Fracture Mechanics Parameters Research Articles

Comparison of the constraint parameters in elastic-plastic fracture mechanics

To describe the effect of crack-tip constraint on the stress field for finite cracked bodies, the following most widely used constraint parameters can be employed in elastic-plastic fracture mechanics, namely, local triaxiality parameter, constraint parameter Q, the second fracture mechanics parameter A using a three-term elastic-plastic asymptotic expansion. To establish the relationship between different constraint parameters, the crack-tip stress fields are employed. Relationship between the crack-tip constraint parameters A, A2, Q and of elastic-plastic fracture mechanics is investigated.

Components of the Fracture Response of Alkali-Activated Slag Composites with Steel Microfibers

Knowledge of the mechanical and primarily fracture parameters of composites with a brittle matrix is essential for the quantification of their resistance to crack initiation and growth, and also for the specification of material model parameters employed for the simulation of the quasi-brittle behavior of structures made from this type of composite. Therefore, the main target of this paper is to quantify the mechanical fracture parameters of alkali-activated slag composites with steel microfibers and the contribution of the matrix to their fracture response. The first alkali-activated slag composite was a reference version without fibers; the others incorporated steel microfibers amounting to 5, 10, 15 and 20% by weight of the slag. Prism specimens with an initial central edge notch were used to perform the three-point bending fracture tests. Load vs. displacement (deflection at midspan) and load vs. crack mouth opening displacement diagrams were recorded during the fracture tests. The obtained diagrams were employed as inputs for parameter identification, the aim of which was to transfer the fracture test response data to the desired material parameters. Values were also determined for fracture parameters using the effective crack model, work-of-fracture method and double-K fracture model. All investigated mechanical fracture parameters were improved by the addition of steel microfibers to the alkali-activated matrix. Based on the obtained results, the addition of 10 to 15% of microfibers by weight is optimal from the point of view of the enhancement of the fracture parameters of alkali-activated slag composite.

J-integral evaluation of repaired cracks in AA7075-T6 structures subjected to uniaxial tensile stresses

Bonded repairs using composite patches over metallic structures have been evaluated as a cost effective method to increase the life of damaged structures. The J-integral is a widely applied fracture mechanics parameter relating to the energy release associated with crack growth and is a measure of the deformation intensity at the crack tip. In practice, the calculated J-integral can be compared with a critical value for the material under consideration to predict fracture. This study aimed at providing an overview of the behavior of a cracked plate of AA7075-T6 alloy repaired with a boron-epoxy patch bonded with FM73 Adhesive layer. The Finite Element Method (FEM) using Abaqus Software 6.14 predicted the performance. The results show a considerable decrease in the value of the J-integral. This is due to the beneficial effect of the patch on the stress state at the crack tip. The best results were obtained from a uni-directional composite fibres orientation of 0°, where the fibers oriented parallel to the direction of load. A parametric analysis has been carried out to evaluate the effect of lay-up, load variation and crack mouth opening on the J-integral. It was found that the crack mouth opening displacement (CMOD) was reduced by 90–97%.

Estimation of the optimum content of fly ash in concrete composite based on the analysis of fracture toughness tests using various measuring systems

Abstract This paper presents the results of compressive strength – fcm and fracture toughness tests of concrete composite modified with the addition of siliceous fly ash (FA). The investigation embraced concrete with 0%, 10%, 20% and 30% FA addition. The parameters of linear and nonlinear fracture mechanics were analysed in this studies, i.e. the critical stress intensity factor – K Ic S and the critical crack tip opening displacement – CTO D c . These parameters were determined based on the results obtained from the MTS 810 press and the Digital Image Correlation (DIC) system with ARAMIS software. Concrete with FA addition up to 23% is characterized by regular fracture toughness and above this limit the fracture toughness gets low. On the other hand, the optimum amount of FA addition causing maximum fracture toughness of the material is 17% ( Fig. 8 ). Furthermore, it was observed that there is a qualitative correlation between parameters: fcm, K Ic S and CTO D c . The values of parameters of fracture mechanics calculated on the basis of data from the ARAMIS software show the behaviour of the structural material exactly at the moment of the initial crack inception. The research results presented show the usefulness of the DIC method in this type of experiments, whereas the article confirmed the high potential of DIC technique in the determination of fracture toughness in concrete composites with FA addition.

Fracture mechanics assessment of divertor vertical target under thermal loading conditions

Since divertor modules undergo extreme thermal loads, lots of stress analyses and several accompanying tests have been carried out for tungsten armored mono- and multi-blocks. However, while noteworthy cracks were found at surface of mono-block during recent high heat flux experiments, there was a little fracture mechanics related research. The objective of present study is to investigate structural integrity of flawed ITER outer vertical target (OVT) based on elastic-plastic fracture mechanics assessment. At first, heat transfer and thermal stress analyses were performed on the mono-block and OVT. Especially, for which two disjunctive heat fluxes were applied at plate and baffle of the OVT as transient condition. Subsequently, parametric fracture mechanics analyses were carried out for the OVT with a postulated surface crack after mapping pre-determined stress profile. In addition, a typical fracture mechanics parameter as well as temperature and stress distributions were also calculated from similar analyses of a mono-block. As results, dependency of J-integral values on crack positions, sizes and locations was discussed, and critical crack sizes were decided by comparing with a representative fracture toughness of plasma facing material.

Fracture Mechanical Properties of Damaged and Hydrothermally Altered Rocks, Dixie Valley‐Stillwater Fault Zone, Nevada, USA

AbstractDamaged and hydrothermally altered rocks are ubiquitous in fault zones, with the degree of damage and type and intensity of alteration varying in space and time. The impact of damage and alteration on hydromechanical properties of fault zones is difficult to assess without characterizing the associated changes to rock and fracture mechanical parameters. To evaluate the mechanical properties of fault rocks from different alteration regimes, we conducted (1) double‐torsion load‐relaxation tests to measure mode‐I fracture toughness (KIC) and subcritical fracture growth index (SCI), (2) uniaxial testing to measure unconfined compressive strength (UCS) and static elastic parameters, and (3) mineralogic and textural characterization of rock from four sites in the footwall of the Dixie Valley‐Stillwater fault zone. Alteration at these sites includes acid sulfate alteration and silicification associated with active fumaroles, intense silicification after calcite and chlorite alteration in an epithermal setting, quartz‐kaolinite‐carbonate alteration from an intermediate‐depth system, and a calcite‐chlorite‐hematite assemblage containing abundant unhealed damage. Silicification is associated with high KIC, SCI, UCS, and increased brittleness, and in precipitation‐dominated settings produces fault cores that are as strong or stronger than adjacent damage zone material. Calcite‐chlorite‐hematite assemblages containing abundant unsealed microfractures are approximately 4–5 times weaker than the granodiorite protolith. Mechanical properties are not predicted by mineralogical composition alone; a key control is the accumulation of damage and degree of healing. Measures of strength increase when mineral precipitation reduces microfracture porosity to <10–15% of total microfracture area. These results show that fault‐proximal weakening or strengthening is influenced by hydrothermal setting.

An advanced assessment of mechanical fracture parameters of sandstones depending on the internal rock texture features

An advanced assessment of mechanical fracture parameters of sandstones depending on the internal rock texture features

High-Temperature Fracture Mechanics Parameter Measurement and Yielding Zone Analysis of Superalloy GH4169 Based on Single-Lens 3D Digital Image Correlation

Fracture mechanics parameters are crucial for evaluating the failure of a material; furthermore, the yielding zone near the crack tip is closely related to the ultimate bearing capacity. How to characterize these parameters has drawn a lot of attention from mechanics researchers. Currently, the digital image correlation (DIC) method, due to its advantage of being able to perform full-field, non-contact measurements, has great potential for application in the measurement of the mentioned parameters. In this paper, a bi-prism-based single lens (BSL) 3D DIC technique was utilized to determine the fracture mechanics parameters and the yielding zone size of the Ni-based superalloy GH4169 at room temperature and 650 °C. In the measurement, the displacement fields of single-edge cracked specimens under a uniaxial tensile load were measured using the BSL 3D DIC system. And then, the J integral and stress intensity factor K at room and high temperature were calculated from the displacement fields. Finally, the J integral calculated using the path integral method (J _ 1) and the J integral converted from the stress intensity factor K (J _ 2) were used to evaluate the yielding condition near the crack tip Yoneyama et al. (Strain 50(2):147–160, 2014), while a specific value was also determined as the critical small-scale yielding load from the variations of J _ 1 and J _ 2. Additionally, the relationship between the yielding zone size rp, calculated from K and the value ∆J = J _ 2 − J _ 1 was established, which was found to be linear. On the rp − ∆J curve, the intercept on the rp axis could be regarded as the critical size of small-scale yielding zone.

Numerical Comparison of Cruciform weld and Butt weld simulation and a Study of Fracture Mechanics on Two Types of Welds

The modeling of the welding is desirable to guess the deformation of the components during manufacture, the position and the magnitude of maximum residual stresses and to envisage metallurgical effects in specific zones. The welding are problems of complex modeling requiring the thermal and structural solutions. This has to lead to the development of several software packages and codes for simulation by finite elements. The welding condition, the properties of the structure and their interactions have significant influences on the thermal and structural responses (temperature history, distortion, and residual stress) in welded structures. This paper presents a finite element procedure for the prediction of welding-induced residual stresses and distortions. Comparison is made with tow numerical example. The first example is a butt welded joint of two plates, while the second is a Cruciform welded joint of two plates with four passes. Moreover, a comparison between the Cruciform weld and the butt-weld which we can obtain the parameters of the linear fracture mechanics; stress intensity factor K and energy release rate G.

Diagnostics of the Engineering State of Steam Pipelines of Thermal Power Plants by the Hardness and Crack Resistance of Steel

We propose a nondestructive method for the diagnostics of the current state of heat-resistant steels after long-term operation in the steam pipelines of thermal power plants (TPP). It is based on measuring the sizes of ferrite grains and the hardness of 15Kh1M1F heat-resistant steel directly on the pipe surface and on the use of the deduced relationship between these characteristics (of the Hall–Petch type). The plot of this relationship contains two rectilinear parts. The first part agrees with the physical ideas concerning the correlation between the grain size and the strength (hardness) of the material. The second part with a rapid decrease in the hardness of steel is connected not only with the subsequent changes in the microstructure of steel but also with the development of the in-service defects scattered in the volume of the metal. To determine the limiting state of degraded steel, we used one of the parameters of fracture mechanics, namely, the effective threshold amplitude of the stress intensity factor (SIF) ΔKth eff determined with regard for the effect of fatigue crack closure. The application of this parameter is substantiated by the detected inversion of the influence of hydrogen on ΔKth eff (from positive to negative) observed as the degree of in-service degradation of steel increases. The indicated inversion is caused by the transformation of the mechanism of fatigue crack growth in the subthreshold part of the fatigue crack growth diagram from transgranular (caused by microshears at the crack tip in each loading cycle) into a brittler mechanism accompanied by the formation of intergranular fragments of mode I fracture in the damaged areas. Therefore, the threshold of cyclic crack-growth resistance corresponding to this inversion is taken as the critical value $$ \varDelta {K}_{\mathrm{th}\;\mathrm{eff}}^c $$ below which the probability of brittle fracture of the exploited steel becomes much higher. By using the constructed correlation dependence between ΔKth eff and the hardness of the metal and the determined critical value $$ \varDelta {K}_{\mathrm{th}\;\mathrm{eff}}^c, $$ we estimate the critical value of hardness. Below this value, the hazard of uncontrolled brittle fracture noticeably increases due to the presence of defects scattered in the bulk of the metal.

Smooth Generalized/eXtended FEM approximations in the computation of configurational forces in linear elastic fracture mechanics

The computation of crack severity parameters in the linear elastic fracture mechanics (LEFM) modeling is strongly dependent on the local quality of the approximated stress fields right at the crack tip vicinity. This work investigates the behavior of extrinsically enriched smooth mesh-based approximations, obtained via $$C^{k}$$ -GFEM framework (Duarte et al. in Comput Methods Appl Mech Eng 196:33–56, 2006), in the computation of $$\mathcal {J}$$ -integral in both pure mode I and mixed-mode loadings for two-dimensional problems of the LEFM. The method of configurational forces is used for this purpose as shown in Steinmann et al. (Int J Solids Struct 38:5509–5526, 2001), for instance, by performing some adaptations according to Hausler et al. (Int J Numer Methods Eng 85:1522–1542, 2011). As such method provides vector quantities, it is also possible to compute the angle $$\theta _{{\mathrm{ADV}}}$$ of probable crack advance. The $$C^{k}$$ -GFEM is quite versatile and shares similar features with the standard FEM regarding the domain partition and numerical integration (Mendonca et al. in Finite Elem Anal Des 47:698–717, 2011). The tests were conducted using three-noded triangular element meshes and numerical integrations were performed using only global coordinates. The evaluations combined different schemes of polynomial and discontinuous/singular (Moes et al. in Int J Numer Methods Eng 46:131–150, 1999) enrichments. The use of a smooth partition of unity (PoU) can influence the accuracy of computed crack severity parameters. The configurational forces computation is favored by the smoothness, reducing the dependence on the way the crack severity parameters are evaluated.

Application of a New, Energy-Based ΔS* Crack Driving Force for Fatigue Crack Growth Rate Description.

This paper presents the problem of the description of fatigue cracking development in metallic constructional materials. Fatigue crack growth models (mostly empirical) are usually constructed using a stress intensity factor ΔK in linear-elastic fracture mechanics. Contrary to the kinetic fatigue fracture diagrams (KFFDs) based on stress intensity factor K, new energy KFFDs show no sensitivity to mean stress effect expressed by the stress ratio R. However, in the literature there is a lack of analytical description and interpretation of this parameter in order to promote this approach in engineering practice. Therefore, based on a dimensional analysis approach, ΔH is replaced by elastic-plastic fracture mechanics parameter—the ΔJ-integral range. In this case, the invariance from stress is not clear. Hence, the main goal of this paper is the application of the new averaged (geometrically) strain energy density parameter ΔS* based on the relationship of the maximal value of J integral and its range ΔJ. The usefulness and invariance of this parameter have been confirmed for three different metallic materials, 10HNAP, 18G2A, and 19th century puddle iron from the Eiffel bridge.

Method comparison for the determination of stretch zone parameters

The fracture behaviour of ductile failing materials is evaluated by parameters of yielding fracture mechanics. According to ISO 12135 the determination of fracture mechanical characteristic values involves, among other things, analysing the stretch zone width (SZW) in the scanning electron microscope (SEM). This procedure is very time-consuming and requires great experience in handling SEM images of fracture surfaces. An alternative method for determining the stretch zone parameters works with 3D elevation profiles of the fracture surface in the stretch zone area taken with a digital microscope. The fracture mechanical parameters determined using the above methods were finally compared. The Ji and δi values of scrap steels resulting from the digital determined SZW show a good agreement with analytically determined crack initiation values (Ji/BL, δi/BL).

Experimental and numerical investigation into the methods of determination of mode I static fracture toughness of rocks

Fracture toughness, as a measure of resistance against crack instability and propagation, is one of the most important parameters in fracture mechanics of rocks and other solid materials. Different methods have so far been proposed in order to determine mode I fracture toughness. In practice, however, considerable differences between their results have been reported. In this study, six conventional tests, including the Single Edge Round Bar Bending test, the Chevron Bend test, the Semi-Circular Bend test, the Straight Notch Disk Bend test, the Brazilian disk test, and the Flattened Brazilian Disk test have been performed on a uniform specimen of gabbro rock for determination of mode I fracture toughness. A notable maximum difference of 42% is observed between the results.The tests are categorized into three groups in terms of their similarities. Several factors which affect the prediction of fracture toughness are investigated by both the numerical and experimental evidences. Distribution of the fracture process zone around the crack tip, is numerically computed using the 3D finite element analysis and based on both the “normal tensile stress” and the “von-Mises” criteria. According to the investigated features, the Chevron Bend test is the most reliable test for determination of the fracture toughness. Furthermore, the distribution of fracture process zone around the crack tip in this test is non-uniform which leads to over estimation of fracture toughness predicted by the effective crack theory.

Moravian greywacke – evaluation of fracture, strength and deformability properties

This contribution brings overview of mechanical properties of greywacke with focus on fracture mechanics parameters. Investigated rock type is clastic sediment, relatively widespread in Moravia region. The rock type is significantly utilized in construction industry. For purposes of this study, Kobeřice quarry was selected as sampling locality. Mechanical properties were investigated by deformation controlled 3-point bending test. Chevron notch was created on specimens in order to study fracture mechanics parameters. Moreover, deformation controlled uniaxial compression tests were carried out, as well. Specimens were equipped with strain gauges; thus, elastic modulus and the Poisson’s ratio could be determined. Splitting tensile test was employed in order to determine tensile strength. Mean value of fracture toughness KIC was determined to 1.85 MPa·m0.5. Mean value of uniaxial compressive strength was observed at level of 211 MPa and tensile strength reached 19.4 MPa. Hence, the tested greywacke was considered as high strength rock. Brittle type of failure occurred during the tests. The obtained results were compared with values reported for clastic sediments from several localities in the Czech Republic. Moravian greywacke reached significantly high strength in comparison to other clastic sedimentary rocks and can be considered as valuable raw material for purposes of construction industry.

Analysis of the cause of the girth gear tooth fracture occurrence at the bucket wheel excavator

Abstract Premature damages and fractures of components and structures of bucket-wheel excavators at open-pit mine often occur in exploitation, caused either by inadequate design or insufficient knowledge of the material properties, welded joints and flaws in component production technology. The bucket-wheel excavator, TAKRAF SRs 2000 × 32/5.0 was employed on the excavation of barren soil for 5.000 h (a few weeks more than a year after the assembly) when the fracture of the tooth of the girth gear, which enables the circular motion of the upper structure of the bucket-wheel excavator, occurred. The gear was, according to the manufacturer’s certificate, made of the cast steel GS 40 MnCrSi3 V. The paper presents calculations of the stress variations cycles’ number for one tooth, as well as of the fracture mechanics parameters – the critical stress intensity factor and critical crack length. It was established that the fracture of the tooth occurred due to an initial crack existing in its base, which originated during the gear’s manufacturing, i.e. due to the so-called manufacturing-in defect.

Fracture toughness of concrete with basalt fiber

The analysis of fracture mechanics parameters of concrete with new types of fibers is essential for the dissemination of their application and development of new methods of structural design.Fracture mechanics parameters are widely used to analyze the material behaviour and also in the design process of selected structures. The paper reports the results of an experimental programme focused on the effect of non-metallic (basalt) fibers on the fracture properties of concrete investigated in Mode I conditions. The changes in concrete properties were analysed on the basis of the critical stress intensity factor KIc, the critical value of crack tip opening displacement (CTODc) and the fracture energy GF. The addition of the basalt fibers had a slight effect on the strength properties of concrete but, at the same time, it had a significant influence on the fracture parameters by the modification of pre-cracking and particularly post-cracking behaviour of the concrete. Results of measuring the toughness and energy-absorption characteristics showed that the specimens reinforced with basalt fibers acquired a great ductile behaviour and energy absorption capacity, compared to ordinary concrete specimens.

DETERMINATION OF THE WILLIAMS SERIES EXPANSION’S COEFFICIENTS USING DIGITAL PHOTOELASTICITY METHOD AND FINITE ELEMENT METHOD

In the present work, photoelastic and finite element methods have been employed to study the near crack tip fields in isotropic linear elastic cracked bodies under mixed mode loading. The investigated fracture results have been obtained for a series of cracked specimens by testing plates with two parallel cracks, two inclined parallel cracks, three-point bend specimens, four-point bend specimens, inclined edge crack triangular shape specimens subjected to symmetric three point bend loading. The multi-parameter Williams series expansion is used for the crack tip field characterization. Digital photoelasticity method is utilized for determination of the Williams series expansions coefficients. The unknown coefficients in the multi-parameter equation are determined using a linear least squares method in an over-deterministic manner. Together with the experimental determination of the fracture mechanics parameters finite element method is invoked to describe the crack tip stress field. Coefficients of higher order terms are either found numerically by finite element method. A good agreement is found between the numerical and experimental results. The significant advantages using multi-parameter equations in the analysis of the stress field are shown and the errors that a study with a limited number of terms produce is demonstrated. The comparison with finite element analysis highlighted the importance and precision of the photoelastic observation for the evaluation of the fracture mechanics parameters. The experimental SIF, T-stress values and coefficients of higher-order terms estimated using the digital photoelasticity method for the extensive series of cracked specimens are compared with finite element analysis (FEA) results, and are found to be in good agreement.

Mixed mode (I+II, I+III) fatigue crack growth description in S355/P355NL1 steel

Fatigue crack growth models (mostly empirical) are usually constructed using stress intensity factor – ΔK in linear-elastic fracture mechanics. Contrary to the kinetic fatigue fracture diagrams (KFFDs) based on ΔK, Kmax new energy diagrams based on strain energy density parameter ΔH, ΔS* demonstrates no sensitivity to mean stress effect expressed by the stress ratio R. According to the dimensional analysis approach ΔH, ΔS* is replaced by elastic-plastic fracture mechanics parameter based on the energy parameter associated with ΔJ energy parameter range. Hence, the main goal of this paper is the application of the new averaged strain energy density parameter ΔS* based on hysteresis loop curves for cracked components under uniaxial as well as multiaxial stress state. The presented approach assumes that the fatigue crack growth increment in the elastic-plastic range is caused by the combination of the maximum value of the energy parameter and its positive part of the range in each cycle of loading. The usefulness and invariance of this parameter have been confirmed in many works.

Thermal and mechanical cyclic tests and fracture mechanics parameters as indicators of thermal shock resistance – case study on silica refractories

The paper discusses alternative methods to assess thermal shock in refractories. Thermal shock performance of two conventional silica bricks and two novice fused silica materials has been studied. Methods involving fracture mechanical tests of monotonic loading, repetitive thermal shock tests and cyclic strain controlled fatigue tests have been utilised. The amorphous fused silica is rather brittle. However low thermal expansion guarantees its superior thermal shock resistance. In-service crystallisation is to happen rather quickly. For crystallised fused silica of the studied morphology the tests coherently predict superior thermal shock resistance due to less brittle failure. Strain controlled fatigue test allows assessment of strain limits in the conditions of cyclic loading and thus combines the benefits of the thermal shock and monotonic fracture mechanics tests. Strain tolerance seems to be the property to correlate the results of the alternative test methods and those with the service loads.