Development of a computational fatigue model for evaluation of weld quality
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Abstract
The current study focuses on the development of a predictive model for assessing the fatigue life of welded joints based on measured weld geometry and applied load. Two different materials (S355 and S960) and two different material thicknesses (2 mm and 8 mm) were considered. Experiments on cruciform joints were conducted to evaluate the fatigue performance for different types of weld geometries. A computational model based on FEM and linear elastic fracture mechanics was developed and adapted to fit the experimental results using optimization and surrogate models.
It is observed that the general fatigue behavior differs for the different materials for the same variation in geometry. The fatigue performance depends on a combination of geometrical parameters. The use of FAT curves according to the weld quality systems, e.g., ISO 5817, is insufficient to describe fatigue properties for welds in thin high strength steel, and different geometries within different weld quality levels can give the same fatigue behavior. It is also concluded that the developed computational model is suitable for further development of weld quality systems.
Keywords
Welded joints Fatigue Fracture mechanics Weld quality Computational model1 Introduction
Many industries are currently making the transition to high strength steel (HSS) in their applications due to the many advantages with its high strength to weight ratio. These materials allow for lightweight designs with high strength while simultaneously keeping the material consumption to a minimum. The fatigue properties do, however, show a high dependency of the weld quality in structural applications manufactured using HSS which requires extensive quality control. This is a problem since recent studies show a weak relation between quality classifications and fatigue properties in the current international standard for weld quality assurance, ISO 5817 [1, 2, 3, 4, 5, 6]. The amount of various weld defects, and the equipment needed to correctly measure them, in the current standard also makes the quality assessment highly inefficient in practice. To allow the introduction of thin HSS in structural applications, a new standard for weld quality assurance is needed which accurately comprises the fatigue aspect. The standard must also be designed to allow for simpler and more efficient means of quality assessment to improve the communication between design and production departments.
The objective of this study is to develop and assess a method for predicting fatigue life in welded joints based on measured weld geometry and applied load. This involves creating a computational model based on finite element methods which is verified with fatigue testing on welded specimens with various defects in steel of different grades and thickness. The paper also aims to reduce the number of evaluated weld defects needed to simplify the quality assessment procedure in a production environment. The developed method is then used to benchmark the international standard along with other corporate standards for fatigue in thin HSS to create a foundation for further development of a new weld quality standard.
2 Weld quality
The quality of a welded joint is quantified as its durability in static or cyclic loading. According to Stenberg [2], the fatigue strength of a welded joint is mainly governed by processinduced residual stresses and geometrical imperfections/defects which introduces stress concentrations near the weld.
Although it is known that the earlier mentioned geometrical features have the most impact on the fatigue life of welds, their mutual influence is different. Further, their relative difference in influence on the fatigue strength is depending on the type of loading, and thus, virtually similar welds do perform differently in separate structures [3, 5].
2.1 Weld quality systems
The current weld quality system available is the international standard, ISO 5817 [2], which defines a set of quality classes based on acceptance limits for different weld geometry features. A weld can then be assigned a specific quality level based on the weld geometry. ISO 5817 identifies the quality classes as D, C, and B where a weld with the highquality level B is equated with a higher performance compared to a weld from the D and C class.

All types of weld imperfections within a weld quality level results in the same fatigue life

By shifting to a level with higher weld quality the resulting fatigue strength is increased with 25%. This roughly corresponds to a doubling of the fatigue life.
Example of acceptance limits for quality level in STD 1810004 [1]
Discontinuity types  VS  VE  VD (normal quality)  VC (high quality)  VB (improved quality) 

Weld class for  Static strength  Fatigue strength  
Cold lap  Permitted  a ≤ 1 mm  a < 0.5 mm  a < 0.1 mm  Not permitted 
Internal lack of fusion  a ≤ 0.2 t  Not permitted  Not permitted  Not permitted  Not permitted 
Weld toe transition radius  No requirements  No requirements  R > 0.3 mm  R > 1 mm  R > 4 mm 
Undercut^{1}  a ≤ 0.2 t [max 2.0 mm]  a ≤ 0.1 t [max 1.0 mm]  a < 0.05 t [max 1.0 mm]  a < 0.04 t [max 1.0 mm]  Not permitted 
Underpassed throat dimension  a ≥ 0.8a  a ≥ 0.9a [max 2.0 mm]  a ≥ 0.9a [max 2.0 mm]  Not permitted  Not permitted 
Edge displacement (linear misalignment)  a ≤ 1.5 t + 0.25 t [max 5.0 mm]  a ≤ 1.0 t  a < 0.1 t  a ≤ 0.05 t  Not permitted 
An annex with further requirements for welds subjected to fatigue have recently been incorporated ISO 5817 which adjusts the imperfection limits for weld class C and B to conform with the general fatigue classes FAT63 and FAT90, respectively. These quality classes are referred to as C63 and B90 [2].
2.2 Digitalized weld quality measurement
The quality of a welded joint has historically been assessed manually using simple mechanical gauges to evaluate the local geometry at discrete points along a weld bead [8].
Recently, more sophisticated assessment procedures have been developed allowing for faster geometry readings with higher accuracy. Stenberg et al. [9] developed a method based on a visual system using the stripe light projection method to measure the local weld geometry. Further, they developed a numerical evaluation algorithm to allow for stable and objective geometry assessments. This concept is now incorporated in the software Winteria® [10] which carries the practice of weld quality assessment into the digital era giving fast and reliable access to the weld information needed for fatigue life assessment of welded structures [8].
3 Experimental setup
3.1 Test specimens
Classification of fatigue specimens, mean local weld geometry
Batch  Series  Throat size, TS [mm]  Leg right, LR [mm]  Leg left, LL [mm]  Toe radius, TR [mm]  Undercut, U [mm]  Qty. 

S355 8 mm  Normal  4.68  6.61  8.26  1.86  0.01  18 
Undercut variation 1  4.22  5.97  7.68  1.62  1.59  6  
Undercut variation 2  4.20  5.94  6.70  1.13  0.74  6  
Toe radius variation 1  3.98  5.64  6.09  0.31  0.01  12  
Toe radius variation 2  4.79  6.77  6.52  0.82  0.01  6  
S355 2 mm  Normal  1.64  2.31  3.09  0.54  0.08  8 
Undercut variation  1.97  2.78  3.09  0.38  0.49  17  
S960 8 mm  Normal  5.38  7.61  7.51  2.02  0.05  18 
Undercut variation 1  4.73  6.69  6.71  1.43  0.38  6  
Undercut variation 2  5.21  7.37  6.55  1.13  1.47  6  
Toe radius variation  4.25  6.00  7.00  0.44  0.02  12  
S960 2 mm  Normal  1.87  2.65  3.18  0.41  0.11  16 
Undercut variation 1  2.03  2.87  3.05  0.45  0.44  6  
Undercut variation 2  2.04  2.89  2.76  0.36  0.43  4  
Leg variation  2.06  2.91  2.57  0.28  0.25  12 
3.2 Test specimens
3.3 Residual stress measurement
The peening effect of sandblasting is known to induce compressive stresses in metallic materials which in turn could affect the fatigue life of the specimens. The first experiment aims to determine the level of induced residual stresses from sandblasting while the second experiment determines the relaxation behavior due to cyclic loading. Xray diffraction technique was used to measure the residual stresses on the surface with Stresstech G3 Xtronic. The residual stress is measured close to the weld toe before and after cyclic loading. The cyclic count is chosen to the relatively low value of 1e4 cycles to allow for the conclusion that, if there is induced residual stresses, the stresses are relaxed after such an early stage that the effect on the fatigue life can be neglected. The load levels are chosen to 110 MPa which corresponds to the low region of recorded fatigue failures to make the above reasoning applicable to all fatigue specimens. This is done for both untreated and sandblasted welds for batches S355 2 mm and S960 2 mm.
4 Computational fatigue model
4.1 Finite element analysis
The complete computational algorithm is built up in two segments where the first segment solves the model to extract and save the position of the largest principal stress. The geometry is then rebuilt in the second segment with an introduced crack at the position of the largest principal stress. The second segment is looped over a predetermined set of crack depths, and information needed to obtain the stress intensity factor is exported for every iteration. By benchmarking the obtained stress intensity factor against an analytical solution of a fracture mechanics problem, with similar characteristics, the mesh size is determined with consideration of the tradeoff between computational time and accuracy.
The heat induced by the weld procedure during the manufacturing of the specimens may result in residual bending deformation of the base plate. This initial curvature will induce additional bending stress in the specimen when straightened out under axial loading and must be accounted for in the analysis. This bending contribution is not possible to model with the symmetric model, hence the introduction of the auxiliary beam section.
The model is solved in two separate load cases where load case one is simple axial loading of the symmetric solid section and the beam acts as an unloaded appendage. The second load case is modeled with a displacement at one end which corresponds to straightening out the bent plate during axial loading. Since linear behavior is assumed, the displacement fields from the two load cases can be superimposed to create one coherent solution.
4.2 Crack propagation modeling
The critical crack length a_{cr} corresponds to the crack length where the stress intensity factor reaches the materials fracture toughness and immediate failure occurs.
This coupling between the SN fatigue data and the fracture mechanics approach is enough to experimentally determine the unknown parameters needed to perform fatigue life calculations with a computational model based on fracture mechanics. The unknown parameters are a_{0}, β, ΔK_{6}, and f(a, geometry).
4.3 Calibration
The computational model is calibrated with the experimental SN data by finding and assigning optimal values for the unknown Paris’s law parameters a_{0}, β, and ΔK_{6} to match the computed and experimental fatigue life. This is done separately for each specimen, and the dependency of weld geometry is obtained. The model is calibrated separately for each specimen batch. For simplicity, ΔK_{6} is set to the representative values of \( 75\ \mathrm{MPa}\sqrt{m} \) and \( 85\ \mathrm{MPa}\sqrt{m} \), for the steel grades S355 and S960 respectively, which reduces the number of unknown parameters. β must be chosen to represent a slope in the SN diagram. The natural approach is to assign one β to each specimen series in a batch where the slope is already obtained by linear fitting of the SN data. The weld geometry parameters assigned to each β is set to the mean values over the respective series.
4.3.1 Determination of a _{0}
For every specimen, the parameter a_{0} is obtained with such a precision that the difference between the computed and experimental fatigue life is virtually zero. Every obtained value of a_{0} is assigned with the geometry parameters for respective specimen.
4.3.2 Multivariate polynomial interpolation
To allow for fatigue life evaluation of an arbitrary weld geometry, the parameters a_{0} and β must be expressed as functions of the weld parameters. This is done using the polynomial interpolation approach where a_{0} and β are used as the function values in Eq. 8.
The obtained linear equation system can be written on the matrix form Ax = B which is solved for the unknown polynomial coefficients. A leastsquare solution is returned if the number of sample points is larger than the number of unknown coefficients, i.e., if the system is overdetermined [12].
With the associated geometry parameters set as the independent variables, a set of linear equations is obtained and the coefficients of the polynomial expressions can be determined. The geometry parameters are assumed to be independent of each other since the dependency is unknown.
4.3.3 Computational model – flow chart
4.4 Benchmark of weld quality systems
Excerpt from ISO 5817 with applicable geometry parameters
Weld class  

Parameter  Thickness  C63  B90 
Toe radius, TR  ≤ 3 mm  Not defined  Not defined 
> 3 mm  Not defined  Not defined  
Undercut, U  ≤ 3 mm  U ≤ 0.1 × thickness  Not permitted 
> 3 mm  U ≤ 0.1 × thickness max: 0.5 mm  U ≤ 0.05 × thickness max: 0.5 mm  
Throat deviation, TD  ≤ 3 mm  TD ≤ 0.2 mm  Not permitted 
> 3 mm  TD ≤ 0.3 mm + 0.1 × throat size max: 1 mm  Not permitted 
Excerpt from Volvo STD 1810004 with applicable geometry parameters
Weld class  

Parameter  VD  VC 
Toe radius, TR  TR ≥ 0.3 mm  TR ≥ 1 mm 
Undercut, U  U ≤ 0.1 × thickness max: 1.5 mm  U ≤ 0.08 × thickness max: 1.5 mm 
Throat deviation, TD  TD ≤ 0.1 × throat size Larger throat is ok  Larger throat is ok 
Range of parameter values used in parameter sweep
Parameter range  

Parameter  t = 8 mm  t = 2 mm 
Toe radius, TR  0.5 mm ≤ TR ≤ 4 mm  0.5 mm ≤ TR ≤ 4 mm 
Undercut, U  0.65 mm ≥ U ≥ 0 mm  0.2 mm ≥ U ≥ 0 mm 
Throat size, TS  4 mm ≤ TS ≤ 4.5 mm  1.8 mm ≤ TS ≤ 2 mm 
The first approach is to define discontinuity domains with acceptance limits corresponding to each weld quality level. For example, the discontinuity domain for weld class VD ranges from its lower acceptance limits up to the acceptance limits for the next class, VC. By computing the fatigue performance for different sets of parameter values within a weld class, and present it on a SN diagram, it is possible to map weld geometries from a discontinuity domain to a fatigue performance domain. By comparing the fatigue performance domains for all weld classes with its corresponding FAT value [13], conclusions can be made on the applicability of the quality systems. The second approach is to determine the fatigue strength corresponding to failure at 1e5 cycles for different sets of weld geometry parameters. These are presented in a diagram which represents the fatigue performance for different variations of geometry parameters.
5 Results
5.1 Fatigue test
5.2 Residual stress relaxation
Residual stress measured in fatigue specimen before and after cyclic loading
Residual stress [MPa]  

Before cyclic loading  After cyclic loading  
Specimen  Load direction  Transverse  Load direction  Transverse 
S355 PL7 1—Sandblasted  −176  −212  −177  −211 
S355 PL7 2—Untreated  −120  −226  −143  −219 
S960 PL7 1—Sandblasted  −290  −322  −298  −355 
S960 PL7 2—Untreated  −20  −207  −19  −208 
The results show no indication of relaxation due to cyclic loading for either material batch. It also shows a difference in compressive stress in the untreated specimens between the two steel grades. Further, the sandblasting influence on compressive stresses in the weld toe is much more significant for the S960 steel.
5.3 Verification of computational model
Figures 14, 15, 16, and 17 show N_{exp} vs. N_{comp} for each material grade illustrating the capability of the computational model. The dashed lines represent 50% deviation in computed fatigue life. The N_{exp}N_{comp} diagrams for 8 mm plate thickness and both material grades show a relatively low difference between computed and experimental fatigue life. The increased scatter of data points for higher fatigue life indicates a loss in performance at higher cycle counts. However, the largest deviation between experimental and computed fatigue life is roughly 50%.
The results for both 2mm batches show great scatter over the whole experimental range reaching a factor of ten in the difference between experimental and computed fatigue life. This indicates a poor model performance for thin plates.
5.4 Benchmarking of weld quality systems
The benchmarking of the weld quality systems is only conducted for 8mm steel thickness since the computational model showed a poor performance for the 2mm specimens.
The results show a large performance span within each quality level for both steel grades and a trend of increased fatigue strength for levels with higher weld quality. The results also show a tendency of overlapping performance between quality levels. Further, the S960 steel grade show better performance at higher load levels but a rapid decline with decreased load levels. By inspection of the fatigue strength at the lower bounds of the quality classes VD and VC, an increase in fatigue strength of roughly 20–30% is found for S355 and 10–25% for S960. The difference varies with the load level. This finding causes an overestimation of life for higher load levels as well as an underestimation of life for lower load levels.
Figures 20 and 21 show the fatigue performance domains corresponding to discontinuities within each weld class from ISO 5817 for the steel grades S355 and S960 respectively.
The results show wide performance spans for both steel grades with some overlapping between the weld classes C63 and B90. By once again comparing the fatigue strength corresponding to the lower bounds of classes C63 and B90, an increase in fatigue strength of 50–60% is found for S355 and 15–60% for steel grade S960.
Figures 22 and 23 show the influence from undercut and toe radius on the fatigue strength corresponding to failure at 1e5 cycles for the two steel grades S355 and S960 respectively. Both diagrams also show the span in variation of the toe radius which the experimental data covers. The colored areas correspond to quality levels within STD 1810004.
The results from the parametric study shows that the fatigue strength for the S355 material is increasing with larger weld toe radius; it also shows that a larger undercut gives lower fatigue strength. The general behavior for the S960 material is partly different showing a lesser influence on the fatigue strength due to change in the toe radius compared to the S355 material. The behavior in fatigue strength for the two materials is very similar for a small toe radius.
6 Conclusions

The developed computational fatigue model is considered to be validated for fillet welded joints with 8mm thickness and could be used as a tool for benchmarking of different weld quality systems and further development and upgrades these systems.

The residual stress shows no relaxation at a nominal stress range of 110 MPa for both material grades, S355 and S960. It is also observed that the sandblasting influence on compressive stresses in the weld toe is much more significant for the S960 steel.

The developed model does not describe the fatigue behavior for the fillet welds with 2mm plate thickness. The ASTM condition [14, 15] for the validity of linear elastic fracture mechanics is not fully satisfied since the crack length is too large in comparison to the thickness of the plates used for the specimens. This tells that the plastic zone near the crack may be relatively large compared to the dimensions of the load carrying area at the weld. This can be one of the reasons for the poor model behavior for the 2mmthick plates.

Fatigue performance depends on a combination of the geometry parameters. The general fatigue behavior due to a change in the geometry parameters and weld quality is different for the fillet welds in S355 and the S960 materials.

Different geometries within different weld quality classes can give the same fatigue behavior. The results show that the fatigue performance for the weld quality levels spans over a large range and that there is overlap between the quality levels. The overlap essentially means that one specimen geometry within one of the quality levels can give the same fatigue performance as a different geometry within a different quality level.
Notes
Acknowledgements
Open access funding provided by Royal Institute of Technology. SCANIA CV is acknowledged for the financial support of this work. Swerea KIMAB is acknowledged for manufacturing the specimens.
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