Fracture Mechanics Considerations Research Articles

Stress Intensity Factors of Continuum Fracture Mechanics at the Nanoscale

The paper presents the analysis of the stress field in the neighborhood of the crack tip by molecular dynamics method implemented in a classical molecular dynamics code LAMMPS (Large-scale Atomic/Molecular Massively Parallel Simulator). The molecular dynamics simulations are aimed at computing continuum fracture mechanics parameters. Stress intensity factors for a copper plate with a central crack under Mode I and Mixed Mode loadings are evaluated with the help of atomistic modelling. The wide class of the computational experiments in LAMMPS is realized. The atomistic values of stress intensity factors are compared with the values obtained from continuum fracture mechanics considerations. It is shown that the continuum fracture theory successfully describes fracture even at extremely confined singular stress field of only several nanometers.

Lattice Discrete Particle Modeling of Size Effect in Slab Scratch Tests

AbstractFor a long time, geomechanicians have used scratch tests to characterize the compressive behavior and hardness of rocks. In recent years, this test has regained popularity in the field of mechanics, especially after a series of publications that highlighted the potential capability of the scratch test to determine the fracture properties of quasi-brittle materials. However, the complex failure mechanisms observed experimentally in scratch tests led to scientific debates and, in particular, raised the question of the size effect. This article intends to provide a better understanding of the problem by using numerical tools and fracture mechanics considerations. To narrow the investigation area, this study focuses on slab scratch tests of quasi-brittle materials and adopts two different numerical methods: (i) the lattice discrete particle model (LDPM) that includes constitutive laws for cohesive fracturing, frictional shearing, and nonlinear compressive behavior, and (ii) the meshless method based on Shepard function and partition of unity (MSPU) implementing linear elastic fracture mechanics (LEFM). The numerical results are further analyzed through Bažant’s size effect law (SEL) with an appropriate mixed-mode fracture criterion. Fracture properties are then calculated and compared to the results of typical notched three-point bending tests. The results show that mixed-mode fracture considerations are of paramount importance in analyzing the fracture process and size effect of scratch tests.

Effect of microstructure and cycling frequency on the torsional fatigue properties of 17-4PH stainless steel

Torsional fatigue tests in the high and very high cycle regime were performed with martensitic stainless steel 17-4PH. Tests were conducted with a servo-hydraulic machine and an ultrasonic equipment at cyclic frequencies of 15–35 Hz and 19 kHz, respectively. Fatigue lifetimes were significantly longer for smooth specimens tested at 19 kHz. Fatigue limits were not affected by testing frequency. This behaviour was explained by the presence of δ ferrite grains, in which crack initiation at conventional frequency is accelerated, but their size is too small to significantly decrease the fatigue limit. In the presence of detrimental defects – i.e. small drilled holes that were introduced into test specimens –, no frequency effect could be observed. The geometry of non-propagating shear cracks emanating from δ ferrite grains and in the martensitic matrix was measured by stepwise polishing of a run-out specimen. Fracture-mechanics considerations suggest that the threshold condition for the propagation of Mode-I cracks determines the fatigue limit under torsional loading.

Numerical determination and experimental verification of the optimum autofrettage pressure for a complex aluminium high‐pressure valve to foster crack closure

AbstractThe determination of the optimum autofrettage pressure enables a clear improvement of the fatigue life for an internally highly pressurized component. The autofrettage process induces residual compressive stress after the release of a single static overload pressure, leading to plastic deformation at the inner wall whereas the outer part is only elastically stressed. This autofrettage pressure is clearly above the subsequent pulsating operating pressure range. Due to the complex geometry of the aluminium valve body, a detailed elastic–plastic finite element analysis is used to determine the critical area and the optimum autofrettage pressure. Based on an experimental stress–strain curve, three important load steps are simulated in a non‐linear way. The FKM guideline is used to assess fatigue life and crack initiation with detailed subsequent experimental verification. Even if small cracks occur, residual compressive stresses prohibit crack growth (nonpropagating crack), which can be analytically verified by fracture mechanical considerations (crack closure effect).

Determination of the influence of a stress-relief heat treatment and additively manufactured surface on the fatigue behavior of selectively laser melted AISI 316L by using efficient short-time procedures

To use Additive Manufacturing (AM) technology for production of safety critical structural components, it is indispensable to investigate thoroughly the materials AM specific microstructure as well as the resulting mechanical and especially cyclic properties. Besides their special microstructure, AM materials show a highly inhomogeneous distribution of residual stresses as well as numerous process induced microstructural notches, e.g. pores in the materials volume and high roughness of additively manufactured surfaces. Therefore, in production of AM components stress-relief heat treatments as well as surface post-processing are commonly used. In the present work, the influence of stress-relief heat treatment as well as the additively manufactured surface condition on the cyclic properties was investigated at selectively laser melted (SLM) specimens made of AISI 316L stainless steel. Specimens were manufactured in horizontal as well as vertical building direction, leading to layer planes oriented parallel and perpendicular to the loading direction, respectively. To reduce the high material and time effort in fatigue investigations, the short-time methods PhyBaLCHT, which is based on cyclic indentation tests and enables a characterization of the materials defect tolerance, as well as load increase tests (LITs) were used for qualitative analyzes of the cyclic deformation behavior. Moreover, the physically based lifetime calculation approach (PhyBaLLIT) was applied for quantitative determination of the fatigue behavior of heat treated specimens, showing excellent correlation to additional constant amplitude tests (CATs), performed for validation. While the heat treatment does not significantly influence the fatigue behavior of vertically built specimens, an increase of fatigue strength could be observed for horizontal building direction, which is mainly caused by an improved defect tolerance. The higher defect tolerance was determined with PhyBaLCHT and could be proved by fracture mechanics considerations using the area-concept. Furthermore, the results show a significantly lower fatigue lifetime for additively manufactured surface condition compared with polished samples, which is more pronounced for vertically built specimens, because of the higher surface roughness of specimens manufactured in this building direction. Moreover, a double-staged S-Nf curve could be observed for specimens with additively manufactured surface, which correlates to the cyclic deformation behavior observed in LITs and CATs.

On the crack-driving force of phase-field models in linearized and finite elasticity

The phase-field approach to fracture has been proven to be a mathematically sound and easy to implement method for computing crack propagation with arbitrary crack paths. Hereby crack growth is driven by energy minimization resulting in a variational crack-driving force. The definition of this force out of a tension-related energy functional does, however, not always agree with the established failure criteria of fracture mechanics. In this work different variational formulations for linear and finite elastic materials are discussed and ad-hoc driving forces are presented which are motivated by general fracture mechanical considerations. The superiority of the generalized approach is demonstrated by a series of numerical examples.

Strength limits in mesoscaled 3Y-TZP ceramics for micro-surgical instruments

Micro-surgical instruments are a new application for mesoscale ceramics formed using the lost mold-rapid infiltration forming (LM-RIF) process. Instrument strength and reliability are the foremost concerns for this sensitive application. It is hypothesized that increasing grain size can improve the damage tolerance of the parts associated with the transformation toughening in the 3Y-TZP material, while retaining high strength. In this work, mesoscale bend bars (314 × 22 × 18 µm) of 3Y-TZP fabricated using the LM-RIF process were heat treated at 1400 °C for 1 h, 8 h, or 16 h, respectively, to obtain samples with different grain sizes. Strength tests were performed under three-point bending and results were evaluated using Weibull statistics. Fractographic and confocal Raman spectroscopic analyses were carried out to interpret the data.Experimental findings showed that the characteristic strength decreased with increasing grain size contrary to the damage tolerance hypothesis. An Orowan-Petch model was recalled to correlate the strength with the flaw size to grain size ratio. At fine grain sizes the strength was controlled by the flaws introduced by the LM-RIF process, whereas at large grain sizes the strength become more grain size controlled. Although larger-grained samples did have a higher propensity to transform, and thus increase toughening, exaggerated grain growth in some of the specimens tested caused an additional flaw population which led to an overall lower strength. Finally, based on the experimental observations and fracture mechanics considerations, we believe that an upper bound of ∼2.5 GPa exists for the strength of mesoscale as-fabricated 3Y-TZP ceramic parts.

Grafting carbon nanotubes onto carbon fibres doubles their effective strength and the toughness of the composite

Bioinspiration can lead to exceptional mechanical properties in a number of biological materials as a result of their internal structure. In particular, the hierarchical arrangement of nano-to macro-components can bring to complex energy dissipation mechanisms and unprecedented resistance to crack growth. In this work, we propose to exploit this approach, combining in a multiscale composite structure carbon nanotubes with conventional carbon fibre reinforcements in a polyvinyl butyral matrix. We show that grafting the nanotubes onto the carbon microfibres improves their interface properties with the matrix considerably, effectively doubling their apparent strength. At the same time, the addition of nanotubes to microfibre reinforcements helps to improve the composite toughness, reaching more than twice the value for the conventional, non-hierarchically reinforced composite. Numerical simulations and fracture mechanics considerations are also provided to interpret the results.

Fatigue assessment of welded joints in API 579-1/ASME FFS-1 2016 - existing methods and new developments

The 3rd Edition of API 579-1/ASME FFS-1 2016 Fitness-For-Service includes a new Part 14 dedicated to fatigue assessment. An important section in this part covers the fatigue assessment of welded joints. In this paper, an overview of the fatigue methods for welded joints is provided and extensions are recommended. First, an overview is given of the classical fatigue method used in the ASME B&PV Code based on smooth bar fatigue curves in conjunction with a fatigue strength reduction factor. In addition, the mesh insensitive structural stress method is outlined using an equivalent stress parameter based on fracture mechanics considerations in conjunction with a master S-N curve based on the analysis of over 2000 high and low cycle S-N test data. The resulting master S-N curve approach is applicable to high cycle fatigue and low cycle fatigue if a Neuber correction is introduced. In this paper, a new structural strain method is presented to extend the early structural stress based master S-N curve method to the low cycle fatigue regime in which plastic deformations can be significant while an elastic core is present. With this new method, some of the inconsistencies of the pseudo-elastic structural stress procedure can be eliminated, such as its use of Neuber’s rule in approximating structural strain beyond yield. The earlier mesh-insensitive structural stress based master S-N curve method can now be viewed as an application of the structural strain method in the high cycle regime, in which structural strains are linearly related to traction-based structural stresses according to Hooke’s law. Thus, both low cycle and high cycle fatigue behavior can now be treated in a unified manner. In the low-cycle regime, the structural strain method characterizes fatigue damage directly in terms of structural strains that satisfy a linear through-thickness deformation gradient assumption, material nonlinear behavior, and equilibrium conditions. A PVRC Joint Industry Project is currently sponsoring work on the structural strain method that will lead to its incorporation in the next edition of API 579-1/ASME FFS-1.

Modeling the lifetime reduction due to the superposition of TMF and HCF loadings in cast iron alloys

The superposition of small amplitude, high frequency loading cycles (HCF) to slow, large amplitude loading cycles (TMF) can significantly reduce the fatigue life. In this work, the combined TMF+HCF loading has been experimentally investigated for a cast iron alloy. In particular, the influence of the HCF frequency of the HCF amplitude and of the location of the superposed HCF cycles has been assessed. It was observed that the HCF frequency has a limited impact on the TMF fatigue life. On the other side, the HCF-strain amplitude has a highly non-linear influence on the TMF fatigue life. A simple estimate for the fatigue life reduction due to the superposed HCF cycles has been derived from fracture mechanics considerations. It is assumed that the number of propagation cycles up to failure can be neglected after a threshold for the HCF loading has been reached. The model contains only two adjustable parameters and can be combined with any TMF life prediction model. The model predictions are compared with the test results for a large range of TMF+HCF loading conditions.

Length scale of interface heterogeneities selects propagation mechanism of frictional slip fronts

We present three-dimensional finite-element simulations showing the propagation of slip fronts at striped heterogeneous interfaces. The heterogeneous area consists of alternating stripes of weaker and stronger frictional properties, which is equivalent to a lower and higher fracture energy, respectively. By comparing the slip front propagation at interfaces that differ solely by the length scale of the heterogeneous pattern, we illustrate that two different propagation regimes exist. Interfaces with wide stripes present slip fronts with propagation speeds that transition from sub-Rayleigh to inter-sonic. Thinner stripes are, however, characterized by the propagation of sub-Rayleigh slip fronts, which are preceded by slip pulses of negligible slip in the weaker stripes. From a macroscopic point of view, an interface with a smaller heterogeneous pattern appears to be stronger than the equivalent coarser interface even though both have the same average properties. The numerical results as well as a theoretical approach based on fracture-mechanics considerations suggest that the origin of these two distinct propagation mechanisms lies in the interaction between the length scales of the cohesive zone and the heterogeneous configuration. We further show by estimating the relevant length scales that the occurring propagation mechanism is influenced by the friction weakening rate of the interface as well as the shear modulus of the bulk material.

Experimental validation of inspection intervals for railway axles accompanying the engineering process

In the paper an example of successful cooperation between an operator, a vehicle manufacturer, a wheelset supplier and a research institute is presented demonstrating the current state of a design procedure which aims at meeting wheelset specification requirements recently adopted by the Deutsche Bahn (DB). Different from the conventional praxis, these requirements incorporate the fracture mechanics approach for determining inspection intervals of railway axles. The procedure includes the wheelset dimensioning based on current railway standards, fracture mechanics considerations to assess subcritical crack propagation starting from a crack size just below the detection limit, and crack propagation tests on full-scale axles under load spectrum representative of in-service conditions. The paper describes different steps of the procedure, while mainly focusing on fracture mechanics – both computational and experimental – issues.

Multilevel approach to lifetime assessment of steam turbines

• Deterministic and probabilistic method of lifetime assessment is presented. • Effect of creep and fatigue damage content on failure probability is analyzed. • Practical application shown by example of lifetime calculation of turbine rotor. This paper presents a multilevel methodology for a steam turbine lifetime assessment based on the damage calculation, probabilistic analysis and fracture mechanics considerations. Creep-fatigue damage calculations serve as a basis for evaluating the current lifetime expenditure and for defining additional steps of analysis. The need for the use of probabilistic analysis results from the inherent uncertainty in estimating the lifetime expenditure primarily caused by scatter in material properties. Fracture mechanics considerations are helpful in determining additional safety margins for components containing cracks. This methodology has been illustrated using an example of the lifetime calculations of a high-temperature steam turbine rotor. The calculations were based on the results of 2D numerical simulations performed for steady state and transient operating conditions.

Improvements of strength and fracture resistance by spatial material property variations

A material with spatial variation in the elastic modulus E can have a much higher apparent fracture resistance and fracture stress than a comparable homogeneous material. The effect occurs due to the strong decrease of the crack driving force, which leads to crack arrest when the crack tip is located in the region with low elastic modulus. From the results of exemplary numerical studies and simple fracture mechanical considerations, models are derived in order to predict the fracture stress and fracture toughness of the inhomogeneous materials. It is shown that high values of fracture stress and fracture toughness can be reached if the amplitude of the E variation is high enough to provide crack arrest and the wavelength of the E variation is small. The beneficial effect of material property variations also occurs if the width of the compliant region is very thin and the loss in stiffness of the structure is almost negligible. The concept is applicable for various types of composite materials; examples are presented.

On the use of spring models to analyse the lateral-torsional buckling behaviour of cracked beams

This paper is focused on the lateral-torsional buckling of cracked or weakened elastic beams. The crack is modelled with a generalised elastic connection law, whose equivalent stiffness parameters can be derived from fracture mechanics considerations. The same type of generalised spring model can be used for beams with semi-rigid connections, typically in the fields of steel and timber engineering. As the basis for the present investigation, we consider a strip beam with fork end supports and exhibiting a single vertical edge crack, subjected to uniform bending in the plane of greatest flexural rigidity. We adopt both direct and variational approaches. In the former, conducted within the framework of the Kirchhoff–Clebsch theory, the effect of prebuckling curvature is taken into consideration. This effect is subsequently neglected in the variationally based analyses. First, the three-dimensional elastic connection law adopted is a direct extension of the planar case, which leads to a paradoxical conclusion: the critical moment is not affected by the presence of the crack, regardless of its location. It is shown that the above paradox is due to the non-conservative nature of the connection model adopted (in the sense that the connection law cannot be derived from a potential). Simple alternatives to this cracked-section constitutive law are proposed, based on conservative moment-rotation laws (quasi-tangential and semi-tangential) and consistent variational arguments. Only one of the proposed alternatives leads to a critical moment that depends on both the torsional and flexural stiffnesses of the spring modelling the cracked cross-section. The analyses are always conducted analytically, yielding closed-form characteristic equations for the buckling moments.

Comparative tectonofractography: fracturing in 19 jointing provinces, experimental results, fracture mechanics considerations and province classification

Comparative tectonofractography: fracturing in 19 jointing provinces, experimental results, fracture mechanics considerations and province classification

Impact of scaling on fracture strength of adhesively bonded fibre-reinforced polymer piping

The development of fibre-reinforced polymer (FRP) piping with high corrosion resistance and specific properties is an attractive engineering proposition with high potential. Advantageous properties make FRP piping a potential candidate for replacing metallic piping structure in the oil and gas industry. Despite the advantages associated with FRP, their application is limited due to, in part, unsatisfactory methods for joining composite subcomponents and inadequate knowledge of failure mechanism under different loading conditions. Aim of the present paper is to study the effect of pipe scaling on the strength of adhesively bonded FRP pipes. Using finite element analysis, a study was performed to investigate dimensional effects on adhesive joint strength based on strength-of-materials and fracture mechanics considerations. Results indicate a shift in failure from adhesive to composite material with increasing pipe diameter. The Tsai-Wu and von Mises failure criteria were employed for the strength analysis of composite pipe sections and the adhesive material, respectively. A fracture mechanics approach was used to assess changes from cohesive failure (within adhesive) to interfacial failure (adhesive/FRP interface) with increasing pipe diameters. © 2011 Published by Elsevier Ltd. Selection and peer-review under responsibility of ICM11

Thermal shock fracture in cross-ply fibre-reinforced ceramic–matrix composites

The onset of matrix cracking due to thermal shock in a range of simple and multi-layer cross-ply laminates comprising a calcium aluminosilicate (CAS) matrix reinforced with Nicalon® fibres is investigated analytically. A comprehensive stress analysis under conditions of thermal shock, ignoring transient effects, is performed and fracture criteria based on either a recently derived model for the thermal shock resistance of unidirectional Nicalon®/glass ceramic–matrix composites or fracture mechanics considerations are formulated. The effect of material thickness on the apparent thermal shock resistance is also modelled. Comparison with experimental results reveals that the accuracy of the predictions is satisfactory and the reasons for some discrepancies are discussed. In addition, a theoretical argument based on thermal shock theory is formulated to explain the observed cracking patterns.

Material model for finite element modelling of fatigue crack growth in concrete

Although fatigue damage of concrete is an important problem in structures subjected to cyclic loading, there are not many highcycle fatigue models available for use in conjunction with advanced concrete material models and nonlinear finite element analysis. The available models that are published in the literature (for instance [1]) usually deal with the low cycled fatigue when it is necessary to perform the numerical nonlinear analysis for all investigated cycles. This approach is definitely not applicable when it comes to high-cycle fatigue when it is usually necessary to consider millions of cycles. The available models (for instance [2]) for high-cycled fatigue are based on linear elastic fracture mechanics considerations and they are not readily applicable to the finite element analysis using the smeared crack approach.The three-dimensional fracture-plastic model [3] in the finite element software ATENA has been extended to capture fatigue damage in tension (however, the model can be easily modified to also consider damage from compressive and tensilecompressive loads). The damage can result in new cracks or growth of existing ones.To keep the material model as simple as possible, the implementation is based on a classical stress based model (S-N or Wöhler curve). The S-N criterion is translated into material damage, which is introduced into the material model on the basis of stress increments at each material point and the number of cycles. The S-N criterion is suitable to initiate damage into the intact material. However, in order to facilitate the necessary crack propagation and extension of a pre-existing damage an additional damage needs to be introduced. It is advantageous to base this damage not on stress cycles but rather on the cycles of crack opening displacements (delta COD). The paper will present the formulation of the new model for the high-cycle fatigue in a form that is suitable for the smeared crack model formulation and the finite element analysis. The model behaviour will be documented on small theoretical examples as well as by comparison with experimental data.

Design against fracture of functionally graded thermal barrier coatings using transformation toughening

This study presents a new theoretical model for design against fracture of zirconia-toughened functionally graded thermal barrier coatings (FG TBCs). A micromechanics-based model, which investigates the effect of the mismatch in material properties of the constituent phases on the transformation toughening mechanism in zirconia-enriched multi-phase composites, has been incorporated with the lamination theory. The developed model enables to engineer ZrO 2-toughened multi-phase FG TBCs with required or pre-determined fracture properties by utilizing the synergetic characteristics of their constituent phases. A simulation for ZrO 2/Ni FG TBC plates subjected to thermal shock loadings has been conducted. The results demonstrated that within the compositional gradation investigated, the substrate metal (Ni)-rich compositional gradation contributed to high fracture-resistant properties based on fracture-mechanics considerations. This tendency was theoretically and experimentally confirmed with results available in the open literature.