Prediction and validation of the transverse mechanical behavior of unidirectional composites considering interfacial debonding through convolutional neural networks
Introduction
Composite materials that are lightweight and have excellent mechanical properties have been used to manufacture advanced engineering structures [1]. To develop composite materials with material properties tailored to users’ requirements, it has been necessary to improve the material properties in terms of strength, stiffness, and toughness under various operating conditions. The demand for shortening the development period and reducing the cost is meanwhile increasing in efforts to meet the market demand for customized and made-to-order products.
To this end, finite element (FE) model-based numerical evaluation of the stiffness and strength according to the microstructure of composite materials has been widely used [[1], [2], [3], [4], [5], [6], [7], [8], [9], [10], [11], [12]] along with experimental and analytical methods. Many studies have employed the representative volume element (RVE) simulating real microstructures to evaluate the material properties of various composites according to various reinforcing constituents to the matrix [[2], [3], [4], [5]]. In particular, to predict the mechanical behavior of unidirectional (UD) composites, many researchers constructed random RVE models and conducted FE simulations considering the random fiber distribution, interphase characteristics, and the elastoplastic behavior of the matrix because it is well known that the matrix and interphase properties dominate the effective properties of UD composites in the transverse direction [[13], [14], [15]]. However, this method also requires high computational costs because the material properties have to be judged in terms of the mean and standard deviation of the simulation results of many RVEs.
To speed up this process, machine learning and deep learning technology were recently introduced to the application of material science to determine the relationship between the input dataset (= microstructure) and output dataset (= material properties) [16]. Machine learning technology analyzes user-provided features, learns from datasets, and makes informed decisions. The support vector machine and logistic regression were used to classify the material phase; artificial neural networks were employed to predict the material properties of the unknown input after training the relationships between input and output datasets [[17], [18], [19], [20]].
In contrast to machine learning, deep learning can extract and learn features independently to make intelligent decisions. Among various deep learning models, the convolutional neural network (CNN) has been popularly adopted for material, microstructure, and defect classification [[21], [22], [23], [24], [25], [26], [27], [28], [29], [30], [31], [32], [33]] as well as discriminative refocusing of microstructural images [34]. Recently, it was also successfully used to predict material properties of binary composites in terms of stiffness, strength, and toughness with reasonable accuracy [[35], [36], [37], [38]]. This success was limited to discrete point-wise information such as stiffness, strength, and toughness. Subsequently, a combined CNN and principal component analysis model was developed to predict the stress-strain (S–S) curve with components of the composite, including randomly assigned hard and soft blocks [39]. This success was remarkable because the datasets of the S–S curve have high dimensionality and thus offer the advantage of predicting the entire S–S history of the structural materials according to the applied strain.
The purpose of the present work is to provide a simple and powerful data-driven model for predicting the transverse mechanical behavior of UD composites. To this end, we use CNN modeling with input datasets consisting of microstructure images and output datasets containing the S–S curves obtained from a transverse tensile simulation of RVEs of UD composites. The accuracy of the proposed model was confirmed by comparing the prediction results of several test datasets having random fiber positions with those of a transverse tensile simulation. It is noted that the accurate prediction of the mechanical behavior was made within only a few seconds for the test dataset with the proposed CNN model learned by the training dataset. Furthermore, we predicted the smoothed S–S curve that includes the entire material response without the principal component analysis that was used in other works [39].
The remainder of this paper is organized as follows. In Section 2, we present the numerical modeling and simulation results of the RVE of UD composites for the preparation input and output dataset. We then provide details of the proposed CNN model in Section 3. Prediction and validation results, including convergence studies, are subsequently presented. Finally, we give concluding remarks.
Section snippets
RVE generation using RSE algorithm
UD composites generally have diverse fiber volume fraction (=) due to mixing ratios with random fiber arrangement. To realize these characteristics of composites in this study, RVEs were generated by setting the fiber radii to 0.37, 0.41, and 0.45 for of 40%, 50%, and 60% with almost 100 circular fibers, respectively, and the RVE size was set to 10.0, which is known to be sufficiently large [5,20]. The random sequential expansion (RSE) algorithm was used to generate random RVEs of the UD
Convolutional neural network (CNN)
A convolutional neural network (CNN) is a neural network model for deep learning that learns from datasets without the need to extract features directly. In this work, we developed a prediction modeling using the CNN toolkit in the MATLAB Deep Learning Toolbox [50]. All of the RVEs used in the transverse tensile simulation were converted to binary images as input datasets, as shown in Fig. 5. The fibers were white pixels; the matrix and interphase were black pixels. The resulting image has a
Convergence study of CNN model
A convergence study of the CNN model was conducted to investigate the prediction performance of the model according to the image resolution and the number of RVE samples. To see the effect of image resolution, a relatively low-level image of 400 × 400 pixels was additionally employed with the same number of RVE samples. Furthermore, the effect of the number of RVE samples was investigated by reducing them from 900 to 600 and 150. We presented S–S curves for three randomly selected RVEs among
Conclusion
In this work, a simple and powerful data-driven CNN model was developed to predict the transverse mechanical behavior of UD composite materials. The relationship between the input datasets (microstructure images) and the output datasets (S–S curves) was trained by the CNN model. It is seen that the CNN model accurately predicts the S–S curves of UD composites showing nonlinear behavior caused by the interphase debonding beyond the elastic limit for unknown test dataset images. Therefore, it is
Author statement
Do-Won Kim: Investigation, Methodology, Software, Writing – original draft. Jae Hyuk Lim: Supervision, Conceptualization, Writing – review & editing. Seungchul Lee: Writing – review & editing.
Declaration of competing interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
Acknowledgement
This work was supported by ‘Space challenge Program’ grant funded by the Ministry of Science and ICT, Republic of Korea (NRF-2020M1A3B8084736).
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