Cohesive Zone Model (CZM)
Cohesive Zone Model (CZM): Theoretical Foundations
What is CZM?
Professor, CZM was also mentioned on the interlaminar delamination page, but can it be used for general fracture as well?
CZM (Cohesive Zone Model) is a versatile fracture model that describes interface failure using a traction-separation law. It is applicable not only to interlaminar delamination but also to adhesive joint debonding, ductile cracking in metals, and concrete cracking.
Traction-Separation Law
Bilinear type:
1. Linear Elasticity — Stress increases with stiffness $K$
2. Damage Initiation — Reaches strength $t^0$
3. Softening — Stress decreases while opening increases
4. Complete Separation — Fracture after consuming energy $G_c$
Advantages of CZM
Summary
The Competing Works of the Dugdale-Barenblatt Model
The cohesive zone model was independently published in 1960 by Dugdale (UK) and Barenblatt (USSR). Dugdale approximated the plastic zone in steel plates as a strip, while Barenblatt formulated a more general attraction relationship. Due to the Cold War, there was no information exchange for several years, and they only learned of each other's papers in the 1970s. Today's CZM was born from the competing works of these two individuals.
Computational Methods for Cohesive Zone Model (CZM)
CZM in FEM
Two implementations:
1. Cohesive Elements — Place thin cohesive elements at the interface (COH3D8, etc.)
2. Surface-based CZM — Set CZM on contact surfaces (no additional elements)
```
*COHESIVE SECTION, RESPONSE=TRACTION SEPARATION
*COHESIVE BEHAVIOR
K_n, K_s, K_t
*DAMAGE INITIATION, CRITERION=QUADS
t_n, t_s, t_t
*DAMAGE EVOLUTION, TYPE=ENERGY, MIXED MODE BEHAVIOR=BK
G_Ic, G_IIc, G_IIIc
```
Mesh Requirements
3 to 5 elements within the process zone. $l_{cz} \approx EG_c/(t^0)^2$.
Summary
Relationship Between TSL Curve Shape and Fracture Toughness
The traction-separation law (TSL) in cohesive zone models has several shapes such as triangular, trapezoidal, and exponential. Different shapes change crack propagation behavior even for the same fracture energy Gc. Trapezoidal shapes often better represent experiments for high-strength adhesives, while exponential shapes fit rubber-based adhesives. The peak strength σmax and area Gc are the minimum required two parameters; using only one of them worsens FEM convergence.
Cohesive Zone Model (CZM) in Practice
CZM in Practice
Interlaminar delamination in composites, strength evaluation of adhesive joints, concrete cracking, fracture in welded joints.
Practical Checklist
Delamination Simulation of Aircraft Panels
For the adhesive interface between carbon fiber reinforced plastic (CFRP) panels and metal frames on the Airbus A380, delamination simulation using cohesive zone models has become a design standard. Setting TSL parameters of Gc=800 J/m² and σmax=50 MPa independently for Mode I and Mode II achieved prediction accuracy of ±15% for damage area after drop impact (from Airbus demonstration tests in the 2010s).
Cohesive Zone Model (CZM): Software & Solver Comparison
CZM Tools
Abaqus CZM Implementation and Contact Elements
In Abaqus/Standard, CZM can be implemented in two ways: surface-based cohesive behavior and dedicated cohesive elements (COH2D4, etc.). Boeing used Abaqus CZM to perform certification analysis for adhesive joints in the B787 wing spar. Analysis of a 300mm×100mm test specimen based on FAA regulations kept prediction error for delamination load within ±10%.
Advanced Technologies
Advanced CZM
Application of CZM to Biomaterials
Since the 2010s, cohesive zone models have also been applied to fracture healing simulations. Converting cortical bone fracture toughness Kc=2.2 MPa√m to CZM parameters can reproduce debonding at bone-implant interfaces. In 2018, a group at KIT predicted bone fixation strength of hip implants using CZM and obtained results matching actual measurements 3 months post-surgery within 10% error.