Fracture Mechanics Parameters Research Articles

Fracture behavior of reactor steel 20MnMoNi 55 in the transition temperature region

The fracture represents the final phase of crack propagation, and the causes of their occurrence or partial crack propagation in the real constructions made of ferritic steels can be different. Along with cracks, influences such as stress concentration and low temperature contribute to fracture being “faster” and have an impact on the fracture mechanics parameters, as well as on the fact that fracture is more likely to occur due to cleavage. The parameters discussed in this study are Jc and rc (parameter, i.e. distance between fatigue crack tip and cleavage initiation site) by testing of C(T)50 specimen in the transition temperature region. Grooved C(T) specimens were made of reactor steel 20MnMoNi 55 with two thickness values, since an additional goal of this study was to present the influence of thickness of tested specimens. Along with it, other parameters that have influence on the understanding of transition temperature region and fracture in this region of ferritic steel are presented.

Influence of discontinuities on fatigue strength using the example of additively manufactured specimens made of AlSi10Mg

Fatigue strength is largely affected by the influence of discontinuities: geometric notches like holes and corners in components, surface notches (roughness), pores and inclusions in the material. Therefore fatigue of structures and materials is a local problem and fatigue strength calculations are best carried out using local approaches such as local stress concept, local strain concept or fracture mechanical concepts. In this investigation, the influence of discontinuities on low cycle and high cycle fatigue strength of materials was examined on the example of additively produced material specimens made of aluminium AlSi10Mg by using a fracture mechanics parameter. Results of fatigue tests on hourglass-specimens made from four different series of 3-D printed specimens are presented. The examination of the fracture surfaces revealed that damage always started from pores located near the surface of the specimens. The fractography gave information about geometry, size and position of the crack-causing pores. The influence of such pores on the fatigue strength of the printed aluminium was investigated by using a modification of Murakami’s √area parameter. The common scatter band of the four test series could thus be reduced significantly.

Photoelastic evaluation of stress fields and coefficients of multi-parameter asymptotic expansion of the crack-tip stress field

In this work, digital photoelasticity method is appliedfor estimation of the crack tip fracture mechanics parameters for a plate with double edge notches and different crack configurations.The digital image processing tool for experimental data obtained from the photoelasticity experiments is developedand utilized. The digital image processing tool is based on the Ramesh approach but allows us to scan the image in any direction and to analyse the image after any number of logical operations. In the digital image processing fringe analysis, the optical data contained in the transmission photoelasticisochromatics were converted into text file and then the points of isochromatic fringes with minimum light intensity were used for evaluating fracture mechanics parameters. The multi-parameter stress field approximation is used. The mixed mode fracture parameters, especially stress intensity factors (SIF) are estimated for specimen configurations like double edge notches and inclined center crack using the proposed algorithm based on the classical over-deterministic method. The effects of higher-order terms in the Williams expansion were analysed for different cracked specimens. It is shown that the higher order terms are needed for accurate characterization of the stress field in the vicinity of the crack tip. The experimental SIF values estimated using the proposed method are compared with analytical/finite element analysis (FEA) results, and are found to be in good agreement.

Fracture parameters of alkali-activated aluminosilicate composites with ceramic precursor: durability aspects

Four sets of alkali-activated aluminosilicate (AAAS) composites based on ceramic precursors were studied in terms of their characterization by mechanical fracture parameters as a basis for considerations of durability. AAAS composites made of brick powder as a precursor and alkaline activator with various silicate moduli (Ms = 0.8, 1.0, 1.2, 1.4, and 1.6) were investigated. The sets of AAAS composites differed in terms of the used filler: quartz sand or brick rubble. Two different precursor particle size ranges of 0–1 mm and 0–0.3 mm were used for both types of filler. The test specimens had nominal dimensions of 40 × 40 × 160 mm and were provided with a notch at midspan after 28 days of hardening. The notches were cut up to 1/3 of the height of the specimens. The specimens were subjected to three-point bending fracture tests during which force vs. deflection (F–d) and force vs. crack mouth opening displacement (F–CMOD) diagrams were recorded. Tensile strength ft,ID and specific fracture energy GF,ID values were identified using the inverse method based on a neural network ensemble. The obtained F–CMOD diagrams were subsequently evaluated using the double-K fracture model supported by the ft,ID and GF,ID values. The double-K model allows the quantification of two different levels of crack propagation: initiation, which corresponds to the beginning of stable crack growth, and unstable crack propagation.

Atomistic Determination of Fracture Mechanics Parameters

Stress intensity factors, T-stresses and higher order coefficients in the Williams series expansion are the fundamental concepts of continuum fracture mechanics for characterizing the stress fields around the crack tip in a homogeneous material in the linear regime. It is well-known that critical values of stress intensity factors stipulate the of materials to growth a crack. Nowadays the modern multi-purpose computational tools such as Simulia Abaqus allow us to calculate T-stresses in cracked specimens and structures along with stress intensity factors. The aim of this study is to understand if one can obtain this fracture parameters of conventional fracture mechanics from atomistic simulations based on molecular dynamics method. The ability to describe fracture processes at atomic scale by means of stress intensity factors, T-stresses and higher-order coefficients will provide the opportunity to take into account many effects such as material microstructures, chemical compositions and concentrations and others. In this study the values of stress intensity factors, T-stress and coefficients of the Williams series expansion are determined using atomistic simulations based on molecular dynamics method with a classical molecular dynamics code Large-scale Atomic/Molecular Massively Parallel Simulator. The over-deterministic method is used to determine SIFs, T-stresses and coefficients of higher-order terms from molecular dynamics modelling of a plate with a central crack. The accuracy of the proposed approach is tested for this rather simple cracked configuration. There is the theoretical analytical solution with all the coefficients of the higher-order terms in the Williams series expansion. The existing theoretical solution allows us to compare the angular distributions of the stress tensor components for a large plane with the central crack. It is shown that results obtained from molecular dynamics simulations and the theoretical analytical solutions coincide qualitatively.

Investigation of Crack Propagation Behaviors in a Fillet Welded Joint Employing X-FEM

A fillet welded joint has been used for ship and offshore structures. During the welding process, unwelded parts remain in the structure. When a crack propagates from the web plate to the joint across the unwelded part, interesting crack propagation (CP) phenomena, i.e., crack front separation and crack coalescing, were observed. In the present study, threedimensional CP simulation is carried out to carefully investigate the fracture behaviors. X-FEM, a powerful computational fracture mechanics analysis method, is adopted. A crack option in an open source CAE software Code Aster is chosen. It is found that a modification is needed to analyze the complicated fracture behaviors appropriately. The analysis control file and source code have been modified to improve accuracy for the evaluation of fracture mechanics parameter and crack path. With the present approach, the complicated fracture phenomena can be solved effectively. The fracture behavior is discussed well with the crack trajectories and history of the fracture mechanics parameters for the propagating crack.

The Size Effect and Microstructure Changes of Granite after Heat Treatment

High temperature can change the mechanical properties of granite, with significant nonlinear characteristics, and at the same time change its microstructure. Therefore, two kinds of granites are used in this paper: one is normal temperature granite and the other is granite treated at 600°C, and a detailed comparative study is made. The fracture toughness of two kinds of rocks was tested by fracture tests, and the results were analyzed by a nonlinear fracture mechanics model (SEL). At the same time, in order to understand the influence of high temperature on the mineral composition and microstructure of granite, XRD, optical microscope, and SEM were used to observe the mineral composition, microcracks, and fracture morphology of granite. The results show the following: (1) high temperature significantly changes the fracture mechanics parameters of granite. The fracture toughness of granite treated at 600°C is significantly lower than that of untreated granite, which is reduced by more than 60%. (2) No obvious size effect was found in the untreated granite, while the size effect of the granite after treatment at 600°C was significant. (3) The granite after high‐temperature treatment showed strong nonlinear characteristics, and the SEL can reasonably describe and explain its nonlinear fracture characteristics. (4) The brittleness of the granite treated at 600°C decreased and the ductility increased. The microscopic morphology of the fracture was rough, with obvious steps and rivers. The microcracks and porosity had increased significantly, but the main components did not change significantly.

Risk assessment based on analytical evaluation of structural integrity and life of drilling rig pipe

Risk assessment procedure based on structural integrity evaluation has been applied to oil drilling rig pipe. The new concept based on application of structural integrity evaluation to assess risk level according to probability and consequence of failure was used. Analytical expressions for surface cracks are used to calculate stress intensity factors for different crack geometries. Oil drilling rig welded pipe integrity has been evaluated analytically by simple application of the Failure Assessment Diagramme (FAD), i.e. by using the ratio of linear elastic fracture mechanics parameter, KI, and its critical value, KIc, in relation with the ratio of applied stress and its critical value, to define the point in FAD. Probability of failure is then taken according to the position of the point in the FAD, corresponding to oil drilling rig welded pipe data. The same logic is employed in the case of cyclic loading, i.e. fatigue crack growth. In that case, structural life is estimated by using Paris law to calculate crack length vs. number of cycles, to be used in risk assessment procedure and by managers to make decision about further use of damaged pipes, based on data provided by engineers.

Influence of rock inclusion composition on the fracture response of cement-based composite specimens

This paper concerns the results of research into the influence of the composition of rock inclusions on the fracture response of cement-based composite specimens. Specially designed specimens of the nominal dimensions 40 × 40 × 160 mm with inclusions in the shape of prisms with nominal dimensions of 8 × 8 × 40 mm were provided with an initial central edge notch with a depth of 12 mm. These specimens, which were made of fine-grained cement-based composite with different types of rock inclusion – amphibolite, basalt, granite, and marble – were tested in the three-point bending configuration. Fracture surfaces were examined via scanning electron microscopy and local response in the vicinity of rock inclusions was characterized via the nanoindentation technique. The aim of this paper is to analyse the influence of the chemical/petrographic composition of rock inclusions on the effective mechanical fracture parameters of cement-based composites, as well as on the microstructural mechanical parameters of the interfacial transition zone. The results of this research indicate the significant dependence of the effective fracture parameters on the petrographic and related chemical composition of the rock inclusions.

Mechanical Fracture and Fatigue Characteristics of Fine-Grained Composite Based on Sodium Hydroxide-Activated Slag Cured under High Relative Humidity

A typical example of an alternative binder to commonly used Portland cement is alkali-activated binders that have high potential as a part of a toolkit for sustainable construction materials. One group of these materials is alkali-activated slag. There is a lack of information about its long-term properties. In addition, its mechanical properties are characterized most often in terms of compressive strength; however, it is not sensitive enough to sufficiently cover the changes in microstructure such as microcracking, and thus, it poses a potential risk for practical utilization. Consequently, the present study deals with the determination of long-term mechanical fracture and fatigue parameters of the fine-grained composites based on this interesting binder. The mechanical fracture parameters are primarily obtained through the direct evaluation of fracture test data via the effective crack model, the work-of-fracture method, the double-K fracture model, and complemented by parameter identification using the inverse analysis. The outcome of cyclic/fatigue fracture tests is represented by a Wöhler curve. The results presented in this article represent the complex information about material behavior and valuable input parameters for material models used for numerical simulations of crack propagation in this quasi-brittle material.

On elastic-plastic and creep fracture mechanics parameters estimates of non-idealized axial through-wall crack in pressurized pipe

The present paper provides engineering estimates for plastic J-integral and crack opening displacement (COD) of a non-idealized axial through-wall crack (TWC) in pipes based on detailed 3-dimensional finite element (FE) analyses. The behaviors of plastic J-integral and COD of a non-idealized axial TWC in typical pressurized pipes in nuclear power plants were systematically investigated. The FE model and analysis procedure employed in this study were verified by comparing the present FE results with the limited existing solutions for pipes with an idealized axial TWC. Based on the FE results, the new plastic influence functions, h1 and h2, which include the effect of a non-idealized TWC on plastic J-integral and COD, are provided as tabular solutions. By employing the plastic influence functions, plastic J-integral and COD of a non-idealized axial TWC along crack front can be directly predicted based on GE/EPRI method. In the present paper, plastic J-integral and COD estimates based on the reference stress concept have also been suggested. Finally, the estimated results were compared with elastic-plastic FE results by using actual stress-strain data and Ramberg-Osgood constants for TP 316 stainless steel. In addition, the engineering estimates proposed in this study were extended to estimating the creep fracture mechanics parameters at elevated temperature. Based on Norton and RCC-MRx creep models, C*-integral and creep COD rate values predicted from the present engineering solutions were validated by comparing with creep FE results. The results provided in this paper demonstrate that the present estimates can be applied to calculating plastic J-integral and COD, C*-integral, and creep COD rate of a non-idealized axial TWC.

Comprehensive fracture tests of concrete for the determination of mechanical fracture parameters

AbstractAdvanced experimental evaluation of the mechanical fracture properties of quasi‐brittle materials is an important part of the design, assessment, and computational modeling of structures made of these materials. The aim is to determine parameters independent of the test configuration or the size of the test specimens. This paper presents the results of an extensive experimental program which is part of the development of a comprehensive multilevel approach for experimental–computational determination of the mechanical fracture parameters of concrete. Three‐point bending and wedge‐splitting tests were performed simultaneously using three different geometrically similar specimen sizes and two well‐separated depths of initial notches. Before the start of the main testing program, the pilot tests that were performed were aimed at the design of the most appropriate concrete mixture. Special attention was paid to the selection of a maximum aggregate grain size. In order to study the process of concrete aging and the development of its mechanical properties, the accompanying destructive and non‐destructive tests were carried out at different ages of hardening. Fracture parameters were evaluated using the effective crack‐length formulation and work‐of‐fracture method. Finally, the size‐independent specific fracture energy was back‐calculated from the measured specific fracture energy.

Application of Fracture Mechanics Parameters to Spherical Storage Tank Integrity Assessment

Application of Fracture Mechanics Parameters to Spherical Storage Tank Integrity Assessment

Consolidated derivation of fracture mechanics parameters and fatigue theoretical evolution models: basic review

Presence of cracks lead to structural steels failure below critical yield strength. The primary aim of the present article is to simplify and consolidate mathematical derivation of stress concentration, fracture stress, stress intensity factor, crack tip opening displacement and J-integral parameters from the first principle as well as application to fatigue. The review explains the mathematical derivation of fracture mechanics parameters from the theoretical concept, including alternatives to fatigue life prediction with strain-based approach method. The stress concentration around a notch can only be performed if the radius of the notch is far greater than zero and the stress field at sharp crack shows singularity when the crack tip radius is equal to zero. Furthermore, blunted crack tip violates stress singularity, while the crack tip opening displacement and J-integral parameters show the solution of a crack extending beyond zero crack tip radius, thus are used to characterize material stress fields with blunted crack tip. The review highlights benefit of characterizing fatigue crack growth with J-integral and crack tip opening displacement parameters over stress intensity factor. This paper would benefit majorly engineers and specialists in nuclear, aviation, oil and gas industries.

Evolution of the fracture mechanics parameters in the vicinity of the hole in conditions of low-cycle fatigue according to the data of modeling a crack with narrow notches

We propose a new method for studying the effect of low-cycle fatigue on the evolution of the fracture mechanics parameters in conditions of loading plane specimens with stress concentrators. Three programs of loading with a constant value of the stress range and different values of the stress ratio, as well as two programs with a constant value of the stress ratio but different stress ranges are considered. One program is common for both cases. All the programs include uniaxial tension-compression. Each program was implemented by testing a batch of the same specimens from seven to nine in each. One specimen from each batch was assigned to assess the durability. The other specimens were brought to various stages of low-cycle fatigue in each program. Experimental data were obtained for cracks of different length which were modeled by a sequence of three narrow notches launched from a through hole in a rectangular specimen. Each notch was exposed to constant external load of the same level. The deformation response to a small increment in the notch length at a constant external load was measured at different stages of low-cycle fatigue using electronic speckle pattern interferometry. The interference fringe patterns used as initial experimental data provided determination of the tangential components of in-plane displacements directly on the notch sides and the values of notch opening were thus determined from the results of direct measurements. The transition from measured displacement components to the values of the stress intensity factor and T-stress was performed using the relationships of a modified version of the crack compliance method based on Williams formulation. Distributions of the fracture mechanics parameters along the notches were obtained at various stages of cyclic loading. The dependences of the crack mouth opening displacement, the stress intensity factor and the T -stress on the number of loading cycles are constructed for the notches of a fixed length at different stages of low-cycle fatigue. It is shown that experimental distributions of the stress intensity factor values over the life time practically coincide for all four combinations of the loading cycle parameters.

Fracture Mechanical Characterization of Adhesively Bonded Wood-Ceramic Interfaces for Mode I Loading

Abstract This study introduces a novel approach for investigating the fracture behavior and technical quality of adhesively bonded wood-ceramic interfaces for Mode I loading. For that, a special test arrangement originally used for quasi-brittle materials was applied. The key benefit of this innovative concept is the ability to describe postcracking behavior that is due to stable and steady recording of load-displacement diagrams. This is a big benefit over common practice techniques from both a mechanical and fracture mechanical point of view. The reason for this is that the quasi-brittle material’s nature of unstable cracking comes into place when the test setup is not stiff enough. Another reason to apply fracture mechanics over continuum mechanics is the ability to identify quantitative parameters that describe the softening process in terms of fracture energy. This is a great benefit over stress-based concepts, such as the stress intensity approach (K-concept), which is not appropriate for adhesively bonded multimaterial interfaces. To demonstrate this new approach, bonded wood-ceramic composites were investigated using four different industrial adhesives from Sika AG (Baar, Switzerland) and Murexin (Wiener Neustadt, Austria). The findings indicated interesting relationships between adhesive bonding strength and crack growth resistance when it comes to changing the material of one bonding partner from wood to ceramic. Polyurethane-based adhesives especially show the highest potential of bonding power and fracture resistance when Mode I loading is applied. Furthermore, acrylate-based adhesives are capable of high improvement gains of both mechanical and fracture mechanical parameters when adhesively bonded wood-ceramic interfaces are investigated. This is a remarkable effect and should be part of future investigations by also incorporating the economical aspects of adhesive selection in terms of benchmarking. Finally, these findings could be used for optimizing the mechanical and chemical properties of hybrid adhesives in the future.

Mechanical properties and fracture parameters of ultra high performance steel fiber reinforced concrete composites made with extremely low water per binder ratios

This study examines the effects of high-volume micro-steel fibers (MSF) content on the mechanical properties, fracture parameters, and ductility of ultra-high performance fiber reinforced concrete (UHPFRCs). The MSFs used in this experiment had an aspect ratio of 37.5 with average length of 6 mm. The investigated parameters include very low water/binder (w/b) ratio and fiber content. Sixteen UHPFRC mixes were examined, eight mixes were made with w/b of 0.12 and eight fiber contents (0%, 1%, 1.5%, 2%, 2.5%, 3%, 3.5, 4%) while the other eight mixes were made with the same fiber contents but with w/b of 0.14. The UHPFRC mixes were examined for various strengths (compressive, splitting tensile, flexural), elastic modulus, and fracture parameters. The experimental results showed that the mixture with 4% of MSFs content and 0.12 w/b ratio exhibited a compressive strength of more than 160 MPa, splitting tensile strength higher than 12 MPa, and modulus of elasticity greater than 43 GPa. Moreover, the results also demonstrated that with increasing MSFs content from 0 to 4% the load–displacement behavior, ductility, and all other fracture parameters were improved significantly.

Review of Methodologies for Structural Integrity Evaluation of Power Modules

AbstractThis paper reviews the previous research on the methodologies for evaluating structural integrity of wire bonds and die-attachments in power modules. Under power module operation, these parts are subjected to repeated temperature variations which induce repeated thermal stress due to the mismatch in coefficients of thermal expansion (CTE) of the constituent materials. Thus, thermal fatigue phenomena are critical issues for the structural integrity of power modules. In the present paper, we also deal with the evaluation methodologies for thermal fatigue in the temperatures over 200 °C, which are expected operational temperatures for wide bandgap semiconductor power modules. The failure models based on the temperature range ΔT widely used in the power electronics community are critically reviewed from a mechanical engineering viewpoint. Detailed discussion is given concerning the superiority of failure models based on the physical quantities such as the inelastic strain range Δεin, the inelastic strain energy density range ΔWin, and the nonlinear fracture mechanics parameter range ΔT* over the conventional ΔT-based failure models. It is also pointed out that the distributed state concept (DSC) approaches based on the unified constitutive modeling and the unified mechanics theory are promising for evaluating the structural integrity of power modules. Two kinds of test methods, a power cycling test (PCT) and a thermal cycling test (TCT), are discussed in the relation to evaluating the lifetimes of wire-liftoff and die attach cracking.

Analysis of Temperature Variation and Thermally-Induced Reflective Cracking Potential in Composite Pavements

Reflective cracking is the major distress in composite pavement and can accelerate the deterioration of the whole structure. This paper analyzes the potential for reflective cracking in composite pavements because of thermal cycles. A heat transfer model was first developed to predict cyclic temperature variations with climatic inputs (solar radiation, wind velocity, air temperature, and humidity). Mechanical models were then employed to analyze thermally-induced reflective cracking potential using fracture mechanics parameters. Both models were validated through field measurement of temperature profile and crack propagation. The temperature profile in composite pavement can be predicted accurately from climate data and typical thermal material properties. Because of the temperature variation and gradient in composite pavement, concrete slabs undergo joint opening and curling deformation and stress concentration occurs at the bottom of the overlay. The loading cycles for initiation and propagation of reflective cracking were predicted by empirical equation and Paris’ law. Increasing overlay thickness can extend the pavement service life, but care is needed as different thicknesses offer varying efficiency. Thicker asphalt overlay mitigates reflective crack potential, especially at the crack initiation phase.

Fracture mechanics analysis method for cracked components under very low cycle fatigue loading

In this study, fracture mechanics analysis was performed to calculate crack growth under very low cycle fatigue loading conditions. The calculation results are compared with 11 experimental datasets concerning through-wall cracked pipes made from three different materials under fully reversed large-amplitude cyclic loading. In the analysis, it was assumed that the crack growth rate under large-amplitude cyclic loading is the linear summation of the fatigue crack growth rate and ductile tearing rate. Relevant fracture mechanics parameters were determined using the reference stress approach. It was found that the calculated failure cycles are around half of those using the experimental data regardless of the material and load amplitude. The most important factors affecting the calculation results were the accuracy of estimating J and ΔJ, and the crack closure coefficient when calculating ΔJ. Their effects on the analysis results are discussed herein.