In this project, we demonstrated stable nanoscale fracture in single-crystal silicon using an in-situ wedge-loaded double cantilever beam (DCB) specimen. The fracture toughness KIC was calculated directly from instrumented measurement of force and displacement via finite element analysis with frictional corrections. Measurements on multiple test specimens were used to show KIC = 0.72 ± 0.07 MPa m1/2 on {111} planes and observe the crack-growth resistance curve in <500 nm increments. The exquisite stability of crack growth, instrumented measurement of material response, and direct visual access to observe nanoscale fracture processes in an ideally brittle material differentiate this approach from prior DCB methods.
Brittle material failure in high consequence systems can appear random and unpredictable at subcritical stresses. Gaps in our understanding of how structural flaws and environmental factors (humidity, temperature) impact fracture propagation need to be addressed to circumvent this issue. A combined experimental and computational approach composed of molecular dynamics (MD) simulations, numerical modeling, and atomic force microscopy (AFM) has been undertaken to identify mechanisms of slow crack growth in silicate glasses. AFM characterization of crack growth as slow as 10-13 m/s was observed, with some stepwise crack growth. MD simulations have identified the critical role of inelastic relaxation in crack propagation, including evolution of the structure during relaxation. A numerical model for the existence of a stress intensity threshold, a stress intensity below which a fracture will not propagate, was developed. This transferrable model for predicting slow crack growth is being incorporated into mission-based programs.
We report analytical relations for the mechanical response of single polymer chains are valuable for modeling purposes, on both the molecular and the continuum scale. These relations can be obtained using statistical thermodynamics and an idealized single-chain model, such as the freely jointed chain model. To include bond stretching, the rigid links in the freely jointed chain model can be made extensible, but this almost always renders the model analytically intractable. Here, an asymptotically correct statistical thermodynamic theory is used to develop analytic approximations for the single-chain mechanical response of this model. The accuracy of these approximations is demonstrated using several link potential energy functions. This approach can be applied to other single-chain models, and to molecular stretching in general.
Background:: Subcritical crack growth can occur in a brittle material when the stress intensity factor is smaller than the fracture toughness if an oxidizing agent (such as water) is present at the crack tip. Objective:: We present a novel bi-material beam specimen which can measure environmentally assisted crack growth rates. The specimen is “self-loaded” by residual stress and requires no external loading. Methods:: Two materials with different coefficient of thermal expansion are diffusion bonded at high temperature. After cooling to room temperature a subcritical crack is driven by thermal residual stresses. A finite element model is used to design the specimen geometry in terms of material properties in order to achieve the desired crack tip driving force. Results:: The specimen is designed so that the crack driving force decreases as the crack extends, thus enabling the measurement of the crack velocity versus driving force relationship with a single test. The method is demonstrated by measuring slow crack growth data in soda lime silicate glass and validated by comparison to previously published data. Conclusions:: The self-loaded nature of the specimen makes it ideal for measuring the very low crack velocities needed to predict brittle failure at long lifetimes.
Fe-Co-2V is a soft ferromagnetic alloy used in electromagnetic applications due to excellent magnetic properties. However, the discontinuous yielding (Luders bands), grain-size-dependent properties (Hall-Petch behavior), and the degree of order/disorder in the Fe-Co-2V alloy makes it difficult to predict the mechanical performance, particularly in abnormal environments such as elevated strain rates and high/low temperatures. Thus, experimental characterization of the high strain rate properties of the Fe-Co-2V alloy is desired, which are used for material model development in numerical simulations. In this study, the high rate tensile response of Fe-Co-2V is investigated with a pulse-shaped Kolsky tension bar over a wide range of strain rates and temperatures. Effects of temperature and strain rate on yield stress, ultimate stress, and ductility are discussed.
Cylindrical dog-bone (or dumbbell) shaped samples have become a common design for dynamic tensile tests of ductile materials with a Kolsky tension bar. When a direct measurement of displacement between the bar ends is used to calculate the specimen strain, the actual strain in the specimen gage section is overestimated due to strain in the specimen shoulder and needs to be corrected. The currently available correction method works well for elastic-perfectly plastic materials but may not be applicable to materials that exhibit significant work-hardening behavior. In this study, we developed a new specimen strain correction method for materials possessing an elastic-plastic with linear work-hardening stress–strain response. A Kolsky tension bar test of a Fe-49Co-2V alloy (known by trade names Hiperco and Permendur) was used to demonstrate the new specimen strain correction method. This new correction method was also used to correct specimen strains in Kolsky tension bar experiments on two other materials: 4140 alloy, and 304L-VAR stainless steel, which had different work-hardening behavior.
We demonstrate the ability to measure R-curves of brittle materials using a method adapted from Theo Fett et al. The method is validated with a NIST standard reference material and demonstrated using Si3N4 of two different microstructures; glass-ceramic, and PZT. As expected, each material's R-curve is seen to be sightly different with glass-ceramics showing the most pronounced R-curve effects. Plans for future applications and experimental efforts are discussed.
Stress intensity factors (SIFs) are used in continuum fracture mechanics to quantify the stress fields surrounding a crack in a homogeneous material in the linear elastic regime. Critical values of the SIFs define an intrinsic measure of the resistance of a material to propagate a crack. At atomic scales, however, fracture occurs as a series of atomic bonds breaking, differing from the continuum description. As a consequence, a formal analog of the continuum SIFs calculated from atomistic simulations can have spatially localized, microstructural contributions that originate from varying bond configurations. The ability to characterize fracture at the atomic scale in terms of the SIFs offers both an opportunity to probe the effects of chemistry, as well as how the addition of a microstructural component affects the accuracy. We present a novel numerical method to determine SIFs from molecular dynamics (MD) simulations. The accuracy of this approach is first examined for a simple model, and then applied to atomistic simulations of fracture in amorphous silica. MD simulations provide time and spatially dependent SIFs, with results that are shown to be in good agreement with experimental values for fracture toughness in silica glass.
Photoluminescent spectral peak positions are known to shift as a function of mechanical stress state. This has been demonstrated at macroscales to determine mean stress and mesoscales to determine mean stress and a quantity related to shear stress. Here, we propose a method to utilize traction-free surface conditions and knowledge of material orientation to solve for two in-plane displacement fields given two measured spectral peak positions measured at a grid of points. It is then possible to calculate the full stress tensor at each measurement point. This is a significant advancement over the previous ability to measure one or two stress quantities. We validate the proposed method using a simple, two-grain geometry and show that it produces the same mean stress and shear stress measure as the existing direct method. We also demonstrate determination of the full stress field in a polycrystalline alumina specimen.
Brittle failure is often influenced by difficult to measure and variable microstructure-scale stresses. Recent advances in photoluminescence spectroscopy (PLS), including improved confocal laser measurement and rapid spectroscopic data collection have established the potential to map stresses with microscale spatial resolution (< 2 μm). Advanced PLS was successfully used to investigate both residual and externally applied stresses in polycrystalline alumina at the microstructure scale. The measured average stresses matched those estimated from beam theory to within one standard deviation, validating the technique. Modeling the residual stresses within the microstructure produced qualitative agreement in comparison with the experimentally measured results. Microstructure scale modeling is primed to take advantage of advanced PLS to enable its refinement and validation, eventually enabling microstructure modeling to become a predictive tool for brittle materials.
Subcritical crack growth can occur in a glass when the stress intensity factor is less than the fracture toughness if water molecules are present. A novel bi-material beam specimen is proposed to investigate environmentally assisted crack growth (EACG). Two materials with different coefficients of thermal expansion are diffusion bonded at high temperature and cooled to the room temperature which introduces residual stress in the beam. A Finite element (FE) model is developed and initially validated with an analytical model. Steady-state crack (SSC) depth at which mode II stress intensity factor (KII) is zero and the corresponding mode I stress intensity factor (KI) value are obtained for different material pairs and thickness ratios of the top and bottom materials using the FE model. Crack propagation path is also predicted. We finally modify the geometry of the specimen to generate non-constant KI values as the crack propagates.
We have developed a novel specimen for studying crack paths in glass. Under certain conditions, the specimen reaches a state where the crack must select between multiple paths satisfying the KII = 0 condition. This path selection is a simple but challenging benchmark case for both analytical and numerical methods of predicting crack propagation. We document the development of the specimen, using an uncracked and instrumented test case to study the effect of adhesive choice and validate the accuracy of both a simple beam theory model and a finite element model. In addition, we present preliminary fracture test results and provide a comparison to the path predicted by two numerical methods (mesh restructuring and XFEM). The directional stability of the crack path and differences in kink angle predicted by various crack kinking criteria is analyzed with a finite element model.
Brittle failure is often influenced by difficult to measure and variable microstructure-scale stresses. Recent advances in photoluminescence spectroscopy (PLS), including improved confocal laser measurement and rapid spectroscopic data collection have established the potential to map stresses with microscale spatial resolution (%3C2 microns). Advanced PLS was successfully used to investigate both residual and externally applied stresses in polycrystalline alumina at the microstructure scale. The measured average stresses matched those estimated from beam theory to within one standard deviation, validating the technique. Modeling the residual stresses within the microstructure produced general agreement in comparison with the experimentally measured results. Microstructure scale modeling is primed to take advantage of advanced PLS to enable its refinement and validation, eventually enabling microstructure modeling to become a predictive tool for brittle materials.
We have developed a novel specimen for studying crack paths in glass. Under certain conditions, the specimen reaches a state where the crack must select between multiple paths satisfying the Kπ 0 condition. This path selection is a simple but difficult benchmark case for both analytical and numerical methods of predicting crack propagation. We document the development of the specimen, using an uncracked and instrumented test case to study the effect of adhesive choice and validate the accuracy of both a simple beam theory model and a finite element model. In addition, we present preliminary fracture test results and provide a comparison to the path predicted by two numerical methods (mesh restructuring and XFEM).
Previous experiments have shown a link between oxidation and strength changes in single crystal silicon nanostructures but provided no clues as to the mechanisms leading to this relationship. Using atomic force microscope-based fracture strength experiments, molecular dynamics modeling, and measurement of oxide development with angle resolved x-ray spectroscopy we study the evolution of strength of silicon (111) surfaces as they oxidize and with fully developed oxide layers. We find that strength drops with partial oxidation but recovers when a fully developed oxide is formed and that surfaces intentionally oxidized from the start maintain their high initial strengths. MD simulations show that strength decreases with the height of atomic layer steps on the surface. These results are corroborated by a completely separate line of testing using micro-scale, polysilicon devices, and the slack chain method in which strength recovers over a long period of exposure to the atmosphere. Combining our results with insights from prior experiments we conclude that previously described strength decrease is a result of oxidation induced roughening of an initially flat silicon (1 1 1) surface and that this effect is transient, a result consistent with the observation that surfaces flatten upon full oxidation.