Welded joints under multiaxial non-proportional loading

Abstract The present paper examines the fatigue behaviour of a fillet-welded tubular T-joint in the so-called H structural component of an agricultural sprayer. Since the experimental measurements, performed in some control locations of the equipment, have highlighted a stress/strain field of random nature, an equivalent deterministic cyclic loading is here defined in order to simplify the fatigue analysis. Such an equivalent loading is able to accumulate damage values equal to the experimental ones in correspondence of the above control locations. The present study shows that it is possible to neglect the actual nature of loading provided that a suitable equivalent deterministic cyclic loading is taken into account.

Such substances are applied by means a pulverisation process, performed by systems named agricultural sprayers.
One of the most common systems is the arm sprayer, that consists of a metal truss structure (named bar), equipped of spray nozzles (Figure 1(a)). The bar is raised and lowered in vertical direction by a structural component, that is named H component due to its shape (Figure 1(b),1(c)).
The H component consists of tubular elements fillet-welded as T-joints (Figure 1(c)). Each Tjoint, made of C25E steel, is composed by a chord (with rectangular hollow cross-section) and a brace (with cylindrical hollow cross-section).

Figure 1.
The present paper examines one of the above T-joints, which are the weakest links of the structural component with respect to the failure. As a matter of fact, high stresses are concentrated near the welds, and cracks are frequently observed after relatively few hours of sprayer service condition (Figure 2).
Note that each maneuver (i.e. shifting the tractor, application of the herbicide on the perimeter of the uncultivated field, application of the herbicide on the cultivated area, braking) was performed twice a day: one when the tractor fuel tank was full, and the other one when the fuel tank was empty.    The present study shows that, even in presence of a random stress/strain field, the fatigue assessment of a metallic structural component can be performed by considering a suitable equivalent deterministic cyclic loading. Such a conclusion can be interesting in industrial applications: as a matter of fact, the nature of random loading is often non-Gaussian, and that makes the problem even more complex.
In details, the paper is organised as follows. In Section 2,

Such a H component consists of fillet-welded tubular T-joints
in as-welded condition. The welding is performed by means a metal inert gas process. The thickness of the tubular components is equal to 4.75mm. The leg length of the fillet welding is equal to 5mm.

Loading condition
The strain field in the H component was measured at locations W1, W2, and W3 (shown in Figure 1(c)), named control locations in the following.
The service condition investigated consists of the maneuvers listed in Table 1. In more detail: Note that each maneuver was performed twice a day: one when the tractor fuel tank was full, and the other one when the fuel tank was empty. Table 1 lists the duration of each maneuver described above, with reference to the time (2000 hours of sprayer operation under typical service condition) after which fatigue damage appeared in the equipment (see Figure 2).

Table 1.
Note that, although the damage numerically computed at locations W1,W2 and W3 after 2000 hours of sprayer operation is lower than the unity, the experimental campaign showed fatigue damage in regions near welding (Figure 2), that is, some material locations along the crack paths were characterized by a damage value equal to the unity.

Results
This Section describes the experimental data and their treatment.
The strain field in the ''H" component was measured at locations W1, W2, and W3, shown in Figure 1(c). More precisely, 8 two tee rosettes mounted on a complete-bridge Wheatstone circuit were arranged on each chord (circuits W1 and W2), whereas two fishbone strain gages mounted on a complete-bridge Wheatstone circuit were arranged on the brace (circuit W3) (Figure 1(d)).
By using the strain measurements coming from the control locations, the principal stress sequences related to the maneuvers listed in Table 1 were determined at the material locations W1, W2, and W3 [29]. The acquisition frequency was equal to 1kHz and the cutoff frequency, in the low pass filter used, was equal to 20Hz. As is indicated in Figure 1  , related to the maneuver named 'Travel on unpaved road -empty fuel tank' in Table 1, are plotted over a time interval of about 210.0 sec.
The rainflow counting procedure is then applied to both  Table 2.
The fatigue properties of welding are also listed in Table 2.
Note that each fatigue parameter in such a    (10 nodes). The adopted discretization is shown in Figure 4, where the finite element mesh is derived from a convergence analysis, being the minimum finite element size equal to about 0.7mm.    Table 1.
Regarding the random procedure, Figure 7 shows some results referred to the stress field at a material location 1 C along a crack path experimentally observed in the chord (Figure 2), near the welding that joints the chord and the brace. Such a location is shown in Figure 8, where the whole crack paths determined through a digitalisation procedure performed on the pictures shown in Figure 2 are also plotted.
It can be observed that shear stress (Figure 7(c)) is shifted with respect to the normal stresses (Figs 7(a) and (b)). The same trend is observed for all maneuvers.   Table 2 for C25E steel. Note that such a stress amplitude represents the amplitude of a cyclic stress that, acting at either location W1 or location W2 for   Table 3).

Figure 9.
Because a shifting of the shear stress with respect to the normal stresses is observed at location 1 C by employing the random procedure (see Figure 7), let us consider an analogous shifting also for the deterministic stress state at location 1 C , so that the stress field at such a location can be described as follows: where  is the pulsation, t is the time, and  is the angle of phase shifting. Different values of  are assumed: 0, 15, 30, 45, 60, 75 and 90 degrees.

FATIGUE STRENGTH ASSESSMENT
According to the results shown in the previous Section, a multiaxial fatigue criterion has to be employed to perform the fatigue assessment of the H component. More precisely, the criterion is applied to a material location at a certain distance from the weld toe.
Such a location is characterised by a damage value equal to the unity, because it is located along the crack path experimentally observed in the chord (Figure 2(b)).
The number of loading cycles to failure, f N , is determined by solving the following equation: According to the Carpinteri criterion, the orientation of critical plane is determined as follows. ) are identified. Then, the normal w to the critical plane is linked to the averaged principal direction 1 through an off-angle  , which is defined as follows ( w belongs to the principal plane 3 1 , and the rotation is performed from 1 to 3 ): The equivalent stress amplitude related to the critical plane, according to the Carpinteri criterion, is given by:

RESULTS AND DISCUSSION
The results in terms of fatigue life, More precisely, the results in Table 4 are determined using the fatigue properties of welding (Table 2), whereas those in Table 5 are derived using the fatigue properties of C25E steel ( Table 2). Table 4. Table 5.
By employing the results listed in Tables    Furthermore, note that the equipment fatigue failure after 2,000 hours is only an estimation, that is, such a value should not be considered as a value with statistical consistency. Figure 10 shows the damage D , averaged on the different values of  (for a given value of n ), against the reference number of loading cycles, n , by employing the fatigue properties of both welding (Figure 10(a)) and steel (Figure 10(b)), with the damage computed through the Carpinteri criterion. The above results are well fitted by logarithmic curves, the equations of which are given by: employing the welding fatigue properties (Figure 10(a)), and: employing the steel fatigue properties (Figure 10(b)).
Using Eq.(13), the reference number of loading cycles to produce a damage equal to 1.0 at the verification location should be equal to 672976, whereas it should be  n 460528 if Eq.(14) were used.

CONCLUSIONS
In the present paper, the fatigue assessment of an agricultural sprayer has been discussed.
More precisely, the T-joint named H component has been examined, because it is the weakest link of the sprayer with respect to the failure.           Table 1:

FIGURES AND TABLES
XYZ is shown in Figure 5.  Table 3.