1 Introduction

Magnesium alloys have been attractive for aerospace and transportation industries because they are the lightest structural metals, and thus, producing components by them could remarkably reduce weight and fuel consumption [1,2,3]. Among magnesium alloys, the rare earth (RE) element-containing system possesses improved comprehensive performances such as mechanical properties [4,5,6,7], casting properties [8] and damping performances [9, 10]. Fatigue property is important for metals because fatigue failure is a main type of failure mode for metal parts [11,12,13]. Therefore, the improvement in fatigue properties of magnesium alloys is of great interest.

During the smelting process of metals, casting defects (i.e. porosity, oxide films and inclusions) are usually formed and deteriorate the fatigue properties of the castings [14,15,16]. With the development of casting technologies and Mg–RE alloys [17,18,19], more and more defect-free Mg castings have been produced. Fatigue properties of defect-free magnesium alloys are mainly dependent on their microstructures [20,21,22]. Generally, RE elements exist in Mg–RE alloys in three forms: second phase particles, solid solution and precipitates [23,24,25]. Different heat treatment processes lead to different microstructures, which significantly influences their fatigue properties and fracture behaviour. Taking Mg–3Nd–0.2Zn–0.5Zr (NZ30K) alloy as an example, in the as-cast state, Nd mainly exists in the secondary phase particles distributed at grain boundaries. After solution treatment, the secondary phase particles disappear and Nd is dissolved into the matrix and exists in the form of solid solution atoms [23]. Further ageing treatment after solution causes the dissolved Nd atoms to precipitate, which leads to higher fatigue strength (~ 85 MPa) than that of the as-cast and T4-treated conditions (~ 70 MPa) [17, 26]. Furthermore, different ageing treatment conditions cause the formation of different precipitates such as β″ (T6: 540 °C × 10 h + 200 °C × 14 h) and β′ (T7: 540 °C × 10 h + 250 °C × 10 h) [23], which leads to different fatigue strengths [26].

Though the effect of heat treatment on high-cycle fatigue of cast Mg alloy containing Nd has been extensively reported [17, 26], comprehensive investigation of the influence of ageing treatment on the low-cycle fatigue (LCF) behaviour of the Mg–Nd alloy is yet to be reported. This study aims to investigate LCF characteristics of the Mg96.47Nd2.9Zn0.21 alloy containing 0.42Zr under peak-aged (T61: 540 °C × 8 h + 200 °C × 14 h) and over-aged (T62: 540 °C × 8 h + 200 °C × 400 h) conditions and then to predict the fatigue life of the alloys using the energy density [27].

2 Experimental

A direct chill casting (casting speed of 100 mm·min−1, water flow of 25 L·min−1 and casting temperature of 730 °C) Mg96.3Nd3Zn0.2Zr0.5 ingot (70 mm in diameter and 2000 mm in length) was used. In this work, the alloy was supplied by National Engineering Research Center of Light Alloys Net Forming and Shanghai Jiao Tong University. The actual chemical composition of the alloy was measured to be Mg96.47Nd2.9Zn0.21Zr0.42 by an Optima 7300DV inductively coupled plasma analysis (ICP). Blanks with dimensions of 16 mm × 16 × mm × 140 mm were cut along the length direction of the ingot for tensile and fatigue test samples. Both peak-aged (T61: 540 °C × 8 h + 200 °C × 14 h) and over-aged (T62: 540 °C × 8 h + 200 °C × 400 h) samples were prepared (Fig. 1).

Fig. 1
figure 1

Variation in hardness of NZ30K alloy samples as a function of time during isothermal aging at 200 °C

Full size image

Room temperature (RT) tensile specimens with gage dimensions Φ6 mm × 30 mm were prepared and then tested using an Instron 5566 tensile machine. For the tensile testing, the crosshead speed of about 1 mm·min−1 was adopted. The LCF test specimens with gage dimensions Φ6mm × 12 mm were prepared and electrolytically polished to improve the surface quality; then, the fatigue testing was carried out using an Instron 8802 fatigue machine under the strain-controlled mode (triangular waveform of R = − 1, frequency of 1 Hz, total strain amplitude in the range of 0.2%–0.6%). Under each condition, three specimens were tested and the average value was employed as the final result. At strain amplitude levels of 0.2% and 0.3%, the fatigue testing was lasted for 104 cycles under the strain-controlled mode, and then, it was converted to the stress-controlled mode (sinusoidal loading of R = − 1, frequency of 30 Hz) for 107 cycles or until the failure of the specimen. Furthermore, some fatigue testing was performed under the constant stress amplitude of 90 MPa (high-cycle fatigue, HCF) until failure for comparison.

The samples for the microstructural observation were chemically etched in an acetic–picric solution (20 ml acetic acid, 60 ml ethanol, 1 ml nitric acid and 19 ml water) and then characterized using an Olympus optical microscope (OM). The fracture surfaces of the fatigue samples were examined using a FEI 250 scanning electron microscope (SEM). The initiation and propagation behaviours of the fatigue cracks on the sample surface were investigated using SEM and OM, respectively.

3 Results and discussion

3.1 Theoretic analysis

Figure 2 shows microstructures of T61- and T62-treated Mg96.47Nd2.9Zn0.21 alloys containing 0.42Zr. The average grain size of the alloys is measured to be 52~56 μm. The beta precipitates are very small, smaller than 200 nm in size, and they cannot be observed in Fig. 2. They can be characterized using transmission electron microscopy (TEM) as Fu [28] reported. In the optical micrographs, other than Mg matrix, only Zr-rich zones (dark areas within grains and at grain boundaries) and some small Zr-containing particles distribute at grain boundaries [29, 30]. Compared with the T61-treated counterpart, T62-treated alloy shows interesting microstructure. The grains with different orientations have different contrasts after etching. Fu [28] pointed that the precipitates in T62-treated alloy are similar to those in the T7-treated counterpart (540 °C × 8 h + 250 °C × 10 h). In the T61-treated condition, the fine plate-shaped β″ precipitates with DO19 structure (a = 0.64 nm, c = 0.52 nm) are the dominant strengthening phase, while β′ precipitates with fcc structure (a = 0.742 nm) are the dominant phase in T62-treated alloy [23]. The β″ precipitates have smaller size and higher density than the β′ precipitates.

Fig. 2
figure 2

OM images of Mg96.47Nd2.9Zn0.21Zr0.42 alloys under a T61-treated and b T62-treated conditions

Full size image

Table 1 shows RT tensile properties of T61- and T62-treated Mg96.47Nd2.9Zn0.21Zr0.42 alloys, and their logarithmic strain–true stress curves are shown in Fig. 3. The alloys exhibit similar yield strength (YS of ~ 150 MPa) and ultimate tensile strength (UTS of ~ 300 MPa), while T62-treated alloy has a better ductility (elongation of ~ 12.6%) than T61-treated counterpart (elongation of ~ 7.1%).

Table 1 Tensile properties of T61- and T62-treated Mg96.47Nd2.9Zn0.21Zr0.42 alloys
Full size table
Fig. 3
figure 3

Logarithmic strain–true stress curves of the T61- and T62-treated Mg96.47Nd2.9Zn0.21Zr0.42 alloys

Full size image

3.2 Cyclic stress response and strain resistance

It was reported that the variations in the stress value and plastic strain value during LCF testing are important [21]. Figure 4a shows the relationship between stress amplitude (\( \sigma_{{{\text{T6}}_{ 1} }} \) and \( \sigma_{{{\text{T6}}_{ 2} }} \)) and number of cycles (Nf) for T61- and T62-treated Mg96.47Nd2.9Zn0.21Zr0.42 alloys at different strain values (0.2%, 0.3% and 0.5%). Table 2 shows the initial and maximum stress amplitudes (ΔσI and ΔσM, respectively) of the samples at different strain values. Apparently, the stress amplitude increases with the increase in the total strain value, and the stress value at the strain value of 0.6% is ~ 88 MPa (T61) and ~ 81 MPa (T62), higher than that at the strain value of 0.2%. At the strain value of 0.2%, the stress amplitudes of both the T61- and T62-treated alloys keep steady during fatigue testing. When the strain value increases to 0.3%, the stress of T61-treated alloy increases and subsequently decreases with the increase in cyclic number, while that of T62-treated counterpart increases slightly during the cyclic loading. On the contrary, at the same strain value, the two aged alloys exhibit the similar initial stress amplitudes. For instance, at the strain value of 0.4%, the maximum stress amplitudes of T61- and T62-treated alloys are 146 and 125 MPa, respectively, increased by 22 and 2 MPa than those at the first cycle (123–124 MPa), indicating that T61-treated alloy could be hardened more than T62-treated counterpart during fatigue. Figure 4b plots the mean stress against the number of cycles for T61- and T62-treated samples. For both samples, the mean stress remains steady. The mean stress of the alloys tested at different stain values is about − 1.01–2.47 MPa (T61) and − 1.41–3.85 MPa (T62), respectively. Therefore, the influence of ageing treatment and strain value on mean stress of the alloys is very marginal.

Fig. 4
figure 4

Variation in a stress amplitude and b mean stress with number of cycles (Nf) for T61- and T62-treated Mg96.47Nd2.9Zn0.21Zr0.42 alloys; c variations in plastic stain amplitude (Δεp/2) during cyclic deformation for alloys

Full size image
Table 2 Cyclic stress amplitudes of T61- and T62-treated Mg96.47Nd2.9Zn0.21Zr0.42 alloys at strains of 0.2%–0.6% (MPa)
Full size table

Figure 4c illustrates the variation in plastic strain amplitude for the alloys during fatigue testing. The increase in the total strain amplitude leads to the increase in the plastic strain value. At the strain amplitude of 0.2%, the plastic strain values of both T61- and T62-treated alloys remain steady during the entire fatigue testing. When the total strain amplitude is above 0.3%, the plastic strain amplitude of T62-treated samples slightly decreases before failure. For T61-treated sample, as the total strain amplitude increases to 0.4%, the plastic strain amplitude decreases and subsequently increases. At the same strain value, the T62-treated sample has a higher plastic strain amplitude than T61-treated counterpart, corresponding to a lower stress response in T62 condition.

3.3 Hysteresis loop and energy density

It is widely acknowledged that the hysteresis loop (or hysteresis energy) is an important fatigue parameter for magnesium alloys [27, 31]. Figure 5a shows stress–strain hysteresis loops of T61- and T62-treated alloys at different cyclic numbers (at the total strain amplitude of 0.4%). For comparison, the compressive tips of the hysteresis loops of the alloys tested at the total strain value of 0.4% were translated to the origin of the coordinates in Fig. 5a. It can be seen that the shape of hysteresis loops of both T61- and T62-treated samples is nearly symmetrical during the entire fatigue testing. Figure 5b shows relationship between total strain energy density (ΔWt) or plastic strain energy density (ΔWp) and cyclic number (Nf) of the alloys at strain value of 0.4%. The value of ΔWp of T61-treated sample keeps steady, decreases and then increases, while that of T62-treated counterparts always remains steady during the fatigue testing. When the cyclic number is below 100, ΔWp value of T62-treated alloy is equivalent to that of T61-treated counterpart. By further increasing the number of cycles, ΔWp value of T61 alloy is lower than that of T62 alloy. In contrast, ΔWt values of the two age-treated alloys are close. Similar results are also observed in the specimens tested at different total strain amplitudes, as shown in Fig. 5c. In addition, the increase in the total strain amplitude leads to the increase in both ΔWt and ΔWp values. The LCF lives of the two treated alloys are also close, which might be because that the values of ΔWt for them are close.

Fig. 5
figure 5

a Stress–strain hysteresis loops at total strain amplitude of 0.4%; b variation in total strain energy density (ΔWt) and plastic strain energy density (ΔWp) with number of cycles for T61- and T62-treated NZ30K alloys tested at total strain amplitude of 0.4%; c relationship between ΔWp or ΔWt and total strain amplitude for Mg96.47Nd2.9Zn0.21Zr0.42 alloys

Full size image

3.4 Fatigue life

It is well known that the LCF lives of the magnesium alloys could be described based upon the Coffin–Manson relation and Basquin laws as follows [3]:

$$ \frac{{\Delta \varepsilon _{{\text{t}}} }}{2} = \frac{{\Delta \varepsilon _{{\text{e}}} }}{2} + \frac{{\Delta \varepsilon _{{\text{p}}} }}{2} = \frac{{\Delta \sigma }}{{2E}} + \left( {\frac{{\Delta \sigma }}{{2K^{\prime } }}} \right)^{{1/n^{\prime } }} = \frac{{\sigma _{{\text{f}}}^{\prime } (2N_{{\text{f}}} )^{b} }}{E} + \varepsilon _{{\text{f}}}^{\prime } (2N_{{\text{f}}} )^{c} $$
(1)

where Δεt, Δεe and Δεp are true strain range, true elastic strain range and true plastic strain range, respectively; E and Δσ are elastic modulus and true stress range, respectively; n′, b, c, K′, σf and εf are cyclic strain hardening exponent, fatigue strength exponent, fatigue ductility exponent, cyclic strength coefficient, fatigue strength coefficient and fatigue ductility coefficient, respectively. Figure 6a shows strain life curves of T61- and T62-treated alloys. At the same strain amplitude, the fatigue lives of the two alloys are close. The parameters in Eq. (1) were calculated by fitting the relationship between lg(Δσ/2) and lg(Δεp/2), lg(Δσ/2) and lg(2Nf), Δεp/2 and lg(2Nf), and the results are shown in Table 3. The LCF lives were predicted based on Eq. (1) and fit well with the experimental data as shown in Fig. 6a; thus, Eq. (1) and the parameters obtained from T61-treated samples could be used to describe the strain–life curves of both T61- and T62-treated alloys.

Fig. 6
figure 6

a Strain life curves of T61- and T62-treated Mg96.47Nd2.9Zn0.21Zr0.42 alloys and b predicted low-cycle fatigue lives using Eqs. (2) and (3)

Full size image
Table 3 Low-cycle fatigue parameters of T61- and T62-treated Mg96.47Nd2.9Zn0.21Zr0.42 alloys
Full size table

It has been reported that both plastic strain and total strain energy densities could be used to predict the LCF lives of magnesium alloys as follows [31]:

$$ N_{\text{f}} = (C/\Delta W_{\text{p}} )^{{\text{1/}m}} $$
(2)
$$ N_{\text{f}} = (C/\Delta W_{\text{t}} )^{{\text{1/}m}} $$
(3)

where m and C are constants. Figure 6b shows the predicted life curves based on Eqs. (2), (3) and experimental data. The values of m and C are determined to be ~ 0.64 and 48 MJ·m−3 in Eq. (2) and 0.35 and 10 MJ·m−3 in Eq. (3), respectively. It can be seen that the predicted values fit well with the experimental results, indicating that the parameters obtained from T61-treated alloy could be also used to predict the fatigue life of T62-treated counterpart.

Weibull data in Fig. 7a show the influence of ageing treatment on HCF life of NZ30K alloys. The fatigue data in Fig. 7a point plot linearly well lnln{1/[1−Fw(Nf)]} vs. ln(Nf), where Fw is 63% probability of failure and Nf is the fatigue life data) [16]. The characteristic fatigue life (N0) of T61-treated alloy is ~ 3.22 × 106 cycles at the stress amplitude of 90 MPa, approximately twice that of T62-treated counterpart.

Fig. 7
figure 7

a Weibull plots showing influence of ageing treatment on HCF life of the Mg96.47Nd2.9Zn0.21Zr0.42 alloys and b true stress–true strain hysteresis loops at maximum stress values of 90–92 MPa and strain values of ~ 0.20% (T61) and ~ 0.25% (T62)

Full size image

Figure 7b shows true stress–true strain hysteresis loops of T61- and T62-treated Mg96.47Nd2.9Zn0.21Zr0.42 alloys at the maximum stress values of 90~92 MPa. T61-treated alloy has lower hysteresis energies than T62-treated counterpart. The higher hysteresis energy was reported to correspond to higher fatigue damage and shorter fatigue life [27]. Therefore, longer fatigue life of T61-treated Mg96.47Nd2.9Zn0.21Zr0.42 alloy tested at stress-controlled loading appears to be due to its lower hysteresis energy and higher matrix strength.

3.5 Fatigue failure and cyclic deformation behaviour

Figure 8 shows SEM images of fatigue crack initiation regions of T61- and T62-treated Mg96.47Nd2.9Zn0.21Zr0.42 alloys. For both alloys, the fatigue failure is mainly originated from the isolated facets within one or two grains located on the surface of the specimens rather than casting flaws. Figure 9 shows fatigue crack initiation and growth path of a small crack on the surface of the alloys. In the peak-aged alloys, precipitates contribute to the cyclic response other than the grain boundary. Both basal and non-basal slip bands are observed on the surface of the peak-aged sample under the continuous loading. It was reported that addition of Nd and Zn would promote the activation of non-basal slip systems [32]. The fatigue crack initiates from the cracked persistent slip bands (PSBs), which is due to the intrusion/extrusion of dislocations–slip and cumulative damage. The cyclic hardening and subsequent softening behaviour in the peak-aged sample might be primarily due to the retarding effect of the fine β″ precipitates on the dislocations–slip and the formation of cracks on the surface of the sample, respectively. In contrast, for the over-aged sample, the fatigue cracks initiate from the cracked grain boundaries. With the increase in the dislocations piled up at grain boundaries, the grain boundaries start to glide to coordinate the deformation and release stress. Continued grain boundary sliding would accelerate the crack of the grain boundary under continuous loading. The interaction mode between precipitates with gliding dislocations is associated with size and number density of the precipitates. The cyclic stress amplitude of the over-aged alloy keeps steady during fatigue testing, which might be due to the relatively homogenous deformation. The cracks in T61-treated sample tend to propagate along the cracked PSBs within grains in the trans-granular mode, while those in T62-treated counterpart propagate along the cracked grain boundaries in the inter-granular mode.

Fig. 8
figure 8

SEM images of fatigue crack initiation region in a T61- and b T62-treated Mg96.47Nd2.9Zn0.21Zr0.42 alloys

Full size image
Fig. 9
figure 9

OM images of fatigue crack initiation and growth path of a small crack in a T61- and b T62-treated Mg96.47Nd2.9Zn0.21Zr0.42 alloys

Full size image

4 Conclusion

The peak-aged and over-aged Mg96.47Nd2.9Zn0.21 alloys containing 0.42Zr have close yield strength and ultimate tensile strength, and T62-treated alloy has higher ductility and plastic strain amplitude, but lower cyclic stress response than T61-treated counterpart.

The influence of ageing treatment on LCF lives of the NZ30K alloys is very marginal, which is attributed to similar total strain energy densities in T61- and T62-treated alloys. In contrast, the ageing treatment significantly affects the HCF lives of the alloys. The shorter fatigue life of T62-treated alloy compared with that of T61-treated counterpart is attributed to the higher hysteresis energy in the over-aged condition. In addition, the LCF lives of the aged Mg96.47Nd2.9Zn0.21Zr0.42 alloys can be predicted using the Coffin–Manson relation and Basquin laws, the energy-based concepts, respectively.

For T62-treated alloy, the stress amplitude slightly increases, which is due to its high ductility and homogenous deformation. In T61 state, the fatigue cracks initiate along the cracked PSBs and then propagate in the trans-granular mode, while in T62 state, the fatigue cracks initiate along grain boundaries and then propagate in the inter-granular mode.