The relationship between the Uniaxial Creep Test and the Small Punch Creep Test of the AZ31 magnesium alloy

Materials Science & Engineering A 614 (2014) 319–325

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Materials Science & Engineering A journal homepage: www.elsevier.com/locate/msea

The relationship between the Uniaxial Creep Test and the Small Punch Creep Test of the AZ31 magnesium alloy M. Lorenzo n, I.I. Cuesta, J.M. Alegre Structural Integrity Group, Escuela Politécnica Superior, Avda. Cantabria s/n, 09006 Burgos, Spain

art ic l e i nf o

a b s t r a c t

Article history: Received 3 June 2014 Received in revised form 16 July 2014 Accepted 17 July 2014 Available online 27 July 2014

In this paper, creep properties of an AZ31 magnesium alloy have been obtained by two different types of creep test: conventional the Uniaxial Creep Test (UCT) and the Small Punch Creep Test (SPCT). The SCPT is currently being studied as an alternative test to obtain the creep properties in those cases where there is not enough material for conducting conventional testing. This test basically consists of punching, under constant load, a small size specimen ð10  10  0:5 mm3 Þ with the ends fixed. The parametric predictive methods on creep, like Larson–Miller and Orr–Sherby–Dorn, are used for comparison. For the reference material used, AZ31 magnesium alloy, SPCT and UCT master curves have been determined, and a correlation between UCT and SPCT results has been established. The activation energy and the failure time predictions obtained from both tests indicate that SPCT is an appropriate method to obtain creep properties for these kinds of materials. & 2014 Elsevier B.V. All rights reserved.

Keywords: Small Punch Creep Test AZ31 Magnesium alloy Larson–Miller Orr–Sherby–Dorn Creep behavior

1. Introduction Generally, the creep behavior of a material is characterized by standardized Uniaxial Creep Test (UCT) [1]. Sometimes, not enough material is available to be able to carry out this test, and the use alternative methods and samples is necessary. One method that is increasingly becoming more popular is the Small Punch Creep Test (SPCT). This test basically consists of punching, under constant load, a specimen of small size ð10  10  0:5 mm3 Þ whose edges are firmly gripped by a die (Fig. 1). The application of the load is made through a spherical head punch or a ball, generally 2.5 mm in diameter. This test was initially developed in the nuclear industry and has been successfully used to obtain the creep properties of in-service components in those cases where there is not sufficient material to carry out standard creep tests, as happens in the case of welds or irradiated materials [2–6]. The experimental setup can be consulted in the CEN code of practice for small punch testing [7]. A recent review [8] indicates that SPCT is a promising method to characterize the full uniaxial creep curve (up to specimen fracture) and for this reason SPCT has attracted much interest from the research community. One of the fundamental tasks in implementing the SPCT is to determine the value of the equivalent load applied in SPCT to

n

Corresponding author. Tel.: þ 34 947 258922. E-mail address: [email protected] (M. Lorenzo).

http://dx.doi.org/10.1016/j.msea.2014.07.053 0921-5093/& 2014 Elsevier B.V. All rights reserved.

obtain the same rupture time to those obtained by the UCT at the same temperature. Due to the complex stress state of the SPCT specimen, which involves complex deformation processes [9], and its variability during testing while constant load is applied, a general expression is difficult to obtain. In recent years, a number of relationships between SPCT load P and UCT stress σ [10,11] have been developed. The CEN Code of Practice for small punch testing [7], in order to provide harmonized guidelines for the SPCT and interpretation of results, contains an experimentally validated expression, derived from the Chakrabarty's membrane stretching framework [12], which correlates the uniaxial equivalent stress with the applied load in SPCT: P ¼ 3:33ksp R  0:2 r 1:2 ho σ

ð1Þ

where R, r and ho are geometrical parameters and ksp is a correction factor to account for the ductility of a specific material that can be initially assumed to be ksp ¼ 1. To determine the ksp value, a series of five SPCT's at constant temperature are recommended, and the results are compared with the Uniaxial Creep Test for the same rupture time. Another aim of this paper is to analyze the viability of the SPCT as an alternative method to the uniaxial test. An attempt has been made to determine if creep parameters obtained with SPCT's are similar to those obtained with UCT's. In creep analysis, one of the most commonly used parametric predicting models using time-temperature is the one proposed by

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Fig. 1. Main dimensions of Small Punch Creep Test device.

Table 1 Chemical composition of the AZ31 magnesium alloy. AZ31% ASTM B90/B90M Al

Zn

Mn

Si

Cu

Ca

Fe

Ni

Others

Mg

2.5–3.5

0.6–1.4

0.2

0.1

0.05

0.04

0.005

0.005

0.3

balance

Larson–Miller (LM) [13]. This model is based on the assumption that the activation energy varies with the applied stress. Another useful correlation used in uniaxial creep was proposed by Orr– Sherby–Dorn (OSD). In this case the activation energy is assumed to be constant and independent of the applied stress [14]. With these two time–temperature parametric prediction methods, “master curves” are obtained from short time tests that can be used for the prediction of long term tests which are not feasible in the laboratory. Consequently, the aim of this paper consists of establishing a correlation between the conventional Uniaxial Creep Test (UCT) and the Small Punch Creep Test (SPCT) in order to characterize the creep behavior of light alloys, based on the more common parametric prediction models in conventional Uniaxial Creep Tests.

continuously measure the creep strain and a constant temperature was maintained using a furnace equipped with three internal thermocouples. A broad experimental Uniaxial Creep Test program has been carried out. The set temperatures were 125 1C, 150 1C and 175 1C, within the range T r 0:5T m for this material. The stress levels were 70 MPa, 90 MPa and 110 MPa. Finally the rolling direction considered were 01,451 and 901. A typical creep strain curve εðtÞ and the corresponding creep strain rate curve ε_ ðtÞ are presented in Fig. 2. In this curve, the typical points are the failure time t f ðhÞ, the minimum creep strain 1 rate ε_ m ðh Þ and the creep strain εf ðmm=mmÞ achieved by the specimen at the failure time. Fig. 3 presents the dependence of the minimum creep strain rate ε_ m with the stress σ at the three different temperature levels tested. Practically parallel trends for various temperatures can be observed, leading one to believe that for this AZ31 magnesium alloy and for the range of stress and temperatures considered, there is not a change on the creep mechanisms in this alloy. Moreover, in Fig. 4 the dependence of the failure time t f versus the stress σ at different temperatures is presented.

2.3. Small Punch Creep Test The Small Punch Creep Tests were performed at loads of 121 N, 171 N and 216 N and at temperatures of 125 1C, 150 1C and 175 1C. In this case, the stress levels, equivalent to the UCT stress σ eq obtained by applying expression (1) proposed from CEN code, were 64 MPa, 90 MPa and 114 MPa respectively. Fig. 5 shows a sketch of the experimental device for these tests. The temperature of the miniature specimen was controlled using a thermocouple placed as close as possible to the specimen. During

2. Experimental procedure 2.1. Material and preparation of test specimens To carry out this study, a rolled sheet of the AZ31 magnesium alloy with a sheet thickness of 1 mm was selected. This AZ31 magnesium alloy is a hexagonal closed packed material (HCP) vulnerable to high temperatures. Magnesium alloys such as AZ31 exhibit excellent mechanical properties, but their creep resistance is poor at temperatures above 125 1C [15]. Table 1 shows the chemical composition of this alloy according to the ASTM [16]. All the necessary specimens for this study were machined from the selected sheet by water jet cutting. They are, as can be seen in the next section, uniaxial creep specimens and small punch specimens. The SPT and SPCT specimens ð10  10  0:5 mm3 Þ were subsequently polished equally from both sides using metallography techniques with abrasive papers with a final grade of 1200 grit to obtain a final thickness ð0:5 mm 7 0:002 mmÞ. The uniaxial tensile and creep specimens were flat, having dimensions ð6  1 mm2 Þ and a gauge length of 25 mm. In this case, the specimens were cut taking the rolling direction into account, classifying them in three types: longitudinal ð01Þ, transverse ð901Þ and diagonal ð451Þto the rolling direction.

Fig. 2. Uniaxial creep ðT ¼ 150 1C; σ ¼ 70 MPaÞ.

strain

εðtÞ

and

creep

strain

rate

ε_ ðtÞ

curves.

2.2. Uniaxial Creep Test Conventional Uniaxial Creep Tests were carried out at a constant engineering stress. A laser extensometer was used to

Fig. 3. Uniaxial stress σ versus minimum creep strain rate ε_ m from the UCT's.

M. Lorenzo et al. / Materials Science & Engineering A 614 (2014) 319–325

the SPCT, the central deflection of the specimen was registered using a COD extensometer. In this case, SPCT curves were plotted using the central creep deflection δðtÞ instead of the creep strain εðtÞ and the creep _ instead of the creep strain rate ε_ ðtÞ, as is shown deflection rate δðtÞ in the example in Fig. 6. The SPCT results of the minimum creep deflection rate 1 δ_ m ðmm h Þ are shown in Fig. 7, whereas the failure times t f ðhÞ obtained by the SPCT's are collected in Fig. 8 for the different temperatures selected. As can be observed, the trend of the curves is similar for both the SPCT's and UCT's with similar temperatures and equivalent stress levels, giving way to the idea that the SPCT can be used to identify whether or not there is a change of creep mechanism as observed in UCT.

321

The Larson–Miller model (LM) is described according to the following expression: LMP ¼ CðT þ log t f Þ

ð2Þ

3. Results 3.1. Larson–Miller–Orr–Sherby–Dorn One of the typical ways for relating the UCT and SPCT is by analyzing commonly used forecasting parametric models, such as Larson–Miller and Orr–Sherby–Dorn.

Fig. 4. Uniaxial stress σ versus time to failure t f from the UCT's.

Gap control

Fig. 6. Small punch creep deflection δðtÞ and minimum creep deflection rate curves δ_ m ðtÞ. ðT ¼ 150 1C; σ eq ¼ 64 MPaÞ.

Fig. 7. Stress σ eq dependence on the minimum creep deflection rate δ_ m for the three temperatures analyzed by the SPCT's.

Weights

Frame SPCT device COD type extensometer

Tube furnace

Adquisition system Tube furnace controller

Specimen

Temperature sensor

Fig. 5. Sketch of the SPCT's experimental devices.

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Fig. 8. Stress σ eq dependence on the failure time t f for the three temperatures analyzed by the SPCT's.

Fig. 9. Constant stress curves by the UCT's.

where C is a material constant that usually takes the value of 20, t f is the failure time in hours and T is the test temperature in Kelvins [13]. The typical value of this material constant C ¼ 20, represents the mean value for a number of alloys, which sometimes leads a reduction of accuracy in forecasting. In this case, the use of values adapted to each material is desirable [17]. On the other hand, the Orr–Sherby–Dorn (OSD) model is described by:   Qc OSD ¼ log t f  ð3Þ 2:303RT where t f and T have the same units as in the previous equation, R is the universal gas constant and Qc is the activation energy in kJ/mol [14]. The main difference between these two forecasting models is that the LM model considers the activation energy to be a function of the applied stress while the OSD considers this activation energy to be independent of the stress level.

Fig. 10. UCT's LMP master curve.

3.2. Results of Uniaxial Creep Tests The constant stress curves by the UCT's, representing the logarithmic failure time versus reciprocal temperature, are presented in Fig. 9 for a range of 70 MPa to 110 MPa. The master curves of the LM and OSD parameters obtained from the results of the tests using the UCT at temperatures of 125 1C, 150 1C and 175 1C are presented in Figs. 10 and 11 respectively. In both cases (LM and OSD), the master curves are obtained from the UCT by two settings of regression: linear and polynomial. Table 2 shows the calculated coefficients of the Larson–Miller fitting master curves as function of the stress in the range from 68 MPa to 109 MPa and using a constant value of C ¼ 14:4 (Expression 2). In the same way, the Orr–Sherby–Dorn coefficients for the master curve fitting were obtained using the value of M ¼ 6606 and the activation energy Q c ¼ 127 kJ=mol (Expression 3), as is showed in Table 3. 3.3. Results of Small Punch Creep Tests Similarly, for the range of 65 MPa (121 N) to 114 MPa (216 N) at temperatures of 125 1C, 150 1C and 175 1C, the constant load curves by the SPCT's are presented in Fig. 12. The master curves using LM and OSD parameters were obtained from the results of the SPCT's, which are presented in Figs. 13 and 14 respectively. The calculated coefficients of the Larson–Miller master curve fitting as function of the stress, using a calculated constant of C ¼ 12:2, are shown in Table 4. Moreover, Table 5 presents the calculated coefficients of the Orr–Sherby–Dorn master curve fitting with M ¼ 5826 and Q c ¼ 112 kJ=mol.

Fig. 11. UCT's OSDP master curve.

Table 2 Fit coefficients for LMP by UCT's. Setting range

Larson–Miller coefficients

σ (MPa)

T (1C)

C

a1

a2

a3

R2

68–109 68–109

125–175 125–175

14.4 14.4

 17.866 0.1269

8199.6  41

9210

0.932 0.940

Table 3 Fit coefficients for OSDP master curve by UCT's with Q c ¼ 127 kJ=mol. Setting range

Sherby–Dorn Sherby–Dorn coefficients

σ (MPa) T (1C)

Qc (KJ/mol)

68–109 68–109

125–175 127 125–175 127

M

a1

a2

a3

R2

6606  0.0419  10.645 0.934 6606 0.0003  0.0903  8.51 0.941

M. Lorenzo et al. / Materials Science & Engineering A 614 (2014) 319–325

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Table 4 Fit coefficients for LMP master curve by SPCT's. Setting range

Larson–Miller coefficients

σeq (MPa)

T (1C)

C

a1

a2

a3

R2

65–114 65–114

125–175 125–175

12.2 12.2

 16.342 0.1523

7271  43

8420

0.94 0.96

Table 5 Fit coefficients for OSDP master curve by SPCT's with Q c ¼ 112 kJ=mol. Setting range

Sherby–Dorn Sherby–Dorn coefficients

σeq (MPa) T (1C)

Qc (KJ/mol)

Fig. 12. Constant load curves by the SPCT's.

65–114 65–114

125–175 112 125–175 112

R2

M

a1

a2

a3

5826 5826

 0.0384 0.0004

 8.8197  0.1019

0.93  6.12 0.97

Fig. 13. SPCT's, LMP master curve.

Fig. 15. UCT's and SPCT's LMP master curves.

Fig. 14. SPCT's, OSDP master curve.

A comparison between both type of test from LMP-master curves and OSDP-master curves is presented in Figs. 15 and 16 respectively. Fig. 16. UCT's and SPCT's OSDP master curves.

4. Analysis and discussion The forecasting methods of Larson–Miller and Orr–Sherby– Dorn employed for predicting the time of failure by SPCT are in agreement with the results obtained by UCT for this alloy AZ31 [18–20]. In general, the values obtained for the constant C in the LM parameter, the constant M in the OSD parameter and the activation energy Q c were somewhat higher in UCT than SPCT. The values of Q c are in good agreement with the values from the literature for this material [19,21–24]. For a similar range of temperatures and equivalent stress levels in UCT, the trend of the failure times in SPCT in a logarithmic scale were the same, as can be seen in Figs. 4 and 8. In general, higher failure times in SPCT's compared to UCT's were obtained, especially at a temperature of 175 1C, as shown in the diagram in

Figs. 4 and 8. Also, in UCT's the failure time for the same stress levels is highest in the transversal direction (901), less in diagonal (451) and the least for the rolling direction (01) for any temperature within the range studied. However, when compared with the equivalent results of the SPCT's, this variation is negligible for the range of temperatures and stress levels used. Equivalent results with the same failure time and temperature (150 1C), using SPCT's and UCT's, have been compared in previous research [25], obtaining a relationship P=σ C 2. With this relationship between load PðNÞ in SPCT and stress σðMPaÞ in UCT, as well as the miniature specimen dimensions and tooling matrix, a new value of the constant ksp ¼ 1:06 for the AZ31 magnesium alloy was calculated, taking a value close to the unit value, as indicated by the CEN code [7].

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Although UCT and SPCT results are very similar, the small differences observed between both tests are justified by the miniature specimen geometry itself and the complex stress state of the SPCT during the creep test. Another important difference with the UCT is that the stress distribution in SPCT changes throughout the test because of a redistribution of the stresses in the specimen [26]. Moreover, in the SPCT specimens, initial plastic deformations appear at the moment when the load is applied, and it causes a large number of dislocations [27,28] compared to the Uniaxial Creep Test. This effect can be also observed in the creep curves, where it can be observed that the primary creep in SPCT's is larger than in UCT's. If UCT and SPCT creep curves are compared, it can be seen that the tertiary creep state, corresponding to an accumulation of damage, is shorter in time or is accelerated in the SPCT's as compared to the UCT's. During the creep test on SPCT's, two deformation mechanisms occur: first bending, associated with primary or stabilized state, and secondly membrane stretching associated with the secondary and tertiary states [29]. At the final (tertiary) creep state, the mechanism in SPCT specimens is the membrane stretching type, which causes a reduction of the thickness of the specimen and gives rise to higher stresses in the moments right before final fracture or failure. At room temperature, the failure mechanism observed in the SPT specimens was brittle (star macro-crack shape), whereas in the range of temperatures between 125 1C and 175 1C, the final fracture observed was ductile (circumferential macro-crack shape), as shown in Fig. 17. However, in the SPCT's the nucleation of the first micro-cavities in the miniature specimen took place in different radial areas. As the testing went on, the stress distribution in the specimen changed and new, more greatly stressed areas appeared. In these areas, growth and coalescence of new micro-voids took place, which progressed to the final failure in a ductile way, showing a final circumferential macro-crack shape as

can be observed in Fig. 18. This circumferential region is located at an approximately constant distance from the center of the punch. In addition to that, the region in which the first cavitation mechanisms occur starts to move, and this can be associated with a combination of climbing and sliding dislocation mechanisms characteristic of this material [30] and governed by the Creep Power-Law-Breakdown [21], since most of the stress levels used are in the high stress regime. However, for lower stress levels the mechanism is associated with grain boundary sliding [22]. The fracture mode and the appearance of a SPCT specimen tested at 175 1C and 121 N and circular crack mode are shown in Fig. 18a. In turn, Fig. 18b shows a detail of the SEM micrographs of the appearance of a fiber surface with dimples and coalescence voids, which is a typical ductile fracture mechanism from the squared area of Fig. 18a. Each dimple is half of one of the micro cavities that were formed and later separated during the process of creep fracture. In this specimen, dimples found are a combination of two types of dimples: O-shaped and U-shaped. In ductile fracture, O-shaped or spherical cavities are caused by uniaxial tensile forces, whereas U-shaped or parabolic cavities are caused by shear forces. It can be noted that this fracture surface is mainly composed of O-shaped or spherical cavities, as shown with arrows in Fig. 18b, which means that most of the forces which cause final fracture are tensile forces. It can be seen that ductile tearing of the edges of the spherical morphology are of the transgranular cracking type. At the bottom of the dimples, particles of β-phase (Mg17Al12) have been found, which are generally thought to be the nucleation center voids formed during the low temperature deformation process [31] as shown by the circle in Fig. 18b. Similarly, in the big dimples in Fig. 18b zones of ripple morphology appear due to serpentine sliding which occurs, because in SPCT's at low creep deflection rates (low creep strain rates in UCT's), there is enough time for this sliding process to take place.

Fig. 17. SEM image of a SPT specimen of the AZ31 tested (a) at room temperature and (b) at 175 1C.

M. Lorenzo et al. / Materials Science & Engineering A 614 (2014) 319–325









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specimen is subjected to during the SPCT's. The ratio calculated for the activation energy was Q cðspctÞ =Q cðuctÞ ¼ 0:88. The methods of extrapolation of creep results based on time– temperature parameters like Larson–Miller and Orr–Sherby– Dorn can be used to predict creep time to failure by Small Punch Creep Test at constant-force. The value of Larson–Miller's C and Orr–Sherby–Dorn's M constant parameters calculated using both types of tests were also in good agreement: C ¼ 12:2, M ¼ 5826 for SPCT and C ¼ 14:4; M ¼ 6606 for UCT. The ratios obtained between these values were: C spct =C uct ¼ 0:85 and M spct =M uct ¼ 0:88. For the forecasting methods of Larson–Miller and Orr–Sherby– Dorn, the master curves fitting (linear and polynomial) as a function of the applied stress, appear to be similar in both types of tests, SPCT's and UCT's, being the forecast model of OSD using a polynomial fitting, the model that better approach the failure time experimentally obtained. In conclusion, the main similarities between the SPCT's and UCT's are that the activation energy and the failure time predictions obtained from both tests indicate that the SPCT is an appropriate method for obtaining creep properties for these kinds of materials.

Acknowledgments The authors are grateful for the funding received from Project MCI Ref: MAT2011-28796-C03-02. References

Fig. 18. (a) SEM image of the typical fracture of the AZ31 tested by the SPCT. (b) Ductile tearing fracture surface at 175 1C.

5. Conclusions

[1] [2] [3] [4] [5] [6] [7] [8]

The main conclusions of this paper are summarized below:

 There are great similarities between the shapes of the creep





curves obtained using SPCT's and UCT's. However, it can be observed that the time associated with each creep stage (primary, secondary and tertiary) is slightly different in both tests. In SPCT's, the primary creep is larger than in UCT's, and the tertiary creep is shorter in SPCT's than in UCT's. These dissimilarities have been attributed to several factors: First, the stress levels used in UCT's are somewhat different from those in SPCT's. While in conventional creep tests the stress state is uniaxial, the small Punch Creep Test is a changing multiaxial stress state. Second, the UCT is more sensitive in the rolling direction, whereas in the SPCT all orientations coexist for the same test, prevailing the one with the smallest creep resistance. The conventional correlation between P and σ, defined by the CEN expression, is appropriate for calculating the creep properties of the AZ31 magnesium alloy using miniature specimens using the SPCT. The value of Qc calculated from the SPCT's was Q cðspctÞ ¼ 112 kJ=mol, whereas from the UCT's it was Q cðuctÞ ¼ 127 kJ=mol. Both are in good agreement with the values from the literature for this material. The small differences between these values have been associated with an increase of dislocations due to the large plastic deformation which the miniature

[9] [10] [11]

[12] [13] [14] [15] [16] [17] [18] [19] [20] [21] [22] [23] [24] [25] [26] [27]

[28] [29] [30] [31]

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