Composite Fracture And Delamination

Chapter 20: Composite Fracture and Delamination

20

Composite Fracture and Delamination 

Summary



Introduction



Requested Solution



FEM Solutions



Modeling Tips



Input File(s)



Video

373

366 367

369 371 373

369

366 MD Demonstration Problems CHAPTER 20

Summary Title

Chapter 20: Composite Fracture and Delamination

Features

• VCCT based crack propagation • Cohesive zone modeling

Geometry

6“ R = 0.5 “ 1.1 “ 0.078 “ 0.6 “

0.9 “

0.9 “

0.6 “

Initial Crack

Material properties

• Isotropic elastic material: E = 5000 ksi,  = 0.3 • Cohesive material for interface elements: Exponential model used • Cohesive energy = 4.409 lb/in; critical opening displacement = 0.005 in

Analysis type

Quasi-static analysis

Boundary conditions

Simply supported as shown in the diagram above

Applied loads

Prescribed vertical displacement

Element type

4-node plane strain; 4-node interface

VCCT properties

• Direct crack propagation by releasing glued contact. • Crack growth resistance = 4.409 lb/in

FE results

1. Plot of deformed shape for VCCT model. 2. Plot of deformed shape for interface element model 3. Force-displacement curve at applied load. 250 Cohesive zone VCCT

Reaction force

200

150

100

50

0

0

0.05

0.1 Vertical displacement

0.15

0.2

CHAPTER 20 367 Composite Fracture and Delamination

Introduction This example models a honeycomb (core) structure with a face sheet between which exists an initial delamination. A hole is drilled in the core part, where a prescribed displacement is applied to the face sheet in order to study the effect of delamination of the face from the core. A plane strain assumption has been used and, for simplicity, the same isotropic material is used for the two parts. The delamination is modeled in two ways: • With glued contact and crack growth using the VCCT option. • With interface elements using a cohesive zone model. Figure 20-1 illustrates the VCCT model. The face sheet is glued to the core. The center part of the face sheet is omitted from the contact body and thus defines the initial cracks. The grid IDs defining the crack tips are shown in Figure 20-2.

Figure 20-1

Definition of Contact Bodies for the VCCT Model

The model using interface elements is shown in Figure 20-3. Here, we do not use contact; instead, there are interface elements between the core and the face which share the grids from the existing meshes. The interface elements have zero thickness, but they are shown with finite thickness in Figure 20-3 (the face part has been moved downwards for better illustration). For the VCCT model, a crack growth resistance is specified. The energy release rate is calculated for each crack at each load level. When this energy release rate is larger than the crack growth resistance, the crack will grow. The growth is accomplished by releasing the glued contact at the crack tip. The next grid along the interface is automatically identified and a new calculation of the energy release rate is performed, and the check for growth repeated. This continues at constant load until either the crack reaches a free boundary or the energy release rate is below the crack growth resistance.

368 MD Demonstration Problems CHAPTER 20

grid 2381

grid 1136

Figure 20-2

Grids for VCCT definition.

Figure 20-3

Delamination Model with Bottom Part moved Downwards to Show the Location of the Delamination Elements

CHAPTER 20 369 Composite Fracture and Delamination

With the interface elements and the cohesive material model, the growth of the delamination occurs by increased damage in the interface elements. Damage could occur at any point along the interface, but in this case, the largest stresses occur where the initial delamination ends, so the largest damage will happen here. When the interface elements have sustained full damage at all integration points, they no longer contribute to the stiffness of the structure.

Requested Solution Requested results are the force-displacement curve of the point where the prescribed displacement is applied and the amount of growth of the initial delamination.

FEM Solutions MD Nastran’s SOL 400 has been used in the analysis. The VCCT option is specified in the bulk data as: VCCT

1

1

2

4.409 0 2381 1

VCCT

2

2

4.409 0 1136

The grid IDs 2381 and 1136 are located as shown in Figure 20-2 Plane strain elements are chosen by the PLPLANE entry on the CQUAD4 option as shown below. PLPLANE 1 PSHLN2 1 + C4

1 1 PLSTRN

1 L

+ +

The delamination elements are defined with the CIFQUAD entry, and the corresponding cohesive property and material are defined as: MCOHE + PCOHE

2 4.409

2 .500E-02 2 2

2

where the exponential option is used for the cohesive material model. The nonlinear iterative control is specified as: NLSTEP + + +

2 GENERAL 30 FIXED 100 MECH PV

1.

+ + +

0 1 0.01

PFNT

Fixed time stepping procedure with total time of 1 is used. Maximum 30 iterations are allowed for each increment. Total 100 numbers of increments are used for fixed time stepping. Output for every single increment is written to the result file. For convergence criterion load equilibrium error with vector component method (PV) is used. Convergence tolerance of 0.01 is used. Pure Full Newton-Raphson Method is used (PFNT) as an iteration method.

370 MD Demonstration Problems CHAPTER 20

The deformed shape at the final load for the two cases is shown in Figure 20-4. It can be seen that the amount of growth of the delamination is the same for the two models. The cohesive zone variant shows the “stretched” interface elements. They are, at this point, fully damaged and do not contribute to the structural stiffness. Figure 20-5 shows a plot of the reaction force versus the prescribed displacement. Here, we clearly see the difference between the two approaches. For VCCT, the interface is rigid until crack growth occurs. The jumps in the reaction force indicate when a new node is released. With a finer mesh, the curve would be smoother. The cohesive zone model shows a different behavior. The initial stiffness is lower as a result of the properties of the cohesive material. Here the interface layer is relatively soft, and the growth of the delamination is smooth. By adjusting the properties of the cohesive material one can adjust the initial stiffness of the interface layer. Thus, the VCCT approach models the interface as rigid while the interface element approach models an elastic interface with initially zero thickness. The values used for the crack growth resistance and the cohesive energy are the same in the two model. This makes sense since these quantities are related – both correspond to the energy needed to break the connection.

a) VCCT

b) Cohesive Zone

Figure 20-4

Deformed Shape at Final Load for the Two Models

CHAPTER 20 371 Composite Fracture and Delamination

250 Cohesive zone VCCT

Reaction force

200

150

100

50

0

0

Figure 20-5

0.05

0.1 Vertical displacement

0.15

0.2

Reaction Force vs. Vertical Displacement

Modeling Tips Both models could be done with higher-order elements for increased accuracy. When glued contact is released in the VCCT model, the midside grid is released whenever a corner grid is released. Hence, although this would give an increased general accuracy of the solution, it would not improve the jagged nature of the force-displacement curve. Some notes on mesh design. In the VCCT model, the meshes on both sides of the glued interface have matching nodes. One of the two grids at the crack tip is identified in the VCCT input. It does not matter which one of the two that is used. It is allowed to use nonmatching meshes for VCCT based crack growth. Figure 20-6 shows an example. Here, the bottom part is glued to the top part (the bottom part is the touching side and the top part the touched side). In this case, it is important that the grid of the touching part is chosen for the VCCT input. This is the grid that would be released in case of crack growth. The touching part should be the part with a finer mesh density. The current interface element model does not use contact. The interface elements and the other elements share nodes. In order to allow a model with independent meshes, one can also use glued contact here. See Figure 20-7 for an example. The interface elements are shown with finite thickness for clarity. The top part of the interface elements are glued to the top part of the model and the bottom part of the interface elements to the bottom part. This way, all three parts can be modeled independently. Similar to the VCCT example above, the touching body (in this case the interface elements) should have a finer mesh density.

372 MD Demonstration Problems CHAPTER 20

crack tip grid Figure 20-6

Example of Mesh for VCCT with Nonmatching Mesh Densities

Figure 20-7

Example of Mesh for Cohesive Zone Model with Nonmatching Mesh Densities

CHAPTER 20 373 Composite Fracture and Delamination

Input File(s) File

Description

nug_20v.dat

Model using the VCCT option

nug_20d.dat

Model using delamination elements

nug_20d.bdf

Model using delamination elements for video

nug_20d_start.SimXpert

Starting model for SimXpert video

Video Click on the image or caption below to view a streaming video of this problem; it lasts about 47 minutes and explains how the steps are performed. 6“ R = 0.5 “ 1.1 “ 0.078 “ 0.6 “

0.9 “

0.9 “

Initial Crack

Figure 20-8

Video of the Above Steps

0.6 “