Testing and Fatigue Life Assessment of Timber Truck Stanchions

: Components of transport trucks are subjected to dynamic cyclic loads. The magnitude of these loads depends on road conditions and cargo mass. Cyclic loads can cause fatigue failure at stress levels signiﬁcantly below the yield strength of the material. When calculating fatigue, it is necessary to determine the actual loads acting on the structure under working conditions. In this study, stanchion displacements of overloaded timber trucks were measured under both static and dynamic loads. For the speciﬁed mass of timber, a history of dynamic loads acting on the stanchion was obtained. Then, based on the ﬁnite element analysis, stress concentration points were determined within the base material and welded joints of the stanchion. The history of maximum stresses at concentration points was determined. Stress ranges and mean stresses for the load history were calculated using the rainﬂow fatigue cycle counting method. Repeats to failure were determined on the basis of the Palmgren–Miner cumulative damage rule and the modiﬁed Goodman correction for the points with the highest stress level. Experimental investigation of the actual load history of the stanchion of signiﬁcantly overloaded timber truck allowed to determine the mileage to potential failure.


Introduction
Timber trucks are commonly used to transport logs on both forest and public roads. Transportation is the most expensive part of the timber production process. The relationship between the volume of timber cargo and its actual weight can be difficult to accurately determine. According to statistical studies, up to 60-80% of timber truck sets in European countries can be overloaded. This means that the timber cargo is heavier than can be carried by the truck within the cargo volume. In such cases, the permissible total weight of a timber truck set can be exceeded by up to 50% [1]. The possibility of significant overload makes it advisable to include it in the design process of truck components. It is particularly important to determine the actual load history for fatigue calculations. In general, the assessment of the fatigue life of structural components is based on determining stress amplitudes and mean stresses and considering S-N diagrams of the materials. The load history for the design process can be accepted with constant amplitude according to standardized load histories (SLHs) or based on measurements under service loads. For load cycles that are not fully reversed, mean stress correction is required [2]. Problems related to fatigue life prediction of constructional elements were raised by authors of numerous publications. Będkowski provided a historical outline of fatigue analysis and described current trends in assessing the fatigue life of engineering structures under service loads [3]. Classification criteria of fatigue failure and stress state components for multiaxial load conditions were also discussed. Mrzygłód and Zieliński [4] and Mrzygłód [5] presented problems related to the numerical implementation of multiaxial high-cycle fatigue criterions in structure optimization. An original method of calculating fatigue life of a soldered construction node based on the two-parameter fatigue characteristics and the linear cumulative damage hypothesis was developed by Szala [6]. Armentani et al. presented findings in [7] on the fatigue behavior of single multiple-riveted lap joints used for aeronautic structures. Both the fatigue life and critical crack size were analyzed. Romanowicz and Szybiński delivered analytical formulas in [8] for determining stresses in the contact area and proposed a methodology for fatigue life assessment of rolling bearings by applying the multiaxial high-cycle fatigue hypothesis. In [9], Romanowicz presented a numerical evaluation of the fatigue load capacity of the cylindrical crane wheel. The application of multiaxial high-cycle fatigue criteria for analyzing the subsurface rolling contact fatigue of structures working in contact conditions was discussed. Studies by Savkin et al. [10] and Jadav et al. [11] referred to the fatigue analysis of truck frames under service loads. In turn, dynamic loads resulting from the actual road roughness were considered in the truck frame fatigue analysis by Zehsaz et al. [12].
Experimental tests are crucial for fatigue failure analysis. These tests may concern the collection of load history data or the execution of fatigue tests for specified load sequences. For example, Yuan et al. presented findings on the fatigue life assessment of a wheel loader [13]. The history of external loads was obtained on the basis of experimental tests involving strain gauge measurements and the load identification model. A cumulative damage theory and a structural stress method were applied to determine the fatigue life of welded components. In the study by Han et al., the method of fatigue strength evaluation of a bogie frame was proposed [14]. Analysis included calculations of cumulative fatigue damage and experimental verification on a full-scale test rig. In addition, an increase in the dynamic factor was assumed in the following fatigue test sequences. Meanwhile, a fatigue life prediction of the end beam of a freight car bogie was developed in the study by Baek et al. [15]. Finite element stress analysis and the fatigue damage prediction based on the rainflow cycle counting method were involved. Load sequences obtained from measurements during starting and braking were used for fatigue tests on the test bench. In [16], Witek presented the analysis of compressor blades subjected to high-cycle fatigue. The study involved the numerical determination of stresses and crack initiation analysis after damage caused by a foreign object. Finite element results were compared with experimental vibration tests. Song et al. presented research on the fatigue life assessment of the purified terephthalic acid filter press of welded shell structure [17]. The tested pressure was determined by experimental analysis, while the finite element method was used for fatigue life calculations and optimization. The thermomechanical model and high-cycle regime were considered. Both the fatigue strength reduction method and the hot-spot method were used to assess the fatigue life of welded joints.
In this paper, the fatigue life of timber truck stanchions operating under significant overload conditions was examined. Experimental tests were carried out to determine the actual loads acting on the stanchion. Then, based on finite element analysis, weak points of the structure and the corresponding stress history were determined. By applying a modified Goodman mean stress correction and the Palmgren-Miner cumulative damage rule, the life to failure of the stanchion was determined.

Experimental Load History Data Collection
An experiment was conducted under operating conditions in order to determine the actual load history of a single stanchion. Two pairs of stanchions with a nominal load of 50 kN were used in tests on local roads. Figure 1 shows the timber truck before the cargo was loaded, and Figure 2 shows the truck during timber loading. Direct measurements of the forces acting on particular points of the stanchion are rather problematic. Therefore, it was decided to measure the transverse displacement of the free end of the stanchion and determine the forces based on the assumed distribution of masses and dimensions of the logs. The measuring system consisted of a displacement transducer mounted on a support fixed to an additional unloaded stanchion and a rigid beam mounted on the loaded stanchion as shown in Figure 3.   The data recorder was placed in the truck cab. The timber truck was loaded with logs and then weighed. The static load was 140 kN, and thus the static overload was 40%. The measured transverse   The data recorder was placed in the truck cab. The timber truck was loaded with logs and then weighed. The static load was 140 kN, and thus the static overload was 40%. The measured transverse   The data recorder was placed in the truck cab. The timber truck was loaded with logs and then weighed. The static load was 140 kN, and thus the static overload was 40%. The measured transverse The data recorder was placed in the truck cab. The timber truck was loaded with logs and then weighed. The static load was 140 kN, and thus the static overload was 40%. The measured transverse displacement of the free end of the stanchion under a static load was 75 mm. The load Appl. Sci. 2020, 10, 6134 4 of 11 distribution per stanchion determined for a static load case is shown in Figure 4. Loads caused by logs that were not in direct contact with the stanchion were also included. Forces for dynamic load cases were determined by multiplying the forces obtained for the static load by the coefficient related to the transverse displacement of the free end of the stanchion. This coefficient is defined as k = x dyn /x stat , where x dyn stands for the transverse displacement under dynamic load and x stat stands for the transverse displacement under static load. The load history obtained from the experiment is shown in Figure 5.
Appl. Sci. 2020, 10, x FOR PEER REVIEW 4 of 11 displacement of the free end of the stanchion under a static load was 75 mm. The load distribution per stanchion determined for a static load case is shown in Figure 4. Loads caused by logs that were not in direct contact with the stanchion were also included. Forces for dynamic load cases were determined by multiplying the forces obtained for the static load by the coefficient related to the transverse displacement of the free end of the stanchion. This coefficient is defined as k = xdyn/xstat, where xdyn stands for the transverse displacement under dynamic load and xstat stands for the transverse displacement under static load. The load history obtained from the experiment is shown in Figure 5.

Finite Element Analysis
Calculations applying finite element analysis were carried out using ANSYS Mechanical software [18]. A finite element model of the stanchion was prepared to identify stress concentration points in the structure and to determine the stress history for these points. The model consisted of 38,384 high-order shell elements generated within mid-surfaces of the stanchion components. The Appl. Sci. 2020, 10, x FOR PEER REVIEW 4 of 11 displacement of the free end of the stanchion under a static load was 75 mm. The load distribution per stanchion determined for a static load case is shown in Figure 4. Loads caused by logs that were not in direct contact with the stanchion were also included. Forces for dynamic load cases were determined by multiplying the forces obtained for the static load by the coefficient related to the transverse displacement of the free end of the stanchion. This coefficient is defined as k = xdyn/xstat, where xdyn stands for the transverse displacement under dynamic load and xstat stands for the transverse displacement under static load. The load history obtained from the experiment is shown in Figure 5.

Finite Element Analysis
Calculations applying finite element analysis were carried out using ANSYS Mechanical software [18]. A finite element model of the stanchion was prepared to identify stress concentration points in the structure and to determine the stress history for these points. The model consisted of 38,384 high-order shell elements generated within mid-surfaces of the stanchion components. The

Finite Element Analysis
Calculations applying finite element analysis were carried out using ANSYS Mechanical software [18]. A finite element model of the stanchion was prepared to identify stress concentration points in the structure and to determine the stress history for these points. The model consisted of 38,384 high-order shell elements generated within mid-surfaces of the stanchion components. The geometry of the welds was also included. Contact elements were defined between the socket and the stanchion beam. The rigid contact was set for a pair of surfaces where the beam and the socket were rigidly bolted. On the other interfaces, the contact with friction was defined. A friction coefficient of 0.15 was assumed. S355J2 structural steel with yield strength of R e ≥ 355 MPa was selected as the material of the stanchion. The finite element model of the stanchion is shown in Figures 6 and 7.
Appl. Sci. 2020, 10, x FOR PEER REVIEW 5 of 11 geometry of the welds was also included. Contact elements were defined between the socket and the stanchion beam. The rigid contact was set for a pair of surfaces where the beam and the socket were rigidly bolted. On the other interfaces, the contact with friction was defined. A friction coefficient of 0.15 was assumed. S355J2 structural steel with yield strength of Re ≥ 355 MPa was selected as the material of the stanchion. The finite element model of the stanchion is shown in Figures 6 and 7.  Stress concentration points were determined based on the von Mises stress distribution under the static load as presented in Figure 8. Points 1 and 2 were identified within weld toes of fillet welds at the end of the reinforcement plates on a rectangular hollow section. Point 3 was found within the toe of a two-sided fillet weld, whereas points 4-6 were selected within the base material. The history of the maximum values of appropriate stress components for further fatigue analysis was determined for each of the above points. Maximum normal stress in the direction of tension was considered for concentration points within the base material. In turn, structural hot-spot stress for welded joints was determined according to the methodology presented in [19]. Assuming relatively coarse mesh with element size equal to material thickness t, hot-spot stress σhs within the weld toe was approximated using Equation (1), where σ0.5t and σ1.5t stand for stresses in reference points located 0.5t and 1.5t away from the weld toe as shown in Figure 9. geometry of the welds was also included. Contact elements were defined between the socket and the stanchion beam. The rigid contact was set for a pair of surfaces where the beam and the socket were rigidly bolted. On the other interfaces, the contact with friction was defined. A friction coefficient of 0.15 was assumed. S355J2 structural steel with yield strength of Re ≥ 355 MPa was selected as the material of the stanchion. The finite element model of the stanchion is shown in Figures 6 and 7.  Stress concentration points were determined based on the von Mises stress distribution under the static load as presented in Figure 8. Points 1 and 2 were identified within weld toes of fillet welds at the end of the reinforcement plates on a rectangular hollow section. Point 3 was found within the toe of a two-sided fillet weld, whereas points 4-6 were selected within the base material. The history of the maximum values of appropriate stress components for further fatigue analysis was determined for each of the above points. Maximum normal stress in the direction of tension was considered for concentration points within the base material. In turn, structural hot-spot stress for welded joints was determined according to the methodology presented in [19]. Assuming relatively coarse mesh with element size equal to material thickness t, hot-spot stress σhs within the weld toe was approximated using Equation (1), where σ0.5t and σ1.5t stand for stresses in reference points located 0.5t and 1.5t away from the weld toe as shown in Figure 9. Stress concentration points were determined based on the von Mises stress distribution under the static load as presented in Figure 8. Points 1 and 2 were identified within weld toes of fillet welds at the end of the reinforcement plates on a rectangular hollow section. Point 3 was found within the toe of a two-sided fillet weld, whereas points 4-6 were selected within the base material. The history of the maximum values of appropriate stress components for further fatigue analysis was determined for each of the above points. Maximum normal stress in the direction of tension was considered for concentration points within the base material. In turn, structural hot-spot stress for welded joints was determined according to the methodology presented in [19]. Assuming relatively coarse mesh with element size equal to material thickness t, hot-spot stress σ hs within the weld toe was approximated Appl. Sci. 2020, 10, 6134 6 of 11 using Equation (1), where σ 0.5t and σ 1.5t stand for stresses in reference points located 0.5t and 1.5t away from the weld toe as shown in Figure 9.
σ hs = 1.5 · σ 0.5t − 0.5 · σ 1.5t (1) Appl. Sci. 2020, 10, x FOR PEER REVIEW 6 of 11 ℎ = 1.5 • 0.5 − 0.5 • 1.5 (1)  The history of maximum hot-spot stress under dynamic load is shown in Figure 10, while maximum normal stress in stress concentration points within the base material is shown in Figure 11.  The history of maximum hot-spot stress under dynamic load is shown in Figure 10, while maximum normal stress in stress concentration points within the base material is shown in Figure 11. The history of maximum hot-spot stress under dynamic load is shown in Figure 10, while maximum normal stress in stress concentration points within the base material is shown in Figure 11.

Rainflow Cycle Counting Method
The rainflow fatigue cycle counting method is used in fatigue analysis to reduce the spectrum of varying stress and obtain simple stress reversals [20]. This method is compared to the rain running down a pagoda roof. The algorithm for counting half-cycles is defined as follows: 1. The stress history plot is rotated by 90° to reflect the direction of the rain that is falling down. Concerning the example of a simple stress history shown in Figure 12, the cycle counting algorithm is as follows: 1. The stress history plot is rotated by 90° so that Figure 13 is obtained. 2. Point A is identified as the largest peak in the stress history.

Rainflow Cycle Counting Method
The rainflow fatigue cycle counting method is used in fatigue analysis to reduce the spectrum of varying stress and obtain simple stress reversals [20]. This method is compared to the rain running down a pagoda roof. The algorithm for counting half-cycles is defined as follows: 1. The stress history plot is rotated by 90° to reflect the direction of the rain that is falling down. Concerning the example of a simple stress history shown in Figure 12, the cycle counting algorithm is as follows: 1. The stress history plot is rotated by 90° so that Figure 13 is obtained. 2. Point A is identified as the largest peak in the stress history.

Rainflow Cycle Counting Method
The rainflow fatigue cycle counting method is used in fatigue analysis to reduce the spectrum of varying stress and obtain simple stress reversals [20]. This method is compared to the rain running down a pagoda roof. The algorithm for counting half-cycles is defined as follows: 1.
The stress history plot is rotated by 90 • to reflect the direction of the rain that is falling down.

2.
Rainflow starts at each successive point of the extreme.

3.
Stress reversals are defined with the assumption that rain falls until one of the following conditions is met: a. It drops on the opposite larger maximum or smaller minimum point; b.
It meets another flow; c.
It falls outside the roof.
Concerning the example of a simple stress history shown in Figure 12, the cycle counting algorithm is as follows: 1.
The stress history plot is rotated by 90 • so that Figure 13 is obtained.

2.
Point A is identified as the largest peak in the stress history.

3.
A-F is identified as the first largest reversal. 4.
F-I is identified as the second largest reversal.

5.
Within the first largest reversal A-F: D-C reversal is identified.

6.
Within the second largest reversal F-I: H-G reversal is identified.
Appl. Sci. 2020, 10, x FOR PEER REVIEW 8 of 11 3. A-F is identified as the first largest reversal. 4. F-I is identified as the second largest reversal. 5. Within the first largest reversal A-F: 6. Within the second largest reversal F-I:  The spectrum of varying stresses obtained from finite element analysis was reduced by applying the above technique. For the analyzed timber truck stanchions, equivalent sets of simple reversal stress cycles were obtained. The effect of stress reduction is presented in Figure 14. Histograms obtained for all the points under consideration include information about the number of reversal stress cycles, corresponding mean stress and stress range. The highest mean stress and the highest stress range are observed from Point 1.

Fatigue Life Calculations
In order to estimate the fatigue life of the stanchion, cumulative fatigue damage and repeats to failure were calculated using the Palmgren-Miner rule [21]. The cumulative damage D is given by Equation (2). Value Ni is the fatigue strength obtained from S-N diagrams, whereas ni indicates the   The spectrum of varying stresses obtained from finite element analysis was reduced by applying the above technique. For the analyzed timber truck stanchions, equivalent sets of simple reversal stress cycles were obtained. The effect of stress reduction is presented in Figure 14. Histograms obtained for all the points under consideration include information about the number of reversal stress cycles, corresponding mean stress and stress range. The highest mean stress and the highest stress range are observed from Point 1.

Fatigue Life Calculations
In order to estimate the fatigue life of the stanchion, cumulative fatigue damage and repeats to failure were calculated using the Palmgren-Miner rule [21]. The cumulative damage D is given by Equation (2). Value Ni is the fatigue strength obtained from S-N diagrams, whereas ni indicates the The spectrum of varying stresses obtained from finite element analysis was reduced by applying the above technique. For the analyzed timber truck stanchions, equivalent sets of simple reversal stress cycles were obtained. The effect of stress reduction is presented in Figure 14. Histograms obtained for all the points under consideration include information about the number of reversal stress cycles, corresponding mean stress and stress range. The highest mean stress and the highest stress range are observed from Point 1.
with unwelded parts, for which fatigue resistance was assessed based on nominal stresses, and FAT100 with two-sided fillet welds and fillet welds at the end of the reinforcement plates on a rectangular hollow section, for which fatigue resistance was assessed based on structural hot-spot stresses.
The results of fatigue life calculations are presented in Table 1. An operating time was calculated by multiplying the number of repeats to failure by a single cycle time of 900 s. The mileage to failure was estimated under the assumption that the average vehicle speed is 50 km/h.

Fatigue Life Calculations
In order to estimate the fatigue life of the stanchion, cumulative fatigue damage and repeats to failure were calculated using the Palmgren-Miner rule [21]. The cumulative damage D is given by Equation (2). Value Ni is the fatigue strength obtained from S-N diagrams, whereas ni indicates the number of cycles for the stress range. Repeats to failure were calculated as R = 1/D.
Since stress cycles obtained as a result of spectrum reduction had non-zero mean stress, the Goodman correction was used when calculating fatigue strength. The modified Goodman relation is given by Equation (3), where σ a and σ m stand for stress amplitude and mean stress, σ u is ultimate tensile strength and σ Nf indicates equivalent fully reversed stress.
Fatigue resistance S-N curves were accepted for the calculations in accordance with [19]. S-N curves are shown in Figure 15. Fatigue classes referred to the structural details as follows: FAT160 with unwelded parts, for which fatigue resistance was assessed based on nominal stresses, and FAT100 with two-sided fillet welds and fillet welds at the end of the reinforcement plates on a rectangular hollow section, for which fatigue resistance was assessed based on structural hot-spot stresses.

Discussion
The results of the fatigue life calculations revealed that the weakest point of the structure belongs to the weld toe of the fillet weld located at the end of the reinforcement plate on the rectangular hollow section. The analyzed region is under tensile stress. The fatigue life obtained for that point was more than 1 million kilometers. Such a result could be accepted as sufficient for the structure under consideration. However, the fatigue life obtained for Point 1 is at least one order of magnitude less than for the other stress concentration points under consideration. The fatigue class FAT100 is assigned to such a weld and is also assigned to the butt weld that could be alternatively considered. In addition, the fatigue strength is determined by the type of weld and not by the strength of the base material. Therefore, neither the use of the butt weld nor the use of steel with higher strength would change the results of fatigue life calculations for welded joints. In order to obtain comparable fatigue life within the entire structure of the stanchion, it is advisable to redesign the node to achieve higher fatigue strength. In the view of high possibility of stanchion overload, the removal of the weld from this location should be considered.

Conclusions
As a result of the experimental test, the load history was obtained for the timber truck stanchions operating under overload conditions of 40%. By applying the finite element analysis, stress concentration points were determined for both welded and unwelded components. For the six selected points, an actual stress history was determined. For the points within the base material, corresponding normal stress was considered, whereas for the points within welds, hot-spot stress was estimated. Fatigue calculations were carried out using the Palmgren-Miner rule and by applying the modified Goodman mean stress correction. The analysis resulted in the determination of the weakest point of the tested structure, which significantly affected the fatigue life under overload conditions.  The results of fatigue life calculations are presented in Table 1. An operating time was calculated by multiplying the number of repeats to failure by a single cycle time of 900 s. The mileage to failure was estimated under the assumption that the average vehicle speed is 50 km/h.

Discussion
The results of the fatigue life calculations revealed that the weakest point of the structure belongs to the weld toe of the fillet weld located at the end of the reinforcement plate on the rectangular hollow section. The analyzed region is under tensile stress. The fatigue life obtained for that point was more than 1 million kilometers. Such a result could be accepted as sufficient for the structure under consideration. However, the fatigue life obtained for Point 1 is at least one order of magnitude less than for the other stress concentration points under consideration. The fatigue class FAT100 is assigned to such a weld and is also assigned to the butt weld that could be alternatively considered. In addition, the fatigue strength is determined by the type of weld and not by the strength of the base material. Therefore, neither the use of the butt weld nor the use of steel with higher strength would change the results of fatigue life calculations for welded joints. In order to obtain comparable fatigue life within the entire structure of the stanchion, it is advisable to redesign the node to achieve higher fatigue strength. In the view of high possibility of stanchion overload, the removal of the weld from this location should be considered.

Conclusions
As a result of the experimental test, the load history was obtained for the timber truck stanchions operating under overload conditions of 40%. By applying the finite element analysis, stress concentration points were determined for both welded and unwelded components. For the six selected points, an actual stress history was determined. For the points within the base material, corresponding normal stress was considered, whereas for the points within welds, hot-spot stress was estimated. Fatigue calculations were carried out using the Palmgren-Miner rule and by applying the modified Goodman mean stress correction. The analysis resulted in the determination of the weakest point of the tested structure, which significantly affected the fatigue life under overload conditions. Author Contributions: Conceptualization, F.L. and E.L.; methodology, F.L. and E.L.; software, F.L.; investigation, E.L.; writing-original draft preparation, F.L.; visualization, F.L. All authors have read and agreed to the published version of the manuscript.