Evaluation of Dislocation Storage by Means of Crystal Plasticity Analysis
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Evaluation of Dislocation Storage by Means of Crystal Plasticity Analysis Tetsuya Ohashi1 and Kazuhisa Asakawa2 1 Kitami Institute of Technology, 2 Graduate student, Kitami Institute of Technology, ABSTRACT A numerical model of two phase metal microstructure of f.c.c. type crystal is made where a harder inclusion of a spherical shape is embedded in softer matrix. The model is subjected to a tensile load and its deformation is analyzed by a finite element crystal plasticity code. Under the tensile load, plastic slip deformation on {111} slip systems take place in the matrix and the density distribution of the geometrically necessary dislocations is evaluated from the gradient of plastic shear strain on slip systems. Obtained results show not only a simple loop structure around the inclusion but also kink wall structure and some smaller loops. Details of the strucuture are discussed.
INTRODUCTION Accumulation of dislocations and their patterning in metal microstructures play important roles in their macroscopic mechanical behavior. We have been, so far, analyzing accumulations of the statistically stored dislocations [1][2] and the geometrically necessary ones by finite element crystal plasticity analysis [3][4]. Dislocations which are trapped during their glide motion by randomly distributed obstacles in microstructure are usually called the statistically stored ones. The density increment of the statistically stored dislocations is proportional to the increment of plastic shear strain. On the other hand, the detailed information of dislocations at obstacles is not obtained by the evaluation of the statistically stored dislocations but depicted from the evaluation of them as the geometrically necessary ones. The density of the geometrically necessary dislocations (abbrebiated as GNDs, hereafter) is obtained from the spacial gradient of the plastic shear strain which is inherently non-uniform at the presence of apparent inhomogeneities. The Orowan loops are well known fine structure of the dislocations which form around inclusions during plastic slip. We have numerically analyzed the plastic slip deformation in microstructure models which include a cuboidal shaped inclusion by means of the crystal plasticity analysis and found that loop shaped dislocation structure was formed around them [4]. In this paper, we examine the slip deformation around a spherical shaped inclusion and fine structure of the geometrically necessary dislocations.
BASIC EQUATIONS Let us consider slip deformation in face centered cubic type crystals, where slip takes place on twelve {111} slip systems. The activation condition of the slip system n is given by the Schmid law; BB5.4.1
Pij( n ) Tij
R
(n)
, Pij( n ) T& ij
R
O
(n) (n) j i
&(n)
,
(n
1,L,12) ,
(1)
and Pij( n )
12 O
(n) (n) i j
b
b
,
(2)
where, Tij and R ( n ) denote the stress and the critical resolved shear stress on the slip system n, The Schmid tensor Pij( n ) is defined by the slip plane normal Oi( n ) and the slip
respectively.
direction bi( n )
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