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Scripta Materialia 58 (2008) 496–499

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Reliability of compressive fracture strength of Mg–Zn–Ca bulkmetallic glasses: Flaw sensitivity and Weibull statistics

Yuan-Yun Zhao,a Evan Mab and Jian Xua,*

aShenyang National Laboratory for Materials Science, Institute of Metal Research, Chinese Academy of Sciences,

72 Wenhua Road, Shenyang 110016, ChinabDepartment of Materials Science and Engineering, The Johns Hopkins University, Baltimore, MD 21218, USA

Received 7 August 2007; revised 29 October 2007; accepted 31 October 2007Available online 20 December 2007

Mg96�xZnxCa4 (x = 30, 25) bulk metallic glasses (BMGs) belong to one of the brittle families of BMGs, yet their compressivefracture strength exhibit surprisingly high uniformity. This strength reliability is also supported by the Weibull modulus valuederived from an analysis based on Weibull statistics. The flaw sensitivity and its obvious composition dependence are discussed.� 2007 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.

Keywords: Bulk amorphous materials; Metallic glasses; Magnesium; Fracture strength; Reliability

As is well documented, the fracture of brittleengineering materials such as oxide glasses and ceramicsdepends on the stress necessary to propagate a critical-sized ‘‘weakest link’’ (flaw or crack) anywhere in thesample. Thus, the flaw-controlled failure of these brittlematerials leads to a considerable variability in theirmechanical properties, and their reliability under load-ing is most commonly characterized using statisticalapproaches such as the classical Weibull statistics frame-work [1–3]. Metallic glasses processed via alloy meltcasting, as a new class of quasi-brittle materials, wouldalso exhibit similar flaw sensitivity and scatter in theirfracture strength. However, despite of the rapid develop-ment of bulk metallic glasses (BMGs) in recent years,their flaw tolerance and reliability under loading is onlybeginning to be documented and analyzed [4], althoughWeibull analysis was occasionally applied to metallicglass ribbons many years ago, before the advent ofBMGs [5,6].

Upon loading of as-cast brittle BMGs, uncontrolla-ble minor flaws in the glass volume (or on its surface)tend to trigger runaway shear banding. The first majordiscrete shear band that cuts across the sample oftenleads to catastrophic fracture. Such strength-limitingflaws may include stress-concentrators such as castingpores, inclusions, surface irregularities or even spatial

1359-6462/$ - see front matter � 2007 Acta Materialia Inc. Published by Edoi:10.1016/j.scriptamat.2007.10.052

* Corresponding author. Tel.: +86 24 23971950; fax: +86 2423971215; e-mail: jianxu@imr.ac.cn

(chemical or topological) heterogeneity. It is obviouslyof interest to find out the strength variability of BMGsin such flaw-sensitive deformation/fracture scenarios.This would allow an assessment of the reliability ofthe macroscopic mechanical properties, which is veryimportant for the application of BMGs as structuralmaterials. Recently, such assessment examining the uni-formity of compressive fracture strength was performedon Zr-based BMGs [4]. A very high Weibull modulus(m) value of 74 was found for the Zr48Cu45Al7 BMG,approaching the range for conventional ductile metals.Meanwhile, it is noteworthy that the m value seems tocorrelate with the intrinsic malleability of BMGs.

Compared with Zr (or Cu and Pd) based BMGs, Mg-based ones are more brittle and flaw-sensitive, eventhough some alloys of them have a satisfactory glass-forming ability (GFA) and form sizable materials[7–11]. In most cases, these BMG materials were fabri-cated via conventional casting. Their failure under com-pressive loading exhibits a typical flaw-controlledbehavior, and the measured apparent fracture strength(rf) is usually lower than their intrinsic yield strength(ry, due to controlled shear banding) [10,12]. Here wereport a Weibull analysis for Mg–Zn–Ca ternary BMGs[11], as they serve as a representative of brittle BMGs. Inaddition, we examine the composition effects on the fail-ure reliability by comparing two BMGs with differingMg content, Mg66Zn30Ca4 vs. Mg71Zn25Ca4. As shownrecently for several Zr-based BMGs [13–15], the

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Figure 2. (a) DSC scans of as-cast 5 and 2 mm diameter rods forMg66Zn30Ca4 and Mg71Zn25Ca4 alloys, respectively. (b) DSC scans ofthe alloys in (a) near their melting temperatures during heating (solidlines) and cooling (dash lines).

Y.-Y. Zhao et al. / Scripta Materialia 58 (2008) 496–499 497

malleability in a given alloy system can be highly depen-dent on composition.

A mixture of pure elements (>99.9 wt.%) of Mg, Caand Zn were melted under an inert atmosphere in aninduction furnace with the nominal composition (inatomic percentage). The master alloy was remelted byinduction melting in a graphite tube and injected in apurified inert atmosphere into the copper mold. Thecross-sectional surfaces of the as-cast rods were ana-lyzed by X-ray diffraction (XRD) using a RigakuD/max 2400 diffractometer with monochromated CuKa radiation. The glass transition and crystallizationbehavior of as-cast glassy rods were investigated by dif-ferential scanning calorimetry (DSC) (Perkin–Elmer,DSC-diamond) with graphite pans under flowing puri-fied argon at a heating rate of 20 K min�1. Uniaxialcompression testing was conducted at room temperaturewith a constant nominal strain rate of 1 · 10�4 s�1. Thetest samples for Weibull analysis were 3.5–4.0 mm inlength and 1.86 mm in diameter, providing a nominalaspect ratio of �2:1 (h/d � 2). Samples 0.85 mm inlength and 1.86 mm in diameter, yielding a nominallow aspect ratio of �1:2 (h/d � 0.5), were also tested.Under this geometrically confined condition, the flaw-controlled fracture can be suppressed such that the ry

of the BMGs can be determined [16,17]. The loadingsurfaces were polished to be parallel to an accuracy ofless than 10 lm.

Starting from the Mg67Zn28Ca5 BMG with a criticalsize (Dc) of 4 mm [11], the GFA of a number of Mg–Zn–Ca compositions at 1 at.% intervals was investi-gated. The best glass former has been located at thecomposition of Mg66Zn30Ca4, with a Dc = 5 mm. AnMg-richer BMG, with Dc not less than 2 mm, was foundat Mg71Zn25Ca4. Figure 1 shows the XRD patterns ofthe as-cast Mg96�xZnxCa4 (x = 30, 25) BMGs at theirDc; both exhibit typical fully amorphous features. Thecorresponding DSC curves are displayed in Figure 2aand b, with the detailed results for the thermal proper-ties listed in Table 1, including the glass transition tem-perature Tg, onset temperature of crystallization Tx1,width of supercooled liquid region DTx (DTx = Tx1 �

Table 1. Critical sizes and thermal properties determined with DSC for the

Alloys Dc (mm) Tg (K) Tx1 (K) DTx (K

Mg66Zn30Ca4 5 351 380 29Mg71Zn25Ca4 2 336 356 29

Figure 1. XRD patterns of the as-cast BMG rods with a diameter of5 mm for Mg66Zn30Ca4 and a diameter of 2 mm for Mg71Zn25Ca4.

Tg), heat of crystallization events DHx, onset tempera-ture of melting events Tm, liquidus temperature TL

and reduced glass transition temperature Trg (Trg =Tg/TL). It was observed that with the increase in theMg content in the BMGs, both the Tg and Tx1 shift tolower temperatures. The different behaviors of the glasstransition and the crystallization seen for these twoglasses suggest likely differences in their intrinsic localstructure, which might lead to different deformationbehaviors. In addition, it is noticed that, in terms ofthe GFA in the ternary alloys, the Mg–Zn–Ca systemis inferior to that of the Mg–Cu–RE (RE = Y, Gd) sys-tems, in which the Dc of the Mg58.5Cu30.5Y11 [7] andMg61Cu28Gd11 [10] is 9 and 12 mm, respectively.

Twenty-five samples were tested for each alloy, andall the stress–strain curves, without any left out, areshown in Figure 3a and b for Mg66Zn30Ca4 andMg71Zn25Ca4 BMG, respectively. For comparison,the ry obtained by testing the low aspect ratio sam-ples (h/d � 0.5) is also included in the figures:930 MPa for the Mg66Zn30Ca4 and 830 MPa for theMg71Zn25Ca4. The apparent fracture strength rf forthe better BMG former Mg66Zn30Ca4 ranges from716 to 854 MPa, with a variation of ±10% about its

Mg–Zn–Ca BMGs fabricated using copper mold casting

) DHx (kJ mol�1) Tm (K) TL (K) Trg

2.7 612 647 0.542.4 611 671 0.50

Figure 4. Weibull plots of compressive fracture strength (rf) takenfrom 25 samples for Mg66Zn30Ca4 (line A) and Mg71Zn25Ca4 (line B)BMGs.

Figure 3. Compressive stress–strain curves from 25 samples for: (a)Mg66Zn30Ca4 and (b) Mg71Zn25Ca4BMGs, together with a curve for asample with low aspect ratio (h:d = 1:2) for each alloy.

498 Y.-Y. Zhao et al. / Scripta Materialia 58 (2008) 496–499

mean value. For the more Mg-rich BMG Mg71Zn25Ca4,the rf ranges from 672 to 752 MPa, with a variation ofonly ±6% about its average. This indicates that withincreasing Mg content in the BMG, both ry and rf

are decreased. Furthermore, it is noticed that the rf

only reaches about 80–90% of their respective ry,namely rf/ry � 0.8–0.9, consistent with the notion thatthe failure is flaw-controlled in all the cases. Addition-ally, the ry of these two Mg–Zn–Ca BMGs is at least�15% lower than that of Mg–Cu–RE (RE = Y, Gd)BMGs [9,10].

The variability of rf in the present as-cast BMGs wasanalyzed using the Weibull statistical method. The Wei-bull equation describes the fracture probability Pf for agiven uniaxial stress r

P f ¼ 1� expf�V ½ðr� rlÞ=r0�mg; ð1Þwhere r0 is a scaling parameter, m is the Weibull modu-lus and V is a normalized volume of the tested sample.The parameter rl denotes the stress at which there is azero failure probability, and is usually taken to be zero[18]. The probability of failure, Pf, was calculated usingthe equation [19–21]

P f ;i ¼ ði� 0:5Þ=n; ð2Þwhere n is the total number of the samples tested and i isthe sample rank in ascending order of failure stress.These results were then plotted in the usual doublelogarithmic form of the Weibull expression

lnfln½1=ð1� P fÞ�g ¼ ln V þ m ln r� m ln r0: ð3ÞFigure 4 shows the Weibull plots in the form suggestedby Eq. (3) for the Mg66Zn30Ca4 (line A) and theMg71Zn25Ca4 (line B) BMGs. As can be seen, in eachcase, a good linear relationship was observed, suggesting

that the experimental data can be reasonably describedby the Weibull distribution equation. Linear least-squares fitting of Eq. (3) to these data gives the Weibullmodulus m as 26 and 41 for the Mg66Zn30Ca4 and theMg71Zn25Ca4, respectively.

Since the m value reflects the degree of variation inthe strength of the samples tested, a higher m value de-notes a narrower distribution of fracture stresses andhigher reliability. In general, Weibull moduli for ductilecrystalline metals and for brittle engineering ceramicmaterials are typically of the order of �100 and �5[22], respectively. Although BMGs, especially Mg-basedmetallic glass, are often regarded as macroscopicallybrittle materials, it is interesting to observe a relativehigh reliability from the rather uniform strength dataand the magnitude of the Weibull moduli. Comparedwith the available m values for the BMGs [4], the mvalue for Mg66Zn30Ca4 is similar to the value for(Zr48Cu45Al7)Y2 (m = 25.5), but smaller than that forZr48Cu45Al7.

In summary, the optimal composition for glass for-mation has been determined for the Mg–Zn–Ca ternarysystem, and it is concluded that the GFA of this systemis not as good as that of the Mg–Cu–Y or Mg–Cu–Gdalloys [7,10]. The apparent compressive fracture strengthvalues measured for a large number of as-cast Mg–Zn–Ca BMGs are rather uniform. This suggests that theflaws in cast BMGs have rather uniform sizes, the mea-sured fracture strength is fairly reliable, and these glassesare reasonably tolerant to minor flaws. A Weibull statis-tical analysis has been performed and the resulting Wei-bull moduli support the indications above. Thesefindings are consistent with the notion that BMGs arecapable of plastic flow which reduces the flaw sensitivity.However, the fracture strength values observed have notreached the intrinsic yield strength, because the nucle-ation of the shear bands can be assisted by minor flaws,and these run-away shear bands cause the macroscopi-cally quasi-brittle behavior. The appreciable differencebetween the two alloys in yield strength (Fig. 3) maybe explained by considering that the yielding in metallicglasses is related to the crossing of a shear flow barrier.

Y.-Y. Zhao et al. / Scripta Materialia 58 (2008) 496–499 499

The height of this barrier scales with the isoconfigura-tional shear modulus [23], which is lower at higher Mgcontent.

The authors gratefully acknowledge stimulating dis-cussions with Professor Y. Li (NUS). This work wassupported by the National Natural Science Foundationof China under Grant No. 50621091 and National BasicResearch Program of China (973 Program) under Con-tract No. 2007CB613906.

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