Showing papers on "Fracture mechanics published in 2017"

Polymer Interface and Adhesion

Abstract: "Interfacial Thermodynamics Molecular Interpretations Interfacial and Surface Tensions of Polymer Melts and Liquids Contact Angles of Liquids on Solid Polymers Surface Tension and Polarity of Solid Polymers Wetting of High-Energy Surfaces Dynamic Contact Angles and Wetting Kinetics Experimental Methods for Contact Angles and Interfacial Tensions Modifications of Polymer Surfaces: Mechanisms of Wettability and Bondability Improvements Adhesion: Basic Concept and Locus of Failure Formation of Adhesive Bond Weak Boundary Layers Effect of Internal Stress and Bond Strength Fracture of Adhesive Bond Fundamentals of Fracture Mechanics Analysis and Testing of Adhesive Bonds Creep, Fatigue, and Environmental Effects Creep and Fatigue of Adhesive Joints Environmental Effects Appendix I: Calculation of Surface Tension and Its Non-polar and Polar Components from Contact Angles By the Harmonic-Mean and the Geometric-Mean Methods Appendix II: Unit Conversion Tables "

A unified phase-field theory for the mechanics of damage and quasi-brittle failure

Abstract: Being one of the most promising candidates for the modeling of localized failure in solids, so far the phase-field method has been applied only to brittle fracture with very few exceptions. In this work, a unified phase-field theory for the mechanics of damage and quasi-brittle failure is proposed within the framework of thermodynamics. Specifically, the crack phase-field and its gradient are introduced to regularize the sharp crack topology in a purely geometric context. The energy dissipation functional due to crack evolution and the stored energy functional of the bulk are characterized by a crack geometric function of polynomial type and an energetic degradation function of rational type, respectively. Standard arguments of thermodynamics then yield the macroscopic balance equation coupled with an extra evolution law of gradient type for the crack phase-field, governed by the aforesaid constitutive functions. The classical phase-field models for brittle fracture are recovered as particular examples. More importantly, the constitutive functions optimal for quasi-brittle failure are determined such that the proposed phase-field theory converges to a cohesive zone model for a vanishing length scale. Those general softening laws frequently adopted for quasi-brittle failure, e.g., linear, exponential, hyperbolic and Cornelissen et al. (1986) ones, etc., can be reproduced or fit with high precision. Except for the internal length scale, all the other model parameters can be determined from standard material properties (i.e., Young’s modulus, failure strength, fracture energy and the target softening law). Some representative numerical examples are presented for the validation. It is found that both the internal length scale and the mesh size have little influences on the overall global responses, so long as the former can be well resolved by sufficiently fine mesh. In particular, for the benchmark tests of concrete the numerical results of load versus displacement curve and crack paths both agree well with the experimental data, showing validity of the proposed phase-field theory for the modeling of damage and quasi-brittle failure in solids.

Stochastic analysis of the fracture toughness of polymeric nanoparticle composites using polynomial chaos expansions

Abstract: The fracture energy is a substantial material property that measures the ability of materials to resist crack growth. The reinforcement of the epoxy polymers by nanosize fillers improves significantly their toughness. The fracture mechanism of the produced polymeric nanocomposites is influenced by different parameters. This paper presents a methodology for stochastic modelling of the fracture in polymer/particle nanocomposites. For this purpose, we generated a 2D finite element model containing an epoxy matrix and rigid nanoparticles surrounded by an interphase zone. The crack propagation was modelled by the phantom node method. The stochastic model is based on six uncertain parameters: the volume fraction and the diameter of the nanoparticles, Young’s modulus and the maximum allowable principal stress of the epoxy matrix, the interphase zone thickness and its Young’s modulus. Considering the uncertainties in input parameters, a polynomial chaos expansion surrogate model is constructed followed by a sensitivity analysis. The variance in the fracture energy was mostly influenced by the maximum allowable principal stress and Young’s modulus of the epoxy matrix.

Bone-like crack resistance in hierarchical metastable nanolaminate steels

Abstract: Fatigue failures create enormous risks for all engineered structures, as well as for human lives, motivating large safety factors in design and, thus, inefficient use of resources. Inspired by the excellent fracture toughness of bone, we explored the fatigue resistance in metastability-assisted multiphase steels. We show here that when steel microstructures are hierarchical and laminated, similar to the substructure of bone, superior crack resistance can be realized. Our results reveal that tuning the interface structure, distribution, and phase stability to simultaneously activate multiple micromechanisms that resist crack propagation is key for the observed leap in mechanical response. The exceptional properties enabled by this strategy provide guidance for all fatigue-resistant alloy design efforts.

Phase field modeling of fracture in anisotropic brittle solids

Abstract: A phase field model of fracture that accounts for anisotropic material behavior at small and large deformations is outlined within this work. Most existing fracture phase field models assume crack evolution within isotropic solids, which is not a meaningful assumption for many natural as well as engineered materials that exhibit orientation-dependent behavior. The incorporation of anisotropy into fracture phase field models is for example necessary to properly describe the typical sawtooth crack patterns in strongly anisotropic materials. In the present contribution, anisotropy is incorporated in fracture phase field models in several ways: (i) Within a pure geometrical approach, the crack surface density function is adopted by a rigorous application of the theory of tensor invariants leading to the definition of structural tensors of second and fourth order. In this work we employ structural tensors to describe transverse isotropy, orthotropy and cubic anisotropy. Latter makes the incorporation of second gradients of the crack phase field necessary, which is treated within the finite element context by a nonconforming Morley triangle. Practically, such a geometric approach manifests itself in the definition of anisotropic effective fracture length scales. (ii) By use of structural tensors, energetic and stress-like failure criteria are modified to account for inherent anisotropies. These failure criteria influence the crack driving force, which enters the crack phase field evolution equation and allows to set up a modular structure. We demonstrate the performance of the proposed anisotropic fracture phase field model by means of representative numerical examples at small and large deformations.

Modeling of internal mechanical failure of all-solid-state batteries during electrochemical cycling, and implications for battery design

Abstract: This is the first quantitative analysis of mechanical reliability of all-solid state batteries. Mechanical degradation of the solid electrolyte (SE) is caused by intercalation-induced expansion of the electrode particles, within the constrains of a dense microstructure. A coupled electro-chemo-mechanical model was implemented to quantify the material properties that cause an SE to fracture. The treatment of microstructural details is essential to the understanding of stress-localization phenomena and fracture. A cohesive zone model is employed to simulate the evolution of damage. In the numerical tests, fracture is prevented when electrode-particle's expansion is lower than 7.5% (typical for most Li-intercalating compounds) and the solid-electrolyte's fracture energy higher than Gc = 4 J m−2. Perhaps counter-intuitively, the analyses show that compliant solid electrolytes (with Young's modulus in the order of ESE = 15 GPa) are more prone to micro-cracking. This result, captured by our non-linear kinematics model, contradicts the speculation that sulfide SEs are more suitable for the design of bulk-type batteries than oxide SEs. Mechanical degradation is linked to the battery power-density. Fracture in solid Li-ion conductors represents a barrier for Li transport, and accelerates the decay of rate performance.

Twisting cracks in Bouligand structures.

Abstract: The Bouligand structure, which is found in many biological materials, is a hierarchical architecture that features uniaxial fiber layers assembled periodically into a helicoidal pattern. Many studies have highlighted the high damage-resistant performance of natural and biomimetic Bouligand structures. One particular species that utilizes the Bouligand structure to achieve outstanding mechanical performance is the smashing Mantis Shrimp, Odontodactylus Scyllarus (or stomatopod). The mantis shrimp generates high speed, high acceleration blows using its raptorial appendage to defeat highly armored preys. The load-bearing part of this appendage, the dactyl club, contains an interior region [16] that consists of a Bouligand structure. This region is capable of developing a significant amount of nested twisting microcracks without exhibiting catastrophic failure. The development and propagation of these microcracks are a source of energy dissipation and stress relaxation that ultimately contributes to the remarkable damage tolerance properties of the dactyl club. We develop a theoretical model to provide additional insights into the local stress intensity factors at the crack front of twisting cracks formed within the Bouligand structure. Our results reveal that changes in the local fracture mode at the crack front leads to a reduction of the local strain energy release rate, hence, increasing the necessary applied energy release rate to propagate the crack, which is quantified by the local toughening factor. Ancillary 3D simulations of the asymptotic crack front field were carried out using a J-integral to validate the theoretical values of the energy release rate and the local stress intensity factors.

Mechanical weathering and rock erosion by climate-dependent subcritical cracking

Abstract: This work constructs a fracture mechanics framework for conceptualizing mechanical rock breakdown and consequent regolith production and erosion on the surface of Earth and other terrestrial bodies. Here our analysis of fracture mechanics literature explicitly establishes for the first time that all mechanical weathering in most rock types likely progresses by climate-dependent subcritical cracking under virtually all Earth surface and near-surface environmental conditions. We substantiate and quantify this finding through development of physically based subcritical cracking and rock erosion models founded in well-vetted fracture mechanics and mechanical weathering, theory, and observation. The models show that subcritical cracking can culminate in significant rock fracture and erosion under commonly experienced environmental stress magnitudes that are significantly lower than rock critical strength. Our calculations also indicate that climate strongly influences subcritical cracking—and thus rock weathering rates—irrespective of the source of the stress (e.g., freezing, thermal cycling, and unloading). The climate dependence of subcritical cracking rates is due to the chemophysical processes acting to break bonds at crack tips experiencing these low stresses. We find that for any stress or combination of stresses lower than a rock's critical strength, linear increases in humidity lead to exponential acceleration of subcritical cracking and associated rock erosion. Our modeling also shows that these rates are sensitive to numerous other environment, rock, and mineral properties that are currently not well characterized. We propose that confining pressure from overlying soil or rock may serve to suppress subcritical cracking in near-surface environments. These results are applicable to all weathering processes.

Brittle Fracture of 2D MoSe2.

Abstract: An in situ quantitative tensile testing platform is developed to enable the uniform in-plane loading of a freestanding membrane of 2D materials inside a scanning electron microscope. The in situ tensile testing reveals the brittle fracture of large-area MoSe2 crystals and measures their fracture strength for the first time.

Fracture behaviour of bamboo fiber reinforced epoxy composites

Abstract: In this work, experimental and numerical study on fracture behaviour of bamboo fiber reinforced epoxy composites is presented. Optimum NaOH concentration for treatment of bamboo fibers was determined through single fiber tensile test and microscopic inspection of fiber surface through SEM (Scanning Electron Microscopy). The results demonstrated that 6% NaOH treated fibers showed maximum ultimate tensile strength of 234 MPa. Single fiber fragmentation test results showed that interfacial adhesion is improved by treating fibers with 6% NaOH. Bamboo fiber reinforced epoxy composite was fabricated using 6% NaOH treated bamboo fibers of length 10 mm, 20 mm and 25 mm with random distribution in epoxy matrix. Mode-I plane strain fracture toughness (K IC ) of bamboo fiber reinforced epoxy composites was investigated based on Linear Elastic Fracture Mechanics (LEFM) approach as per ASTM D5045 . Results showed that composites having 25 mm length of fibers had the largest K IC value of 2.67 MPa.m 1/2 , whereas composites with 10 mm fiber length showed lowest value of fracture toughness K IC of 1.61 MPa.m 1/2 . SEM results revealed that fiber breakage, matrix cracking, fiber matrix debonding and fiber pull out are major causes of failure of composite. Simulation/modelling of crack propagation in CT (Compact Tension) specimen by using FEA software ABAQUS ® showed similar results as experimental values.

Multi-phase-field modeling of anisotropic crack propagation for polycrystalline materials

Abstract: A new multi-phase-field method is developed for modeling the fracture of polycrystals at the mi-crostructural level. Inter and transgranular cracking, as well as anisotropic effects of both elasticity and preferential cleavage directions within each randomly oriented crystal are taken into account. For this purpose, the proposed phase field formulation includes: (a) a smeared description of grain boundaries as cohesive zones avoiding defining an additional phase for grains; (b) an anisotropic phase field model; (c) a multi-phase field formulation where each preferential cleavage direction is associated with a damage (phase field) variable. The obtained framework allows modeling interactions and competition between grains and grain boundary cracks, as well as their effects on the effective response of the material. The proposed model is illustrated through several numerical examples involving a full description of complex crack initiation and propagation within 2D and 3D models of polycrystals.

Effect of minor alloying elements on crack-formation characteristics of Hastelloy-X manufactured by selective laser melting

Abstract: Two batches of pre-alloyed Hastelloy-X powder with different Si, Mn and C contents were used to produce specimens by Selective Laser Melting (SLM). Cracks with various morphologies were found in some of the parts. Two major reasons that control crack formation and propagation were considered: (i) internal strain accumulation due to the thermal cycling that is characteristic to SLM processing; (ii) crack formation and propagation during solidification. This phenomenon, known as hot tearing, is frequently found in conventional casting and is dependent on chemical composition. Using thermodynamic software simulation, the temperature vs fraction of solid curves was used to determine hot tearing sensitivity as a function of Si, Mn and C content. It was found that low Si and C contents help in avoiding crack formation whereas cracking propensity was relatively independent of Mn concentration. Hence, the cracking mechanism during SLM is believed to be as follows: crack initiation is mainly induced during solidification and is dependent on the content of minor alloying elements such as Si and C, whereas crack propagation predominantly occurs during thermal cycling. If microstructures free of micro-cracks after solidification can be generated with optimised SLM parameters, these manufactured parts can sustain the internal strain level and, thus, crack formation and propagation can be avoided.

Effects of Defects, Surface Roughness and HIP on Fatigue Strength of Ti-6Al-4V manufactured by Additive Manufacturing

Abstract: The additive manufacturing (AM) is expected to be the promising manufacturing process for high strength or hard steels such as Ti-6Al-4V for the aerospace industry components having complex shapes. However, disadvantage or challenge of AM is presence of defects which are inevitably contained in the manufacturing process. This paper focuses on the effects of defects, surface roughness and Hot Isostatic Pressing (HIP) process on the fatigue strength of a Ti-6Al-4V manufactured by AM. The guide is presented for the fatigue design and development of high quality and high strength Ti-6Al-4V by AM processing based on the combination of the statistics of extremes on defects and the √area parameter model. Defects were mostly gas porosity and those made by lack of fusion. Many pores which were formed near surface were eliminated by HIP and eventually HIP improved fatigue strength drastically to the level of the ideal fatigue limit to be expected from the hardness. Surface roughness had strong detrimental influence on fatigue strength. The method for estimating the effective size √areaeffmax of irregularly shaped defects and interacting adjacent defects was proposed from the viewpoint of fracture mechanics. Although the statistics of extremes analysis is useful for the quality control of AM, the particular surface effect and interaction effect of adjacent defects must be carefully considered. The effective defect size for adjacent defects is much larger than a single defect. Since the orientations of defects in AM materials are random, a defect in contact with specimen surface has a higher influence (termed as the effective defect size √areaeff) than the real size of the defect from the viewpoint of fracture mechanics. Considering the volume and number of productions of components, the lower bound of the fatigue limit σwl based on √areaeffmax can be determined by the √area parameter model.

Modeling of internal mechanical failure of all-solid-state batteries during electrochemical cycling, and implications for battery design

Abstract: This is the first quantitative analysis of mechanical reliability of all-solid state batteries. Mechanical degradation of the solid electrolyte (SE) is caused by intercalation-induced expansion of the electrode particles, within the constrain of a dense microstructure. A coupled electro-chemo-mechanical model was implemented to quantify the material properties that cause a SE to fracture. The treatment of microstructural details is essential to the understanding of stress-localization phenomena and fracture. A cohesive zone model is employed to simulate the evolution of damage. In the numerical tests, fracture is prevented only if electrode-particle's expansion is lower than 7.5% and the solid-electrolyte's fracture energy higher than $G_c = 4$ J m$^{-2}$. Perhaps counter-intuitively, the analyses show that compliant solid electrolytes (with Young's modulus in the order of E$_{SE} = 15$ GPa) are more prone to micro-cracking. This result, captured by our non-linear kinematics model, contradicts the speculations that sulfide SEs are more suitable for the design of bulk-type batteries than oxide SEs. Mechanical degradation is linked to the battery power-density. Fracture in solid Li-ion conductors represents a barrier for Li transport, and accelerates the decay of rate performance.