Engineering Failure Analysis 36 (2014) 155–165

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Engineering Failure Analysis

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Fracture failure analysis of AISI 304L stainless steel shaft

1350-6307/$ - see front matter � 2013 Elsevier Ltd. All rights reserved.http://dx.doi.org/10.1016/j.engfailanal.2013.09.013

⇑ Corresponding author. Tel.: +98 918 385 3445.E-mail address: Shzangeneh@aut.ac.ir (Sh. Zangeneh).

Sh. Zangeneh ⇑, M. Ketabchi, A. KalakiMining and Metallurgical Engineering Department, Amirkabir University of Technology, Tehran, Iran

a r t i c l e i n f o

Article history:Received 8 June 2013Received in revised form 13 September 2013Accepted 20 September 2013Available online 2 October 2013

Keywords:Failure analysisAgitator shaftFinite element analysisAISI 304L stainless steel

a b s t r a c t

Fracture failure analysis of an agitator shaft in a large vessel is investigated in the presentwork. This analysis methodology focused on fracture surface examination and finite ele-ment method (FEM) simulation using Abaqus software for stress analysis. The results showthat the steel shaft failed due to inadequate fillet radius size and more importantly markingdefects originated during machining on the shaft. In addition, after visual investigation ofthe fracture surface, it is concluded that fracture occurred due to torsional–bending fatigueduring operation.

� 2013 Elsevier Ltd. All rights reserved.

1. Introduction

In order to mixing of fluids, mechanically stirred vessels are widely used for variety of purposes such as homogenizingsingle or multiple phases in terms of concentration of components, physical properties, and temperature. Processing duringmechanical mixing occurs under either laminar or turbulent flow conditions, depending on the impeller Reynolds number,defined as Re = qND2/l. For Reynolds numbers below than about Re 6 10, the process is laminar which is called as creepingflow. Fully turbulent conditions are achieved at Reynolds numbers higher than about Re P 104, and the flow which has a Rey-nolds number between these two regimes would be considered as transitional flow [1].

Typically, a large vessel consists of three main parts: agitator shaft with impeller, top structure with motor and gearboxand fixed vessel to foundation including anchor bolting. The agitator shaft consists of two parts, namely, upper shaft andlower shaft. These two parts are tightly connected by means of a rigid coupling to construct the main shaft [2]. General viewof the investigated shaft is illustrated in Fig. 1. The agitator shaft was mainly made of an austenitic stainless steel to resist thecorrosive media in the vessel. Since shafts are subjected to fluctuating loading of combined bending and torsion with variousdegrees of stress concentration, the main problem would fundamentally be fatigue loading [3].

In general, shafts are an important component used for power transmission in machinery and mechanical equipment.Failures of such components and structures have engaged scientists and engineers extensively in an attempt to find theirmain causes and thereby offer methods for their possible prevention [4–7]. In this study, failure investigation of an agitatorshaft of a typical large vessel was considered. The aim of this study is to understand the main reason of fracture and avoid theloss of product and time due to shaft failure and happening of similar cases.

2. Experimental procedure

The failed shaft was inspected macroscopically and microscopically by means of optical and scanning electron micros-copy (SEM) while a great care was taken to avoid damage of fracture surfaces. Atomic absorption spectrometry was

Flange connection

(4 each at 90˚) Baffles

Electric motor

Impeller (3 blades)

Upper shaft

Lower shaft

Top structure

Fig. 1. General arrangement of the vessel with agitator.

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employed to determine chemical composition of the alloy. Room-temperature tensile and impact (Charpy) tests were per-formed in conformity with the ASTM E-8 and ASTM E-23 standards requirements, respectively. Test-samples for impact(Charpy) toughness are made in compliance with the ASTM-E23 of the size 10 � 10 � 55 mm, with the U notch of 2 mmdepth and with the 1 mm radius on top of the notch. The tests were made on instrumented Charpy pendulum and the ob-tained results showed that in all the tested specimens, major fracture energy (85%) was used for crack initiation while itsminor portion (15%) was spent on the crack propagation. To determine the hardness of the alloy, Brinell hardness (HRB) mea-surements were carried out on several points from the outer surface to the central zone of the polished surface of the shaft.

3. Results and discussion

3.1. Chemical composition

According to manufacturer’s documents, the shaft was made from AISI 304L stainless steel. Table 1 shows the atomicabsorption spectroscopy analysis which is compared with the related standard [8]. As it can be seen the chemical composi-tion of the failed shaft meets the specified requirement.

3.2. Mechanical properties

Table 2 summarizes the measured results of uniaxial tension tests. Compared to the qualified values, the shaft had a goodquality in ductility, the average yield stress 274 ± 15 MPa and ultimate stress 595 ± 10 MPa.

The all values of impact toughness were above the minimal required values of 116 J. It has to be mentioned that scatteredmechanical data is mainly due to inhomogeneity of the cast material. In addition, the hardness of various sites of the failedshaft was determined and listed in Table 2. Vividly, it can be seen that the measured hardness met the standard ones [9].

Table 1Chemical composition of failed shaft and AISI 304L stainless steel.

Composition Carbon Manganese Phosphorus Sulfur Silicon Chromium Nickel Nitrogen Iron

Failed shaft 0.029 1.05 0.035 0.011 0.44 18.1 9 – Balance304L stainless steel 0.03 max. 2.00 max. 0.045 max. 0.030 max. 0.75 max. 18.0–20.0 8.0–12.0 0.10 max. Balance

Table 2Mechanical properties of failed shaft.

Mechanical properties 0.2% Yield strength (MPa) Ultimate tensile strength (MPa) Elongation (%) Hardness (HRB) Charpy test (J)

Failed shaft 274 ± 15 595 ± 10 95 ± 3 110 ± 8 116 ± 3

Fig. 2. Fracture surface of the failed shaft at flange connection.

Sh. Zangeneh et al. / Engineering Failure Analysis 36 (2014) 155–165 157

3.3. Fracture surface interpretations

As shown in Fig. 2, the fracture surface has the typical characteristics of a fatigue failure. After crack initiation, propaga-tion of the crack happened over about 3/4 of the shaft cross section which was caused by rotational-bending load. It can bededuced that fatigue is a high-cycle, low-stress type and that propagation occurred under low nominal stresses covering ofmore than 3/4 of the shaft cross section by fatigue crack [10]. In general, three different locations of fracture were evaluated;surfaces of the shaft, radial zone and final fracture zone.

High number of machining grooves which were formed during manufacturing process were revealed by careful macro-scopic examination of the exterior surface of the agitator shaft (Fig. 3a). More surface roughness leads to less fatigue strengthdue to the fact that valleys of rough surfaces act as stress concentration sites. Under higher magnification, some micro cracksdue to improper machining process originated on the surface of agitator shaft (Fig. 3b). Since a very large fraction of fatiguelife is spent in the initiation of crack in high cycle fatigue, fatigue life decrease severely when such micro cracks exist on ashaft [11].

Radial zone contains both many radial coarse lines directed to center and concentric circles about center. In early phasesof crack initiation, each crack propagates at different planes (Fig. 4a) and eventually some steps occur between neighborplanes named ratchet marks. Ratchet marks formation is one of the important factors showed low stress with high stressconcentration as illustrated in Fig. 4b. Fracture surface of radial zone with typical fatigue striation is shown in Fig. 5a. Somesections flattened by the rubbing of crack surfaces during the compressive component of the stress cycle are shown in Fig. 5a.Based on Bates–Clark equation (Eq. (1)) [12], stress intensity factor (SIF) during cyclic crack growth can be easily calculatedby knowing elastic modulus and striation spacing, which for the shaft case, the values of E and striation spacing (according toFig. 5b) were 193 GPa and approximately 1.7 lm, respectively. Thus stress intensity would be calculated 102 MPa

pmin in

the failed shaft.

Striation Spacing ¼ 6ðDK=EÞ2 ð1Þ

To calculate Dr, a simple geometry such as the one shown in Fig. 6a was chosen i.e. a cylindrical shaft with a surface crackwith elliptical shape, in a plane perpendicular to the shaft axis (direction of loading). The crack shape is defined by means ofthe lengths a and b representing the semi-axes of the ellipse (Fig. 6b). The stress intensity factor for the geometry and modeof loading is:

DK ¼ Yast aD

� �Drð

ffiffiffiffiffiffipap

Þ ð2Þ

where Dr is the axial stress range, a is the crack length and Y� aD

� �is a dimensionless function given by following equation:

Fig. 3. (a) Macroscopic examination of the exterior surface of the shaft revealed a number of machining grooves and (b) microscopic examination showsmicro cracks on the surface of failed shaft.

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Y�aD

� �¼ 0:473� 3:286

aD

� �þ 14:797

aD

� �2� ��1

2 aD

� �� a

D

� �2� ��1

4

: ð3Þ

The asterisk is used to indicate only one geometric parameter (the crack depth a) is required, i.e., it is a simplified ap-proach in which the aspect ratio a/b and the curvilinear coordinate s are not considered. This was taken, since a represen-tative geometry (the cylinder with a straight-fronted edge crack) is employed, and the global character of the fracturecriterion is achieved, respectively [13]. Therefore, striation fatigue based on SEM observation shown in Fig. 5b was takennearly 2 mm of shaft surface. So, a value is nearly 2 mm, and also the diameter of the failed shaft under investigation was100 mm. As a result, Yast a

D

� �and axial stress range Dr would be 4.14 and 311 MPa, respectively.Final fracture zone has a

diameter of about 25 mm. The size of this zone provides information on how big the load. That is, the smaller the size is,the lower the load applied. As it can be clearly seen in Fig. 2, when it comes to the comparison, the size of final fracture zoneis smaller than the shaft diameter. Thus, the nominal applied loads are fairly low and the shaft material is highly ductile andtough. Note that because of a distance between the shaft center and zone center, if the shaft is subjected to bending accom-panied by torsion, the final fracture zone relocates from center to edge of the shaft. Under higher magnification, one can seethe typical dimple features (Fig. 7a). Carbide/matrix interface which is shown in (Fig. 7b), was very weak contributed tointerfacial separation. In this case, carbides were responsible for the void nucleation.

3.4. Calculation of torque acting on the shaft

Torque calculation on the shaft during process determined through delivered power to a given fluid at a constant rota-tional speed [2]. The power consumed by a mixer can be obtained by the following equation:

P ¼ Npqn3D5

gc

!ð4Þ

Cracks initiation zones

Ratchet Marks

a

b

Fig. 4. (a) Cracks initiation zones on flange connection and (b) ratchet marks.

Fig. 5. (a) Striation fatigues at fracture surface, some flattened surface indicated by red arrow and (b) striation spacing. (For interpretation of the referencesto color in this figure legend, the reader is referred to the web version of this article.)

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D

2b

a

a

b

Fig. 6. Geometry of analysis: (a) 3D view of the shaft and (b) 2D sketch of the cracked section.

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where q is density of fluid (lb/ft3), Da is impeller diameter (ft), n is the speed of impeller (rps), g is Newton’s law conversionfactor and Np is power number which depends on Reynolds number (NRe), Froude number (NFr) and impeller type based onfollowing equation:

Np ¼ /nD2

aql

;n2Da

g; S1; . . . ; S9

!ð5Þ

As given in Eq. (5) the power number, Np, also is a function of ratio of tank to impeller diameter (T/D), height of impellerabove vessel floor to impeller diameter (Z/D), length of impeller blade to impeller diameter (L/D), impeller diameter to widthof blade (D/W), tank diameter to baffle width (T/B), liquid depth in vessel to impeller diameter (H/D), number of impellerblades (n), pitch/angle (Degree) and number of baffles (n), all of which included to the above equation as shape factorsS1,. . .,S9 respectively. In general, if Reynolds number goes over 104, based on available information [2] Np will be constantand independent of liquid viscosity. Furthermore, changes in NFr have not any significant effect on Np. Therefore, Eqs. (4)-(5) can be rewritten as independent of NRe and NFr.

Np ¼Pgc

n3D5aq¼ /ðS1; . . . ; S9Þ ð6Þ

Regarding the available information [1], power number for three flat blades is 2.58. For pitched blade turbines, changingthe blade angle h would change the power number by Np � (sinh)2 [2]. As a result, when blades make a 45� angle with shaft,Np is 0.4 times the value when blades are parallel with a shaft, which means the power number will be changed to 1.032based on S8 shape factor. Some necessary data taken from the specification sheet of vessel are given in Table 3. The torquecan be calculated 372 NM in accordance to P = xT = 2pnT.

Fig. 7. (a) Final fracture zone of the failed shaft shows the typical dimple features and (b) interfacial separation of carbide/matrix interface.

Table 3Necessary data extracted from the specification sheet of vessel.

Definition Impeller diameter Viscosity Density Acceleration of gravity Speed of impeller

Values 3.44 ft 1.34 � 10�3 lb/ft s 69 lb/ft3 32.17 ft/s2 1.17 rps

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3.5. Stress analysis by Abaqus program

In this study, the commercial Abaqus software was employed to analyze stress propagation at start-up regime of the shaftduring mixing operation. The 3D geometry model of the agitator shaft is shown in Fig. 8a. As shown, all parts such as shafts,flange connection and bolts (Fig. 8b) used to fasten flange were modeled and assembled to this analysis. Mechanical behaviorof shaft material was imported into the software by calibration tool in order to use exact data for the simulation. Bolt loadsdefined by concentrate force in their length to fasten flanges. In order to define the contacts among bodies and position themrelative to each other in only one global coordinate system in which shafts and bolts would be identical with practical placesin the process, contact surfaces and contact pairs are also defined.

Before performing the simulation, several assumptions were made: (1) shaft weight was not to be taken into consider-ation, since during mixing operation, the axial (upward) forces created by impeller due to blade angle of 45� are oppositeto the shaft weight, (2) drum pressure acts as a hydrostatic pressure equally over the shaft and has no effect on the generalyielding, thus, it helps to increase the yield of the shaft material. (3) operation temperature (216� C) is a moderate temper-ature for the shaft material and at this temperature the properties of the material do not change considerably but ductilityand fracture toughness increase moderately at high temperatures up to around 350� C and (4) the material is assumed to beisotropic and homogeneous.

In order to study numerical simulations of the agitator shaft, hexahedral brick elements C3D20R which are the quadraticreduced-integration elements were adopted. These elements are not susceptible to shear locking, even when subjected tocomplicated states of stress. Therefore, these elements are also generally the best choice for the most general stress/displace-

Fig. 8. (a) 3D geometry model of the agitator shaft and (b) intake flange connection.

Fig. 9. Stress contours at different stages of the analysis during the start-up of the shaft calculated according to the Von Mises’ criterion in the incrementaltimes of (a) 10�4, (b) 3 � 10�4, (c) 7 � 10�4 and (d) 10�3 s, respectively.

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ment simulations. The mesh is graded in a way such that there is a higher mesh density at shaft to flange connection. Thisimproves the accuracy of the solution around the shaft without tremendously increasing the computational time. Mesh inthe all parts generated by sweep method. Abaqus/CAE creates swept meshes by internally generating the mesh on an edge or

Fig. 10. Stress contours at different stages of the analysis during the start-up of the shaft with a single machining groove with a depth of 0.2 mm calculatedaccording to the Von Mises’ criterion in the incremental times of (a) 10�4, (b) 3 � 10�4, (c) 7 � 10�4 and (d) 10�3 s, respectively.

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face and then sweeping that mesh along a sweep path. Normally, a higher mesh density provides for higher accuracy but alsoincreases the computational time, therefore, a trade-off between time and accuracy becomes crucial. In this case, three dif-ferent mesh densities were investigated. The shaft were initially meshed with 7855 elements with a higher mesh densitycloser to the shaft to flange and then mesh density changed from 10,165 to 11,705 in order to reach successful convergent.After obtaining the torque (372 NM), it was applied to a reference point 2 (Rp-2) which was coupled to lower position of theshaft (impeller location). Also, constant rotating speed of 70 rpm defined to the reference point 1 (Rp-1) in the upper positionof the model (electric motor location). In addition, some constraints were applied for conformity to the real shaft operation.

Dynamic analysis in Abaqus/Standard uses implicit time integration method to calculate the transient dynamic responseof a system. These time integration operators are implicit, which means that the operator matrix must be inverted and a setof simultaneous nonlinear dynamic equilibrium equations must be solved at each time increment. This solution is done iter-atively using Newton’s method [14]. Fig. 9a–d shows stress contours at different stages of the analysis during the start-up ofthe shaft calculated according to the Von Mises’ criterion in the incremental times of 10�4, 3 � 10�4, 7 � 10�4 and 10�3 s,respectively. As can be seen in Fig. 9a–d, stress waves propagated into the upper shaft in a very short period of time, howeverdue to abrupt change in the cross section of shaft to flange, stress raised at shaft/flange connection until the flow stressreached to the bolts and then the stress relaxed by flowing through the bolts to the lower shaft caused the shaft to rotate.Although stress highly increased up to 101 MPa at the location of crack initiation at shaft to flange connection in a short per-iod of time (7 � 10�4 s), this can be neglected by considering mechanical properties of the shaft. In general, fracture of theshaft originates at points of stress concentration either inherent in design or introduced during fabrication or operation. Inthis case, the design features that cause concentrated stress is inadequate fillet radius size. Furthermore, stress concentrationproduced during fabrication as a result of machining grooves.

Depending on the variables of machining technique and the quality of the cutting tool, machining can lead to fairly sharpgrooves. To understand the effect of machining grooves on stress concentration, a single machining mark with a depth of0.2 mm was considered based on roughness measurements. Surface roughness used here was based on the difference be-tween the highest peak and the lowest one. Fig. 10a–d shows stress contours at different stages of the analysis along witha single machining mark with a depth of 0.2 mm at start-up of the shaft calculated according to the Von Mises’ criterion inthe incremental times of 10�4, 3 � 10�4, 7 � 10�4 and 10�3 s, respectively. Fig. 11a–b shows the effect of 0.2 mm machininggroove on stress concentration during the start-up of the shaft at the time of 7 � 10�4 s at higher magnification. Also, it can

Fig. 11. Effect of a single machining groove with a depth of 0.2 mm in a start-up of the shaft at the time of 7 � 10�4 s (a) side view and (b) root of machiningmark.

Fig. 12. Stress contours at steady state operation of the shaft calculated according to the Von Mises’ criterion.

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Sh. Zangeneh et al. / Engineering Failure Analysis 36 (2014) 155–165 165

be seen that such a circumferential groove increased stress concentration to as much as 50% the smooth one at start-up time.The number of such machining marks with the size of more than 0.2 mm originated during fabrication process (Fig. 3a), soeach one play a crucial role in decreasing fatigue life and eventually contributed to failure of the shaft. In general, the majordefects that originate during machining are machining grooves, grinding burns and cracks. Machining grooves are extremelydangerous in critical rotating parts, with life limited by fatigue. Because of their stress-raising effect, machining defects arethe preferred sites for fatigue crack initiation. A large number of service failures occur due to improper machining.

Static analysis in Abaqus/Standard was carried out to understand stress distribution during steady state operation of theshaft. Fig. 12 depicts stress contours in the assembled agitator shaft. As it is clear due to inadequate fillet radius size, stressraised at shaft/flange connection, but the obtained maximum stress, i.e. 6 MPa, is not comparable with the one occur duringstartup. Therefore, an increase in stress at shaft/flange connection might occur mostly in the service during startup or othertransient conditions.

4. Conclusion

Experimental and numerical simulation of the agitator AISI 304L stainless steel shaft was studied. Results showed thatmechanical properties (uniaxial tension, impact and hardness tests) and chemical composition of the failed shaft were inacceptable range. Calculations showed that torque applied to the shaft during mixing operation at constant speed of70 rpm was approximately 372 NM. Stress analysis based on the boundaries conditions mentioned earlier showed that inthe smooth shaft at 7 � 10�4 s of starting time, stress raised up to 101 MPa within shaft to flange connection. This valuein the shaft with a single machining groove with depth of 0.2 mm increases as much as 50%. In addition, Static analysisshowed that stress rose at flange/shaft connection up to 6 MPa in steady state operation. On the basis of all the above stated,it can be concluded that inadequate fillet radius size and more importantly machining grooves on the shaft surface was themain cause of the shaft failure.

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