Engineering Failure Analysis 18 (2011) 1279–1294

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Engineering Failure Analysis

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Research on fatigue cracks in composite dowel shear connection

P. Harnatkiewicz a,⇑, A. Kopczynski a, M. Ko _zuch b, W. Lorenc b, S. Rowinski b

a Dept. of Mechanical Engineering, Wrocław University of Technology, Wrocław, Polandb Dept. of Civil Engineering, Wrocław University of Technology, Wrocław, Poland

a r t i c l e i n f o a b s t r a c t

Article history:Received 4 June 2010Received in revised form 17 March 2011Accepted 23 March 2011Available online 3 April 2011

Keywords:Composite dowelContinuous shear connectionFatigue cracksFE strength analysisFE fatigue analysis

1350-6307/$ - see front matter � 2011 Elsevier Ltddoi:10.1016/j.engfailanal.2011.03.016

⇑ Corresponding author.Tel.: +48 71 320 3860; faE-mail addresses: piotr.harnatkiewicz@pwr.wroc

Last year, extensive research was conducted on a modern type of continuous shear connec-tors – the composite dowel PreCo-Beam (2001) [1] and innovative composite constructionswere designed and built. As this shear connection is to be applied mainly for bridges, prob-lems concerning fatigue behavior arise Berthellemy et al. (2009) [2]. Complicated stressdistribution from external loads in steel dowels combined with different manufacturingtechnologies and resulting eigenstresses make the stress patterns in steel dowels verycomplex, and the problem of fatigue cracks even more complicated. This study presentsinvestigations undertaken after completion of the PreCo-Beam project [1], which is a partof research to be conducted years 2009–2011 at Wrocław University of Technology.

General information on an approach to estimating the fatigue resistance of compositedowels is presented, focusing on a description of stress analysis in steel dowels, and theimpact of the manufacturing method on fatigue lifespan. The background to a detailed fati-gue numerical analysis is presented, as are the initial results obtained from numerical sim-ulations. These are verified against the background of experimental tests results.

� 2011 Elsevier Ltd. All rights reserved.

1. Introduction

A modern type of continuous shear connection, the composite dowel, is an increasingly promising solution for compositebeams (Fig. 1). This innovative shear connection is implemented in a construction method where the connection betweenthe halved steel girder and concrete is provided by steel dowels manufactured using a special cutting line of the web of asteel section or plate. Different shapes of cutting line are possible. For the purposes of this paper, a puzzle shape (Fig. 1c)and clothoidal shape (Fig 1d) are presented-the first shape (PZ) was strongly investigated and tested, and so it is a good ref-erence for scientific investigations, and the second shape (CL), which was ultimately developed, was implemented for indus-trial production. Contrary to the standard solution using welded studs (Fig. 2a), an upper flange is not needed for completionof the composite girder (Fig. 2b), and it is thus possible to implement economic and robust prefabricated steel–concrete com-posite girders [3].

Composite dowels have developed rapidly over the last few years, especially in the course of the European PreCo-Beamresearch project [1]. Today, primary design rules are available [1,3] together with efficient manufacturing technology [2]. Themanufacture of steel dowels is fully automatic (Fig. 3), contrary to the typical solution employing welded studs (Fig. 4),where additional manpower is needed. Therefore, economically, composite dowels are a very attractive solution for bridgeengineering and being used increasingly often (Fig. 5), especially for spans constructed over railway lines (Fig. 5b and c)where rapid production of the superstructure is especially important.

. All rights reserved.

x: +48 71 320 3123..pl (P. Harnatkiewicz), wojciech.lorenc@pwr.wroc.pl (W. Lorenc).

Fig. 1. Composite dowel shear connection: (a) general scheme and terminology, (b) spatial location of steel dowels and reinforcement, (c) geometry ofclothoidal shape (CL), (d) geometry of puzzle shape (PZ).

Fig. 2. Shear connections used in bridges – steel part of section with steel connectors and sketch final composite section: (a) welded studs, (b) compositedowels.

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The important thing concerning structures under cyclic loads, like bridges, is that fatigue cracks can appear in the steelstructure, and these can lead to a sudden failure of the girder [4]. Such a situation has also been shown experimentally intests of composite dowel shear connections with the PZ shape [2]. This phenomenon is common in steel structures (andhence composite structures, regardless of the type of shear connection), but in composite beams constructed with compositedowels it is very specific, as is presented in [2]. Following up on conclusions reached in the PreCo-Beam project [1], the aimof this study was to improve investigations of fatigue behavior in the steel part; fatigue in the concrete part can be neglected.Research focused on crack initiation and crack propagation has been started, and is to be finished in the year 2011. The ap-proach taken to the problem, initial conclusions, and methodology used are presented in this paper.

Within the implemented PreCo-Beam project [1], the PZ shape was mainly analyzed [2]. This shape was tested in astrength materials laboratory, where cracked elements were obtained [1,2] and these provided the basis for the currentstudy as, according to predictions, the nature of the cracks was confirmed by a detailed metallographic analysis. Currently,the shape CL is being produced [2] which, after primary testing, shows much better fatigue characteristics. It is anticipated

Fig. 3. Technology of fabrication of steel dowels currently used in industry.

Fig. 4. Technology of fabrication of welded studs.

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that the nature of crack initiation and subsequent crack propagation should be universal for any reasonable shapes. Thecracks obtained in the PreCo-Beam project are valuable testing materials and a good technical reference for current studiesand the calibration of numerical tools.

The main goal of this publication is:

� to present a general approach to the problem of fatigue resistance of composite dowels,� to propose numerical tools and algorithms for calculation and methods of numerical modeling,� to calibrate numerical tools on the basis of existing results of fatigue tests with the PZ shape, and to conduct resistance

analysis and investigate fatigue durability,� to draw conclusions from the studies using the CL shape.

After that, detailed, extensive research on the CL shape finally developed can be conducted, as initial test results alreadyexist. This should contribute towards determining the fatigue durability of constructions with a composite dowel shear con-nection, and detailed design guidance for fatigue calculations will be provided. This will lead to more economical design, asthe rough fatigue models currently used are definitely on the safe side.

2. State-of-the-art

The classic headed studs (Figs. 2a and 4) are the form of shear connection being most often used. In classic beams withheaded stud connectors found in the compression zone of the cross section, cracks do not have a chance to propagate, and so

Fig. 5. Examples of structures implemented: (a) cross section of first railway bridge with composite dowels constructed in Poland in 2009, (b) prefabricatedcomposite girder of aforementioned railway bridge, (c) road viaduct in Austria (picture by SSF Ingenieure), (d) road viaduct in Poland.

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the appearance of cracking in this type of connector does not lead to damage of the construction. In a situation where crack-ing appears in a place where the flange is under tension, then the possible further propagation of the cracking does not threa-ten the construction because a crack, after achieving zero axis stress, will eventually stop in the compression zone of thecross section. Furthermore, the path of a crack is usually long and it is generally easy to discover any fatigue damage duringbridge area inspection.

For composite dowels, theory currently in favor is that in which the bearing of steel in a shear connection is determined(because of local yielding and fatigue of the materials) on the basis of the maximum reduced stresses for local yielding andthe main stresses for fatigue [12]. The superposition of stress at the toe of the steel dowel appears due to the appearance oflongitudinal shear in the connection (local action) and bending of the composite section (global action) [12]. This has beenconfirmed by testing [1], and it is assumed that fatigue cracks in a shear connection can be dangerous if the shear connectionis in a tensile cross section area, as they can lead to a failure of the bottom flange. Finding the critical point at the toe of thedowel is a complicated task, as is determining the stress distribution from global and local action, but an approach to this hasbeen finally established, and is presented [12]. It was developed using the assumption that shape is the only important factorand the factor of size can be eliminated from the investigation if the unit length of the connection is considered [12] – thisway, stress values next to the critical point at the toe of steel dowel depend on two shape coefficients, Ael and b, dependentonly on the shape of the dowel.

According to [12], the stress value rs of any type at the critical point at the toe of a steel dowel can be estimated using theformula:

rs ¼ rL þ rG ¼1

AelV � Sy

Iy � tw

� �þ b M � z

Iyþ N � 1

F

� �ð1Þ

where V, M and N denote the global transversal force, bending moment and normal force, respectively, in the compositebeam, Iy, Sy and F are the second moment of area of composite section, the moment of area of the steel part and the areaof composite section, respectively, and z and tw are the distance of the bottom line of the steel dowel from the neutral axisof the composite section and web thickness, respectively. The values of the coefficients depend on what type of stress is con-sidered (reduced stress, principal stress). Eq. (1) is a simple design formula [2] derived with appropriate approximation [12]from a more general approach describing the behavior of steel dowels [12]. This general approach is synthetically presentedin Fig. 6 for the criteria of yielding of the puzzle shape.

In Fig. 6 and Eq. (1), Ael is the shape coefficient concerning the local action, and b is the shape coefficient concerning theglobal action (notch factor) [5] and denotes vL for the longitudinal shear, rN for the nominal stress in the web from globalaction, tw for web thickness, and fy for the nominal yield stress of steel. The solution in Fig. 6 is calculated for positive values

Fig. 6. Design concept for yielding of steel dowels for the PZ shape, presented for the entire vL–rN space [12] (dashed line is a Mises ellipse for a regular steelplate under shear and axial stress).

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of coordinates, while the rest is only an estimate. If a detailed category concerning fatigue is assumed instead of the nominalyield stress of steel, the same approach can be implemented for studying fatigue. This way of considering fatigue and theprincipal stress coefficients for the PZ shape (Fig. 1c) is calculated using the finite element method [12]: Ael = 0.097 andb = 1.82. More information and data for the CL shape can be found in the final report of PreCo-Beam project [1].

In addition, according to [5] the detailed category for a gas-cut steel sheet is conservatively accepted as Drc = 125 MPa inagreement with PN-EN 1993-1-9. The values of the scope of modified stresses is determined on the basis of EC 1993-1-9, inagreement with the formula:

k � Drs 6 kc � 125=cMf ð2Þ

where: kc is the accumulated stress factor (determined thanks to FEM results) and k is the damage replacement factor (forbridges according to EN 1993-2).

The partial factor is selected depending on the accepted assessed method of measuring durability (the method of toler-ated damages or the method of unconditional lifespan of a construction) as well as on the consequences of damage. It is pro-posed in [1] that a connector may not be damage tolerant, with high consequences of failure, hence cMf = 1.35 which isdisputable but certainly safe.

The fundamental calculation of load history which is a complicated task for steel dowels subjected to both local and glo-bal action. A proposition by Barthellemy is given in [2]. One must pay attention to the spectrum of stress (it is usually nothomogeneous) and to the total, as stresses are calculated according to Palmgren-Miner. This can be easily accomplished forlaboratory tests and constant amplitude, but may become extremely complicated for realistic structures – a simple designmodel does not yet exist.

2.1. Numerical models

As part of [1], extensive parametric analyzes with the aid of the finite elements method in ABAQUS software were con-ducted. The problems of geometric non-linearity, including because of the contact between steel and concrete, as well as theproblems of the physical non-linearity of steel and concrete are presented in [6]. Based on those analyzes [1,6], it was deter-mined that for, the purposes of fatigue analysis, those models in which linear material models are adopted (excluding rein-forcing bars) will be sufficiently accurate, and the only source of non-linearity is the contact at the steel–concrete interface.The approach of small sliding formulation [8] describing the contact is sufficiently accurate for the purposes of fatigue anal-ysis, and means that the problem becomes linear in the context of a variable part of loading (double the amplitude of loadingresults in double the stresses, if the static part of the loading is ignored). It is essential to introduce cracks in the concrete atthe geometry stage [12]. The above assumptions were accepted for the purposes of this analysis.

2.2. Tests concerning fatigue cracks under cyclic loads

NPOT specimens and beam specimens with the PZ shape were tested under cyclic loads to obtain fatigue cracks [1]. GradeS460 steel and grade C70/85 concrete were used for the specimens tested. NPOT is a new type of composite specimen devel-oped in the course of PreCo-Beam to ensure propagation of fatigue cracks – the structure of this specimen is presented in[1,2]. Tests conducted proving the appearance of fatigue cracks and the phenomenon of crack propagation toward the lower

Fig. 7. NPOT specimen after tests [2]: (a) general view after cutting along concrete part, (b) fatigue crack in steel dowel.

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flange were presented in [2]. A detailed microscopic study of the crack of an NPOT specimen (Fig. 7) [2] was conducted in thecourse of PreCo-Beam project [1]. As fatigue cracks also appeared in beam specimens, the steel parts that failed because ofpropagating fatigue cracks during tests under cyclic loads are studied in detail within the current study (Fig. 8). One should

Fig. 8. Testing setup for C16SC beam [1]: (a) general view and load values, (b) geometry of the model and boundary conditions, (c) sketch of fatigue cracksin steel part, (d) photograph of fatigue cracks in steel part.

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note that the force level during testing was set high enough to produce fatigue cracks, and the beams were designed so as toenable crack propagation – the upper stress limit was close to the nominal yielding stress.

The first fatigue analyzes were done for the NPOT model by analyzing a fragmentary model in the form of a steel doweltogether with the contiguous web using Code Aster software [2]. Loads in the form of compressive stresses acting on thetooth were adapted by analyzing the contact stresses of the steel–concrete interface obtained from the FEM model madefor the entire composite element using ABAQUS software [12]. Details of the analysis are presented in [2]. The principalstresses (maximal tension) corresponding to the amplitude of variable loading in the course of the research (constant ampli-tude) calculated using Code Aster software amounted to 281 MPa, and corresponded with those determined in the ABAQUSsoftware [12]. The fatigue analysis performed made it possible to describe the durability (number of cycles to failure) at1.21 � 105 adapting the ‘‘signed von Mises’’ as a criterion, and at 1.76 � 105 adapting the principal stresses as the criterion,assuming the 125 MPa fatigue category. The crack obtained during the research corresponds in terms of its location with thepredictions of FEM [2], as does the number of cycles which led up to the appearance of the crack (3.50 � 105). Cracks in thebeams have not previously been analyzed in detail, and they are the subject of consideration in this report. The beam C16SCwas selected as being representative from among the two identical beams (C15SC and C156C) that have been tested [1]; bothbeams were tested 2 mln cycles with the same load conditions and failure mechanisms of steel dowels for both of them arethe same [1]. This way situation presented in Fig. 8 is to be representative. Beam C16SC was studied under cyclic loading ofconstant amplitude as per Fig. 8. After 2.09 � 106 cycles of loading with a frequency of 2.4 Hz, it was cut open, and it wasobserved that fatigue cracks had developed (Fig. 8d). It should be noted that the crack which appeared in model NPOT after3.50 � 105 cycles of loading led to the complete destruction of the structure after 1.30 � 106 cycles of loading, while in thebeams, the fatigue cracks which developed did not lead to the complete destruction of the structure after 2.00 � 106 cycles ofloading, and the values of stresses at the base of the tooth were very close in the NPOT specimen and in the beams, both inrelation to the constant and the cyclically variable part of the loading. The above note will be relevant in the context of futureanalyzes concerning the propagation of fatigue cracks in beams. Moreover, it should be emphasised that, after the NPOTelements were cut open, fragments of concrete tightly adhering to the front surfaces of the steel teeth were observed, whichallows for the conclusion that the concrete was not destroyed during the fatigue testing. Likewise, the arrangement ofstresses in the steel dowel did not change significantly with the increasing number of cycles during testing at constantamplitude.

2.3. Eigenstresses

As a result of modification of eigenstresses after a hot rolled beam is longitudinally cut, two T-beams are obtained, whosedeformations are usually similar to the required structure pre-cambering, but very often need to be additionally straight-ened. Hence, the problem of eigenstresses caused by beam cutting and straightening appears, as does the issue of modelingthis phenomenon by FEM techniques. Cutting the beam into two parts causes the redistribution of eigenstresses. This prob-lem is very complex, and initial results of the study were presented in [7]. This problem is beyond the scope of the currentstudy and will be introduced later on.

3. Fabrication of steel dowels

The PZ shape came from cutting a web with a shape that consists of cut circles having the same radii, as well asstraight lines. This way, after having cut the web of the rolled I-beam, two T-sections are created without web materialloss. The CL shape arises from cutting the web with such a shape that consists of clothoids and straight lines – this way,after cutting the web of the rolled I-beam, two T-sections are created, and the web refuse is regained from the cut, aspresented in Fig. 3.

The fatigue durability of steel connectors depends on the shape of the cut (PZ, CL) as well as the method of cutting. A cur-rent, widely-used production method is the gas cut method, mostly because of its cost. However, this method reduces thefatigue durability of the metal connectors. During cutting, as a result of burning oxygen and acetylene, a lot of heat energy issupplied to the element, which disrupts the crystallographic structure in the material in the area of the cut. Additionally, thesurface of the cut contains a lot of grooves, which constitute areas of concentrated stress. It is suggested that uneven surfacesand sharp edges be removed by machining and that they then be subjected to a process such as shot peening. A better

Fig. 9. CL-type beams.

Fig. 10. CL type gas-cutting of a steel connector for beams with reduced height of web: (a) cutting process, (b) resulting geometry, (c) twice-heated area dueto repeated flame re-lighting.

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technology for cutting steel connectors may turn out to be plasma cutting. The surface of the cut will be smoother than thatmade by gas cutting, and the heat affecting zone would seem to be better if this technology is used. Plasma cutting technol-ogy is starting to be used more often by prefabrication plants, despite the higher production costs involved. For the needs offatigue testing at Wrocław University of Technology, the beams with CL-shaped dowels were produced from an IPE 500beam from S355 J2 steel (Fig. 9).

During cutting (Fig. 10), situations unsafe for fatigue load arose, in which the cutting burner lost its flame. This wascaused by technical conditions of the device as well as the ready-state of the cut element. It should be emphasized thatin those parts where the burner had to be re-lit, the location of the cut was heated again (Fig. 10c). This is an unsafe situation,because such an occurrence in the geometric notches (stress concentration) would reduce the fatigue durability of the steelconnector. Unfortunately, such situations can happen randomly and are not dependent on the production plant. Thus, whenthese steel parts are mass-produced, the problem is essentially impossible to control.

The plasma cutting method is safer for construction because it offers better cutting surface quality and eliminates theunevenness (grooves) that is typical of gas cutting. So far, the impact of technology on fatigue durability has not been tested,but a simple visual comparison of the surfaces of both cutting technologies is possible (Fig. 11a,b).

To summarize: fatigue durability is affected not only by the shape of the cut itself, but also by factors associated with thetechnology of producing the construction, such as:

Fig. 11. Different technologies of fabrication of CL shape: (a) plasma cut, (b) gas cut.

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� the characteristics of the material after cutting,� the state of the cut surface and number of flaws (cutting technology, speed of cutting, amount of energy supplied),� the characteristics of the residual stresses resulting from cutting,

4. FE-analysis

The numerical models M1 and M2 which were used in the analysis were constructed independently by two researchteams representing, respectively, the Department of Civil Engineering (M1) and the Department of Mechanical Engineering(M2), of the Wrocław University of Technology. The M1 model was built by adapting the Lorenc [12] model constructed forthe purposes of analyzing beams under constant cyclic loading within the PreCo-beam [1]. The M2 model was constructedfor purposes of this study and directed to durability analysis. Both models refer to the fatigue studies of beam C16SC by [1](Fig. 8) and have the same geometry and material properties. The construction of two models by independent teams consid-erably limits the possibility of random errors being made, and enables the control of results already in the modeling stage. Inboth cases, an ABAQUS software application was utilized, and the symmetry of the model was exploited in two planes. Ulti-mately, for advanced fatigue analyzes, the M2 model was used. The values of the Youngs’s modulus and Poisson’s ratio ap-plied in the models are 210 GPa and 0.30 for steel, and 38.5 GPa and 0.167 for concrete, respectively. The crack patternapplied in the geometry [12] was according to that recorded during tests for upper load level (Pmax at Fig. 8). The assumedfriction coefficient was 0.30 [6].

When analyzing the results from the M1 model (Fig. 12), the results of the FEM calculations in the Code Aster [2] softwarewere referred to, which were carried out for the purposes of analyzing the NPOT specimen [1]. This was the first fatigue spec-imen, during which the propagating fatigue cracks were obtained for a composite dowel shear connection. The states ofstresses at the base of dowel No. 4 of beam C16CS (Fig. 12) and at the base of the dowel in the NPOT model [2] as wellas the maximum values of stresses are very similar (264 MPa for the most stressed dowel of the beam, and 281 MPa forthe dowel in the NPOT specimen), with the difference in the values of stresses amounting to only 6%. The classic approachin accordance with EN-1993-1-9 and presented in Section 2 used in the design of steel structures with regard to fatiguestresses refers to the amplitude of principal stresses. Applying this simple criterion, as was done for the NPOT model [2],the durability was determined according to (3) as the number of loading cycles N = 1.21 � 105, assuming a 125 MPa fatiguecategory for the edge and Dr1 = 264 MPa as the amplitude of the principal stress:

Fig. 12.elemenprincip

N ¼ Exp Ln 2� 106� �

� 3 � LnDr1

125

� �� �: ð3Þ

The method of discretization of the steel part and the values obtained in the NPOT model according to [2] (Code Aster)and the NPOT model according to [12] (ABAQUS) are convergent, which is presented in [2]. It is similar in the case of com-paring the M1 beam model and the NPOT model according to [12]. All three models are therefore convergent and reliable inthe context of the results obtained, and have been confirmed experimentally. Until now, the fragmentary model of the NPOTelement (Code Aster) was used in fatigue analysis [2], and the durability set in Code Aster software on the basis of the‘‘signed von Mises’’ criterion (N = 1.21 � 105) [2] is about 31% less than that determined on the basis of principal stresses

FE model M1 of composite dowels: (a) geometry of the model of the entire composite beam, (b) net of finite elements, (c) narrowness of net of finitets in critical regions, (d) geometry of steel part, (e) geometry of concrete part, (f) principal stress layout for entire model – maximal tension, (g)al stress layout in steel dowel – maximal tension.

Fig. 14. Discrete model M2 (support is located at right).

Fig. 13. Geometry and boundary conditions of the beam being modelled.

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(N = 1.76�105) [2], in accordance with Eq. (3) – by analyzing the NPOT specimen and assuming the largest value of principalstresses Dr1 = 281 MPa in Eq. (3). The same conclusion can thus be applied to the M1 beam model, and so the durabilitydetermined assuming the ‘‘signed von Mises’’ criterion will be about 31% smaller, i.e., N = 0.69 � 2.12 � 105 = 1.46 � 105

in the case of dowel No. 4 of the C16CS beam. The calculated values are convergent with the results of the studies, duringwhich very clearly developed cracks in the web [1] were observed after 2.09 � 106 cycles of loading. Similarly, convergencewas obtained for the NPOT model, as already presented in [2]. Against the background of experimental research of the classicapproach used in the design of steel structures with regard to fatigue according to EN-1993-1-9, analysis of the states ofstresses with the aid of FEM in ABAQUS software and fatigue analysis with the aid of FEM in Code Aster software, the M1model was assumed to be correct and reliable in the context of analyzing the stresses, with the ‘‘signed von Mises’’ takenas the correct criterion in defining the fatigue durability of a connection of the composite dowels type.

Following the assumptions for the M1 model of the same geometry (Fig. 12), the same material properties and boundaryconditions are used for the M2 model, but different meshing techniques and finite element sizes and types are used; ele-ments with full and reduced integration elements are applied in the model.

Due to the appearance of double symmetry in the shear connection, a 1/4-model was prepared. The values of force Pmin

and Pmax (Fig. 8) were applied to the M2 model, contrary to the DP used in the M1 model – this is because durability analysisis to be carried out after calculation of the stresses. Hence, the force value for the 1/4-model is 0.25 P.

In the next step, meshing of the shear connection was carried out by covering the finite elements with a net. Size of ele-ments in critical regions is about 1.5 mm. Taking advantage of the double symmetry of the analyzed construction allowed fora more dense net on the finite elements, which significantly influenced the accuracy and the duration of calculations.

The discrete model of the entire structure consisted of 74318 C3D6, C3D8R and C3D4 type elements [8] as shown inFig. 14. The boundary conditions were done in the way that is closest to its fastening to a hydraulic press (Fig. 13) on whichstatic and cyclic testing had been previously performed [1].

The shear connection was supported in a way approximating realistic conditions, in which the steel connector in themodel is an integral part of the steel cross section, participates in distributing the internal forces from global load effects(both bending moment in the beam), and is an element that assured the transfer of the longitudinal shear between steeland concrete. To allow consideration of the contact conditions for the spatial deformation description, it is necessary to ac-cept the contact bonds for additional unknowns which are Fourier factors. This made the analysis very complicated [8] in the‘‘post-processing’’ model and numerical fatigue analysis. The definition of the contact problem is one of the key elements ofthe mechanical system of a shear connection beam. In the numerical beam model, the contact between the surface of thetooth and the structure of the concrete around it is taken into consideration. The contact ‘‘master slave’’ type algorithms uti-lized in the FEM calculations are not treated equally [8]. In performing the numerical calculations, one of them fulfills therole of the master–superior in relation to the other, which is yielding. Due to the similar density of the netting of the finiteelements, selection of the superior surface was determined by adapting the netting on those surfaces. This was a conse-quence of wanting to achieve better results. Ultimately, for the superior surface, a toothed surface was chosen as the contactsurface. The friction factor is a characteristic value for two contact surfaces, but it is not a stable characteristic. This can be

P. Harnatkiewicz et al. / Engineering Failure Analysis 18 (2011) 1279–1294 1289

dependent on the speed of skidding, the value of normal stress, and also the temperature. The value of this factor can also bedependent on the actual finish of the surface contact. As a result of a lack of adequate experimental data, the value was trea-ted as stable, since this provided a close enough value.

The numerical analysis of composite beams was made in the code ABAQUS [8]. To solve non-linear balance equation sys-tems, the ABAQUS code takes advantage of the iterative – incremental Newton–Raphson method and carries out the integra-tion using the central difference method according to the proposed scheme by Hughes and Winget [8]. One should rememberthat, when examining the issue of contact for the balance equation system for the shear connection analyzed, the kinematicand static border conditions were supplemented with additional limitations, the so-called Hertz–Signorir–Moureau condi-tions which resulted from using a contact bond [8].

In the construction analyzed, these limitations were implemented by utilizing the fine function, based on the addition ofpotential energy into the functional of the additional part with the fine factor. This part is responsible for the resilient energybrought out by the force, and which results from the cast limitations of a certain value of the above factor. The physical inter-pretation of the fine factor is introducing additional stiffness in the system in the direction of a restricted degree of freedom.The formulation of the contact issue in the form of the fine function does not introduce additional unknowns to the analyzedequation, which makes it possible to obtain the desired outcome.

The steel beam was made of steel S460 M. The material S460 M is indicated in the EN-10025-4/2004 Standard and the EN10 113 (1993-04-000) Standard as – 1.8827/S460 M. A model of the material according to the standard is presented in theTable 1.

The standard values of fatigue strength presented in the table above were utilized in numerical fatigue calculations. Thedata from the axial tensile specimen presented in Fig. 15 confirm that the stresses in the material did not exceed its actualyield during fatigue testing.

Table 1Material properties for S460 in MPa according to EN 10113.

Material Material number Rm (MPa) Re (MPa) rW,zd,N (MPa) rSch,zd,N (MPa) rW,b,N (MPa) sW,s,N (MPa) sW,t,N (MPa)

S460 M 1.8827 530 460 240 220 265 140 155

where Rm, tensile strength; Re, yield strength; rW,zd,N, material fatigue limit for tension- compression stress; rSch,zd,N, material fatigue limit for zero-tensionstress; rW,b,N, material fatigue limit for completely reversed normal stress for bending; sW,s,N, material fatigue limit for completely reversed shear stress; andsW,t,N, material fatigue limit for completely reversed shear stress for torsion.

Fig. 15. Results of tensional tests for steel S460M cut out from the beam web.

Fig. 16. Reduced (Mises) stress in the entire steel part of the M2 model.

Fig. 17. Reduced (Mises) stress in steel dowels of the M2 model.

Fig. 18. First principal (maximal tension) stress in steel dowels of the M2 model.

Fig. 19. Third principal (maximal compression) stress in steel dowels of the M2 model.

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On the basis of the calculations performed using the finite elements method, a spatial field stress in the tested construc-tion was achieved. This is presented for the steel part in Figs. 16–19 for upper load level Pmax. The stress state in the concretepart is beyond the scope of this study; it was extensively dealt with in [6,12] for ultimate static load conditions.

5. Durability analysis

On the basis of the numerical calculations carried out, experimental testing was primarily confirmed, pointing to the lim-ited fatigue resistance of a shear connection for assigned load conditions. A fatigue numerical analysis was made using theFALANCS code [9] and a Virtual Lab-Durability environment [10]. During the numerical analysis, attention was focused ontesting the behavior of the steel connector of a shear connection, given that its durability limits the life of the shear connec-tion. One of the more important steps was preparing the model for numerical fatigue analysis, because it was necessary toimport the calculation model from ABAQUS without losing information on the stress state of the connector resulting fromthe interaction between the concrete and steel where they are in contact. Fig. 20 shows a fatigue calculating algorithm basedon FEM results, which was used in the later parts of this article.

To outline the fatigue durability of the steel connector, a Jiang-a multi-axial material model was used [9]. Using this mate-rial model is a consequence of relying on the calculations of stress criteria of the critical plane. This criterion was used be-cause of the appearance of a multi-axial stress state in the shear connection and its effectiveness in this type of multi-axialintensive state of the construction [11].

For numerical investigations, this is implemented in the model by means of material a characteristic. In general, the ref-erence value of fatigue strength at 2 � 106 cycles is assumed to be 120 MPa [5] for a gas-cut edge for steel dowels at thisstage.

The material model used for FE fatigue analysis was defined on the basis of SN curve data for steel S460 M (Fig. 21), usingNE (number of cycles at endurance limit), SE (Load amplitude value at endurance limit), N1 (Number of cycles at the inter-mediate point), S1 (Load amplitude at the intermediate point-k1), k1 (inverse slope of the lower segment), k2 (inverse slopeof the upper segment) and Smax (tensile strength).

Fig. 20. Data flow in the stress-life approach used.

Fig. 21. Representation of the SN curve.

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Although the SN curve is often graphed with elastic stress amplitude on the vertical axis, other measures of load could beused, such as bending moment or force amplitude. In addition to the SN curves as described above (Wöhler type), forS460 Msteel the following material parameters were used: SE = 80 MPa, NE = 1 � 106, S1 = 80 MPa, k1 = 5, k2 = 5.

In the calculations, Goodman corrections were used. For calculations with the Goodman correction, the mean stress andamplitude are plotted on the correction diagram, and the point is resolved back to the vertical axis to determine the equiv-alent stress amplitude. This is an important factor, as the mean stress values are high at the critical points of steel dowels.TheFE fatigue analysis was performed for the full 3D critical plane (normal).

In summary, the numerical fatigue analysis was carried out in the following ways:

� Number of Critical Planes – 18.� Number of In-Plane Directions for 3D Critical Plane – 9.� Number of Out-Of-Plane Directions for 3D Critical Plane – 9.� Fatigue Parameter – full 3D critical plane normal, Goodman correction.

Fig. 22. Damage location (discontinuous) in the third steel dowel of the M2 model.

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In Figs. 22 and 23, the damage fatigue layout for one cycle is presented. The figures present the following:

� Damage location.� Fatigue damage.

The durability obtained from the numerical calculations is significantly lower than that determined by the methodsclassically applied in construction, e.g., (3), which is consistent with expectations. The fatigue calculations carried outillustrate the usefulness of the latest algorithms and approaches applied in mechanics in the fatigue analysis of a new typeof shear connection; an interpretation of results in both the qualitative and quantitative senses is possible. Based on theanalysis carried out, a methodology for proceeding with the fatigue analysis of a composite dowel type connection was pro-posed and attention was then paid to the principal problems to be solved.

Fig. 23. Fatigue damage in the third steel dowel of the M2 model.

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6. Conclusions

In this paper, the latest research work on the fatigue resistance of composite dowel shear connections were presented.The assumptions, research methods and initial results of FEA were shown. Special attention was paid to methods of proto-typing a virtual analysis and numerical methods of estimating fatigue lifespan, which are part of the project 2502/B/T02/2009/37 (a national project funded by the Polish government), which is being conducted in cooperation between two depart-ments of Wroclaw University of Technology – the Civil Engineering Department and the Mechanical Engineering Depart-ment. The conducted work will bring researchers closer to a solution of the problem of the fatigue resistance of shearconnections with composite dowels. The detailed conclusions are:

(1) FEM analysis has shown that the stress level of the PZ-shaped elements during the research with [1] was highenough for the possibility of low-cycle fatigue of those elements what resulted in propagating fatigue cracks.Because the exterior loads during the research were assumed to be on a reasonable level in terms of the longitudinalshear forces per unit length and the bending moment in the composite cross section, it can be stated that the PZshape is unsuitable in construction applications because its fatigue durability is too low. Increasing the thicknessof the web could result in the outcome becoming uneconomical. Because the CL shape exhibits significantly betterfatigue parameters than the PZ shape [2], and because the technology of its fabrication has already been masteredindustrially, ultimately, in further analyzes the focus was only on the CL shape, while the PZ shape was only treatedas a valuable academic case, since numerous studies and theoretical analyzes have been carried out on the PZ shape,but not yet on the CL shape.

(2) Current knowledge allows us to confirm that, in the case of loads leading to high-cycle fatigue, i.e., those which arerelatively small in relation to the limiting load capacity of the connection, no meaningful change in the state of stressesin the steel dowels will occur with an increase in the number of cycles, and therefore it will be possible to apply classicdesign algorithms based on the accumulation of damages and the Palmgren–Miner summation.

(3) A hypothesis arises: fatigue durability, understood to be a crack of small depth, i.e., such that there exists no redis-tribution of forces between the steel dowels, will occur only from the state of stresses in the dowel’s critical regionand the state of the cut in the surface of the steel sheet – therefore, the problem will be reduced to the precisedefining of the state of stresses and the defining of the fatigue durability of a standard tensioned specimen fabri-cated from currently produced steels and cut with the aid of the technologies used in the manufacture of steel dow-els. Such research is currently being conducted. Because it is predicted that one defined shape (CL) will be used andthe size of the dowels in not a factor here [12], after carrying out advanced analyzes with the methods presented inthis paper and confirming these with the aid of experimental studies, it will be possible to provide a very simpledesign criterion. Research into beams with the CL shape is currently being conducted. The propagation of crackin the bending element is a much more complex problem, and at the same time an important one. The speed ofpropagation of crack depends on the state of stresses, which in turn changes through the redistribution of forcesbetween the dowels as a result of the propagating crack. According to the authors, the fundamental factor respon-sible for the speed of propagation of a significantly developed crack will be the state of normal stresses in the web,which is the effect of the bending of the composite cross section. It can be stated in this context that the largeststresses on the edge of the dowel are responsible for the initiation of the crack, and are the effect of the superpo-sitioning of the local and global effects, while in principle the global effects determine the speed of propagation.Appropriate analyzes relating to the propagation of scratches are currently being conducted. It is necessary to definethe criterion of fatigue for the steel dowel – currently, cracks of ‘‘small’’ depth are being analyzed (in the case of theaxially tensioned specimens, this constitutes a breaking up of the specimen). Rejecting the criterion in the form ofthe breaking up of the bottom flange as possible for consideration in the study stage only, it is proposed that thecriterion be in the form of a defined length of cracks. This criterion should result from either a quantitative condi-tion of the redistribution of force between the dowels as a result of the propagating crack, or should be definedbecause of the possibility of following the progress of crack during inspections periods of structures (e.g. every5 years) – in that case, the minimum length of a crack cannot be smaller than the height of the concrete coveredregion of the steel web as measured from the bottom of the concrete slab to the base of the dowels (typically circa60 mm).

(4) The fatigue study of the CL-shaped beams subjected to the same loading as the PZ-shaped beams (Fig. 9) has beencompleted. After two million cycles, no fatigue cracks were observed, which even at this stage allows the conclusionto be drawn that the fatigue durability of the CL shape is superior. Moreover, one of the beams studied was subjectedto variable loadings double in size in order to induce low-cycle fatigue and then to investigate the propagation ofcracks. Propagating cracks were produced. An analysis of the two extreme cases with the aid of the methods presentedin this article, and the fatigue study of tensioned steel specimens cut out using different techniques (oxy-cutting,plasma-cutting, water-cutting) will allow definite conclusions to be reached on the fatigue durability of the CL shapecurrently being used in structures. Since currently, for the purposes of designing CL shapes, assumptions favoringsafety are being used, the above conclusions will lead a reduction in the costs of structures and to their rational designand implementation.

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(5) It is questionable whether a connector may be damage-tolerant with serious consequences of failure, according to [1].Under certain circumstances, considering those conditions which have an impact on the possibility of crack propaga-tion, this strong criterion could be relaxed. It is an important issue if fatigue governs the resistance of shear connec-tion. As the partial factor cMf differs from 1.00 to 1.35 the possible economical benefits are evident.

(6) For a detailed and reliable fatigue design of the CL shape, the entire loop according to Fig. 6 must first be established.This is done by FE calculations supported by beam tests with a large number of strain gauges at the steel dowels –these tests have recently been completed, and the results will soon be presented.

Since tests of beams with the clothoidal shape have already been completed, it is planned that a clear method of evalu-ating the fatigue resistance of the connections as well as the values of partial factors for estimating fatigue resistance accord-ing to EN 1993-1-9 will be available soon. These will be published in a separate paper, together with the results of tests andnumerical calculations for the clothoidal shape.

Acknowledgements

The research presented herein is undertaken on the basis of the results and conclusions obtained during the Preco-beaminternational research project financed by the European Commision (RFCS), and so the authors, representing the Dept. of Ci-vil Engineering of Wrocław University of Technology, would like to express their appreciation for the work of all partnersinvolved in PreCo-Beam [1] established as the state of the art and a starting point for current research; especially, the inputof Jacques Barthellemy from SETRA on fatigue is of great importance for current research. We also acknowledge our coop-eration with Guenter Seidl from SSF Ingenieure, conducting research on the fatigue behavior of composite dowels in thespring of 2010 in Germany together with Martin Mensinger from TU Muenchen.

This work has been carried out as part of MNiSW National Project No. 2502/B/T02/2009/37. The financial support of theMNiSW of the Polish government is gratefully acknowledged and also scholarship START from Polish Foundation of Science.

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