- Email: [email protected]
Stress distributions and crack growth in riveted lap joints fastening thick steel plates
Engineering Failure Analysis 91 (2018) 370–381
Contents lists available at ScienceDirect
Engineering Failure Analysis journal homepage: www.elsevier.com/locate/engfailanal
Stress distributions and crack growth in riveted lap joints fastening thick steel plates
T
⁎
Jackeline Kafie-Martineza, , Peter B. Keatinga, Pranav Chakra-Varthyb, José Correiac, Abílio de Jesusc a
Texas A&M University at College Station, TX, United States Indian Institute of Technology, Gandhinagar, India c Faculty of Engineering, University of Porto, Portugal b
A R T IC LE I N F O
ABS TRA CT
Keywords: Riveted lap joints Fatigue life Finite element analysis Railroad bridges Residual stress
Single shear lap joints have been a common method to fasten steel plates in railroad bridges and can be highly susceptible to fatigue cracking under the cyclic loading bridges experience. To better comprehend the fatigue process of these connections, it is important to understand the stress state near the rivet hole. While the fatigue behavior of these riveted connections has been studied, few have been carried out on stress distribution and crack formation in riveted lap joints fastening thick steel plates. This study is to provide information regarding the stress distributions developed in a single shear lap joint connecting plates of varying thicknesses. Results from the stress contour analysis are utilized to detect possible regions for fatigue crack nucleation under cyclic heavy axle loads. The study also provides information regarding the fatigue crack geometry typically found in single shear lap joints.
1. Introduction Rivets were widely used as mechanical fasteners in railroad bridges constructed after the 1900's through the 1960's, when the introduction of high strength bolts replaced the use of rivets [1]. These riveted railway bridges were not originally designed taking into account fatigue [2], furthermore, if fatigue was taken into account, it was based on limited understanding and knowledge of the phenomenon [3,4]. This was due to many reasons: first, fatigue cracking in these early structures was infrequent [5,6]. Second, axle loads in train configurations prior to the 1960s rarely exceeded 20 tons (40,000 lbs), creating an almost negligible effect on the fatigue damage of railroad bridges [7]. Finally, the fatigue phenomenon was only intensively investigated after the second half of the 20th century [2], were welding began to be used as the preferred method for fabrication of steel bridges. There are a large number of old riveted railroad bridges that are still in operation today. The average age of these riveted railway bridges is reaching 100 years old [7]. Moreover, as the railroad industry increase their carloads, these bridges are subjected to increasing axle loads. Freight cars have increased from 85 tons, commonly used before 1960, to a range of 131.5 tons to 143 tons (263,000 lbs–286,000 lbs) used today [7]. Furthermore, in 2011 alone, it was reported that approximately 1600 railcars of 157.5 tons (315,000 lbs) were in service on Class I railroads [8,9]. With the ever increasing freight car weights, the old riveted railroad bridges are being subjected to larger and more frequent stress ranges that they were originally intended for. Since most of the riveted railroad bridges in service have passed the 80 years' service lifetime, the proper maintenance and remaining fatigue life of these bridges is a major concern. It is imperative to investigate the effect of heavy axle loads in fatigue damage of these structures.
⁎
Corresponding author. E-mail address: [email protected] (J. Kafie-Martinez).
https://doi.org/10.1016/j.engfailanal.2018.04.048 Received 29 January 2018; Received in revised form 16 April 2018; Accepted 29 April 2018 Available online 03 May 2018 1350-6307/ © 2018 Elsevier Ltd. All rights reserved.
Engineering Failure Analysis 91 (2018) 370–381
J. Kafie-Martinez et al.
With the current fatigue provisions [10], the life of the components can be estimated by identifying the fatigue detail category and specifying the critical stress range it will experience during its lifetime. However, when utilizing a fracture mechanics approach, much more information regarding the stress state and crack (geometry and size) is needed; but it could also provide a more accurate fatigue life estimation. Current fatigue S-N curves are based on fatigue life of welded connections; experimental results have shown that fatigue life of riveted connections typically fall within Category C and D. The S-N curves can provide a robust estimation, however, in some cases, a more accurate calculation is needed. 2. Riveted lap joints To understand the fatigue process within riveted lap joints, detailed knowledge of the stress state is required. Studies have demonstrated that clamping force is a principal variable influencing the fatigue resistance of riveted connections typical in old railroad bridges [11]. The presence of residual stresses resulting from rivet installation complicate the analysis of crack formation and propagation. In comparison with high strength bolts, the clamping stresses on rivets are generally lower in magnitude and not as predictable due to an increased variability in magnitude [2,3]. The use of different riveting techniques, either in-shop or on-site, may entail different clamping force magnitudes and variable load-carrying capacities in member and in joints [12]. The presence of clamping stress affects the nucleation location and the path of fatigue cracks at rivet holes. It will also dictate the magnitude of the compression stress between faying surfaces, this leads to transmitting a portion of the applied load by friction [13]. This study is to provide information regarding the stress state near the rivet hole due to thermal contraction during the installation. Additionally, it describes how the residual stress combines with external surface traction to yield the stress distribution typically found near rivet holes. The stress state near the rivet hole will be used to study fatigue crack propagation in this area. 2.1. Previous studies Skorupa et al. [13] conducted fatigue tests on riveted lap joints, typically found in aircraft fuselages, to understand the effects of thickness and clamping stress of rivets on fatigue life, crack initiation and crack growth. It was found that cracks always initiate at the faying surface at the outer rivet rows and that the crack geometry and growth were affected by the clamping stress. Lower clamping stress produced quarter elliptical cracks which propagated through the rivet row, whereas higher clamping stress produced semi elliptical cracks that propagated away from the rivet row towards the edge. Sanches et al. [14] performed a fatigue simulation of a double shear riveted joint. Both, crack initiation and propagation were accounted for. Effects of various variable model inputs such as friction, clamping stress, as well as the crack initiation size definition were assumed in the probabilistic form to generate S-N curves. For the investigated riveted joint, the fatigue crack initiation was the dominating damage mechanism. The proposed S-N curve did not show good agreement with the existing code-based S-N curves. Skorupa et al. [15] analyzed the fatigue behavior in riveted lap joints and evaluate quantitatively the influence of several variables on the joint fatigue behavior. It was concluded that: fatigue cracks in riveted lap joint always start in one of the end rivet rows on the faying surface of the loaded sheet; sheet thickness, rivet type and clamping stress can have a significant impact on all aspects of the joint fatigue response; increasing the rivet clamping stress yields a longer fatigue life regardless of the sheet thickness; and that riveting imperfections can have a profound influence on the joint fatigue performance. Zhou [16] conducted a study to measure the magnitude of clamping residual stress in riveted members from demolished bridges approximately 60 years of age. The measured clamping stress varied from 34 to 165 MPa (5 to 24 ksi), with an average of about 83 MPa (12 ksi) and a standard deviation of about 41 MPa (6 ksi). Zhou [16] also performed a two-dimensional finite element model to examine the distribution of normal and frictional stresses on the contact surfaces. The presence of a crack was not considered in the model. It was reported that a temperature change of 204 °C (400 °F) during the cooling process in the rivet caused a clamping stress of about 262 MPa (38 ksi). Correia et al. [17] presented a comparison between two alternative finite element models to predict the fatigue strength of a single shear and single rivet connection. A finite element model using solid elements in its entirety is compared to a finite element model using a combination of shell elements for the plates, and solid elements for the rivet. Both steel plates and rivet were modeled as isotropic and elastic material. The simulations were performed using the Augmented Lagrange contact algorithm, and null gap between plates and rivet was considered. A through thickness crack was assumed and a stress ratio R equivalent to 0.1 was assumed. The study works with clamping stress ranging from 0 to 300 MPa. The research concluded that crack initiation phase is dominant for high cycle fatigue and that the numerical analysis assuming an initial crack size of 0.6 mm agreed well with experimental data. Correia et al. [17] based his finite element model in the studies presented by De Jesus et al. [2] and Correia et al. [18]. De Jesus et al. [2] proposed a methodology to generate probabilistic stress life data for a riveted shear splice, which can be applied into probabilistic fatigue assessments. Correia et al. [18] uses the same 3-D FE model of a riveted joint to assess the elastic stress concentration and the stress intensity factor to assess the crack initiation and crack propagation phases, respectively. This data was used to derive probabilistic S-N fields for riveted connections. The parameters in the analysis that were assumed in a probabilistic form were: clamping stress, friction, the initial crack size and the coefficient C of the Paris's Law. All the above authors presented excellent work and insight into their finite element model. However, the stress distributions per se were not reported, as well as the effect of the plate thickness in the residual clamping stress. Additionally, this study investigates the effect of the plate thickness on the crack geometry developed due to cyclic loads. Some authors, such as De Jesus et al. [19], Correia et al. [20], Lesiuk et al. [21,22,23] and Raposo et al. [24] have studied the mechanical properties of puddle irons/old mild steels as well as riveted connections used in old riveted steel bridges. De Jesus et al. 371
Engineering Failure Analysis 91 (2018) 370–381
J. Kafie-Martinez et al.
Fig. 1. Dimensions and boundary conditions of the lap joint, top view.
[19] presented a study on assessing the strain-life and fatigue crack growth data using samples of original material removed from five Portuguese metallic riveted bridges. Their study also included the monotonic and cyclic elastoplastic properties for the old mild steels. Lesiuk et al. [21–23] has also been studying the mechanical properties and the microstructural degradation effect, the fatigue crack propagation and crack closure effects in old low carbon steels after 100-years of operating time. More recently, Raposo et al. [24] presented a review paper on mechanical characteristics of old mild steels and puddled iron from old riveted steel bridges, such as, monotonic tensile strength, chemical composition, microstructures, hardness, notch toughness, and fatigue crack propagation. The mechanical properties of the materials from the old steel bridges are of great importance as they can be used in fatigue studies and damage assessment of these structures. 2.2. Finite element model of a single shear lap joint In order to obtain a detailed stress state in a single shear lap joint, a finite element model was performed. Dimensions of the lap joint are illustrated in Figs. 1 and 2. The three-dimensional finite element model was developed using ABAQUS© software. The model attempts to replicate the residual stresses developed during the installation process, as well as to provide information on how the residual stresses superimpose with mechanical tensile stresses. The stress distributions will later be utilized to identify possible regions for crack propagation, as well as, perform a fatigue life assessment through a fracture mechanics approach. The model consists of two analyses steps. The first step is a thermo-mechanical analysis where the residual stress was simulated by specifying different initial temperatures between contacting plates and rivet. This provides an analytical methodology to generate the clamping stress. The second step consists on applying a tensile mechanical traction, σ, at x = 800 mm (31.5 in.). The second step will use the stresses found in step 1 as the initial condition. Therefore, the results of step 2 are the superimposed stresses. Two predefined fields where necessary to state the initial temperature of the rivet (1000 °C or 1832 °F) and of the plates (20 °C or 68 °F). The mechanical boundary conditions used are the following: 1. The left edge of the outer plate, that is when x = 0, is pinned supported. 2. The beginning 200 mm (7.9 in.) segment of the outer plate (x = 0 to 200 mm) and the end 200 mm (7.9 in) of the segment of the inner plate (x = 600 to 800 mm) are constrained in the y and z direction. A thermal boundary condition is set to define the final state: the entire system (both plates and the rivet) reach ambient temperature. Additionally, contacting surfaces between rivet and plates' surfaces were necessary to avoid penetration of one surface over the other. The three contact properties specified were the following: tangential behavior, normal behavior and a clearance dependent thermal conductance. The tangential behavior was specified as a Penalty Friction Formulation assuming a coefficient of friction equivalent to 0.3. The normal behavior was defined as hard contact pressure overclosure. The hard contact relationship minimizes the penetration of the slave surface into the master surface at the constraint locations and does not allow the transfer of tensile stress across the interface. There are three possible constraint enforcement methods in ABAQUS: the direct method, the penalty method and the augmented Lagrange method. In this investigation, the default constraint enforcement method was used. The default constraint enforcement method depends on interaction properties as follows: the penalty method is used by default for finite-sliding, surface-tosurface contact (including general contact) if a hard pressure-overclosure relationship is in effect; the augmented Lagrange method is
Fig. 2. Dimensions and boundary conditions of the lap joint, transverse view. 372
Engineering Failure Analysis 91 (2018) 370–381
J. Kafie-Martinez et al.
Table 1 Material properties of steel at room temperature. Young's modulus, E Poisson's ratio, υ Yield Stress, σy Ultimate Stress, σut Specific Heat, cp Linear Thermal Expansion, α Thermal Conductivity, λa Mass Density, ρ
193 GPa 0.28 248 MPa 400 Mpa 440 J/kg °C 12 × 10−6/ °C 53.3 W/m °C 7850 kg/m3
used by default for three-dimensional self-contact with node-to-surface discretization if a hard pressure-overclosure relationship is in effect; the direct method is the default in all other cases. Finally, separation after contact is allowed. For this reason, it was necessary to specify the material's thermal gap conductance, that is, how the conductance differs in a steel-air-steel interface scenario. The finite element model is non-linear due to the contact problem. The Nlgeom option must be enabled to account for large strain plastic deformations. Steel properties commonly utilized for A36 are presented in Tables 1 and 2. Even though it is common to have steel A502 for steel structural rivets, no distinction was made between the plates and the rivet steel in the finite element model. The difference in material properties for steel A36 and A502 is not expected to produce significant effect in the results. Moreover, the crack is expected to develop in the plates, therefore, A36 is used for the entire geometry. Except for the material's density, the dependence of the material properties with respect to temperature was considered. For more detailed information regarding the finite element model as well as steel thermal properties refer to Ref. [25]. The steel rivet and steel plates were modeled using an 8-node thermo-mechanically coupled brick, called C3D8RHT in ABAQUS. A refined mesh near the rivet hole area is necessary since a large stress concentration is expected in this area. Since preliminary findings suggest that fatigue crack growth usually emanates from the rivet hole, and that plate thickness plays an important role in the residual stress distributions around the area, it was deemed necessary to perform a mesh convergence study. The objective of the mesh convergence study is to determine the optimum size of elements necessary to have good accurate results. Therefore, the plate thickness of the base model, 12.7 mm, was divided into 5, 10, 15 and 20 elements resulting in element thicknesses of 2.54 mm, 1.27 mm, 0.85 mm and 0.64 mm respectively. Fig. 3 shows the mesh of the riveted joint. Figs. 4 and 5 show how the stress distributions varied for the different adopted meshes. For the longitudinal stress, Fig. 4, the major discrepancy appears to be right under the rivet head. However, stress near the interface are of most importance, since this region would most likely surrender to fatigue, as it will be explained later. On the other hand, the clamping stress (Fig. 5) present small discrepancy on the top half of the plate thickness, but, once again, clamping stress near the interface is of most importance. For this reason, and in order to save computational time, an element thickness of 1.27 mm (10 elements) throughout the plate thickness was adopted. 2.3. Deformations The usage of overclosure hard contact surfaces prevented the contacting surfaces from penetrating one another; it also allows them to separate and loose contact as needed. Therefore, the use of contact surfaces gives a realistic deformed shape. The deformation of the model is always important to check since by comparing it to the expected real deformations of the component one can rest assure the model simulates the real behavior. In this specific case, as the rivet cools and contracts, the plates are compressed and consequently warp. As shown in Fig. 6, the plates are bended under tensional loading. Fig. 7 shows the undeformed and deformed shape of the joint, as the rivet cools, it shrinks, and a gap is formed between rivet shank and the plates. 2.4. Stress distributions The stress contours for residual and total stress for both plates and the rivet are shown, see Figs. 8, 9, and 10. The total stress consists of the residual stress in combination with a tensile traction of 20 MPa. It is important to note that the stress contours for both plates shown here present the stresses along the contacting surfaces, since crack propagation is more likely to happen throughout this Table 2 Interface contact thermal conductance for steel-air-steel with a normal grinding surface finish and zero contact pressure. Gap [mm]
Interfacial Thermal Conductance [W/m2 °C]
0.0 0.5 1.0 1.5
2500 50 25 0
373
Engineering Failure Analysis 91 (2018) 370–381
J. Kafie-Martinez et al.
Outer plate
Inner plate
Surface Interaction
Refined mesh around rivet hole Fig. 3. Mesh of the riveted lap joint using an 8-node thermos-mechanically coupled brick. Surface interaction was defined for every contacting surface.
Fig. 4. Longitudinal stress distribution assuming different number of elements throughout the plate thickness. 374
Engineering Failure Analysis 91 (2018) 370–381
J. Kafie-Martinez et al.
Fig. 5. Clamping stress distribution assuming different number of elements throughout the plate thickness.
Fig. 6. Deformed shape of the riveted lap joint, longitudinal view (deformation scale factor of 15).
surface. Another important observation is that residual stresses are completely symmetrical; meanwhile, when combined with the mechanical traction, the stresses lose symmetry. Fig. 11 shows how the clamping stress changes with temperature range. It is quite interesting to note that the clamping stress does not significantly change for a temperature range larger than 280 °C. On the other hand, the computational time is much larger when a ΔT of 980 °C is used. Hence, in the event of a preliminary study one can assume a 280 °C < ΔT < 980 °C to have an estimation of the magnitude of the clamping stress. When 280 °C < ΔT ≤ 980 °C, the average clamping stress is 260 MPa. This agrees with the value computed by Zhou [26]. Zhou [26] reported a clamping stress of about 262 MPa (38 ksi) for a temperature change of 204 °C (400 °F). Moreover, studies have shown that the initial tension of an ordinary rivet driven with a hydraulic riveter can reach 214 MPa (31,000 lb/in2) [27,28]. Wilson and Thomas [29] reported an average initial tension of 241 MPa (35,000 lb/in2) for carbon-steel rivets, driven by either a hydraulic riveting machine or a pneumatic hand-riveting hammer. It is important to clarify that for Fig. 11 an average clamping stress along the plate thickness was used. The stress distributions were also obtained assuming three other plate thicknesses, 6.35 mm (¼ in.), 7.94 mm (5/16 in.), and 25.4 mm (1 in.) shown in Fig. 12 and Fig. 13. In Fig. 12 and Fig. 13 stress vs. plate thickness are presented on the left graph and stress vs. normalized plate thickness are shown on the right. Fig. 12 shows how the clamping changes for each plate: it can be as high as 340 MPa for the 7.94 mm-thick plate or as low as 100 MPa for a 25.4-mm thick plate. Note also that the thickest plate, has the lowest 375
Engineering Failure Analysis 91 (2018) 370–381
J. Kafie-Martinez et al.
Fig. 7. Transverse view of the riveted lap joint (a) undeformed and (b) deformed.
Fig. 8. Longitudinal stresses (MPa) (a) residual (b) residual plus mechanical.
clamping stress along the faying surfaces. Moreover, the clamping stress S33 is not directly responsible for fatigue crack propagation. Fatigue cracks in rivets usually start at the rivet hole, and propagate perpendicular due to the fluctuations of the longitudinal stress, S11. Hence, the longitudinal stress S11 vs. plate thickness and normalized plate thickness are shown in Fig. 13. This longitudinal residual stress, S11, can hinder fatigue crack propagation if it is of a compressive type, or can accelerate fatigue crack propagation if it is of a tensile nature. The 25.4 mm -thick plate exhibits tensile residual stress near the faying surfaces, and if combined with a remote mechanical tension load, this area can become a hot-spot for fatigue cracks. Furthermore, Figs. 14 and 15 present how the stress distributions along the z and y axes are affected by an increase in the remote tensile load. Fig. 14 shows that for a remote tension of 10 MPa (1.5 ksi) and 15 MPa (2.2 ksi), the total stress along the plate thickness is under compression. However, in the case of a larger remote tension, say 20 MPa (2.9 ksi), the faying surface is the first region to come under tension, which suggests a crack will most likely propagate there.
376
Engineering Failure Analysis 91 (2018) 370–381
J. Kafie-Martinez et al.
Fig. 9. Longitudinal stresses (MPa) (a) residual (b) residual plus mechanical for the inner plate.
2.5. Crack growth in riveted lap joints It is very well known that fatigue cracks are likely to emanate from the rivet hole for two reasons. First, the punching or drilling of the hole introduces imperfections in the material and second, the hole in the plate produces a stress concentration in the area. In order to develop a fatigue assessment of a riveted joint using fracture mechanics concepts, one must be clear on the location of the fatigue crack along with its shape and its initial size. Experimental data usually depicts the location, final crack length, and the cause of a fatigue crack, however only a handful of studies go to the extent on describing the shape the crack takes along the propagation phase. The initial crack size assumed in order to provide an accurate fatigue life estimation is generally a matter of debate. Moreover, the initial crack size is usually chosen as that length that correlates well with experimental data. Sanchez et al. [30] performed an excellent investigation relating the effect of punching and drilling processes on local microstructural damage leading to crack initiation. A fracture surface analysis was performed and concluded that in the majority of the cases of punched plates crack begins at the transition zone between the cut and the tearing zones. As the crack grows and gets to the closest corner, it develops as a corner crack to obtain a front shape close to a quarter of a circumference. Furthermore, and contrary to punched plates, it is not easy to determine the place where the crack begins in drilled specimens. The local damage that is produced through the punching causes a significant loss in fatigue resistance when compared to drilled holes. Shahani and Kashani [31] modeled two symmetric through thickness crack. It states that this crack geometry is an approximation of the real geometry occurring during fatigue loading of the specimen, since due to secondary bending, cracks would initiate and grow during a port of the fatigue life time as a part through cracks (typically with the quarter ellipse shape) [32]. Skorupa et al. [13] reported the crack growth in riveted fuselage lap joints. A particularly large number of works documented the influence of the clamping force on the crack initiation. It concluded that depending on the rivet type and the clamping force, fatigue cracks tend to initiate and propagate in the net cross section at the edge of the hole on the faying surface. Fatigue cracks can also initiate outside the rivet hole, but propagating through the hole, usually shifted above the net cross section. Harris et al. [33] describes the failure progression for a riveted lap joint: it starts with small corner cracks (6 μm) located at the edge of the rivet hole and faying surface for the outer rivets (in the case there are several rivet rows), the corner crack propagates through the thickness, and then the through' crack propagates until the K value for the rivet-loaded crack is equal to that for a double377
Engineering Failure Analysis 91 (2018) 370–381
J. Kafie-Martinez et al.
Fig. 10. Longitudinal stresses (MPa) (a) residual (b) residual plus mechanical for the outer plate.
edge crack subjected to only remote stress. Zhou [16] conducted fatigue test on eighteen full scale riveted bridge girders under both constant and variable amplitude loads. Tests were conducted to failure and detailed examination of growth of cracks from rivet holes showed that the cracks were typically elliptical corner cracks. Propagation of the crack from an initial corner type to a through-the-thickness crack constituted the major portion of fatigue crack growth. Most of the studies in riveted lap joints done so far are related to aircraft structures, where sheet thickness is typically within 1–4 mm (0.04–0.16 in.). Riveted plates found in railroad bridges can have a thickness up to 25.4 mm (1 in.). Therefore, crack propagation for aircraft structures is different from bridges. However, in steel bridges, where the steel plates are usually thicker than 12.7 mm (0.5 in.), a “crack emanating from a round hole” is not applicable. For thicker plates, the crack will still emanate from the edge of the rivet hole but the crack will most likely be of an elliptical shape. Most of the fatigue life will be spent in propagating the 378
Engineering Failure Analysis 91 (2018) 370–381
J. Kafie-Martinez et al.
Fig. 11. Average clamping stress along the plate thickness versus temperature range.
Fig. 12. Clamping stress field variation throughout the plate thickness for different plate thicknesses.
Fig. 13. Longitudinal residual stress field variation throughout the plate thickness for 6.35 mm, 7.94 mm, 12.7 mm, and 25.4 mm (1/4-in, 5/16in,1/2-in, and 1-in respectively) thick plates.
crack depth through the plate thickness. In the former case, fatigue life consists on the number of stress cycles that are required to take the crack from a length Lo to a critical length, Lc. In the latter case, the crack growth is different: because of its elliptical shape, the crack will have a length c and a depth a. Each of these, length and depth, will grow based on the magnitude of the stress intensity
379
Engineering Failure Analysis 91 (2018) 370–381
J. Kafie-Martinez et al.
Fig. 14. Thermal and mechanical stresses along the plate thickness in the riveted lap joint.
Fig. 15. Thermal and mechanical stresses along the y-axis in the riveted lap joint.
factor at the crack front in these two specific directions. Finally, predictions of the lap joint fatigue behavior accounting for the contribution of fretting remain in an academic interest range. Theoretical and experimental investigation on fretting damage indicate that the source of crack nucleation caused by fretting is a sharp peak in the tangential stress due to fretting at the edge of the contact zone [34]. 3. Summary and conclusions A three dimensional finite element models were developed to obtain the residual stress field generated during a hot-driven riveting process. The model simulates the generation of stress in the material being fastened as the rivet contracts due to a decrease of temperature. The distribution of residual thermal stress and the combination of thermal with mechanical stresses in a single shear steel riveted lap joint were developed. A parametric study was carried out to determine the effect of plate thickness in the development of residual stress. The plate thickness plays an important role on the stress distributions on the sense that, thinner plates are benefit by the clamping force generated during the rivet installation process, since it induces a localized compressive stress that hinders crack initiation and propagation. Thinner plates will exhibit slower fatigue crack growth rate and a higher residual stress effect. Moreover, this beneficial effect fades away in thicker plates. The thicker the plate, the less the beneficial effect of the clamping along the faying surfaces. Additionally, fatigue cracks are most likely to form at the contacting surfaces between plates, due to the low clamping stress in the area; therefore, it is more likely to surrender to fatigue under a remote mechanical tension load. Literature review shows that fatigue cracks in riveted joints emanate from the rivet hole along the faying surfaces. Fatigue cracks 380
Engineering Failure Analysis 91 (2018) 370–381
J. Kafie-Martinez et al.
in steel riveted plates can be assume quarter elliptical corner crack emanating from a hole. The stress distributions, and the geometry and size of fatigue cracks will later be used to conduct a fatigue life assessment utilizing a fracture mechanics approach. Acknowledgment The authors would like to thank the American Association of Railroads and Texas A&M High Performance Research Computing for their continuous support. References [1] B. Solomon, North American Railroad Bridges, Crestline Books, 2016 (256 pages). [2] A. De Jesus, H. Pinto, A. Fernandez-Canteli, E. Castillo, J. Correia, Fatigue assessment of a riveted shear splice based on a probabilistic model, Int. J. Fatigue 32 (2009) 453–462. [3] B. Akesson, Fatigue Life of Riveted Steel Bridges, Taylor and Francis Ltd, London, United Kingdom, 2010, p. 184. [4] H.S. Reemsnyder, Fatigue life extension of riveted connections, J. Struct. Div. 101 (12) (1975) 2591–2608. [5] J.W. Fisher, G.L. Kulak, I.F.C. Smith, A Fatigue Primer for Structural Engineers, N. S. B, Alliance, 1998. [6] D. Mertz, Steel bridge design handbook: design for fatigue, US Department of Transportation Federal Highway Administration FHWA -IF-12-052-Vol. 12, vol. 12, 2012. [7] J.F. Unsworth, Heavy Axle Load (HAL) Effects on Fatigue Life of Steel Bridges, Presented at the TRB 2003 Annual Meeting, 2003. [8] C. Barkan, Introduction to Rail Transportation, University of Illinois at Urbana-Champaign, 2012. [9] W.-F. Chen, L. Duan, Chapter 23: Railroads, Bridge Engineering Handbook, CRC Press, 2000. [10] P.B. Keating, J.W. Fisher, Evaluation of fatigue tests and design criteria on welded details, NCHRP REPORT 286, National Cooperative Highway Research Program, Washington, D.C., 1986, p. 286. [11] J.M. Out, J.W. Fisher, B.T. Yen, Fatigue strength of weathered and deteriorated riveted members, October 1984. (DOT/OST/P-34/85/016) 138p, Fritz Laboratory Reports, 1984, p. 2282. [12] A. Pipinato, C. Pellegrino, O.S. Bursi, C. Modena, High-cycle fatigue behavior of riveted connections for railway metal bridges, J. Constr. Steel Res. 65 (2009) 2167–2175. [13] A. Skorupa, M. Skorupa, T. Machniewicz, A. Korbe, An experimental investigation on crack initiation and growth in aircraft fuselage riveted lap joints, Mat. Sci. Forum 726 (2012) 211–217. [14] R.F. Sanches, A. De Jesus, A.M.P. Correia, A. Da Silva, A. Fernandes, A probabilistic fatigue approach for riveted joints using Monte Carlo Simulation, J. Constr. Steel Res. 110 (2015) 149–162. [15] A. Skorupa, M. Skorupa, T. Machniewicz, A. Korbel, Fatigue crack location and fatigue life for riveted lap joints in aircraft fuselage, Int. J. Fatigue 58 (2014) 209–217. [16] Y. Zhou, Fatigue strength evaluation of riveted bridge members, Degree of Doctor of Philosophy in Civil Engineering, Civil Engineering, Lehigh University, Bethlehem, Pennsylvania, 1994. [17] A.M.P. Correia, A. De Jesus, A. Silva, B. Pedrosa, C. Rebelo, R.A.B. Calcada, FE simulation of S-N curves for a riveted connection using two-stage fatigue models, Adv. Comput. Design 2 (4) (2017) 333–348. [18] A.M.P. Correia, A. De Jesus, A.L.L. Da Silva, J.F.N.D.A. Silva, A procedure to derive probabilistic fatigue strength data for riveted joints, Presented at the International Conference on Bridge Maintenance, Safety and Management (IABMAS '10), Pennsylvania, USA, 2010. [19] A. De Jesus, A. Da Silva, M.V. Figueiredo, A.M.P. Correia, A.S. Ribeiro, A. Fernandes, Strain-life and crack propagation fatigue data from several Portuguese old metallic riveted bridges, Eng. Fail. Anal. 18 (1) (2011) 148–163. [20] A.M.P. Correia, et al., Statistical analysis of fatigue crack propagation data of materials from ancient portuguese metallica bridges, Frat. Integ. Strut. 42 (2017) 136–146. [21] G. Lesiuk, M. Szata, M. Bocian, The mechanical properties and the microstructural degradation effect in an old low carbon steels after 100-years operating time, Archiv. Civil Mech. Eng. 15 (2015) 786–797. [22] G. Lesiuk, M. Szata, Kinetics of fatigue crack growth and crack paths in the old puddled steel after 100-years operating time, Frat. Int. Strut. 34 (2015) 290–299. [23] G. Lesiuk, P. Kucharski, A.M.P. Correia, A. De Jesus, C. Rebelo, L. Simoes da Silva, Mixed mode (I+II) fatigue crack growth in puddle iron, Eng. Fract. Mech. 185 (2017) 175–192. [24] P. Raposo, A.M.P. Correia, G. Lesiuk, I. Valente, A. De Jesus, R.A.B. Calcada, Mechanical characterization of ancient Portuguese riveted bridge steels, Eng. Struct. Technol. 9 (4) (2017) 214–225. [25] J. Kafie-Martinez, P.B. Keating, Finite element modeling for clamping stresses developed in hot-driven steel structural riveted connections, Int. J. Civil Environ. Struct. Construct. Architect. Eng. 11 (5) (2017) 560–565. [26] M. Zhou, Fracture Mechanics Analysis on the Resistance of Welded Details under Variable Amplitude Long Life Loading, Civil Engineering, Texas A&M University, 1993 (Master of Science). [27] J.M. Friedland, Stresses in Rivets Used in Direct Tension, Engineering News, Feb. 17, 1916. [28] “The effects of stresses produced in materials by riveting,” Zeitschrift des Vereins Deutscher Ingenieure, 56 (47) (1890) Nov. 23, 1912. [29] W.M. Wilson, F.P. Thomas, Fatigue tests of riveted joints, Engineering Experiment Station Bulletin No. 302, May 31, 1938. [30] L. Sanchez, F. Gutiérrez-Solana, D. Pesquera, Fatigue behavior of punched structural plates, Eng. Fail. Anal. 11 (2004) 751–764. [31] A.R. Shahani, H.M. Kashani, Fracture mechanics-based life prediction of a riveted lap joint, J. Comput. Appl. Res. Mech. Eng. 4 (1) (2014) 1–17. [32] P.M.G.P. Moreira, P.F.P. de Matos, P.P. Camanho, S.D. Pastrama, P.M.S.T. de Castro, Stress intensity factor and load transfer analysis of a cracked riveted lap joint, Int. J. Fatigue 28 (4) (2007) 1263–1270. [33] C.E. Harris, R.S. Piascik, J. Newman Jr., A practical engineering approach to predicting fatigue crack growth in riveted lap joints, Proc. of Internation Conference on Aeronautial Fatigue, 1999 (W.A. Seattle). [34] A. Skorupa, M. Skorupa, Riveted Lap Joints in Aircraft Fuselage, (2012).
381
Contents lists available at ScienceDirect
Engineering Failure Analysis journal homepage: www.elsevier.com/locate/engfailanal
Stress distributions and crack growth in riveted lap joints fastening thick steel plates
T
⁎
Jackeline Kafie-Martineza, , Peter B. Keatinga, Pranav Chakra-Varthyb, José Correiac, Abílio de Jesusc a
Texas A&M University at College Station, TX, United States Indian Institute of Technology, Gandhinagar, India c Faculty of Engineering, University of Porto, Portugal b
A R T IC LE I N F O
ABS TRA CT
Keywords: Riveted lap joints Fatigue life Finite element analysis Railroad bridges Residual stress
Single shear lap joints have been a common method to fasten steel plates in railroad bridges and can be highly susceptible to fatigue cracking under the cyclic loading bridges experience. To better comprehend the fatigue process of these connections, it is important to understand the stress state near the rivet hole. While the fatigue behavior of these riveted connections has been studied, few have been carried out on stress distribution and crack formation in riveted lap joints fastening thick steel plates. This study is to provide information regarding the stress distributions developed in a single shear lap joint connecting plates of varying thicknesses. Results from the stress contour analysis are utilized to detect possible regions for fatigue crack nucleation under cyclic heavy axle loads. The study also provides information regarding the fatigue crack geometry typically found in single shear lap joints.
1. Introduction Rivets were widely used as mechanical fasteners in railroad bridges constructed after the 1900's through the 1960's, when the introduction of high strength bolts replaced the use of rivets [1]. These riveted railway bridges were not originally designed taking into account fatigue [2], furthermore, if fatigue was taken into account, it was based on limited understanding and knowledge of the phenomenon [3,4]. This was due to many reasons: first, fatigue cracking in these early structures was infrequent [5,6]. Second, axle loads in train configurations prior to the 1960s rarely exceeded 20 tons (40,000 lbs), creating an almost negligible effect on the fatigue damage of railroad bridges [7]. Finally, the fatigue phenomenon was only intensively investigated after the second half of the 20th century [2], were welding began to be used as the preferred method for fabrication of steel bridges. There are a large number of old riveted railroad bridges that are still in operation today. The average age of these riveted railway bridges is reaching 100 years old [7]. Moreover, as the railroad industry increase their carloads, these bridges are subjected to increasing axle loads. Freight cars have increased from 85 tons, commonly used before 1960, to a range of 131.5 tons to 143 tons (263,000 lbs–286,000 lbs) used today [7]. Furthermore, in 2011 alone, it was reported that approximately 1600 railcars of 157.5 tons (315,000 lbs) were in service on Class I railroads [8,9]. With the ever increasing freight car weights, the old riveted railroad bridges are being subjected to larger and more frequent stress ranges that they were originally intended for. Since most of the riveted railroad bridges in service have passed the 80 years' service lifetime, the proper maintenance and remaining fatigue life of these bridges is a major concern. It is imperative to investigate the effect of heavy axle loads in fatigue damage of these structures.
⁎
Corresponding author. E-mail address: [email protected] (J. Kafie-Martinez).
https://doi.org/10.1016/j.engfailanal.2018.04.048 Received 29 January 2018; Received in revised form 16 April 2018; Accepted 29 April 2018 Available online 03 May 2018 1350-6307/ © 2018 Elsevier Ltd. All rights reserved.
Engineering Failure Analysis 91 (2018) 370–381
J. Kafie-Martinez et al.
With the current fatigue provisions [10], the life of the components can be estimated by identifying the fatigue detail category and specifying the critical stress range it will experience during its lifetime. However, when utilizing a fracture mechanics approach, much more information regarding the stress state and crack (geometry and size) is needed; but it could also provide a more accurate fatigue life estimation. Current fatigue S-N curves are based on fatigue life of welded connections; experimental results have shown that fatigue life of riveted connections typically fall within Category C and D. The S-N curves can provide a robust estimation, however, in some cases, a more accurate calculation is needed. 2. Riveted lap joints To understand the fatigue process within riveted lap joints, detailed knowledge of the stress state is required. Studies have demonstrated that clamping force is a principal variable influencing the fatigue resistance of riveted connections typical in old railroad bridges [11]. The presence of residual stresses resulting from rivet installation complicate the analysis of crack formation and propagation. In comparison with high strength bolts, the clamping stresses on rivets are generally lower in magnitude and not as predictable due to an increased variability in magnitude [2,3]. The use of different riveting techniques, either in-shop or on-site, may entail different clamping force magnitudes and variable load-carrying capacities in member and in joints [12]. The presence of clamping stress affects the nucleation location and the path of fatigue cracks at rivet holes. It will also dictate the magnitude of the compression stress between faying surfaces, this leads to transmitting a portion of the applied load by friction [13]. This study is to provide information regarding the stress state near the rivet hole due to thermal contraction during the installation. Additionally, it describes how the residual stress combines with external surface traction to yield the stress distribution typically found near rivet holes. The stress state near the rivet hole will be used to study fatigue crack propagation in this area. 2.1. Previous studies Skorupa et al. [13] conducted fatigue tests on riveted lap joints, typically found in aircraft fuselages, to understand the effects of thickness and clamping stress of rivets on fatigue life, crack initiation and crack growth. It was found that cracks always initiate at the faying surface at the outer rivet rows and that the crack geometry and growth were affected by the clamping stress. Lower clamping stress produced quarter elliptical cracks which propagated through the rivet row, whereas higher clamping stress produced semi elliptical cracks that propagated away from the rivet row towards the edge. Sanches et al. [14] performed a fatigue simulation of a double shear riveted joint. Both, crack initiation and propagation were accounted for. Effects of various variable model inputs such as friction, clamping stress, as well as the crack initiation size definition were assumed in the probabilistic form to generate S-N curves. For the investigated riveted joint, the fatigue crack initiation was the dominating damage mechanism. The proposed S-N curve did not show good agreement with the existing code-based S-N curves. Skorupa et al. [15] analyzed the fatigue behavior in riveted lap joints and evaluate quantitatively the influence of several variables on the joint fatigue behavior. It was concluded that: fatigue cracks in riveted lap joint always start in one of the end rivet rows on the faying surface of the loaded sheet; sheet thickness, rivet type and clamping stress can have a significant impact on all aspects of the joint fatigue response; increasing the rivet clamping stress yields a longer fatigue life regardless of the sheet thickness; and that riveting imperfections can have a profound influence on the joint fatigue performance. Zhou [16] conducted a study to measure the magnitude of clamping residual stress in riveted members from demolished bridges approximately 60 years of age. The measured clamping stress varied from 34 to 165 MPa (5 to 24 ksi), with an average of about 83 MPa (12 ksi) and a standard deviation of about 41 MPa (6 ksi). Zhou [16] also performed a two-dimensional finite element model to examine the distribution of normal and frictional stresses on the contact surfaces. The presence of a crack was not considered in the model. It was reported that a temperature change of 204 °C (400 °F) during the cooling process in the rivet caused a clamping stress of about 262 MPa (38 ksi). Correia et al. [17] presented a comparison between two alternative finite element models to predict the fatigue strength of a single shear and single rivet connection. A finite element model using solid elements in its entirety is compared to a finite element model using a combination of shell elements for the plates, and solid elements for the rivet. Both steel plates and rivet were modeled as isotropic and elastic material. The simulations were performed using the Augmented Lagrange contact algorithm, and null gap between plates and rivet was considered. A through thickness crack was assumed and a stress ratio R equivalent to 0.1 was assumed. The study works with clamping stress ranging from 0 to 300 MPa. The research concluded that crack initiation phase is dominant for high cycle fatigue and that the numerical analysis assuming an initial crack size of 0.6 mm agreed well with experimental data. Correia et al. [17] based his finite element model in the studies presented by De Jesus et al. [2] and Correia et al. [18]. De Jesus et al. [2] proposed a methodology to generate probabilistic stress life data for a riveted shear splice, which can be applied into probabilistic fatigue assessments. Correia et al. [18] uses the same 3-D FE model of a riveted joint to assess the elastic stress concentration and the stress intensity factor to assess the crack initiation and crack propagation phases, respectively. This data was used to derive probabilistic S-N fields for riveted connections. The parameters in the analysis that were assumed in a probabilistic form were: clamping stress, friction, the initial crack size and the coefficient C of the Paris's Law. All the above authors presented excellent work and insight into their finite element model. However, the stress distributions per se were not reported, as well as the effect of the plate thickness in the residual clamping stress. Additionally, this study investigates the effect of the plate thickness on the crack geometry developed due to cyclic loads. Some authors, such as De Jesus et al. [19], Correia et al. [20], Lesiuk et al. [21,22,23] and Raposo et al. [24] have studied the mechanical properties of puddle irons/old mild steels as well as riveted connections used in old riveted steel bridges. De Jesus et al. 371
Engineering Failure Analysis 91 (2018) 370–381
J. Kafie-Martinez et al.
Fig. 1. Dimensions and boundary conditions of the lap joint, top view.
[19] presented a study on assessing the strain-life and fatigue crack growth data using samples of original material removed from five Portuguese metallic riveted bridges. Their study also included the monotonic and cyclic elastoplastic properties for the old mild steels. Lesiuk et al. [21–23] has also been studying the mechanical properties and the microstructural degradation effect, the fatigue crack propagation and crack closure effects in old low carbon steels after 100-years of operating time. More recently, Raposo et al. [24] presented a review paper on mechanical characteristics of old mild steels and puddled iron from old riveted steel bridges, such as, monotonic tensile strength, chemical composition, microstructures, hardness, notch toughness, and fatigue crack propagation. The mechanical properties of the materials from the old steel bridges are of great importance as they can be used in fatigue studies and damage assessment of these structures. 2.2. Finite element model of a single shear lap joint In order to obtain a detailed stress state in a single shear lap joint, a finite element model was performed. Dimensions of the lap joint are illustrated in Figs. 1 and 2. The three-dimensional finite element model was developed using ABAQUS© software. The model attempts to replicate the residual stresses developed during the installation process, as well as to provide information on how the residual stresses superimpose with mechanical tensile stresses. The stress distributions will later be utilized to identify possible regions for crack propagation, as well as, perform a fatigue life assessment through a fracture mechanics approach. The model consists of two analyses steps. The first step is a thermo-mechanical analysis where the residual stress was simulated by specifying different initial temperatures between contacting plates and rivet. This provides an analytical methodology to generate the clamping stress. The second step consists on applying a tensile mechanical traction, σ, at x = 800 mm (31.5 in.). The second step will use the stresses found in step 1 as the initial condition. Therefore, the results of step 2 are the superimposed stresses. Two predefined fields where necessary to state the initial temperature of the rivet (1000 °C or 1832 °F) and of the plates (20 °C or 68 °F). The mechanical boundary conditions used are the following: 1. The left edge of the outer plate, that is when x = 0, is pinned supported. 2. The beginning 200 mm (7.9 in.) segment of the outer plate (x = 0 to 200 mm) and the end 200 mm (7.9 in) of the segment of the inner plate (x = 600 to 800 mm) are constrained in the y and z direction. A thermal boundary condition is set to define the final state: the entire system (both plates and the rivet) reach ambient temperature. Additionally, contacting surfaces between rivet and plates' surfaces were necessary to avoid penetration of one surface over the other. The three contact properties specified were the following: tangential behavior, normal behavior and a clearance dependent thermal conductance. The tangential behavior was specified as a Penalty Friction Formulation assuming a coefficient of friction equivalent to 0.3. The normal behavior was defined as hard contact pressure overclosure. The hard contact relationship minimizes the penetration of the slave surface into the master surface at the constraint locations and does not allow the transfer of tensile stress across the interface. There are three possible constraint enforcement methods in ABAQUS: the direct method, the penalty method and the augmented Lagrange method. In this investigation, the default constraint enforcement method was used. The default constraint enforcement method depends on interaction properties as follows: the penalty method is used by default for finite-sliding, surface-tosurface contact (including general contact) if a hard pressure-overclosure relationship is in effect; the augmented Lagrange method is
Fig. 2. Dimensions and boundary conditions of the lap joint, transverse view. 372
Engineering Failure Analysis 91 (2018) 370–381
J. Kafie-Martinez et al.
Table 1 Material properties of steel at room temperature. Young's modulus, E Poisson's ratio, υ Yield Stress, σy Ultimate Stress, σut Specific Heat, cp Linear Thermal Expansion, α Thermal Conductivity, λa Mass Density, ρ
193 GPa 0.28 248 MPa 400 Mpa 440 J/kg °C 12 × 10−6/ °C 53.3 W/m °C 7850 kg/m3
used by default for three-dimensional self-contact with node-to-surface discretization if a hard pressure-overclosure relationship is in effect; the direct method is the default in all other cases. Finally, separation after contact is allowed. For this reason, it was necessary to specify the material's thermal gap conductance, that is, how the conductance differs in a steel-air-steel interface scenario. The finite element model is non-linear due to the contact problem. The Nlgeom option must be enabled to account for large strain plastic deformations. Steel properties commonly utilized for A36 are presented in Tables 1 and 2. Even though it is common to have steel A502 for steel structural rivets, no distinction was made between the plates and the rivet steel in the finite element model. The difference in material properties for steel A36 and A502 is not expected to produce significant effect in the results. Moreover, the crack is expected to develop in the plates, therefore, A36 is used for the entire geometry. Except for the material's density, the dependence of the material properties with respect to temperature was considered. For more detailed information regarding the finite element model as well as steel thermal properties refer to Ref. [25]. The steel rivet and steel plates were modeled using an 8-node thermo-mechanically coupled brick, called C3D8RHT in ABAQUS. A refined mesh near the rivet hole area is necessary since a large stress concentration is expected in this area. Since preliminary findings suggest that fatigue crack growth usually emanates from the rivet hole, and that plate thickness plays an important role in the residual stress distributions around the area, it was deemed necessary to perform a mesh convergence study. The objective of the mesh convergence study is to determine the optimum size of elements necessary to have good accurate results. Therefore, the plate thickness of the base model, 12.7 mm, was divided into 5, 10, 15 and 20 elements resulting in element thicknesses of 2.54 mm, 1.27 mm, 0.85 mm and 0.64 mm respectively. Fig. 3 shows the mesh of the riveted joint. Figs. 4 and 5 show how the stress distributions varied for the different adopted meshes. For the longitudinal stress, Fig. 4, the major discrepancy appears to be right under the rivet head. However, stress near the interface are of most importance, since this region would most likely surrender to fatigue, as it will be explained later. On the other hand, the clamping stress (Fig. 5) present small discrepancy on the top half of the plate thickness, but, once again, clamping stress near the interface is of most importance. For this reason, and in order to save computational time, an element thickness of 1.27 mm (10 elements) throughout the plate thickness was adopted. 2.3. Deformations The usage of overclosure hard contact surfaces prevented the contacting surfaces from penetrating one another; it also allows them to separate and loose contact as needed. Therefore, the use of contact surfaces gives a realistic deformed shape. The deformation of the model is always important to check since by comparing it to the expected real deformations of the component one can rest assure the model simulates the real behavior. In this specific case, as the rivet cools and contracts, the plates are compressed and consequently warp. As shown in Fig. 6, the plates are bended under tensional loading. Fig. 7 shows the undeformed and deformed shape of the joint, as the rivet cools, it shrinks, and a gap is formed between rivet shank and the plates. 2.4. Stress distributions The stress contours for residual and total stress for both plates and the rivet are shown, see Figs. 8, 9, and 10. The total stress consists of the residual stress in combination with a tensile traction of 20 MPa. It is important to note that the stress contours for both plates shown here present the stresses along the contacting surfaces, since crack propagation is more likely to happen throughout this Table 2 Interface contact thermal conductance for steel-air-steel with a normal grinding surface finish and zero contact pressure. Gap [mm]
Interfacial Thermal Conductance [W/m2 °C]
0.0 0.5 1.0 1.5
2500 50 25 0
373
Engineering Failure Analysis 91 (2018) 370–381
J. Kafie-Martinez et al.
Outer plate
Inner plate
Surface Interaction
Refined mesh around rivet hole Fig. 3. Mesh of the riveted lap joint using an 8-node thermos-mechanically coupled brick. Surface interaction was defined for every contacting surface.
Fig. 4. Longitudinal stress distribution assuming different number of elements throughout the plate thickness. 374
Engineering Failure Analysis 91 (2018) 370–381
J. Kafie-Martinez et al.
Fig. 5. Clamping stress distribution assuming different number of elements throughout the plate thickness.
Fig. 6. Deformed shape of the riveted lap joint, longitudinal view (deformation scale factor of 15).
surface. Another important observation is that residual stresses are completely symmetrical; meanwhile, when combined with the mechanical traction, the stresses lose symmetry. Fig. 11 shows how the clamping stress changes with temperature range. It is quite interesting to note that the clamping stress does not significantly change for a temperature range larger than 280 °C. On the other hand, the computational time is much larger when a ΔT of 980 °C is used. Hence, in the event of a preliminary study one can assume a 280 °C < ΔT < 980 °C to have an estimation of the magnitude of the clamping stress. When 280 °C < ΔT ≤ 980 °C, the average clamping stress is 260 MPa. This agrees with the value computed by Zhou [26]. Zhou [26] reported a clamping stress of about 262 MPa (38 ksi) for a temperature change of 204 °C (400 °F). Moreover, studies have shown that the initial tension of an ordinary rivet driven with a hydraulic riveter can reach 214 MPa (31,000 lb/in2) [27,28]. Wilson and Thomas [29] reported an average initial tension of 241 MPa (35,000 lb/in2) for carbon-steel rivets, driven by either a hydraulic riveting machine or a pneumatic hand-riveting hammer. It is important to clarify that for Fig. 11 an average clamping stress along the plate thickness was used. The stress distributions were also obtained assuming three other plate thicknesses, 6.35 mm (¼ in.), 7.94 mm (5/16 in.), and 25.4 mm (1 in.) shown in Fig. 12 and Fig. 13. In Fig. 12 and Fig. 13 stress vs. plate thickness are presented on the left graph and stress vs. normalized plate thickness are shown on the right. Fig. 12 shows how the clamping changes for each plate: it can be as high as 340 MPa for the 7.94 mm-thick plate or as low as 100 MPa for a 25.4-mm thick plate. Note also that the thickest plate, has the lowest 375
Engineering Failure Analysis 91 (2018) 370–381
J. Kafie-Martinez et al.
Fig. 7. Transverse view of the riveted lap joint (a) undeformed and (b) deformed.
Fig. 8. Longitudinal stresses (MPa) (a) residual (b) residual plus mechanical.
clamping stress along the faying surfaces. Moreover, the clamping stress S33 is not directly responsible for fatigue crack propagation. Fatigue cracks in rivets usually start at the rivet hole, and propagate perpendicular due to the fluctuations of the longitudinal stress, S11. Hence, the longitudinal stress S11 vs. plate thickness and normalized plate thickness are shown in Fig. 13. This longitudinal residual stress, S11, can hinder fatigue crack propagation if it is of a compressive type, or can accelerate fatigue crack propagation if it is of a tensile nature. The 25.4 mm -thick plate exhibits tensile residual stress near the faying surfaces, and if combined with a remote mechanical tension load, this area can become a hot-spot for fatigue cracks. Furthermore, Figs. 14 and 15 present how the stress distributions along the z and y axes are affected by an increase in the remote tensile load. Fig. 14 shows that for a remote tension of 10 MPa (1.5 ksi) and 15 MPa (2.2 ksi), the total stress along the plate thickness is under compression. However, in the case of a larger remote tension, say 20 MPa (2.9 ksi), the faying surface is the first region to come under tension, which suggests a crack will most likely propagate there.
376
Engineering Failure Analysis 91 (2018) 370–381
J. Kafie-Martinez et al.
Fig. 9. Longitudinal stresses (MPa) (a) residual (b) residual plus mechanical for the inner plate.
2.5. Crack growth in riveted lap joints It is very well known that fatigue cracks are likely to emanate from the rivet hole for two reasons. First, the punching or drilling of the hole introduces imperfections in the material and second, the hole in the plate produces a stress concentration in the area. In order to develop a fatigue assessment of a riveted joint using fracture mechanics concepts, one must be clear on the location of the fatigue crack along with its shape and its initial size. Experimental data usually depicts the location, final crack length, and the cause of a fatigue crack, however only a handful of studies go to the extent on describing the shape the crack takes along the propagation phase. The initial crack size assumed in order to provide an accurate fatigue life estimation is generally a matter of debate. Moreover, the initial crack size is usually chosen as that length that correlates well with experimental data. Sanchez et al. [30] performed an excellent investigation relating the effect of punching and drilling processes on local microstructural damage leading to crack initiation. A fracture surface analysis was performed and concluded that in the majority of the cases of punched plates crack begins at the transition zone between the cut and the tearing zones. As the crack grows and gets to the closest corner, it develops as a corner crack to obtain a front shape close to a quarter of a circumference. Furthermore, and contrary to punched plates, it is not easy to determine the place where the crack begins in drilled specimens. The local damage that is produced through the punching causes a significant loss in fatigue resistance when compared to drilled holes. Shahani and Kashani [31] modeled two symmetric through thickness crack. It states that this crack geometry is an approximation of the real geometry occurring during fatigue loading of the specimen, since due to secondary bending, cracks would initiate and grow during a port of the fatigue life time as a part through cracks (typically with the quarter ellipse shape) [32]. Skorupa et al. [13] reported the crack growth in riveted fuselage lap joints. A particularly large number of works documented the influence of the clamping force on the crack initiation. It concluded that depending on the rivet type and the clamping force, fatigue cracks tend to initiate and propagate in the net cross section at the edge of the hole on the faying surface. Fatigue cracks can also initiate outside the rivet hole, but propagating through the hole, usually shifted above the net cross section. Harris et al. [33] describes the failure progression for a riveted lap joint: it starts with small corner cracks (6 μm) located at the edge of the rivet hole and faying surface for the outer rivets (in the case there are several rivet rows), the corner crack propagates through the thickness, and then the through' crack propagates until the K value for the rivet-loaded crack is equal to that for a double377
Engineering Failure Analysis 91 (2018) 370–381
J. Kafie-Martinez et al.
Fig. 10. Longitudinal stresses (MPa) (a) residual (b) residual plus mechanical for the outer plate.
edge crack subjected to only remote stress. Zhou [16] conducted fatigue test on eighteen full scale riveted bridge girders under both constant and variable amplitude loads. Tests were conducted to failure and detailed examination of growth of cracks from rivet holes showed that the cracks were typically elliptical corner cracks. Propagation of the crack from an initial corner type to a through-the-thickness crack constituted the major portion of fatigue crack growth. Most of the studies in riveted lap joints done so far are related to aircraft structures, where sheet thickness is typically within 1–4 mm (0.04–0.16 in.). Riveted plates found in railroad bridges can have a thickness up to 25.4 mm (1 in.). Therefore, crack propagation for aircraft structures is different from bridges. However, in steel bridges, where the steel plates are usually thicker than 12.7 mm (0.5 in.), a “crack emanating from a round hole” is not applicable. For thicker plates, the crack will still emanate from the edge of the rivet hole but the crack will most likely be of an elliptical shape. Most of the fatigue life will be spent in propagating the 378
Engineering Failure Analysis 91 (2018) 370–381
J. Kafie-Martinez et al.
Fig. 11. Average clamping stress along the plate thickness versus temperature range.
Fig. 12. Clamping stress field variation throughout the plate thickness for different plate thicknesses.
Fig. 13. Longitudinal residual stress field variation throughout the plate thickness for 6.35 mm, 7.94 mm, 12.7 mm, and 25.4 mm (1/4-in, 5/16in,1/2-in, and 1-in respectively) thick plates.
crack depth through the plate thickness. In the former case, fatigue life consists on the number of stress cycles that are required to take the crack from a length Lo to a critical length, Lc. In the latter case, the crack growth is different: because of its elliptical shape, the crack will have a length c and a depth a. Each of these, length and depth, will grow based on the magnitude of the stress intensity
379
Engineering Failure Analysis 91 (2018) 370–381
J. Kafie-Martinez et al.
Fig. 14. Thermal and mechanical stresses along the plate thickness in the riveted lap joint.
Fig. 15. Thermal and mechanical stresses along the y-axis in the riveted lap joint.
factor at the crack front in these two specific directions. Finally, predictions of the lap joint fatigue behavior accounting for the contribution of fretting remain in an academic interest range. Theoretical and experimental investigation on fretting damage indicate that the source of crack nucleation caused by fretting is a sharp peak in the tangential stress due to fretting at the edge of the contact zone [34]. 3. Summary and conclusions A three dimensional finite element models were developed to obtain the residual stress field generated during a hot-driven riveting process. The model simulates the generation of stress in the material being fastened as the rivet contracts due to a decrease of temperature. The distribution of residual thermal stress and the combination of thermal with mechanical stresses in a single shear steel riveted lap joint were developed. A parametric study was carried out to determine the effect of plate thickness in the development of residual stress. The plate thickness plays an important role on the stress distributions on the sense that, thinner plates are benefit by the clamping force generated during the rivet installation process, since it induces a localized compressive stress that hinders crack initiation and propagation. Thinner plates will exhibit slower fatigue crack growth rate and a higher residual stress effect. Moreover, this beneficial effect fades away in thicker plates. The thicker the plate, the less the beneficial effect of the clamping along the faying surfaces. Additionally, fatigue cracks are most likely to form at the contacting surfaces between plates, due to the low clamping stress in the area; therefore, it is more likely to surrender to fatigue under a remote mechanical tension load. Literature review shows that fatigue cracks in riveted joints emanate from the rivet hole along the faying surfaces. Fatigue cracks 380
Engineering Failure Analysis 91 (2018) 370–381
J. Kafie-Martinez et al.
in steel riveted plates can be assume quarter elliptical corner crack emanating from a hole. The stress distributions, and the geometry and size of fatigue cracks will later be used to conduct a fatigue life assessment utilizing a fracture mechanics approach. Acknowledgment The authors would like to thank the American Association of Railroads and Texas A&M High Performance Research Computing for their continuous support. References [1] B. Solomon, North American Railroad Bridges, Crestline Books, 2016 (256 pages). [2] A. De Jesus, H. Pinto, A. Fernandez-Canteli, E. Castillo, J. Correia, Fatigue assessment of a riveted shear splice based on a probabilistic model, Int. J. Fatigue 32 (2009) 453–462. [3] B. Akesson, Fatigue Life of Riveted Steel Bridges, Taylor and Francis Ltd, London, United Kingdom, 2010, p. 184. [4] H.S. Reemsnyder, Fatigue life extension of riveted connections, J. Struct. Div. 101 (12) (1975) 2591–2608. [5] J.W. Fisher, G.L. Kulak, I.F.C. Smith, A Fatigue Primer for Structural Engineers, N. S. B, Alliance, 1998. [6] D. Mertz, Steel bridge design handbook: design for fatigue, US Department of Transportation Federal Highway Administration FHWA -IF-12-052-Vol. 12, vol. 12, 2012. [7] J.F. Unsworth, Heavy Axle Load (HAL) Effects on Fatigue Life of Steel Bridges, Presented at the TRB 2003 Annual Meeting, 2003. [8] C. Barkan, Introduction to Rail Transportation, University of Illinois at Urbana-Champaign, 2012. [9] W.-F. Chen, L. Duan, Chapter 23: Railroads, Bridge Engineering Handbook, CRC Press, 2000. [10] P.B. Keating, J.W. Fisher, Evaluation of fatigue tests and design criteria on welded details, NCHRP REPORT 286, National Cooperative Highway Research Program, Washington, D.C., 1986, p. 286. [11] J.M. Out, J.W. Fisher, B.T. Yen, Fatigue strength of weathered and deteriorated riveted members, October 1984. (DOT/OST/P-34/85/016) 138p, Fritz Laboratory Reports, 1984, p. 2282. [12] A. Pipinato, C. Pellegrino, O.S. Bursi, C. Modena, High-cycle fatigue behavior of riveted connections for railway metal bridges, J. Constr. Steel Res. 65 (2009) 2167–2175. [13] A. Skorupa, M. Skorupa, T. Machniewicz, A. Korbe, An experimental investigation on crack initiation and growth in aircraft fuselage riveted lap joints, Mat. Sci. Forum 726 (2012) 211–217. [14] R.F. Sanches, A. De Jesus, A.M.P. Correia, A. Da Silva, A. Fernandes, A probabilistic fatigue approach for riveted joints using Monte Carlo Simulation, J. Constr. Steel Res. 110 (2015) 149–162. [15] A. Skorupa, M. Skorupa, T. Machniewicz, A. Korbel, Fatigue crack location and fatigue life for riveted lap joints in aircraft fuselage, Int. J. Fatigue 58 (2014) 209–217. [16] Y. Zhou, Fatigue strength evaluation of riveted bridge members, Degree of Doctor of Philosophy in Civil Engineering, Civil Engineering, Lehigh University, Bethlehem, Pennsylvania, 1994. [17] A.M.P. Correia, A. De Jesus, A. Silva, B. Pedrosa, C. Rebelo, R.A.B. Calcada, FE simulation of S-N curves for a riveted connection using two-stage fatigue models, Adv. Comput. Design 2 (4) (2017) 333–348. [18] A.M.P. Correia, A. De Jesus, A.L.L. Da Silva, J.F.N.D.A. Silva, A procedure to derive probabilistic fatigue strength data for riveted joints, Presented at the International Conference on Bridge Maintenance, Safety and Management (IABMAS '10), Pennsylvania, USA, 2010. [19] A. De Jesus, A. Da Silva, M.V. Figueiredo, A.M.P. Correia, A.S. Ribeiro, A. Fernandes, Strain-life and crack propagation fatigue data from several Portuguese old metallic riveted bridges, Eng. Fail. Anal. 18 (1) (2011) 148–163. [20] A.M.P. Correia, et al., Statistical analysis of fatigue crack propagation data of materials from ancient portuguese metallica bridges, Frat. Integ. Strut. 42 (2017) 136–146. [21] G. Lesiuk, M. Szata, M. Bocian, The mechanical properties and the microstructural degradation effect in an old low carbon steels after 100-years operating time, Archiv. Civil Mech. Eng. 15 (2015) 786–797. [22] G. Lesiuk, M. Szata, Kinetics of fatigue crack growth and crack paths in the old puddled steel after 100-years operating time, Frat. Int. Strut. 34 (2015) 290–299. [23] G. Lesiuk, P. Kucharski, A.M.P. Correia, A. De Jesus, C. Rebelo, L. Simoes da Silva, Mixed mode (I+II) fatigue crack growth in puddle iron, Eng. Fract. Mech. 185 (2017) 175–192. [24] P. Raposo, A.M.P. Correia, G. Lesiuk, I. Valente, A. De Jesus, R.A.B. Calcada, Mechanical characterization of ancient Portuguese riveted bridge steels, Eng. Struct. Technol. 9 (4) (2017) 214–225. [25] J. Kafie-Martinez, P.B. Keating, Finite element modeling for clamping stresses developed in hot-driven steel structural riveted connections, Int. J. Civil Environ. Struct. Construct. Architect. Eng. 11 (5) (2017) 560–565. [26] M. Zhou, Fracture Mechanics Analysis on the Resistance of Welded Details under Variable Amplitude Long Life Loading, Civil Engineering, Texas A&M University, 1993 (Master of Science). [27] J.M. Friedland, Stresses in Rivets Used in Direct Tension, Engineering News, Feb. 17, 1916. [28] “The effects of stresses produced in materials by riveting,” Zeitschrift des Vereins Deutscher Ingenieure, 56 (47) (1890) Nov. 23, 1912. [29] W.M. Wilson, F.P. Thomas, Fatigue tests of riveted joints, Engineering Experiment Station Bulletin No. 302, May 31, 1938. [30] L. Sanchez, F. Gutiérrez-Solana, D. Pesquera, Fatigue behavior of punched structural plates, Eng. Fail. Anal. 11 (2004) 751–764. [31] A.R. Shahani, H.M. Kashani, Fracture mechanics-based life prediction of a riveted lap joint, J. Comput. Appl. Res. Mech. Eng. 4 (1) (2014) 1–17. [32] P.M.G.P. Moreira, P.F.P. de Matos, P.P. Camanho, S.D. Pastrama, P.M.S.T. de Castro, Stress intensity factor and load transfer analysis of a cracked riveted lap joint, Int. J. Fatigue 28 (4) (2007) 1263–1270. [33] C.E. Harris, R.S. Piascik, J. Newman Jr., A practical engineering approach to predicting fatigue crack growth in riveted lap joints, Proc. of Internation Conference on Aeronautial Fatigue, 1999 (W.A. Seattle). [34] A. Skorupa, M. Skorupa, Riveted Lap Joints in Aircraft Fuselage, (2012).
381