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Fatigue failure analysis of a spring for elevator doors
Engineering Failure Analysis 17 (2010) 731–738
Contents lists available at ScienceDirect
Engineering Failure Analysis journal homepage: www.elsevier.com/locate/engfailanal
Fatigue failure analysis of a spring for elevator doors R. Rivera *, A. Chiminelli, C. Gómez, J.L. Núñez Laboratorio de Materiales y Simulación Computacional del Área de Investigación, Desarrollo y Servicios Tecnológicos, Instituto Tecnológico de Aragón, C/María de Luna 8, 50018 Zaragoza, Spain
a r t i c l e
i n f o
Article history: Available online 10 September 2009 Keywords: Fatigue failure Inclusions Spring
a b s t r a c t The present work details a study performed for the determination of the causes of the premature rupture of a spring from an elevator door control mechanism. The study is based on the general methodology applicable to failure analysis. The results obtained in the experimental analysis and the analytical calculations lead to the conclusion that the fracture of the spring was caused by a mechanical fatigue mechanism whose origin is related to the presence in the periphery of the material of inclusions and superficial folds (stress concentrators), probably aggravated by the tensional state derived from the lack of alignment in the application of the load on the spring with respect to its axial axis. Ó 2009 Elsevier Ltd. All rights reserved.
1. Introduction The present article describes the procedure applied and the results obtained of a failure analysis of a tension spring belonging to the door control mechanism of an elevator in order to determine the causes of its premature rupture in service. The methodology is mainly based on experimental techniques commonly used for failure analysis [1]. The first phase of the study was the compilation of information regarding the component and its operation. Subsequent to the visual inspection of the spring, the fracture was characterized at macro and microscopic level (SEM). From these first analyses, the rupture mechanism was determined, and together with the study of the material fabrication process and the spring design verification through analytic calculations, the failure causes of the component was identified and classified as design, use/maintenance or fabrication failure. The spring analysed corresponds to those used in certain opening/closing mechanisms for doors in which they are submitted to cyclic tension–tension loads. These components are usually made with mild steel specific for springs, such as the SH designation according to EN-10270-1. The geometric characteristics of the analysed spring and the chemical composition of the associated steel are shown in Tables 1 and 2 respectively. Loads generated during the door operation have been established experimentally using dynamometric cells in real door assemblies. The results obtained from these measurements are shown in Table 3. Under these loads, a minimum of 1,200,000 work cycles without fissures, cracks or permanent deformations that could affect the component operation is required. The following sections describe the procedure and the results obtained in the present study.
* Corresponding author. Tel.: +34 976010000; fax: +34 976716298. E-mail address: [email protected] (R. Rivera). 1350-6307/$ - see front matter Ó 2009 Elsevier Ltd. All rights reserved. doi:10.1016/j.engfailanal.2009.08.018
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R. Rivera et al. / Engineering Failure Analysis 17 (2010) 731–738
Table 1 Geometric characteristics of the spring analysed. Mean diameter (mm) Wire diameter (mm) Spring length without loads (mm)
10 1.2 530
Table 2 Steel composition of the spring (designation SH considering EN-10207-1). Element
Min.
Max.
Carbon (%) Copper (%) Manganese (%) Silicon (%) Phosphorus (%) Sulfur (%)
0.35
1.00 0.2 1.20 0.3 0.035 0.035
0.5 0.1
Table 3 Loads acting on the spring in service. Position
Length (mm)
Load (N)
Door open Door closed
780 1010
26 43
2. Experimental analysis 2.1. Macroscopic analysis The sample is constituted by a spring fragment of 127 mm length. The surface fracture to be analysed is located in one of the sides, see Fig. 1. On the opposite side of the fracture location, the spring coil suffers from some plastic deformation in the material and loss of linearity from the axle of the strain transmission. Macroscopic anomalies are not detected in the outer surface of the spring. There is a continuous mark on the inner surface of the spring coil, see Fig. 2.
2.2. Macrofractographic analysis A macrofractographic analysis of the spring fracture has been carried out by means of stereoscopic magnification. The fracture progresses across one of the coils of the spring according to several planes with different orientations. The surface shows marks oriented in the direction of the fracture propagation. These marks allow the origin of the fracture to be
Fig. 1. General macrograph of the spring fragment.
R. Rivera et al. / Engineering Failure Analysis 17 (2010) 731–738
733
Fig. 2. Detailed macrograph of the spring side where the fracture is located, inner surface.
Fig. 3. Spring fracture scheme.
located in the inner surface of the spring, in the proximity of the superficial mark appearing on the inner surface of the spring coil, see Fig. 3. The area of origin of the rupture is characterized as a flat fracture, with elliptical marks concentrically distributed in the origin zone. These macrocharacters of the fracture are consistent with the actuation of a mechanical fatigue mechanism [2]. The area of the fracture associated with the fatigue mechanism, origin and progression, corresponds approximately to 50% of the total fracture area. This seems to suggest that the tensional level was medium when the fracture took place. Finally, the remainder of the fracture surface is associated with the final fracture zone and apparently presents a ductile macromorphology characterized by a dull surface with the presence of deformation of the material. 2.3. Scanning electron microscopy (SEM) and X-ray dispersion analysis (EDS) The microfractographic analysis of the surface fracture was carried out by means of an electronic microscope SEM EDX Hitachi S-3400 N, variable pressure with EDX Röntec XFlash of Si(Li). As a result of this analysis, the origin and the progression of the fracture was characterized by the presence of fatigue striations perpendicular to the direction of the fracture progression. This morphology is characteristic of the actuation of a mechanical fatigue mechanism [3], see Fig. 4. Some inclusions are detected in a sector of the inner surface of the spring linked to the origin of the fracture. The elemental nature of the inclusions determined by X-ray dispersion analysis (EDS) is composed of silicon, sulphur, aluminium, potassium, calcium and oxygen [4], see Fig. 5. The surface of the final fracture zone shows ductile dimples that are formed by microvoid coalescence [3], see Fig. 6. 2.4. Light microscopic analysis Additionally, metallographic tests were prepared from a longitudinal section of the spring that contained the fracture surface in a zone close to the fracture origin and a transversal section of the spring, see Fig. 7.
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R. Rivera et al. / Engineering Failure Analysis 17 (2010) 731–738
Fig. 4. Electronic micrograph of the origin zone of the fracture.
Fig. 5. Electronic micrograph and EDS spectrum of the inclusions connected with the origin of the fracture.
The material microstructure of the spring can be observed in Figs. 8 and 9. The continuous mark located on the inner surface of the spring coil is related to the presence of folds and superficial plastic deformation of the material associated with the manufacturing processes of the spring, see Fig. 8. The main fracture of the spring is located next to the superficial mark. Parallel secondary cracks to the main fracture are detected. They offer the same progression and morphology as the main fractures and are located in the proximity of the superficial mark, see Fig. 9. There are folds and inclusions (impurities) in the surface of the spring near the fracture surface with a depth of 30 lm in the analysed section, see Fig. 9. 2.5. Vickers hardness measurements In order to complete the material characterization, Vickers hardness measurements (HV0, 3) were carried out according to UNE-EN ISO 6507-1:2006 on the section analysed by light microscopy . The test results are included in Table 4. The values of the material hardness are consistent with the thermomechanical treatment of the spring.
R. Rivera et al. / Engineering Failure Analysis 17 (2010) 731–738
Fig. 6. Electronic micrograph of the final fracture zone.
Fig. 7. Location of the analysed sections.
Fig. 8. Optical micrograph in etching condition of the inner surface of the coil adjacent to the fracture.
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R. Rivera et al. / Engineering Failure Analysis 17 (2010) 731–738
Fig. 9. Optical micrograph in etching condition of the inner surface of the fractured coil.
Table 4 Vickers hardness measurements (HV0, 3). Reference
HV0, 3 hardness
Average HV0, 3 hardness
Spring – zone near the failure
692 700 680
691
Spring – zone far from the failure
673 671 664
669
3. Fatigue life verification The results obtained from the failure analysis were verified with an analytic calculation to estimate the fatigue life of the springs and to check that the rupture was not a consequence of a design/selection failure. The analysis carried out covers the following points: – Maximum shear stress calculation in helicoidal springs with circular wire section under axial load (main spring axis). – Determination of ultimate shear strength and fatigue shear strength for the spring material. – Security factor calculation for current spring design considering fatigue conditions and ‘‘infinite life” design using the Goodman model.
3.1. Maximum shear stress calculation in service conditions The maximum shear stress (smax) in the spring wire can be calculated as a sum of a direct shear stress and a stress associated to the torsional moment generated by the axial force [5]:
smax ¼
4F
p d2
þ
8F D
p d3
ð1Þ
where F is the axial force acting on the spring, D is the mean diameter and d is the wire diameter. Defining the spring index C = D/d, the previous equation can be arranged as follows:
smax ¼ K s
8F D
p d3
with
Ks ¼ 1 þ
1 2C
where Ks is the correction factor of direct shear stress.
ð2Þ
R. Rivera et al. / Engineering Failure Analysis 17 (2010) 731–738
737
When the spring is working under fatigue loads, it is necessary to consider also the curvature effect [5]. This effect appears as an overload, concentrated in the inner face of the spring coil. Both corrections (direct shear stress and curvature effect) can be integrated in what is called the Wahl factor (KW):
KW ¼
4 C 1 0:615 þ 4C4 C
ð3Þ
Under fatigue conditions, the stresses can be considered as the sum of two components, an alternating shear stress sa and a mean shear stress sm. The curvature effect must be applied only to the alternating shear stresses, the components that may cause fatigue [5].
sa ¼ K W
8 Fa D
p d3
sm ¼ K s
8 Fm D
p d3
ð4Þ
where Fa y Fm are the alternating and mean forces respectively and can be calculated through the following expressions:
Fa ¼
F max F min 2
Fm ¼
F max þ F min 2
ð5Þ
being Fmax = 43 N and Fmin = 26 N (Table 3). From these expressions and the values defined in Table 1 it has been obtained that:
sa ¼ 147:3 MPa and sm ¼ 538:9 MPa 3.2. Ultimate and fatigue shear strength determination The ultimate shear strength Ssu and the fatigue shear strength in inverted alternating stress cycles Sse (fatigue resistance in cases in which the mean shear stresses are null) are factors of major importance in fatigue spring design. Both parameters are wire diameter dependent, and are usually estimated from experimental values and semi-empirical expressions. In this context, it is possible to find various calculation models proposed in the literature, the majority of them offering similar results. In the present work, a model analogous to that suggested in the SAE Spring Manual [6] has been used, which has been demonstrated to work correctly in numerous cases. This model is defined for a life of 10 million cycles, equivalent to an ‘‘infinite life” design. The ultimate shear strength Ssu and the fatigue shear strength Sse can be calculated through this model from the ultimate traction strength Stu by means of the following expressions:
Ssu ¼ 0:5 Stu
ð6Þ
Sse ¼ 0:15 Stu
ð7Þ
Considering a value for Stu of 2285 MPa (EN-10270-1) estimated from the hardness values obtained experimentally:
Ssu ¼ 1142:5 MPa and Sse ¼ 342:75 MPa
3.3. Security factor calculation for fatigue As mentioned above, the security factor calculation has been carried out considering the Goodman model [2,5–7], one of the most widely used and recognized criteria in fatigue design of components. The criterion is expressed analytically through the following equation:
sa Sse
þ
sm Ssu
¼
1 n
ð8Þ
Substituting in (8), taking into account the strength values Ssu and Sse calculated in the previous section, the security factor obtained for the spring analysed is n = 1.12. This result verifies that the spring is appropriate for the service conditions specified and the cycles estimated for the component. 4. Conclusions Based on the results of the experimental analysis performed on the spring fragment and the analytical calculations, it can be concluded that the fracture of the spring is related with a manufacturing failure, being the consequence of the actuation of a mechanical fatigue mechanism whose origin is related with the existence in the periphery of the material of inclusions and folds (stress concentrators) in the inner surface of the spring. The fracture mechanism could possibly be assisted by the tensional state derived from the misalignment of the load application on the spring.
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R. Rivera et al. / Engineering Failure Analysis 17 (2010) 731–738
Acknowledgements The authors are grateful to the INSTITUTO DE CARBOQUÍMICA of Zaragoza (CSIC) for its collaboration with the SEM characterization. References [1] [2] [3] [4] [5] [6] [7]
Failure analysis and prevention. ASM handbook, vol. 11. Metals Park (OH, USA): ASM International; 2002. Fatigue and fracture. ASM handbook, vol. 19. Metals Park (OH, USA): ASM International; 1996. Fractography, 9th ed. In: ASM handbook, vol. 12. Metals Park (OH, USA): ASM International; 1992. Failure analysis and prevention, 9th ed. ASM handbook, vol. 11. Metals Park (OH, USA): ASM International; 1992. Shigley M. Mechanical engineering design. Mc Graw Hill; 1990. Spring design manual. SAE; 1996. Dieter G. Mechanical metallurgy, fatigue of metals. Mc Graw Hill; 1988.
Contents lists available at ScienceDirect
Engineering Failure Analysis journal homepage: www.elsevier.com/locate/engfailanal
Fatigue failure analysis of a spring for elevator doors R. Rivera *, A. Chiminelli, C. Gómez, J.L. Núñez Laboratorio de Materiales y Simulación Computacional del Área de Investigación, Desarrollo y Servicios Tecnológicos, Instituto Tecnológico de Aragón, C/María de Luna 8, 50018 Zaragoza, Spain
a r t i c l e
i n f o
Article history: Available online 10 September 2009 Keywords: Fatigue failure Inclusions Spring
a b s t r a c t The present work details a study performed for the determination of the causes of the premature rupture of a spring from an elevator door control mechanism. The study is based on the general methodology applicable to failure analysis. The results obtained in the experimental analysis and the analytical calculations lead to the conclusion that the fracture of the spring was caused by a mechanical fatigue mechanism whose origin is related to the presence in the periphery of the material of inclusions and superficial folds (stress concentrators), probably aggravated by the tensional state derived from the lack of alignment in the application of the load on the spring with respect to its axial axis. Ó 2009 Elsevier Ltd. All rights reserved.
1. Introduction The present article describes the procedure applied and the results obtained of a failure analysis of a tension spring belonging to the door control mechanism of an elevator in order to determine the causes of its premature rupture in service. The methodology is mainly based on experimental techniques commonly used for failure analysis [1]. The first phase of the study was the compilation of information regarding the component and its operation. Subsequent to the visual inspection of the spring, the fracture was characterized at macro and microscopic level (SEM). From these first analyses, the rupture mechanism was determined, and together with the study of the material fabrication process and the spring design verification through analytic calculations, the failure causes of the component was identified and classified as design, use/maintenance or fabrication failure. The spring analysed corresponds to those used in certain opening/closing mechanisms for doors in which they are submitted to cyclic tension–tension loads. These components are usually made with mild steel specific for springs, such as the SH designation according to EN-10270-1. The geometric characteristics of the analysed spring and the chemical composition of the associated steel are shown in Tables 1 and 2 respectively. Loads generated during the door operation have been established experimentally using dynamometric cells in real door assemblies. The results obtained from these measurements are shown in Table 3. Under these loads, a minimum of 1,200,000 work cycles without fissures, cracks or permanent deformations that could affect the component operation is required. The following sections describe the procedure and the results obtained in the present study.
* Corresponding author. Tel.: +34 976010000; fax: +34 976716298. E-mail address: [email protected] (R. Rivera). 1350-6307/$ - see front matter Ó 2009 Elsevier Ltd. All rights reserved. doi:10.1016/j.engfailanal.2009.08.018
732
R. Rivera et al. / Engineering Failure Analysis 17 (2010) 731–738
Table 1 Geometric characteristics of the spring analysed. Mean diameter (mm) Wire diameter (mm) Spring length without loads (mm)
10 1.2 530
Table 2 Steel composition of the spring (designation SH considering EN-10207-1). Element
Min.
Max.
Carbon (%) Copper (%) Manganese (%) Silicon (%) Phosphorus (%) Sulfur (%)
0.35
1.00 0.2 1.20 0.3 0.035 0.035
0.5 0.1
Table 3 Loads acting on the spring in service. Position
Length (mm)
Load (N)
Door open Door closed
780 1010
26 43
2. Experimental analysis 2.1. Macroscopic analysis The sample is constituted by a spring fragment of 127 mm length. The surface fracture to be analysed is located in one of the sides, see Fig. 1. On the opposite side of the fracture location, the spring coil suffers from some plastic deformation in the material and loss of linearity from the axle of the strain transmission. Macroscopic anomalies are not detected in the outer surface of the spring. There is a continuous mark on the inner surface of the spring coil, see Fig. 2.
2.2. Macrofractographic analysis A macrofractographic analysis of the spring fracture has been carried out by means of stereoscopic magnification. The fracture progresses across one of the coils of the spring according to several planes with different orientations. The surface shows marks oriented in the direction of the fracture propagation. These marks allow the origin of the fracture to be
Fig. 1. General macrograph of the spring fragment.
R. Rivera et al. / Engineering Failure Analysis 17 (2010) 731–738
733
Fig. 2. Detailed macrograph of the spring side where the fracture is located, inner surface.
Fig. 3. Spring fracture scheme.
located in the inner surface of the spring, in the proximity of the superficial mark appearing on the inner surface of the spring coil, see Fig. 3. The area of origin of the rupture is characterized as a flat fracture, with elliptical marks concentrically distributed in the origin zone. These macrocharacters of the fracture are consistent with the actuation of a mechanical fatigue mechanism [2]. The area of the fracture associated with the fatigue mechanism, origin and progression, corresponds approximately to 50% of the total fracture area. This seems to suggest that the tensional level was medium when the fracture took place. Finally, the remainder of the fracture surface is associated with the final fracture zone and apparently presents a ductile macromorphology characterized by a dull surface with the presence of deformation of the material. 2.3. Scanning electron microscopy (SEM) and X-ray dispersion analysis (EDS) The microfractographic analysis of the surface fracture was carried out by means of an electronic microscope SEM EDX Hitachi S-3400 N, variable pressure with EDX Röntec XFlash of Si(Li). As a result of this analysis, the origin and the progression of the fracture was characterized by the presence of fatigue striations perpendicular to the direction of the fracture progression. This morphology is characteristic of the actuation of a mechanical fatigue mechanism [3], see Fig. 4. Some inclusions are detected in a sector of the inner surface of the spring linked to the origin of the fracture. The elemental nature of the inclusions determined by X-ray dispersion analysis (EDS) is composed of silicon, sulphur, aluminium, potassium, calcium and oxygen [4], see Fig. 5. The surface of the final fracture zone shows ductile dimples that are formed by microvoid coalescence [3], see Fig. 6. 2.4. Light microscopic analysis Additionally, metallographic tests were prepared from a longitudinal section of the spring that contained the fracture surface in a zone close to the fracture origin and a transversal section of the spring, see Fig. 7.
734
R. Rivera et al. / Engineering Failure Analysis 17 (2010) 731–738
Fig. 4. Electronic micrograph of the origin zone of the fracture.
Fig. 5. Electronic micrograph and EDS spectrum of the inclusions connected with the origin of the fracture.
The material microstructure of the spring can be observed in Figs. 8 and 9. The continuous mark located on the inner surface of the spring coil is related to the presence of folds and superficial plastic deformation of the material associated with the manufacturing processes of the spring, see Fig. 8. The main fracture of the spring is located next to the superficial mark. Parallel secondary cracks to the main fracture are detected. They offer the same progression and morphology as the main fractures and are located in the proximity of the superficial mark, see Fig. 9. There are folds and inclusions (impurities) in the surface of the spring near the fracture surface with a depth of 30 lm in the analysed section, see Fig. 9. 2.5. Vickers hardness measurements In order to complete the material characterization, Vickers hardness measurements (HV0, 3) were carried out according to UNE-EN ISO 6507-1:2006 on the section analysed by light microscopy . The test results are included in Table 4. The values of the material hardness are consistent with the thermomechanical treatment of the spring.
R. Rivera et al. / Engineering Failure Analysis 17 (2010) 731–738
Fig. 6. Electronic micrograph of the final fracture zone.
Fig. 7. Location of the analysed sections.
Fig. 8. Optical micrograph in etching condition of the inner surface of the coil adjacent to the fracture.
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R. Rivera et al. / Engineering Failure Analysis 17 (2010) 731–738
Fig. 9. Optical micrograph in etching condition of the inner surface of the fractured coil.
Table 4 Vickers hardness measurements (HV0, 3). Reference
HV0, 3 hardness
Average HV0, 3 hardness
Spring – zone near the failure
692 700 680
691
Spring – zone far from the failure
673 671 664
669
3. Fatigue life verification The results obtained from the failure analysis were verified with an analytic calculation to estimate the fatigue life of the springs and to check that the rupture was not a consequence of a design/selection failure. The analysis carried out covers the following points: – Maximum shear stress calculation in helicoidal springs with circular wire section under axial load (main spring axis). – Determination of ultimate shear strength and fatigue shear strength for the spring material. – Security factor calculation for current spring design considering fatigue conditions and ‘‘infinite life” design using the Goodman model.
3.1. Maximum shear stress calculation in service conditions The maximum shear stress (smax) in the spring wire can be calculated as a sum of a direct shear stress and a stress associated to the torsional moment generated by the axial force [5]:
smax ¼
4F
p d2
þ
8F D
p d3
ð1Þ
where F is the axial force acting on the spring, D is the mean diameter and d is the wire diameter. Defining the spring index C = D/d, the previous equation can be arranged as follows:
smax ¼ K s
8F D
p d3
with
Ks ¼ 1 þ
1 2C
where Ks is the correction factor of direct shear stress.
ð2Þ
R. Rivera et al. / Engineering Failure Analysis 17 (2010) 731–738
737
When the spring is working under fatigue loads, it is necessary to consider also the curvature effect [5]. This effect appears as an overload, concentrated in the inner face of the spring coil. Both corrections (direct shear stress and curvature effect) can be integrated in what is called the Wahl factor (KW):
KW ¼
4 C 1 0:615 þ 4C4 C
ð3Þ
Under fatigue conditions, the stresses can be considered as the sum of two components, an alternating shear stress sa and a mean shear stress sm. The curvature effect must be applied only to the alternating shear stresses, the components that may cause fatigue [5].
sa ¼ K W
8 Fa D
p d3
sm ¼ K s
8 Fm D
p d3
ð4Þ
where Fa y Fm are the alternating and mean forces respectively and can be calculated through the following expressions:
Fa ¼
F max F min 2
Fm ¼
F max þ F min 2
ð5Þ
being Fmax = 43 N and Fmin = 26 N (Table 3). From these expressions and the values defined in Table 1 it has been obtained that:
sa ¼ 147:3 MPa and sm ¼ 538:9 MPa 3.2. Ultimate and fatigue shear strength determination The ultimate shear strength Ssu and the fatigue shear strength in inverted alternating stress cycles Sse (fatigue resistance in cases in which the mean shear stresses are null) are factors of major importance in fatigue spring design. Both parameters are wire diameter dependent, and are usually estimated from experimental values and semi-empirical expressions. In this context, it is possible to find various calculation models proposed in the literature, the majority of them offering similar results. In the present work, a model analogous to that suggested in the SAE Spring Manual [6] has been used, which has been demonstrated to work correctly in numerous cases. This model is defined for a life of 10 million cycles, equivalent to an ‘‘infinite life” design. The ultimate shear strength Ssu and the fatigue shear strength Sse can be calculated through this model from the ultimate traction strength Stu by means of the following expressions:
Ssu ¼ 0:5 Stu
ð6Þ
Sse ¼ 0:15 Stu
ð7Þ
Considering a value for Stu of 2285 MPa (EN-10270-1) estimated from the hardness values obtained experimentally:
Ssu ¼ 1142:5 MPa and Sse ¼ 342:75 MPa
3.3. Security factor calculation for fatigue As mentioned above, the security factor calculation has been carried out considering the Goodman model [2,5–7], one of the most widely used and recognized criteria in fatigue design of components. The criterion is expressed analytically through the following equation:
sa Sse
þ
sm Ssu
¼
1 n
ð8Þ
Substituting in (8), taking into account the strength values Ssu and Sse calculated in the previous section, the security factor obtained for the spring analysed is n = 1.12. This result verifies that the spring is appropriate for the service conditions specified and the cycles estimated for the component. 4. Conclusions Based on the results of the experimental analysis performed on the spring fragment and the analytical calculations, it can be concluded that the fracture of the spring is related with a manufacturing failure, being the consequence of the actuation of a mechanical fatigue mechanism whose origin is related with the existence in the periphery of the material of inclusions and folds (stress concentrators) in the inner surface of the spring. The fracture mechanism could possibly be assisted by the tensional state derived from the misalignment of the load application on the spring.
738
R. Rivera et al. / Engineering Failure Analysis 17 (2010) 731–738
Acknowledgements The authors are grateful to the INSTITUTO DE CARBOQUÍMICA of Zaragoza (CSIC) for its collaboration with the SEM characterization. References [1] [2] [3] [4] [5] [6] [7]
Failure analysis and prevention. ASM handbook, vol. 11. Metals Park (OH, USA): ASM International; 2002. Fatigue and fracture. ASM handbook, vol. 19. Metals Park (OH, USA): ASM International; 1996. Fractography, 9th ed. In: ASM handbook, vol. 12. Metals Park (OH, USA): ASM International; 1992. Failure analysis and prevention, 9th ed. ASM handbook, vol. 11. Metals Park (OH, USA): ASM International; 1992. Shigley M. Mechanical engineering design. Mc Graw Hill; 1990. Spring design manual. SAE; 1996. Dieter G. Mechanical metallurgy, fatigue of metals. Mc Graw Hill; 1988.