A multiscale elasto-plastic damage model for the nonlinear behavior of 3D braided composites
Introduction
3D braided composites possess several advantages over traditional composites, such as higher impact strengths, better damage tolerance and fatigue resistance. Therefore, they have been applied widely in many fields, e.g., engine blades, helmet, artificial stent, etc. [1,2]. In the past few decades, the material stiffness has been widely studied and various satisfactory methods have been proposed to predict the stiffness properties [3,4]. However, due to the variability of the properties for constituents, the natural multiscale properties and the expensive experimental expenses, it is difficult to predict the strength and reveal the damage behavior for 3D braided composites by means of experiments alone. Therefore, a reliable analytical model needs to be established to characterize the damage behavior for 3D braided composites, while reducing the number of experiments.
During the manufacture process, several defects may be generated due to the temperature difference from the curing temperature to the room temperature. When subjected to external loads, the material is more likely to be damaged which is expressed as stiffness degradation and final fracture. Meanwhile, owing to the stress concentration around the defects, the unrecoverable plastic deformation will also occur. Thus, the mechanical properties for 3D braided composites depend on both damage and plasticity. Neglecting either of them cannot characterize the mechanical performance well. Some researchers have applied the elastic damage model to determine the nonlinear material behavior for braided composites [[5], [6], [7]]. Wang et al. used the elastic damage model based on the fast Fourier transform (FFT) to investigate the progressive damage behavior for 3D braided composites [5]. The elastic damage model was adopted to characterize the damage and failure behavior for triaxial braided composites under multiaxial stress state [6]. Applying the maximum principal stress criterion and combining with micro-CT, the in-plane tensile damage behavior of the 3D orthogonal woven composites was studied by Zeng et al. [7]. However, the effects of plasticity for epoxy matrix was not considered in these works, while the phenomenon has been clearly observed from experiment [8]. On the contrary, the plastic model was used alone in some studies to investigate the nonlinear properties for braided composites [9,10]. Applied the J2 plastic theory for epoxy matrix, the compressive properties of braided composites were studied by Fang et al. [9]. Song et al. considered the inelastic deformation for matrix and studied the nonlinear behavior of triaxial braided composites under compression [10]. However, the stiffness degradation for matrix material was not considered in these works. It should be noted that the nonlinear behavior of 3D braided composites is controlled by both damage and plasticity. Meanwhile, many elasto-plastic damage models have been proposed to characterize the mechanical behavior of concrete and unidirectional composites [[11], [12], [13]]. To the best of the author's knowledge, there are no studies focusing on the elasto-plastic damage behavior for braided composites besides of our previous work [14]. In the previous work [14], a coupled elasto-plastic damage model was established to evaluate the effects of damage and plasticity, and the plastic model of epoxy matrix was based on the von Mises yield criterion. This model could not reflect the different mechanical behavior in tension and compression which has been observed by experiment [15]. When the external load is applied to the braided composites, some matrix materials are subjected to tension and some matrix materials are under compression. Thus, an accurate elasto-plastic damage model that can characterize the different mechanical properties of matrix material under tension and compression needs to be established.
On the other hand, due to the natural multiscale characteristics of 3D braided composites, focusing on the mechanical behavior at one scale cannot reveal the failure mechanism of materials. Thus, it is necessary to develop a multiscale analysis model to capture the mechanical behavior at different scales. Dong et al. adopted a two-scale method to predict the stiffness of braided composites with internal defects while the damage behavior was not involved [16]. Yu et al. predicted the mechanical properties of braided composites via two-scale method (i.e., mesoscale and macroscale), while the microscale properties and damage behavior were not considered [17]. Zhao et al. proposed a multiscale model to simulate the impact damage of triaxially braided composites and the results showed great agreement with experiments [18]. The multiscale analysis method is an effective way to predict the mechanical performance for composites, and the satisfactory results of multiscale damage analysis for 3D braided composites have not been obtained at now.
On the basis of the aforementioned argument, it is necessary to establish a model to couple the plasticity and damage for constituents on the different scales. In this paper, a multiscale elasto-plastic damage model is proposed to evaluate the nonlinear mechanical performance of 3D braided composites and it is validated with the corresponding experiment.
Section snippets
Multiscale elasto-plastic damage model
The mechanical properties of 3D braided composites are affected by the material inhomogeneity which may come from multiple scales, e.g. the fiber arrangement at microscale and the braiding structure at mesoscale. Considering the mechanical behavior at one scale alone cannot characterize the properties accurately. The multiscale method is predominant which can capture and transfer the valid information among different scales. Here we adopt a sequential multiscale method to implement the
Multiscale analysis for the 3D braided composites
The proposed multiscale analysis method is applied to investigate the nonlinear mechanical behavior of 3D four-directional braided composites under unidirectional tension. The numerical simulations are compared with corresponding experiments to verify the accuracy of the proposed model.
Microscale analysis
The stress-strain curves of TDE-86 epoxy matrix under uniaxial tension and compression are determined by the experiments. Hardening curves are transformed from the stress-strain curves and used in the numerical implementation. The value of plastic Poisson's ratio is given from reference [34]. In order to validate the proposed model, the experiment of Bisphenol-A epoxy matrix is used [15]. Applying the UMAT to a standard 3D hexahedral element, the comparison of numerical simulation and
Conclusions
In this paper, a multiscale elasto-plastic damage model is proposed to characterize the nonlinear behavior of 3D braided composites. Microscale constituents consist of fiber, matrix and interface, which are consistent with the mesoscale ones. The elastic damage model is applied to degrade the stiffness of fiber. A coupled elasto-plastic damage model is proposed to integrate the effects of both plasticity and damage. A bilinear constitutive relation is adopted to investigate the properties of
Acknowledgements
This work was supported by Beijing Natural Science Foundation (1184017) and National Natural Science Foundation of China (11802018 and 11732002). And, the first author would like to acknowledge beneficial technical discussions with Dr. Xiaoming Bai.
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