Chapter 4:Multiscale and Multilevel Modeling of Composites 175 0.9 0.8 7 0.6 05 0.4 0.3 02 (b) 0.9 07 0.6 0.5 0.4 0.3 0.2 (c) Fig.4.7.Progressive damage plot from (a)lower damage state to (c)higher damage state.White lines indicate damage saturation,i.e.,cracks
Fig. 4.7. Progressive damage plot from (a) lower damage state to (c) higher damage state. White lines indicate damage saturation, i.e., cracks Chapter 4: Multiscale and Multilevel Modeling of Composites 175
176 Y.W.Kwon among subdomains within each domain while the average particle volume fraction was equal to the domain particle volume fraction.By doing so, local stress effect due to inhomogeneous microstructure in a composite can be studied [28,31]. Comparing the stress-strain curves between uniform and nonuniform particle distribution cases for the whole specimen,the nonuniform distri- bution case resulted in much lower failure strength and strain values as illustrated in Fig.4.6.A nonuniform particle distribution resulted in locally higher stresses and strains than the uniform case.This caused crack initia- tions earlier for the nonuniform case and eventually earlier failure as shown in Fig.4.7.The figure plots damage parameter distributions as damage increases.The lighter color in the gray scale indicates a greater damage state.The highest damage is represented by white,which denotes cracks. This study also provided information regarding what would be a useful failure criterion for such a composite discussed above.Because the compo- site has much stronger and stiffer particles than the matrix,failure in the matrix did not affect much the effective stress at the composite level. Hence,the composite stresses would not be a good choice for a failure cri- terion at the macrolevel.On the other hand,the composite strains represent the damage very closely,and would be a good selection for a failure crite- rion at the macrolevel. 4.3 Fibrous Composites 4.3.1 Multiscale Analysis for Fibrous Composites Fiber-reinforced composites can be constructed by multiple layers.Every layer has long unidirectional fibers embedded in a matrix material,and the fiber orientation of each layer is generally varied from layer to layer.For the fibrous composite,the multiscale analysis hierarchy is depicted in Fig.4.8.Comparing to the particulate composite,the fibrous composite requires one more step for the multiscale analysis,which is the Lamination Module7,14-16,191. As illustrated in Fig.4.8,the overall hierarchy has a Stiffness Loop and a Stress Loop for a complete cycle.The same modules are also used for both loops.First of all,the fiber and matrix material and geometric properties are used in the Fibrous Module to determine the effective
among subdomains within each domain while the average particle volume fraction was equal to the domain particle volume fraction. By doing so, local stress effect due to inhomogeneous microstructure in a composite can be studied [28, 31]. Comparing the stress–strain curves between uniform and nonuniform particle distribution cases for the whole specimen, the nonuniform distribution case resulted in much lower failure strength and strain values as illustrated in Fig. 4.6. A nonuniform particle distribution resulted in locally higher stresses and strains than the uniform case. This caused crack initiations earlier for the nonuniform case and eventually earlier failure as shown in Fig. 4.7. The figure plots damage parameter distributions as damage increases. The lighter color in the gray scale indicates a greater damage state. The highest damage is represented by white, which denotes cracks. failure criterion for such a composite discussed above. Because the composite has much stronger and stiffer particles than the matrix, failure in the matrix did not affect much the effective stress at the composite level. Hence, the composite stresses would not be a good choice for a failure criterion at the macrolevel. On the other hand, the composite strains represent the damage very closely, and would be a good selection for a failure criterion at the macrolevel. 4.3 Fibrous Composites 4.3.1 Multiscale Analysis for Fibrous Composites Fiber-reinforced composites can be constructed by multiple layers. Every layer has long unidirectional fibers embedded in a matrix material, and the fiber orientation of each layer is generally varied from layer to layer. For the fibrous composite, the multiscale analysis hierarchy is depicted in Fig. 4.8. Comparing to the particulate composite, the fibrous composite requires one more step for the multiscale analysis, which is the Lamination Module [7, 14–16, 19]. As illustrated in Fig. 4.8, the overall hierarchy has a Stiffness Loop and a Stress Loop for a complete cycle. The same modules are also used for both loops. First of all, the fiber and matrix material and geometric properties are used in the Fibrous Module to determine the effective Y.W. Kwon This study also provided information regarding what would be a useful 176
Chapter 4:Multiscale and Multilevel Modeling of Composites 177 Stiffness Loop Finite Fibrous Lamination Element Module Module Analysis Microlevel Mesolevel Macrolevel Macrolevel (fibers and (fibrous (laminated (composite matrix) composite) composite) structure) Fibrous Lamination Finite Module Module Element Analysis Stress Loop Fig.4.8.Multiscale analysis hierarchy for a fibrous composite material properties of a unidirectional fibrous composite.These composite properties are used for each lamina with its orientation of fibers with respect to the global coordinate system.The "Lamination Module"computes the effective properties of the laminated composite.Then,those properties are used for finite element analysis of a laminated composite structure.This completes the Stiffness Loop.Then,the reverse order is used to decompose stresses and strains at the macrolevel into those in the microlevel,i.e., stresses and strains in the fiber and matrix materials. Once microlevel stresses and strains are computed,damage and/or failure criteria are applied to them.Because damage and failure are described at the constituent level,damage and failure modes are simplified and physics-based.At the microlevel,there are three potential damages and failures:fiber breakage,matrix cracking,and interface debonding.Different damage or failure criteria can be applied to those three different damage modes
Fig. 4.8. Multiscale analysis hierarchy for a fibrous composite material properties of a unidirectional fibrous composite. These composite properties are used for each lamina with its orientation of fibers with respect to the global coordinate system. The “Lamination Module” computes the effective properties of the laminated composite. Then, those properties are used for finite element analysis of a laminated composite structure. This completes the Stiffness Loop. Then, the reverse order is used to decompose stresses and strains at the macrolevel into those in the microlevel, i.e., stresses and strains in the fiber and matrix materials. Once microlevel stresses and strains are computed, damage and/or failure criteria are applied to them. Because damage and failure are described at the constituent level, damage and failure modes are simplified and physics-based. At the microlevel, there are three potential damages and failures: fiber breakage, matrix cracking, and interface debonding. Different damage or failure criteria can be applied to those three different damage modes. Microlevel (fibers and matrix) Mesolevel (fibrous composite) Macrolevel (composite structure) Fibrous Module Finite Element Analysis Finite Element Analysis Fibrous Module Stiffness Loop Stress Loop Macrolevel (laminated composite) Lamination Module Lamination Module Chapter 4: Multiscale and Multilevel Modeling of Composites 177