NG-18-11-R01 A Model for Crack Propagation in Steel

A treatment of crack propagation in steel, in terms of stress and strain rather than energy, is derived which takes into account the time rate of plastic deformation at the crack tip. Formulations of (1) the yielding of steel in terms of dislocation dynamics, and (2) a simple crack model responsive to plastic

relaxation are developed. These describe the stress-strain behavior of low-carbon steel, predict strain-rate sensitivity and yield delay times, and estimate rates of stress application on the material in advance of the moving model crack. Together, they define, in a consistent way, the maximum stress and

plastic-zone size in front of the model crack as a function of nominal stress and crack speed.

The calculations indicate that dynamic-yield-stress values attained in front of a fast-moving crack can exceed the brittle-fracture stress. The maximum stress generated by the crack increases with crack velocity but is relatively insensitive to nominal stress. Finally, the treatment suggests that both the minimum stress for crack propagation and the terminal velocity of brittle fractures may be governed by a limiting plastic-zone size.