Numerical Approach to Determine Crack Path and Delamination Growth in Composite Structures

Issue #18 - July 9th, 2009

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This Week's Feature Composite Example

Numerical Approach to Determine Crack Path and Delamination Growth in Composite Structures

(a) Tension Test (b) Three-Point Bending Test   Figure 1 - Predicted delamination process at the interface of flange and skin for a composite skin/stringer joint

Fracture mechanics based Discrete Cohesive Zone Modeling (DCZM) or Continuum Cohesive Zone Modeling (CCZM) approach is widely used in simulation of crack propagation and delamination growth (Figure 1) in composite structures; however, its effectiveness is limited as it requires prior identification of the crack path, which is usually obtained from test. This limitation makes DCZM/CCZM a test duplication tool for simulating fracture propagation rather than a test prediction one. Reliance on testing alone hinders the analysis process and reduces its potential benefits. The shortcoming of the DCZM/CCZM approach can fortunately be overcome with finite element/micro-mechanics based Progressive Failure Analysis (PFA) to determine analytically the crack path under increased stress.

Augmentation to Multi-scale Progressive Failure Analysis: 

A novel methodology is implemented in GENOA [1] to address the limitation of DCZM/CCZM with respect to crack path requirement for the analysis. GENOA is state of the art durability and damage tolerance (D&DT), and life and reliability prediction software. It is dedicated for the evaluation of composite structures made from tape, 2/3-D weave and braids, fiber metal laminates, and sandwich construction.

The methodology works in two consecutive steps:

1. PFA strength/strain based evaluation to determine the crack path;
2. Crack propagation analysis using DCZM/CCZM based on crack path predicted by PFA. 

The methodology combines the best of both capabilities: damage initiation and progression and failure initiation and crack path prediction via PFA and crack propagation/delamination via DCZM. PFA and DCZM are briefly described next. This is followed by examples to illustrate and validate the integrated PFA/DCZM approach.

The PFA approach [2] increments the load to failure while evaluating strength and strain composite failure criteria to identify loads that produce damage initiation and propagation, and fracture initiation. When it comes to modeling stress singularities such as those near crack fronts, PFA may have some limitations, which can be addressed by switching to linear elastic fracture mechanics method once fracture is initiated. In the fracture mechanics approach, nodes along the pre-defined crack path are initially tied together with DCZM elements and then released when mode I (crack opening), II (crack shearing or sliding) and III (crack tearing) components of strain energy release rate exceed the mixed-mode fracture criteria [3]. DCZM element is a spring type element and a triangle type cohesive law is applied as the spring internal force.

Application: A composite skin/stringer flange (lap type) joint [4] (Figure 2) subjected to tension and three-point bending load is used to validate the new methodology in GENOA. The skin lay-up consists of 14 plies ([0/45/90/-45/45/-45/0]s) and the flange consists of 10 plies ([45/90/-45/0/90]s). The flange and the skin are bonded together with CYTEC 1515 [5], a grade-5 film adhesive, with a final thickness of 0.102 mm [6]. Each ply in the flange and the skin is made of IM6/3501-6 graphite epoxy pre-preg tape with a nominal thickness of 0.188 mm. The material properties of both the unidirectional tape and adhesive are taken from references [5,6,7]. Figure 3 shows a side view of the ply lay-up setup. 

 

Figure 2 - Co-cured Skin/Stringer Joint [4]

 

Figure 3 - Ply lay-up setup in GENOA (side view)

As noted by Kruger et al [6], the kin/stringer flange joint specimens that were tested were subjected to tension and 3-point bending. These two tests are simulated numerically using the two steps approach described earlier: PFA followed by DCZM.

Tension: PFA evaluation is performed first to predict the crack path under tension load. Then the crack path is used as input to DCZM along with fracture toughness data from literature. This two steps approach indicated a delamination load of 22.2 kN. If we are to rely on PFA alone for this delamination growth simulation example, we would obtain a delamination load comparable to the one from DCZM. 

Three-point Bending: DCZM predicted a delamination load of 403.2 N using crack path obtained from PFA. If we are to run PFA for the whole simulation, we would obtain a delamination load of 417N independent of DCZM. The analysis shows that the flange is delaminated from the skin due to the failure of the adhesive (Mode I and II failure), just as the test results indicated. 

The use of PFA stand alone has a distinct advantage over DCZM stand alone as it is capable of assessing micro crack formation under increased loading. Unlike PFA, DCZM does not capture any damage in skin or flange before the onset of delamination. This phenomena is evident in Figures 4 and 5, which show the PFA and DCZM methodology predicted delamination at the interface of a skin/stringer flange specimen for the two loading cases. The red area in Figure 4b indicates the damage in the specimen as predicted by PFA. 

 

(a) Tension                                                          (b) Three-Point Bending

Figure 4 - PFA predicted delamination at the interface of a skin/stringer specimen

 

(a) Tension                                                             (b) Three-Point Bending

Figure 5 - DCZM predicted delamination at the interface of a skin/stringer specimen

Figure 6 gives a comparison of DCZM simulation results guided by PFA predicted crack path. The load displacement for the tension and three point bending specimen obtained from GENOA using PFA followed by DCZM are compared to experimental results. Results from PFA stand alone simulation are also plotted and compared to those from experiment [6]. The results from simulation match well with the test data. The predicted delamination loads are within the upper and lower bounds of the test data [4,6]. In addition, the predicted delamination pattern in each case is consistent with the experimental observations. The literature data focused mainly on delamination load. Therefore post-peak load behavior cannot be validated in these simulations for the PFA and DCZM approach.

 

(a) Tension                                                           (b) Three-Point Bending

Figure 6 - Comparison of simulation using the PFA and new methodology with experimental results for a skin/stringer specimen under two loading cases

Conclusions: 

The delamination process of the flange from the skin due to adhesive failure for a skin/stringer flange specimen under tension or three-point bending is successfully simulated and predicted using a two step numerical approach: PFA followed by DCZM (CCZM). This development transforms the cohesive modeling capability from test duplication tool to a test prediction one. The PFA predicted fracture path needs to be qualified by the engineer before proceeding to step 2 (that is DCZM evaluation).  This technology provides an effective mean to determine the initiation and propagation of delamination in composite structures while minimizing the test efforts. 

References: 
1. GENOA Durability and Damage Tolerance Software, Alpha STAR Corp, Long Beach, CA 2009, www.ascgenoa.com

2. Garg, M., Abumeri, G. H., and Huang, D., 2008. "Predicting Failure Design Envelop for Composite Material System Using Finite Element and Progressive Failure Analysis Approach," SAMPE May 2008, Long Beach. Click here to email us for the technical publication.

3. Xie, D., Garg, M., Huang, D., and Abdi, F., 2008. "Cohesive zone model for surface cracks using finite element analysis," May 2008 AIAA, Illinois. Click here to email us for the technical publication.

4. Camanho, P. P., Davila, C. G., and Pinho, S. T., 2003. "Fracture analysis of composite co-cured structural joints using decohesion elements," Fatigue & Fracture of Engineering Materials & Structures, Vol.27, Issue 9, pp745-757. Click here to email us for the technical publication.

5. CYTEC 1515 product sheet.

6. Krueger, R., Cvitkovich, M. K., O?Brien, T. K., and Minguet, P. J., 2000. "Testing and analysis of composite skin/stringer flange debonding under multi-axial loading," Journal of Composite Material, Vol.34, No.15, pp1263-1300. Click here to email us for the technical publication.

7. http://casl.ucsd.edu/data_analysis/carpet_plots.htm

Click here to read the full technical product data sheet of GENOA.

This issue was brought to you by Alpha STAR Corporation.

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