Roberto Ballarini

Structural basis for the fracture toughness of the shell of the conch Strombus gigas

Natural composite materials are renowned for their mechanical strength and toughness: despite being highly mineralized, with the organic component constituting not more than a few per cent of the composite material, the fracture toughness exceeds that of single crystals of the pure mineral by two to three orders of magnitude. The judicious placement of the organic matrix, relative to the mineral phase, and the hierarchical structural architecture extending over several distinct length scales both play crucial roles in the mechanical response of natural composites to external loads. Here we use transmission electron microscopy studies and beam bending experiments to show that the resistance of the shell of the conch Strombus gigas to catastrophic fracture can be understood quantitatively by invoking two energy-dissipating mechanisms: multiple microcracking in the outer layers at low mechanical loads, and crack bridging in the shells tougher middle layers at higher loads. Both mechanisms are intimately associated with the so-called crossed lamellar microarchitecture of the shell, which provides for ‘channel’ cracking in the outer layers and uncracked structural features that bridge crack surfaces, thereby significantly increasing the work of fracture, and hence the toughness, of the material. Despite a high mineral content of about 99% (by volume) of aragonite, the shell of Strombus gigas can thus be considered a ‘ceramic plywood’, and can guide the biomimetic design of tough, lightweight structures.

Nano measurements with micro-devices: mechanical properties of hydrated collagen fibrils

The mechanical response of a biological material to applied forces reflects deformation mechanisms occurring within a hierarchical architecture extending over several distinct length scales. Characterizing and in turn predicting the behaviour of such a material requires an understanding of the mechanical properties of the substructures within the hierarchy, the interaction between the substructures, and the relative influence of each substructure on the overall behaviour. While significant progress has been made in mechanical testing of micrometre to millimetre sized biological specimens, quantitative reproducible experimental techniques for making mechanical measurements on specimens with characteristic dimensions in the smaller range of 10–1000 nm are lacking. Filling this void in experimentation is a necessary step towards the development of realistic multiscale computational models useful to predict and mitigate the risk of bone fracture, design improved synthetic replacements for bones, tendons and ligaments, and engineer bioinspired efficient and environmentally friendly structures. Here, we describe a microelectromechanical systems device for directly measuring the tensile strength, stiffness and fatigue behaviour of nanoscale fibres. We used the device to obtain the first stress–strain curve of an isolated collagen fibril producing the modulus and some fatigue properties of this soft nanofibril.

Stress-strain experiments on individual collagen fibrils.

Collagen, a molecule consisting of three braided protein helices, is the primary building block of many biological tissues including bone, tendon, cartilage, and skin. Staggered arrays of collagen molecules form fibrils, which arrange into higher-ordered structures such as fibers and fascicles. Because collagen plays a crucial role in determining the mechanical properties of these tissues, significant theoretical research is directed toward developing models of the stiffness, strength, and toughness of collagen molecules and fibrils. Experimental data to guide the development of these models, however, are sparse and limited to small strain response. Using a microelectromechanical systems platform to test partially hydrated collagen fibrils under uniaxial tension, we obtained quantitative, reproducible mechanical measurements of the stress-strain curve of type I collagen fibrils, with diameters ranging from 150-470 nm. The fibrils showed a small strain (epsilon < 0.09) modulus of 0.86 +/- 0.45 GPa. Fibrils tested to strains as high as 100% demonstrated strain softening (sigma(yield) = 0.22 +/- 0.14 GPa; epsilon(yield) = 0.21 +/- 0.13) and strain hardening, time-dependent recoverable residual strain, dehydration-induced embrittlement, and susceptibility to cyclic fatigue. The results suggest that the stress-strain behavior of collagen fibrils is dictated by global characteristic dimensions as well as internal structure.

Electrostatically actuated failure of microfabricated polysilicon fracture mechanics specimens

Polysilicon fracture mechanics specimens have been fabricated using standard microelectromechanical systems (MEMS) processing techniques, and thus have characteristic dimensions comparable with typical MEMS devices. These specimens are fully integrated with simultaneously fabricated electrostatic actuators which are capable of providing sufficient force to ensure catastrophic crack propagation from blunt notches produced using micromachining. Thus, the entire fracture experiment takes place on–chip, without any external loading source. Fracture has been initiated using both monotonic and cyclic resonance loading. A reduction in the nominal toughness under cyclic loading is attributed to subcritical growth of sharp cracks from the micromachined notches in the fracture mechanics specimens. Fatigue fracture has been observed in specimens subjected to as many as 109 cycles, and environmental corrosion is implicated in at least some aspects of the fatigue.

Fracture toughness of polysilicon MEMS devices

Abstract Polysilicon fracture mechanics specimens have been fabricated using standard microelectro-mechanical systems (MEMS) processing techniques, with characteristic dimensions comparable to typical MEMS devices. These specimens are fully integrated with simultaneously fabricated electrostatic actuators that are capable of providing sufficient force to ensure catastrophic crack propagation. Thus, the entire fracture experiment takes place on-chip, eliminating the difficulties associated with attaching the specimen to an external loading source. The specimens incorporate atomically sharp cracks created by indentation, and fracture is initiated using monotonic electrostatic loading. The fracture toughness values are determined using finite element analysis (FEA) of the experimental data, and show a median value of 1.1 MPa m 1/2 .

The Fracture Toughness of Polysilicon Microdevices: A First Report

Polysilicon microfracture specimens were fabricated using surface micromachining techniques identical to those used to fabricate microelectromechanical systems (M devices. The nominal critical J-integral (the critical energy release rate) for crack initiation, Jc, was determined in specimens whose characteristic dimensions were o the same order of magnitude as the grain size of the polysilicon. Jc values ranged from 16 to 62 Nym, approximately a factor of four larger than Jc values reported for single crystal silicon.

Monte Carlo simulation of effective elastic constants of polycrystalline thin films

A Monte Carlo finite element model is developed for predicting the scatter in the nominal elastic constants of a thin film aggregate of cubic crystals. Universal results for the nominal plane strain Youngs modulus and Poissons ratio are presented as functions of the number of grains within a unit volume, and two parameters that quantify the level of the crystalline anisotropy. The predictions are compared with formulae that are derived for plane strain Voigt and Reuss bounds.

Effect of Rim Thickness on Gear Crack Propagation Path.

Abstract : Analytical and experimental studies were performed to investigate the effect of rim thickness on gear tooth crack propagation. The goal was to determine whether cracks grew through gear teeth or through gear rims for various rim thicknesses. A finite element based computer program (FRANC, FRacture ANalysis Code) simulated gear tooth crack propagation. The analysis used principles of linear elastic fracture mechanics. Quarter-point, triangular elements were used at the crack tip to represent the stress singularity. The program had an automated crack propagation option in which cracks were grown numerically using an automated re-meshing scheme. Crack tip stress intensity factors were estimated to determine crack propagation direction. Gears with various backup ratios (rim thickness divided by tooth height) were tested to validate crack path predictions. Gear bending fatigue tests were performed in a spur gear fatigue rig. From both predictions and tests, gears with backnp ratios of 3.3 and 1.0 produced tooth fractures while a backup ratio of 0.3 produced rim fractures. For a backup ratio of 0.5, the experiments produced rim fractures and the predictions produced both rim and tooth fractures, depending on the initial geometry of the crack.

Crack growth in cement-based composites

Abstract A model that can be used to predict Mode I crack growth in cement-based composites is presented. The region ahead of a crack tip, where nonlinear deformations and aggregate interlock occur, is modeled as an extension of the actual stress-free crack subjected to a closing pressure that depends on the crack face displacements. In the case of concrete, crack propagation is assumed to occur when the crack opening displacement at the tip of the actual crack reaches a critical value. To predict results, the elastostatics problem of a layer containing a vertical edge crack was solved using a Greens function approach together with integral transform techniques. Stress intensity factors and crack opening displacements were obtained by numerically solving a singular integral equation. The closing pressure function and critical crack tip opening displacement were taken from experimental data for various materials, and the model was applied to the analysis of experiments performed on initially notched concrete and fiber-reinforced mortar beams.

Fracture mechanisms of the Strombus gigas conch shell: implications for the design of brittle laminates

Flexural strength, crack-density evolution, work of fracture, and critical strain energy release rates were measured for wet and dry specimens of the Strombus gigas conch shell. This shell has a crossed-lamellar microarchitecture, which is layered at five distinct length scales and can be considered a form of ceramic “plywood”. The shell has a particularly high ceramic (mineral) content (99.9 wt%), yet achieves unusually good mechanical performance. Even though the strengths are modest (of the order 100 MPa), the laminated structure has a large strain to fracture, and a correspondingly large work of fracture, up to 13 kJ m−2. The large fracture resistance is correlated to the extensive microcracking that occurs along the numerous interfaces within the shell microstructure. Implications of this impressive work of fracture for design of brittle laminates are considered.