Life analysis of the bolted joint

The paper deals with the fatigue damage calculation of 2 types of computation model of bolted joints. The study is performed via a numerical analysis with support of finite element method (FEM) software ANSYS. One model was created with a thread on the bolt, another was only bolt with cylindrical surfaces, the second model was greatly simplified. It will be evaluated the fatigue damage for both types of models. Subsequently both types of computational models will be compared in dependence on the accuracy of the results and the speed of the calculation. There are also the theoretical backgrounds for preloaded bolted joint, which was used for calculation of preload load prescribed on body of screws.


Introduction
The high strength bolted joints are often used in a variety of engineering industry. Usage of equipment in multiple applications (customer requirements) requires reassessing already defined limits. For efficient and reliable use of the equipment, it is necessary for the manufacturers to guarantee the same life of the components under the required operating conditions [1][2][3].
Fatigue assessment of bolted joints are considered in fatigue problem areas and requires research. The problem of determining the threaded joints fatigue strength and damage has been investigated for many years [14][15][16]. Fatigue limit affected by the stress gradients, size effect and surface quality for high reliability in industry are also in the problem areas. Offshore and subsea applications where bolted joints are the critical points can be found on wellheads, drilling risers, structural connections, flanges, and similar. Drill pipe threaded connections are susceptible to fatigue damage because of high stress concentration due to the geometry and high mean stress induced by preload [4][5][6][7].

Preload force calculation
For calculating the preload force, the value of torque on the torque wrench used to tighten the bolt or the nut was used (torque in screw thread + torque under the nut).
Internal thread diameters are: D -major diameter, D2 -pitch diameter, D1 -minor diameter. External thread diameters are: d -major diameter, d2 -pitch diameter, d1 -minor diameter. Pitch of thread is shown as P and H = 0.86 P (Fig. 1).  -friction angle (dry friction, no movement) taking into account the thread profile, where: f -coefficient of friction between nut (screw head) and material After getting into formulas, force for preload was given 24981 N.

FEM simulation
Finite elements model consists of screw, nut, two plates a two washer one is under screw and the second is on nut (Fig. 2). Screws which have been contemplated in the simulation are metric screws M8. The analysis was designed as a static analysis in a position which is one screw connects two plates (Fig. 2).
For purpose of this paper was used two types of connection with screw, the fist type is when screw is without thread and the second type is whit using screw with thread (Fig. 2). For the best results were generated contact areas between the individual components. Between head of screw and top washer, top washer and top plate, top plate and bottom plate, bottom plate and bottom washer, bottom washer and nut were prescribed symmetric frictional contacts with value of friction 0.2. Then in model where was used thread is prescribed between nut and screw frictional contact with coefficient of frictional 0.1 on thread. In model without thread is prescribed between screw and nut bonded contact.

Loads and boundary conditions
For the screw was prescribe preload on volume of screw model which was calculated according analytical formulas presented in this paper (1). Value of preload force is 24981 N.
In simulation, two steps were used, first step was used for load screw with preload force then in second step load of preload force in screw was lock. First step was only used for preload screw. Subsequently, external force on plates was considered in second step.
Therefor load of value 1000 N was prescribed on both plate, it is shown of red colour (Fig. 4) and on the opposite side of plates was prescribed fixed support shown with blue colour on figure 3.

Life calculation of bolts
For calculation of bolt service life was used data from experimental measurement for material 42CrMo4 which is typical for bolt of strength grade 10.9 (Fig. 5). The definition of the S -N curve model in the double logarithmic system is that the linear damage accumulation is done with the amplitude stress tensor of the particular hysteresis [8][9][10][11][12][13]. Fatigue damage was evaluated after 1•10 6 cycles on both models. The chosen location for damage evaluation was selected on the axes of the screws. The course of the damage on the screws axis is shown on the graph. With red colour is represent model of screw with thread and model of screw without thread is represent with blue colour (Fig. 6). The course of both types of models to length of 12 mm is similar, then model with thread starts to have bigger value like model without thread. Model with thread has maximum value of 0.82 at length about 17 mm therefor maximum value of model without thread is 0.67 at length 18.4 mm. Fig. 6. Graph of dependence of the damage to the distance on the screw axis for both types of models

Conclusion
Two types of screw connections models were created. One was considered with thread on screw and between threads on screw and nut was contact with friction. Another was without thread and between screw and nut was only bonded contact. Preload force of same value was prescribed on body of screws for both models. Preload force was calculated according analytical relationships from tightened torque. There were also prescribed force and on the opposite side fixed support on plates between bolt connections. After the numerical analysis, the fatigue analysis of the screws was evaluated.
The analysis shows that the model which has been considered with thread on the screw is more accurate because the value of damage is there a greater (Fig. 6). Overleaf computing time of model with thread was 9 h 21 m while in model without thread it was only 5 h 31 m with using an appropriate number of elements to achieve optimal results. The model using a thread is recommended to use in calculations where there is a requirement for accuracy in area of bolt connection. The model without thread is suitably used in assemblies where such connections are large number and the calculation is not focused on the area of the bolt connection.
The part of the results of this work was supported by grants VEGA 1/0795/16 and KEGA 017ŽU-4/2017. with thread without thread