Engineering Failure Analysis 29 (2013) 167–179

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Engineering Failure Analysis

journal homepage: www.elsevier .com/locate /engfai lanal

A new approach to enhancement of fatigue life of rail-end-boltholes

1350-6307/$ - see front matter � 2012 Elsevier Ltd. All rights reserved.http://dx.doi.org/10.1016/j.engfailanal.2012.12.001

⇑ Corresponding author.E-mail address: duncheva@tugab.bg (G.V. Duncheva).

Galya V. Duncheva a,⇑, Jordan T. Maximov b

a Department of Machine Elements, Technical University of Gabrovo, 5300 Gabrovo, Bulgariab Maksimov Konsult AD, 5300 Gabrovo, Bulgaria

a r t i c l e i n f o

Article history:Received 21 September 2012Received in revised form 19 November 2012Accepted 3 December 2012Available online 27 December 2012

Keywords:Cold workingFatigue failureFinite element analysisRailway engineeringResidual stress

a b s t r a c t

The object of this paper is bolted joint railroads as the accent is put on the material behav-iour around the bolted holes. The fatigue failure around rail-end-bolt holes is particularlydangerous, since it leads to derailment of trains and consequently, to inevitable accidents.Moreover, the cracking at rail-ends, which starts from bolt hole surface, causes prematurerails replacement. It is well-known that the presence of residual compressive hoop stressesaround the bolted holes closes the existing first mode cracks and impedes the formation ofnew ones and thereby extends the fatigue life of the holed components. In this article anew approach to enhancement of fatigue life of rail-end-bolt holes has been developedon the basis of a novel method and tool for cold expansion (CE) of holes, patented by theauthors. The major advantage of the method is in imparting around the holes of beneficialresidual compressive hoop stresses which are symmetric toward the middle longitudinalplane of the rail and thus the axial stress gradient is minimum. The developed approachconsists in setting and solving a multi-objective optimization task of the CE of the rail-end-bolt holes. Because of the specificity of the studied problem, the optimal solutionhas been found by finite element (FE) simulations. For that purpose generalized FE modelof the object has been developed. Through this model the critical point around the outsideholes has been localized and the cycle of variation of hoop stresses has been determinedtaking into consideration assembly stresses. On the basis of adapting the generalized FEmodel of the rail joint to simulating the CE process, a comparison between the cases withand without CE of rail-end-bolt holes has been made. On this basis the optimal degree of CEand the successive hole treatment have been found. After simulating the CE process by thedetermined optimal degree of CE, the beneficial effect of implementing the new approachhas been proved.

� 2012 Elsevier Ltd. All rights reserved.

1. Introduction

Railway transport is acquiring greater significance in the development of modern transport. This tendency is a direct con-sequence from the energy and environmental crises. In this aspect research directed to higher safety, long life and economyof components composing railways, is becoming more and more topical.

Building of high-speed railway lines is related to the so-called continuously welded rails. However, bolted joint railwayscannot be done away with by 100% – in broken country and curvilinear railroad tracks they have no alternative. There are alarge number of bolted rail joints in heavy lines and mountainous lines. In Bulgaria, for instance, bolted joint railroads are

168 G.V. Duncheva, J.T. Maximov / Engineering Failure Analysis 29 (2013) 167–179

64.4% of the railway network and their overall extended length is 4760 km [1]. Two joint bars or fishplates and four bolts areused to connect the ends of adjoining rails. When the remaining conditions are the same, reliability, service life as well asmaintenance and repair activities depend on the state of components composing rail joints: rail ends, joint bars and bolt con-nections (Fig. 1).

The elements in a rail joint are subjected to cyclic and impact loads as a result of passing of trains [2,3]. The cyclic impactload is particularly dangerous owing to the difference in levels of the joined rail ends. This difference is a direct effect of thesagging of the rail when a wagon wheel is on its end. At the same time it is necessary to analyze the change in operatingstresses, taking into account the assembly stresses resulting from bolt pretension.

The dynamic character of loads causes fatigue in material in rail joint elements and respectively provokes originating andgrowth of fatigue cracks. In this aspect the zones around bolt holes are potentially dangerous as natural stress raisers. Amode of failure in bolted joints is fatigue crack initiation and growth from the bolt holes in the end rail (Fig. 2). The fatiguefailure around rail-end-bolt holes is particularly dangerous since it leads to derailment of trains and consequently to inev-itable accidents. At the same time, the cyclic bending and contact stresses due to passing of wheels cause different defects inrail heads, at their very ends. As a result surface or internal cracks, breaking out or plastic deformation occur. Damages orbreaking of rail joints to a great extent are due to the cyclic character of bending stresses acting vertically and sideways[3]. And whereas the exploitation of railroads can continue when flaws appear in the rail heads, the breaking of rail endsdirectly jeopardizes the safety of this sort of transport. Therefore, the fatigue failure around bolted holes is of limiting impor-tance to the safety of railway transport, service life and maintenance and repair activities of bolted joint railroads.

It is well-known that the fatigue life of structural holed components, subjected to cyclic load, can be increased by gen-erating compressive normal stresses around the holes. These beneficial residual compressive stresses significantly reducethe maximum values of the operating tensile stresses arising at the critical points of the components and thus impedethe formation of first mode cracks. A common approach to impart beneficial residual stresses around a hole is coldworking

Fig. 1. Bolted rail joint components.

Fig. 2. Typical cracks originating at rail-end-bolt hole.

G.V. Duncheva, J.T. Maximov / Engineering Failure Analysis 29 (2013) 167–179 169

process having temperature lower than the recrystalization temperature of the respective metal. There are two groups ofmethods to realize this approach. The first group includes burnishing technologies (ball and roller burnishing, deep rolling),shot peening, etc. A common disadvantage of these methods is relatively shallow zones of residual stresses imparted aroundthe apertures. The second group imparts beneficial residual stresses in significant depth and can be divided into two sub-groups: tool impact on the front surfaces of the plate; tool impact on the hole surface. The following methods correspondwith the first subgroup: ring groove coining [4], pad coining [5] (entitled ‘‘stress coining’’ by the inventor), ‘‘improving fati-gue life of holes’’ [6], stress wave [7]. The second subgroup includes: ball or solid mandrel coldworking [8], pre-stressing offastener holes by tapered pin and tapered sleeve [9], split sleeve cold expansion [10], cold working by seamless tubularmember [11], split mandrel coldworking [12], cold work of holes by rotational mandrel and tubular seamless sleeve madeof shape memory alloy [13], etc.

It is well known that coldworking of holes is in the basis of prevention of originating and growth of fatigue cracks aroundrail-end-bolt holes. Implementing this approach, the FTI company has developed RailTec system, based on split sleeve coldexpansion (CE) method and especially adapted to rail-end-bolt holes [14]. The essence of this approach is in generating afield of residual compressive stresses around the hole, due to pulling a tool with a diameter greater than the diameter ofthe preliminary drilled hole. After ceasing the action of the tool on the hole, the plastically deformed layer of metal aroundthe hole appears to be pressed at the expense of the reversible deformations of the elastically deformed layers around it. Thecreated residual compressive field closes the existing cracks like a bracket and impedes the formation and growth of newones. Since the cracks around the bolted holes originate mainly from the hole periphery (first mode cracks), hoop normalstresses are of practical importance. The beneficial effect is in enhancement of fatigue life by 3–10 times and significant sav-ings from reduced supervision of railroads, current maintenance and rail replacement costs [14].

Although this type of pre-stressing of rail-end bolt holes has been of great advantage over recent years, it bears the dis-advantages inherent in the mandrel coldworking and split sleeve CE methods: significant and nonsymmetric with respect tothe middle plane of the rail gradient of the residual hoop (circumferential) stresses due to axial force flow passing throughthe rail; considerable surface upset; non-symmetric expansion in circumferential direction; a need for throw away (dispos-able one-time use) pre-lubricated split sleeve.

In publications on rail joints, research on the state of rail heads dominates, employing the FE approach [2,15,16]. To studythe growth of fatigue cracks around bolted holes, an analytical and experimental approach was applied [17], as well as the FEapproach [18,19]. In these studies it was accentuated on fracture mechanics of rail ends, instigated by growth of fatiguecracks around untreated bolted holes.

It is well-known that the non-uniform residual stress distribution through the plate thickness, produced by mandrel cold-working methods, reduces the beneficial effect from these stresses on the fatigue life of the corresponding holed component.To overcome this problem, a novel method and tool have been developed and presented in the article. The present study isdirected to optimization of CE process of bolted holes in rails of 60 EN 13674-1:2011 type, carried out by novel patentedmethod and tool according to BG Patent No. 66052 [20]. According to the invention the process is carried out by input axialaction applied to a pin with a conical working part. As a result, simultaneous displacement in radial direction of the workingparts of the tool of ‘sector’ type is provoked. The latter act on the hole surface performing CE process, similar to the process ofmere radial expansion. Thus an axial force flow does not pass through the plate (the passage of such force flow is typical of allmandrel coldworking methods, including split sleeve cold expansion and split mandrel coldworking). As a result, the zone ofresidual hoop normal stresses formed around the hole, is symmetric as regards the middle plane and has a minimum axialgradient. Besides that the surface upset is very slightly pronounced.

Due to rail end geometry, holes at the ends should not be considered as closely positioned i.e. residual stress zone aroundthe first treated hole will alter initial conditions before CE of the second hole. Therefore, for rails of specific geometry andmaterial, besides depending on the degree of cold expansion (DCE), determined by circumferential linear deformation et;0

at a point of the hole surface in percentage, the residual stress distribution around the holes will also depend on the sequenceof treating the holes. On the other hand, owing to rail specific geometry, residual stress zones generated around the holes,will be characterized by certain inhomogeneity. Therefore, it is necessary to optimize the parameters of CE process of rail-end-bolt holes. A process will be optimal if it ensures relatively most intensive and homogeneous zones around both holescombined with comparatively low energy consumption.

Taking into account the listed considerations, the major objective of this study is to develop an approach to enhancementof fatigue life of rail-end-bolt holes, determining the parameters of CE process, carried out using a novel patented methodand tool, to provide maximum intensive and homogeneous zones of residual compressive hoop stresses under the conditionsof minimum DCE, respectively, minimum expenses and time for its realization.

The following major problems have been solved to attain the objective:

� Determining the variation cycle of operating stresses taking into account mounting stresses resulting from tightening thebolts;� Optimization of the novel CE process of rail-end-bolt holes by determining DCE and the sequence of hole treatment;� Evaluation of beneficial effects of CE of bolted holes on the basis of comparison between both cases: with or without CE.

The finite element (FE) approach has been applied due to the specifics of the matter being studied to solve the above-listed problems.

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2. Determining the cycle of operating stresses taking into consideration assembly stresses

This study is directed to:

� Localization of the endangered zone around rail-end-bolt holes;� Determining the maximum mounting stress and the stress caused by passing wheels taking into account dynamic-

response factor taken from other scientific publications [4];� Determining the variation cycle of hoop normal stress at the endangered point.

2.1. Generalized FE model of rail joint

2.1.1. General characterizationABAQUS FE package is used [21]. Generalized FE model of rail joint is shown in Fig. 3.The geometry of the rail joint components is subjected to the assumption that the system being analyzed is symmetrically

loaded with respect to the longitudinal plane of the rails. The rails that have been modeled are in accordance with [22]. Therail ends at the joint are 350 mm long and they have been modeled by means of solid 3D FEs. The rail ends length is chosen ina way to eliminate the boundary effect’ influence on the stress distribution around the inside bolted hole. The FE model con-sists of: rail ends – 15441 linear hexahedral elements type C3D8R; joint bar – 18052 linear tetrahedral elements type C3D4;wheel – 10347 tetrahedral elements type C3D4; bolted connections – 4512 hexahedral elements type C3D8R. The extensionsof rail ends are 12:5 m long each and are modeled as beam 3D FEs – 80 line elements of B32 type. This approach allows moreaccurate simulation of the studied problem without unnecessary aggravation of the calculating procedure. To this end, dis-placements of the final 3D sections of rail ends were needed, identical to those of the respective contact node of beam FEs,and constraints of ‘‘coupling’’ type were imposed. The ends of the two rails were mounted with an 8 mm gap [2]. This gaplength is conformed to the mean value of dispersion of the assembly gap.

2.1.2. Constitutive modelsIn fact, the rails material is elastic–plastic, and the constitutive models of rail head and of the remaining part (web and

foot) of them are different in the general case. The stress–strain curve for the zone around the holes (web of the rail) has beenobtained at Metal Testing Laboratory at the Technical University of Gabrovo (Fig. 4). To this effect, from the web of the re-placed rail a sample is cut, from which a round test specimen for uniaxial tensile test is made. The stress measure in ABAQUSv. 6.5-1 is Cauchy or ‘‘true’’ stress, which corresponds to the force per current area, and the strain measure is a logarithmicstrain [21]. The latter is commonly used in metal plasticity. One motivation for this choice in this case is that, when true

Fig. 3. Generalized FE model of bolted rail joint.

Fig. 4. Experimental stress–strain curve of the rail web.

G.V. Duncheva, J.T. Maximov / Engineering Failure Analysis 29 (2013) 167–179 171

stress is plotted versus logarithmic strain, tension, compression and torsion test results coincide closely [21]. If nominalstress-nominal strain (rnom � enom) data are obtained from a uniaxial test for isotropic material, a simple conversion to truestress-logarithmic strain (rtrue � eln) exists in ABAQUS:

rtrue ¼ rnomð1þ enomÞ ð1Þ

eln ¼ lnð1þ enomÞ ð2Þ

Logarithmic plastic strain values are used in ABAQUS to define the strain hardening behavior:

epln ¼ eln �

rtrue

E; ð3Þ

where E is Young’s modulus. A nonlinear kinematic hardening model of elastic–plastic rate-independent material is defined.These data are entered in ABAQUS as a point set (rtrue � eln).

The material model of the joint bar is also elastic–plastic and corresponds to C30 DIN 17200 steel. Elastic behavior hasbeen assumed for bolts and wheel with Young’s modulus and Poisson’ratio respectively: E ¼ 2:15� 105 MPa and m = 0.31;E ¼ 2� 105 MPa and m = 0.3 .

2.1.3. InteractionsBetween the rails and joint bar, joint bar and bolts, as well as between the rails and wheel, tangential and normal contact

has been defined with friction coefficient of 0.15. The elastic foundation of rails has a coefficient of 20.6925 N/mm2. The casewhen the ends of 3D rails are on elastic foundation has been dealt with. The elastic supports of beam FEs are modeled bymeans of spring FEs with rigidity of 28907 N=mm [3]. They are defined at a spacing of 600 mm, corresponding to the spacingof the sleepers (Fig. 3).

2.1.4. Boundary conditionsThe geometrical boundary conditions are in conformity with the symmetry and physical character of the problem being

studied – all degrees of freedom of the final nodes of the last beam FSs have been eliminated, except rotation around theirown axes; bolt axes are restricted to move, except along their own axes; the final section of joint bar is restricted only in theinitial analysis step.

The analysis contains two active steps: bolt pretension and wheel loading. Pretension, respectively formation of mountingstresses is simulated by means of preset displacements of the middle sections of the bolt shanks corresponding to pretensionmoment of 500 Nm, respectively, to axial force in bolts of 104166 N [2].

The major problem of this study: determining the variation cycle of circumferential normal stresses at an endangeredpoint from the hole periphery, has been solved in quasi-static mode, i.e. for different positions of the wheels, a series ofnumerical simulations have been conducted.

2.2. Determining the variation cycle of hoop normal stresses

For accurate determination of the operating cycle, preliminary analyses have been made and the effect of a four-axial wa-gon has been simulated. Static load of 80 kN has been assumed with dynamic-response factor of 1.367 [3]. It has been foundthat when the wheel which is closest to middle of rail joint, is at a distance of over 3:6m, stresses in rail joint are practicallyequal to mounting stresses (due to bolt pretension). On this basis it has been assumed that the operating cycle of loading therail joint is formed as a result of loading two adjacent wheels at a distance of 1:8 m. For the cases when one of the wheels isin the middle of the rail joint or near it, the impact load is calculated with dynamic-response factor of 2.4 [3]. On this basisthe wheel load is set by means of pressure.

Fig. 5. A scheme of loading of bolted rail joint.

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Fig. 5 shows 10 successive positions of the pair of wheels on the basis of which the variation cycle of hoop normal stressesat the endangered point has been determined.

It has been found that the endangered point is the most external point from the outside hole periphery of the rail end(Fig. 5, position 1). On the basis of FE results, obtained for this point, the variation cycle of rt; MPa has been obtained(Fig. 6). The cycle starts from the magnitude of mounting stresses (bolt pretension), which cause considerable tension atthe endangered point: rt � 258 MPa. As it could be expected, when one of the wheels is in the middle of the rail joint (posi-tions 6 and 9 in Fig. 5), rt ; MPa changes sharply. Obviously, the variation cycle of hoop normal stresses rt at the endangeredpoint is entirely tensile and considerable dynamism is exhibited. Therefore, especially around the end bolted holes, there areprerequisites for initiating and growth of fatigue cracks of first type.

3. FE optimization of CE process of rail-end-bolt holes

3.1. Generalized 3D FE model of the CE process

In accordance with the study objective, a 3D FE model of the CE process has been developed, realized with a tool accord-ing to BG Patent No. 66052 [20]. According to the patent, the tool consists of a pin with external conical working part and a

Fig. 6. Cycle of alteration of hoop stress in critical point.

G.V. Duncheva, J.T. Maximov / Engineering Failure Analysis 29 (2013) 167–179 173

sleeve split into a number of sectors. CE process is performed by axial motion of the mandrel. The latter reacts with respec-tive internal conical surfaces of the sectors. As a result, simultaneous displacement of sectors is instigated and each sectormoves radially in direction of its symmetric plane. In this concrete case the process was simulated by means of a tool con-taining 8 sectors.

Two holes at the end of rail of 60 EN 13674-1:2011 type, 350 mm long are object of CE. Bolted holes have rated diameterof / 33 mm and the length, equal to the thickness of rail web, is 16:5 mm. The distance between the hole centers is 165 mm.

The developed 3D model of the studied process is shown in Fig. 7. The conical mandrel is modeled as a ‘‘rigid body’’,whereas the rail and the number of sectors – as hard deformable bodies. Second order FEs, type C3D20R are used. The mate-rial of the rail is elastic–plastic with Young’s modulus E ¼ 2:06� 105 MPa and Poisson’s ratio m = 0.3. The behavior of the railmaterial in the plastic region is based on a model of nonlinear kinematic hardening, obtained on the basis of half cycle tensiletest (Fig. 4). Elastic behavior has been assumed for the set of sectors.

The CE process is simulated in the desired sequence and DCE by synchronized in pseudo-time defined displacements ofthe mandrels-sectors couples. The latter are set by tabulated functions. Between the interacting surfaces of mandrels andsectors, tangential and normal contact is defined with friction coefficient of 0.08, and between the sectors and holes – tan-gential and normal contact with friction coefficient of 0.15.

Constraints imposed on rail end are illustrated in Fig. 7, and constraints imposed on mandrels-sectors couples depend onthe physical nature of the process and the sequence of treating the holes. At the beginning of the process both tools are in-serted into the holes and interactions between the contacting external working surfaces of the sectors and the respective

Fig. 7. FE model of the novel CE process.

174 G.V. Duncheva, J.T. Maximov / Engineering Failure Analysis 29 (2013) 167–179

parts of the surface of rail-end holes are set. The sectors which treat the second hole are freed along y and z axes during CE ofthe first hole, to be able to self-adjust with respect to the second hole.

3.2. Methodology of the study

3.2.1. Basic stagesThe optimization of the CE process of the bolted holes contains the following stages:

� Stage I: Planned numerical experiment: the external hole is subjected to CE first and then the internal hole – variant A;� Stage II: Planned numerical experiment: the internal hole is subjected to CE first and then the external hole – variant B;� Stage III: Multi-objective optimization of each variant (A and B). On the basis of the optimization, the variant which pro-

vides a more intensive and uniform compression zone around holes, at lower DCE is chosen. The satisfaction of the lastcondition guarantees lower energy expenses.

3.2.2. Governing factors and objective functionsA planned numerical experiment of 32 type is conducted [23]. The governing factors x1 and x2 are degrees of cold expan-

sion DCE_1 and DCE_2 in percentage respectively of the first and second holes according to the analyzed variant – A or B. Thefactor levels in natural and coded form, as well as corresponding radial displacements are shown in Table 1.

The experimental design is shown in Table 2, where the axial motions of the mandrels are denoted by h1 and h2 appliedrespectively to the first and second holes for CE.

For each experimental point from FE results, the following objective functions are taken into account or calculated:

� rresDP;n - standardized value of the residual hoop normal stress at the critical point (the most external point from the exter-

nal hole periphery, Fig. 5) towards the yield limit.� St_1 - arithmetic-mean value of the residual hoop normal stresses rres

t for the nodes from the periphery (entrance face) ofthe first hole for the respective variant;� St_2 - arithmetic-mean value of the residual hoop normal stresses rres

t for the nodes from the periphery (entrance face) ofthe second hole for the respective variant;� St_1norm - standardized value of St_1 towards the yield limit;� St_2norm - standardized value of St_2 towards the yield limit;� DeltaSt_1 - absolute value of the difference between St_1 and maximum stress rres

t1;max at a point from the first hole periph-ery, read as an algebraic number:

Table 2Optima

No.

123456789

DeltaSt 1 ¼ jSt 1� rrest1;maxj ð4Þ

� DeltaSt_2 - absolute value of the difference between St_2 and maximum stress rrest2;max at a point from the second hole

periphery, read as an algebraic number:

DeltaSt 2 ¼ jSt 2� rres

t2;maxj ð5Þ

Table 1Governing factors and variation levels.

Factor levels

Coded: xi; i ¼ 1; 2 �1 0 1Natural: ~xi; i ¼ 1%; 2% 1 3 5Radial displacements (mm) 0.165 0.495 0.825

l composed second-order design.

x1 x2 ~x1 ~x2 h1; mm h2; mm

�1 �1 0.165 0.165 9.4528 9.45280 �1 0.495 0.165 28.3585 9.45281 �1 0.825 0.165 47.2642 9.4528�1 0 0.165 0.495 9.4528 28.3585

0 0 0.495 0.495 28.3585 28.35851 0 0.825 0.495 47.2642 28.3585�1 1 0.165 0.825 9.4528 47.2642

0 1 0.495 0.825 28.3585 47.26421 1 0.825 0.825 47.2642 47.2642

G.V. Duncheva, J.T. Maximov / Engineering Failure Analysis 29 (2013) 167–179 175

� DeltaSt_1norm – standardized value of DeltaSt_1 towards the yield limit;� DeltaSt_2norm - standardized value of DeltaSt_2 towards the yield limit;� req,norm - standardized maximum equivalent stress req, reached during CE, towards ultimate tensile strength rult.

3.2.3. Optimization task formulationTo find the optimum values of the degrees of CE: DCE_1 and DCE_2, a multi-objective task has been fulfilled. To this end,

by means of QStatLab [23] in succession, for both diagrams (variants A and B) regression models of the objective functionsgiven in 3.2.2 are found:

� fDP,n is the model of rresDP;n:

– for variant A:

fDP;n A ¼ �1:2656844� 0:13611833x1 þ 0:00249333x2 þ 0:08864167x21 � 0:00119333x2

2 ð6Þ

– for variant B:

fDP;n B ¼ �1:2349311þ 0:04742833x1 � 0:11768x2 þ 0:07106167x21 þ 0:05207667x2

2 ð7Þ

� fSt_1 and fSt_2 are the models of respectively St_1norm and St_2norm, as follows:– for variant A:

fSt 1 A ¼ �1:4383333� 0:18316667x1 þ 0:00233333x2þþ0:1135x2

1 � 0:00225x41

ð8Þ

fSt 2 A ¼ �1:3283333� 0:03666667x1 � 0:15766667x2þþ0:10133333x2

2 � 0:045x1x2ð9Þ

– for variant B:

fSt 1 B ¼ �1:3206667� 0:21283333x1 þ 0:00116667x2 þ 0:0675x21 ð10Þ

fSt 2 B ¼ �1:3981111� 0:028x1 � 0:17916667x2 þ 0:09166667x21 þ 0:06216667x2

2: ð11Þ

� fDSt_1 and fDSt_2 are the models of respectively DeltaSt_1norm and DeltaSt_2norm, as follows:– for variant A:

fDSt 1 A ¼ 0:26566667þ 0:03833333x1 þ 0:00183333x2 þ 0:00333333x21 þ 0:0025x1x2 ð12Þ

fDSt 2 A ¼ 0:180888889� 0:00683333x1 þ 0:04383333x2 ð13Þ

– for variant B:

fDSt 1 B ¼ 0:18066667þ 0:02933333x1 � 0:013x21 � 0:0035x1x2; ð14Þ

fDSt 2 B ¼ 0:2838889� 0:19016667x1 þ 0:05383333x2 þ 0:21416667x21 � 0:03283333x2

2 ð15Þ

� fM is the model of req,norm:– for variant A:

fM A ¼ 1:017þ 0:061x1 þ 0:06x2 � 0:069x1x2; ð16Þ

– for variant B:

fM B ¼ 1:0186667þ 0:03066667x1 þ 0:0545x2 þ 0:02733333x21 � 0:0585x1x2 ð17Þ

The optimization has been carried out, and the following restrictive conditions have been adopted:

(1) Condition guaranteeing maximum in absolute value residual hoop normal stress at the critical point:

fDP;n A !min; fDP;n B !min; ð18Þ

(2) Condition for achieving maximum averaged intensity of the compression zone generated around the holes:

fSt 1 !min; f St 2 !min; ð19Þ

176 G.V. Duncheva, J.T. Maximov / Engineering Failure Analysis 29 (2013) 167–179

(3) Condition for creating a compression zone close in intensity, around both holes:

Table 3Functio

VariVariVariVari

FSt ¼ jfSt 1 � fSt 2j ! 0; ð20Þ

(4) Condition guaranteeing that at none of the points of the periphery of both holes after CE there will be tensile circum-ferential normal stresses:

D1 ¼ jfSt 1j � fDSt 1 > 0D2 ¼ jfSt 2j � fDSt 2 > 0

: ð21Þ

(5) Condition directed to achieving maximum homogeneity of the zones of residual circumferential normal stresses in cir-cumferential direction, generated around each hole;

fDSt 1 !min; fDSt 2 !min; ð22Þ

(6) Condition for strength – it is guaranteed that during CE at no point of the rail the maximum stress rult will be reachedwhich the material can bear:

fM A < 1; fM B < 1: ð23Þ

The optimization problem is in finding the values of xi, i = 1,2, which satisfy simultaneously conditions (18)–(23).

3.3. Optimization outcomes

The optimization is conducted using QStatLab in accordance with the genetic algorithm [23]. The found coded optimumvalues of the governing factors and their corresponding target and constraint functions obtained from the optimum solutionare shown in Table 3. On the basis of the optimum values found x1 and x2, additional numerical simulations have been con-ducted. The calculated target and constraint functions on the basis of obtained FE results are very close to those, obtainedfrom multi-objective optimizations (Table 3).

Obviously, variant A ensures a more intensive and uniform compressive zone around the internal hole of the rail end (inthis case – the second hole), since the natural values DCE 1 ¼ 1:8364% and DCE 2 ¼ 3:2524% correspond to x1 and x2. On thecontrary, variant B leads to a more intensive compressive zone around the external hole (the second hole) but the inhomo-geneity of the residual stress zone is more strongly marked. Regardless of this, an essential advantage of variant B is the pro-vision of a residual circumferential normal stress greater in absolute value at the endangered point due to higher DCE of theexternal hole (DCE 1 ¼ 2:1214%; DCE 2 ¼ 2:7348%). Owing to this reason, it is purposeful CE of rail-end-bolt holes to be car-ried out according to variant B. On the other hand, the case when both holes are treated at the same DCE is of practical inter-est. Therefore, a numerical simulation in accordance with variant B has been carried out additionally. Identical DCE havebeen set, close to the optimum value of the second hole obtained for variant B: DCE 1 ¼ DCE 2 ¼ 2:8%. Fig. 8 shows the dis-tribution of rres

t along the periphery of the two holes for the three analyzed cases: variant A, variant B and variant B at oneand the same DCE. In all cases, specific ellipticity of the generated compressive zone is observed which is due to the higherradial rigidity of the rails in vertical direction. CE, performed according to variant B, ensures a more intensive compressivezone around the external hole, as well as greater differences between the zones around the two holes. Evidently, CE, carriedout at DCE = 2.8% according to variant B creates sufficiently intensive and relatively homogeneous zones around the twoholes.

The FE results for the distribution of rrest around the external hole with respect to a local cylindrical coordinate system,

obtained for the 5th experimental point, variant B are shown in Fig. 9a. Fig. 9b shows charts visualizing the distribution ofrres

t in axial direction through the critical point and along a generating line from the hole, contacting with the middle of oneof the sectors. Such character of residual stress distribution is observed in all analyzed cases. Obviously, CE, performed usingthe patented tool, creates almost ideally symmetric zone of residual stresses versus the middle longitudinal plane of the rail.With a view of these results, for FE study of the CE effect on the cycle of stress variation, FE model can be employed whichhas a symmetry plane coinciding with the longitudinal symmetry plane of the rails. Consequently, the generalized FE modelof a rail joint, described in Section 2.1 can be adapted to this end.

n values.

x1 x2 fDP,n fSt_1 fSt_2 FSt fDSt_1 fDSt_2 fM

ant A from optimization �0.5818 0.1262 �1.1534 �1.2929 �1.3220 0.0291 0.2445 0.1904 0.9942ant A from FE simulation �1.0393 �1.1684 �1.3069 0.1385 0.2315 0.1974 0.7459ant B from optimization �0.4394 �0.1326 �1.225 �1.214 �1.343 0.1290 0.1651 0.4011 0.9999ant B from FE simulation �1.2079 �1.1276 �1.3789 0.2513 0.1594 0.2576 0.7643

(a) (b) (c)Fig. 8. Distribution of rres

t in circumferential (hoop) direction: (a) variant A; (b) variant B; (c) variant B with constant DCE = 2.8%.

(a) (b)Fig. 9. Distribution of rres

t for the outside hole: (a) general view; (b) graphical representation in an axial direction of the hole.

G.V. Duncheva, J.T. Maximov / Engineering Failure Analysis 29 (2013) 167–179 177

4. FE study of the effect from CE of bolted holes

4.1. FE model

The aim of this part of the study is to evaluate the effect of CE performed using the new tool by comparing to the casewithout CE.

Generalized FE model of the rail joint, described in Section 2.1 has been used, complemented by the required active stepssimulating CE of bolt holes – successively: ‘‘expansion-1’’, ‘‘stress recovery-1’’, ‘‘expansion-2’’ and ‘‘stress recovery-2’’. Withthe intention of comparing, only one rail was subjected to CE up to reaching DCE of 2.8%.

(a) (b)Fig. 10. Comparison between the cases without and with CE.

178 G.V. Duncheva, J.T. Maximov / Engineering Failure Analysis 29 (2013) 167–179

4.2. Comparison between the case without CE and with CE

The hoop normal stresses formed at the critical point, corresponding to position 8 in Fig. 5, are the object of comparison.This position is chosen because it provokes maximum stresses in the cycle obtained in Section 2.2 (Fig. 6). Fig. 10 shows dia-grams illustrating the formation of hoop normal stresses at the critical point from the external hole in both cases – respec-tively, without and with CE.

As it can be seen in Fig. 10b, considerable residual compressive hoop stress is generated after CE: rrest � �249MPa. The

compressive zone which is smaller in absolute value compared to the zone obtained on the basis of FE model, described inSection 3.1, is due to the linear FEs, used in generalized FE model of the rail joint. The bolt pretension causes partial unload-ing, but the compressive field remains considerable rt � �217 MPa. For comparison, in the case without CE the bolt preten-sion causes significant tension �rt � 258 MPa in the vicinity of the critical point. Obviously, for the case with CE the loadfrom the wheels additionally reduces the zone of residual compressive stresses, but the compressive zone remains consid-erable in absolute value - rt � 190 MPa.

5. Conclusions

� A new approach to enhancement of fatigue life of rail-end-bolt holes has been developed on the basis of a novel methodand tool for CE of holes, patented by the authors. The major advantage of the method is in imparting around the holes ofbeneficial residual compressive hoop stresses which are symmetric toward the middle longitudinal plane of the rail andthus the axial stress gradient is minimum. The developed approach consists in setting and solving a multi-objective opti-mization task of the CE of the rail-end-bolt holes through generalized FE model of the rail bolted joint.� Through generalized FE model the critical point around external holes has been localized and the variation cycle of hoop

stresses has been determined taking into consideration assembly stresses.� The generalized FE model of the rail joint has been adapted to simulating the CE process. On this basis the optimal degree

of CE and the successive holes treatment have been found. The optimum constant DCE of 2:8% has been fixed. This valueof DCE guarantees high intensity and homogeneity of the compressive field around the holes. The two holes must be coldexpanded in internal-external sequence.� It has been proved that CE, performed employing the novel tool, ensures almost ideally symmetric compressive zone in

relation to the middle longitudinal plane of the rails since the process is very close to mere radial expansion. Therefore,the CE process, carried out by means of the novel tool, practically excludes the axial gradient of the compressive zonegenerated around the holes. This gradient is a direct result of the deformation wave passing in axial direction and it isinherent to mandrel coldworking methods.� A comparison between the cases with and without CE of rail-end-bolt holes has been made. After CE process simulation at

certain optimum DCE, the CE beneficial effect has been proved.

G.V. Duncheva, J.T. Maximov / Engineering Failure Analysis 29 (2013) 167–179 179

Acknowledgements

This work is a part from Project No. SIP-02-27/18.05.2009 ‘‘A Novel Method for Enhancement of Fatigue Life and Load-Carrying Capacity of Structural Components with Fastener Holes’’. The project is implemented with the financial supportof European Union and Republic of Bulgaria, European Regional Development Fund, Operational Programme: ‘‘Developmentof the Competitiveness of the Bulgarian Economy 2007–2013’’, Measure: 1.1.1.: ‘‘Support for the Creation and Developmentof Innovative Start up Companies’’ 2007 BG 1610003/1.1.1-01/2007.

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