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Purpose

Figure 1 - Change in perfect lattice created by program CRACK.

The program reads in the following information:

• the atom positions for the perfect lattice,
• the lattice elastic constants,
• the orientation of lattice,
• the surface energy of the surface exposed by the crack, and
• the desired stress intensity (in units of the Griffith's critical stress intensity, which the program calculates).

• the values of critical and applied stress intensity
  
  and either
  
  
  • the positions of the atoms after the crack is in place (Figure 6), or
  
  or
  
  • the perfect lattice positions along with the displacements needed to move the atoms to their positions under a crack at Griffith's Critical Stress Intensity (Figure 5).

Usage

elastic.fil

This file contains all the Voight elastic constants (C11, C12, etc.) for the lattice. Comments can appear anywhere in the file, and they must start with the character #.

The elastic constants can appear in the following format:

     C11
     C12 C22
     C13 C23 C33
     C14 C24 C34 C44
     C15 C25 C35 C45 C55
     C16 C26 C36 C46 C56 C66

This is the lower half the symmetric elastic constant matrix, for the material in standard orientation, that is x, y and z are the 100, 010 and 001 lattice directions. The units for the elastic constants are erg/cm² (note that one Mbar equals 10¹² erg/cm²). For common lattice symmetries the elastic constants C14, C24, C34, etc., will equal zero.

The position of the elastic constants on each line is not important. It is only required that they appear in above order.

Figure two shows an example of an elastic constant file.

Figure 2 - File containing elastic constants.

# Elastic constants for Voter-Chen Ni # in units of ergs/cm^3 2.48e+12 1.52e+12 2.48e+12 1.52e+12 1.52e+12 2.48e+12 0.00 0.00 0.00 1.32e+12 0.00 0.00 0.00 0.00 1.32e+12 0.00 0.00 0.00 0.00 0.00 1.32e+12

orient.fil

This command parameter names the file with information on the lattice orientation. Like the elastic.fil above, comments can appear anywhere in the file, and must begins with the character #. The data lines in the file contain the miller indices which indicate which lattice directions lie along the x, y and z direction. In the example below (Figure 3), the lattice orientation is given as [111] in the x direction, [1-10] in the y, and [11-2] in the z direction.

In the example, one direction appears on each line, however the data must be spread in any fashion among the lines. It only required that they appear in the proper order.

Figure 3 - File of orientation vectors.

# Orientation (x,y,z) = (111) (1-10) (11-2) 1 1 1 1 -1 0 1 1 -2

coordinate.fil

This file contains the coordinates for atom in the perfect lattice. Like the above two files, comments beginning with the character # can appear anywhere in the file. The first data line in the file must contain the number of atom coordinates that follow. There may be any number of text before the number appears on the line. The remaining data lines must each contain four numbers, the atom type (an integer) and the x, y and z coordinates. Figure 4 shows an example that was used to make the example in Figure 1.

Figure 4 - First 11 lines of file containing atom coordinates (full input data file - 30KB).

# Atomic coordinates for fcc Ni PARTICLE 768 1 1.0162 3.1113 0.3594 1 1.0162 1.8667 2.5147 1 1.0162 0.6223 4.6703 1 1.0162 0.6223 0.3594 1 3.0483 0.6223 1.7963 1 1.0162 4.3556 2.5147 1 1.0162 1.8667 6.8260 1 1.0162 4.3556 6.8260 1 1.0162 3.1113 4.6703

surfe

This is the relaxed surface energy, in units of erg/cm², of the exposed surface within the crack. This is the surface facing the y direction (see Figure 1).

x y

This is the position of the crack tip within the perfect lattice, in angstroms.

cratio

This parameters specifies a fraction the Griffith's Critical Stress Intensity. This is an optional parameter. If it is not specified, then the program output looks like Figure 5. Here the atom positions of the perfect lattice are given along with the displacement needed to obtained the atom positions for a cracked lattice at Griffith's Critical Strength Intensity. A crack at any fraction of the Griffith's Critical Strength Intensity can be obtained by applying that fraction of the displacement to the perfect lattice positions.

If cratio is specified then the output looks like Figure 6. In this case, the coordinates give the atom positions for the cracked lattice.

Figure 5 - First 11 lines of output file with perfect lattice positions and displacements. Notice that the first two lines are comments (beginning with #) that report the calculated theoretical critical stress intensity and the applied stress intensity.

# Theoretical Critical Stress Intensity (erg/cm^2.5) 5.421088e+07 # Applied Stress Intensity (erg/cm^2.5) 5.421088e+07 DISP 768 1 1.0162 3.1113 0.3594 0.5753 -2.1858 0.0000 1 1.0162 1.8667 2.5147 0.6530 -2.1848 0.0000 1 1.0162 0.6223 4.6703 0.7244 -2.1853 0.0000 1 1.0162 0.6223 0.3594 0.7244 -2.1853 0.0000 1 3.0483 0.6223 1.7963 0.7524 -1.9803 0.0000 1 1.0162 4.3556 2.5147 0.4900 -2.1880 0.0000 1 1.0162 1.8667 6.8260 0.6530 -2.1848 0.0000 1 1.0162 4.3556 6.8260 0.4900 -2.1880 0.0000 1 1.0162 3.1113 4.6703 0.8135 -3.0912 0.0000

Figure 6 - First 11 lines of output file with coordinates of cracked lattice that was used to make the example in Figure 1 (full output data file - 30KB). Notice that the first two lines are comments (beginning with #) that report the calculated theoretical critical stress intensity and the applied stress intensity.

# Theoretical Critical Stress Intensity (erg/cm^2.5) 5.421088e+07 # Applied Stress Intensity (erg/cm^2.5) 8.131632e+07 PARTICLE 768 1 1.8791 -0.1674 0.3594 1 1.9958 -1.4106 2.5147 1 2.1029 -2.6556 4.6703 1 2.1029 -2.6556 0.3594 1 4.1769 -2.3481 1.7963 1 1.7512 1.0735 2.5147 1 1.9958 -1.4106 6.8260 1 1.7512 1.0735 6.8260

Example

1. G. C. Sih and H. Liebowitz, Fracture: An Advanced Treatise, edited by H. Liebowitz (Academic Press, New York and London, 1968), Vol. 2, p. 125
   
   
2. C. S. Becquart, P. C. Clapp and J. A. Rifkin, Molecular dynamics simulations of surface reconstruction at the edges of a crack in ruthenium aluminum, J. Mater. Res., 9 (3), 548-552 (1994).
   
   
3. C. S. Becquart, D. Kim, J. A. Rifkin and P. C. Clapp, Fracture properties of metals and alloys from molecular dynamics simulations, Materials Science and Engineering, A170, 87-94 (1993).
   
   
4. A. F. Voter and S. F. Chen, Accurate Interatomic Potentials for Ni, Al and Ni₃Al, MRS Syposia Proceedings 82, 175 (1987).