Phase field modeling and simulation of coupled fracture and twinning in single crystals and polycrystals

被引:66
|
作者
Clayton, J. D. [1 ,2 ]
Knap, J. [1 ]
机构
[1] US Army, Res Lab, Aberdeen Proving Ground, MD 21005 USA
[2] Univ Maryland, A James Clark Sch Engn, College Pk, MD 20742 USA
关键词
Phase field; Fracture; Twinning; Elasticity; Crystals; Finite strain; NONLINEAR ELASTICITY; BRITTLE-FRACTURE; CONTINUUM; DEFORMATION; MICROSTRUCTURE; PROPAGATION; PLASTICITY; MECHANICS; CRITERION; EVOLUTION;
D O I
10.1016/j.cma.2016.01.023
中图分类号
T [工业技术];
学科分类号
08 ;
摘要
A phase field theory incorporating both fracture and deformation twinning behaviors in crystalline solids is described and implemented in finite element calculations. A variational approach is used to derive governing equations for quasi-static loading. The constitutive theory accounts for possible anisotropy of surface energy of fracture, enabling preferential cleavage on intrinsically weak crystallographic plane(s). Both linear elastic and nonlinear elastic models for bulk material behavior are addressed, the latter via compressible neo-Hookean elasticity. Numerical implementation is undertaken via the finite element method, wherein nodal degrees of freedom are displacement components and order parameters associated with twinning shear and local elastic stiffness reduction from fracture. Three dimensional simulations are reported, with solutions obtained via incremental energy minimization subjected to appropriate boundary and irreversibility constraints. Two sets of calculations are considered: a single crystal with a geometric notch, from which a crack and/or twin may extend upon mode I or mode II loading, and simple tension of a polycrystal consisting of grains with various lattice orientations. Results from the first set of calculations demonstrate a tendency for fracture before twinning when surface energies of the two mechanisms are equal, and a tendency for twinning to delay fracture when the fracture energy substantially exceeds the twin boundary energy. Results from the second set demonstrate effects of relative orientations of cleavage planes to habit planes (parallel or perpendicular), effects of initial orientation distributions, and effects of secondary grain boundary phases differing in strength and stiffness from surrounding crystals. Published by Elsevier B.V.
引用
收藏
页码:447 / 467
页数:21
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