Staatliche Mater ialprufungsanstalt (MPA), Univeristy of Stuttgart,
Abstract
The failure mechanisms in AlSi-cast alloys with various microstructures ofthe Si-eutectic are studied by in-situ tensile tests in a scanning electron mi-croscope. On the basis of these observations the failure criteria and criticalfailure stresses are determined. Crack initiation and subsequent crack prop-agation is simulated with the Finite Elemente Method using the recently-introduced method of multiphase elements and an automatic element eli-mination technique.
As a result of the experimentally observed failure mechanisms a two-criteria model was applied which enables the simulation of crack initiationin the Si-particles by a normal stress criterion as well as subcritical crackgrowth in the matrix using Rice & Tracey's local damage parameter.
1 Introduction
The mechanical properties of sub-eutectic AlSi-cast alloys are determinedby the microstructure of the Si-eutectic. Lamellar particles which are usu-ally present in the eutectic can be modified by addition of antimony (Sb) toobtain a globular structure [1], resulting in remarkably improved fracturebehaviour. This is reflected in an increase of the critical strain to failurefrom 1 % in the non-modified to 13 % in the Sb-modified structure. Theseobservations are well known from macroscopic tensile tests.
With respect to the optimisation of the mechanical properties it isnecessary to obtain an understanding of the failure mechanisms on a micro-scopic scale. The analysis of the structurally determined fracture behaviour
is the objective of the experimental and numerical microstructural investi-gations presented in this paper. Modelling of real microstructures with theFinite Elemente Method (FEM) allows the simulation of special fractureinitiating situations taking into account the occurrence of several phases aswell as external notches.
2 Overview
The failure mechanisms were investigated for the AlSi-cast alloys of the typeAlSiTMg with lamellar and Sb-modified globular structure of the Si-eutectic(figure 1).
(a) (b)
Figure 1: AlSiTMg, (a) lamella-shaped structure of the Si-eutectic, (b)Sb-modified, globular structure of the Si-eutectic.
In-situ tensile testing in a scanning electron microscope (SEM) is asimple method to accurately investigate the course of events during the fail-ure in such materials. However, it seems worth noting that the observationsare limited to the surface region while the failure event may well occur inthe volume of the material. The concentration of stress in a small region isnecessary to study all details of the crack initiation. For this reason notchedspecimens with an elastic stress concentration factor of OLK— 6 and a slen-der ligament were used. The specimens were loaded in a quasi-static tensiletest with a cross-head speed of 0.1 /zm/s as shown schematically in figure2. On the basis of the experimental observations the failure stress of theSi-particles in the eutectic was determined by FE-calculations.
Furthermore, the fracture behaviour of AlSi-cast alloys was directlysimulated by FE-modelling using
• the method of multiphase elements (MME) [2] in which the Gaussianpoints of one element may be assigned to different phases. (The FE-mesh can then be independent of the structure.)
Figure 2: SEM in-situ tensile specimen and tensile test (schematic).
• an automatic element elimination technique (EET) [3]. The crackpath is simulated by the elimination of elements which exceed a pre-defined failure criterion.
The MME and EET were developed for use with the FE-programLARSTRAN [4]. A linear-elastic behaviour with a Young's modulus of116 GPa [5] was assumed for the Si-particles in the FE-models. The stress-strain diagram of the matrix was adjusted to literature data [6].
3 Results
3.1 Experimental study of the failure process
As expected, the alloy with the lamellar Si-eutectic showed macroscopicallyalmost linear-elastic fracture behaviour. Local yielding of the matrix wasobserved in the notch ground region at approximately 70 % of the globalfailure load. Brittle fracture in the Si-particles occurred at 90 % of theglobal failure load.
In the case of the Sb-modified structure a macroscopic elastic-plasticbehaviour was observed. First deviations from the linear-elastic behaviourin the stress-strain diagram are connected with the brittle fracture of Si-particles. Especially in the notch ground region a strong plastification ofthe matrix in conjunction with particle failure was observed. An exampleis depicted in figure 3.
The metallographic investigation of the crack faces confirmed the roleof the Si-particles as fracture initiating defects. Particles with the longestaxis parallel as well as perpendicular to the direction of normal stress failat about the same load although the geometry of the particles would favour
Figure 3: Particle cracking and local yielding in the notch ground region(AlSiYMg, Sb-modified).
the failure of the parallel oriented particles.Since the Si-particles are the "weak link" in the microstructure a dif-
ferent fracture behaviour is observed for the two alloys. For small globularSi-particles the cracks formed by particle fracture are much smaller than forthe lamellar Si-eutectic. In the lamellar Si-eutectic, the fracture of particlesoriented perpendicular to the loading axis immediately introduces relativelylong critical cracks which result in macroscopically brittle failure. Rathersurprisingly at first sight, in both microstructures cracks were observedsometimes in the notch ground and sometimes in the centre of the speci-men. We conclude from these observations that the first crack initiation isdetermined almost exclusively by the local conditions and is not stronglydetermined by the (mild) global stress concentration from the notch. More-over, a precise determination of the failure initiating event should include afully SD-analysis.
3.2 Determination of the fracture stress of Si-particles
Further SEM in-situ tensile tests were performed for an AlSilTCu alloy withlarge, primary precipitated Si-particles. The fracture of these particles canbe observed more easily and thus be correlated to the globally applied frac-ture load. Since the tests are performed in-situ in a SEM the geometry andlocation of cracked Si-particles with regard to the notch ground is known.The stress distribution in the specimen was then calculated using the FE-program ANSYS 5.1 [7]. Assuming the average material properties of theAlSi-cast alloy and plane stress conditions, the stress components a% and
(jy were calculated for the global load which caused particle fracture.Finally, a model (c.f. figure 4) which takes into account the different
mechanical properties of the two phases was generated to derive the failurestress of the Si-particles. The cell was loaded with the stresses determinedin the previous model. Assuming a normal stress criterion for brittle frac-ture a failure stress of 225 MPa was determined for the particle shown infigure 4.
17%1%%
Sic
J I - P A R T I C L E
Figure 4: Stress distribution of the normal stress cr^ at a Si-particle.
However, since these results were obtained from 2D-calculations, thestress values obtained are somewhat to low. By comparison of 2D- and 3D-calculations for a simple cylindrical particle, the actual (3D) failure stresswas estimated to be about 36 % higher. Thus, a failure stress of 310 MPawas applied as the failure criterion for the Si-particles in the FE-simulations.
3.3 Simulation of crack initiation
Crack initiation was simulated on the basis of the SEM in-situ tensile testsfor an AlSiTMg alloy with lamellar structure. Using the MME a cell repre-sentative of the two-phase microstructure cell was embedded into the centralregion of a 2D-model of the in-situ tensile specimen with 12764 triangularelements (figure 5). Plane strain boundary conditions were imposed.
The stages of crack initiation were simulated with a two-criteria model.Elements which were assigned to the Si-particles are eliminated on the basis
Figure 5: FE-model of the SEM in-situ tensile specimen and (a) modelof the real structure cell (assignment of phases to the Gaussianpoints in the elements) in comparison to (b) the simulated realstructure.
of a normal stress criterion if the maximum normal stress exceeds 310 MPa.A local damage parameter D based on Rice and Tracey's void growth model[8] was used as the failure criterion for the subcritical crack growth in thematrix (1). In agreement with simulations of the crack path in an Al/SiCmetal matrix composite [6] the criterion for element elimination was set to
where rj is the stress triaxiality and tpi the plastic strain.Figure 6 gives an overview of the calculated stages of crack initiation.
As a result of the stress concentration the first cracks are formed in Si-particles in the notch ground region at a total strain of 0.2 %. At the tipof these cracks the damage parameter locally exceeds the critical value at
Figure 6: Crack initiation in the real structure cell with eliminated el-ements (white), stress distribution a? at total strains of (a)0.2 %, (b) 0.25 %, (c) 0.26 % and (d) 0.27 %. Loading axiscorresponds to figure 5.
The calculation qualitatively shows very good agreement with the ex-perimental results. For the one specimen simulated here, crack initiationwas experimentally observed at a total strain of 0.18 %. A large number ofeliminated elements are assigned to these Si-particles. Thus, failure of thesimulated AlSi-cast alloys is mainly determined by brittle fracture of theSi-particles. However, the calculated location of the crack initiation differsfrom the experiment where the first crack was observed in the centre ofthe ligament which again emphasises the necessity of a fully SB-analysis.Studies of 3B-microstructures are in preparation.
4 Summary
The failure mechanisms of AlSi-cast alloys of the type AlSiTMg were studiedexperimentally and with corresponding FE-simulations. In-situ tensile testsperformed in a SEM showed the different stages of failure, crack initiationby brittle fracture of the Si-particles, ductile crack growth by failure of thematrix and instable crack propagation.
The two alloys under consideration behave very differently. It wasfound that the failure of large lamellar particles may immediately form cri-tical cracks and lead to a macroscopic linear-elastic behaviour. The failure ofglobular particles causes much shorter cracks which results in a macroscopicelastic-plastic behaviour. Assuming a normal stress criterion, the failurestress of the particles was estimated by FE-modelling and a direct compar-ison with in-situ investigations on a model alloy with large Si-particles.
Using the MME and EET the fracture behaviour was simulated. Fol-lowing the experimentally observed failure course a two-criteria model wasdeveloped. Failure of the Si-particles which occurs before matrix failurewas simulated by a normal stress criterion. Element elimination in thematrix was performed by Rice fc Tracey's local damage parameter. Theresults of the FE-simulation accurately reproduce the experimental resultswith respect to the total strain which causes the crack initiation. However,the precise location of crack initiation is not reproduced accurately, whichdemonstrates the necessity of a fully 3D-analysis.
Acknowledgements
This research work is part of the COST-512 program supported by BMBF(contract No. 03K 8004).
References
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