Showing papers on "Fracture mechanics published in 2014"

ISRM-Suggested Method for Determining the Mode I Static Fracture Toughness Using Semi-Circular Bend Specimen

Abstract: The International Society for Rock Mechanics has so far developed two standard methods for the determination of static fracture toughness of rock. They used three different core-based specimens and tests were to be performed on a typical laboratory compression or tension load frame. Another method to determine the mode I fracture toughness of rock using semi-circular bend specimen is herein presented. The specimen is semi-circular in shape and made from typical cores taken from the rock with any relative material directions noted. The specimens are tested in three-point bending using a laboratory compression test instrument. The failure load along with its dimensions is used to determine the fracture toughness. Most sedimentary rocks which are layered in structure may exhibit fracture properties that depend on the orientation and therefore measurements in more than one material direction may be necessary. The fracture toughness measurements are expected to yield a size-independent material property if certain minimum specimen size requirements are satisfied.

Fracture initiation and propagation in intact rock – A review

Abstract: The initiation and propagation of failure in intact rock are a matter of fundamental importance in rock engineering. At low confining pressures, tensile fracturing initiates in samples at 40%–60% of the uniaxial compressive strength and as loading continues, and these tensile fractures increase in density, ultimately coalescing and leading to strain localization and macro-scale shear failure of the samples. The Griffith theory of brittle failure provides a simplified model and a useful basis for discussion of this process. The Hoek–Brown failure criterion provides an acceptable estimate of the peak strength for shear failure but a cutoff has been added for tensile conditions. However, neither of these criteria adequately explains the progressive coalition of tensile cracks and the final shearing of the specimens at higher confining stresses. Grain-based numerical models, in which the grain size distributions as well as the physical properties of the component grains of the rock are incorporated, have proved to be very useful in studying these more complex fracture processes.

Material and bond properties of ultra high performance fiber reinforced concrete with micro steel fibers

Abstract: For investigating the effect of fiber content on the material and interfacial bond properties of ultra high performance fiber reinforced concrete (UHPFRC), four different volume ratios of micro steel fibers (Vf = 1%, 2%, 3%, and 4%) were used within an identical mortar matrix. Test results showed that 3% steel fiber by volume yielded the best performance in terms of compressive strength, elastic modulus, shrinkage behavior, and interfacial bond strength. These parameters improved as the fiber content was increased up to 3 vol.%. Flexural behaviors such as flexural strength, deflection, and crack mouth opening displacement at peak load had pseudo-linear relationships with the fiber content. Through inverse analysis, it was shown that fracture parameters including cohesive stress and fracture energy are significantly influenced by the fiber content: higher cohesive stress and fracture energy were achieved with higher fiber content. The analytical models for the ascending branch of bond stress-slip response suggested in the literature were considered for UHPFRC, and appropriate parameters were derived from the present test data.

Phase field approximation of dynamic brittle fracture

Abstract: Numerical methods that are able to predict the failure of technical structures due to fracture are important in many engineering applications. One of these approaches, the so-called phase field method, represents cracks by means of an additional continuous field variable. This strategy avoids some of the main drawbacks of a sharp interface description of cracks. For example, it is not necessary to track or model crack faces explicitly, which allows a simple algorithmic treatment. The phase field model for brittle fracture presented in Kuhn and Muller (Eng Fract Mech 77(18):3625---3634, 2010) assumes quasi-static loading conditions. However dynamic effects have a great impact on the crack growth in many practical applications. Therefore this investigation presents an extension of the quasi-static phase field model for fracture from Kuhn and Muller (Eng Fract Mech 77(18):3625---3634, 2010) to the dynamic case. First of all Hamilton's principle is applied to derive a coupled set of Euler-Lagrange equations that govern the mechanical behaviour of the body as well as the crack growth. Subsequently the model is implemented in a finite element scheme which allows to solve several test problems numerically. The numerical examples illustrate the capabilities of the developed approach to dynamic fracture in brittle materials.

Phase field modeling of fracture in rubbery polymers. Part I: Finite elasticity coupled with brittle failure

Abstract: This work presents a new phase field model for rate-independent crack propagation in rubbery polymers at large strains and considers details of its numerical implementation. The approach accounts for micro-mechanically based features of both the elastic bulk response as well as the crack toughness of idealized polymer networks. The proposed diffusive crack modeling based on the introduction of a crack phase field overcomes difficulties associated with the computational realization of sharp crack discontinuities, in particular when it comes to complex crack topologies. The crack phase field governs a crack density function, which describes the macroscopic crack surface in the polymer per unit of the reference volume. It provides the basis for the constitutive modeling of a degrading free energy storage and a crack threshold function with a Griffith-type critical energy release rate, that governs the crack propagation in the polymer. Both the energy storage as well as the critical energy release due to fracture can be related to classical statistical network theories of polymers. The proposed framework of diffusive fracture in polymers is formulated in terms of a rate-type variational principle that determines the evolution of the coupled primary variable fields, i.e. the deformation field and the crack phase field. On the computational side, we outline a staggered solution procedure based on a one-pass operator split of the coupled equations, that successively updates in a typical time step the crack phase field and the displacement field. Such a solution algorithm is extremely robust, easy to implement and ideally suited for engineering problems. We finally demonstrate the performance of the phase field formulation of fracture at large strains by means of representative numerical examples.

Fracture Mechanics Tests in Adhesively Bonded Joints: A Literature Review

Abstract: Fracture mechanics characterization tests for adhesive joints are analyzed and reviewed in order to understand their advantages and disadvantages. Data reduction techniques for analytical methods are summarized to understand the improvements implemented in each test. Numerical approaches are also used complementing tests information. Both linear and non-linear methods to obtain the fracture energy release rate are presented. Pure mode I and mode II tests are described. Simple mixed-mode tests, varying only the specimen geometry, with limited mode-mixity are also presented. Performing a wider mode-mixity range requires sophisticated apparatus that are studied in detail. There is no general agreement about the test suitability for mixed-mode fracture assessment of adhesive joints. A universal test that can easily be performed and give accurate results is essential to optimize the expensive testing at the design stage.

60 Years of Hall-Petch: Past to Present Nano-Scale Connections

Abstract: Pioneering research results reported in the early 1950’s by E. O. Hall and N. J. Petch on iron and steel materials have led to an expanded description of the grain size dependence of the complete stress­strain behavior of a wider range of materials and including assessments of other mechanical properties such as the ductile to brittle transition behavior and the hardness of materials, particularly, of nanocrystalline materials. The dislocation pile-up model that was presented originally for the inverse square root of grain diameter dependence of material strength has endured. Most recently, the pile-up model description has been more definitely associated with the Griffith theory of achieving a critical stress concentration at the tip of a crack; and, the Hall-Petch analysis has been connected to the macro-scale description of the fracture mechanics stress intensity parameter. These topics and other “60 years of Hall-Petch” type researches are tracked over time in the present report while giving special emphasis to current order-of-magnitude strength improvements that are reported for metals with nanopolycrystalline grain diameters.

Phase-field models for brittle and cohesive fracture

Abstract: In this paper we first recapitulate some basic notions of brittle and cohesive fracture models, as well as the phase-field approximation to fracture. Next, a critical assessment is made of the sensitivity of the phase-field approach to brittle fracture, in particular the degradation function, and the use of monolithic versus partitioned solution schemes. The last part of the paper makes extensions to a recently developed phase-field model for cohesive fracture, in particular for propagating cracks. Using some simple examples the current state of the cohesive phase-field model is shown.

Synthesis, mechanical properties, and in vitro biocompatibility with osteoblasts of calcium silicate-reduced graphene oxide composites.

Abstract: Calcium silicate (CaSiO3, CS) ceramics are promising bioactive materials for bone tissue engineering, particularly for bone repair. However, the low toughness of CS limits its application in load-bearing conditions. Recent findings indicating the promising biocompatibility of graphene imply that graphene can be used as an additive to improve the mechanical properties of composites. Here, we report a simple method for the synthesis of calcium silicate/reduced graphene oxide (CS/rGO) composites using a hydrothermal approach followed by hot isostatic pressing (HIP). Adding rGO to pure CS increased the hardness of the material by ∼40%, the elastic modulus by ∼52%, and the fracture toughness by ∼123%. Different toughening mechanisms were observed including crack bridging, crack branching, crack deflection, and rGO pull-out, thus increasing the resistance to crack propagation and leading to a considerable improvement in the fracture toughness of the composites. The formation of bone-like apatite on a range of C...

Effective toughness of heterogeneous media

Abstract: We propose a versatile approach to computing the effective toughness of heterogeneous media. This approach focusses on the material property independent of the details of the boundary condition. The key idea is what we call a surfing boundary condition, where a steadily propagating crack opening displacement is applied as a boundary condition to a large domain while the crack set is allowed to evolve as it chooses. The approach is verified and used to study examples in brittle fracture. We demonstrate that effective toughness is different from effective or weighted surface area of the crack set. Furthermore, we demonstrate that elastic heterogeneity can have a profound effect on fracture toughness: it can be a significant toughening mechanism and it can lead to toughness asymmetry wherein the toughness depends not only on the direction but also on the sense of propagation. The role of length-scale is also discussed.

Thermodynamically consistent algorithms for a finite-deformation phase-field approach to fracture

Abstract: SUMMARY Phase-field approaches to fracture offer new perspectives toward the numerical solution of crack propagation. In this paper, a phase-field method for finite deformations and general nonlinear material models is introduced using a novel multiplicative split of the principal stretches to account for the different behavior of fracture in tension and compression. An energy-momentum consistent integrator is developed and applied to the arising nonlinear coupled phase-field model. This approach is thermodynamically consistent in the sense that the first law of thermodynamics if fulfilled with respect to the dissipation function. The capabilities and the performance of the proposed approach is demonstrated in several representative examples. Copyright © 2014 John Wiley & Sons, Ltd.

Quasi-static and dynamic fracture behaviour of rock materials: phenomena and mechanisms

Abstract: An experimental investigation is conducted to study the quasi-static and dynamic fracture behaviour of sedimentary, igneous and metamorphic rocks The notched semi-circular bending method has been employed to determine fracture parameters over a wide range of loading rates using both a servo-hydraulic machine and a split Hopkinson pressure bar The time to fracture, crack speed and velocity of the flying fragment are measured by strain gauges, crack propagation gauge and high-speed photography on the macroscopic level Dynamic crack initiation toughness is determined from the dynamic stress intensity factor at the time to fracture, and dynamic crack growth toughness is derived by the dynamic fracture energy at a specific crack speed Systematic fractographic studies on fracture surface are carried out to examine the micromechanisms of fracture This study reveals clearly that: (1) the crack initiation and growth toughness increase with increasing loading rate and crack speed; (2) the kinetic energy of the flying fragments increases with increasing striking speed; (3) the dynamic fracture energy increases rapidly with the increase of crack speed, and a semi-empirical rate-dependent model is proposed; and (4) the characteristics of fracture surface imply that the failure mechanisms depend on loading rate and rock microstructure

Ductile Fracture Simulation of Structural Steels under Monotonic Tension

Abstract: This paper aims to predict ductile fracture of mild steel under monotonic loading only from the test results of notchless tensile coupons. A simple fracture model based on the concept of a ...

Effect of Stress Triaxiality on the Flow and Fracture of Mg Alloy AZ31

Abstract: The microscopic damage mechanisms operating in a hot-rolled magnesium alloy AZ31B are investigated under both uniaxial and controlled triaxial loadings. Their connection to macroscopic fracture strains and fracture mode (normal vs shear) is elucidated using postmortem fractography, interrupted tests, and microscopic analysis. The fracture locus (strain-to-failure vs stress triaxiality) exhibits a maximum at moderate triaxiality, and the strain-to-failure is found to be greater in notched specimens than in initially smooth ones. A transition from twinning-induced fracture under uniaxial loading to microvoid coalescence fracture under triaxial loading is evidenced. It is argued that this transition accounts in part for the observed greater ductility in notched bars. The evolution of plastic anisotropy with stress triaxiality is also investigated. It is inferred that anisotropic plasticity at a macroscopic scale suffices to account for the observed transition in the fracture mode from flat (triaxial loading) to shear-like (uniaxial loading). Damage is found to initiate at second-phase particles and deformation twins. Fracture surfaces of broken specimens exhibit granular morphology, coarse splits, twin-sized crack traces, as well as shallow and deep dimples, in proportions that depend on the overall stress triaxiality and fracture mode. An important finding is that AZ31B has a greater tolerance to ductile damage accumulation than has been believed thus far, based on the fracture behavior in uniaxial specimens. Another finding, common to both tension and compression, is the increase in volumetric strain, the microscopic origins of which remain to be elucidated.