Track I: Fracture, Damage, and Defect Mechanics
Symposium IA: The Theoretical, Experimental, and Computational Aspects of Fracture Mechanics
Wednesday July 26, 2017 – Session 1A – 10:15am to 12:15pm
Location: 440 Curry Student Center
Session Chair: Maurizio M. Chiaramonte, Princeton University
|10:15am||D. S. Kammer*||Invited: Simulation of Dynamic Shear Crack Propagation along weak Interfaces with Various Stress Distributions|
|Abstract: The propagation of shear cracks along weak interfaces is a long-standing problem of great importance to earthquake source mechanics and engineering (composite materials). Observed propagation speeds range from slow fronts  up to supershear velocities [1,2,3], which considerably affects wave radiation from the interface. In recent work, several stress-based criteria were used to predict the propagation speed for a given stress state . Generally, it was observed and predicted that higher shear stresses lead to faster cracks. However, none of these criteria could explain the wide spread of velocities observed for a given stress level. In this study, we analyze the propagation speed of slip fronts for various stress distributions using numerical simulations; and demonstrate that dynamic linear elastic fracture mechanics (LEFM) provides a unifying framework to predict the observed phenomena. The underlying principle is based on energetic considerations by comparing the released potential energy with the dissipated fracture energy. A large excess of potential energy results in faster cracks. LEFM provides a unique relationship and thus a quantitative prediction of crack propagation speed. It shows that any (admissible) propagation speed can be observed at a given point with a given stress state – it depends on the available energy and thus on the stress drop along the crack as well as the problem geometry. We compare our results to experimental observations . These findings give us fundamental insight into the governing mechanism of rupture propagation, which is essential for a beforehand estimation of wave radiation of an upcoming earthquake.|
|10:35am||G. Phlipot* | D. M. Kochmann||Fracture of Periodic Truss Lattices Investigated by a Quasicontinuum Technique|
|Abstract: Advances in fabrication techniques have enabled the creation of lattice metamaterials consisting of a sizeable number of truss members that have been shown to exhibit high strength and stiffness-to-weight ratios, among other desirable properties. While many properties of these materials are well understood, the response of truss lattices undergoing fracture has not been studied as thoroughly. This is partly due to the fact that fracture simulations require modeling a large number of truss members, which has limited most studies to two dimensions or linear elasticity. However, by using an extension of the quasicontinuum (QC) method, a multiscale modeling tool originally designed to significantly reduce the computational expense of atomic lattice simulations by coarse-graining and energy sampling techniques, the cost of truss lattice fracture simulations can be greatly reduced. We make use of a three-dimensional, high-performance, adaptive, fully nonlocal QC code to model fracture of multiple lattice topologies. Each lattice site in the simulation is equipped with rotational and translational degrees of freedom, and beam potentials are used as inter-lattice-site interactions. We predict the fracture toughness of two- and three-dimensional brittle lattice topologies by enforcing the continuum K-field displacements to the periphery of large, coarse-grained meshes with notches, and comparing the largest stress near the notch with the yield stress of the constituent material. We present results on how the fracture toughness of these lattice topologies varies with crack orientation, and with relative density. The effect of geometric and material nonlinearity on the fracture properties is also investigated by using corotational beam interactions and by introducing plasticity and failure of the constituent material.|
|10:55am||K. Alidoost* | M. Feng | P. H. Geubelle | D. A. Tortorelli||Energy Release Rate Approximation for Surface Cracks using Topological Derivatives|
|Abstract: Topological derivatives provide the variation of a functional when an infinitesimal hole is introduced into the domain. In a previous study, the authors developed a first-order approximation of the energy release rate associated with a small surface crack at any boundary location and at any orientation using a first-order topological derivative . This approach offers significant computational advantages over other methods because (i) it requires only a single analysis while other methods require an analysis for each combination of location and orientation, and (ii) it is performed on the non-cracked domain, removing the need to create very fine meshes in the vicinity of crack tips.
This initial study, however, was limited to small cracks in 2-D domains. In this work, a higher-order approximation of the energy release rate is developed using higher-order topological derivatives. In addition to the stress state present at the crack initiation point, this higher-order approximation incorporates the derivatives of the stress state computed on the uncracked domain in the expected direction of crack propagation. The derivatives of the stress state are computed using an asymptotic expansion for the tractions along the crack surface as the crack length approaches zero. Higher-order approximations allow the analyst to accurately treat longer cracks and determine for which crack lengths the first-order approximation is accurate.
In this presentation, we begin by reviewing the first-order approximation of the energy release rate. We then combine this first-order approximation with Abaqus FEA so that simply by supplying an ODB file the first-order approximation of the energy release rate is computed for a crack at any boundary location and at any orientation. In this way, we promptly identify the critical combinations of boundary locations and orientations that reach the critical energy release rate at the smallest crack lengths. Subsequently, we introduce the higher-order approximations of the energy release rate and the asymptotic expansion used to calculate them. We conclude by showing how these higher-order approximations (i) increase the accuracy of the approximation when treating long cracks, and (ii) are used to predict for what crack sizes the first-order approximation is accurate.
|11:15am||J. Fan* | R.Stewart | T. Xu||Crack-Tip Simulation Accuracy by XGP Multiscale Methods|
|Abstract: The success in using the GP, short for the generalized particle dynamics method (Fan, 2009), with cohesive zone method (CZM) to bridge crack propagation at the atomistic and mesoscopic scale (Eng. Fract. Mech, 155, 2016) brings more attention to its central issue: simulation accuracy verification of crack-tip behavior. This is fundamentally important in determining whether the analysis is significant or nonsense. Unfortunately, this kind of accuracy verification including the model size effect has been researched the least. This is mainly due to a lack of effective method to verify the accuracy of atomisticlly-based multiscale crack analysis, shortcomings of existing multiscale methods in developing large model with high accuracy and a lack of basic understanding and effective scheme to investigate and control the model size effects.
All these issues are addressed in this presentation with new concepts and new methods. Specifically, accuracy verification with the classical continuum solutions is developed after handling two types of data with one being continuous and the other is point-wise. The basic issue for improving the existing multiscale scheme is addressed by an extension of the GP method in which the model inner region consists of core atomistic region surrounded by several succeeding higher scales of particles. Since FE nodes are connected only with the outmost particles where the deformation gradient is smooth the extended GP can avoid artificial effects on the most interesting atomic regions. This is quite different from the quasicontinuum (QC) and other direct coupling methods which directly connect FE nodes with atoms. This new method are confirmed with analytical solutions of an edge-crack in a two dimensional plate. Its applications by using an asymptotic approach for model size effects show that there exists a problem-dependent critical model size, LCR, above which may not be necessary under a given error tolerance and below which the obtained traction-separation (TS) curve of cohesive fracture model may underestimate material resistance measured by the critical energy release rate, GIC, as well as overestimate the initial strain for BCC to FCC phase transformation near the crack-tip.
|11:35am||Z. Meng* | M. A. Bessa | W. Xia | W.K. Liu | S. Keten||Predicting the Macroscopic Fracture Energy of Epoxy Resins from Atomistic Molecular Simulations|
|Abstract: Predicting the macroscopic fracture energy of highly cross-linked glassy polymers from atomistic simulations is challenging due to the size of the process zone being large in these systems. Here, we present a scale-bridging approach that links atomistic molecular dynamics simulations to macroscopic fracture properties on the basis of a continuum fracture mechanics model for two different epoxy materials. Our approach reveals that the fracture energy of epoxy resins strongly depends on the functionality of epoxy resin and the component ratio between the curing agent (amine) and epoxide. The most intriguing part of our study is that we demonstrate that the fracture energy exhibits a maximum value within the range of conversion degrees considered (from 65% to 95%), which can be attributed to the combined effects of structural rigidity and post-yield deformability. Our study provides physical insight into the molecular mechanisms that govern the fracture characteristics of epoxy resins and demonstrates the success of utilizing atomistic molecular simulations toward predicting macroscopic material properties.|
|11:55am||Z. Liu* | M. Fleming | W. K. Liu||A Consistent Concurrent Framework for Multiscale Material Failure Based on Self-Consistent Clustering Analysis|
|Abstract: Accurate and efficient computational methods for predicting fracture and damage are essential to design and failure analysis of engineering materials with heterogeneous microstructural properties. Successful material models need to capture the non-trivial inter-dependence between material constituents at small scales that lead to dramatic performance effects in the macroscale response. Mechanistic understanding of this structure-property relation will also enable a collection of material microstructural database, which will accelerate material design and manufacturing. Traditional fracture mechanics and continuum damage mechanics are phenomenological methods which are not sensitive to the material microstructures, requiring extensive testing and model calibration for new materials. In this work, we aim to solve the damage problem using a multiscale data-driven modeling framework, so that the macroscale material law is directly extracted from the homogenization of the microscale model.
A new three-step homogenization scheme is presented, where the strain localization is distributed in the RVE and the microscale equilibrium condition becomes well-posed even with the strain softening effect. The homogenization will continuously provide the effective behavior in the localization region, which is independent of the RVE size. The only material length parameter in the concurrent simulation is in the macroscale, and it can be measured or calibrated from numerical or physical experiments. The microscale RVE homogenization can capture the complex damage mechanism due to material heterogeneities, and explicitly provide a microstructure-sensitive material damage model for the macroscale without predefining the form.
To increase the efficiency of the multiscale concurrent calculations, the self-consistent clustering analysis (SCA) with a new generalized formulation is proposed. By grouping material points with similar mechanical behavior into clusters, the number of degrees of freedom can be greatly reduced. With the microstructural database built in the offline stage, a reduced Lippmann-Schwinger equation is formulated and solved using a self-consistent scheme in the online stage. By comparing with direct numerical simulations (DNS) for plastic materials, the proposed method is shown to be accurate, with good convergence under refinement and computationally efficient. In the concurrent simulation, the predicted macroscale fracture patterns are observed to be sensitive to the combinations of microscale constituents, showing the capability of the SCA microstructural database.
Thursday July 27, 2017 – Session 1A – 10:15am to 12:15pm
Location: 440 Curry Student Center
Session Chair: Maurizio M. Chiaramonte, Princeton University
|10:15am||A. T. Akono*||Invited: Ductile-to-Brittle Transition in Scratch Testing via the Energetic Size Effect Law: Macroscopic and Microscopic Length Scales|
|Abstract: The scratch test consists in pulling a diamond stylus across the surface of a weaker material. In the 1810s, the scratch resistance was formulated into a scale, Mohs’ Hardness Scale, by the German Mineralogist Friedrich Mohs. Nowadays, with the advent of instrumented scratch testing, scratch testing is widely applied in several fields of science and engineering including polymer damage, metal wear, thin film quality control, and strength of rocks. A novel application of scratch testing is for the fracture analysis of materials via scratch testing. In this study, we apply the energetic Size Effect Law to analyze scratch tests. At the macroscopic scale, we consider tests carried out with a prismatic blade. At the microscopic scale, we focus on progressive-load scratch tests using a Rockwell C diamond probe.
Our first step is to utilize Dimensional Analysis to connect the scratch force to the probe geometry and material characteristic. In order to apply the energetic size effect law, we define the nominal strength and nominal size at both the macroscopic and microscopic levels. The type II size effect law is then articulated to model the ductile-to-brittle transition during scratch tests. The theoretical developments are later implemented into an experimental procedure to assess the solid fracture toughness and characteristic length directly from scratch tests measurements. The theoretical framework is validated at first on homogeneous materials such as paraffin wax, polycarbonate, polyacetal, and aluminum. An excellent agreement is found between the theoretical predictions and measurements from conventional fracture testing methods such as three-point bending tests on single-edge notched specimens. The theoretico-experimental framework is then extended to an extensive characterization campaign including conventional Portland cement paste, natural shale and organic-rich shale.
In a second step, we seek to connect the small-size expansion and the large-size expansion. To this end, we employ the universal size effect law. In that fashion, we can seamlessly bridge the strength asymptote and the linear elastic fracture mechanics asymptote. Thus, scratch tests provide a convenient and reliable tool to yield both the strength and fracture characteristics of materials.
|10:35am||J. Segurado | A. Cruzado | S. Lucarini | J. LLorca*||Modeling of Fatigue Fracture of Inconel 718 by Means of Crystal Plastic and Computational Homogenization|
|Abstract: The mechanical performance of Ni-based polycrystalline superalloys is closely related to their microstructure and models able to predict the behavior as function of the microstructure are fundamental to improve the design, reducing the weight and increasing the performance. Computational homogenization is used here to connect macroscopic behavior and microstructure by finite element simulations of representative volume elements (RVE) of the polycrystalline microstructure, which take into account the grain size and shape distributions as well as the texture in the polycrystal. The behavior of each grain follows a phenomenological crystal plasticity model that accounts for the elasto-visco-plastic behavior of the crystal including all the specific features of this alloy: Bauschinger effect, cyclic softening, mean stress relaxation and ratcheting.This approach has been applied to predict the low cycle fatigue (LCF) of Inconel 718 alloy. The CP parameters were obtained combining micromechanical tests  and inverse analysis of macroscopic cyclic tests. The fatigue life estimation was based on simulating the polycrystalline cyclic plastic behavior until the stable cycle to extract some Fatigue Indicator Parameters (FIP) that link cyclic response to fatigue crack initiation. A power-law was proposed for the relation between FIP and number of cycles to initiation and the two parameters of the law were obtained from two experimental fatigue test. The model was able to predict the fatigue life under LCF in a wide range of strain amplitudes, including the characteristic dual slope Coffin-Manson response of this alloy, as well as other experimental trends: the influence of the strain ratio on the fatigue life and the increase in the scatter at low strain amplitudes.|
|10:55am||B. Haghgouyan | C. Hayrettin | Th. Baxevanis* | I. Karaman | D.C. Lagoudas||On the Experimental Evaluation of the Fracture Toughness of Shape Memory Alloys|
|Abstract: The unique properties of Shape Memory Alloys (SMAs) result from a reversible, diffussionless solid–to–solid transformation from austenite to martensite and vice versa under applied mechanical load and/or temperature variations. Furthermore, sufficient mechanical loading, applied to the material in the twinned martensite phase results in detwinning by reorientation of a certain number of variants. Most of the SMA fracture toughness values reported in literature are based on the premise of Linear Elastic Fracture Mechanics (LEFM) despite the fact that the tests do not comply with the small-scale yielding assumption associated with the aforementioned nonlinearities in the SMA response. Actually, according to the experimental data, the requirement of small-scale yielding in SMAs yields specimen sizes that are prohibitively large. Here, a methodology is developed for measuring the fracture toughness using the J-integral as a fracture criterion, for which the requirements on specimen sizes are much less strict than those for a valid stress intensity factor, Kvalue, according to LEFM. The proposed methodology differs from the corresponding one used in conventional elastic–plastic materials in an effort to accommodate the Young’s moduli mismatch between the two phases and the negligible crack tip blunting. Finite element analysis is employed to validate the methodology while experimental data from NiTi compact tension (CT) specimens are interpreted accordingly. In addition to providing the fracture toughness values of NiTi SMAs, unprecedented conclusions concerning the temperature dependence of fracture toughness are drawn.|
|11:15am||S. Lavenstein* | B. Crawford | G. Sim | P. Shade | M. Uchic | C. Woodward | J. El-Awady||High Frequency in situ Fatigue of Nickel-Base Superalloy Microcrystals|
|Abstract: Micro-scale mechanical testing has become a popular way to measure the strength of materials and to identify their deformation mechanisms. To date, most studies have been limited to monotonic loading (i.e., bulk indentation, compression, tension, or bending). Although the cyclic response of materials are of great importance, micro-scale fatigue tests to-date have been limited in the number of loading cycles that can be completed in a practical amount of time. Here, we present a novel in situ, high-cycle fatigue testing methodology using a combination of Focused Ion Beam (FIB) fabrication and nanoindentation. The cyclic loading is imposed by using high frequency actuator dynamics. The amplitude and frequency of the oscillating force can be optimized to the desired values. Utilizing this methodology, we conduct a systematic study on the effect of crystal size on the fracture and fatigue life of microcantilever nickel-base superalloys under different loading conditions. The crack initiation and propagation in the microcantilever is monitored by observing changes in the beams dynamic stiffness and SEM imaging.|
|11:35am||A. Louhghalam* | T. Petersem | F-J. Ulm||Effect of Thermo-Chemo-Mechanical Eigenstress on Durability of Concrete: A Fracture Mechanics Approach|
|Abstract: Durability of concrete structures depends on the risk of fracture due to different environmental stressors such as Alkali silica relation (ASR), freeze thaw, drying and autogenous shrinkage. These distresses result in chemical evolutions of material properties at the nano-scale, that lead to formation of thermo- chemo- and hygro-mechanical eigenstresses at the continuum level. While these eigenstresses cannot do any work, they can lead to fracture and significant loss of durability.By way of example, we study the risk of fracture in concrete pavements and relate that to eigenstresses due to different distress mechanism. We model the pavement as an Euler Bernoulli beam on elastic foundation representing the subgrade with a crack passing through pavement thickness. We take into account the change of axial and flexural compliance of the beam section due to the existence of crack as a function of crack depth  and determine the energy release rate of the system due to eigenstress forces and moments, by taking into account their coupled actions. We then use the energy release rate in a linear elastic fracture mechanics framework to estimate the risk of fracture. The fracture criterion provides scaling relationships between the eigenstresses due to environmental stressors and material and structural properties of the pavement and sub-grade. We then discuss the applicability of the results in design of fracture resistant material both at material and structural scale. Finally we compare the results with the solution of a two-dimensional problem of a partially cracked film on a half-space substrate in a plane strain condition to determine the range of validity of the simplified model.|
|11:55am||S. Nadimpalli | P. Thompson*||Effect of Temperature on the Fracture Behavior of Cu/sac305/Cu Solder Joints|
|Abstract: The objective of the present study is to examine the effect of temperature on the fracture behavior of Cu-SAC305-Cu joints. To this end, double cantilever beam (DCB) specimens, consisting of a thin layer of Sn96.5Ag3.0Cu0.5 (SAC305) solder sandwiched between two copper bars, fabricated under standard surface mount (SMT) processing conditions are fractured under various temperatures with a MTS machine equipped with an environment chamber. The load-displacement behavior corresponding to crack initiation and the subsequent toughening before ultimate failure and the displacements near crack tip are recorded and used to calculate the fracture energy release rates. The fracture surfaces and the crack path analyses are conducted with a scanning electron microscope to understand the effect of temperature on the mechanism of fracture. As temperature increased, the fracture toughness decreased and corresponding failure mechanisms were analyzed.
Thursday July 27, 2017 – Session 2A – 1:30pm to 3:10pm
Location: 440 Curry Student Center
Session Chair: K. Ravi-Chander, University of Texas at Austin
|1:30pm||M. Vasoya | L. Ponson | V. Lazarus*||Invited: Bridging Micro to Macroscale Fracture Properties in Highly Heterogeneous Brittle Materials: Some Fundamental Lessons Learned from a Simple Example|
|Abstract: The effect of strong toughness heterogeneities on the macroscopic failure properties of brittle solids is investigated in the context of planar crack propagation. The basic mechanism at play is that the crack is locally slowed down or even trapped when encountering tougher material. The induced front deformation results in a selection of local toughness values that reflects at larger scale on the material resistance. To unravel this complexity and bridge micro to macroscale in failure of strongly heterogeneous media, we propose a homogenization procedure based on the introduction of two complementary macroscopic properties : An apparent toughness defined from the loading required to make the crack propagate and an effective fracture energy defined from the rate of energy released by unit area of crack advance. The relationship between these homogenized properties and the features of the local toughness map is computed using an iterative perturbation method. This approach is applied to a circular crack pinned by a periodic array of defects invariant in the radial direction, that gives rise to two distinct propagation regimes : A weak pinning regime where the crack maintains a stationary shape after reaching an equilibrium position and a fingering regime characterized by the continuous growth of localized regions of the fronts while other part remain trapped. Our approach successfully bridges micro to macroscopic failure properties in both cases and illustrates how small scale heterogeneities can drastically affect the overall failure response of brittle solids. On a broader perspective, we believe that our approach can be used as a powerful tool for the rational design of heterogeneous brittle solids and interfaces with tailored failure properties.|
|1:50pm||A. Elbanna*||How We Learned to Stop Worrying and to Start Loving Dynamic Rupture Nonlinearities|
|Abstract: The Finite Difference (FD) and the Spectral Boundary Integral (BI) Method have been used extensively to model spontaneously propagating shear cracks in a variety of engineering and geophysical applications. This study proposes a new method, referred to herein as the “Hybrid Method”, in which the two methods are combined. Benefiting from the flexibility of FD and the efficiency of SBI, this method is capable of solving a wide range of fracture problems in a computationally efficient way.In the Hybrid Method, nonlinearities or heterogeneities are confined to a virtual narrow strip that includes the fault or the wave source. This strip, then, is discretized using a FD scheme in space and time while the virtual boundaries of the strip are handled using the SBI formulation that represents the two elastic half spaces outside the strip. Modeling the elastodynamic response in these two halfspaces is carried out by an Independent Spectral Formulation before joining them to the strip with the appropriate boundary conditions. Dirichlet and Neumann boundary conditions are imposed on the strip and the two half-spaces, respectively, at each time step to propagate the solution forward. We illustrate that this implementation provides an exact truncation of the wave field in the near field and provides an exact absorbing boundary condition for the discretized bulk. We further demonstrate the accuracy and efficiency of the method using several examples and demonstrate the coupling using both explicit and implicit schemes. This approach is more computationally efficient than pure FD and expands the range of applications of SBI beyond the current state of the art potentially allowing the simulation of earthquake cycles with bulk nonlinearities.|
|2:10pm||Y. Barak* | A. Srivastava | S. Osovski||The Effect of Loading Rate on Ductile Fracture Toughness and Fracture Surface Roughness – An Experimental Study|
|Abstract: A material’s crack growth resistance depends on its resistance to the creation of new free surfaces, as well as its deformation characteristics, particularly those related to dissipation, which in turn are strongly influenced by the material’s microstructure and the imposed loading conditions. However, it is not clear what is the relation, if any, between a material’s crack growth resistance and the roughness of the corresponding fracture surface. Recently, a correlation between the crack growth resistance and statistical features of the fracture surface roughness was suggested to exist based on numerical calculations [1,2]. Here, we present an experimental validation regarding the role of loading rate on the measured fracture toughness and fracture surface roughness. The toughness of Aluminum alloy 6061-T6 was probed at quasi static and dynamic loading regimes, using double edge notched specimens. Dynamic loading experiments were held using a standard Hopkinson (Kolsky) tensile apparatus along with a high-speed camera, whereas quasi static loading was achieved using an Instron 4483 machine. The experimentally measured toughness obtained using digital image correlation (DIC), as well as the measured surface roughness obtained from stereographic SEM images are to exhibit a correlation similar to that found in .|
|2:30pm||G. Albertini* | D. S. Kammer||Propagation Speed Instability in Rapid Mode II Fracture in Heterogeneous Media|
|Abstract: Dynamic shear crack propagation along a weak interface has been widely studied for homogeneous, uniform conditions. A seed crack, whose length exceeds Griffith’s critical length, will become dynamic and asymptotically accelerates towards the Rayleigh wave speed. After a well-defined propagation distance, the crack will jump to supershear velocities if the applied shear load is supercritical (Burridge 1973; Andrews 1976).
We relax the assumption of homogeneous media and investigate dynamic shear fracture in heterogeneous media using two-dimensional finite-element simulations and a linear slip-weakening cohesive law. We consider bulk inclusions with contrasting stiffness while preserving constant interface properties. These inclusions have shown to affect the dynamic crack propagation and, under certain circumstances, to promote supershear transition (Albertini and Kammer 2017).
In this study, we focus on an unstable propagation regime, which occurs in setups with specific inclusion distances. Even though all interface and material properties are constant in the direction of crack propagation, the rupture presents oscillations of acceleration and deceleration. After an initial acceleration phase the speed oscillates with constant wavelength and amplitude. The amplitude of this oscillations scales with the material contrast. Wave reflection at the boundaries of the inclusions are a possible underlying source of fracture speed oscillation. We consider the near-tip strain fields to assess how wave reflection affects the dynamic energy release rate. We further analyze the frequency of the far field particle displacement and determine the effect of fracture speed oscillation on high frequency radiation.
|2:50pm||M. M. Chiaramonte*||Mapped Finite Element Methods for Simulating Crack Path Instabilities in Quenched Plates|
|Abstract: Crack path instabilities are observed in rapidly quenched rectangular glass plates whereby wavy crack patterns form as a result of the induced temperature gradients. The peculiar characteristic of these instabilities is that the speed of propagation is several order of magnitudes lower that the Rayleigh wave speed. Experimental studies [7, 5, 6] as well as analytical results [4, 1, 3] have shown the dependence of the instabilities on certain geometrical, material, and experimental parameters (e.g. plate width, material toughness, speed of quenching ect.). By perturbing this parameters cracks are observed to propagate along a straight line, oscillate with a periodic sinusoidal or semi-circle like morphology, or propagate in a chaotic manner.
In this talk we will formulate the problem of a crack propagating in a thermally strained plate. We describe a novel higher-order computational framework for the numerical solution of the problem centered around Mapped Finite Element Methods . We verify the convergence of the results and validate them against experiments. We reveal crack behaviors not previously observed. Particularly we discuss periods of sudden crack propagation, followed by temporary arrest and crack kinking. We identify various crack morphologies: sinusoidal, wave-like, semi-circle, kinked and flattened oscilla- tions. We investigate the frequency content of the oscillatory crack paths and study their relation to the dominating problem parameters. Additionally, we identify two new thresholds in phase space corresponding to the transition from oscillatory propagation to rapid propagation and arrest, as well as from permanent crack arrest to temporary crack arrest followed by kinking and branching.
Thursday July 27, 2017 – Session 3A – 3:25pm to 5:25pm
Location: 440 Curry Student Center
Session Chair: Ahmed Elbanna, University of Illinois at Urbana-Champaign
|3:25pm||T. Siegmund*||Invited: Bone Tissue Anisotropy is Related to Microcrack Formation|
|Abstract: This study is concerned with the formation of microcracks in trabecular bone. The formation of such microcracks is of relevance to bone integrity and fracture risk in an aging human population. The study, in particular, is concern with the mechanics of the formation and propagation of linear microcracks as these are primarily observed in in-vivo damaged bone. We report on a computational biomechanics model of trabecular bone in which both bone tissue heterogeneity as well tissue anisotropy are accounted for. Tissue heterogeneity follows from the x-ray energy absorption characteristics as determined by a micro-CT scan and anisotropy is imposed as a synthetic texture and emerges from the bone remodeling process. Fracture is accounted for with a XFEM model such that microcrack planes are defined by bone tissue anisotropy.We demonstrate that this approach leads to the model prediction of linear microcracks in close spatial arrangement agreement with observation on in-vivo developed microcracks. This deformation and failure response is highly damage tolerant on the overall trabecular bone level and can be seen as a strategy for tissue toughness and failure resistance.|
|3:45pm||S. Nobakhti* | S. Shefelbine||Multiscale Characteristics of Bone Toughness|
|Abstract: Bone achieves toughness through structural hierarchy and various toughening mechanisms acting at different length scales. At the nanoscale, bone is a composite of collagen molecules and hydroxyapatite mineral crystals. Alterations in quantity/quality of the collagen and mineral at the nanoscale influence other properties such as porosity, tissue mineral density and the matrix elasticity at the micro-scale and consequently, the strength and toughness at the whole bone level. Previous studies on bovine  and human  bone have proposed that bone’s toughness derives from its mechanical heterogeneity. It is generally believed that the elastic modulus is positively correlated to the amount of mineral in bone  and therefore, toughness should be primarily affected by the bone mineral content and distribution. Genetically altered mouse models of bone pathology allow us to examine how molecular defects alter the bone mineral and drive whole bone toughness across length-scales.
We generated whole bone crack resistance curves in notched three-point bending experiments on the femur for mouse models of bone pathology. We measured degree of mineralization with quantitative backscattered scanning electron microscopy and the elastic modulus with nanoindentation of the tibia. Mineral to matrix ratio was measured in the humerus by thermogravimetric analysis and crystal size was measured on humerus with wide angle x-ray diffraction.
We found that degree of mineralization, the elastic modulus, and fracture toughness varied significantly across mouse models. Toughness was generally lower in highly mineralized bone, bone lacking anisotropic arrangement of the collagen fibrils, and porous highly-vascularized bone. Crystal size was not correlated to the degree of mineralization nor the tissue elastic modulus. By examining a wide range of pathologic mice spanning the spectrums of strength and ductility we will better understand the critical contributors to toughness.
|4:05pm||A. Mesgarnejad | C. Pan* | S. Shefelbine | A. Karma | R. Erb||Crack Paths in Anisotropic Biomimetic Composites Textured by Magnetic Particles|
|Abstract: Lightweight biocomposites such as nacre, bone, and bamboo exhibit remarkable strength and toughness derived from multiple toughening mechanisms. The fracture properties of these biocomposites remain insufficiently understood at a fundamental level due, in part, to the geometrical complexity of crack paths within the material. Cracks in homogeneous, elastic, isotropic materials propagate normal to the principle stress axis, while cracks in hierarchically structured composites can strongly deflect from this axis leading to an increase in crack length that requires significant energy to propagate. Crack deflection is indicative of enhanced fracture toughness; however, the influence of the anisotropic properties and macroscopic heterogeneity on crack propagation is still poorly understood. Understanding the role of anisotropy and heterogeneity in crack deflection is key to elucidating the remarkable toughness of biocomposites and applying these findings to the biomimetic design of lightweight engineering materials.Here we present an experimental approach to fabricate and characterize the fracture of anisotropic and heterogeneous materials. We use micron-size alumina platelets coated with super paramagnetic iron oxide nanoparticles positioned in an acrylate – urethane co-polymer matrix to texture the anisotropic structures inside the material. The reinforcement can be aligned into designed patterns by an external magnetic field. Therefore the anisotropy of the composite can be tuned by controlling the alignment patterns as well as the concentration of the magnetic particles in the matrix. We also use a computational method to approach this cracking behavior to show the crack path found in our experiment can be theoretically and computationally predicted on the size scale of our sample.|
|4:25pm||A. Mesgarnejad* | C. Pan | S. Shefelbine | R. Erb | A. Karma||Crack Kinking in Anisotropic Bio-Mimetic Composites|
|Abstract: Lightweight bio-composites such as nacre, bone, and bamboo exhibit a unique combination of high strength and fracture toughness. However, how those remarkable mechanical properties relate to the underlying composite structure of those materials remains poorly understood. While cracks in elastically isotropic and homogeneous materials propagate normal to the principle stress axis, cracks in composite materials can strongly deflect from this axis, thereby contributing to increased toughness. We combine experiments using a biomimetic composite and continuum scale phase-field modeling to show that crack kinking can result from a strong fracture toughness anisotropy induced by alignment of small platelets of a hard phase embedded inside a soft polymer matrix without macroscopic heterogeneities. Furthermore, we interpret both experimental and phase-field results within the framework of linear elastic fracture mechanics extended to anisotropic materials. We investigate fracture in a geometry where a tensile crack is induced to propagate in a direction perpendicular to the hard-phase platelets. The experimental results demonstrate the existence of a transition from straight to kinked crack propagation above a critical fracture energy anisotropy. We find that those transitions can be reproduced quantitatively by numerical simulations of a phase-field model that incorporates an anisotropic fracture energy. We show that the results of both experiments and simulations can be understood in the framework of a previously derived force balance condition at the crack tip (Hakim and Karma, (JMPS 57(2), pp.342-368, 2009), which relates the modes I and II stress-intensity factors to the fracture energy.|
|4:45pm||H. Chai*||On the Deformation and Fracture Behaviour of Tooth Enamel|
|Abstract: The main forms of damage under ball contact applied to the central fossa are median radial cracks and cylindrical cracks originating from a contact region and radial or ring cracks initiating from the DEJ across from such a spot. These types of damage may greatly weaken the enamel coat. Analytical relationships for these failure modes are provided that provide useful insight into the design of prosthetic crowns. An interesting aspect of the anisotropic material properties of tooth enamel is the elimination of cone cracking, which otherwise can lead to rapid tooth ware, especially in the presence of liquids. This deficiency may be overcome using an anisotropic material design mimicking tooth enamel.|
|5:05pm||Y. Zhang* | H. Chai||Interfacial Fracture Resistance of Graded Zirconia-Glass Ceramics for Dental Prostheses|
|Abstract: In recent years, zirconia-based restorative systems (i.e., porcelain-veneered zirconia and monolithic zirconia) have emerged as promising materials for all-ceramic prostheses due primarily to their superior mechanical properties, aesthetics and biocompatibilities. However, the susceptibility to porcelain fracture as well as the poor fusion and resin-cement bonding capability of zirconia prevent the widespread use of such material systems. We hypothesize that such clinical deficiencies may be substantially mitigated by infiltrating an in-house feldspathic glass into the bonding surfaces of zirconia, creating a graded zirconia-glass structure for superior bonding capabilities. Our test data show that glass-infiltration at the veneering surface can effectively prevent veneer chipping and delamination while that at the cementation surface can increase the interfacial fracture energy of zirconia by over a factor of 3, to a level consistent with feldspathic ceramic. The fracture energy at the porcelain/zirconia interface was determined by a four-point-bending test with the thin porcelain veneer in tension, whereas that for the zirconia/resin cement interface was measure using the wedge-loaded double-cantilever-beam test. The much improved interfacial fracture resistance, together with the increased resistance to flexural and contact damage, edge chipping and delamination found in previous studies, suggest that functionally graded zirconia can be considered as a viable material option for dental restorations.
Friday July 28, 2017 – Session 1A – 10:15am to 12:15pm
Location: 440 Curry Student Center
Session Chair: Maurizio M. Chiaramonte, Princeton University
|10:15am||C. M. Landis*||Invited: Phase-field Modeling of Fatigue Fracture|
|Abstract: I will present some recent work on phase-field modeling of fatigue fracture. Over the last decade, the phase-field approach to fracture has been shown to be a useful tool for modeling complex crack path evolution. Features including the nucleation, turning, branching, and merging of cracks as a result of quasi-static mechanical and dynamic loadings are captured without the need for extra constitutive rules for these phenomena. This presentation will provide a brief summary of the phase-field approach to fracture mechanics problems. I will discuss how a modified J-integral can be used to gain insight into the fatigue crack growth law when the “phase-field viscosity” parameter is utilized in the theoretical framework. I will then present some simulations on the crack path evolution during fatigue crack growth. These simulations will be compared to experimental results on an aluminum alloy.|
|10:35am||P. Kabir* | K. Mendu | A-T. Akono||Fluid-Rock Reactions in Mt Simon Sandstone via Scratch Testing|
|Abstract: Geologic carbon sequestration in deep saline aquifers is an emerging approach for mitigating climate change by trapping CO2 in suitable geological formations. The Illinois Basin- Decatur Project (Mt Simon formation) has resulted in the injection of 1-million metric tons of CO2 over three years into the reservoir at 2200 m depth. Mt Simon formation in Illinois is a siliciclastic formation consisting of primarily quartz, feldspar, clays. Despite many investigations, the effect of supercritical CO2 on the host rock is not fully known. The research objective is to model an experimental framework to explore the influence of brine-CO2-rock interactions on microstructure, composition, and mechanical characteristics of the rock. Furthermore, a full knowledge of geochemical reactions in reservoir conditions and their implications on mechanical integrity will inform exploratory field studies of CO2 geological capture and storage. The first step consists in formulating novel methodologies to experimentally evaluate the mechanical behavior across several length-scales. To this end, we employ cutting-edge tribology-based microscopic testing methods. For instance, the scratch test consists in drawing a sharp diamond stylus across the surface of a weaker material under a linearly increasing load. The basic idea is to tune the geometry so as to activate fracture processes in the bulk of the micron-size material volume probed. Moreover, by application of advanced nonlinear mechanical theories, the force and depth curves are correlated to intrinsic material fracture characteristics. In this study, we combine microscopic scratch testing and electron probe microanalysis methods to monitor changes in structure and mechanical characteristics as a function of the exposure time to water vapor. Scanning electron microscopy confirms the presence of fracture surfaces generated during the scratch tests. The surface roughness was characterized by atomic force microscope to evaluate the influence of the specimen preparation protocol on the measured fracture characteristics. High-resolution scanning electron microscopy is utilized to shed light on microstructure and chemical modifications following chemical reactions between various mineralogical phases and water. The experimental framework provides a blueprint for future investigations to understand geochemical reactions in Mt Simon sandstone.|
|10:55am||S. Julien* | K.T. Wan||Fracture Mechanics of the Finite-Punch Shaft-Loaded Blister Test at the Bending and Stretching Limits|
|Abstract: Thin-film adhesion is important in a number of areas, such as the photovoltaic (PV) solar industry, as well as the adhesion of biological cells and tissues. In the PV industry, a PV module consists of one or more thin films—polymer encapsulants, the PV wafer, and a protective backsheet—laminated to a rigid substrate—the module front glass. Measurement of adhesion, therein, is important because adhesive failures can occur due to prolonged exposure to the environment. The shaft-loaded blister test is a well-known method for measuring the adhesive strength of thin films, wherein a hole is etched through the substrate to the film, and a cylindrical shaft is inserted through the hole and driven against the film. The applied shaft force causes the film to form the shape of a blister, growing in size and gradually debonding from the substrate. The debond energy of the filmsubstrate interface can be computed from the applied force and blister size. Models relating the debond energy to these measured quantities already exist in the literature for the idealized pointload configuration—wherein the contact area between the shaft and the film is a single point, and the model reduces to a simple, elegant relationship. However, the more realistic scenario encountered in experiments is that in which the punch forms a finite contact area with the film. This more-difficult-to-analyze model has received less attention in the literature. In the present work, we analyze this scenario, for the particular case in which the shaft is cylindrical and flat-ended. We show that, for a sufficiently large blister diameter—relative to the diameter of the punch—the solution approaches that of the point load. Conversely, for a small to intermediate blister diameters, our results suggest that our derived analytical model may be used to quantitatively relate the debond energy to the measured quantities. Ultimately, the model will be applicable to measuring the adhesion in PV modules, as well as the adhesive strength of other thin-film systems of interest.|
|11:15am||T. Zhu* | G. Li | S. Muftu | K. T. Wan||Revisiting the Constrained Blister Test to Measure Thin Film Adhesion|
|Abstract: Thin film adhesion has significant impacts in nanotechnology and life science. Dillard first introduced the constrained blister test by restricting the blister height using a planar plate. Xu and Liechti investigated structured acrylate layers on a polyethylene terephthalate carrier film with a “modified” constrained blister, where uniform pressure is applied to a freestanding membrane clamped at the periphery until it makes adhesive contact with a top plate. Long analyzed the experimental data of a pressurized elastomeric film adhering on a planar substrate from Flory based on large deformation using rubber hyperelasticity. In this study, a solid-mechanics model for the constraint blister based on small strain approximation, linear elasticity and zero-range surface force. And it differs from Xu’s work as we consider the lock-up membrane stress at the adhesion surface.
Here we consider two loading configurations based on fixed grips and fixed load. A thin film is clamped at the periphery to form a circular freestanding diaphragm before a uniform pressure, p, is applied to inflate it into a blister. To measure adhesion-delamination, one loading configuration is to constrain the blister height, w0, by a rigid plate that leads to an adhesion contact circle of radius c. Depressurization causes shrinkage of the contact until complete detachment of the plate. Measurement of (p, w0, c) allows one to determine the adhesion energy, γ. Another loading configuration is to apply a dead load (or weight) F on the constraining plate now allowed for vertical translational freedom. The coupled F and p lower the constraining plate, delaminate the film, and ultimately detach the plate at pull-off. Theoretical model is constructed to track the interrelationship between the measureable quantities. An interesting outcome from the model is that the loading-unloading hysteresis. And the results have good consistence with large deformation model in Long’s work.
|11:35am||K. Vijaykumar* | H. Kesari||Effective Toughness of Interfaces|
|Abstract: Regularized variational fracture models (RVFMs) provide a straight forward way for simulating the evolution of complex crack patterns in elastic solids. In RVFM, cracks are modeled using a continuous scalar field, termed the damage field, which takes values between zero (undamaged) and unity (fully broken). The displacement field and the damage field are evolved simultaneously so that the system moves in a direction which reduces the total free energy. This methodology makes it feasible to simulate the evolution of complex fracture paths in a straightforward manner . We modify the energy functional in the traditional RVFM to introduce interfaces by varying the fracture toughness of the solid spatially. This allows us to introduce interfaces of arbitrary geometries in the solid. We simulate classical interfacial fracture problems, such as the kinking of a crack out of a weak interface, to ascertain the accuracy of the modified RVFM. The model is suitable to study crack paths in elastically heterogeneous media such as metal matrix composites (MMC’s) and structural bio-materials. It has been experimentally observed that these materials show an effective toughness that is different from that of their constituent phases. It is believed that this difference is due to mechanisms such as crack arresting and crack bridging, which originate from the presence of weak interfaces. The modified RVFM can be used for determining the effective toughness in such composite materials.|
|11:55am||A. Vasudevan* | T. Grabois | L. Ponson||Triangular Fracture Patterns in Polymeric Materials as the Signature of Shear Induced Crack Front Instability|
|Abstract: Polymeric materials like PMMA under certain loading conditions show stick-slip crack propagation where the crack oscillates between slow and fast crack growth despite being driven at a constant loading rate. In PMMA, when a crack transits from a fast (slip regime) to a slow propagation (stick regime), the transition occurs always through the occurrence of triangular patterns on the fracture surface. These patterns are formed through a heterogeneous transition along the front and they show characteristic angles close to 15-25 degrees. In this work, we characterize this instability and determine the basic mechanism at the origin of the out-of-plane excursions of the front under dominantly tensile loading conditions. To decipher the triangular patterns, we study both the in-plane front deformations that is revealed by Wallner lines and the out-of-plane front deviations inferred from the fracture surface that we scan after failure using an interferometric profilometer. Assuming a small amount of mode II (in-plane shear), using a crack front perturbation approach in 3D developed by Movchan et. al.(1998), we are able to understand well the in-plane and the out-of-plane shape of the triangles. According to the crack front perturbation approach, an in-plane perturbed crack when subjected to a mode II causes the crack to kink non-uniformly and this response of the crack explains well the growth of the triangular patterns. Finally, the onset of the instability which have been seen in other materials like hydrogels and rubber will also be discussed.