The influence of mechanical constraints introduced by β annealed microstructures on the yield strength and ductility of Ti-6Al-4V

Abstract

Discussed is a computational study of the influence of the microstructure’s geometric morphology on the yield strength and ductility of Ti-6Al-4V. Uniaxial tension tests were conducted on physical specimens to determine the macroscopic yield strength and ductility of two microstructural variations (mill annealed and β annealed) to establish comparisons of macroscopic properties. A multi-experimental approach was utilized to gather two dimensional and three dimensional data, which were used to inform the construction of representative β annealed polycrystals. A highly parallelized crystal plasticity finite element framework was employed to model the deformation response of the generated polycrystals subjected to uniaxial tension. To gauge the macroscopic response’s sensitivity to the morphology of the geometry, the key geometrical features - namely the number of high temperature β phase grains, α phase colonies, and size of remnant secondary β phase lamellae - were altered systematically in a suite of simulations. Both single phase and dual phase aggregates were studied. Presented are the calculated yield strengths and ductilities, and the resulting trends as functions of geometric parameters are examined in light of the heterogeneity in deformation at the crystal scale.

Introduction

Ti-6Al-4V is the most widely used titanium alloy, and is commonly used for critical components in many different engineering applications - desirable because of the concurrence of high strength, corrosion resistance, and low weight (Lütjering and Williams, 2007). The thermomechanical processes the raw material is subjected to during manufacture have the potential to introduce a wide variety of microstructures, in turn altering the deformation response of the material. Representing two extremes of attainable microstructures are the mill annealed microstructure and the β annealed microstructure. Experimental observation has shown that the two microstructures are markedly different in terms of their geometric features and deformation response (Ding, Guo, Wilson, 2002, Semiatin, Knisley, Fagin, Barker, Zhang, 2003). The presence of two crystallographic phases, including a hexagonal crystallographic phase that exhibits strong elastic and plastic anisotropy (Kelly, Groves, 1970, Tomé, Kocks, 1985) adds complexity to the material’s deformation response. How the microstructure effects the deformation response can be understood by considering the mechanical constraints that exist between the two crystallographic phases when equilibrium and compatibility are enforced. Understanding the microstructure-property relationship - specifically in regards to the estimation of the yield strength and ductility - is crucial in an alloy with such ubiquity, wide microstructural variability, and complex crystal scale behavior.

Simulating the deformation of these microstructures provides insight into the development of plasticity at the crystal scale, and the influence that the microstructure has on the resulting macroscopic behavior. Mathematical frameworks exist that describe the behavior of plastically deforming materials at the crystal scale (Asaro, Needleman, 1985, Marin, Dawson, 1998b). These crystal plasticity equations are often implemented in a finite element computational framework (Marin and Dawson, 1998a). Due to constraints on computational capabilities, studies have historically been limited to simplified representations of microstructures (Raabe, Zhao, Mao, 2002, Sarma, Dawson, 1996, Zhang, Zhang, McDowell, 2007), idealized models for the study of texture evolution (Philippe et al., 1995), or detailed microstructural representations of limited scale (Barton and Dawson, 2002). Indeed, while other modeling techniques (e.g. mean field approaches such as the Taylor model or Sachs model) are able to estimate an aggregate’s macroscopic response, high fidelity finite element modeling allows for a better understanding of the microstructure’s influence on such a response by considering the spatial arrangement of grains and phases. The development of more efficient computational architectures, coupled with the use of highly parallelized code has allowed for the use of larger meshes, and thus the inclusion of fine geometric detail. Recent experimental and computational studies suggest that deformation occurs heterogeneously across individual grains, necessitating the use of high fidelity representations of microstructures in order to accurately predict the deformation response (Obstalecki, Wong, Dawson, Miller, 2014, Wong, Obstalecki, Miller, Dawson, 2015).

Representation of a microstructure for use in such simulations is dependent on the experimental identification of key geometric features. Two dimensional methods, such as optical microscopy and EBSD provide detailed depictions of surface features of microstructures, yet are lacking due to their failure to elucidate three dimensional features. Recent developments in both destructive (Echlin et al., 2012) and non-destructive (Lienert et al., 2011) orientation mapping techniques allow for the construction of three dimensional maps - providing not only detailed information about the geometric features of a microstructure, but also the spatial distribution of crystallographic orientations. A multi-experimental approach allows for a better understanding of a microstructure’s geometric morphology. These data, in turn, may be used to inform the generation of a potentially infinite number of randomly generated microstructure representations that contain features similar to those observed. Voronoi tessellations have proven to be an effective way to represent generic polycrystals (Barbe, Decker, Jeulin, Cailletaud, 2001, Watanabe, Zbib, Takenouchi, 1998), and techniques and implementation have recently evolved to efficiently facilitate the creation of large polycrystals and attendant robust finite element meshes (Quey et al., 2011). While sufficient in representing main features of the mill annealed microstructure, Voronoi tessellations alone are insufficient in accurately representing the fine details of the β annealed microstructure.

In this paper, we focus specifically on how attributes of the β annealed microstructure introduce mechanical constraints that affect the material’s macroscopic properties. A method is described that creates an idealized version of the β annealed microstructure that includes the experimentally observed fine geometric features. A highly parallelized crystal plasticity finite element framework is used to simulate the deformation response. Details of the geometry are altered to gauge their influence on macroscopic behavior, and lower bound estimates on the yield strength and ductility are found. Following presentation of the macroscopic properties, concurrent responses at the crystal scale are examined. The influence of structure-imposed constraints within the microstructure on the intensity of deformation heterogeneity is demonstrated with contrasting images of evolving deformation rate banding for defining features of the microstructure. Further, the propensity for microstructure features to constrain slip activity to one or two systems is investigated in detail. The differences in responses at the crystal scale provide a better understanding of the particular features that most influence the trends observed at the macroscopic scale.