Strength characteristics of a composite laminate with a center hole under biaxial tensile loading

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STRENGTH CHARACTERISTICS OF A COMPOSITE LAMINATE WITH A CENTER HOLE UNDER BIAXIAL TENSILE LOADING

ПРОЧНОСТНЫЕ СВОЙСТВА СЛОИСТОГО КОМПОЗИТА С ЦЕНТРАЛЬНЫМ ОТВЕРСТИЕМ ПРИ БИАКСИАЛЬНОМ РАСТЯЖЕНИИ

Сюй Чуанси, Магистрант Департамент Прочности Композитов, Нанкинский Университет Космонавтики и Астронавтики

Нанкин, Китай

Ушаков А.М., к.т.н. доцент, Доцент каф. Технологии ф-та Авиационные Двигатели,

Московский Авиационный Институт Москва, Российская Федерация

Аннотация: представленная статья посвящена разработке полезной модели, работающей непосредственно с биаксиальным растяжением композитных пластин в присутствии концентратора напряжений, называемой как прогрессивная модель разрушения, и реализованная путем параметрического программирования в ANSYS.

Introduction

In modem time, most of the analytical and experimental work is limited to uniaxially loaded laminates. Very little work has been reported on the behavior of such laminates with stress concentrations under biaxial states of stress. Stress distributions in composites around holes or cracks, have been treated analytically using linear anisotropic elasticity and finite-element methods [1, pp.73-100]. Inhomogeneity of the material, nonlinearity of response near failure and the complex interaction of failure modes near notches make it difficult to predict biaxial behavior on the basis of uniaxial response.

1. Progressive Damage Analysis

For biaxial testing, there are always two types of shapes: Center thinning specimens and Split arm specimens. The general configuration of the cruciform specimen was adopted as split arm specimens like previous studies [2, pp.121-123]. In order to guarantee the uniform strain field can be generated in the circular gauge region located at the center of the specimen under biaxial loadings, a number of parametric studies were carried out through FEA to refine the design, especially determination of dimensions and selection of proper tab materials.

1.2 Cruciform model dimension

Based on [3, pp.36-39]. The geometry of specimen was selected to be cruciform shape. The size for length and width is 300 mm X 300 mm, arm width is 40 mm. The center area of 40mmx40mm size has a circular opening, with a diameter of 6 mm. The slot width is 2.5 mm, 1.75 mm is reserved above the edge of the central region in order to ensure the slot of arms does not affect the stress distribution in the central area, therefore the slot length is 123.25 mm. The geometry of whole specimen and center area are shown on Figure 1 (a) and (b).

1.3 Finite Element Model

Finite element method was chosen as the numerical tool for modeling and analysis in this study; for this purpose, ANSYS standard was used. A full-size model was created with conventional solid elements, Solid185. From a convergence study on the effect of mesh fineness on the accuracy of results, a structured meshing scheme was chosen with 169856 elements and 190468 nodes as shown in Figure 2.

1.2 Static Analysis

In order to make a reconfirmation of the specimen design, the cruciform specimen with an open hole was modeled and analyzed in ANSYS to check if strain in the gauge region is as uniform as expected when biaxial loadings are applied. Static analysis was performed on the specimen with slots and without slots, respectively. The tensile loads of 200 MPa were applied on the two perpendicular arm ends. The calculating results of 0^o ply and 90^o ply in specimen were selected to make a comparison. The stress and strain contours of the specimen are shown on Figure 3.

From Figure 3, some results can be concluded: (1) Stress distribution in gauge area with slots is almost the same to that without slots, which means slots don't affect stress field in central area a lot. (2) The specimen with slots reduces the stress concentration at the chamfer compared to that without slots. Above all, it can ensure failure happens from the hole instead of chamfer, which means current design is adequate.

1.4 Progressive Damage Model

A progressive damage model was incorporated in the simulation using parametric programming implemented into ANSYS. The main mechanical properties of the UD lamina are given in Table 1. The stacking sequence of laminates was selected to be [0/90]4s. The nominal thickness of the cured laminates was about 2.0 mm. In this scheme, the material properties of a failed element are degraded, or damaged, once a specified failure criterion is met. To this effect, Tsai Wu's quadratic failure criterion [4, pp.68-78] was chosen as the damage initiation criterion. Among various methodologies used to degrade the material properties on the onset of failure, the one used by Chang [5, pp.840-841] was implemented where the elements of the elastic stiffness matrix were degraded based on the mode of failure, either fiber or matrix dominated.

For finite element model, the end of left arm was constrained by X-axis and Z-axis direction, end of bottom arm was constrained by Y-axis and Z-axis direction, while a uniform tensile displacement in the positive direction of the Y axis and the positive direction of the X axis is applied to the upper end and the right end, respectively. Displacements applied in either direction could be varied so as to obtain different combinations of the stresses (a_±, a₂) on the onset of ultimate failure. These values would lie on the locus of the failure envelope.

Three biaxial ratios were chosen to study, ultimate damages of which were shown in Figures 4-6. Six colors were selected to display each damage mode shown in Table 2.

As shown on Figure 4, the total damage of laminate (under biaxial ratio=1) mainly includes fiber and matrix tensile failure; in both 0^o and 90^o plies, there are almost presented fiber tensile failure along diagonal direction from the hole; especially in 0^o ply, fiber damage evolved from vertical slots, while from horizontal slots in 90° ply.

For both cases (biaxial ratio=2 and =3), the total damage in 0^o ply mainly includes matrix and fiber failure, while fiber failure dominates in 90^o ply. damage would both evolve to horizontal slots either in 0^o ply or 90^oply due to applied force in Y-axis more than in X-axis. The most difference between these two conditions is that there exists another fiber damage path biased toward the Y-axis in both 0^o and 90^o ply mainly due to more force applied in Y-axis under bigger biaxial ratio compared to the other one.

2. Results and Analysis

Zhang [6, pp.41-43] has made biaxial tensile experiments of orthogonal laminates containing a hole, from which the resulting data were extracted to evaluate the reliability of the progressive damage model.

2.1 Load-Displacement Curves

Based on simulations, the load-displacement curves for open-hole specimens under different biaxial loading schemes can be obtained. By adding data of experiment, the comparisons between experiment and simulation have been shown on Figure 7.

For equal biaxial loading condition, the load-displacement curve is almost linear during loading process. After ultimate failure, the applied force decreases suddenly, which means the specimen has brittleness. For other two cases (biaxial ratio=2 and =3), except linearity, the force in Y-axis of experiment can decrease a little during latter loading period due to interface debonding. Also, for biaxial ratio= 3, the load in X-axis can stand more time after that in Y-axis reaches the limit.

2.2 Failure Envelope.

Conclusion

Progressive damage model was utilized to analyze the damage evolution of specimen. During designing model, a cruciform shape with four slots on arms were selected by comparison of results with static analysis. In addition, damage mechanisms in ultimate failure phase under three different loading schemes were displayed, accompany with the load-displacement curve, from which ultimate strength can be obtained. Based on the predicting results of FEA, the failure envelopes for open-hole laminates were established and compared to experiments.

Acknowledgements

Very grateful to tutor A.M. Ushakov for his technical, financial and moral support.

Bibliography

1. Rybicki, E.F. and Hopper, A.T. Analytical Investigation of Stress Concentrations Due to Holes in Fiber-Reinforced Plastic Laminated Plates; Three-Dimensional Models, Air Force Materials Lab. Report, AFML-TR-73- 100 (June 1973).

2. Tiernan P, A. Design optimization of biaxial tensile test specimen using finite element analysis [J]. International Journal of Material Forming, 2014, 7:117 123.

3. Jia Wenbin. Analysis and Research on Low Velocity Impact Damage and Residual Strength under Biaxial Load of Composite Laminated Plates [D]. Nanjing: Nanjing University of Aeronautics and Astronautics, 2016.

4. Tsai, S.W. and Wu, E.M. A General Theory of Strength for Composite Anisotropic Materials, Journal of Composite Materials, 1971,5: 58-80.

5. FU-KUO CHANG and KUO-YEN CHANG. A Progressive Damage Model for Laminated Composites Containing Stress Concentrations, Journal of Composite Materials, 1987,5:834-855

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