Probabilistic fracture of Ti–6Al–4V made through additive layer manufacturing
Introduction
The Ti–6Al–4V alloy is the most widely used titanium alloy with applications in jet engines, airframes and biomedical implants. Consequently, its mechanical behavior has been studied extensively. For example, Zhang et al. (2007) made use of a crystal plasticity model to describe the mechanical response of a Ti–6Al–4V alloy to cyclic loading. Przybyla and McDowell (2011) introduced a microstructure-sensitive extreme value probabilistic framework to compare the fatigue failure of four different Ti–6Al–4V microstructures. Khan et al. (2012) formulated an anisotropic criterion with tension-compression asymmetry to describe the yield behavior of Ti–6Al–4V. The tension/compression asymmetry, anisotropic yielding and anisotropic strain-hardening in Ti–6Al–4V ingots has also been characterized experimentally and modeled at the macroscopic level by Tuninetti et al. (2015). A theoretical model predicting the spacing of periodic adiabatic shear bands during high speed machining of Ti–6Al–4V has been prosed by Ye et al. (2013). Li et al. (2014) observed an increase in the ductility of Ti–6Al–4V during ring expansion experiments at strain rates above about 7 × 103/s.
In aerospace engineering, Ti–6Al–4V components are traditionally manufactured through intense milling of bulk parts, the hot-forming of sheets and assembly welding (Tersing et al., 2012). Additive Layer Manufacturing (ALM) provides a promising cost-effective alternative to traditional machining. Historically, ALM has been intensively used for rapid prototyping, where shape is more important than the mechanical properties of the manufactured parts. Examples are the selective laser sintering with metal powders (Agarwala et al., 1995, Kruth et al., 2003, Levy et al., 2003) or the development of 3D printing with polymers (Levy et al., 2003, Wendel et al., 2008). The mechanical properties of components made from metal powders are often affected by contaminations that are associated with the high surface-to-volume ratio of powders. To the best of the authors' knowledge, ALM components built from powder stock are not yet used in the safety critical load carrying structures of modern jet engines.
Wire-feed processes feature a lower surface-to-volume ratio and thus a lower risk of contamination (Brandl et al., 2008). Other advantages of wire over powder include material availability, cost and quality. Brandl et al., 2008, Brandl et al., 2009 presented an argon flooded open ALM system composed of a Nd:YAG laser beam and a wire-feeder mounted on a 6-axis robot. Baufeld et al., 2009, Baufeld and Van der Biest, 2009, Baufeld et al., 2010 proposed the so-called Shaped Metal Deposition (SMD) process composed of a tungsten inert gas welding torch mounted on a 6-axis robot. The ALM part is built from wire stock on a 2-axis table inside a closed chamber with argon atmosphere. As compared to laser made parts, the SMD parts feature a lower nitrogen contamination (Baufeld et al., 2011).
The basic mechanical performance of ALM materials are typically characterized through uniaxial tension experiments (e.g. Baufeld et al., 2011). In view of using ALM parts in load carrying structures, the multi-axial material response needs to be known. A first objective of the present paper is to characterize experimentally and model numerically the average large deformation response of SMD made Ti–6Al–4V. Given the stochastic nature of the fracture response of ALM materials, a second objective of this work is to formulate and calibrate a probabilistic stress-state dependent fracture initiation model for SMD made Ti–6Al–4V. In Section 2, the macro- and microstructure of an SMD produced Ti–6Al–4V box structure is characterized. Subsequently, a comprehensive plasticity and fracture testing program is executed which includes the tensile testing of smooth, notched and central hole specimens as well as selected shear, bending and punch experiments. In Section 3, a non-associated plasticity model is presented along with a probabilistic formulation of the Hosford–Coulomb fracture initiation model. Finite element simulations are performed for all experiments to determine the loading paths to fracture in terms of the stress triaxiality, the Lode parameter and the equivalent plastic strain. Based on the hybrid experimental-numerical results, the four material parameters of the probabilistic fracture initiation model are identified. The final discussion is primarily concerned with the third objective of this work, which is the comparison of the observed ALM material fracture response with that of conventional Ti–6Al–4V sheet stock, and the identification of the physical origin of the observed randomness in the ALM-made Ti–6Al–4V fracture response.
Section snippets
ALM component
SMD is a Rolls-Royce patented technology being developed for high-value industrial applications at the University of Sheffield Advanced Manufacturing Research Centre. Fig. 1 shows a schematic and a photograph of the manufacturing process. The SMD equipment consists of a 6-axis KUKA KR16 robot with a Gas Tungsten Inert Gas (GTAW) welding head, linked to a 2-axis manipulator, housed in a full sealed chamber. A 1.2 mm diameter Ti–6Al–4V wire (part ⑤ in Fig. 1b) is fed through the GTAW welding head
Plasticity
A simple quadratic plasticity model is employed to provide a first approximation of the inelastic material response. Note that the effect of the third stress invariant on the plastic behavior of the mixed HCP–BCC microstructure of the Ti–6Al–4V alloy is neglected in the context of the present paper. The reader is referred to the literature (e.g. Cazacu et al., 2006) for a proper treatise of this aspect. Due to the uncertainty in the ALM material response, it is still considered as a second
Model calibration and validation
A combined analytical and numerical approach is taken to identify the model parameters. The finite element models are therefore presented first before detailing the calibration procedures and comparing the simulation predictions with the experiments.
Discussion
The particular feature of the current Ti–6Al–4V material is the organization of the microstructures in domains that are due to prior beta grains. This causes macroscopic material heterogeneity at the millimeter scale in addition to the conventional microscopic heterogeneity of a polycrystalline material. To shed more light on the effect of the macroscopic heterogeneity on the material response, the DIC measured surface strain fields are analyzed. In addition, we also performed selected fracture
Conclusions
A comprehensive experimental program is performed to characterize the plasticity and fracture response of Ti–6Al–4V components made through Additive Layer Manufacturing (ALM). A wire-feed process has been used instead of a powder-based technique to reduce the risk of contaminations during manufacturing. For reference, we also performed all experiments on conventional Ti–6Al–4V sheets made through casting followed by rolling. While the experimental results for the sheet stock showed a high
Acknowledgments
The authors would like to thank Alexandre Tanguy and Dr. Eva Heripré (LMS – Ecole Polytechnique) for their help with the microscopic analysis. Thanks are also due to Professor Tomasz Wierzbicki (MIT) for valuable discussions. The partial financial support through the MIT Industrial Fracture Consortium and the CNRS is gratefully acknowledged.
References (39)
- et al.
A new model of metal plasticity and fracture with pressure and Lode dependence
Int. J. Plast.
(2008) - et al.
Wire based additive layer manufacturing: comparison of microstructural and mechanical properties of Ti-6Al-4 V components fabricated by laser-beam deposition and shaped metal deposition
J. Mater. Process. Technol.
(2011) - et al.
A ductile damage criterion at various stress triaxialities
Int. J. Plast.
(2008) - et al.
Orthotropic yield criterion for hexagonal closed packed materials
Int. J. Plast.
(2006) - et al.
A modified damage model for advanced high strength steel sheets
Int. J. Plast.
(2011) - et al.
Hybrid experimental-numerical analysis of basic ductile fracture experiments for sheet metals
Int. J. Solids Struct.
(2010) - et al.
Formation of α-Widmanstätten structure: effects of grain size and cooling rate on the Widmanstätten morphologies and on the mechanical properties in Ti6Al4V alloy
J. Alloys Compd.
(2001) - et al.
Fracture characteristics of a cold-rolled dual-phase steel
Eur. J. Mech. A/Solids
(2011) - et al.
A finite strain, finite band method for modeling ductile fracture
Int. J. Plast.
(2012) - et al.
A new approach for ductile fracture prediction on Al 2024-T351 alloy
Int. J. Plast.
(2012)
Deformation induced anisotropic responses of Ti-6Al-4V alloy part II: a strain rate and temperature dependent anisotropic yield criterion
Int. J. Plast.
Void growth and coalescence in ductile solids with stage III and stage IV strain hardening
Int. J. Plast.
Rapid manufacturing and rapid tooling with layer manufacturing (LM) technologies, state of the art and future perspectives
CIRP Ann. Manuf. Technol.
Effects of deformation rate on ductility of Ti-6Al-4V material
Procedia Eng.
Modeling of shear ductile fracture considering a changeable cut-off value for stress triaxiality
Int. J. Plast.
Experiments and modeling of anisotropic aluminum extrusions under multi-axial loading–part II: ductile fracture
Int. J. Plast.
An assessment of isotropic constitutive models for ductile fracture under high and low stress triaxiality
Int. J. Plast.
Evaluation of associated and non-associated quadratic plasticity models for advanced high strength steel sheets under multi-axial loading
Int. J. Plast.
Simulated microstructure-sensitive extreme value probabilities for high cycle fatigue of duplex Ti-6Al-4V
Int. J. Plast.
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