|
Damage and Failure Analysis of Composite Materials
Progressive Damage Modeling of Composites Modeling Damage and Failure of Polymer Matrix Composites The objective of this study was to incorporate a new composite damage constitutive model into the DYNA3D finite element code developed at Lawrence Livermore National Laboratory. The composite damage model used was for progressive damage of polymer matrix composites as developed at the Stanford University composites and structures group. The DYNA3D code used is an explicit three-dimensional finite element code for the nonlinear dynamic analysis of materials and structures. The composite damage model used is based on the work of Professor Fu-Kuo Chang and the thesis project of Dr. Iqbal Shahid [1993]. The implementation of the model into DYNA3D was performed by Dr. Steven Kirkpatrick as an independent research project with the assistance of Prof. Chang and Dr. Shahid.
The technical difficulties of this research program arise from the incompatibilities of the current form of the Chang-Shahid damage model with the DYNA3D code architecture. The damage model was developed for design analysis of flat plate structures subjected to in-plane loadings (2-dimensional static problems). DYNA3D is a three dimensional general purpose code for the dynamic analysis of materials and structures. Thus, the damage model needed to be reformulated to be implemented into DYNA3D in a computationally efficient manner.
The Chang-Shahid damage model used in this program was initially obtained from the PDCOMP computer code developed by Dr. Shahid as part of his PhD. thesis research. As implemented in the PDCOMP code the damage model combines design failure criteria based on polynomial functions of stress components with progressive damage and degradation modeling for analyses of static in-plane loadings of symmetric laminate composite plates of various geometries both with and without cutouts and stress concentrations. The model makes an assumption of a continuous anisotropic elastic body with degraded moduli in the damaged regions. As incorporated in PDCOMP, the Chang-Shahid damage model is a laminate constitutive model where the entire laminate is evaluated at any point in the plate.
The input parameters for PDCOMP are the geometry, material, layup, and loading. PDCOMP is designed to statically increment the load up to the point where the ultimate failure load is reached. The PDCOMP code performs both stress analysis and damage development in parallel in each time step. Failure mechanisms of matrix cracking, fiber-matrix shear-out, and fiber breakage are considered. If the calculated stresses are below failure levels the load is incremented. However, if the calculated stresses are above the failure levels the progressive damage analyses is performed.
In the progressive damage analyses, damage is incremented, properties are degraded and updated, and stresses and deformations updated. This loop is performed iteratively until an updated state is determined with damage and stresses that are on or below the failure surfaces and in equilibrium with the applied load. If this updated damage state is below the ultimate failure load the loads are again incremented and the process continues. The analyses performed to determine updated stiffnesses is based on elastic analyses of cracked plies within a laminate and the resulting effective reduction in stiffness. Thus the resulting stiffness update calculations require evaluation of complex mathematical expressions and require significant computational effort if evaluated for a significant number of elements and time steps. The failure criteria used in PDCOMP are separated to account for different damage mechanisms of fiber breakage, fiber-matrix shear-out, and matrix cracking.
The technical difficulties of this research program arise from the incompatibilities of the current form of the Chang-Shahid damage model with the DYNA3D code architecture. The damage model was developed for design analysis of flat plate structures subjected to in-plane loadings (2-dimensional static problems). DYNA3D is a three dimensional general purpose code for the dynamic analysis of materials and structures. Thus, the damage model needed to be reformulated to be implemented into DYNA3D in a computationally efficient manner.
The Chang-Shahid damage model used in this program was initially obtained from the PDCOMP computer code developed by Dr. Shahid as part of his PhD. thesis research. As implemented in the PDCOMP code the damage model combines design failure criteria based on polynomial functions of stress components with progressive damage and degradation modeling for analyses of static in-plane loadings of symmetric laminate composite plates of various geometries both with and without cutouts and stress concentrations. The model makes an assumption of a continuous anisotropic elastic body with degraded moduli in the damaged regions. As incorporated in PDCOMP, the Chang-Shahid damage model is a laminate constitutive model where the entire laminate is evaluated at any point in the plate.
It was not feasible to directly tie the damage model code PDCOMP to the DYNA3D finite element constitutive model subroutine due to the computationally intensive analyses and algorithms performed in PDCOMP. In addition, the single integration point solid elements in DYNA3D require a laminae constitutive model as apposed to the laminate constitutive model in PDCOMP. Thus the approach for implementing the composite damage model into DYNA3D was to modify the code PDCOMP to output moduli and strength curves as a function of crack density for each ply in the layup. These material behavior curves are then used as the input conditions for the composite constitutive model in DYNA3D. Each ply in the layup is then analyzed in DYNA3D using a different material number with properties specified by the associated strength and moduli curves which are input in the load curve cards.
An advantage of this approach is that the information from the progressive damage model can be implemented into DYNA3D as material input properties and thus the calculations required in the constitutive model can be greatly reduced. PDCOMP is run only once through with crack densities incremented and strengths and moduli for each ply is calculated. Thus this approach is much more computationally efficient than tying subroutines of PDCOMP directly into DYNA3D. The disadvantage of this approach is that much of the additional analyses performed by PDCOMP was lost and thus further development of the DYNA3D constitutive model was needed. For example, PDCOMP would iteratively calculate the change in crack densities that would occur for a given load increment. For DYNA3D a similar damage evolution equation or algorithm needed to be developed. Other modifications were needed to obtain three dimensional failure criteria since other than in-plane loading conditions were possible.
A series of quasistatic tensile tests on various laminates were simulated with the DYNA3D version of the progressive damage model. The predictions compared well with those of PDCOMP and the experimental data. A second type of demonstration calculation was performed to demonstrate the performance of the progressive damage model for a dynamic problem with out-of-plane loadings. The problem analyzed was the response of a composite panel loaded by a low velocity ball nose impactor. Results of tests and previous analyses for this example are given by Choi and Chang. This problem was chosen because it demonstrates the capabilities of the model for a dynamic problem with out-of-plane loadings. The damage mechanisms observed in the tests were primarily matrix cracking and delamination.
A sketch of the test setup for the ball impact tests is shown in Figure 1. The mass of the impactor (with base mass) totaled 0.16 kg. The spherical nosed impactor was made of steel and had a radius of 0.635 cm. The impacted panel was 10 cm long and 7.6 cm wide and firmly clamped at either end as shown in Figure 13. The other two edges of the specimen were free. The extent of damage produced in the impacted panels was determined by x-radiographs. The damage observed in a cross-ply T300/976 carbon/epoxy panels at 6.7 m/s is shown in Figure 2a. The corresponding calculation of damage in the DYNA3D impact simulation is shown in Figure 2b. The overall agreement between experiments and calculations for the low velocity impact is good.
The progressive damage model appears to be a useful tool for analysis of laminate composite structures. The class of problems for which the model was originally developed was static in-plane tensile loading of structures. The development to include the model into DYNA3D extends the model to general three-dimensional dynamic analyses of composite structures. The initial comparisons of the model in DYNA3D indicate that the updated model can be used to calculate low velocity impact damage that may occur in problems such as a tool dropped on a composite aircraft panel as shown in Figure 3. Application of the model for problems with significantly different loading conditions or higher loading rates may require further validation or development.
References
- I. Shahid, "Progressive Failure Analysis of Laminated Composites subjected to In-Plane Tensile and Shear Loads," PhD. Dissertation, Stanford University, April 1993.
- Choi, H.Y. and Chang, F.K., "A Model for Predicting Damage in Graphite/Epoxy Laminated Composites Resulting from Low-Velocity Point Impact."
For inquiries or comments, please contact:
Dr. Steven Kirkpatrick
Principal Engineer
e-mail: skirkpatrick@ara.com
Dr. Robert T. Bocchieri
Principal Engineer
e-mail: rbocchieri@ara.com
This research was performed in cooperation the Stanford University Structures and Composites Laboratory.
|
