GRD Journals- Global Research and Development Journal for Engineering | Volume 4 | Issue 5 | April 2019 ISSN: 2455-5703
Fracture of Bone-Like Microstructure under Three-Point Bending Test James Rickgauer Department of Materials Science and Engineering Texas A&M University
Timothy D. Allen Department of Materials Science and Engineering Texas A&M University)
Abstract Composite materials with staggered structure show exceptional mechanical properties despite its brittle and weak building blocks. For instance, the fundamental structure of bone and bone-like materials is a staggered arrangement of nano-scale hard minerals in a soft protein matrix. Underrating how bone-like structure increases strength and toughness could benefit the manufacturing of composite materials. In this paper, the effect of building block dimensions of staggered minerals on crack formation, crack propagation is studied. Cohesive zone model in finite element method context is employed to model damage and failure of the interface between two building blocks. A three-point bending test is performed on the structure with different building block dimensions, and results are compared in the form of force-displacement and energy release rate curves. The results indicate that the increase in the aspect ratio, leads to a increase in the strength, stiffness, and energy release rate in the three-point bending test. Although decrease in the aspect ratio prevents sudden failure of the structure and catastrophic failure. Keywords- Bone-Like, Finite Element, Cohesive Zone Model, Fracture, Three-Point Bending
I. INTRODUCTION Nature builds material with outstanding mechanical properties that exceed their own building blocks properties. Some studies show that the hierarchical structure of these materials is the main reason behind their amazing properties [1–4]. On the other hand, in some other studies [1,5,6], optimum flaw tolerance size due to the geometry of the structure was introduced as the main reason for higher strength and toughness. Understanding the structure-property relationship for such structures and finding the optimum geometry in order to have high strength, stiffness and fracture toughness could help the manufacturing of this type of composites. Dimensional analysis of nacre-like structure has previously been studied numerically [7,8] and analytically [7,9]. An analytical solution to mortar-brick structure shows an increase in strength, stiffness, and decrease in fracture toughness by increasing the aspect ratio [9]. However, in the mentioned study the mortar is modeled as elastic-perfect plastic. Increase in fracture toughness by increasing the length of the minerals was shown in another analytical study [7]. In this paper, the second approach, the concept of flaw tolerance, due to the optimum size of building blocks is evaluated. The main focus is on the maximum bearing load, stiffness, and energy release rate of staggered structure with a different aspect ratio of minerals. The assumption is that minerals are solid and failure only happens in the mortar (interface) of the structure. However, some studies have shown that when the interface becomes too strong, the failure occurs in the mineral tablets [8,10–12].
II. MATERIALS AND METHODS The main difference here is the utilization of only one material type, minerals, in the staggered structure. These minerals could be any stiff nano-scale bio-molecules which interact with adjacent molecules through van der Waals forces. Here the same type of interaction is assumed for all sides of the minerals for simplicity and the effect of geometry parameters (Figure 1) on fracture and failure of the staggered structure will be evaluated. The minerals are modeled as linear elastic isotropic material with E=70000 MPa, and Ď‘=0.3 and the interface is modeled as cohesive material with linear elastic and softening region as shown in Figure 2. The properties for cohesive material is defined in table 1.
Fig. 1: Shape and overlap of minerals, a, b and c are length, width, and overlap of minerals respectively. The interactions are shown in blue arrows, and the same type of interaction is assumed for all directions
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Fracture of Bone-Like Microstructure under Three-Point Bending Test (GRDJE/ Volume 4 / Issue 5 / 006)
To study the effect of geometry on the fracture and failure of staggering materials, three-point bending simulations have been performed for different aspect ratios of minerals. The structure for the largest aspect ratio is shown in Figure 3. The dimension of the beam is 100Ă—6 mm with 1mm thickness, and plane strain condition is assumed for all the simulations. Automatic stabilization with 0.001 dissipated energy fraction has been used in the static analysis to improve solution convergence.
Fig. 2: The loading-unloading path for cohesive material. [6] Max_s1 (MPA) 80
Max_s2 (MPA) 80
Max_s3 (MPA)
Failure disp (mm)
E/Enn
80 0.038 6666 Table1: Properties of the cohesive element
G1/Ess
G2/Ett
6666
6666
Fig. 3: Shape and overlap of minerals, a, b and c are lengths, width, and overlap of minerals respectively. The interactions are shown in blue arrows, and the same type of interaction is assumed for all directions
III. RESULTS AND DISCUSSION Three-point bending simulation has been done on staggered structure with four different aspect ratio, R=33.33, R=16.66, R=8.33 and R=4.166 and for all cases c/a=0.5. For each case failure mechanism, force-displacement curve and energy release rate are evaluated. In Figure 4, the failure mechanism for different aspect ratio are shown. As the aspect ratio of minerals decreases, more localization of damage around the area in the middle of the beam occurs, due to the fact that crack follows the shortest path from bottom to the top and by decreasing the aspect ratio, the path gets shorter and shorter (moving in y-direction rather than in xdirection). This should result in lower strength and toughness of the structure. Figure 5a,b compares the force-displacement and energy release rate for different aspect ratio. As mentioned above, due to the shorter path to failure for cases with a lower aspect ratio, the strength, and energy release rate is lower for these cases. Figure 5,b mainly shows that failure is more abrupt in the cases with higher aspect ratio with a higher overall energy release rate. Also, the step-shaped curves in energy release rate figure show how crack propagates in x and y-direction. The propagation in y-direction makes the sudden vertical jump in curves and propagation in the x-direction, causes a more smooth increase in energy release rate. Besides, Figure 5, a indicates that not only the strength but also the bending stiffness of the staged structure reduce at a lower aspect ratio of minerals. The same results were observed in the analytical study of the brick-mortar structure [9], although that study was done for elastic-perfect plastic mortar under tension test. Figure 6 represents more clear results for variation of maximum load, stiffness, and energy release rate with respect to change in the aspect ratio of minerals. The variation shows possible optimum size for higher aspect ratios as the values seem to be approaching a plateau.
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Fracture of Bone-Like Microstructure under Three-Point Bending Test (GRDJE/ Volume 4 / Issue 5 / 006)
Fig. 4: Three-point bending of staggered structure with different aspect ratio. For higher aspects ratio, the crack has to move more in ydirection rather than x-direction
(a) (b) Fig. 5: Three-point bending test results for staggered structure with different aspects ratios. (a) Force-displacement curves. (b) Energy release rate-time period curves
(a)
(b)
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Fracture of Bone-Like Microstructure under Three-Point Bending Test (GRDJE/ Volume 4 / Issue 5 / 006)
Fig. 6: Variation of Ultimate force, Stiffness and energy release rate with respect to aspect ratio are shown in (a), (b) and (c) respectively
IV. CONCLUSION In this paper, the effect of aspect ratio on the fracture and failure of a three-point bending specimen was evaluated. The results indicate that the increase in the aspect ratio, leads to a increase in the strength, stiffness, and energy release rate in the three-point bending test. Although decrease in the aspect ratio prevents sudden failure of the structure and catastrophic failure. More simulations are necessary to conclude the optimum aspect ratio for optimum strength, stiffness, and energy release rate.
ACKNOWLEDGMENTS The authors would like to thank Mehdi Shishehbor for helpful discussions on modeling, and introducing this journal to us.
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