Research Paper
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−  ==  +  The objective of this research is to study the influence of morphology on fracture and debonding of silicon particles embedded in an Al1%Si matrix. The fracture and deboning is caused by applied tensile and compressive cyclic loading conditions. Finite element method is used to study these effects to accurately represent particle geometry, particle interactions, and the stressstrain behavior of the aluminum matrix. A cluster of 4 to 8 silicon particle inclusion is chosen for the study over infinite array of inclusion or single isolated inclusion. Silicon particles are modeled with linear elastic constitutive relationship and matrix material using internal state variable cyclic plasticity model. A two level design of experiments method is used to test 16 sets of combination made with 7 variables; relative particle size, shape, spacing, configuration, alignment, grouping and matrix microporosity. Results of the study demonstrates the dominance of shape and alignment during initial phases fracturing and debonding and spacing during later phases. Local intensification of stresses in induced by particle debonding in Al1%Si matrix. This intensification of stresses is higher than that of particle fracture. Enhancement is spacing due to consecutive fracturing in the cluster becomes a dominant factor due to large local intensification of stresses as mentioned above. 
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+  animation=  
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+  images=  
+  {{paper_figureimage=image 1.pngimage caption= Fig. 1. Schematic demonstrating the different parameters considered in the present finite element study. The parameter ranges were determined by examining actual micrographs of a modified cast A356 aluminum alloy}}  
+  
+  {{paper_figureimage=Image 2.pngimage caption=Figure 2. This is a plot of the accessibility of each grain boundary structure for an asymmetric tilt grain boundary. For complex boundaries, a large number of boundaries may need to be sampled to find the "global" minimum energy boundary.}}  
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+  methodology= Two level design of experiments (DOE) method is used to study the effects of seven parameters at their chosen range of conditions is shown in Fig.1. A total of 16 significant combinations of the 7 morphological parameters at their extreme conditions are chosen for the study, shown in the following Table 1. The extremes for these parameters are based on micrographical observations from an A365 aluminum alloy study which constitutes silicon particles. Finite element cases were created for all 16 combinations with following assumptions;  
+  # Traces of other element are not considered in the model though that are generally present in the alloy to promote hardening and other casting properties.  
+  # The silicon particles are assumed to behave in an isotropic linear elastic. The Al matrix material is described using an internal state variable plasticity model with coupled micro void growth.  
+  # Temperature and strain rate dependence on the plasticity of the model were not considered. Experimental data regression is thoroughly used to generate constants for the model  
+  In Fig 2, stressstrain model output is compared to experimental output for cycles 1, 2, and 10. A point of saturation is attained at the end of 10 cycles in both cases. Maximum tensile principal stress is an important study parameter which is the proposed cause of fracture in Si particles. Debonding is studied on the basis of hydrostatic stresses on particle matrix interface. The screening of the two significant parameters is listed under table 2.  
+  
+  material model=  
+  {{Template:LAMMPS}}  
+  
+  
+  input deck= See [[LAMMPS Input Deck for Grain boundary generation]]  
+  
+  
+  results=  
+  <table width="100%" cellspacing="3" cellpadding="5">  
+  <tr>  
+  <td colspan="2">This methodology has resulted in structures that agree with HRTEM images and grain boundary energies that agree with experimentallymeasured grain boundary energies. Figure 3 shows an example plot of the grain boundary energy versus inclination angle for a complex grain boundaries in Cu (Sigma 3 asymmetric grain boundaries). This system of boundaries displays a phase transformation at the boundary to the orthorhombic 9R phase for inclination angles of 7090 degrees. The methodology used above agrees nicely with experimental results and previous atomistic calculations of Wolf and coworkers.  
+  </td>  
+  </tr>  
+  <tr>  
+  <td align="center">  
+  <table>  
+  <tr>  
+  <td> [[Image:Al_100STGBs.gifthumb300px Al <100> symmetric tilt grain boundaries.]]</td>  
+  <td> [[Image:Al_110STGBs.gifthumb300px Al <110> symmetric tilt grain boundaries.]]</td>  
+  </tr><tr>  
+  <td> [[Image:Cu_001STGBs.gifthumb300px Cu <100> symmetric tilt grain boundaries.]]</td>  
+  <td> [[Image:Cu_110STGBs.gifthumb300px Cu <110> symmetric tilt grain boundaries.]]</td>  
+  </tr>  
+  </table>  
+  </td>  
+  <td valign="top">  
+  [[image:plot_gb_energy.jpgthumb400pxFigure 3. Plot of the grain boundary energy as a function of inclination angle for asymmetric tilt grain boundaries in Cu.]]  
+  </td>  
+  </tr>  
+  </table>  
+  
+  
+  
+  
+  acknowledgement=M.A. Tschopp would like to acknowledge funding provided under an NSF graduate fellowship for the initial work. Continued funding for investigating structureproperty relationships in grain boundaries under the NEAMS (Nuclear Energy Advanced Modeling and Simulation) program is also acknowledged.  
+  
+  references= The initial methodology was used in the following papers:  
+  }}  
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[[Category: Research Paper]]  [[Category: Research Paper]] 
Revision as of 14:47, 5 May 2015
AbstractThe objective of this research is to study the influence of morphology on fracture and debonding of silicon particles embedded in an Al1%Si matrix. The fracture and deboning is caused by applied tensile and compressive cyclic loading conditions. Finite element method is used to study these effects to accurately represent particle geometry, particle interactions, and the stressstrain behavior of the aluminum matrix. A cluster of 4 to 8 silicon particle inclusion is chosen for the study over infinite array of inclusion or single isolated inclusion. Silicon particles are modeled with linear elastic constitutive relationship and matrix material using internal state variable cyclic plasticity model. A two level design of experiments method is used to test 16 sets of combination made with 7 variables; relative particle size, shape, spacing, configuration, alignment, grouping and matrix microporosity. Results of the study demonstrates the dominance of shape and alignment during initial phases fracturing and debonding and spacing during later phases. Local intensification of stresses in induced by particle debonding in Al1%Si matrix. This intensification of stresses is higher than that of particle fracture. Enhancement is spacing due to consecutive fracturing in the cluster becomes a dominant factor due to large local intensification of stresses as mentioned above. Author(s): {{{authors}}} 


MethodologyTwo level design of experiments (DOE) method is used to study the effects of seven parameters at their chosen range of conditions is shown in Fig.1. A total of 16 significant combinations of the 7 morphological parameters at their extreme conditions are chosen for the study, shown in the following Table 1. The extremes for these parameters are based on micrographical observations from an A365 aluminum alloy study which constitutes silicon particles. Finite element cases were created for all 16 combinations with following assumptions;
In Fig 2, stressstrain model output is compared to experimental output for cycles 1, 2, and 10. A point of saturation is attained at the end of 10 cycles in both cases. Maximum tensile principal stress is an important study parameter which is the proposed cause of fracture in Si particles. Debonding is studied on the basis of hydrostatic stresses on particle matrix interface. The screening of the two significant parameters is listed under table 2.  
Material ModelLargescale Atomic/Molecular Massively Parallel Simulator (LAMMPS) 

Input Data 

Results


AcknowledgmentsM.A. Tschopp would like to acknowledge funding provided under an NSF graduate fellowship for the initial work. Continued funding for investigating structureproperty relationships in grain boundaries under the NEAMS (Nuclear Energy Advanced Modeling and Simulation) program is also acknowledged.  
ReferencesThe initial methodology was used in the following papers: 