Pablo D. Zavattieri

A grain level model for the study of failure initiation and evolution in polycrystalline brittle materials. Part I: Theory and numerical implementation

Abstract A model is presented to analyze material microstructures subjected to quasi-static and dynamic loading. A representative volume element (RVE) composed of a set of grains is analyzed with special consideration to the size distribution, morphology, chemical phases, and presence and location of initial defects. Stochastic effects are considered in relation to grain boundary strength and toughness. Thermo-mechanical coupling is included in the model so that the evolution of stress induced microcracking, from the material fabrication stage, can be captured. Intergranular cracking is modeled by means of interface cohesive laws motivated by the physics of breaking of atomic bonds or grain boundary sliding by atomic diffusion. Several cohesive laws are presented and their advantages in numerical simulations are discussed. In particular, cohesive laws simulating grain boundary cracking and sliding, or shearing, are proposed. The equations governing the problem, as well as their computer implementation, are presented with special emphasis on selection of cohesive law parameters and time step used in the integration procedure. This feature is very important to avoid spurious effects, such as the addition of artificial flexibility in the computational cell. We illustrate this feature through simulations of alumina microstructures reported in part II of this work. A technique for quantifying microcrack density, which can be used in the formulation of continuum micromechanical models, is addressed in this analysis. The density is assessed spatially and temporally to account for damage anisotropy and evolution. Although this feature has not been fully exploited yet, with the continuous development of cheaper and more powerful parallel computers, the model is expected to be particularly relevant to those interested in developing new heterogeneous materials and their constitutive modeling. Stochastic effects and other material design variables, although difficult and expensive to obtain experimentally, will be easily assessed numerically by Monte Carlo grain level simulations. In particular, extension to three-dimensional simulations of RVEs will become feasible.

The stomatopod dactyl club: a formidable damage-tolerant biological hammer.

Hammering Home the Lesson Stomatopods are marine crustaceans that use hammerlike claws for defense and to attack their prey. The claws undergo repeated high-velocity and high-force impacts. Weaver et al. (p. 1275; see the Perspective by Tanner) used a variety of techniques to examine the structure, mechanical behavior, and toughening mechanisms of the claw of the Peacock Mantis shrimp. The claws composite structure is optimized for toughness, which helps to prevent the complete failure that might arise from the claws repetitive hammering. The structure of mantis clubs is optimized to prevent complete failure caused by repetitive impacts. Nature has evolved efficient strategies to synthesize complex mineralized structures that exhibit exceptional damage tolerance. One such example is found in the hypermineralized hammer-like dactyl clubs of the stomatopods, a group of highly aggressive marine crustaceans. The dactyl clubs from one species, Odontodactylus scyllarus, exhibit an impressive set of characteristics adapted for surviving high-velocity impacts on the heavily mineralized prey on which they feed. Consisting of a multiphase composite of oriented crystalline hydroxyapatite and amorphous calcium phosphate and carbonate, in conjunction with a highly expanded helicoidal organization of the fibrillar chitinous organic matrix, these structures display several effective lines of defense against catastrophic failure during repetitive high-energy loading events.

Tablet-level origin of toughening in abalone shells and translation to synthetic composite materials

Nacre, the iridescent material in seashells, is one of many natural materials employing hierarchical structures to achieve high strength and toughness from relatively weak constituents. Incorporating these structures into composites is appealing as conventional engineering materials often sacrifice strength to improve toughness. Researchers hypothesize that nacres toughness originates within its brick-and-mortar-like microstructure. Under loading, bricks slide relative to each other, propagating inelastic deformation over millimeter length scales. This leads to orders-of-magnitude increase in toughness. Here, we use in situ atomic force microscopy fracture experiments and digital image correlation to quantitatively prove that brick morphology (waviness) leads to transverse dilation and subsequent interfacial hardening during sliding, a previously hypothesized dominant toughening mechanism in nacre. By replicating this mechanism in a scaled-up model synthetic material, we find that it indeed leads to major improvements in energy dissipation. Ultimately, lessons from this investigation may be key to realizing the immense potential of widely pursued nanocomposites.

Grain level analysis of crack initiation and propagation in brittle materials

A study on the accuracy of cohesive models for capturing dynamic fragmentation of ceramic microstructures is presented. The investigation consists of a combined experimental/numerical approach in which microcracking and damage kinetics are examined by means of plate impact recovery experiments. The numerical analysis is based on a 2-D micromechanical stochastic finite element analysis. The model incorporates a cohesive law to capture microcrack initiation, propagation and coalescence, as well as crack interaction and branching, as a natural outcome of the calculated material response. The stochasticity of the microfracture process is modeled by introducing a Weibull distribution of interfacial strength at grain boundaries. This model accounts for randomness in grain orientation, and the existence of chemical impurities and glassy phase at grain boundaries. Representative volume elements (RVE) of ceramic microstructure with different grain size and shape distributions are considered to account for features observed in real microstructures. Normal plate impact velocity histories are used not only to identify model parameters, but also to determine under what conditions the model captures failure mechanisms experimentally observed. The analyses show that in order to capture damage kinetics a particular distribution of grain boundary strength and detailed modeling of grain morphology are required. Simulated microcrack patterns and velocity histories have been found to be in a good agreement with the experimental observations only when the right grain morphology and model parameters are chosen. It has been found that the addition of rate effects to the cohesive model results in microcrack diffusion not observed experimentally.

A finite deformation continuum\discrete model for the description of fragmentation and damage in brittle materials

Abstract A dynamic finite element analysis of large displacements, high strain rate deformation behavior of brittle materials is presented in total Lagrangian coordinates. A continuum\discrete damage model capable of capturing fragmentation at two size scales is derived by combining a continuum damage model and a discrete damage model for brittle failure. It is assumed that size and distribution of potential fragments are known a priori, through either experimental findings or materials properties, and that macrocracks can nucleate and propagate along the boundaries of these potential fragments. The finite deformation continuum multiple-plane microcracking damage model accounts for microcracks within fragments. Interface elements, with cohesive strength and reversible unloading before debonding, between potential fragments describe the initiation of macrocracks, their propagation, and coalescence leading to the formation of discrete fragments. A surface-defined multibody contact algorithm with velocity dependent friction is used to describe the interaction between fragments and large relative sliding between them. The finite element equations of motion are integrated explicitly using a variable time step. Outputs are taken at discrete time intervals to study material failure in detail. The continuum\discrete damage model and the discrete fragmentation model, employing interface elements alone, are used to simulate a ceramic rod on rod impact. Stress wave attenuation, fragmentation pattern, and overall failure behavior, obtained from the analyses using the two models, are compared with the experimental results and photographs of the failing rod. The results show that the continuum\discrete model captures the stress attenuation and rod pulverization in agreement with the experimental observations while the pure discrete model underpredicts stress attenuation when the same potential fragment size is utilized. Further analyses are carried out to study the effect of potential fragment size and friction between sliding fragments. It is found that compared with the continuum\discrete damage model, the discrete fragmentation model is more sensitive to the multi-body discretization.

A grain level model for the study of failure initiation and evolution in polycrystalline brittle materials. Part II: Numerical examples

Abstract Numerical aspects of the grain level micromechanical model presented in part I are discussed in this study. They include, an examination of solution convergence in the context of cohesive elements used as an approach to model crack initiation and propagation; performance of parametric studies to assess the role of grain boundary strength and toughness, and their stochasticity, on damage initiation and evolution. Simulations of wave propagation experiments, performed on alumina, are used to illustrate the capabilities of the model in the framework of experimental measurements. The solution convergence studies show that when the length of the cohesive elements is smaller than the cohesive zone size and when the initial slope of the traction-separation cohesive law is properly chosen, the predictions concerning microcrack initiation and evolution are mesh independent. Other features examined in the simulations were the effect of initial stresses and defects resulting from the material manufacturing process. Also described are conditions on the selection of the representative volume element size, as a function of ceramic properties, to capture the proper distance between crack initiation sites. Crack branching is predicted in the case of strong ceramics and sufficient distance between nucleation sites. Rate effects in the extension of microcracks were studied in the context of damage kinetics and fragmentation patterns. The simulations show that crack speed can be significantly varied in the presence of rate effects and as a result crack diffusion by nucleation of multiple sites achieved. This paper illustrates the utilization of grain level models to predict material constitutive behavior in the presence, or absence, of initial defects resulting from material manufacturing. Likewise, these models can be employed in the design of novel heterogeneous materials with hierarchical microstructures, multi-phases and/or layers.

A computational model of ceramic microstructures subjected to multi-axial dynamic loading

A model is presented for the dynamic finite element analysis of ceramic microstructures subjected to multi-axial dynamic loading. This model solves an initial-boundary value problem using a multi-body contact model integrated with interface elements to simulate microcracking at grain boundaries and subsequent large sliding, opening and closing of microcracks. An explicit time integration scheme is adopted to integrate the system of spatially discretized ordinary differential equations. A systematic and parametric study of the effect of interface element parameters, grain anisotropy, stochastic distribution of interface properties, grain size and grain morphology is carried out. Numerical results are shown in terms of microcrack patterns and evolution of crack density, i.e., damage kinetics. The brittle behavior of the microstructure as the interfacial strength decreases is investigated. Crack patterns on the representative volume element vary from grains totally detached from each other to a few short cracks, nucleated at voids, except, for the case of microstructures with initial flaws. Grain elastic anisotropy seems to play an important role in microfracture presenting higher values of crack density than the isotropic case. The computational results also show that decreasing the grain size results in a decrease in crack density per unit area at equal multiaxial dynamic loading. Histograms of crack density distribution are presented for the study of the stochasticity of interface parameters. Finally, a strong dependency with grain shape is observed for different microstructures generated using Voronoi Tessellation. The micromechanical model here discussed allows the study of material pulverization upon unloading. The qualitative and quantitative results presented in this article are useful in developing more refined continuum theories on fracture properties of ceramics.

Bio-inspired impact-resistant composites

Through evolutionary processes, biological composites have been optimized to fulfil specific functions. This optimization is exemplified in the mineralized dactyl club of the smashing predator stomatopod (specifically, Odontodactylus scyllarus). This crustaceans club has been designed to withstand the thousands of high-velocity blows that it delivers to its prey. The endocuticle of this multiregional structure is characterized by a helicoidal arrangement of mineralized fiber layers, an architecture which results in impact resistance and energy absorbance. Here, we apply the helicoidal design strategy observed in the stomatopod club to the fabrication of high-performance carbon fiber-epoxy composites. Through experimental and computational methods, a helicoidal architecture is shown to reduce through-thickness damage propagation in a composite panel during an impact event and result in an increase in toughness. These findings have implications in the design of composite parts for aerospace, automotive and armor applications.

OPTIMIZATION STRATEGIES IN UNSTRUCTURED MESH GENERATION

SUMMARY We propose a new optimization strategy for unstructured meshes that, when coupled with existing automatic generators, produces meshes of high quality for arbitrary domains in 3-D. Our optimizer is based upon a non-differentiable definition of the quality of the mesh which is natural for finite element or finite volume users: the quality of the worst element in the mesh. The dimension of the optimization space is made tractable by restricting, at each iteration, to a suitable neighbourhood of the worst element. Both geometrical (node repositioning) and topological (reconnection) operations are performed. It turns out that the repositioning method is advantageous with respect to both the usual node-by-node techniques and the more recent differentiable optimization methods. Several examples are included that illustrate the efficiency of the optimizer.

Three-dimensional digital image correlation to quantify deformation and crack-opening displacement in ductile aluminum under mixed-mode I/III loading

Fractures in ductile thin-sheet structures, such as a fuselage or automobile panels, often occur under complex loading conditions. In particular, under remote mixed-mode I/III loading conditions, a cracked structure is subjected to a combination of in-plane tension and large out-of-plane tearing deformation, which may lead to crack tip fields consisting of all three fracture modes (modes I, II, and III). Understanding such fracture events in ductile materials is an important component of the structural integrity analysis of load-bearing structures containing ductile, thin sheets. Due to the complex nature of mixed-mode I/III fracture in ductile thin-sheet materials, reports of experimental investigations are very limited in the literature. We configure three-dimensional digital image correlation (3D-DIC) systems to acquire full-field deformations during the loading and stable tearing processes. The full-field deformation measurements are used to characterize the stable crack extension behavior of an aluminum alloy undergoing quasistatic and dynamic mixed-mode I/III loading. Results confirm that 3D-DIC is an excellent methodology for measuring 3-D deformations in the presence of large out-of-plane warping and motion, both dynamically and statically. Data obtained during the fracture process indicate that the introduction of a mode III component into the loading process alters the crack tip displacement and strain fields relative to those measured in the nominally mode I loading. Furthermore, the measured crack-opening displacement (COD) values during quasistatic and impact mixed-mode I/III fracture show that (1) COD is nearly constant for crack extension beyond 2 mm and (2) COD under combined-mode I/III loading is four times larger than observed during mixed-mode I/II or mode I fracture of the same material, indicating that the magnitude of the critical COD is a function of loading mode in highly ductile, thin-sheet materials.