A numerical study to assess the role of pre-stressed inclusions on enhancing fracture toughness and strength of periodic composites

Abstract

A rational design for simultaneous toughening and strengthening in composites would be significant for myriad applications in fracture-related problems. Nacre simultaneously exhibits extremely high toughness (approximately 3000 times the constituent materials) and high strength, being one of the classic examples of the brilliant solutions nature can come up with based on necessity. Several experimental studies have suggested that the underlying “brick and mortar” microstructure of the nacre could be responsible for the high performance (high strength and high toughness). However, it has been realized that the engineered composites can not achieve the desired performance by only mimicking the “brick and mortar” structure. Naturally, the question arises whether there is any additional mechanism that is possibly responsible for the high-performance of nacre and may be mimicked in the engineered composites to achieve the desired high performance. In this study, numerical simulations show that the design of high-performance engineered composites can be achieved by introducing pre-stress in the inclusions. We have carried out mode-I and mode-II fracture simulations in periodic composites with both hard and soft pre-stressed inclusions to assess their role in the performance of composites. For modeling crack propagation in mode I, we have adopted the surfing boundary conditions proposed by Hossain et al. (2014), and appropriately extended it for modeling crack propagation in mode II. The present work indicates that a study on the existence of a pre-stressed condition of the platelets in the nacre may be a topic of research interest to explore the origin of the high performance of the nacre.

Appendix

1.1 Appendix A1: Convergence plot

After mesh refinement and convergence study for the numerical model, the domain is discretized using 114962 triangular elements and 57480 nodes. Note that the length of the element edges is considered as an immediate measure of the mesh refinement level adopted in our simulations. Mesh is not refined in the crack propagation direction. However, after convergence study, a mesh with maximum size 0.025 yields good results. A convergence plot for the same is shown in Fig. 1. The minimum and maximum size of the elements are 0.021 mm and 0.025 mm, respectively, and the corresponding areas are 0.0376 $\text {mm}^2$ and 0.0703 $\text {mm}^2$, respectively (Fig. 13).

1.2 Appendix A2: Effect of periodicity

This sections shows the effect of periodicity. We test-run simulations with increasing domain size and compute normalized J-integral (the path remains same for all the domains). A compressive prestress load of 250 MPa is applied to the hard inclusions to study the effect. Note that the inclusion size and spacing between them for all the domain remain the same. From Fig. 14b, we observe that a convergence is achieved beyond 21 $\times$ 21 inclusions. It also shows that a compressive prestress force in the inclusions shows an increase in the fracture toughness in all the test-domains. Figure 14a shows that fracture strength is also converged after 21 $\times$ 21 inclusions. Next, to study the effect of inclusion shape, we test run with square shaped, circular shaped and triangular shaped inclusions on the converged domain, i.e., 21 $\times$ 21 inclusion domain. It is observed is that with hard inclusions, there is not much change in the J-integral, i.e, the shape of the inclusions are have a negligible effect with hard inclusions (even with applied compressive prestressing in the inclusions).