In the past decade, high-frequency mechanical impact (HFMI) has significantly developed as a reliable, effective, and user-friendly method for post-weld fatigue strength improvement technique for welded structures. During this time, period 46 documents on HFMI technology or fatigue improvements have been presented within Commission XIII of the International Institute of Welding. This paper presents one possible approach to fatigue assessment for HFMI-improved joints. Stress analysis methods based on nominal stress, structural hot spot stress, and effective notch stress are all discussed. The document considered the observed extra benefit that has been experimentally observed for HFMI-treated high-strength steels. Some observations and proposals on the effect of loading conditions like high mean stress fatigue cycles, variable amplitude loading, and large amplitude/low cycle fatigue cycles are given. Special considerations for low stress concentration details are also given. Several fatigue assessment examples are provided in an appendix. A companion paper has also been prepared concerning HFMI equipment, proper procedures, safety, training, quality control measures, and documentation has also been prepared. It is hoped that these guidelines will provide stimulus to researchers working in the field to test and constructively criticize the proposals made with the goal of developing international guidelines relevant to a variety of HFMI technologies and applicable to many industrial sectors. The proposal can also be used as a means of verifying the effectiveness of new equipment as it comes to the market.
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- D :
Damage sum for variable amplitude loading
- f y :
IIW fatigue class, i.e., the nominal stress range in megapascals corresponding to 95 % survival probability at 2 × 106 cycles to failure (a discrete variable with 10–15 % increase in stress between steps)
IIW thickness correction factor
- k R :
Strength reduction factor for stress ratio, 1 ≥ k R > 0
- K :
- m :
Slope of the S–N line 1 × 104 ≤ N < 1 × 107 cycles
Slope of the S–N line 1 × 107 cycles ≤ N
- L :
Characteristic length used to compute f(t)
- N :
- R :
- t :
- X N :
Improvement factor in life for HFMI treated welds at Δσ equal to the FAT class of the as-welded joint: N f = X N × 2 × 106
- \( \rho \) :
Weld toe radius
- σ :
- Δ\( \sigma \) :
- eff :
- eq :
Equivalent (stress range)
- f :
Failure (cycles) or fictitious (weld toe radius)
- k :
Corresponding to the knee point of the S–N curve
- S :
Structural hot spot stress
- max :
Maximum value: during one cycle for constant amplitude loading or during one repetition of the spectrum for variable amplitude loading
- min :
- nom :
- w :
Value computed using the effective notch method
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Support for this work has been partially provided by the LIGHT research program of the Finnish Metals and Engineering Competence Cluster (FIMECC), the Finnish Funding Agency for Technology and Innovation (TEKES), and the European Union’s Research Fund for Coal and Steel (RFCS) Research Program under grant agreement n° RFSR-CT-2010-00032: "Improving the fatigue life of high-strength steel welded structures by post-weld treatments and specific filler material."
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Appendix I: Characteristic nominal stress S–N curves for HFMI-improved welded joints for high-strength steels
Appendix II: Examples
2.1 Example 1: Nominal stress design for a detail subjected to high R ratio
Consider the case of a welded detail which in the as-welded condition corresponds to FAT 63. The joint is fabricated from f y = 960 MPa steel and will be subjected to R = 0.5 loading.
What is the suitable characteristic line for design?
Based on Fig. 7, an increase of eight fatigue classes can be claimed for R ≤ 0.15. The resulting S–N curve FAT 160 (63) is shown in Appendix I as Fig. I-3. Based on Table 3, the S–N curve for R = 0.5 is reduced by three fatigue classes with respect to R ≤ 0.15 loading so the characteristic curve is considered to represent five FAT class improvement, i.e., FAT 112 (63). This is shown in Fig. II-1. With respect to Fig. 9, the limitation on the maximum stress range that can be applied to a weld in order to claim benefit from HFMI treatment in this example is Δσ = 384 MPa. This value would correspond to N ≈ 4,220 cycles. The characteristic line shown in Fig. II-1 is therefore considered to be valid over the entire life range shown.
2.2 Example 2: Nominal stress design for a detail subjected to variable amplitude loading
Consider the case of a longitudinal welded attachment from steel with f y = 700 MPa, subject to variable amplitude loading. The target fatigue life is 1 × 107 cycles. Each load cycle has R = 0 and Δσ eq = 0.20 × Δσ max based on Eq. 3.
Will HFMI be an effective improvement technology for this design case?
In the as-welded condition, a typical longitudinal attachment is FAT 71. According to Fig. 7, a detail fabricated from f y = 700 MPa shows six fatigue class improvement due to HFMI. The resulting characteristic S–N curve is FAT 140 (71); see Appendix I Fig. I-2.
This characteristic curve intersects 1 × 107 cycles at Δσ eq = 102 MPa. Based on the design load spectrum, the maximum stress which occurs is 102/0.20 = 510 MPa. According to Fig. 9, the maximum allowable stress range for f y = 700 MPa at R = 0 is 560 MPa. Thus, HFMI is expected to be fully effective for this component.
For comparison purposes, the characteristic fatigue life for a FAT 71 welded joint subjected to Δσ eq = 102 MPa would have a characteristic fatigue life of N f = 675,000 cycles. Therefore, for this design case, HFMI is computed to result in a fatigue life increase of 14.8×. See Fig. II-2.
2.3 Example 3: structural hot spot based assessment for a detail subjected to variable amplitude loading
Consider an HFMI-treated non-load-carrying structural detail which is subjected to variable amplitude loading for which the cycle range distribution is approximately log-linear. Assume that Δσ eq = 0.387 × Δσ max when computed according to Eq. 3 with D = 0.5. Each cycle has R = −1. The structure is fabricated from S960 steel. The computed structural stress concentration is K s = 1.21.
Construct the characteristic line and compare it to experimental results.
As shown in Fig. 10 or Tables 4 and 6, a non-load-carrying detail fabricated from S960 (f y = 960 MPa) steel treated by HFMI has a resulting structural hot spot S–N characteristic curve of FAT 250 with the requirement that K s,min = 1.4. Because the computed K s < K s,min, K s,min is used to compute Δσ s,eq. The loading is R = −1 so Δσ s,eq = (0.387 × 2) × K s,min × σ max. Results are shown in Fig. II-2. From the data table, it can be seen that the maximum nominal stress range for the first two experimental points exceed the limiting curves in Fig. 9. Therefore, the FAT 250 line is not necessarily expected to be conservative with these two points since the beneficial residual stresses may relax out. A conservative approach would be to assume that joints with such high nominal stresses behave according to the as-welded line. Alternatively, the effective notch method with a FAT 225 S–N curve could be using ρ f = ρ + 1 mm with ρ as the actual HFMI groove radius. As mentioned in “Section 4,” this is a topic requiring further study. For comparison purposes, Fig. II-2 also shows the experimental data with Δσ s,eq computed using K s (rather than K s,min) and D = 1.0 in Eq. 3 instead of the recommended D = 0.5.
2.4 Example 4: effective notch stress-based assessment for a detail subjected to variable amplitude loading
Consider an HFMI-treated structural detail which is subjected to variable amplitude loading for which the cycle range distribution is approximately Gaussian. Assume that Δσ eq = 0.504 × Δσ max when computed according to Eq. 3 with D = 0.5. Each cycle has R = −1. The structure is fabricated from S700 steel.
Construct the characteristic line and compare with experimental results.
As shown in Fig. 12 or Table 5, a detail fabricated from S700 (f y = 700 MPa) steel treated by HFMI has a resulting effective notch method characteristic S–N curve of FAT 400. Because the loading is R = −1, Δσ w, eq = (0.504 × 2) × σ w, max. If it is assumed that K s = 1.22 and K w = 2.08, the maximum nominal stress range for all of the experimental points would be below the limiting curves in Fig. 9. Therefore, the FAT 400 is expected to be conservative with respect to 95 % of all of the experimental data. Results are shown in Fig. II-3. It is clear that the experimental data are conservative with respect to the characteristic line. For comparison purposes, Fig. II-3 also shows the experimental data with Δσ w,eq computed using D = 1.0 in Eq. 3 instead of the recommended D = 0.5.
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Marquis, G.B., Mikkola, E., Yildirim, H.C. et al. Fatigue strength improvement of steel structures by high-frequency mechanical impact: proposed fatigue assessment guidelines. Weld World 57, 803–822 (2013). https://doi.org/10.1007/s40194-013-0075-x
- High-frequency mechanical impact (HFMI)
- Weld toe improvement
- Fatigue improvement
- High-strength steels
- Fatigue design
- Hot spot stress
- Effective notch stress