Elastic Foundation Solution for the Energy Release Rate and Mode Partitioning of Face/Core Debonds in Sandwich Composites

2019 ◽  
Vol 86 (12) ◽  
Author(s):  
George A. Kardomateas ◽  
Niels Pichler ◽  
Zhangxian Yuan
Keyword(s):  
Energy Release Rate ◽  
Closed Form ◽  
Energy Release ◽  
Elastic Foundation ◽  
Release Rate ◽  
Sandwich Beam ◽  
Integral Approach ◽  
Closed Form Expression ◽  
Sandwich Composites ◽  
Sandwich Construction

Abstract The goal of this paper is to derive closed form expressions for the energy release rate and mode partitioning of face/core debonds in sandwich composites, which include loading in shear. This is achieved by treating a finite length sandwich beam as having a “debonded” section where the debonded top face and the substrate (core and bottom face) are free and a “joined” section where a series of springs (elastic foundation) exists between the face and the substrate. The elastic foundation analysis is comprehensive and includes the deformation of the substrate part (unlike other elastic foundation studies in the literature) and is done for a general asymmetric sandwich construction. A J-integral approach is subsequently used to derive a closed form expression for the energy release rate. In the context of this elastic foundation model, a mode partitioning approach based on the transverse and axial displacements at the beginning of the elastic foundation (“debond tip”) is proposed. The results are compared with finite element results and show very good agreement.

scholarly journals Closed form solution for the energy release rate and mode partitioning of the single cantilever beam sandwich debond from an elastic foundation analysis

2020 ◽  
pp. 109963622093290
Author(s):  
George A Kardomateas ◽  
Zhangxian Yuan
Keyword(s):  
Energy Release Rate ◽  
Closed Form ◽  
Energy Release ◽  
Elastic Foundation ◽  
Cantilever Beam ◽  
Release Rate ◽  
Closed Form Solution ◽  
Integral Approach ◽  
Sandwich Composite ◽  
Closed Form Expression

The goal of this paper is to derive closed form expressions for the energy release rate and mode partitioning offace/core debonds for the Single Cantilever Beam Sandwich Composite testing configuration, which is loaded with an applied shear force and/or bending moment. This is achieved by an elastic foundation approach, in which a finite length sandwich beam is treated as having a free “debonded” section and a “joined” section where a series of springs exists between the face and the substrate (core and bottom face). The elastic foundation analysis is done for a general asymmetric sandwich construction. A J-integral approach is subsequently used to derive a closed form expression for the energy release rate. It is also shown that the energy release rate is very close to the differential energy stored in the springs at the beginning of the elastic foundation, i.e. the energy released by the “broken” differential spring element as the debond propagates. In the context of this elastic foundation model, a mode partitioning measure is defined based on the transverse and axial displacements at the beginning of the elastic foundation. Since the normal springs account for the transverse compressibility of the core but not for the shear, a correction for the shear of the substrate is included by deriving the expression for the corresponding shear angle and accounting for the additional horizontal “tip” displacement. The results are compared with finite element results for a range of core materials and show very good agreement.

The Initial Post-buckling and Growth Behavior of Internal Delaminations in Composite Plates

1993 ◽  
Vol 60 (4) ◽  
pp. 903-910 ◽  
Author(s):  
G. A. Kardomateas
Keyword(s):  
Energy Release Rate ◽  
Closed Form ◽  
Energy Release ◽  
Release Rate ◽  
Plate Thickness ◽  
Composite Plates ◽  
Growth Behavior ◽  
Mode I ◽  
Perturbation Procedure ◽  
Post Buckling

The initial post-buckling and growth behavior of delaminations in plates is studied by a perturbation procedure. In this work, no restrictive assumptions regarding the delamination thickness and plate length are made, i.e., the usual thin film assumptions are relaxed. The perturbation procedure is based on an asymptotic expansion of the load and deformation quantities in terms of the distortion parameter of the delaminated layer, the latter being considered a compressive elastica. Closed-form solutions for the load and midpoint delamination deflection versus applied compressive displacement during the initial post-buckling phase are derived. Moreover, closed-form expressions for the energy release rate and the mixity ratio (i.e., Mode II versus Mode I) at the delamination tip are produced. A higher Mode I component is found to be present during the initial post-buckling phase for delaminations of increasing ratio of delamination thickness over plate thickness, h/T (i.e., delaminations further away from the surface). Moreover, the-energy release rate corresponding to the same applied strain is larger for a higher h/T ratio. The reduced growth resistance of these configurations is verified by experimental results on unidirectional composite specimens with internal delaminations.

Closed-Path J-Integral Analysis of Bridged and Phase-Field Cracks

2016 ◽  
Vol 83 (6) ◽  
Author(s):  
Roberto Ballarini ◽  
Gianni Royer-Carfagni
Keyword(s):  
Energy Release Rate ◽  
Energy Release ◽  
Release Rate ◽  
Momentum Tensor ◽  
Integral Approach ◽  
J Integral ◽  
Damaged Material ◽  
Energetic Balance ◽  
Material Separation ◽  
Definition Of

We extend the classical J-integral approach to calculate the energy release rate of cracks by prolonging the contour path of integration across a traction-transmitting interphase that accounts for various phenomena occurring within the gap region defined by the nominal crack surfaces. Illustrative examples show how the closed contours, together with a proper definition of the energy momentum tensor, account for the energy dissipation associated with material separation. For cracks surfaces subjected to cohesive forces, the procedure directly establishes an energetic balance à la Griffith. For cracks modeled as phase-fields, for which no neat material separation occurs, integration of a generalized energy momentum (GEM) tensor along the closed contour path that traverses the damaged material permits the calculation of the energy release rate and the residual elasticity of the completely damaged material.

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