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Option: crack

Syntax

-crack <I|II|III> <stress|strain> <Ks> <p1> <p2> <ξ> <n> <μ> <ν>

Description

This option inserts a straight crack in the system. The equations used by this option can be found e.g. in L.B. Freund, Dynamic fracture mechanics.

The user has to provide the following parameters:

• I|II|III: mode of the crack, must be I (opening), II (in-plane shear) or III (out-of-plane shear).
• stress|strain: decides if the crack is built assuming plane stress or plane strain, respectively.
• K_s: stress intensity factor (in GPa.Å^1/2).
• p₁, p₂: coordinates of the crack in the plane normal to the crack tip line (see ξ below), by order of permutation X, Y, Z: if ξ=Z then p₁ is the position along X and p₂ the position along Y; if ξ=Y then p₁ is along Z and p₂ along X; if ξ=X then p₁ is along Y and p₂ along Z. The positions <p₁> and <p₂> are usually given in Å. It is also possible to give them with respect to the box dimensions with the keyword BOX and an operation (see this page).
• ξ: direction of the line of the crack tip, must be x, y or z.
• n: direction normal to the plane of cut (also normal to the surfaces forming the crack lips), must be x, y or z, and must be different from ξ.
• μ: shear modulus of the material (in GPa).
• ν: Poisson ratio of the material.

If plane stress is used then κ=(3-ν)/(1+ν); otherwise (i.e. assuming plane strain) κ=3-4ν.

For a mode I crack (opening crack) the displacements applied to any atom in the system are:

       ux1 = (Ks/2μ) √r/2π cos(θ/2) [κ - 1 + 2sin2(θ/2)]

       ux2 = (Ks/2μ) √r/2π sin(θ/2) [κ + 1 - 2cos2(θ/2)]

where x₃ is the direction <ξ> of the crack line, and x₂ the normal to the plane of cut (i.e. x2=<n>), r is the distance of the atom to the crack tip, and θ is the angle between the plane normal to <n> and the segment formed by the atom and the crack tip. In addition for a mode I crack the box is elongated along x2 by (Ks/μ)√pos2/2π(κ+1).

For a mode II crack (in-plane shear crack) the displacements are:

       ux1 = (Ks/2μ) √r/2π sin(θ/2) [κ + 1 + 2cos2(θ/2)]

       ux2 = -(Ks/2μ) √r/2π cos(θ/2) [κ - 1 - 2sin2(θ/2)]

And finally for a mode III crack (out-of-plane shear crack):

       ux3 = (Ks/μ) √r/2π sin(θ/2)

In addition to these displacements, Atomsk also computes the theoretical (continuum) stresses associated with the crack and saves the Voigt components σ_xx, σ_yy, σ_zz, σ_yz, σ_xz and σ_xy as auxiliary properties for each atom.

In linear elastic materials a mixed-mode problem can be treated by using this option three times to add up the three contributions:

       u = umodeI + umodeII + umodeIII

If a selection was defined (with the option -select) then the displacements described above are applied only to selected atoms.

Default

By default no crack is introduced at all.

Examples

• atomsk initial.xyz -crack I stress 20 30.0 0.5*BOX z y 90 0.3 crack.cfg

  This will read initial.xyz and insert a mode I crack along Z, assuming plane stress, the crack lips being normal to ξ=Y, using a stress intensity factor K_s=20 GPa.Å^1/2, a shear modulus μ=90 GPa and a Poisson ratio ν=0.3. The crack will be at X=30 Å and in the center of the box along Y. The result will be output to crack.cfg.

• atomsk initial.xyz -crack I stress 40 30 0.5*BOX z y 90 0.3 -crack II stress 10 30 0.5*BOX z y 90 0.3 -crack III stress 10 30 0.5*BOX z y 90 0.3 crack.cfg

  This will read initial.xyz and insert a crack by adding three contributions of modes I, II and III. The result will be output to crack.cfg.

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