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International Journal of Fatigue journal homepage: www.elsevier.com/locate/ijfatigue

Quantitative evaluation of fatigue life of cast aluminum alloys by non-destructive testing and parameter model Y. Tijani a,b,⇑, A. Heinrietz b, T. Bruder b,c, H. Hanselka a,b a

System Reliability and Machine Acoustics SzM, University of Technology, Magdalenenstr., 4, 64289 Darmstadt, Germany Fraunhofer Institute for Structural Durability and System Reliability LBF, Bartningstr., 47, 64289 Darmstadt, Germany c BMW Group, Knorrstr., 147, 80788 Munich, Germany b

a r t i c l e

i n f o

Article history: Received 31 January 2012 Received in revised form 8 April 2013 Accepted 28 May 2013 Available online xxxx Keywords: Cast aluminum alloys Non-destructive testing Finite element simulation Fatigue calculation Parameter model

a b s t r a c t The presence of production-related defects in cast aluminum alloy components leads to reduction in their fatigue strength. The optimal use of their high strength-to-weight beneﬁts is thereby restricted. There are numerous qualitative approaches relating the defects characteristics to fatigue analysis. This work presents a method to quantitatively evaluate the fatigue life of defect-prone cast aluminum alloys. The investigation was carried-out by non-destructive analysis of cast aluminum alloy samples using X-ray computed tomography. The microstructural discontinuities were characterized and quantiﬁed in terms of defect size, morphology and distance to specimen surface. These were subsequently used as input in a new parameter model for fatigue life calculation. The results correlate with fatigue experiments and ﬁnite-element calculations. This approach provides the possibility to extensively evaluate the fatigue properties of cast aluminum alloy components based on non-destructive test methods. It guarantees an improvement of control mechanisms within the scope of quality assurance. Ó 2013 Elsevier Ltd. All rights reserved.

1. Introduction The requirement for weight reduction in automotive applications has led to increase in the use of aluminum castings [1,2]. It is primarily due to the high strength-to-weight ratio associated with cast aluminum alloys. This is in addition to the castability of components with complex geometries which can be accomplished more easily with aluminum alloys. Consequently, cast aluminum alloys present an outstanding balance of cost, properties and light weight leading to fuel efﬁciency at relatively lower cost. However, the production chain of cast aluminum components consists of physical processes that introduce pores and inclusions in the end products. These defects decrease the performance of the components by ultimately reducing the fatigue properties. Gas and shrinkage pores are some of the most common production-related defects encountered during casting of aluminum alloys, see e.g. [3,4]. The presence of pores results in microstructural discontinuities. They serve as internal geometrical notches which are usually unintended. Under applied external load, there is a high possibility of local stress concentration at the pore region. This leads to fatigue crack initiation and a subsequent reduction in fatigue strength of the cast aluminum alloy components. There are ⇑ Corresponding author at: Fraunhofer Institute for Structural Durability and System Reliability LBF, Bartningstr., 47, 64289 Darmstadt, Germany. Tel.: +49 6151 705 668. E-mail address: [email protected] (Y. Tijani).

many improvements in the industry which tend to eliminate or reduce the amount of defects. However, the production-related defects cannot be completely avoided without incurring additional costs. The evaluation of local stresses and strains by means of stress concentration factors, Kt, around external geometrical discontinuities have been reported, see e.g. [5]. These notches are usually due to non uniform cross section of the components. Fatigue life of a notched member can be predicted by using fracture mechanics approach [6]. Similarly, many models have been reported to predict the impact of defects on fatigue strength in metals [7]. Moreover, for pores originating from aluminum casting process, it has been observed that surface or near surface pores lead to fatigue crack initiation, see [8,9]. In Fig. 1, a shrinkage pore close to the specimen surface is found to have initiated the fatigue crack. In general, the knowledge of pore size, type and distribution is sufﬁcient to determine a crack-initiating pore. However, it is necessary to consider the characteristic pore parameters so as to obtain a quantitative estimation of fatigue life of cast aluminum alloys. The parameters include their sizes, morphologies and locations in the material’s microstructure. The use of computed tomography and ﬁnite element analysis to study or characterize the effect of pores on fatigue properties in cast aluminum alloys has been previously reported [10–12]. This latest work presents an approach to quantitatively calculate the fatigue life of cast aluminum alloys based on information about the pore parameters which are obtained from computed tomography data. A parameter model was

0142-1123/$ - see front matter Ó 2013 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.ijfatigue.2013.05.017

Please cite this article in press as: Tijani Y et al. Quantitative evaluation of fatigue life of cast aluminum alloys by non-destructive testing and parameter model. Int J Fatigue (2013), http://dx.doi.org/10.1016/j.ijfatigue.2013.05.017

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Fig. 1. Scanning electron microscope images showing location of crack initiation on the fracture surface of cast AlSi9Cu3 specimen (left) and a shrinkage pore that initiated the crack (right).

developed and implemented for cast AlSi8Cu3 alloy by using FE calculations and computer tomography. The model was veriﬁed by fatigue experiments on the investigated AlSi8Cu3 specimens as well as AlSi7Mg0.3 specimens.

2. Methodology 2.1. Materials Cast aluminum alloys EN AC-46200 (AlSi8Cu3) and EN AC42100 (AlSi7Mg0.3) were produced by low pressure die casting. Extensive information on the cast parameters and the experimental procedure, including the diagram indicating the geometry and dimensions of the fatigue samples are presented in [13]. The un-notched specimens were round with gauge length of 30 mm and diameter of 8 mm. The total specimen length was 100 mm. The AlSi8Cu3 samples were heat-treated using T5 tempering, artiﬁcially aged at 250 °C for 6 h, and had tensile strength Rm = 179 MPa; yield strength Rp0.2 = 132 MPa; elongation at fracture A = 0.9% and Brinell hardness of 96 HB. The AlSi7Mg0.3 samples were heat-treated using T6 tempering and had tensile strength Rm = 272 MPa; yield strength Rp0.2 = 194 MPa; elongation at fracture A = 8.7% and Brinell hardness of 93 HB. As indicated in [13], fatigue experiments were carried-out on the specimens by using a 25 kN servo-hydraulic machine at room temperature. Under constant-amplitude axial loading, the stress-controlled tests were conducted at stress ratio R = 1 and frequency f = 80 Hz.

2.2. Non-destructive testing by computed tomography The non-destructive analysis of fatigue samples from cast aluminum alloys EN AC-46200 (AlSi8Cu3-T5) is presented. With a reconstruction diameter of 20 mm, a maximum voxel size of 23 lm was achieved due to the specimen size of 100 mm. The fatigue samples were reconstructed by using AvizoÒ software. The microstructural discontinuities of the samples were analyzed to obtain quantitative information on pore sizes, morphologies and distance to specimen surface, see Fig. 2. In the investigated samples, the shrinkage pores were the dominant population of defects. In this work, the investigated specimens were selected to ensure presence of pores with maximum volume of 4 mm3 [13]. With voxel size of 23 lm, the largest cast pores can be easily analyzed using AvizoÒ. However, the analysis of cast pores of diameter less than 0.2 mm would not be reliable (for realistic 3D analysis, there

should be minimum of 10 voxels/particle). The investigated samples have pore diameter greater than 0.2 mm. 2.3. Finite element model of cast aluminum alloy specimens The effect of pores on the local stress in cast aluminum alloy samples was investigated by ﬁnite element analysis using AbaqusÒ Standard. The material was considered to be linear-elastic with Young’s modulus, E = 70 GPa and Poisson ratio, m = 0.33. The 3D meshes are composed of 50,000–75,000 and 300,000–500,000 quadratic elements for spherical and non-spherical pores respectively. The pore inﬂuence is characterized by its stress concentration factor, Kt. The higher the value of Kt, the lower is the fatigue life of the aluminum alloy sample. 2.3.1. Stress concentration factor of spherical pores A linear elastic 3D FE calculation was carried-out on modeled spherical pores. These represent gas pores which are usually round in shape. The inﬂuence of pore size (diameter) and location (distance between pore surface and sample surface) on the stress concentration factor Kt was determined. The Kt is deﬁned as the ratio of the maximum principal stress rmax to the nominal stress rn. Fig. 3 shows the stress concentration factor as a function of pore distance–diameter ratio. distance to surface At pore pore < 0:5, Kt progressively increases. This indidiameter cates that Kt is high if the pore is close to the surface. Kt decreases distance to surface at pore pore > 0:5 which shows that Kt is reduced if the pore diameter is far away from the surface. Fig. 3 is comparable to the work of Borbély et al. [14] where elastic–plastic FE calculations were performed to investigate size-distance to surface effect as a function of normalized maximum stress component. The distance to surface was measured from the middle of the pore. In comparison to Fig. 3, it was established in [14] that the normalized maximum stress component of a tensile-stressed specimen containing spherical cavities is most severe for a cavity lying just underneath the surface and less severe for cavities lying deeper beneath the surface. 2.3.2. Stress concentration factor of non spherical pore For shrinkage pores, the FE calculation was performed on the 3D reconstructed microstructure of the specimens obtained from CT scan. The CT images provide very realistic morphological information of the pores. After generating the shrinkage pores as surface models using AvizoÒ, the defects were exported to AbaqusÒ for FE analysis. In the reported work, the meshes were generated from 3D images using AbaqusÒ. A linear elastic calculation was

Please cite this article in press as: Tijani Y et al. Quantitative evaluation of fatigue life of cast aluminum alloys by non-destructive testing and parameter model. Int J Fatigue (2013), http://dx.doi.org/10.1016/j.ijfatigue.2013.05.017

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1mm

(a)

4 2

3

5

6 1 7

1mm Voxel size = 23 micron in x, y and z directions

(b) Fig. 2. (a) Image from the 2D stack and (b) the 3D reconstruction of internal structure of an AlSi8Cu3 specimen showing the shrinkage pores.

6

Section 2.3.1, a mathematical relationship that characterizes the inﬂuence of pore diameter on Kt was established,

Stress Concentration, Kt [ ]

3D FEM computation

K t;1 ¼ f ðSÞ

5

ð2Þ

Similarly, a mathematical relationship was determined to characterize the inﬂuence of pore location on Kt,

K t;2 ¼ f ðDÞ

4

3

2 0

0,5

1

1,5

2

2,5

3

Distance to surface/Pore diameter [ ] Fig. 3. Stress concentration factor of spherical pores as a function of distance– diameter ratio.

carried-out with nominal stress of 90 MPa. One of the models is shown in Fig. 4. It was observed that the highest stresses occur at the pores in the regions between the pores and the specimen surface.

For values of Kt,1 = Kt,2, the corresponding values of S and D were noted. By applying scientiﬁc data mining technology [15] as provided in EureqaÒ, the combined inﬂuence of S and D on Kt was established. EureqaÒ is a free software tool for detecting equations and hidden mathematical relationships in raw data. It identiﬁes the simplest mathematical formulas which could describe the underlying mechanisms that produced the data. In EureqaÒ, three columns of variables were deﬁned: (i) Column 1: Values of Kt,1 = Kt,2. (ii) Column 2: Corresponding values of D i.e. pore distance to surface. (iii) Column 3: Corresponding values of S i.e. pore size given as pore diameter. The modeling task to be set was given as:

column 1 ¼ f

2.4. Parameter model A parameterization of the FE calculation indicates that the stress concentration factor at the pore depends on the pore size S, the distance to the surface D and the pore morphology M, i.e.

K t ¼ f ðS; D; MÞ

ð1Þ

A mathematical function was developed to predict the combined impact of pore size and pore distance to surface on the stress concentration factor. From the FE calculation described in

ð3Þ

column 2 column 3

ð4Þ

Eq. (4) corresponds to a mathematical relationship that provides Kt value from ratio DS. Correlation coefﬁcient was selected as ﬁtness metric which speciﬁes the error to measure when optimizing solutions. The solution with highest correlation coefﬁcient of 0.99 was selected and this is given by the relation

Kt ¼ f

pﬃﬃﬃ D 0:71R 0:31 ¼ 2:74 þ 0:6R pﬃﬃﬃ 1:1 þ pﬃﬃﬃ 2:21 R S R pﬃﬃ R R

ð5Þ

R

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(a) (b) fixed support (u1 = u2 = u3 = 0)

(c) (d) Fig. 4. FE-model of the specimen AlSi8Cu3-T5 showing (a) meshed surface of the pore with highest value of maximum principal stress, (b) an assembly of the reconstructed defects with stress direction and boundary condition, (c) pore with highest value of maximum principal stress after FE calculation and (d) the stress distribution around the pore with highest value of maximum principal stress.

distance to surface where R ¼ DS ¼ pore pore and R – 0. diameter The relationship in Eq. (5) accounts for the variability in the FE calculations that is attributed to the approximation errors. The parametric equation, therefore, exhibits some minima and maxima but the maximum deviation due to the errors amounts to only about 0.3%. For the purpose of numerical stability, the value of Kt was taken as 2.05 for R > 3.5. It can be observed that Eq. (5) is only valid for pores that are round or spherical in shape. This is true for many gas pores but clearly not applicable to determine the stress concentration factor of shrinkage pores. The inﬂuence of pore morphology on the local stress was further investigated using the CT images and the modeled spherical pores. Fig. 5 shows the morphological deviation of the pores with respect to a perfect sphere. In addition to the deviation according to pore shape, it can also be observed in Fig. 5 that

the pore volume also inﬂuences the deviation: the larger shrinkage pores have higher deviation than the smaller shrinkage pores as shown in the two different ﬁts according to the range of pore volumes. The dependence of non-spherical pore shape on the stress concentration factor can be analytically determined by the deviation of pore shape from a sphere, Mdev i.e.

Mdev ¼ f ðMÞ ¼

Maximum Feret Diameter Þ ð6:Volume Area

ð6Þ

By combining the two mathematical functions in Eqs. (5) and (6), the stress concentration factor of a pore can be predicted as:

Kt ¼

! pﬃﬃﬃ 0:71R 0:31 2:74 þ 0:6R pﬃﬃﬃ 1:1 þ pﬃﬃﬃ 2:21 R Mdev R pﬃﬃR R R

ð7Þ

On the assumption that the gas pores are spherical, Mdev is equal to 1 for gas pores and Eq. (7) reduces to Eq. (5). Hence Eq. (7) is applicable to both gas and shrinkage pores. In general, the parametric relationship is the same for all stress levels. But it will produce different results for different specimens based on the pore parameters (R, Mdev) and the mechanical property which is described in the next section.

3 Gas pores Shrinkage pore, volume 0.5 - 2 mm³ Shrinkage pore, volume 2 - 4 mm³

6V/A (mm)

2

3. Result and discussion 1

The inﬂuence of gas and shrinkage pores on the local stresses with respect to their sizes, locations and shapes can be quantitatively computed from Eq. (7).

0 0

1

2

3

Max. Feret (mm) Fig. 5. Deviation factor for spherical pores and shrinkage pores of different volume.

3.1. Correlation between FE results and parameter model For veriﬁcation of the parameter model in Eq. (7), further FE calculations were performed on both the modeled spherical pores and

Please cite this article in press as: Tijani Y et al. Quantitative evaluation of fatigue life of cast aluminum alloys by non-destructive testing and parameter model. Int J Fatigue (2013), http://dx.doi.org/10.1016/j.ijfatigue.2013.05.017

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the shrinkage pores from CT scans. The relevant parameters – size, shape and location of the pores- in the new FE calculations were speciﬁcally selected to be different from those used in the development of the parameter model. From the new FE calculations, the stress concentration factors were determined, Kt (FE calculation). Furthermore, the relevant parameters of the newly analyzed spherical and shrinkage pores were used as input in Eq. (7) to generate a Kt relationship. Correlation plots of both Kt values are shown in Fig. 6a and b. It can be observed that the Kt values for spherical pores are more accurately predicted. Although R2 = 0.9 is acceptable for shrinkage pores, a better correlation can be achieved upon an improvement in the 3D image analysis.

Table 1 Comparison between experimental fatigue life of AlSi8Cu3-T5 specimens and results of parameter model. Specimen A B C

Specimen

The knowledge of Kt provides an evaluation of the fatigue life based on the pore parameters as described above. However, it excludes the impact of the material behavior which is characteristic to each material depending on its mechanical properties, among other considerations. In order to include the inﬂuence of the material characteristics in the calculation of fatigue life, the effective stress concentration factor Kf is used i.e.

D E

! pﬃﬃﬃ 0:71R 0:31 Kf ¼ 2:74 þ 0:6R pﬃﬃﬃ 1:1 þ pﬃﬃﬃ 2:21 R :M dev g R pﬃﬃ R R

ð8Þ

where g is the notch sensitivity factor of the material obtained using [16]. By deﬁning the fatigue life Nf as the number of loading cycles required before failure occurs [17], the fatigue life of a pore-prone specimen Npore can be expressed as:

Nk

Fatigue life (parameter model)

50 80 90

1.00 E+7 1.79 E+5 1.71 E+4

1.00 E+7 1.78 E+5 1.85 E+4

Stress amplitude

ra (MPa)

Fatigue life (experiment)

Fatigue life (parameter model)

80 90

1.00 E+7 1.22 E+6

1.00 E+7 1.09 E+6

a run-out at stress amplitude of 50 MPa while crack initiation was mostly observed between 60 MPa and 110 MPa depending on the maximum pore volume. As reported in [13], fractographic investigations indicate crack initiation from oxide in only 5% of the specimens. Due to insufﬁcient detectability of oxide by CT scans, this work is focused on prediction of fatigue lives of specimens with cast pores. Table 1 shows the experimental fatigue life for 3 specimens and the calculated values from the parameter model. Furthermore, the parameter model was also veriﬁed by fatigue experiments on AlSi7Mg0.3-T6 specimens [13], see Table 2. In general, the model predictions lie within the 90% conﬁdence level of the fatigue experiments.

R

Npore ¼

Fatigue life (experiment)

Table 2 Comparison between experimental fatigue life of AlSi7Mg0.3-T6 specimens and results of parameter model.

3.2. Estimation of fatigue life and comparison with experiment

1

Stress amplitude

ra (MPa)

ð9Þ

rpore K f ðporeÞ k rk

4. Conclusions

where Nk and rk are the number of cycles and corresponding fatigue strength of pore-free specimens; k is the slope of the S–N curve of the pore-free specimens; rpore is the stress level applied on the pore-prone specimen; Kf(pore) is the effective stress concentration due to the presence of pore (it combines the stress concentration Kt with the mechanical properties of the material). By obtaining the effective stress concentration factor from Eq. (8) and using the fatigue property of a pore-free specimen as a reference, the fatigue life of a pore–prone aluminum alloy specimen can be determined. The pore-free specimens used in this work were produced from high purity continuously cast ingots [13]. The prediction of the parameter model was veriﬁed by fatigue experiments presented in [13]. In all the tested specimens that were selected for comparison, crack initiated from pores. As shown on the S–N curve of AlSi8Cu3 specimens reported in [13], there was

A parameter model was developed based on characteristic pore parameters obtained from computed tomography. The method provides the value of stress concentration factor of pores. In combination with information on the fatigue behavior of a pore-free aluminum alloy, the method predicts the fatigue life of pore-prone aluminum samples. There are good agreements between the results of the parameter model and ﬁnite element analysis on one hand, and results of the parameter model and experimental fatigue tests on the other hand. The most accurate simulation of fatigue behavior of cast aluminum samples should consider cyclic plasticity. The parameter model was however derived from linear-elastic FE calculations of the material microstructure. With the model predictions within 90% conﬁdence level of the fatigue experiments, the presented method shows that a simpler approach can estimate

8 R² = 0.9991

5

K t, FE calculation [ ]

K t, FE calculation [ ]

6

4

3

R² = 0.9135

7 6 5 4

2

3 2

3

4

5

K t, Parameter model [ ]

(a)

6

3

4

5

6

7

8

K t, Parameter model [ ]

(b)

Fig. 6. Correlation between stress concentration factors from FE calculation and parameter model for (a) modeled spherical pores and (b) shrinkage pores from CT scans.

Please cite this article in press as: Tijani Y et al. Quantitative evaluation of fatigue life of cast aluminum alloys by non-destructive testing and parameter model. Int J Fatigue (2013), http://dx.doi.org/10.1016/j.ijfatigue.2013.05.017

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the pore inﬂuence on material fatigue. Nonetheless, this method does not totally eliminate the necessity for elastic–plastic simulation with its attendant higher computational requirements. In general, the approach offers a new option to quantitatively determine the fatigue life of cast aluminum alloy components based on nondestructive analysis. It is expected to improve control mechanisms within the scope of quality assurance. Acknowledgments

[6]

[7] [8]

[9] [10]

The presented work was a part of the research Project IGF 295 ZN of the Research Association Casting Technology (FVG), Düsseldorf, Germany. It was sponsored by the Federal Ministry of Economics and Technology (BMWi) through the German Federation of Industrial Research Associations (AiF) under the program for the promotion of joint industrial research and development (IGF). It was based on a decision of the German Parliament.

[11]

[12]

[13]

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Please cite this article in press as: Tijani Y et al. Quantitative evaluation of fatigue life of cast aluminum alloys by non-destructive testing and parameter model. Int J Fatigue (2013), http://dx.doi.org/10.1016/j.ijfatigue.2013.05.017