Fracture and mode mixity analysis of shear deformable composite beams

Abstract

To analyse delaminated composite beams with high accuracy under mixed-mode I/II fracture conditions first-, second-, third-and Reddy's third-order shear deformable theories are discussed in this paper. The developed models are based on the concept of two equivalent single layers and the system of exact kinematic conditions. To deduce the equilibrium equations of the linearly elastic system, the principle of virtual work is utilised. As an example, a built-in configuration with different delamination position and external loads are investigated. The mechanical fields at the delamination tip are provided and compared to finite element results. To carry out the fracture mechanical investigation, the J -integral with zero-area path is introduced. Moreover, by taking the advantage of the J -integral, a partitioning method is proposed to determine the ratio of mode-I and mode-II in-plane fracture modes. Finally, in terms of the mode mixity, the results of the presented evaluation techniques are compared to numerical solutions and previously published models in the literature.Keywords Delamination · Energy release rate · Mixed-mode I/II fracture · J -integral · Higher-order beam theories IntroductionAs the composite materials play important role in the industrial applications [11], the strong adhesion between the laminated layers is essential and must remain reliable even at high strains and high stresses [15]. Presence and propagation of a delamination in lightweight composite materials [35,38] can significantly decrease the load bearing capability of the structure [7,26,28], modify the dynamic properties [6,20,27,39,40], and furthermore, they can easily lead to sudden and catastrophic failure of the brittle mechanical system. Thus, the description [22,36] and the avoidance [10,59] of an interlaminar failure, which may take place because of low-velocity impact [5,24], blast loading [32,37], manufacturing defects [16][17][18] and free edge effects [13], are inevitable from engineering point of view.The application of the linear elastic fracture mechanics is one possibility to characterise the interlaminar fracture resistance of conventional high performance composites with inherent brittleness [8,9]. The critical value of the energy release rate G c , which can be considered as a material property, is suitable to characterise the strength of an interface layer between two elastic plies [19]. Like any other material parameters, mechanical tests must be carried out to be determined. In the case of fracture mechanical investigation, as linear elastic fracture mechanics works only if the location, size andshape of the crack are known, the experiments must be B. Kiss (B) · A. Szekrényes

Enhanced beam and plate finite elements with shear stress continuity for compressible sandwich structures

“…For sandwich beams, four conditions should be fulfilled due to Cauchy's Postulate (action and reaction on surfaces) if there is no external shear load on the outer surfaces of the face sheets [44][45][46][47]:…”

“…=C2xx * a * * 2 * b * h * * 3 * (2 * a + 3 * h)/(20 * Le) Ke[12,45]=C2xx * a * * 2 * b * h * * 3 * (−2 * a − 3 * h)/(20 * Le) Ke[12,46]=C2xx * a * * 2 * b * h * * 3 * (2 * a + 3 * h)/240 Ke[12,47]=C2xx * a * * 2 * b * h * * 3 * (2 * a + 3 * h)/240 Ke[12,48]=3 * C2xx * a * * 2 * b * h * * 3 * (2 * a * * 2 + 4 * a * h + 3 * h * * 2) /(80 * Le) Ke[12,49]=3 * C2xx * a * * 2 * b * h * * 3 * (−2 * a * * 2 − 4 * a * h − 3 * h * * 2)/(80 * Le) Ke[12,50]=C2xx * a * * 2 * b * h * * 3 * (2 * a * * 2 + 4 * a * h + 3 * h * * 2)/320 Ke[12,51]=C2xx * a * * 2 * b * h * * 3 * (2 * a * * 2 + 4 * a * h + 3 * h * * 2)/320 Ke[12,56]=−39 * G1xz * Le * h * * 2/140 Ke[12,57]=−27 * G1xz * Le * h * * 2/280 Ke[12,58]=−11 * G1xz * Le * * 2 * h * * 2/280 Ke[12,59]=13 * G1xz * Le * * 2 * h * * 2/560 Ke[12,60]=−39 * G1xz * Le * h * * 2/140 Ke[12,61]=−27 * G1xz * Le * h * * 2/280 Ke[12,62]=−11 * G1xz * Le * * 2 * h * * 2/280 Ke[12,63]=13 * G1xz * Le * * 2 * h * * 2/560 Ke[13,13]=3 * b * h * * 5 * (5 * C1xx * h * * 2 + 70 * C2xx * a * h + 78 * G1xz * Le * * 2)/(2800 * Le) Ke[13,14]=b * h * * 5 * (−5 * C1xx * h * * 2 − 70 * C2xx * a * h + 78 * G1xz * Le * * 2)/11200 Ke[13,15]=b * h * * 5 * (−5 * C1xx * h * * 2 − 70 * C2xx * a * h − 132 *…”

Testing mechanical performance of adhesively bonded composite joints in engineering applications: an overview

“…tedious. [114,115] To facilitate treatment a number of corrections are proposed.- [116][117][118] During the test, force P and the crack length a needs to be measured simultaneously to evaluate G I . While P is measurable in a straightforward manner (force sensor), measurements and interpretation of a is less obvious and debatable .…”

Higher-order semi-layerwise models for doubly curved delaminated composite shells

“…where it is important to highlight that the multiplicator matrices of the undelaminated region (l = 2) are equally involved for both sides of the equation [69]. Equation (46) means eight conditions.…”