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Failure analysis of a SAE 4340 steel locking bolt
Engineering Failure Analysis 11 (2004) 915–924 www.elsevier.com/locate/engfailanal
Failure analysis of a SAE 4340 steel locking bolt M.T. Milan a, D. Spinelli a
a,* ,
W.W. Bose Filho a, M.F.V. Montezuma a, V. Tita
b
Nemaf (N ucleo de Ensaios de Materiais e Analises de Falhas), Department of Materials, Aeronautics and Automotive Engineering, University of Sao Paulo, Av. Trabalhador Sao-carlense 400, Sao Carlos 13566-590, Brazil b Department of Mechanical Engineering, Engineering School of S~ao Carlos – University of S~ao Paulo, CEP: 13566-590, S~ao Carlos, SP, Brazil Received 12 December 2003; accepted 18 December 2003 Available online 6 March 2004
Abstract Several SAE 4340 steel locking bolts used to assemble speed reducer housings fractured after a few hours of operation. Micrographic and macrographic analyses, scanning electron microscopy techniques, tensile, impact and hardness testing were used to fully characterize the component and material properties. Stress calculations were performed using both Neuber analysis and Finite Element Analysis (FEA) and the results were compared. Cracks nucleated at the root of the last engaged thread due to a combination of high local stresses in this region, surface defects, non-uniformity of the thread root and low toughness of the material. After nucleation, the crack propagated by fatigue until the catastrophic failure. 2004 Elsevier Ltd. All rights reserved. Keywords: Fasteners; Fatigue; Finite element analysis; Thread rolling; Stress concentrations
1. Introduction Several locking bolts used for assembly speed reducer housings fractured after a few hours of operation. One example of the bolt fracture surfaces can be seen in Fig. 1. In all cases, the fracture took place starting from the root of the last engaged thread. The bolt was manufactured out of a SAE 4340 steel, quenched and tempered in order to result in the mechanical properties given in Table 1. Dimensions and geometry of the bolt are given in Fig. 2. Threads were cold rolled after the heat treating, machined to a root radius of 0.577 mm and angle of 60, as specified for the metric thread M100 4h13. A
*
Corresponding author. Tel.: +55-016-271-9333/+55162739577; fax: +55-016-271-9241/+552739590. E-mail address: [email protected] (D. Spinelli).
1350-6307/$ - see front matter 2004 Elsevier Ltd. All rights reserved. doi:10.1016/j.engfailanal.2003.12.003
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M.T. Milan et al. / Engineering Failure Analysis 11 (2004) 915–924
Nomenclature enom nominal strain et total elongation E YoungÕs modulus En Charpy energy K monotonic strain hardening coefficient Kt elastic stress concentration factor Kr stress concentration factor Ke strain concentration factor n monotonic strain hardening exponent r thread root radius RA Reduction of area Snom nominal stress Sy (0.2%) 0.2% offset yield strength t thickness e local strain c coefficient of load relief r local stress rr true ultimate tensile strength ryy thread root longitudinal stress FEA Finite Element Analysis HBS Brinell hardness measured using steel indenter UTS ultimate tensile strength
Fig. 1. Fractured bolt.
Table 1 Nominal mechanical properties, as specified by the manufacturer UTS (MPa)
Sy (0.2%) (MPa)
et (%)
HBS
En (J)
1100–1300
>900
>10
335–385
35
M.T. Milan et al. / Engineering Failure Analysis 11 (2004) 915–924
917
Fig. 2. Dimensions and geometry of the bolt. The nut and the fractured region are also shown schematically. All dimensions are in mm.
tensile pre-stress of approximately 492 MPa was applied to the bolt by a hydraulic system in order to assemble the nut on the housing.
2. Methods
• • • • • • • • •
The following procedures were applied in the current investigation: Chemical analysis; Macrographic analysis; Micrographic analysis; Hardness measurements; Impact testing; Tensile testing; Scanning electron microscopy; Neuber analysis; Finite element analysis.
3. Results and analysis 3.1. Chemical analysis Chemical analysis results are presented in Table 2. The obtained values are within the intervals specified for the SAE 4340 steel.
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M.T. Milan et al. / Engineering Failure Analysis 11 (2004) 915–924
Table 2 Chemical analysis results (in wt%)
Nominal Obtained
C
Si
Mn
P
S
Cr
Ni
Mo
0.38–0.43 0.40
0.15–0.35 0.22
0.60–0.80 0.70
0.03 max 0.027
0.04 max 0.01
0.70–0.90 0.86
1.65–2.00 1.75
0.20–0.30 0.21
Fig. 3. Fracture surface of the bolt.
Fig. 4. Detail of the probable region of crack nucleation.
3.2. Macrography Fig. 3 shows a macrograph of the fracture surface of the bolt where both slow and fast fracture regions are clearly observed. Additionally, beach marks can be observed on the fracture surface, which is a typical feature of the fatigue crack propagation mechanism. Fig. 4 details the most likely region of crack nucleation at the thread root, revealing several surface irregularities.
M.T. Milan et al. / Engineering Failure Analysis 11 (2004) 915–924
919
Fig. 5. Optical micrograph of the thread root immediately below the fracture surface (Nital 2%).
3.3. Micrography Fig. 5 depicts a micrograph of a transverse section of the threaded region immediately below the fracture surface. The deformation lines due to the rolling process are seen below the thread root. The microstructure consists of ferritic regions alternating with tempered martensite and/or bainite regions. The root is not uniform and several geometrical irregularities are observed. The measured thread root radius was approximately 0.340 mm and therefore smaller than the specified value for the M100 thread, which is 0.577 mm. 3.4. Mechanical properties Mechanical properties are presented in Table 3. Tensile test results and hardness values indicated that the material is in accordance with the nominal limits specified by the manufacturer (Table 1). However, Charpy impact tests revealed lower values of absorbed energy than specified in Table 1, suggesting that the heat treatment procedure could have caused embrittlement of the steel. 3.5. Fractography Fig. 6 presents the most likely region of crack nucleation, where a large number of surface defects are seen on the thread. These defects are probably a consequence of the debris crushed between the roller and Table 3 Actual mechanical properties Tespiece
UTS (MPa)
rr a (MPa)
Sy (0.2%) (MPa)
et (%)
RA (%)
E (GPa)
Kb (MPa)
nb
HBS
En (J)
1 2 3 4
1288 1238 1228 1238
1350 1291 1277 1286
1071 1020 1014 1018
15 13 16 14
58 55 53 54
184 183 188 188
1721 1675 1659 1724
0.0725 0.0755 0.0749 0.0814
350 360 363 355
23.5 18.7 20.9 –
Average
1248
1301
1031
14
55
186
1695
0.0760
357
21.0
a b
Calculated using rr ¼ Sr ð1 þ eÞ. Measured for plastic strain above 0.2%.
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M.T. Milan et al. / Engineering Failure Analysis 11 (2004) 915–924
Fig. 6. (a) Most likely region of crack nucleation. (b) Region indicated by the arrow.
the thread during the rolling process. These defects contribute to increase the stress concentration factor in this region. 3.6. Neuber analysis The stress concentration factor, Kt , is given by the ratio between the local stress, r, in the discontinuity and the nominal stress, Snom , applied to the net section containing the discontinuity: Kt ¼
r Snom
ð1Þ
:
For threaded sections, Neuber [1] proposed the following equation for the determination of Kt : Kt ¼ 1 þ 2
tc 1=2 r
;
ð2Þ
where t is the notch depth, r is the root radius and c is the coefficient of load relief due to the decrease in the stress concentration factor caused by a series of identical closely spaced notches or grooves. In the present case, t ¼ 2:454 mm and c ¼ 0:44 [1]. Therefore, a Kt value of 4.56 for the measured root radius, r ¼ 0:340 mm, was found. If the nominal root radius r ¼ 0:577 mm is considered, then Kt ¼ 3:74. Eqs. (1) and (2) are valid provided that the local stresses remain below the yield strength of the material. Considering the nominal tensile pre-stress of 492 MPa applied to the bolt in order to assemble the nut, for both root radii analyzed (0.340 and 0.577 mm) the estimated local stresses calculated according to Eq. (1) are higher than the yield strength of the material and therefore, localized plastic deformation occurs at the notch root. In this case, r is related to Snom by the following relation: Kr ¼
r Snom
for r > Sy :
ð3Þ
In terms of strain, the above equation can be rewritten as: Ke ¼
e enom
for r > Sy :
ð4Þ
M.T. Milan et al. / Engineering Failure Analysis 11 (2004) 915–924
921
However, it is well known that the elastic Kt can be correlated to Kr and Ke through the following relationship [2]: Kt ¼
pffiffiffiffiffiffiffiffiffiffi Kr Ke :
ð5Þ
Substituting Eqs. (3) and (4) in Eq. (5) and rearranging this equation, it is found that r and e are correlated by the equation of a hyperbola: 2
re ¼
ðKt Snom Þ : E
ð6Þ
Additionally, r and e are related by the true stress–strain curve: e¼
r r 1n þ ; E K
ð7Þ
where K and n are the monotonic strain hardening coefficient and monotonic strain hardening exponent, respectively. Inserting Eq. (7) into Eq. (6), the local stress, r, can be obtained:
2 r r 1n ðKt Snom Þ : þ r¼ E K E
ð8Þ
The above equation can be determined analytically by iteration techniques or graphically through the intersection of the true stress–strain curve and NeuberÕs hyperbola. Fig. 7 shows the results obtained for the present investigation. Calculated values show that the estimated local stress at the thread root is almost as high as the ultimate tensile strength (UTS) of the material. Considering the nominal root radius (r ¼ 0:577 mm) the calculated stress was approximately 1184 MPa which is 91% of the UTS. Instead, if the measured root radius is taken into account (r ¼ 0:340 mm), the local stress is 1233 MPa (95% of UTS). However, these results must be seen with some care because the nut
1600
σ (local stress) (MPa)
UTS= 1301MPa 1233MPa 1200 1184MPa Neuber´s hiperbola for r=0.340mm Neuber´s hiperbola for r=0.577mm True stress-strain curve
800
400
0
0
0.02
0.04
0.06
0.08
0.1
ε (local strain) Fig. 7. True stress–strain curve and NeuberÕs hyperbola obtained for the bolt.
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M.T. Milan et al. / Engineering Failure Analysis 11 (2004) 915–924
was not taken into account in the stress concentration factor calculations. It is well known that bolts typically fail from the last engaged thread due to the higher stress concentration that occurs in this region [3]. Therefore, the stress results provided by Neuber analysis are likely to be non-conservative. 3.7. Finite element stress analysis The finite element code ANSYS was used to determine the stress distribution in the locking bolt when subjected to the load and constraints of operational conditions. In order to reduce the complexity of the analysis, a bi-dimensional model was used to simulate the bolt geometry. A uniform tensile stress of 492 MPa was applied to the modeled bolt either with or without the nut assembled in order to simulate the assembling loading conditions. In the latter case, for the sake of simplicity, it was assumed that the housing to which the bolt is assembled is perfectly rigid, i.e., the applied stress is totally transmitted to the bolt and no stress relaxation occurs. Fig. 8 shows a schematic representation of both situations. The finite element ‘‘Plane 42’’ used in the analysis is the 4-node with two degrees of freedom in each node (x and y displacements), assuming an axisymmetric stress state. The mesh contains 25,975 nodes and 25,088 elements. The nut-thread contact was simulated by restricting the normal displacements on the lower surface of the thread, as seen in Fig. 9. The true stress–strain curve was used as the input information for the elasto-plastic material model, assuming Von Mises yield criterion, multilinear isotropic hardening and associative flow rule. Results show that when the load is applied to the bolt without the nut assembled, the estimated longitudinal stress at the thread root, ryy , remains nearly constant in all threads. For the actual root radius
Fig. 8. Schematic representation of the constraints and loading conditions imposed on the simulated bolt: (a) without the nut; (b) with the nut.
M.T. Milan et al. / Engineering Failure Analysis 11 (2004) 915–924
923
Fig. 9. Details of the mesh near the threaded region: (a) without the nut; (b) with the nut.
(r ¼ 0:340 mm), ryy is estimated as approximately 1260 MPa. When the nominal root radius is considered (r ¼ 0:577 mm), the estimated ryy yields a value of 1150 MPa. These results compare very well with those obtained by Neuber analysis. However, when the nut is assembled on the threaded region of the bolt, a different picture emerges. In this case, for both root radii considered in the analysis, there is a peak stress at the last engaged thread, which is higher than the UTS of the material (Fig. 10). Although this peak stress is likely to be a conservative value because the housing is not perfectly rigid, it is a close approximation of the actual true stress developed at the thread root. Therefore, if the nut is taken into account, the conclusion is that a crack will nucleate at the root of the last engaged thread when the bolt is loaded in tension and the nut is assembled.
30 25 Nut region Last engaged thread
Thread
20 15 10
1760MPa r=0.340mm
5
FEA results for r=0.577mm FEA results for r=0.340mm
0
0
500
1000
1620MPa r=0.577mm
1500
Thread root longitudinal stress, σyy (MPa) Fig. 10. Thread root longitudinal stress against thread position.
2000
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M.T. Milan et al. / Engineering Failure Analysis 11 (2004) 915–924
As soon as the crack initiates, the peak ryy stress is partially relieved and the crack propagates by fatigue until the catastrophic failure takes place.
4. Conclusions The locking bolt used for assembling speed reducer housings failed due to the high stresses developed at the thread root as a consequence of the applied assembly load. Additionally, it is important to highlight that other factors such as surface defects, thread root radius smaller than the nominal value and low toughness of the material also contributed to the crack nucleation process.
5. Recommendations (a) (b) (c) (d)
Reduce the assembly load. Increase the thread radius. Reassess the heat treatment procedure in order to increase the toughness properties of the steel. Improve the control of the surface rolling process to avoid defects and non-uniformity of root radius.
Acknowledgements Thanks are due to the Department of Mechanical Engineering – School of Engineering of S~ao Carlos – USP for providing access to the Finite Element Code ANSYS used in this work and to Renk Zanini S.A. – Brazil for authorizing the publication of this work.
References [1] Neuber H. Theory of notch stress: principles for exact calculation of strength with reference to structure form and materials. Washigton DC, USA: Office of Technical Services, Department of Commerce; 1964. [2] Bannantine JA, Comer JJ, Handrock JL. Fundamentals of metal fatigue analysis. New Jersey: Prentice-Hall Inc.; 1990. [3] Peterson RE. Stress concentration factors. New York: Wiley; 1974.
Failure analysis of a SAE 4340 steel locking bolt M.T. Milan a, D. Spinelli a
a,* ,
W.W. Bose Filho a, M.F.V. Montezuma a, V. Tita
b
Nemaf (N ucleo de Ensaios de Materiais e Analises de Falhas), Department of Materials, Aeronautics and Automotive Engineering, University of Sao Paulo, Av. Trabalhador Sao-carlense 400, Sao Carlos 13566-590, Brazil b Department of Mechanical Engineering, Engineering School of S~ao Carlos – University of S~ao Paulo, CEP: 13566-590, S~ao Carlos, SP, Brazil Received 12 December 2003; accepted 18 December 2003 Available online 6 March 2004
Abstract Several SAE 4340 steel locking bolts used to assemble speed reducer housings fractured after a few hours of operation. Micrographic and macrographic analyses, scanning electron microscopy techniques, tensile, impact and hardness testing were used to fully characterize the component and material properties. Stress calculations were performed using both Neuber analysis and Finite Element Analysis (FEA) and the results were compared. Cracks nucleated at the root of the last engaged thread due to a combination of high local stresses in this region, surface defects, non-uniformity of the thread root and low toughness of the material. After nucleation, the crack propagated by fatigue until the catastrophic failure. 2004 Elsevier Ltd. All rights reserved. Keywords: Fasteners; Fatigue; Finite element analysis; Thread rolling; Stress concentrations
1. Introduction Several locking bolts used for assembly speed reducer housings fractured after a few hours of operation. One example of the bolt fracture surfaces can be seen in Fig. 1. In all cases, the fracture took place starting from the root of the last engaged thread. The bolt was manufactured out of a SAE 4340 steel, quenched and tempered in order to result in the mechanical properties given in Table 1. Dimensions and geometry of the bolt are given in Fig. 2. Threads were cold rolled after the heat treating, machined to a root radius of 0.577 mm and angle of 60, as specified for the metric thread M100 4h13. A
*
Corresponding author. Tel.: +55-016-271-9333/+55162739577; fax: +55-016-271-9241/+552739590. E-mail address: [email protected] (D. Spinelli).
1350-6307/$ - see front matter 2004 Elsevier Ltd. All rights reserved. doi:10.1016/j.engfailanal.2003.12.003
916
M.T. Milan et al. / Engineering Failure Analysis 11 (2004) 915–924
Nomenclature enom nominal strain et total elongation E YoungÕs modulus En Charpy energy K monotonic strain hardening coefficient Kt elastic stress concentration factor Kr stress concentration factor Ke strain concentration factor n monotonic strain hardening exponent r thread root radius RA Reduction of area Snom nominal stress Sy (0.2%) 0.2% offset yield strength t thickness e local strain c coefficient of load relief r local stress rr true ultimate tensile strength ryy thread root longitudinal stress FEA Finite Element Analysis HBS Brinell hardness measured using steel indenter UTS ultimate tensile strength
Fig. 1. Fractured bolt.
Table 1 Nominal mechanical properties, as specified by the manufacturer UTS (MPa)
Sy (0.2%) (MPa)
et (%)
HBS
En (J)
1100–1300
>900
>10
335–385
35
M.T. Milan et al. / Engineering Failure Analysis 11 (2004) 915–924
917
Fig. 2. Dimensions and geometry of the bolt. The nut and the fractured region are also shown schematically. All dimensions are in mm.
tensile pre-stress of approximately 492 MPa was applied to the bolt by a hydraulic system in order to assemble the nut on the housing.
2. Methods
• • • • • • • • •
The following procedures were applied in the current investigation: Chemical analysis; Macrographic analysis; Micrographic analysis; Hardness measurements; Impact testing; Tensile testing; Scanning electron microscopy; Neuber analysis; Finite element analysis.
3. Results and analysis 3.1. Chemical analysis Chemical analysis results are presented in Table 2. The obtained values are within the intervals specified for the SAE 4340 steel.
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M.T. Milan et al. / Engineering Failure Analysis 11 (2004) 915–924
Table 2 Chemical analysis results (in wt%)
Nominal Obtained
C
Si
Mn
P
S
Cr
Ni
Mo
0.38–0.43 0.40
0.15–0.35 0.22
0.60–0.80 0.70
0.03 max 0.027
0.04 max 0.01
0.70–0.90 0.86
1.65–2.00 1.75
0.20–0.30 0.21
Fig. 3. Fracture surface of the bolt.
Fig. 4. Detail of the probable region of crack nucleation.
3.2. Macrography Fig. 3 shows a macrograph of the fracture surface of the bolt where both slow and fast fracture regions are clearly observed. Additionally, beach marks can be observed on the fracture surface, which is a typical feature of the fatigue crack propagation mechanism. Fig. 4 details the most likely region of crack nucleation at the thread root, revealing several surface irregularities.
M.T. Milan et al. / Engineering Failure Analysis 11 (2004) 915–924
919
Fig. 5. Optical micrograph of the thread root immediately below the fracture surface (Nital 2%).
3.3. Micrography Fig. 5 depicts a micrograph of a transverse section of the threaded region immediately below the fracture surface. The deformation lines due to the rolling process are seen below the thread root. The microstructure consists of ferritic regions alternating with tempered martensite and/or bainite regions. The root is not uniform and several geometrical irregularities are observed. The measured thread root radius was approximately 0.340 mm and therefore smaller than the specified value for the M100 thread, which is 0.577 mm. 3.4. Mechanical properties Mechanical properties are presented in Table 3. Tensile test results and hardness values indicated that the material is in accordance with the nominal limits specified by the manufacturer (Table 1). However, Charpy impact tests revealed lower values of absorbed energy than specified in Table 1, suggesting that the heat treatment procedure could have caused embrittlement of the steel. 3.5. Fractography Fig. 6 presents the most likely region of crack nucleation, where a large number of surface defects are seen on the thread. These defects are probably a consequence of the debris crushed between the roller and Table 3 Actual mechanical properties Tespiece
UTS (MPa)
rr a (MPa)
Sy (0.2%) (MPa)
et (%)
RA (%)
E (GPa)
Kb (MPa)
nb
HBS
En (J)
1 2 3 4
1288 1238 1228 1238
1350 1291 1277 1286
1071 1020 1014 1018
15 13 16 14
58 55 53 54
184 183 188 188
1721 1675 1659 1724
0.0725 0.0755 0.0749 0.0814
350 360 363 355
23.5 18.7 20.9 –
Average
1248
1301
1031
14
55
186
1695
0.0760
357
21.0
a b
Calculated using rr ¼ Sr ð1 þ eÞ. Measured for plastic strain above 0.2%.
920
M.T. Milan et al. / Engineering Failure Analysis 11 (2004) 915–924
Fig. 6. (a) Most likely region of crack nucleation. (b) Region indicated by the arrow.
the thread during the rolling process. These defects contribute to increase the stress concentration factor in this region. 3.6. Neuber analysis The stress concentration factor, Kt , is given by the ratio between the local stress, r, in the discontinuity and the nominal stress, Snom , applied to the net section containing the discontinuity: Kt ¼
r Snom
ð1Þ
:
For threaded sections, Neuber [1] proposed the following equation for the determination of Kt : Kt ¼ 1 þ 2
tc 1=2 r
;
ð2Þ
where t is the notch depth, r is the root radius and c is the coefficient of load relief due to the decrease in the stress concentration factor caused by a series of identical closely spaced notches or grooves. In the present case, t ¼ 2:454 mm and c ¼ 0:44 [1]. Therefore, a Kt value of 4.56 for the measured root radius, r ¼ 0:340 mm, was found. If the nominal root radius r ¼ 0:577 mm is considered, then Kt ¼ 3:74. Eqs. (1) and (2) are valid provided that the local stresses remain below the yield strength of the material. Considering the nominal tensile pre-stress of 492 MPa applied to the bolt in order to assemble the nut, for both root radii analyzed (0.340 and 0.577 mm) the estimated local stresses calculated according to Eq. (1) are higher than the yield strength of the material and therefore, localized plastic deformation occurs at the notch root. In this case, r is related to Snom by the following relation: Kr ¼
r Snom
for r > Sy :
ð3Þ
In terms of strain, the above equation can be rewritten as: Ke ¼
e enom
for r > Sy :
ð4Þ
M.T. Milan et al. / Engineering Failure Analysis 11 (2004) 915–924
921
However, it is well known that the elastic Kt can be correlated to Kr and Ke through the following relationship [2]: Kt ¼
pffiffiffiffiffiffiffiffiffiffi Kr Ke :
ð5Þ
Substituting Eqs. (3) and (4) in Eq. (5) and rearranging this equation, it is found that r and e are correlated by the equation of a hyperbola: 2
re ¼
ðKt Snom Þ : E
ð6Þ
Additionally, r and e are related by the true stress–strain curve: e¼
r r 1n þ ; E K
ð7Þ
where K and n are the monotonic strain hardening coefficient and monotonic strain hardening exponent, respectively. Inserting Eq. (7) into Eq. (6), the local stress, r, can be obtained:
2 r r 1n ðKt Snom Þ : þ r¼ E K E
ð8Þ
The above equation can be determined analytically by iteration techniques or graphically through the intersection of the true stress–strain curve and NeuberÕs hyperbola. Fig. 7 shows the results obtained for the present investigation. Calculated values show that the estimated local stress at the thread root is almost as high as the ultimate tensile strength (UTS) of the material. Considering the nominal root radius (r ¼ 0:577 mm) the calculated stress was approximately 1184 MPa which is 91% of the UTS. Instead, if the measured root radius is taken into account (r ¼ 0:340 mm), the local stress is 1233 MPa (95% of UTS). However, these results must be seen with some care because the nut
1600
σ (local stress) (MPa)
UTS= 1301MPa 1233MPa 1200 1184MPa Neuber´s hiperbola for r=0.340mm Neuber´s hiperbola for r=0.577mm True stress-strain curve
800
400
0
0
0.02
0.04
0.06
0.08
0.1
ε (local strain) Fig. 7. True stress–strain curve and NeuberÕs hyperbola obtained for the bolt.
922
M.T. Milan et al. / Engineering Failure Analysis 11 (2004) 915–924
was not taken into account in the stress concentration factor calculations. It is well known that bolts typically fail from the last engaged thread due to the higher stress concentration that occurs in this region [3]. Therefore, the stress results provided by Neuber analysis are likely to be non-conservative. 3.7. Finite element stress analysis The finite element code ANSYS was used to determine the stress distribution in the locking bolt when subjected to the load and constraints of operational conditions. In order to reduce the complexity of the analysis, a bi-dimensional model was used to simulate the bolt geometry. A uniform tensile stress of 492 MPa was applied to the modeled bolt either with or without the nut assembled in order to simulate the assembling loading conditions. In the latter case, for the sake of simplicity, it was assumed that the housing to which the bolt is assembled is perfectly rigid, i.e., the applied stress is totally transmitted to the bolt and no stress relaxation occurs. Fig. 8 shows a schematic representation of both situations. The finite element ‘‘Plane 42’’ used in the analysis is the 4-node with two degrees of freedom in each node (x and y displacements), assuming an axisymmetric stress state. The mesh contains 25,975 nodes and 25,088 elements. The nut-thread contact was simulated by restricting the normal displacements on the lower surface of the thread, as seen in Fig. 9. The true stress–strain curve was used as the input information for the elasto-plastic material model, assuming Von Mises yield criterion, multilinear isotropic hardening and associative flow rule. Results show that when the load is applied to the bolt without the nut assembled, the estimated longitudinal stress at the thread root, ryy , remains nearly constant in all threads. For the actual root radius
Fig. 8. Schematic representation of the constraints and loading conditions imposed on the simulated bolt: (a) without the nut; (b) with the nut.
M.T. Milan et al. / Engineering Failure Analysis 11 (2004) 915–924
923
Fig. 9. Details of the mesh near the threaded region: (a) without the nut; (b) with the nut.
(r ¼ 0:340 mm), ryy is estimated as approximately 1260 MPa. When the nominal root radius is considered (r ¼ 0:577 mm), the estimated ryy yields a value of 1150 MPa. These results compare very well with those obtained by Neuber analysis. However, when the nut is assembled on the threaded region of the bolt, a different picture emerges. In this case, for both root radii considered in the analysis, there is a peak stress at the last engaged thread, which is higher than the UTS of the material (Fig. 10). Although this peak stress is likely to be a conservative value because the housing is not perfectly rigid, it is a close approximation of the actual true stress developed at the thread root. Therefore, if the nut is taken into account, the conclusion is that a crack will nucleate at the root of the last engaged thread when the bolt is loaded in tension and the nut is assembled.
30 25 Nut region Last engaged thread
Thread
20 15 10
1760MPa r=0.340mm
5
FEA results for r=0.577mm FEA results for r=0.340mm
0
0
500
1000
1620MPa r=0.577mm
1500
Thread root longitudinal stress, σyy (MPa) Fig. 10. Thread root longitudinal stress against thread position.
2000
924
M.T. Milan et al. / Engineering Failure Analysis 11 (2004) 915–924
As soon as the crack initiates, the peak ryy stress is partially relieved and the crack propagates by fatigue until the catastrophic failure takes place.
4. Conclusions The locking bolt used for assembling speed reducer housings failed due to the high stresses developed at the thread root as a consequence of the applied assembly load. Additionally, it is important to highlight that other factors such as surface defects, thread root radius smaller than the nominal value and low toughness of the material also contributed to the crack nucleation process.
5. Recommendations (a) (b) (c) (d)
Reduce the assembly load. Increase the thread radius. Reassess the heat treatment procedure in order to increase the toughness properties of the steel. Improve the control of the surface rolling process to avoid defects and non-uniformity of root radius.
Acknowledgements Thanks are due to the Department of Mechanical Engineering – School of Engineering of S~ao Carlos – USP for providing access to the Finite Element Code ANSYS used in this work and to Renk Zanini S.A. – Brazil for authorizing the publication of this work.
References [1] Neuber H. Theory of notch stress: principles for exact calculation of strength with reference to structure form and materials. Washigton DC, USA: Office of Technical Services, Department of Commerce; 1964. [2] Bannantine JA, Comer JJ, Handrock JL. Fundamentals of metal fatigue analysis. New Jersey: Prentice-Hall Inc.; 1990. [3] Peterson RE. Stress concentration factors. New York: Wiley; 1974.