Chambart, Marion Estelle

Kok, Piet

Molinari, Jean-François

Richart, Nicolas

Taheri Mousavi, Seyedeh Mohadeseh

Infoscience - École polytechnique fédérale de Lausanne

Revealing microstructural parameters influencing strength and toughnessof silicon nitrideSeyedeh Mohadeseh Taheri Mousavi†∗, Jean-Francois Molinari†, Marion Chambart†, NicolasRichart†, Piet Kok‡† LSMS, ENAC, E´cole Polytechnique Fe´de´rale de Lausanne, Lausanne, SwitzerlandMohadeseh.taherimousavi@epfl.ch, Jean-francois.molinari@epfl.chMarion.chambart@epfl.ch, Nicolas.richart@epfl.ch‡Automotive applications, Tata steel, NetherlandsPiet.kok@tatasteel.comKeywords: Silicon nitride, dynamic loading, finite element modeling, cohesive element.ABSTRACTDiscovering microstructural features which influence macroscopic properties has appealed to manyresearchers. In many materials (including silicon nitride), a slight change in microscopic propertiescan bring a huge difference in their macro-scale behavior, increasing the number of potential industrialapplications. Materials scientists are able to monitor the grain size, the amount of porosity and of secondphase material within silicon nitride, which alters the macro-scale toughness and strength. There isa strong interest in developing robust numerical methods for simulating damage mechanisms in thismaterial. In this paper, we study the influence of needle-shaped grains, which are found in siliconnitride, on mechanical strength and toughness. This calls for addressing the numerical challenge ofcapturing both its intergranular and transgranular cracking, a topic which has been overlooked in theliterature [3].We present a two-dimensional finite-element framework for modeling silicon nitride at the microscale.The microstructure is constructed using a Voronoi tessellation, in which a clustering technique wasused to append a given needle-shaped grains density. The cohesive element framework developed byDugdale [2] is utilized for considering fracture within the microstructure. We resort to the cohesivelaw proposed by Camacho [1] for modeling crack opening, whereas the bulk behavior is considered asisotropic and elastic. As in the hexagonal structure of Si3N4 grains, cleavage planes have an angle of60 degrees with one another [4], we generated a discretization which was aligned with those randomlyoriented planes (see figure 1), all the while keeping a sufficient mesh quality.Figure 1: Silicon nitride microstructure whose elements are aligned with cleavage planes 0 5 10 15 20 25 30 35 40 45 0  0.5  1  1.5  2  2.5Average stress (MPa) Time(ns)Strain rate = 5*10^5/s10000 elements20000 elements30000 elementsFigure 2: Studying the mesh convergence of our approachConsequently, the discretization which consists of equilateral elements could be utilized to denote thecrystal structure of the grains. This original approach for transgranular cracking does not require (acomputationally intensive) remeshing procedure and data transferring for aligning the elements withcleavage planes. This allows the study of much larger microstructures than was done in [3]. It alsoshould be mentioned that the number of cracks inside a grain is not limited. The cohesive properties forintergranular and transgranular cracking were gathered in the literature and given some randomness tocapture the microstructural diversity in grain boundaries and material defects.We first present results concerning mesh dependency. Consequently, we chose a microstructure withthree different discretizations, but under the same loading conditions (strain rate= tensile, ...). As it isshown in figure 2, the same strength was obtained for all three microstructures. Moreover, the finalamounts of dissipated energy have a satisfactory agreement, although we do not expect an exact matchdue to the randomness in fracture parameters. Several physical parametric studies were performed. Inparticular, the calculations reveal a strong rate dependence in the presence of needle shapes. Increasingthe strain rate yields higher dissipated energy and higher strength. We observe as well that it increasesthe percentage of trans-granular fracture (which in conjunction to a broader crack network, is one ofthe reasons for the observed strain rate hardening). In another parametric study, the microstructure wasvaried. We show that when needle grains are more numerous and coarser, the specimen’s toughnessincreases. A detailed examination of the crack paths reveals that needles cause more deflections, whichincreases the material’s resistance to crack propagation, but also increases the probability of trans-granular fracture.References[1] G.T. Camacho and M. Ortiz. Computational modeling of impact damage in brittle materials. Solidand Structures, 33:2899–2938, 1996.[2] D.S. Dugdale. Yielding in steel sheets containing slits. Mechanics and Physics of Solids, 8:100–104, 1960.[3] R.H. Kraft and J.F. Molinari. A statistical investigation of the effects of grain boundary propertieson transgranular fracture. Acta Materialia, 56(17):4739–4749, 2008.[4] F.L. Riley. Silicon nitride and related materials. American Ceramic Society, 83(2):245–265, 2000.

Revealing microstructural parameters influencing strength and toughness of silicon nitride

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Revealing microstructural parameters influencing strength and toughness of silicon nitride

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