PSI - Issue 23

Yoshitaka Umeno et al. / Procedia Structural Integrity 23 (2019) 348–353 Author name / Structural Integrity Procedia 00 (2019) 000 – 000

3

350

A

B

B

O

O

O

n

C

Fig. 1: Molecular formula of PC and its CG representation.

2.2. Simulation Cells and Condition for Deformation Analyses Simulation cells of different sizes as shown in Fig. 2 were prepared. The small cell (Fig. 2(a)) consists of more than 4,000 CG particles, which is equivalent to ~30,000 atoms and is used for comparison with the AA model and long-time calculations for deformation analyses at low strain rates. The large cell (Fig. 2(b)), which includes more than 130,000 CG particles (equivalent to ~10 6 atoms), is used for investigation of multiaxial effect in larger scale. The three-dimensional periodic boundary condition was imposed on both the simulation cells. Molar masses of molecules were given uniformly for each simulation cell for simplification. Another cell with a medium size (~113 Å , not shown) having about 16,400 CG particles is used for analyses of the effect of molar mass (Sec. 3.3). Simulation cells were deformed by applying external strain at constant strain rates, ˙ε . The wide range of strain rate, ˙ε = 10 -9 -10 -4 fs -1 , was applied to investigate the rate effect, and other analyses were carried out at ˙ε = 10 -6 fs -1 . The following four types of tension were tested; the uniaxial stress ( σ xx = σ yy = 0, ε zz = ˙ε t ; tension with Poisson contraction), the uniaxial strain ( ε xx = ε yy = 0, ε zz = ˙ε t ; tension without Poisson contraction), uniform biaxial tension ( σ xx = 0, ε yy = ε zz = ˙ε t ) and uniform triaxial tension ( ε xx = ε yy = ε zz = ˙ε t ). Note that triaxial stress occurs under the condition of the uniaxial strain, i.e. , σ xx , σ yy ≠ 0.

(b)

~225 Å

(a)

~72 Å

Fig. 2: Simulation cells of PC for deformation analyses; (a) small cell and (b) large cell.

3. Result and Discussion

3.1. Effect of Loading Mode on Deformation Behavior Figure 3 (a) shows stress-strain relationships obtained with the large simulation cells under various tensile loading types. The stress-strain relationships can be categorized into two types; the uniaxial and uniform biaxial tension results in the ductile behavior, while the brittleness was observed in uniaxial tension with transverse strain constrained and uniform triaxial tension. The yield stress is ~100 MPa in the former cases and ~250 MPa in the latter. These tendencies in the stress-strain relationships are corresponding to the structural change during deformation. Figures 3 (b) and (c) show snapshots of the simulation cell after deformation under different loading modes. In the ductile cases, molecules in the cell deform uniformly along the tensile direction. Conversely, in the brittle cases, it is observed that voids are