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Double cantilever cohesive crack

A classic DCB under opening displacement. The interface follows a cohesive law: linear response, then a process zone, then softening. The chart is the load-displacement path of a refined XEFG solution.

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Stage: Elastic
Left-node δ = 0.000 mm
Top +δ · Bottom −δ
view ×150 (true scale invisible)
Load–Displacement (refined XEFG)
Spline Current (I)(II)(III)
0 (I) 0.140 (II) 0.270 (III) 0.320 0.450
Load ($F$): 0.00 kN
Upper-left $u_y$: +0.000 mm
Lower-left $u_y$: −0.000 mm
Crack length ($a$): 120 mm
Peak traction: 0.00 MPa
Tip traction: 0.00 MPa
State: Elastic
Cohesive traction along ligament $\sigma(x)$
Ahead of crack tip — green elastic · amber softening · gap = broken
Traction–separation law $\sigma(\delta_n)$
Points = active cohesive stations (current openings)

Specimen & Kinematics

  • Length / height: 400 mm × 200 mm
  • Initial notch $a_0$: 120 mm
  • $\delta$ on the curve: vertical displacement of the upper/lower left load nodes (not CMOD)
  • Motion: upper-left node $u_y=+\delta$, lower-left $u_y=-\delta$; arms meet at crack tip $x=a$
  • Support: pinned at right midplane

Cohesive Zone Traction Law

  • $\sigma_c$: 10 MPa peak cohesive strength
  • $\delta_0$: 0.02 mm damage initiation
  • $\delta_f$: 0.08 mm complete separation
  • Purple arrows on the midplane = local cohesive tractions (length ∝ $\sigma$)