VSI: Fatigue of Welded Joints – Current State-of-the-Art A NOVEL PROCEDURE FOR DAMAGE EVALUATION OF FILLET-WELDED JOINTS

In the present paper, a novel procedure for fatigue resistance assessment of fillet-welded joints under complex random loading is proposed. It consists of two consecutive steps: (1) computation of the stress tensor at the verification point; (2) evaluation of damage and, consequently, fatigue life. The procedure exploits the multiaxial critical plane-based criterion by Carpinteri et al. for random loading. A case study, represented by a mechanical component of an arm sprayer used in agriculture, is examined in order to assess such a procedure. A comparison between experimental and numerical results in terms of crack nucleation location is performed.


INTRODUCTION
Fillet-welded joints, in the form of "T" joint, lap joint and corner joint, represent the most common connections in welded structures. Three approaches have been proposed in Ref. [5]: (i) nominal stress 5 approach, (ii) structural hot spot stress approach, (iii) effective notch stress approach.
As a matter of fact, the stress range may include or exclude the local stress raising effect coming from (1) discontinuity due to a structural detail of welded joint and (2) weld toe transition. More precisely: (i) Nominal stress approach: the stress range is computed or measured by exluding the local stress raising effect due to both discontinuity and transition; (ii) Structural hot spot stress approach: the stress range is computed or measured by including the local stress raising effect due to the above discontinuity, but excluding that due to the above transition; (iii) Effective notch stress approach: the stress range is computed or measured by including the local stress raising effect due to both discontinuity and transition.   The paper is organised as follows. Section 2 is dedicated to the description of the novel procedure. In Section 3, the case study is presented by giving details on the geometry and the stress field that characterise the fillet T-joint examined, and on the damage evaluation. The results obtained are discussed in Section 4, and conclusions are summarised in Section 5.

THE NOVEL PROCEDURE
Firstly, the proposed procedure requires to compute the stress state at the verification point and then the accumulated damage at the same point.

Computation of the stress tensor components at the verification point
Let us consider the point H in Figure 3, assumed as the hot spot, and the extrapolation path perpendicular to the weld [5].

Figure 3.
The stress state at a generic point along the above path is biaxial, that is, the stress tensor components different from zero are ,, xy  and xy  . In order to compute the values of such components at the hot spot, the extrapolation equation derived through the structural hot spot stress approach for type "a" hot spot and coarse mesh [5] is employed, that is: where the stresses with the subscripts 0.5T and 1.5T are those at two reference points which are 0.5T and 1.5T away from H along the extrapolation path, respectively, being T the plate thickness.

Damage and fatigue life computation
In order to compute damage and consequently the fatigue life, the multiaxial critical plane-based criterion by Carpinteri and the weight function   Wt is given by: The normal w to the critical plane is assumed to belong to the principal plane ˆ1 3 , and its direction is determined by rotating 1axis towards 3 -axis of an angle expressed by (in degrees): Once the critical plane passing through the verification point is identified, a local frame uvw is adopted, where the u-direction is represented by the intersection line between the critical plane and the wZ plane, and v forms an orthogonal frame with u and w .
The stress vector w S at the verification point may be decomposed as follows: where N is perpendicular to the critical plane, whereas C lies on such a plane and may be decomposed in two components, u C and v C , along the directions u and v , respectively.
Let us consider the scalar series A reduction procedure is performed on N -series in order to preserve only peaks and valleys of this series, and a new one, named * N -series, is obtained. As an example, let us consider three terms of the N -series, that is, The indexes of the latter terms are registered in a vector of two components, 12 ( , ) kk  K : in this case, . The reduction procedure operates as follows: In such a way, the number of terms for the N -and * N -series is the same and equal to n .
A reduction procedure is also performed on the C -series in order to preserve only the vectors that maximise the amplitude of C between a peak and a valley of the N -series. In more detail, if we consider the above case, i.e.
, the following amplitudes are computed according to the definition by Papadopoulos [26]: Then, if In such a way, the number of terms for C -and * C -series is the same and equal to n . The above two conditions on the C amplitudes are graphically shown in Figure 4. Furthermore, a numerical example of the above reduction procedure is reported in Ref. [20]. The rainflow counting method is applied to the * N -series. For each counted reversal, the maximum value of * N and the amplitude of * C computed as proposed in Ref. [26] are registered in order to determine the following equivalent stress amplitude: The damage accumulated during the observation period where cr D is the critical damage.

APPLICATION OF THE NOVEL PROCEDURE: A CASE STUDY
The case study here examined is represented by the top fillet-welded T-joint on the right-hand side of the H component shown in Figure   5, which is the weakest T-joint with regard to fatigue failure under service condition [21], as has been experimentally observed. The welding has been performed by means of a metal inert gas process.
The leg length of welding is equal to 5mm. 13

Multiaxial random stress field
The random stress field in the T-joint has been determined by employing both experimental measurements and finite element analysis  Table 1, together with how many times each maneuver is repeated during T .  Figure 5), whereas two fish-bone strain gauges have been arranged on one of the two braces (see point W3 in Figure 5).
For each of the manuevers listed in Table 1 Figure 5.
The material is C25E steel, whose mechanical properties are listed in Table 2

Damage evaluation
Let us consider the polar frame Or shown in Figure 6. The line starting from point O with an orientation  can be considered as a generic extrapolation path according to the structural hot spot stress approach (described in Section 2.1). Therefore, the generic 16 hot spot is the point at the intersection between such a line and the weld toe.  Table 1), and each value obtained is then multiplied by the number of times that a given maneuver is repeated during the observation time interval T (see last column of Table   1).
The fatigue parameters used in such a calculation refer to welding material, and are listed in Table 3. The total damage is determined by summing the damage accumulated for each maneuver during T . Table 3.
Both stress tensor and damage calculation are repeated by varying 

RESULTS AND DISCUSSION
In Figure 7, the probability density function of the stresses  (Figure 7(a)) and 6 m  (Figure 7(b)). Such an orientation is that along which the accumulated total damage is maximum with respect to the other orientations, whereas the maneuvers   (Figure 7(c)) and 6 m  (Figure 7(d)). From such curves, the number of loading cycles for which the maximum value or amplitude of the above stresses is greater than a given value can be deduced.  In Figure 9, the value of total damage is plotted against  in the chord (Figure 9(a)) and in the brace (Figure 9(b)).
An  increment of 15° is selected. can be concluded that the procedure proposed seems to identify, with significant accuracy, the region on the weld toe where cracks are expected to nucleate.

CONCLUSIONS
A novel procedure for fatigue resistance assessment of welded joints under complex random loading has been herein proposed.