Lattice Orientation Effects on Void Growth and Coalescence in FCC Single Crystals
Lattice orientation eﬀects on void growth and coalescence in fcc single crystals G.P. Potirniche a, J.L. Hearndon a, M.F. Horstemeyer a,b,*, X.W. Ling a
a Center for Advanced Vehicular Systems, Mississippi State University, Box 5405, MS 39762, United States b Department of Mechanical Engineering, Mississippi State University, Box 5405, MS 39762, United States
Received 10 March 2005 Available online 28 September 2005
Void growth and coalescence in fcc single crystals were studied using crystal plasticity under uni- axial and biaxial loading conditions and various orientations of the crystalline lattice. A 2D plane strain unit cell with one and two cylindrical voids was employed using three-dimensional 12 poten- tially active slip systems. The results were compared to ﬁve representative orientations of the tensile axis on the stereographic triangle. For uniaxial tension conditions, the void volume fraction increase under the applied load is strongly dependent on the crystallographic orientation with respect to the tensile axis. For some orientations of the tensile axis, such as  or , the voids exhibited a growth rate twice as fast compared with other orientations (, ). Void growth and coales- cence simulations under uniaxial loading indicated that during deformation along some orientations with asymmetry of the slip systems, the voids experienced rotation and shape distortion, due mainly to lattice reorientation. Coalescence eﬀects are shown to diminish the inﬂuence of lattice orientation on the void volume fraction increase, but noteworthy diﬀerences are still present. Under biaxial load- ing conditions, practically all diﬀerences in the void volume fraction for diﬀerent orientations of the tensile axes during void growth vanish. These results lead to the conclusion that at microstructural length scales in regions under intense biaxiality/triaxiality conditions, such as crack tip or notched regions, the plastic anisotropy due to the initial lattice orientation has only a minor role in inﬂuenc- ing the void growth rate. In such situations, void growth and coalescence are mainly determined by the stress triaxiality, the magnitude of accumulated strain, and the spatial localization of such plastic strains.
During the past decades, extensive research has been performed in the area of ductile fracture of polycrystalline metals. Void nucleation, growth, and coalescence have been studied both experimentally (Gurland and Plateau, 1963; Beachem and Yoder, 1973; Clayton and Knott, 1976; Hayden and Floreen, 1969; Wilsdorf, 1983; Garrison and Moody, 1987) and theoretically (McClintock, 1968; Rice and Tracey, 1969; Gurson, 1977; Budianski et al., 1982; Tvergaard, 1990; Faleskog and Shih, 1997; Horstemeyer et al., 2000a,b,c). To clarify the conditions leading to final fracture in isotropic materials, computational void growth and coalescence studies employed mainly unit cell models. Faleskog and Shih (1997) analyzed the interaction effects between the triaxiality, plastic yielding and various size voids interacting for void coalescence. In their analysis, void coalescence first developed by one void that rapidly enlarged, and created a larger triaxiality field around smaller voids distributed throughout the material. Coalescence processes and a decrease in the load carrying capacity continued until the microscopic ligaments failed due to the cleavage along crystallographic planes. They concluded that the primary process in ductile failure in high-strength metals is by microvoid cavitation and link-up.
Coalescence was also indicated to occur when the deformation mode changed from an axisymmetric to a uniaxial type, as indicated in a paper by Koplik and Needleman (1988). The influence of various issues, such as void spacing, void shape and strain hardening coefficient, was addressed by Pardoen and Hutchinson (2000) and by Horstemeyer and Ramaswamy (2000b). Horstemeyer et al. (2000c), using axisymmetric and planar unit cells, analyzed void growth and coalescence at the micromechanical length scale in two materials, a stainless steel and an aluminum alloy, and they concluded that coalescence is determined by an intervoid ligament distance (ILD). Li et al. (2000) used both an axisymmetric unit cell model and a plane stress model to evaluate the void growth in a matrix with varying strain hardening exponents. High triaxiality and intense plastic straining were found to be the main causes for the accelerated void growth. Li et al. considered that in addition to the stress triaxiality and accumulated plastic strain, void growth is determined also by a ‘‘third factor’’ called ‘‘the third invariant of generalized strain rate’’ (Li et al., 2000). Under conditions of constant triaxiality, the void growth is more pronounced if this third strain invariant is assumed to vanish. Void interaction for different void arrangements by using cubic and hexagonal unit cells was analyzed by Kuna and Sun (1996),and they found that the stress–strain curve indicated differences in the body-centered void arrangements with respect to the other unit cell types, which was explained by the differences in the plastic collapse mechanism between these void arrangements. The effect of void clustering on ductile fracture was also studied by Benson (1995). He found that void cluster size has a significant effect on the fracture strain, while the ultimate strain is almost insensitive to this parameter. This dependence manifested very strongly only after the cluster size has reached a critical value, and he concluded that, at least theoretically, the cluster can be replaced by an equivalent larger void.
Recent developments in the damage mechanics area consider the influence of microstructural conditions, such as inclusions (Bonfoh et al., 2004; Siruguet and Leblond,2004a,b) and crystallographic slip within single crystals (Gan and Kysar, 2005). The inﬂuence of plastic anisotropy on damage evolution was investigated by Qi and Bertram (1999) by considering the process of creep damage in fcc single crystals. By using a creep-damage model for single crystals they noticed major diﬀerences in the creep strain and the accumu- lated damage depending on crystal orientation with respect to the tensile axis (, , or ). Shu(1998) used an elasto-viscoplastic strain gradient crystal lasticity theory to study the void growth under uniaxial and biaxial strain ﬁelds. By using a double slip orientation model developed by Rashid and Nemat-Nasser (1992), Shu observed a size scale eﬀect as the ratio between the unit cell considered for analysis and void embedded in this unit cell was changed, which led him to the conclusion that small voids have the ten- dency to grow slower than big voids, also noted by Horstemeyer and Ramaswamy (2000b). A similar result was obtained by Tvergaard and Niordson (2004), who applied a non-local elastic–plastic model to study the growth of voids comparable with a charac- teristical material length. Wen et al. (2005) extended Gurson model to account for the void size eﬀect. They found that, for small strains, void size has practically no eﬀect on the stress–strain curve at small void volume fractions, the void size becoming signiﬁcant only at large void volume fractions.
Orsini and Zikry (2001) studied the void growth and interaction in fcc copper crystals using ﬁnite element analysis by employing a unit cell with a cluster of four voids arranged in periodic and random void arrangements. Their study employed a rate-dependent for- mulation of crystal plasticity, and they analyzed only one orientation of the crystalline lattice, namely a double slip orientation with the tensile axis in the direction ½-11 2]. The results of their study illustrated that the rotation of the crystalline lattice and plastic activity on slip systems was concentrated mainly in the ligament region between the voids. The hydrostatic stress also increased in this region to approximately twice yield stress. Their very interesting study lacked the consideration of diﬀerent orientations for the crystalline lattice as well as the inﬂuence of biaxiality/triaxiality on void growth and coalescence. Void growth in hcp single crystals has been analyzed by O'Regan et al. (1997) using ﬁnite element analysis and a constitutive theory that implemented a triple slip model. They found that the relative angles between the slip systems had a greater role in determining the void growth rate than the orientation of the lattice with respect to the tensile axis. More recently, Kysar et al. (2005) analyzed the case of circular void embedded in a single crystal in plane strain conditions using slip-line theory. They found that the stress and deformation state are heterogeneous, with sectors around the void, where individual slip systems are active.
The goal of this study is to computationally simulate the processes of growth and coa- lescence of voids embedded in single crystals and to elucidate the inﬂuences of crystallo- graphic plastic slip on the mechanics of void enlargement. The complexity of plastic anisotropy at the crystallographic level is simulated by considering ﬁve representative ori- entations on the stereographic triangle. The tractions on the unit cell model considered are applied both uniaxially and biaxially, and the implications on the evolution of the void growth are studied. This study represents an eﬀort toward a multiscale approach to dam- age mechanics and ductile fracture, considering that growth and oalescence of voids oc- curs many times in very small and localized regions, notch radii and shear bands of intensely plastic strains.
The paper is organized as follows. Section 2 brieﬂy introduces crystal plasticity consti- tutive theory used in this study to describe the matrix behavior. Section 3 describes the finite element model used in this study. Section 4 presents the results and discussion on the void volume fraction evolution and stress–strain behavior for various crystallographic orientations. Section 5 presents the main conclusions.
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