Multiaxial Kitagawa analysis of A356-T6

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Abstract

Experimental Kitagawa analysis has been performed on A356-T6 containing natural and artificial defects. Results are obtained with a load ratio of R = −1 for three different loadings: tension, torsion and combined tension–torsion. The critical defect size determined is 400 ± 100 μm in A356-T6 under multiaxial loading. Below this value, the microstructure governs the endurance limit mainly through Secondary Dendrite Arm Spacing (SDAS). Four theoretical approaches are used to simulate the endurance limit characterized by a Kitagawa relationship are compared: Murakami relationships [Murakami Y. Metal fatigue: effects of small defects and nonmetallic inclusions, Elsevier; 2002], defect-crack equivalency via Linear Elastic Fracture Mechanics (LEFM), the Critical Distance Method (CDM) proposed by Susmel and Taylor [Susmel L, Taylor D. Eng Fract Mech 2008;75:15] and the gradient approach proposed by Nadot and Billaudeau [Nadot Y, Billaudeau T. Eng Fract Mech 2006;73:1]. It is shown that the CDM and gradient methods are accurate; however fatigue data for three loading conditions is necessary to allow accurate identification of an endurance limit.

Introduction

The tensile fatigue behaviour of A356-T6 has been the subject of study by a number of researchers [1], [2], [3], [4], [5], [6], [7]. In almost all related studies, casting defects such as intermetallic inclusions, porosity, shrinkages and oxide films have been shown to be present at the origin of the failure. In cases where defects were not present, the basic microstructure [8], [9] has been shown to determine the fatigue life. The presiding microstructural factor in this latter case is Secondary Dendrite Arm Spacing (SDAS) which decides the overall strength of the material. By processing samples of A356 via Hot Isostatic Pressing (HIP) to eliminate porosity, Gao et al. [8] compared the influence of SDAS and porosity on the tensile endurance limit. It was found that the fatigue limit was significantly increased either through HIP or halving the SDAS. While the effects of porosity and SDAS are not mutually exclusive, the role SDAS plays is less important when the material contains defects. Another microstructural characteristic that participates in fatigue mechanisms is the secondary eutectic phase. Fatigue crack initiation has been found to occur at silicon particles within this phase [5], [9] in samples that were free of defects. However, in the majority of prior studies, the authors did not explicitly quantify the critical defect size. One exception is the work of Brochu et al. [5] where an experimental Kitagawa relationship was developed for rheocast A357, a similar alloy to A356. This study demonstrated a critical defect size of 150 μm under fully reversed (R = −1) tensile loading. In terms of multiaxial fatigue behaviour, only two previous studies are available for A356 [9], [10]. De-Feng et al. [10] performed tension–torsion fatigue testing on thin-wall specimens in the low-cycle regime (104 cycles). McDowell et al. [9] performed torsional High-Cycle Fatigue (HCF) testing, however these tests were conducted with deformation control.

The fatigue life prediction of nominally defective materials such as A356 is of great importance to industry and has been the subject of considerable study. Linear Elastic Fracture Mechanics (LEFM) has been shown to only apply to the study of long cracks where stress fields are homogeneous and not affected by local plasticity, making it inappropriate to be applied on short cracks [11]. Therefore, treating defects as cracks and leveraging analytical approaches based on LEFM may not always be appropriate. Using experimental assessments of local plasticity through microhardness measurements, Murakami [12] has shown that fatigue behaviour can be assessed for some materials through empirical relations based on applied stress and hardness. In terms of more advanced computational and analytical assessments, there are two stress-based approaches as highlighted by Atzori et al. [13]. The first are local methods which dictate that an effective stress must be reached around a defect to affect the fatigue resilience [14], [15] or nominal stress methods where the fatigue or endurance limit of the material is defined in terms of a nominal applied stress [16]. Most recently, Critical Distance Theory [17] has been shown to successfully correlate fatigue behaviour with a critical distance from a defect that is material dependent. Other studies have shown that the stress gradient around a defect is a more practical indicator of fatigue resilience [18], [19], [20].

The objective of the present study is to investigate the influence of casting defects on the HCF behaviour of A356-T6. Kitagawa-type analysis is performed with experimental results for three different scenarios: tension, torsion and combined loading. The critical defect size from a multiaxial standpoint is then defined. Finally, four different approaches to simulating the evolution of the endurance limit with increasing defect sizes are compared for each of the loading cases. This is done to determine the best method for simulating the endurance limit based on defect size for this industrially relevant alloy.

Section snippets

Material and experimental conditions

The material employed in this study was Low-Pressure Die Cast (LPDC), strontium modified A356 (Al–7Si–0.3Mg) in the T6 condition with a typical chemical composition given in Table 1. The majority of fatigue specimens were cut from a wedge-shaped casting, and a lesser number were cut directly from an automotive wheel casting. While both casting types were made with permanent steel dies, the wheel casting was actively cooled during solidification while the wedge casting was left to cool

Experimental results

Experimental fatigue test results are given in Fig. 2, Fig. 4, Fig. 6 in the form of bi-linear Kitagawa diagrams for each of the loading cases. The fracture surfaces were first examined macroscopically, and these observations guided Scanning Electron Microscopy (SEM) analysis of the initiation area. The goal of SEM observations (Fig. 3, Fig. 5, Fig. 7) was to clearly identify the initiation site and where possible, measure the initiating defect. Multiaxial fracture surfaces were found to be

Simulation of multiaxial Kitagawa relationships

Four standard models to predict the endurance limit of defective materials were employed to simulate the behaviour of A356-T6. What follows is a presentation of each model, followed by a comparison of the results of each model to experimental data in Section 5. The following models are able to predict the Kitagawa relationships for tension, torsion and combined loading:

  • 1.

    Linear Elastic Fracture Mechanics (LEFM) approach whereby a defect is considered equivalent to a crack.

  • 2.

    Murakami relationships

Comparison between simulations and experimental results

Fig. 8, Fig. 9, Fig. 10 present the predictions made by each of the four approaches compared with experimental results for the three loading cases. Under tension Fig. 8, the CDM and Gradient approaches describe the experimental results quite well. However, this is likely due to the single experimental point employed for identification of the necessary parameters. The trend of the fatigue limit versus defect size is also well described. Murakami’s equation leads to non-conservative results, but

Conclusion

  • For A356-T6 submitted to multiaxial fatigue loading, fatigue cracks can initiate either on casting defects or inside the microstructure. Both scales are in competition for the localization of cyclic plastic deformation that leads to the initiation of a crack.

  • When a crack initiates at a defect, the various types of defect can be characterized by area: natural defects were found to have the same endurance limit as artificial defects.

  • The critical defect size has been found to be 400 ± 100 μm in

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