Steel Design FATIGUE FAILURE OF BOLTED CONNECTIONS S.F. Stiemer

FATIGUE FAILURE OF BOLTED CONNECTIONS

ABSTRACTAn overview of the fatigue process and behaviour of fatigue loading is given. Bolted connections in both tension and shear are discussed in detail with emphasis placed on the location of failure, fatigue design curves, influence of preloading, joint stiffness, and contact area. Anchor bolts are also briefly discussed. Design requirements as per CSA S16.1-99 and AISC LRFD-1999 are given. Various methods on how to minimize fatigue problems are presented.

1 INTRODUCTION

Under certain conditions a material may fail due to the repeated application of loads that are not large enough to cause failure in a single application. This phenomenon is referred to as fatigue failure. The existence of fatigue failure implies that, under repeated stresses, materials undergo some internal progressive, permanent structural changes. Fatigue failures are often more dangerous than other typical failures because they generally occur suddenly, without significant prior deformations. Figure 1 shows a fatigue induced fracture surface.

Fatigue failure in bolted connections is generally caused by repeated cycles of tension loading. Although failures under repeated cyclic compression loads are know, these are rare and will be ignored in this discussion.

Figure 1. Fracture surface of a typical paper clip broken by 6 cycles of repeated bending (80x).1

2 THE FATIGUE PROCESS

Fatigue failure will only occur if the following essential conditions are present: cyclic tensile loads, stress levels above a threshold value, fatigue susceptible material, and a flaw in the material. If these conditions are present, then the following events can occur, leading to fatigue failure (Figure 2):

1. Crack initiation

2. Crack growth

3. Crack propagation

4. Final rupture

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Figure 2. Fatigue sequence - the stages of failure are: (1) initiation, (2) growth, (3) propagation, and (4) rupture. 2

2.1 CRACK INITIATION

Generally, fatigue cracks will originate on a free surface at a point of high stress concentration in the material. This may often be due to a pre-existing flaw in the material; or perhaps a human made discontinuity, such as the root of a thread, a tool mark, corrosion, or any point at which there is a sharp change in size or shape of the material. It would be safe to say that no connection is entirely free from defects of this type.

2.2 CRACK GROWTH

As the part is subjected to cyclic tensile loads, the material around the stress concentrations undergoes a slip mechanism. Slip occurs by the movement of dislocation – displacement of the atomic matrix. Under cyclic loading, reverse slip on adjacent slip planes may lead to the formation of extrusions and intrusions at the surface. These will act as the starting point of the crack. Initially the crack will grow along the slip plane, but will eventually change direction until it is growing in a plane perpendicular to the principle tensile stress.

2.3 CRACK PROPAGATION

Fatigue cracks will propagate under shear and tensile loads, but not under compressive loading since these cracks will close rather than open. During each tensile loading cycle, very high stresses occur at the crack tip (due to the stress concentrating effect of the sharp crack), causing the

crack to propagate into the still undamaged material ahead of it. The crack only propagates a finite distance in each loading cycle; this advance may by as much as 25 m/cycle.1 The back stresses exerted on the material during unloading cause deformation markings often called striations or beach marks, as shown in Figure 3.

Figure 3. Micrograph of fatigue fracture, with characteristic beach marks.1

2.4 FINAL RUPTURE

The crack grows more rapidly as stress levels increase. The process of crack growth is repeated until the crack reaches some critical length, at which time a sudden failure occurs, in either a ductile or brittle manner, depending on the characteristics of the material.

The fatigue life of a bolt and connection depends a great deal on the location and magnitude of the initial crack, but more importantly on factors such as bolt and joint stiffness, initial preload, alloy content, heat treatment, location and magnitude of external tension loads, etc. Therefore, there is a lot of scatter in the fatigue life of a bolted connection, making it difficult to accurately determine.

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3 BEHAVIOUR OF FATIGUE LOADING

The fatigue life, or endurance, of a material refers to the number of repeated cycles of loading (N) that a material will undergo before it fails. N will depend on the particular set of loading conditions. However, the general rule of thumb is that the higher the fatigue stress levels, the fewer number of loading cycles are required to cause failure. In most well designed bolted joints, however, fatigue failure will occur under high-cycle loading. Fatigue data is most commonly presented in terms of S-N curves (maximum stress versus the number of cycles), as shown in Figure 4.

Figure 4. S-N Curve for varying magnitude of altering stress.2

As Figure 4 shows, the material undergoes a definite fatigue limit. That is, it may withstand infinite cycles of loading without failing, as long as the applied stress is less than the fatigue limit. Although S-N curves are often produced based on tension loading along the axis of the fastener, it is important to recognize that if the fastener is subjected to some other form of stress as well as tension, its fatigue life will be adversely affected. Shear stress for example, would make it more susceptible to fatigue. There are many factors that will affect the fatigue life, each resulting in a different S-N curve. The major factors in order of importance that affect fatigue life are:

1. Shape of the connection.

2. Magnitude of stress excursions or variations.

3. Mean stress level.

4. Choice of material.

Other conditions such as corrosive environments and extreme temperatures also can affect the fatigue performance.

4 BOLTED CONNECTIONS LOADED IN TENSION

A typical bolted connection loaded in tension is shown in Figure 5.

Figure 5. Bolted connection loaded in tension. 3

4.1 LOCATION OF FAILURE

The tread in a bolt acts as a notch and therefore a high stress concentration is caused at the root of the tread. At locations where two threads meet the stress concentrations can be even higher, i.e. at the runout of the thread and where the thread and nut first engages the thread of the bolt. In addition, the head-shank transition is also a stress concentration.

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A bolt and nut loaded axially, as shown in Figure 6, has three possible fatigue crack initiation locations:

a. Head-shank transition

b. Runout of thread

c. Thread at nut

Figure 6. Axially loaded bolt with possible fatigue crack locations. 3

In standard bolts, the radius at the bolt-head shank transition is usually large enough to prevent fatigue cracks at this point.

Normally, if fatigue cracks occur, they will be located at the first engagement of the threads of the bolt and nut (point c in Figure 6), and can be 2 to 4 times the mean value. 3 This is due to the load transfer from nut to bolt. The contacting thread faces of the bolt and nut will give rise to extra bending stresses in the threads. Also, the load is unevenly distributed between the contacting faces of the bolt and nut, with the stresses being higher at the first thread of engagement. This will depend on the thread form, pitch, and differences in Young’s modulus where different materials are used. The load transfer can become more uniform by plastic deformation of the bolt.

4.2 THE INFLUENCE OF PRELOAD AND JOINT STIFFNESS

A bolt in a connection will see a portion of any external load, Fb, applied to the joint. The magnitude of the mean load on the bolt depends on the preload of the bolt. The magnitude of the load excursion (Fb) depends on:

1. The magnitude of the external tension load.

2. The bolt-to-joint stiffness ratio (Kb/Kj).

3. Whether or not the external tension load exceeds the critical load required to separate the joint (depends on the magnitude of the initial preload).

The effect of preloading, where there is tensile loading on the bolted connection, is illustrated for a flange connection in Figures 7 and 8. The thickness of the flange is assumed to be large enough to neglect bending flexibility and possible prying forces.

Figure 7. Flange connection with non-preloaded bolts. 3

Figure 8. Flange connection with preloaded bolts. 3

Where there is no preload, (Figure 7), and thus no contact force on the facing surfaces of the flanges, the external tensile force F t applied on the connection will be transferred directly to the bolts, Fb. Therefore, there will be a variation of the force in the bolts and a corresponding displacement between the opposing flanges. The connection can be considered to act as a two-spring system.

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In the case with a preload force Fv, this force will initially be in equilibrium with the contact force Fc on the contact area of the flanges, (Figure 8). These two flanges act like one as long as the external load F t

is less than the preload Fv. As a result, the external load applied to the bolts will change very little. As shown in the diagram, the increase in the external force is compensated largely by a decrease of the contact force Fc and small increases in the forces in the bolt Fb. Only the elastic deformation of the two flanges will cause change in the bolt load. The flanges, however, are relatively stiff compared to the bolt area and therefore this effect is minimal. But, the load in the bolts will increase rapidly as soon as the contact surfaces separate due to the external force surpassing the preload force Fv. When this has occurred the situation is equivalent to the non-preloaded case. As long as the external load F t is below the preload force Fv the situation can be considered as a three-spring system.

The amount of variation of the forces in the bolts due to the variation in the external load is dependent on the stiffness ratio of the flange and bolt (Figure 9). The more flexible the bolt, the less force variation it will undergo. Using more washers or using spring washers will increase the bolt’s length, thereby making the bolt more flexible. Inserting gaskets between the flanges will make the flange assembly more flexible, leading to possible detrimental effects. The flange thickness must also be adequate to reduce bending flexibility; otherwise the location on the contact forces may become critical.

4.3 THE INFLUENCE OF THE LOCATION OF THE CONTACT AREA

When the bolts of the connection are subjected to a preload force, contact forces are induced on the connecting surface. The location of the developed contact forces will affect the fatigue life of the connection.

Figures 10 and 11 shows an example where the flange thickness is much smaller than in Figures 7 and 8 and is, therefore, more susceptible to bending. In this figure, introducing shims develops contact forces. In both cases, the bolts are tightened to the same preload. A schematic model of the relevant spring system is shown in Figure 10, while Figure 11 shows the measured bolt forces with respect to an external load.

Figure 9. The effect of varying Fb and Kb /Kj ratios. (Note that the initial preload is the same in each case). 2

Figure 10. Flange connection with different location of contact forces. 3

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Figure 11. Measured bolt forces with respect to an external load. (Dashed line represents FT, solid line represents FB). 3

4.3.1 Contact Area at the Centre

When the contact force is located in the centre, Figure 10a, there is effectively a very stiff spring in the middle compared to the two flexible springs representing the flexible bolts and flange edges. This situation is very similar to having a very low Kb /Kj ratio, and the variation of magnitude in the bolts will not be too great if the preload force is not exceeded. This is shown in Figure 11a, with the applied external tension force plotted in a dashed line, and the force in the bolt plotted with a solid line.

4.3.2 Contact Area at the End of Flanges

When the contact force is located near the edge of the flanges, Figure 10b, the stiffness of the bolts is relatively large compared to the outer flange. This situation is very similar to having a relatively high Kb /Kj

ratio, and as a result the variation of the external force will cause variation of the bolt forces of nearly equal magnitude, as shown in Figure 11b.

In general the most favourable condition with respect to the fatigue resistance is to have the contact area as close as possible to where the tensile force is acting. This is shown in Figure 12.

Figure 12. Different locations of contact area: Going from (a) to (c) the bolts will experience more load variation with the same variation of the external forces. 3

5 BOLTED CONNECTIONS LOADED IN SHEAR

A typical bolted connection loaded in shear is shown in Figure 13. In these types of connections, load is transferred from one piece to the other via cover plates.

5.1 LOAD TRANSFER AND STRESS CONCENTRATION

5.1.1 Non-Preloaded Bolts

In the case of non-preloaded bolts, the applied force is transferred via bearing between the plates and the shank of the bolt, as indicated in Figure 13a. These types of connections are inadequate for variable loads that change sign as significant displacements will occur due to the clearance between the hole and bolt shank. Load transfer of this type is very concentrated at the location were the shank bears against the holes.

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In these connections the stress is concentrated around the hole. Since the bolt shank is also loaded in bearing, it too will experience high stress concentrations, (Figure 14a).

Figure 13. Example of a bolted connection loaded in shear. 3

5.1.2 Preloaded Bolts

When the bolts are preloaded, the applied force is transferred by friction between the plate surfaces. High Strength Friction Grip Bolts (HSFG) are used to obtain the necessary compressive stresses between the plates to enable the load to be transferred by friction. The load is transferred over a large area around the bolt (Figure 14b), and therefore the load transfer is not as great as in the non-preloaded bolt case. These types of connections can be used when the variable load changes sign.

For preloaded-bolts there are no stress concentration at the hole. In fact the stresses may even be less than the nominal stresses. This is due to the fact that the load has been transferred to an area around the hole.

5.2 LOCATION OF FAILURE

5.2.1 Non-Preloaded Bolts

The crack will occur at the hole due to the large stress concentration. Another potential failure location could be in the bolt as a result of the variable shear load applied to the shank at the shear plane. If this type of connection is used, the threaded part of the bolt should not be located in the shear plane, as the notch effect could drastically reduce the fatigue resistance, (Figure 14a).

5.2.2 Pre-Loaded Bolts

In the case of non-preloaded bolts, the stress concentrations do not generally occur near the hole. The contact pressure decreases radially from the hole. Fatigue cracks will usually develop in the gross section of the plate (see Figure 14b), were the contact pressure is not high enough to prevent slip.

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Figure 14. Stress and possible crack location of a bolted connection loaded in shear. 3

5.3 FATIGUE DESIGN CURVE FOR BOLTS IN SHEAR

In the case of non-preloaded bolts, there are two possible failures – the shank of the bolts and the gross section of the plate. Both should be checked against relevant design curves. Canadian and American design codes provide information for fatigue failure of gross plate cross-sections, but none is available for failure of a bolt shank in shear.

In the case of preloaded bolts, the bolts themselves will not fail provided that the pre-load is sufficient to prevent slip in the connection. The plates fall into the same design category as in the non-preloaded case. However, since the failure does not occur near the holes, the gross section of the plate can be used for calculating fatigue stresses.

6 ANCHOR BOLTS

Anchor bolts have some different fatigue resistance characteristics in comparison to the normal bolts that have been discussed thus far.

Test results have shown that the bolt diameter and the thread size do not influence fatigue behaviour; the fatigue lives were almost identical as normal bolts. 3

The way the bolt is formed also affects the fatigue resistance. Anchor bolts with rolled threads perform better than those with cut threads. This is due to the residual compressive stresses that are formed when the bolt has been rolled. Also, cut threads leave a sharp notch at the location of thread termination, which acts as a potential point of stress concentration.

The number of nuts also affects fatigue performance. More nuts can substantially increase the connection’s resistance.

Another important factor that must be taken into account is the effect of prying action, which will increase the applied force.

7 PREDICTING FATIGUE LIFE

There are several methods for predicting fatigue life; essentially they all involve the concept of the gradual accumulation of damage during the process of cyclic loading. The two most common methods are based on linear cumulative damage, and the Palmgren Miner’s Rule.

The linear cumulative damage is based on specific S-N data for each particular specimen type. This method is adopted in many design codes

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including the Canadian CSA S16.1-94 and American AISC LRFD-1999, which are discussed in a later section. A formatted spreadsheet has also been developed to implement the fatigue requirements of these codes.

The Palmgren Miner rule is used to determine the level of fatigue damage.In the calculation procedure, the existing number of stress cycles n i are divided by the allowed number of stress cycles N i, and added for each stress cycle. If this total is less than 1.0 the connection has not failed in fatigue. Miner’s rule follows the expression:

7.1 CSA S16.1-94 FATIGUE REQUIREMENTS4

Fatigue requirements are addressed in Section 14 of the CSA S16.1-94. The code states that fatigue is generally not a design consideration for buildings such as commercial or residential. However, industrial buildings may have members, such as crane girders, for which fatigue is a design consideration; other structures such as amusement rides and sign supports, for example may also be susceptible to fatigue.

When looking at the fatigue limit state, emphasis is placed on fatigue cracks that result from live load effects and those that result in local distortions. It is also important to determine the number of cycles to which a detail may be subjected.

When carrying out the fatigue resistance analysis, only variable and impact loads contribute to the stress range. Further, the designer only needs to consider regions that are subjected to tensile stresses or stress reversals. Compressive stress regions may be ignored.

Fatigue design in this specification is based on experimental data in which various fatigue susceptible details were tested to develop corresponding S-N curves. Details are assigned to one of eight stress range categories (A to E1). Appendix K illustrates various details and gives some guidance on how to assign a detail to a category. Figure 15 shows the allowable stress range versus the number of stress cycles for each category.

Figure 15. CSA fatigue resistances for categories A to E1 CSA S16.1-94

The fatigue life of a detail is inversely proportional to the cube of the stress range for values above the constant threshold stress range. The detail is considered to be satisfactory in fatigue if the applied stress range is less than that corresponding to the expected number of cycles of loading for the design life of the structure, as shown below.

fsr = calculated stress range at the detail due to the passage of the fatigue

load

Fsr = fatigue resistance, including adjustment for the number of stress range cycles for each passage of load

= fatigue life constant pertaining to the detail category [Table 4(a)]

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n = number of stress range cycles at given detail passage of the moving load [Table 4(b)]

N = number of passages of the moving load

Fsrt = constant amplitude threshold stress range [Table 4(a)]

For the fatigue resistance of high strength tension bolts, the code requires that the bolts are tensioned to the required pre-load and that prying action is considered.

From reviewing the detail categories given in Appendix K, we can see that the code gives very little guidance on how to check a bolted connection for fatigue resistance. It is left up to the designer to use his/her judgement.

7.2 AISC LRFD-1999 FATIGUE REQUIREMENTS5

Fatigue requirements are addressed in Section K3 of the AISC LRFD-1999. The AISC fatigue criteria are very similar to those found in CSA S16.1-94; however, there are additional requirements given for bolts and threaded parts.

The considered stress range is defined as “the magnitude of the change in stress due to the application or removal of the unfactored live load. In the case of a stress reversal, the stress range shall be computed as the numerical sum of maximum repeated tensile and compressive stresses or the numerical sum of maximum shearing stresses of opposite direction at the point of probable crack initiation.” 5

No evaluation of fatigue resistance is required if the live load stress range is less than the threshold stress range, FTH, or if the number of cycles of application of live load is less than 2 x 104.

As in the CSA S16.1-94, the fatigue life of a detail is inversely proportional to the cube of the stress range for values above the constant threshold stress range. The detail is considered to be satisfactory on fatigue if the applied stress range is less than that corresponding to the expected number of cycles of loading for the design life of the structure, as shown below. (Note all calculations shown are in SI units).

.

FSR = design stress range, (MPa)

FTH = threshold fatigue stress range, maximum stress range for indefinite design life [Table A-K.3.1], (MPa)

Cf = Constant [Table A-K3.1]

N = number of stress range fluctuations in design life

= number of stress range fluctuations per day x 365 x years of design life

The AISC LRFD also has additional requirements for bolts and threaded parts. For mechanically fastened connections loaded in shear, the maximum range of stress in the connected material at service loads shall not exceed the design stress computed using the equation given above. For high-strength bolts, common bolts, and threaded anchor bolts with cut, ground or rolled threads, the maximum range of tensile stress on the net tensile area from applied axial load and moment plus load due to prying action shall not exceed the design stress range computed using the equation above. The factor Cf shall be taken as 3.9 x 108 (as for category E’). The threshold stress, Fth shall be taken as 48 MPa (as for category D). The net tensile area for metric bolts is given as:

P = pitch, (mm/thread)

db = nominal diameter (body or shank diameter), (mm)

When dealing with bolts and threaded parts, the designer must also consider any prying action and the relative stiffness of the connected parts.

Although the AISC LFD does provide a little more guidance than the CSA S16.1-94, it still does not adequately take into account all of the

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effects, which may influence the fatigue life of a bolted connection. It is, therefore, left to the designers to use their professional judgment.

8 MINIMIZING FATIGUE PROBLEMS

There are many steps that a designer can take to minimize fatigue related problems. Each of these is related to the conditions that are necessary for fatigue to occur: cyclic tensile loads, stresses above an endurance limit, a susceptible material, and an initial flaw. In general, most of the steps that we can take are intended to reduce stress levels (and concentrations) and/or to reduce the load excursion seen by the bolt.

8.1 MINIMIZING STRESS LEVELS

The following are just a few of the steps that a designer can take to minimize stress levels. Many of these are incorporated in ‘fatigue resistant fasteners’, which are available from some fastener manufacturers.

Rolling treads instead of cutting them provides a smother thread finish (fewer initial cracks). The rolling process induces a residual compressive stress in the bolts, which acts as a compressive preload, thereby helping to reduce the tensile load excursions.

A generous fillet between the head and shank will reduce stress concentrations. The exact shape is also important; an elliptical fillet, for example, is better than a circular one.2 Increasing the radius of a circular fillet will also help

If the face of the nut, the undersides of the bolt head, and/or joint surface are not perpendicular to the thread axis and the boltholes, the fatigue life can be seriously affected.2

Bolts under tension see stress concentrations at the head-to-shank fillet, first threads to engage the nut, and at the thread run-out. Anything that may impose additional loading to these regions will be detrimental. Some of these situations are shown in Figure 16.

Figure 16. Joints should be designed so that maximum loads do not fall on stress concentration points of the fastener.2

The thread run-out should be gradual rather than abrupt. It has been suggested that a taper of 15o should be used to minimize stress concentrations at this critical point (Figure 17). 2

Figure 17. Thread run-out should be gradual.2

Anything that can be done to minimize corrosion will reduce the possibilities of crack initiation and/or crack growth and will, therefore, extend fatigue life.

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Figure 18 shows a proposed fastener, which, because of its geometry, can greatly reduce stress concentrations and, therefore increase the fatigue life of the connection.

Figure 18. Flanges, dished, and undercut nut and bolt head used to improve stress distribution.2

8.2 REDUCING LOAD VARIATIONS

Nothing can help extend the fatigue life of a bolt or joint more dramatically than a reduction in load variations.

It will greatly help to correctly identify and apply the maximum safe preload that the joint can withstand. Minimizing the bolt-to-joint stiffness ratio, (as well as proper location of contact forces), so that the load excursions and external loads will be seen by the joint and not the bolt will reduce fatigue problems.

9 CONCLUSIONS

Fatigue failure of bolted connections is a serious problem in steel structures, as the failure happens suddenly without prior warning. It occurs in areas were the applied stress is cyclic and tensile in nature, and where there is a stress concentration.Bolted connections are commonly used in both tension and shear, each with varying fatigue characteristics. The fatigue life of the connection depends on many factors including: the magnitude of the varying applied load, duration of the varying load, fastener geometry, preloading of the bolt, relative stiffness of the bolt and joint and the contact area.Designing to withstand fatigue related failures are addressed in both the Canadian CSA S16.1-94 and American AISC LRFD-1999 design codes. These codes provide a method that is based on experimental testing to

determine if the applied stress range is within the desired limit for a required number of load cycles. This may be relatively accurate for normal steel members or welded connections; however, it does not adequately address bolted connections, as there are numerous connection types that do not fall under a prescribed design category. It is therefore up to the designers to use their judgment or undergo further rigorous analysis in order to determine if the connection is adequate to resist fatigue.By minimizing stress levels or reducing load variations, the designer may make the connection less prone to fatigue failure.

REFERENCES

1Young J., Mindess S, Gray R. and Bentur A. 1998. The Science and Technology of Civil Engineering Materials. Prentice Hall: 152-175.

2Bickford J. 1990. An Introduction to the Design and Behaviour of Bolted Joints, 2nd Edition. Marcel Dekker: 467-494.

3http://www.kuleuven.ac.be/bwk/materials/Teaching/master/toc.htm, November 2003.

4Canadian Institute of Steel Construction. 1997. Handbook of Steel Construction, 7nd Edition. CISC.

5American Institute of Steel Construction. 1999. Load and Resistance Factor Design Specification for Steel Buildings. CISC.

10 CREDITS

The text above has been based on a term project done by Mr. Chris

Meisl for the CIVL510 course in 2003.

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