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On the behaviour of non-propagating cracks in steel and aluminium castings
Engineering Fracture Mechanics 220 (2019) 106670
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On the behaviour of non-propagating cracks in steel and aluminium castings
T
M. Schuscha , R. Aigner, S. Pomberger, M. Oberreiter, M. Leitner, M. Stoschka ⁎
Christian Doppler Laboratory for Manufacturing Process based Component Design, Montanuniversität Leoben, Franz Josef-Straße 18, Leoben 8700, Austria
ARTICLE INFO
ABSTRACT
Keywords: Non-propagating cracks Stress intensity factor Casting Aluminium Steel
Casting defects as well as sharp notches can serve as initial points for fatigue cracks under cyclic loading. On the contrary, the cyclic material crack resistance counteracts to crack propagation. Hence, an incipient crack can arrest completely, even though a constant cyclic load is applied. Considering a short propagating crack, the local stress intensity factor, which represents the crack growth driving force, increases due to the crack extension, yet crack arrest may occur. Such an arresting of growing cracks can be traced back to an increase of the materials resistance in terms of crack closure effects. This paper deals with the evaluation of the cyclic short crack behaviour and the assessment of non-propagating cracks for cast aluminium and cast steel in terms of the Frost diagram. At first, single edge notched bending specimens are machined out of both cast materials and investigated in regard to their fracture mechanical short and long crack growth behaviour under varying stress ratios. Moreover, the data is analysed in terms of the short crack resistance (R-curve) and the subsequent long crack growth behaviour. Secondly, detectable surface porosity defects, regarding the aluminium material, and sharp surface notches, as in case of cast steel, are investigated by a linear elastic finite-element simulation to evaluate the local stress concentration factors numerically. Finally, Frost diagrams are set up for both materials and well approved by the detected non-propagating cracks. A final comparison of the investigated fatigue test data points and the Frost diagrams reveals a sound agreement validating the applicability of the presented approach.
1. Introduction This work contributes to the material characterization regarding non-propagating cracks originating from defects and sharp notches in aluminium and steel castings. Special focus is laid on the evaluation of the material dependent short- and long crack behaviour. Investigations of non-propagating cracks originating from material flaws and sharp notches have already been thoroughly researched [1–8]. Tanaka et al. extended the assessment model by additionally considering the crack closure effects [9–11]. Relating to mixed-mode conditions, Susmel and Taylor investigated the behaviour non-propagating cracks under in-phase mode I and II loading [12]. Verreman and Limodin set up a relation between the stress concentration factor Kt and the normalized stress intensity factor kn [13]. In a more recent work, Aman shows the influence of adjacent flaws on the material’s fatigue and non-propagating cracks [14]. Furthermore, Chapetti and Guerrero introduced an approach for the assessment of the notch sensitivity and size effect of bunt and
⁎
Corresponding author. E-mail address: [email protected] (M. Schuscha).
https://doi.org/10.1016/j.engfracmech.2019.106670 Received 1 April 2019; Received in revised form 19 August 2019; Accepted 9 September 2019 Available online 17 September 2019 0013-7944/ © 2019 Elsevier Ltd. All rights reserved.
Engineering Fracture Mechanics 220 (2019) 106670
M. Schuscha, et al.
sharp notches [15]. Larrosa et al. formulated an approach, which utilizes the short crack growth and a finite element simulation for a direct determination of the fatigue limits, which also considers the influence of the components boundaries [16]. Sadananda et al. introduced a feasible assessment model, which calculates the minimum stress intensity factor of a growing crack for the evaluation of non-propagating cracks [17]. Steimbreger and Chapetti analysed the influence of weld undercuts on the fatigue strength of steel and aluminium materials based on Frost’s approach [18]. In general, the distinctive fatigue life behaviour of sharp and blunt notches can be assessed in terms of Kt and Kf , whereas Kt represents the stress concentration factor and Kf the notch fatigue factor under constant amplitude cyclic loading. As an incipient crack from a sharp notch propagates, the crack growth driving force, defined as the stress intensity factor (SIF), increases in case of a constant loading amplitude. Hence, this material behaviour is representative for short cracks. As the materials crack growth resistance is diversified by numerous effects, the initial crack may rest and a further propagation of the crack can only be affected by increasing the applied cyclic load. As summarized in [8], such non-propagating cracks have already been detected and researched in case of: (1) (2) (3) (4) (5) (6) (7) (8)
Cracks originating from sharp notches. Free surface short cracks. Microstructural inhomogeneities obstructing crack propagation. Blunting of cracks in low-strength ductile materials. Application of local overloads. Cracks growing in a plastic zone caused by compression-compression loads. Short cracks in creeping materials. Crack growth subjected to oxide- and plasticity-induced crack closure.
Considering a component with inherent micro-cracks caused by the manufacturing process, two factors establish the short crack growth behaviour: the stress intensity factor as the propagations driving force and the material’s varying resistance. The linear elastic SIF is related to the externally applied load. The material can also exhibit either an increasing or decreasing resistance relying on local inhomogeneities in the microstructure or affected by crack closure effects [19]. For a continuous crack growth it is crucial that the net driving force is greater than the material’s resistance. Additionally to the external load, the internal stresses also have to be taken into account to obtain an effective crack growth driving force, which can be either in tensile or compression stress state. Finally the net stress fields, that result from both internal and external loads, have to exceed the material’s resistance to support further crack growth. Therefore, non-propagating cracks occur as the net driving force drops beyond the materials resistance. In order to assess the occurrence of non-propagating cracks in aluminium and cast steel alloys, following steps are performed:
• Firstly, crack propagation tests are conducted enabling the determination of the material’s crack growth resistance. Additionally, • • •
the long crack threshold value is converted into the threshold value, which is valid for V-notches with distinct opening angles for a proper assessment of the relating specimens. Secondly, both Frost diagrams are set-up based on the prior determined data for the assessment of the non-propagating cracks. Thirdly, linear elastic finite element analysis of defects and V-shaped notches at which non-propagating cracks could be determined are performed in order to assess the local stress concentration factor Kt . Finally, the fatigue test data points including non-propagating cracks are compared to the Frost diagram to validate the applicability of the presented approach. Therefore, this work scientifically contributes to following main topics:
• Development of Frost diagrams for aluminium and steel cast alloy based on crack propagation tests considering crack closure effects. • Study of non-propagating cracks for surface imperfections in case of aluminum cast alloy evaluating the linear-elastic stress concentration by numerical analysis. • Implementation of the notch stress intensity factor (NSIF) concept into the Frost approach for V-notched steel cast material considering the notch opening angle.
2. Crack growth resistance and non-propagating cracks In case of a short crack the material’s resistance corresponds to the effective stress intensity factor threshold Kth, eff . As the SIF, caused by an external load and the internal stresses, exceeds the effective threshold, the short crack starts to grow. Accompanying to the crack growth, an increase in the crack resistance occurs which can be attributed to the build-up of crack closure effects [20]. This behaviour can evaluated as the cyclic crack resistance (R-) curve [21,22]. Depending on the material and manufacturing condition, the crack resistance can increase with the crack extension from the small (effective) Kth, eff to the long crack threshold range Kth, lc , as illustrated in Fig. 1. Thus, the R-curve describes the transition of the threshold Kth starting from Kth, eff at a crack extension a = 0 mm towards the long crack threshold Kth, lc . The shift from short- to long crack growth threshold can be expressed in terms of an exponential function, see Eq. (1), utilizing the characteristic lengths li and the weighting factors i [20]. The parameter li can be considered as imaginary length scales, that 2
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Fig. 1. Representative structure of an R-curve.
describes the built-up of the crack closure effects and therefore affect the shape of the resistance curve, details see [20]. n
Kth = Kth, eff + ( Kth, lc
Kth, eff )· 1
i · exp i=1
a li
(1)
The long crack growth behaviour is not a representative statement of the material’s intrinsic resistance since it inherits crack closure effects driven by cyclic crack flanks contact, unless the experimental tests run at stress ratios R 0.7 [22,23]. It is well known that the stress ratio has a significant influence on the material’s long crack threshold [21–25]. As the incipient short crack reaches the long crack threshold, the common linear elastic fracture mechanical law by Paris and Erdogan [26] can be utilized to assess further crack propagation. Concerning the assessment of sharp notches, Frost analysed the fatigue behaviour of notched plates and cylindrical bars under cyclic tensile and rotating bending tests [27]. Thereby, an relation between the long crack threshold and the plain fatigue limit range 0 was found regarding the assessment of notched specimens. The experimental results exceeded the estimated limits for very high stress concentration factors Kt . As it is illustrated in Fig. 2, the consideration of the long crack threshold deduces a region of nonpropagating cracks. If a cyclic loaded sharp notch is located in this area, an incipient crack will probably start to propagate, depending on the previously stated factors. Yet, based on the effective materials resistance behaviour, short propagating cracks can be arrested, if the crack-tip driving force is smaller than the long crack threshold Kth, lc . The branch point between the linear elastic notch mechanics curve and the fracture mechanically determined limit is known as the characteristic stress concentration factor K t . In addition, it should be stated that the Frost diagram reports the notch fatigue limit as function of the stress concentration factor Kt for a constant notch depth a [29,28]. 3. Materials and threshold testing In this work two different materials are utilized regarding the assessment of non-propagating cracks: representing a common steel
Fig. 2. Representative structure of Frost diagram. 3
Engineering Fracture Mechanics 220 (2019) 106670
M. Schuscha, et al.
Table 1 Nominal chemical composition of the investigated materials in weight percent [30,31]. G21Mn5 + N
C [%] 0.17–0.23
Mn [%] 1.1–1.3
Si [%] −0.6
Cr [%] −0.3
P [%] −0.02
S [%] −0.015
EN AC-46200
Si [%] 7.5–8.5
Cu [%] 2.0–3.5
Fe [%] 0.8
Mn [%] 0.15–0.65
Mg [%] 0.05–0.55
Ti [%] 0.25
Fig. 3. SENB specimen geometry for fracture mechanical testing.
in casting application, the G21Mn5 steel in a normalized condition as well as an Al-Si-cast alloy with T6 heat treatment as specified in EN AC-46200 are studied. An overview of the corresponding nominal chemical compositions are given in Table 1. According to the material standards [30–32] the yield and ultimate tensile strengths for EN AC-46200 and G21Mn5 are YS, Al = 277 MPa, UTS, Al = 326 MPa and YS, St = 300 MPa, UTS, St = 480 –620 MPa , respectively. All fracture mechanical tests were conducted on single edge notched bending specimens (SENB), according to the standard ASTME647 [33]. The specimen geometry exhibits a total length of 80 mm , a height of 24 mm and a width of 12 mm , as illustrated in Fig. 3. Furthermore, an initial notch with a depth of 4 mm is milled. Subsequently, the initial notches are sharpened by means of razor blade polishing. Afterwards, the specimens are pre-cracked in terms of a compression-compression loading at a stress ratio R = 20 until an incipient crack with a length between 100 and 200 µm is determined. The experimental investigations are performed on a RUMUL® Testtronic resonance test rig with an axial bending load at R = 1 and R = 0 stress ratios with an average frequency of 160 Hz regarding the aluminium and 190 Hz for the cast steel specimens at room temperature. Referring to the test procedure, an increasing K method with a constant K step is applied as recommended in [34]. The crack propagation is measured by the DC potential drop method. A subsequent assessment of the fracture mechanical test data considering the short crack growth behaviour facilitates material depended crack resistance curves. As depicted in Fig. 4, both materials exhibit an effective threshold Kth, eff , which represents the intrinsic material resistance. A short crack propagation by a leads to an increase of the local threshold. Due to a fully reversed crack-tip opening under an alternating stress ratio R = 1, the crack closure effects take a significantly higher influence on the long crack growth threshold, which is expressed by the more distinct increase of the R-curve. On the contrary, the tumescent stress ratio R = 0 leads to a comparably narrower increase in the crack resistance, due to the reduced crack closure effects. Comparing the fracture mechanical results of both materials, a similar behaviour throughout the propagation from short to long crack can be observed. Differences in the Rcurve behaviour between both materials can be mostly attributed to a variation in the built-up of crack closure, such as plasticity-,
Fig. 4. Resistance curves of both materials for alternating and tumescent stress ratios. 4
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Fig. 5. Crack growth behaviour of the investigated materials under R =
1 and R = 0 .
Fig. 6. Aluminium plain tension–compression specimen.
roughness- and oxide-induced effects. As the crack resistance is fully built-up and further propagation is present, the crack growth law by Paris and Erdogan [26] is applicable. The transition into the constant growth section is assessed via utilization of the modified NASGRO equation [21]. The results of the data analysis are illustrated in Fig. 5. Applicable for both materials, the tumescent load curves reach the steady Paris slope [26] earlier than the alternating results, which tend to converge to this slope at higher stress intensity values. The evaluated data of both materials are utilized for the assessment of non-propagating cracks in terms of the related Frost diagrams. Therefore, cracks that originated from sharp notches or defects and subsequently ceased their propagation, are further on evaluated according to their local stress concentration factor Kt and the applied stress . 4. Utilization of the Frost diagram The experimental investigations concerning the aluminium material are conducted under a tumescent tension–compression stress ratio utilizing an plain flat specimen geometry, as it is illustrated in Fig. 6. The specimens feature an as-casted surface on the top, that is intended to act as the primary failure origin. The remaining surfaces at the test cross section are machined and grinded during the manufacturing process to prevent fatigue failures from these surfaces. A subsequent microscopic analysis of the run-out specimen, that are exceeding ten million load cycles, exhibit surface defects, which were cut-opened during the manufacturing process. Further on, small cracks, which originated from these defects during the fatigue testing, were detected. Fig. 7 illustrates a representative surface defect and the corresponding cracks on both sides of the flaw.
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Fig. 7. Non-propagating crack detected on the free surface of the aluminium specimen No.1.
Regarding the assessment of the local stress concentration factor Kt , the shape and size of each surface defect is obtained by measuring of the flaw subsequently to the surface analysis and further integrated into an Abaqus® linear elastic finite-element model. Thereby, the boundary as well as the loading conditions are set accordingly to the experimental testing conditions, whereas the loading magnitude is set to 1 MPa. Furthermore, the finite element model is defined with quadratic elements with a reduced integration under a plain stress state. The global element size is set to 0.02 mm , whereby a refined mesh of 4.4·10 4 mm is utilized at the critical areas for a proper Kt assessment. Fig. 8 depicts the results of a finite element simulation of the surface flaw found on the specimen’s surface as well as a summarizing table of the stress concentration factors of all detected NPC’s. In case of the specimen one, which is illustrated in Figs. 7 and 8, the crack emanating from the lower tip is considered and therefore a stress concentration Kt = 5.8 is utilized for the further investigation, as marked in 8. Hence, an material related Frost diagram for the EN AC-46200 can be obtained representing the four different data points, as it is illustrated in Fig. 9.
Fig. 8. FEM simulation pertaining the determination of K t and evaluated stress concentration factors.
Fig. 9. NPC assessment: cracks originated from a defect in aluminium. 6
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Fig. 10. Notched steel specimens: 45°, 90° and 135°.
As can be seen in the figure, all test results are within the range of the NPC predicted area by the Frost diagram and therefore give a sound agreement between the tested material behaviour and the fracture mechanical approach. It should be noted that in case of aluminium castings the examined defects are shaped quite closely as cracks. Hence, the long crack threshold can be applied directly, caused by the crack-like flaws in the material in terms of size and shape. Further information on the statistically distributed defects in EN AC-46200 and the corresponding fatigue assessment is given in [32,35–37]. In terms of the G21Mn5 material, three different round bar specimen geometries, featuring V-notches with 45°, 90° and 135° opening angle, are utilized in the experimental investigations. Further, the notch tip of the specimens are designed with a notch root radius of 0.1 mm to achieve a high notch acuity and therefore an utmost high stress concentration. Fig. 10 illustrates the investigated cast steel specimens. Relating to these V-notched cast steel specimens, the NSIF concept [28,38–40] has to be applied for the determination of the corresponding long crack threshold KthV . The tests are performed on a rotating bending test rig and therefore an alternating stress ratio is applied. Details about the experimental investigations and the numerical NSIF assessment of the notched specimens are provided in depth in [41]. Due to the varying opening angle of the specimen geometries, the angle depended KIV, th has to be determined separately for each specimen geometry. According to Atzori et.al., the opening-angle dependent NSIF threshold can be established either based on the Finite-Volume Energy, the Fracture Mechanics or the Point Method approach [28]. Evaluating the rotating bending tests, the NSIF threshold is determined by utilizing the Point Method within the corresponding expressions. According to Fig. 11, the stress path along the notch bisector line can be defined as follows
(r , 0) =
KIV . 2 r
(2)
Relating to the fracture mechanical based equation, the El-Haddad length a0 [5] is specified by
a0 =
1
Kth, lc
2
(3)
0
Fig. 11. Stress path along the bisector line of the V-notch. 7
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Fig. 12. Non-propagating crack obtained on the fracture surface of notched cast steel specimen.
If a notch is subjected to mode I loading, the Point Method determines a distance of a0 /2 from the notch tip, where the plain specimen’s fatigue limit [28] is present. Therefore Eq. (2) is modified by the result of the Point Method, which enables the following expression: 0
KIV, th
=
2
( ) a0 2
(4)
Subsequently the El-Haddad length a0 is substituted to achieve a relation between Kth, lc and
KIV, th =
2 2
(1/2
))
(1 2 ) 0
KthV
[28].
K th2 , lc
(5)
It is well known, that the stress singularity at a crack tip with parallel flanks equals 0.5. But in terms of an open V-notch, the local stress singularity depends on the notch opening angle, as stated in [42]. Williams introduced the angle dependent eigenvalue , which is utilized to calculate stress singularity with the simple equation = 1 . Rotating bending specimens, which also endured ten million load cycles, are also designated as run-out samples. After cyclic testing the specimens are cooled-down in liquid nitrogen to force a material embrittlement and subsequent burst-fractured broken. A light-optical fracture surface analysis exhibits a circumferential crack on the run-out specimen, that is recognizable by a darker surface colour. The discolouration can be explained by the non-propagating cracks. An incipient crack starts to grow from the surface and stops as soon as the materials resistance exceeds the applied load, causing the occurrence of multiple NPC’s. The remaining load cycles lead to a recurrent contact between the crack flanks and therefore to a wear of the crack flanks. Fig. 12 depicts a 45° V-notched fracture surface containing a circumferential crack with a mean depth of 80 µm . In addition to the 45° specimen, NPC’s also can be found at three 90° and at two 135° geometries. As stated before, the different notch-opening angles require an individual assessment of each notch geometry. Therefore, linear elastic finite-element simulations are conducted regarding the determination of the particular stress concentration factors. The applied mesh was set to global size of 0.5 mm , whereby a local refinement to 1·10 3 mm is set for the determination of Kt . Furthermore, an axisymmetric model exhibiting full-integration Fourier CAXA84 elements is utilized. The results of the numerical simulations are illustrated in Fig. 13.
Fig. 13. Result of the FEM simulation of the 45° V-notched specimen and the evaluated K t factors of all geometries.
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The identified non-propagating cracks are illustrated as Frost diagram in Fig. 14, depicting the 45° notched specimen results in green, 90° in blue and 135° in red. Despite different stress concentration factors and distinct applied stresses, the NPC results show a sound agreement with the individual areas of non-propagating cracks. Whereas, the 45° data point (1) corresponds with the Frost design curve for 45°, the 90° data points (2,3,4) are between 10–23% below the Frost design curve for 90° and the 135° points (5,6) are 17–23% below the corresponding design curve for 135° .
Fig. 14. NPC assessment of cracks originated from sharp notches in cast steel.
5. Summary and conclusions Initial fatigue crack growth tests utilizing SENB specimen contribute to the assessment of short and long crack growth behaviour of cracks in aluminium and steel cast materials. Different stress ratios are studied during the fracture mechanical tests. The results of the investigations show a similar fracture mechanical tendency between both materials for each stress ratio. Furthermore, the investigated long crack threshold values are utilized for the development of a Frost diagram for each material. In terms of the aluminium cast material EN AC-46200, non-propagating cracks of sizes up about 100 µm , which have originated from small surface defects, are assessable. Concerning the analysis of the cast steel G21Mn5, sharp V-notched round bar specimens are tested under rotating bending, which possess also non-propagating cracks exhibiting a size of 80 µm within the early crack-growth stages. Summarizing, the investigations show a good applicability of the Frost diagram regarding non-propagating cracks in aluminium and steel castings, respectively. According to the presented research methodology, non-propagating cracks are observed after the specimen endured the given number of run-out load cycles. A review pertaining the occurrence of NPC and the assessment during growth and arresting of cracks can be investigated in more detail in further work. Based on the results of this paper following scientific conclusions can be drawn.
• The Frost diagram represents a feasible tool concerning the assessability of non-propagating cracks occurring at microstructural inhomogeneities in aluminium alloys. This extends the application from notches to casting imperfections such as defects. • The introduction of the NSIF concept into the Frost approach concerning the assessment of non-propagating cracks emanating from sharp V-notched cast steel exhibits a satisfying applicability considering the investigated notch geometries with the opening angles 45°, 90° and 135°.
Acknowledgements The financial support by the Austrian Federal Ministry for Digital and Economic Affairs and the National Foundation for Research, Technology and Development is gratefully acknowledged. Furthermore, the authors would like to thank the industrial partners BMW AG and Nemak Dillingen GmbH for the excellent mutual scientific cooperation within the CD-laboratory framework. Also I would like to acknowledge the industrial partner Siemens Mobility GmbH for their significant scientific collaboration within the CD-laboratory framework. References [1] [2] [3] [4] [5]
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[37] Aigner R, Pusterhofer S, Pomberger S, Leitner M, Stoschka M. A probabilistic Kitagawa-Takahashi diagram for fatigue strength assessment of cast aluminium alloys. Mater Sci Eng: A 2019;745:326–34. https://doi.org/10.1016/j.msea.2018.12.108. [38] Atzori B. Estimation of the fatigue strength of light alloy welds by an equivalent notch stress analysis. In: Cumulative fatigue damage conference - University of Seville 2003 cumulative fatigue damage conference, vol. 24, no. 5; 2002. p. 591–9. https://doi.org/10.1016/S0142-1123(01)00113-X. [39] Atzori B, Lazzarin P. A three-dimensional graphical aid to analyze fatigue crack nucleation and propagation phases under fatigue limit conditions. Int J Fract 2002;118(3):271–84. https://doi.org/10.1023/A:1022965909483. [40] Atzori B, Lazzarin P, Meneghetti G. Fracture mechanics and notch sensitivity. Fatigue Fract Eng Mater Struct 2003;26(3):257–67. https://doi.org/10.1046/j. 1460-2695.2003.00633.x. [41] Schuscha M, Leitner M, Stoschka M. Development of a generalized Kitagawa diagram for cast G21Mn5 steel. MATEC Web Conf 2018;165:14010. https://doi.org/ 10.1051/matecconf/201816514010. [42] Williams ML. Stress singularities resulting from various boundary conditions in angular corners of plates in extension. J Appl Mech 1952;19:526–8.
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Engineering Fracture Mechanics journal homepage: www.elsevier.com/locate/engfracmech
On the behaviour of non-propagating cracks in steel and aluminium castings
T
M. Schuscha , R. Aigner, S. Pomberger, M. Oberreiter, M. Leitner, M. Stoschka ⁎
Christian Doppler Laboratory for Manufacturing Process based Component Design, Montanuniversität Leoben, Franz Josef-Straße 18, Leoben 8700, Austria
ARTICLE INFO
ABSTRACT
Keywords: Non-propagating cracks Stress intensity factor Casting Aluminium Steel
Casting defects as well as sharp notches can serve as initial points for fatigue cracks under cyclic loading. On the contrary, the cyclic material crack resistance counteracts to crack propagation. Hence, an incipient crack can arrest completely, even though a constant cyclic load is applied. Considering a short propagating crack, the local stress intensity factor, which represents the crack growth driving force, increases due to the crack extension, yet crack arrest may occur. Such an arresting of growing cracks can be traced back to an increase of the materials resistance in terms of crack closure effects. This paper deals with the evaluation of the cyclic short crack behaviour and the assessment of non-propagating cracks for cast aluminium and cast steel in terms of the Frost diagram. At first, single edge notched bending specimens are machined out of both cast materials and investigated in regard to their fracture mechanical short and long crack growth behaviour under varying stress ratios. Moreover, the data is analysed in terms of the short crack resistance (R-curve) and the subsequent long crack growth behaviour. Secondly, detectable surface porosity defects, regarding the aluminium material, and sharp surface notches, as in case of cast steel, are investigated by a linear elastic finite-element simulation to evaluate the local stress concentration factors numerically. Finally, Frost diagrams are set up for both materials and well approved by the detected non-propagating cracks. A final comparison of the investigated fatigue test data points and the Frost diagrams reveals a sound agreement validating the applicability of the presented approach.
1. Introduction This work contributes to the material characterization regarding non-propagating cracks originating from defects and sharp notches in aluminium and steel castings. Special focus is laid on the evaluation of the material dependent short- and long crack behaviour. Investigations of non-propagating cracks originating from material flaws and sharp notches have already been thoroughly researched [1–8]. Tanaka et al. extended the assessment model by additionally considering the crack closure effects [9–11]. Relating to mixed-mode conditions, Susmel and Taylor investigated the behaviour non-propagating cracks under in-phase mode I and II loading [12]. Verreman and Limodin set up a relation between the stress concentration factor Kt and the normalized stress intensity factor kn [13]. In a more recent work, Aman shows the influence of adjacent flaws on the material’s fatigue and non-propagating cracks [14]. Furthermore, Chapetti and Guerrero introduced an approach for the assessment of the notch sensitivity and size effect of bunt and
⁎
Corresponding author. E-mail address: [email protected] (M. Schuscha).
https://doi.org/10.1016/j.engfracmech.2019.106670 Received 1 April 2019; Received in revised form 19 August 2019; Accepted 9 September 2019 Available online 17 September 2019 0013-7944/ © 2019 Elsevier Ltd. All rights reserved.
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sharp notches [15]. Larrosa et al. formulated an approach, which utilizes the short crack growth and a finite element simulation for a direct determination of the fatigue limits, which also considers the influence of the components boundaries [16]. Sadananda et al. introduced a feasible assessment model, which calculates the minimum stress intensity factor of a growing crack for the evaluation of non-propagating cracks [17]. Steimbreger and Chapetti analysed the influence of weld undercuts on the fatigue strength of steel and aluminium materials based on Frost’s approach [18]. In general, the distinctive fatigue life behaviour of sharp and blunt notches can be assessed in terms of Kt and Kf , whereas Kt represents the stress concentration factor and Kf the notch fatigue factor under constant amplitude cyclic loading. As an incipient crack from a sharp notch propagates, the crack growth driving force, defined as the stress intensity factor (SIF), increases in case of a constant loading amplitude. Hence, this material behaviour is representative for short cracks. As the materials crack growth resistance is diversified by numerous effects, the initial crack may rest and a further propagation of the crack can only be affected by increasing the applied cyclic load. As summarized in [8], such non-propagating cracks have already been detected and researched in case of: (1) (2) (3) (4) (5) (6) (7) (8)
Cracks originating from sharp notches. Free surface short cracks. Microstructural inhomogeneities obstructing crack propagation. Blunting of cracks in low-strength ductile materials. Application of local overloads. Cracks growing in a plastic zone caused by compression-compression loads. Short cracks in creeping materials. Crack growth subjected to oxide- and plasticity-induced crack closure.
Considering a component with inherent micro-cracks caused by the manufacturing process, two factors establish the short crack growth behaviour: the stress intensity factor as the propagations driving force and the material’s varying resistance. The linear elastic SIF is related to the externally applied load. The material can also exhibit either an increasing or decreasing resistance relying on local inhomogeneities in the microstructure or affected by crack closure effects [19]. For a continuous crack growth it is crucial that the net driving force is greater than the material’s resistance. Additionally to the external load, the internal stresses also have to be taken into account to obtain an effective crack growth driving force, which can be either in tensile or compression stress state. Finally the net stress fields, that result from both internal and external loads, have to exceed the material’s resistance to support further crack growth. Therefore, non-propagating cracks occur as the net driving force drops beyond the materials resistance. In order to assess the occurrence of non-propagating cracks in aluminium and cast steel alloys, following steps are performed:
• Firstly, crack propagation tests are conducted enabling the determination of the material’s crack growth resistance. Additionally, • • •
the long crack threshold value is converted into the threshold value, which is valid for V-notches with distinct opening angles for a proper assessment of the relating specimens. Secondly, both Frost diagrams are set-up based on the prior determined data for the assessment of the non-propagating cracks. Thirdly, linear elastic finite element analysis of defects and V-shaped notches at which non-propagating cracks could be determined are performed in order to assess the local stress concentration factor Kt . Finally, the fatigue test data points including non-propagating cracks are compared to the Frost diagram to validate the applicability of the presented approach. Therefore, this work scientifically contributes to following main topics:
• Development of Frost diagrams for aluminium and steel cast alloy based on crack propagation tests considering crack closure effects. • Study of non-propagating cracks for surface imperfections in case of aluminum cast alloy evaluating the linear-elastic stress concentration by numerical analysis. • Implementation of the notch stress intensity factor (NSIF) concept into the Frost approach for V-notched steel cast material considering the notch opening angle.
2. Crack growth resistance and non-propagating cracks In case of a short crack the material’s resistance corresponds to the effective stress intensity factor threshold Kth, eff . As the SIF, caused by an external load and the internal stresses, exceeds the effective threshold, the short crack starts to grow. Accompanying to the crack growth, an increase in the crack resistance occurs which can be attributed to the build-up of crack closure effects [20]. This behaviour can evaluated as the cyclic crack resistance (R-) curve [21,22]. Depending on the material and manufacturing condition, the crack resistance can increase with the crack extension from the small (effective) Kth, eff to the long crack threshold range Kth, lc , as illustrated in Fig. 1. Thus, the R-curve describes the transition of the threshold Kth starting from Kth, eff at a crack extension a = 0 mm towards the long crack threshold Kth, lc . The shift from short- to long crack growth threshold can be expressed in terms of an exponential function, see Eq. (1), utilizing the characteristic lengths li and the weighting factors i [20]. The parameter li can be considered as imaginary length scales, that 2
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Fig. 1. Representative structure of an R-curve.
describes the built-up of the crack closure effects and therefore affect the shape of the resistance curve, details see [20]. n
Kth = Kth, eff + ( Kth, lc
Kth, eff )· 1
i · exp i=1
a li
(1)
The long crack growth behaviour is not a representative statement of the material’s intrinsic resistance since it inherits crack closure effects driven by cyclic crack flanks contact, unless the experimental tests run at stress ratios R 0.7 [22,23]. It is well known that the stress ratio has a significant influence on the material’s long crack threshold [21–25]. As the incipient short crack reaches the long crack threshold, the common linear elastic fracture mechanical law by Paris and Erdogan [26] can be utilized to assess further crack propagation. Concerning the assessment of sharp notches, Frost analysed the fatigue behaviour of notched plates and cylindrical bars under cyclic tensile and rotating bending tests [27]. Thereby, an relation between the long crack threshold and the plain fatigue limit range 0 was found regarding the assessment of notched specimens. The experimental results exceeded the estimated limits for very high stress concentration factors Kt . As it is illustrated in Fig. 2, the consideration of the long crack threshold deduces a region of nonpropagating cracks. If a cyclic loaded sharp notch is located in this area, an incipient crack will probably start to propagate, depending on the previously stated factors. Yet, based on the effective materials resistance behaviour, short propagating cracks can be arrested, if the crack-tip driving force is smaller than the long crack threshold Kth, lc . The branch point between the linear elastic notch mechanics curve and the fracture mechanically determined limit is known as the characteristic stress concentration factor K t . In addition, it should be stated that the Frost diagram reports the notch fatigue limit as function of the stress concentration factor Kt for a constant notch depth a [29,28]. 3. Materials and threshold testing In this work two different materials are utilized regarding the assessment of non-propagating cracks: representing a common steel
Fig. 2. Representative structure of Frost diagram. 3
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Table 1 Nominal chemical composition of the investigated materials in weight percent [30,31]. G21Mn5 + N
C [%] 0.17–0.23
Mn [%] 1.1–1.3
Si [%] −0.6
Cr [%] −0.3
P [%] −0.02
S [%] −0.015
EN AC-46200
Si [%] 7.5–8.5
Cu [%] 2.0–3.5
Fe [%] 0.8
Mn [%] 0.15–0.65
Mg [%] 0.05–0.55
Ti [%] 0.25
Fig. 3. SENB specimen geometry for fracture mechanical testing.
in casting application, the G21Mn5 steel in a normalized condition as well as an Al-Si-cast alloy with T6 heat treatment as specified in EN AC-46200 are studied. An overview of the corresponding nominal chemical compositions are given in Table 1. According to the material standards [30–32] the yield and ultimate tensile strengths for EN AC-46200 and G21Mn5 are YS, Al = 277 MPa, UTS, Al = 326 MPa and YS, St = 300 MPa, UTS, St = 480 –620 MPa , respectively. All fracture mechanical tests were conducted on single edge notched bending specimens (SENB), according to the standard ASTME647 [33]. The specimen geometry exhibits a total length of 80 mm , a height of 24 mm and a width of 12 mm , as illustrated in Fig. 3. Furthermore, an initial notch with a depth of 4 mm is milled. Subsequently, the initial notches are sharpened by means of razor blade polishing. Afterwards, the specimens are pre-cracked in terms of a compression-compression loading at a stress ratio R = 20 until an incipient crack with a length between 100 and 200 µm is determined. The experimental investigations are performed on a RUMUL® Testtronic resonance test rig with an axial bending load at R = 1 and R = 0 stress ratios with an average frequency of 160 Hz regarding the aluminium and 190 Hz for the cast steel specimens at room temperature. Referring to the test procedure, an increasing K method with a constant K step is applied as recommended in [34]. The crack propagation is measured by the DC potential drop method. A subsequent assessment of the fracture mechanical test data considering the short crack growth behaviour facilitates material depended crack resistance curves. As depicted in Fig. 4, both materials exhibit an effective threshold Kth, eff , which represents the intrinsic material resistance. A short crack propagation by a leads to an increase of the local threshold. Due to a fully reversed crack-tip opening under an alternating stress ratio R = 1, the crack closure effects take a significantly higher influence on the long crack growth threshold, which is expressed by the more distinct increase of the R-curve. On the contrary, the tumescent stress ratio R = 0 leads to a comparably narrower increase in the crack resistance, due to the reduced crack closure effects. Comparing the fracture mechanical results of both materials, a similar behaviour throughout the propagation from short to long crack can be observed. Differences in the Rcurve behaviour between both materials can be mostly attributed to a variation in the built-up of crack closure, such as plasticity-,
Fig. 4. Resistance curves of both materials for alternating and tumescent stress ratios. 4
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Fig. 5. Crack growth behaviour of the investigated materials under R =
1 and R = 0 .
Fig. 6. Aluminium plain tension–compression specimen.
roughness- and oxide-induced effects. As the crack resistance is fully built-up and further propagation is present, the crack growth law by Paris and Erdogan [26] is applicable. The transition into the constant growth section is assessed via utilization of the modified NASGRO equation [21]. The results of the data analysis are illustrated in Fig. 5. Applicable for both materials, the tumescent load curves reach the steady Paris slope [26] earlier than the alternating results, which tend to converge to this slope at higher stress intensity values. The evaluated data of both materials are utilized for the assessment of non-propagating cracks in terms of the related Frost diagrams. Therefore, cracks that originated from sharp notches or defects and subsequently ceased their propagation, are further on evaluated according to their local stress concentration factor Kt and the applied stress . 4. Utilization of the Frost diagram The experimental investigations concerning the aluminium material are conducted under a tumescent tension–compression stress ratio utilizing an plain flat specimen geometry, as it is illustrated in Fig. 6. The specimens feature an as-casted surface on the top, that is intended to act as the primary failure origin. The remaining surfaces at the test cross section are machined and grinded during the manufacturing process to prevent fatigue failures from these surfaces. A subsequent microscopic analysis of the run-out specimen, that are exceeding ten million load cycles, exhibit surface defects, which were cut-opened during the manufacturing process. Further on, small cracks, which originated from these defects during the fatigue testing, were detected. Fig. 7 illustrates a representative surface defect and the corresponding cracks on both sides of the flaw.
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Fig. 7. Non-propagating crack detected on the free surface of the aluminium specimen No.1.
Regarding the assessment of the local stress concentration factor Kt , the shape and size of each surface defect is obtained by measuring of the flaw subsequently to the surface analysis and further integrated into an Abaqus® linear elastic finite-element model. Thereby, the boundary as well as the loading conditions are set accordingly to the experimental testing conditions, whereas the loading magnitude is set to 1 MPa. Furthermore, the finite element model is defined with quadratic elements with a reduced integration under a plain stress state. The global element size is set to 0.02 mm , whereby a refined mesh of 4.4·10 4 mm is utilized at the critical areas for a proper Kt assessment. Fig. 8 depicts the results of a finite element simulation of the surface flaw found on the specimen’s surface as well as a summarizing table of the stress concentration factors of all detected NPC’s. In case of the specimen one, which is illustrated in Figs. 7 and 8, the crack emanating from the lower tip is considered and therefore a stress concentration Kt = 5.8 is utilized for the further investigation, as marked in 8. Hence, an material related Frost diagram for the EN AC-46200 can be obtained representing the four different data points, as it is illustrated in Fig. 9.
Fig. 8. FEM simulation pertaining the determination of K t and evaluated stress concentration factors.
Fig. 9. NPC assessment: cracks originated from a defect in aluminium. 6
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Fig. 10. Notched steel specimens: 45°, 90° and 135°.
As can be seen in the figure, all test results are within the range of the NPC predicted area by the Frost diagram and therefore give a sound agreement between the tested material behaviour and the fracture mechanical approach. It should be noted that in case of aluminium castings the examined defects are shaped quite closely as cracks. Hence, the long crack threshold can be applied directly, caused by the crack-like flaws in the material in terms of size and shape. Further information on the statistically distributed defects in EN AC-46200 and the corresponding fatigue assessment is given in [32,35–37]. In terms of the G21Mn5 material, three different round bar specimen geometries, featuring V-notches with 45°, 90° and 135° opening angle, are utilized in the experimental investigations. Further, the notch tip of the specimens are designed with a notch root radius of 0.1 mm to achieve a high notch acuity and therefore an utmost high stress concentration. Fig. 10 illustrates the investigated cast steel specimens. Relating to these V-notched cast steel specimens, the NSIF concept [28,38–40] has to be applied for the determination of the corresponding long crack threshold KthV . The tests are performed on a rotating bending test rig and therefore an alternating stress ratio is applied. Details about the experimental investigations and the numerical NSIF assessment of the notched specimens are provided in depth in [41]. Due to the varying opening angle of the specimen geometries, the angle depended KIV, th has to be determined separately for each specimen geometry. According to Atzori et.al., the opening-angle dependent NSIF threshold can be established either based on the Finite-Volume Energy, the Fracture Mechanics or the Point Method approach [28]. Evaluating the rotating bending tests, the NSIF threshold is determined by utilizing the Point Method within the corresponding expressions. According to Fig. 11, the stress path along the notch bisector line can be defined as follows
(r , 0) =
KIV . 2 r
(2)
Relating to the fracture mechanical based equation, the El-Haddad length a0 [5] is specified by
a0 =
1
Kth, lc
2
(3)
0
Fig. 11. Stress path along the bisector line of the V-notch. 7
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Fig. 12. Non-propagating crack obtained on the fracture surface of notched cast steel specimen.
If a notch is subjected to mode I loading, the Point Method determines a distance of a0 /2 from the notch tip, where the plain specimen’s fatigue limit [28] is present. Therefore Eq. (2) is modified by the result of the Point Method, which enables the following expression: 0
KIV, th
=
2
( ) a0 2
(4)
Subsequently the El-Haddad length a0 is substituted to achieve a relation between Kth, lc and
KIV, th =
2 2
(1/2
))
(1 2 ) 0
KthV
[28].
K th2 , lc
(5)
It is well known, that the stress singularity at a crack tip with parallel flanks equals 0.5. But in terms of an open V-notch, the local stress singularity depends on the notch opening angle, as stated in [42]. Williams introduced the angle dependent eigenvalue , which is utilized to calculate stress singularity with the simple equation = 1 . Rotating bending specimens, which also endured ten million load cycles, are also designated as run-out samples. After cyclic testing the specimens are cooled-down in liquid nitrogen to force a material embrittlement and subsequent burst-fractured broken. A light-optical fracture surface analysis exhibits a circumferential crack on the run-out specimen, that is recognizable by a darker surface colour. The discolouration can be explained by the non-propagating cracks. An incipient crack starts to grow from the surface and stops as soon as the materials resistance exceeds the applied load, causing the occurrence of multiple NPC’s. The remaining load cycles lead to a recurrent contact between the crack flanks and therefore to a wear of the crack flanks. Fig. 12 depicts a 45° V-notched fracture surface containing a circumferential crack with a mean depth of 80 µm . In addition to the 45° specimen, NPC’s also can be found at three 90° and at two 135° geometries. As stated before, the different notch-opening angles require an individual assessment of each notch geometry. Therefore, linear elastic finite-element simulations are conducted regarding the determination of the particular stress concentration factors. The applied mesh was set to global size of 0.5 mm , whereby a local refinement to 1·10 3 mm is set for the determination of Kt . Furthermore, an axisymmetric model exhibiting full-integration Fourier CAXA84 elements is utilized. The results of the numerical simulations are illustrated in Fig. 13.
Fig. 13. Result of the FEM simulation of the 45° V-notched specimen and the evaluated K t factors of all geometries.
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The identified non-propagating cracks are illustrated as Frost diagram in Fig. 14, depicting the 45° notched specimen results in green, 90° in blue and 135° in red. Despite different stress concentration factors and distinct applied stresses, the NPC results show a sound agreement with the individual areas of non-propagating cracks. Whereas, the 45° data point (1) corresponds with the Frost design curve for 45°, the 90° data points (2,3,4) are between 10–23% below the Frost design curve for 90° and the 135° points (5,6) are 17–23% below the corresponding design curve for 135° .
Fig. 14. NPC assessment of cracks originated from sharp notches in cast steel.
5. Summary and conclusions Initial fatigue crack growth tests utilizing SENB specimen contribute to the assessment of short and long crack growth behaviour of cracks in aluminium and steel cast materials. Different stress ratios are studied during the fracture mechanical tests. The results of the investigations show a similar fracture mechanical tendency between both materials for each stress ratio. Furthermore, the investigated long crack threshold values are utilized for the development of a Frost diagram for each material. In terms of the aluminium cast material EN AC-46200, non-propagating cracks of sizes up about 100 µm , which have originated from small surface defects, are assessable. Concerning the analysis of the cast steel G21Mn5, sharp V-notched round bar specimens are tested under rotating bending, which possess also non-propagating cracks exhibiting a size of 80 µm within the early crack-growth stages. Summarizing, the investigations show a good applicability of the Frost diagram regarding non-propagating cracks in aluminium and steel castings, respectively. According to the presented research methodology, non-propagating cracks are observed after the specimen endured the given number of run-out load cycles. A review pertaining the occurrence of NPC and the assessment during growth and arresting of cracks can be investigated in more detail in further work. Based on the results of this paper following scientific conclusions can be drawn.
• The Frost diagram represents a feasible tool concerning the assessability of non-propagating cracks occurring at microstructural inhomogeneities in aluminium alloys. This extends the application from notches to casting imperfections such as defects. • The introduction of the NSIF concept into the Frost approach concerning the assessment of non-propagating cracks emanating from sharp V-notched cast steel exhibits a satisfying applicability considering the investigated notch geometries with the opening angles 45°, 90° and 135°.
Acknowledgements The financial support by the Austrian Federal Ministry for Digital and Economic Affairs and the National Foundation for Research, Technology and Development is gratefully acknowledged. Furthermore, the authors would like to thank the industrial partners BMW AG and Nemak Dillingen GmbH for the excellent mutual scientific cooperation within the CD-laboratory framework. Also I would like to acknowledge the industrial partner Siemens Mobility GmbH for their significant scientific collaboration within the CD-laboratory framework. References [1] [2] [3] [4] [5]
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