the ground surface when the applied stress ranges were above a certain stress level. It seems that previously embedded flaws were exposed or became nearer to the surface as a result of the toe grinding operation. Although the probability of crack initiation from a flaw was reduced in ground joints, the replica method clearly demonstrated that the majority of the fatigue cracks (a total of eleven, Table 3) initiated at flaws. This was consistent with the observation that these cracks initiated in weld metal, not in the parent metal where the SCF due to the groove produced by grinding was the highest for the ground joints.
Although fatigue lives of both as-welded and ground welds can be characterised by the crack growth process, there were some differences between the two, resulting in increased fatigue life for the latter. Examination of the various factors affecting the fatigue crack growth calculations indicates that the beneficial effects of toe grinding can be attributed to the following two aspects:
- Reduced stress intensity factor range, ΔK, when compared at the same nominal stress range and crack size. This was attributed again to two factors, the stress intensity magnification factor Mk and crack shape. Firstly, by toe grinding, Mk was significantly reduced. Secondly, because of the severe stress concentration along the weld toe, cracks in as-welded joints tend to adopt a lower aspect ratio. This was often enhanced by multiple crack initiation and coalescence of these cracks, Figure 7(b). On the other hand, the aspect ratio of cracks in ground joints was significantly higher and the fatigue life, or at least the majority of the fatigue life, of a specimen was dominated by growth of a single crack. This difference can be readily seen by comparing the fracture surfaces of the as-welded and ground joints in Figure 7. When approaching a through-thickness crack, the aspect ratio of the crack in the as-welded joint was 0.12, but was about 0.35 for the crack in the ground weld. ΔK decreases with increase in a/2c and consequently that for the ground joints was less than that for the as-welded joints at the same crack depth and applied stress range.
- Crack growth rates. The average growth rate for cracks growing from the ground weld toes was significantly lower than that for the as-welded joints. As described before, the crack growth parameter A for the as-welded joints was estimated to be A=2.5x10-13, significantly greater than the average value of A=1.3x10-13 found in the ground joints. This difference can be explained by the possible difference in residual stresses, and hence effective stress ratio, between the two types of joint, crack growth rate being influenced by stress ratio. Through residual stress measurements, it has been estimated that there is a sharp decrease in residual stresses through the plate thickness. This finding was related to a similar type of welded joint to the one tested in the present work but in 20mm thick by 250mm wide steel plate with a yield strength of 530MPa. Residual stress reached the maximum value of about 270MPa near the surfaces at the weld toes and decreased sharply with increasing distance from the surface, becoming compressive at the centre of the plate. It then increased again towards the back surface. At a depth of 0.8mm from the surface, which was the grinding depth in the current investigation, the residual stress decreased to about 150MPa (reduced by 44%). By grinding, a further reduction in residual tensile stresses or even the creation of compressive stresses can be expected. Thus, although the actual magnitudes of the residual stresses in the present specimens may have been lower than those investigated in , it does seem likely that the reduced crack growth rates observed in the ground joints are attributable to a more favourable residual stress state.
The above discussion can also explain the behaviour of ground joints in high strength steels. As toe grinding reduces the chance of crack initiation from flaws, crack initiation life is expected to be important in the total fatigue endurance. As a result, high strength steels (yield strength of about 700MPa) benefit more from toe grinding: a fatigue strength increase of over 100% was observed in the review by Booth. On the other hand, some specimens of high strength steels only saw an increase of about 30%, similar to the average increase found in low and medium strength steels (yield strength of 240-400MPa). It is likely that the high strength steel ground joints contained flaws, which offset any potential benefit from tensile strength. The large data scatter in S-N curves typically observed for ground joints[12,15,25] also supports this speculation.
The present results highlight the importance of welding flaws, which would be innocuous in an as-welded joint, in toe ground welds. Clearly, every effort should be made to avoid them or grind them out but a serious practical limitation is the problem of detecting such small flaws by current NDT methods. However, if they can be avoided it seems that a significant crack initiation period will be required before a fatigue crack starts to propagate, potentially leading to much greater improvement in fatigue life than that obtained from the present test specimens, and that the parent metal at the base of the groove produced by toe grinding is the most likely crack initiation site. Furthermore, on the basis of the rather limited current experimental data on crack initiation free from any flaws, it seems that a reasonable estimate of the crack initiation endurance can be obtained using the local approach proposed by Lawrence et al.
Based on a study of fatigue crack initiation and growth in toe ground fillet welded joints, the following conclusions were drawn:
- A replica method for detecting crack initiation from ground joints was successfully developed. It enabled the detection of surface cracks as little as 0.1mm in length.
- Burr grinding increased the fatigue endurance of the fillet welds by a factor of at least 4.6.
- It was revealed by the replica method that, even in ground joints, most cracks initiated from flaws on or just beneath the ground surface, consistent with the observation of initiation of these cracks in the weld metal.
- The fatigue performance of ground joints was predicted well using fracture mechanics fatigue crack growth analysis for endurance ≤106 cycles.
- Compared to as-welded joints, the increased fatigue performance of ground joints was attributed to i) reduced stress intensity magnification factor Mk; ii) reduced ΔK due to more favourable fatigue crack front shapes; and iii) slower crack growth rates possibly related to reduced tensile residual stresses.
- Reasonable estimates were made of the crack initiation endurances for those joints where crack initiation did not occur from flaws using the Lawrence approach.
This work was supported by the Industrial Members of TWI. In addition, the authors would like to thank the staff of the Fatigue Laboratory in carrying out the experimental work.
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