Crack Propagation Commands

The Crack Settings on this page activate crack propagation and select various propagation options.

Propagate Command

The Propagate command sets the criterion used for crack propagation in MPM calculations and optionally sets a crack propagation direction method and traction law material to use on new crack surfaces. In scripted files, the command is

Propagate (crit),<(dir)>,<(traction)>

In XML files, the command, which must be in the [[Crack Settings|<Cracks> block, is:

<Propagate criterion='(critNum)' direction='(dirNum)' traction='(traction)'/>

where (crit) and optionally (dir) are the crack propagation criterion and the method to select the crack propagation direction.

Crack Propagation Criterion

The crack propagation criterion is one of the following options (which can be set by number or name, although XML files must use a number):

• 0:"none" for no propagation.
• 1:"max energy release" for crack growth based on stress intensity factors and a single critical stress intensity factor (K_Ic). The propagation condition is based on the maximum energy release rate (also known as the maximum hoop stress criterion). The default propagation direction is in the direction of the maximum energy release rate (or the direction of maximum hoop stress).
• 2:"steady state" for crack initiation when total energy release rate (J) reaches a critical value (specified by J_Ic) or when the time reaches a specified time. Once the crack has initiated, the crack grows at a specified constant speed. It may be stopped at any predetermined maximum length. The default propagation direction is self-similar propagation.
• 3:"energy balance" for crack growth by a dynamic energy balancing scheme. The research for this option is in progress and it is not yet meant for general use. The default propagation direction is self-similar propagation.
• 4:"energy density" for crack growth based on stress intensity factors and a single critical stress intensity factor (K_Ic). The propagation condition is based on the minimum strain energy density. The default propagation direction is in the direction of minimum strain energy density.
• 5:"elliptical" for crack growth based on stress intensity factors and two critical stress intensity factors (K_Ic and K_IIc). The default propagation direction is the direction of maximum energy release rate. The criterion for crack growth is
  
        [math]\displaystyle{ \left({K_I\over K_{Ic}}\right)^p + \left({K_{II}\over K_{IIc}}\right)^q = 1 }[/math]
  
  
• 6:"max ctod" for crack growth if the crack tip opening displacement at the crack tip exceeds δ_Ic or δ_IIc if one or both are specified. The default propagation direction is self-similar propagation.
• 7:"critical err" for crack growth when energy release rate exceeds J_Ic. The default propagation direction is self-similar propagation.

Crack Propagation Direction

Each crack propagation criterion has a default method for determination of the crack propagation direction. If desired, that direction can be changed using the option (dir) parameter using one of the following options (which can be set by number or name, although XML files must use a number):

• 0:"default" to use the default direction for the above criterion.
• 1:"self similar" to grow in the same direction as the crack tip crack segment.
• 2:"cod normal" to grow normal to a vector between the top and bottom surface at the crack tip.
• 3:"cod hoop" to estimate the direction of maximum energy release rate based on the normal and shear crack opening displacements. This direction is similar to the default direction for "max energy release" criterion above, but can be used on any type of material.
• 4:"initial" to grow in the crack tip direction defined by the initial crack geometry.

Traction Law in Wake of Propagation

The optional parameter #3 can define a <a href="material.html">material ID</a> for a previously defined <a href="tractionlaws.html">traction law material</a>. When this parameter is used, new crack surfaces created by crack propagation will be initialized with the provided traction law material. To set #3 without specifying a direction rule in #2, set #2 to the default value (or 0). Note that any crack that propagates into a traction law material must use a frictionless contact law. If any initial crack particles have a traction law material, the crack will automatically be converted to a frictionless contact crack. If the initial crack, however, has no traction laws, you must be sure to create that crack as a frictionless crack.

Maximum Hoop Stress Direction

In max energy release rate (or max hoop stress), the crack direction is at angle θ (which is ccw from self similar growth) and obeys

      [math]\displaystyle{ \cos\theta = {3R^2 + \sqrt{1+8R^2} \over 1+9R^2} \quad {\rm and} \quad \sin\theta = \mp\sqrt{1-\cos^2\theta} = \mp\left | R(3\cos\theta - 1)\right| }[/math]

where R = K_II/K_I. The second term is negative or positive depending on K_II being positive or negative. In the limit of K_I to zero, cos θ = 1/3 for crack direction of -70.5 (or +70.5) degrees. This method requires K_I and K_II which can only be done for isotropic (and subclasses), mooney, heisotropic (and subclass), and viscoelastic. All use initial, low strain modulus to calculate stress intensity factors.

Above is same as

      [math]\displaystyle{ \tan {\theta\over 2} = {1\over 4}\left({1\over R} \mp \sqrt{{1\over R^2} + 8}\right) }[/math]

where negative of positive is determined by sign of K_II.

in cod hoop direction, the code uses the max energy release rate method, but assumes R = δ_t/δ_n or ratio of the sliding and opening crack opening displacements. This method can be used for any material.

Propagation Length

PropagateLength <PropagateLength>2.5</PropagateLength>

Alternate Propagation Criterion

AltPropagate <AltPropagate criterion='7' direction='4' traction='0'/>

Notes

1. Crack propagation and direction criteria are based on <a href="material.html">material properties</a> that must be set in the analysis.
2. Crack propagation occurs in the material defined by the tip material parameter #3 when <a href="newcrack.html">defining cracks</a>.
3. The Propagate command defines the default propagation, direction, and traction law material for all materials. If desired, a specific material can override these defaults using the criterion, direction, and traction <a href="material.html">material property</a> settings.