Showing papers on "Fracture mechanics published in 2021"

Intrinsic toughening and stable crack propagation in hexagonal boron nitride

Abstract: If a bulk material can withstand a high load without any irreversible damage (such as plastic deformation), it is usually brittle and can fail catastrophically1,2. This trade-off between strength and fracture toughness also extends into two-dimensional materials space3–5. For example, graphene has ultrahigh intrinsic strength (about 130 gigapascals) and elastic modulus (approximately 1.0 terapascal) but is brittle, with low fracture toughness (about 4 megapascals per square-root metre)3,6. Hexagonal boron nitride (h-BN) is a dielectric two-dimensional material7 with high strength (about 100 gigapascals) and elastic modulus (approximately 0.8 terapascals), which are similar to those of graphene8. Its fracture behaviour has long been assumed to be similarly brittle, subject to Griffith’s law9–14. Contrary to expectation, here we report high fracture toughness of single-crystal monolayer h-BN, with an effective energy release rate up to one order of magnitude higher than both its Griffith energy release rate and that reported for graphene. We observe stable crack propagation in monolayer h-BN, and obtain the corresponding crack resistance curve. Crack deflection and branching occur repeatedly owing to asymmetric edge elastic properties at the crack tip and edge swapping during crack propagation, which intrinsically toughens the material and enables stable crack propagation. Our in situ experimental observations, supported by theoretical analysis, suggest added practical benefits and potential new technological opportunities for monolayer h-BN, such as adding mechanical protection to two-dimensional devices. Single-crystal monolayer hexagonal boron nitride is unexpectedly tough owing to its asymmetric lattice structure, which facilitates repeated crack deflection, crack branching and edge swapping, enhancing energy dissipation.

Studies of Fracture Toughness in Concretes Containing Fly Ash and Silica Fume in the First 28 Days of Curing.

Abstract: This paper presents the results of the fracture toughness of concretes containing two mineral additives. During the tests, the method of loading the specimens according to Mode I fracture was used. The research included an evaluation of mechanical parameters of concrete containing noncondensed silica fume (SF) in an amount of 10% and siliceous fly ash (FA) in the following amounts: 0%, 10% and 20%. The experiments were carried out on mature specimens, i.e., after 28 days of curing and specimens at an early age, i.e., after 3 and 7 days of curing. In the course of experiments, the effect of adding SF to the value of the critical stress intensity factor—KIcS in FA concretes in different periods of curing were evaluated. In addition, the basic strength parameters of concrete composites, i.e., compressive strength—fcm and splitting tensile strength—fctm, were measured. A novelty in the presented research is the evaluation of the fracture toughness of concretes with two mineral additives, assessed at an early age. During the tests, the structures of all composites and the nature of macroscopic crack propagation were also assessed. A modern and useful digital image correlation (DIC) technique was used to assess macroscopic cracks. Based on the conducted research, it was found the application of SF to FA concretes contributes to a significant increase in the fracture toughness of these materials at an early age. Moreover, on the basis of the obtained test results, it was found that the values of the critical stress intensity factor of analyzed concretes were convergent qualitatively with their strength parameters. It also has been demonstrated that in the first 28 days of concrete curing, the preferred solution is to replace cement with SF in the amount of 10% or to use a cement binder substitution with a combination of additives in proportions 10% SF + 10% FA. On the other hand, the composition of mineral additives in proportions 10% SF + 20% FA has a negative effect on the fracture mechanics parameters of concretes at an early age. Based on the analysis of the results of microstructural tests and the evaluation of the propagation of macroscopic cracks, it was established that along with the substitution of the cement binder with the combination of mineral additives, the composition of the cement matrix in these composites changes, which implies a different, i.e., quasi-plastic, behavior in the process of damage and destruction of the material.

A coupled mechano-chemical peridynamic model for pit-to-crack transition in stress-corrosion cracking

Abstract: We introduce a coupled mechano-chemical peridynamic model to describe stress corrosion cracking. In this model, two mechanisms, stress-dependent anodic dissolution and diffuse corrosion layer-assisted fracture, are considered to influence pitting and crack propagation in stress corrosion cracking. Diffusion peridynamic bonds (acting as dissolution bonds at the solid/liquid interface) and mechanical peridynamic bonds are used to represent the interactions between material points. Mechanical bonds can be damaged by mechanical stretching or by anodic dissolution. The magnitude of the dissolution fluxes for diffusion peridynamic bonds depends on both mechanical deformation and the applied electrical potential. The coupling between anodic dissolution and mechanical damage leads to cracks that initiate in the corrosion damage layer and propagate into the bulk. A 2D three-point bending/corrosion test demonstrates the concept. We verify the model in 3D using an experimental test from the literature for the case of stress-corrosion cracking process in a steam turbine steel sample. The model's results capture the pit-to-crack transition time, the pit size and shape at fracture, as well as the morphology of cracks that spring from, and connect the pits.

A generalized 2D Bézier-based solution for stress analysis of notched epoxy resin plates reinforced with graphene nanoplatelets

Abstract: In this study, a robust Bezier-based multi-step method is extended to accurately solve the governing fourth-order complex partial differential equation (PDE) in linear elastic fracture mechanics (LEFM) problems. The Bezier technique was first introduced by the authors to solve initial value problems in one dimension. Now, the method is further extended to simultaneously solve Boundary Value Problems (BVPs) in orthogonal directions. To examine the accuracy and performance of the present method, the first-mode normalized stress intensity factor (SIF) of a 2D epoxy resin plate having an initial edge crack and reinforced with randomly oriented graphene nanoplatelets (GnP) is determined and compared with the associated exact analytical solution using the Bayesian statistical analysis. Besides, the impact of GnP aspect ratio on the normalized crack opening displacement (COD) of the reinforced matrix is elaborated for the first time in the literature. Results of the present study suggest that GnPs with maximum aspect ratio are most effective to enhance elastic properties of the plate and potentially limit the edge crack propagation. Specifically, inclusion of 0.5 and 1.0% of needle-shaped GnPs in a notched epoxy resin plate decrease the maximum normalized COD by 33 and 50%, respectively, while for square-shaped GnPs, these reductions are limited to 20 and 37%, respectively.

A general phase-field model for fatigue failure in brittle and ductile solids

Abstract: In this work, the phase-field approach to fracture is extended to model fatigue failure in high- and low-cycle regime. The fracture energy degradation due to the repeated externally applied loads is introduced as a function of a local energy accumulation variable, which takes the structural loading history into account. To this end, a novel definition of the energy accumulation variable is proposed, allowing the fracture analysis at monotonic loading without the interference of the fatigue extension, thus making the framework generalised. Moreover, this definition includes the mean load influence of implicitly. The elastoplastic material model with the combined nonlinear isotropic and nonlinear kinematic hardening is introduced to account for cyclic plasticity. The ability of the proposed phenomenological approach to naturally recover main features of fatigue, including Paris law and Wohler curve under different load ratios is presented through numerical examples and compared with experimental data from the author’s previous work. Physical interpretation of additional fatigue material parameter is explored through the parametric study.

The effect of pulse current changes in PCGTAW on microstructural evolution, drastic improvement in mechanical properties, and fracture mode of dissimilar welded joint of AISI 316L-AISI 310S stainless steels

Abstract: In this paper, the effect of pulse current changes in the Pulsed Current Gas Tungsten Arc Welding (PCGTAW) on the various properties of dissimilar welding of AISI 316L-AISI 310S stainless steels was investigated. 10 mm thickness steel sheets were joined by the PCGTAW process with the background current (Ib) of 55, 70 and 85A, as well as the peak current (Ip) of 110, 130 and 150A. Then, optical microscopy (OM) and Field Emission Scanning Electron Microscopy (FE-SEM) techniques were used to study the microstructural evolution in different areas of the welded joints. Also, tensile, Charpy impact and Vickers microhardness tests were used to evaluate the effect of the pulsed current changes on mechanical properties. Finally, the fracture surfaces of Charpy impact and tensile tests samples were studied by FE-SEM. The weld metal (WM) microstructure consisted of austenite dendrites together with a low amount of delta ferrite in the grain-boundaries. Results also showed that by increasing Ib and decreasing Ip, the microstructure of the WM was changed from columnar dendritic to coaxial, and a very fine, dendritic one. This condition led to the reduction of the size of the dendrites and the amount of delta ferrite ingrain boundaries of the WM, as well as a reduction in the width of Unmixed Zone (UMZ) area. Moreover, all the welded joints were fractured from the AISI 316L stainless steels side. However, the results of the Charpy impact and microhardness tests showed that with the above variation in the welding parameters, hardness value and fracture energy of the WM increased significantly. Fractography of the surfaces showed a completely ductile fracture for both tensile and Charpy impact tests samples.

Phase field modeling of fracture in Functionally Graded Materials: Γ-convergence and mechanical insight on the effect of grading

Abstract: A phase field (PF) approximation of fracture for functionally graded materials (FGM) using a diffusive crack approach incorporating the characteristic length scale as a material parameter is herein proposed. A rule of mixture is employed to estimate the material properties, according to the volume fractions of the constituent materials, which have been varied according to given grading profiles. In addition to the previous aspects, the current formulation includes the internal length scale of the phase field approach variable from point to point, to model a spatial variation of the material strength. Based on the ideas stemming from the study of size-scale effects, Γ -convergence for the proposed model is proved when the internal length scale is either constant or a bounded function. In a comprehensive sensitivity analysis, the effects of various model parameters for different grading profiles are analyzed. We first prove that the fracture energy and the elastic energy of FGM is bounded by their homogeneous constituents. Constitutive examples of boundary value problems solved using the BFGS solver are provided to bolster this claim. Finally, crack propagation events in conjunction with the differences with respect to their homogeneous surrogates are discussed through several representative applications, providing equivalence relationships for size-scale effects and demonstrating the applicability of the current model for structural analysis of FGMs.

An assessment of phase field fracture: crack initiation and growth

Abstract: The phase field paradigm, in combination with a suitable variational structure, has opened a path for using Griffith's energy balance to predict the fracture of solids. These so-called phase field fracture methods have gained significant popularity over the past decade, and are now part of commercial finite element packages and engineering fitness- for-service assessments. Crack paths can be predicted, in arbitrary geometries and dimensions, based on a global energy minimization-without the need for ad hoc criteria. In this work, we review the fundamentals of phase field fracture methods and examine their capabilities in delivering predictions in agreement with the classical fracture mechanics theory pioneered by Griffith. The two most widely used phase field fracture models are implemented in the context of the finite element method, and several paradigmatic boundary value problems are addressed to gain insight into their predictive abilities across all cracking stages; both the initiation of growth and stable crack propagation are investigated. In addition, we examine the effectiveness of phase field models with an internal material length scale in capturing size effects and the transition flaw size concept. Our results show that phase field fracture methods satisfactorily approximate classical fracture mechanics predictions and can also reconcile stress and toughness criteria for fracture. The accuracy of the approximation is however dependent on modelling and constitutive choices; we provide a rationale for these differences and identify suitable approaches for delivering phase field fracture predictions that are in good agreement with well-established fracture mechanics paradigms. This article is part of a discussion meeting issue 'A cracking approach to inventing new tough materials: fracture stranger than friction'.