Features of Nonlinear Response
Consider first the case with GIc = 1.27N/mm. As the end-shortening increases to beyond the critical value, delamination occurs with about 12 elements (each 0.25mm long) failing one after another in quick succession. The load drops slightly but thereafter recovers to increase further. During this stage more elements fail with a total delamination growth of 9mm when the end-shortening of 2mm is reached. At this time the tangential stiffness of the structure has reduced significantly with the load beginning to level off. The behavior for GIc = 0.637N/mm is similar, except that delamination growth begins a little early, the load drop is more pronounced. And the total delamination growth is 18mm. Fig. 15 shows the axial compression vs. end shortening relationship.
Fig. 15. Static Response of Sandwich Column, Case II
Notwithstanding the actual magnitudes of the loads involved, qualitatively there is a significant difference between the delamination behavior under static loading of the Cases I and II considered here (cf. Fig. 13 and Fig. 16). It is somewhat paradoxical to see that delamination growth is minimal for the present case of a slender column with thin facing sheets whereas it was extensive for the case of stouter column with thicker facing sheets. Careful examination of the deformed shape of the member as it evolves indicates that the delamination growth is influenced by overall bending of the entire column and highly localized rotation of the facing sheet that occurs at the crack tip. If the overall bending is such as to cause longitudinal tension at the facing sheet, delamination growth comes to a stand still; if it is such as to cause longitudinal compression in the delaminating facing sheet with a pronounced curvature, the sheet in the vicinity of the crack tip tends to rotate and come into contact with the core inhibiting delamination growth. Thus we may conclude the delamination growth is not a significant factor in a slender sandwich column having thin facings under static loading. There are other modes of failure, such as face sheet wrinkling and its interaction with overall bending which cause failure of the member (El-Sayed, S., 2002).
Fig. 16. Static Response, Case II: Deformed shape at end shortening = 2mm
The delamination phenomena in sandwich members are studied using cohesive layer models- designated as UMAT and UEL models. When applied to a test case, it was found that the UMAT model which has a finite thickness can predict initiation of delamination growth as well as rate of growth of delamination, but is unable to predict large delamination growth due to an inherent deficiency. The UEL model which has zero initial thickness is capable of tracing the entire delamination history. Apart from the critical value of strain energy release rate in the opening mode, the parameter that influences crack initiation is the strength of the cohesive model material; for sandwich delamination problems using the actual strength of the core material in conjunction with the proposed models gave satisfactory results.
Delamination was studied in a member carrying a prescribed end-shortening. Two cases are considered, the Case I of a column which was relatively stout with relatively thick facing sheets and Case II, a slender column with thin facing sheets. The overall bending of the member (in case II) had a significant influence in inhibiting the crack growth by virtue of contact between the facing sheet and the core in the quasi-static load application.
ABAQUS/Standard User’s Manual, “UMAT: Define a Material’s Mechanical Behavior,” Hibbitt, Karlsson and Sorensen, Inc., Pawtucket, RI, Vol. 6.3, 2001, pp. 126.96.36.199-188.8.131.52.
ABAQUS/Standard User’s Manual, “UEL: Define an Element,” Hibbitt, Karlsson and Sorensen, Inc., Pawtucket, RI, Vol. 6.3, 2001, pp. 184.108.40.206-220.127.116.11.
Abot, J. L., “Fabrication, Testing and Analysis of Composite Sandwich Beams”, Ph. D. Thesis, Northwestern University, Evanston, Illinois, 2000.
Alfano, G. and Crisfield, M. A., “Finite Element Interface Models for the Delamination Analysis of Laminated Composites: Mechanical and Computational Issues,” International Journal for Numerical Methods in Engineering, Vol. 50, 2001, pp. 1701-1736.
El-Sayed, S. and Sridharan, S., “Cohesive Layer Models for Predicting Delamination Growth and Crack Kinking in Sandwich Structures,” International Journal of Fracture, Vol. 117, No. 1, Sept. 2002, pp. 63-84.
Li, X., “Debonding fracture of foam core the tilted sandwich structure,” Ph. D. Thesis, Florida Atlantic University, Boca Raton, Florida, 2000.
Li, Y. and Sridharan, S., “Performance of Two Distinct Cohesive Layer Models for Tracking Composite Delamination”, International Journal of Fracture, in press, 2005.
Li, Y. and Sridharan, S., “Investigation of Delamination Caused by Impact Using a Cohesive Layer Model”, AIAA Journal, Vol.43,No.10,2005, pp.2243-2250.
Sridharan, S., “Displacement-based mode separation of strain energy release rates for interfacial cracks in bi-material media”, International Journal of Solids and Structures, Vol. 38, 2001, pp. 27876803.