# International Journal of Fracture (INT J FRACTURE )

Publisher: Springer Verlag

## Description

The International Journal of Fracture is an outlet for original analytical numerical and experimental contributions which provide improved understanding of the mechanisms of micro and macro fracture in all materials and their engineering implications. The Journal is pleased to receive papers from engineers and scientists working in various aspects of fracture. Contributions emphasizing empirical correlations unanalyzed experimental results or routine numerical computations while representing important necessary aspects of certain fatigue strength and fracture analyses will normally be discouraged; occasional review papers in these as well as other areas are welcomed. Innovative and in-depth engineering applications of fracture theory are also encouraged. In addition the Journal welcomes for rapid publication concise Letters in Fracture and Micromechanics which serve the Journal 's Objective. Letters include: Brief presentation of a new idea concept or method; new experimental observations or methods of significance; short notes of quality that do not amount to full length papers; discussion of previously published work in the Journal and Letters Errata.

• Impact factor
1.25
Show impact factor history

Impact factor
.
Year
• 5-year impact
1.31
• Cited half-life
0.00
• Immediacy index
0.21
• Eigenfactor
0.01
• Article influence
0.67
• Website
International Journal of Fracture website
• Other titles
International journal of fracture, Fracture
• ISSN
0376-9429
• OCLC
1771045
• Material type
Periodical, Internet resource
• Document type
Journal / Magazine / Newspaper, Internet Resource

## Publisher details

• Pre-print
• Author can archive a pre-print version
• Post-print
• Author can archive a post-print version
• Conditions
• Authors own final version only can be archived
• Publisher's version/PDF cannot be used
• On author's website or institutional repository
• On funders designated website/repository after 12 months at the funders request or as a result of legal obligation
• Published source must be acknowledged
• Must link to publisher version
• Set phrase to accompany link to published version (The original publication is available at www.springerlink.com)
• Articles in some journals can be made Open Access on payment of additional charge
• Classification
​ green

## Publications in this journal

• ##### Article: Investigation of fatigue crack growth characteristics of NR/BR blend based tyre tread compounds
[Hide abstract]
ABSTRACT: Tyre tread directly comes in contact with various road surfaces and is prone to damage due to cuts from sharp objects during service. As tyres undergo millions of fatigue cycles, these cuts propagate continuously and lead to catastrophic failure. Therefore fatigue crack growth (FCG) characteristics should be an essential criterion for tread compound selection. The present study investigates FCG behavior of blends comprising of Natural Rubber (NR) and Polybutadiene Rubber (BR) over a wide range of tearing energy. Pure shear specimens with a notch on both edges were tested in a Tear Analyser. Rapid increase in FCG rate after a certain strain level was observed. This transition point appeared in a strain range of 20–35 %, depending on the blend composition. The higher BR containing compounds exhibited better FCG characteristics below the transition point but reversal of ranking was seen above this point. The influence of temperature, R ratio, waveforms and cure system on FCG characteristics was also investigated in NR and 60–40 NR/BR blend compounds. Higher FCG rate was achieved under pulse loading compared to the sine waveform. The relaxation time between pulse cycles played an important role. With an increase in relaxation time, FCG rate decreases significantly. The higher sensitivity towards R ratio was observed in NR compound. The 60–40 NR/BR blend showed higher FCG rate with increase in temperature compared to the NR compound. The NR compound with high Sulfur/Accelerator (S/Ac) ratio showed better FCG characteristics whereas for 60–40 NR/BR blend with low S/Ac ratio achieved superior FCG characteristics.
International Journal of Fracture 07/2014; 188(1).
• ##### Article: Estimation of cracking and damage mechanisms of rock specimens with precut holes by moment tensor analysis of acoustic emission
[Hide abstract]
ABSTRACT: This work presents an experiment on the acoustic emission (AE) of coarse grain granites with two square-shaped precut holes under uniaxial loading. Studies were carried out on the temporal–spatial evolution behavior of micro-cracks by AE mechanisms with the use of the simplex location method and the moment tensor theory, with further analysis in comparing the numerical simulations using the software RFPA $$^\mathrm{2D}$$ (Rock Failure Process Analysis). The results show that during the loading process, from beginning to rock failure, shear-mode micro-cracks are prominent, constituting more than 60 % of the total events; next most common are tensile-mode micro-cracks a less than 35 % of the total events. Variations of micro-cracks of the three modes during the loading process have the same increase tendency, i.e. fewer were generated in the initial loading stage, with a rapid increase when the stress values are between 40 and 60 % of the peak stress, and a rate dimunition before rock failure. It is observed that the tensile stress concentration is prone to appear at the tops of the two holes in the form of tensile type cracks, while the shear stress concentration usually appears at the bottom in the middle region of the specimen in the form of shear type cracks. The findings of the present work may serve as guidance for the prevention of roof and floor collapse in the stope exploration of mines.
International Journal of Fracture 07/2014; 188(1).
• ##### Article: Experiments and modeling of edge fracture for an AHSS sheet
[Hide abstract]
ABSTRACT: With the emergence of advanced high strength steels (AHSSs) and other light–weight materials, edge fracture has been one of the important issues evading reliable prediction using CAE tools. To study edge fracture behavior of AHSS, a comprehensive hole expansion test (HET) program has been carried out on a DP780 sheet. Specimen with three different edge conditions (milled edge, water jet cut edge and punched edge) are manufactured and tested. Results reveal that the hole expansion ratio (HER) of the present DP780 sheet is around 38 % for milled specimen and water jet cut specimen, and about 14 % for punched specimen. A novel method of a central hole specimen tension is also introduced for edge fracture study, showing a similar trend as found in HET. The paper briefly presents a procedure and the results for a full calibration of the DP780 sheet for plasticity and fracture, where a hybrid testing/simulation method is used to obtain parameters for Hill 48 plasticity model and modified Mohr–Coulomb fracture model. The finite element simulation gives an accurate prediction of HER, as well as the load displacement response and specimen deflection distribution in the hole expansion tests on uncracked material. The correlation between simulation and tests on central hole specimen also turns out to be very good. The paper also presents a very interesting insight of the initiation and propagation of cracks from the hole edge during a hole expansion test by numerical simulation in comparison with testing observation. The number of final cracks are accurately predicted. Other new aspects of the present paper include an improved 3D DIC measurement technique and a simplified analytical solution, from which a rapid estimation of displacement and hoop strain field can be made (see “Appendix 2”).
International Journal of Fracture 06/2014; 187(2).
• ##### Article: On the fracture of small samples under higher order strain gradient plasticity
[Hide abstract]
ABSTRACT: In this work we perform Finite Element simulations within the framework of large deformation elasto-viscoplasticity on a material that is sensitive to the gradients of plastic strain and incorporates a single intrinsic length scale parameter. Both small scale yielding simulations and those on a finite sized sample show that large stress enhancements can occur at the tip of a notch due to gradient effects. The amount of plastic strain and opening stress that can be expected at the notch tip depends on an interplay between the notch radius, specimen dimensions and boundary conditions. It is shown that cleavage can be the favored criterion for failure in even a ductile material when the notch radius is small compared to the intrinsic length scale. Moreover, for large intrinsic length scales, failure may not always initiate at a notch but may be triggered away from it due to the presence of a boundary impermeable to dislocations.
International Journal of Fracture 06/2014; 187(2).
• ##### Article: Cracks at rounded V-notch tips: an analytical expression for the stress intensity factor
[Hide abstract]
ABSTRACT: An analytical expression for the stress intensity factor related to a crack stemming from a blunted V-notch tip is put forward. The analysis is limited to mode I loading conditions, as long as the crack length is sufficiently small with respect to the notch depth. The proposed formula improves significantly the predictions of a recently introduced relationship, by considering a notch amplitude dependent parameter. Its values are estimated through a finite element analysis: different notch amplitudes, ranging from $0^{\circ }$ to $180^{\circ }$ , and different crack length to root radius ratios, ranging from 0 to 10, are taken into account. The evaluation of the apparent generalized fracture toughness according to equivalent linear elastic fracture mechanics concludes the paper.
International Journal of Fracture 06/2014; 187(2).
• ##### Article: A simplified method for the evaluation of fatigue crack front shapes under mode I loading
[Hide abstract]
ABSTRACT: Two-dimensional elastic or elasto-plastic models dominate the current fatigue crack growth assessment and life prediction procedures for plate components with through-the-thickness cracks. However, as demonstrated in many theoretical and experimental papers, the stress field near the crack tip is always three-dimensional and, as a result, the fatigue crack front is not straight. It is normally curved towards the plate faces. Over the past few years there were a number of very careful numerical studies focusing on the evaluation of fatigue crack front shapes. However, the application of the direct numerical techniques to fatigue phenomena is a very tedious and time consuming process and, sometimes, it is quite ambiguous. In the current paper we develop a simplified method for the evaluation of the front shapes of through-the-thickness fatigue cracks. Further, we validate the developed method against experimental results, investigate the influence of various parameters on the crack front shapes at stable (steady-state) propagation and analyse the differences in the results of fatigue crack growth evaluation obtained with two- and three-dimensional approaches.
International Journal of Fracture 06/2014; 188(2):203-211.
• ##### Article: The unacknowledged risk of Himalayan avalanches triggering
[Hide abstract]
ABSTRACT: A “universal” model for avalanche triggering, as well as for collapse of suspended seracs, is presented based on Quantized Fracture Mechanics, considering fracture, friction, adhesion and cohesion. It unifies and extends the classical previous approaches reported in the literature, including the role of the slope curvature. A new size-effect, that on mountain height rather than the classical one on snow slab thickness, is also discussed and demonstrated thanks to glaciers data analysis from the World Glacier Inventory (http://nsidc.org/data/glacier_inventory/browse.html, 2014). The related most noteworthy result is that snow precipitation needed to trigger avalanches at 8,000 m could be up to 4 times, with a realistic value of 1.7 times, smaller than at 4,000 m. This super-strong size-effect may suggest that the risk of Himalayan avalanches is today still unacknowledged. A discussion on the recent Manaslu tragedy concludes the paper.
International Journal of Fracture 06/2014; 187(2).
• ##### Article: Nanostructural scaling effect in fracturing homogeneous solids
[Hide abstract]
ABSTRACT: The scaling effect (power law dependence of number of newly-formed damages on damage size) during fracturing is inherent in heterogeneous materials, such as composites, concrete, rocks, etc., in which multi-site damaging takes place. Fracturing brittle homogeneous materials do not exhibit this phenomenon due to the lack of pre-failure damage accumulation at the microscopic scale level. This work is to determine the role of structural heterogeneity in the process of primary defect nucleation occurring in conventional homogeneous materials. We present highly resolved time series of fractoluminescence (FL) emitted during multiple chemical bond breakage in shock-damaged silica glass and single crystals $\upalpha \hbox {-SiO}_{2}$ and $\upalpha \hbox {-SiC}$ . The statistical analysis of the time series has shown that the energy distributions of FL pulses followed the power law indicative of long-range interactions between primary damage events. This scaling phenomenon is caused by the multiplicity of newly formed damaged sites at the level of structural heterogeneity. At the same time, the microscopic and larger damage formation reflected in the acoustic emission time series did not exhibit the presence of long-range interactions between growing brittle cracks.
International Journal of Fracture 06/2014; 187(2).
• ##### Article: A model for predicting crack initiation in forged M3:2 tool steel under high cycle fatigue
[Hide abstract]
ABSTRACT: AISI type M3 class 2 tool steel (or in German designation DIN: HS6-5-3 tool steel) is most commonly used in tooling industry, and also in some engine parts. Those components are usually subjected to cyclic stresses and mostly fail by fatigue. Fatigue crack initiation in this material occupies large fraction of total lifetime and strongly depends on microstructural features of primary and eutectic carbides, such as shape, shape ratio, volume fraction, the distribution of carbides as well as load ratio. To model fatigue initiation mechanisms of forged M3:2 tool steel, McDowell’s model was modified and developed for different length-scales. For fatigue crack formation and short crack growth, a hierarchical approach was used and the life time of these stages were estimated based on the local cyclic plasticity. Through this relation the effect of microstructural features on both fatigue crack formation and short crack growth in the material were identified. The results of the proposed model have explicitly reflected the influence of microstructural features on both fatigue crack formation and propagation in forged M3:2 tool steel. Moreover, the model can be used for improving the fatigue resistance of a tool steel component.
International Journal of Fracture 05/2014; 187(1).
• ##### Article: Interlaminar Fracture Testing Method for CFRP Using Tensile Loading with Acoustic Emission Analysis
[Hide abstract]
ABSTRACT: A method is described to characterize the uniformity of interlaminar fracture toughness of laminated carbon-fiber-reinforced polymer (CFRP) composites fabricated by the modified vacuum assisted resin transfer molding process. To prepare specimens for Mode I fracture toughness tests, pieces were sectioned from the inlet and vent regions of a CFRP plate ([+30/-30]6), with a starter crack inserted. The specimens were packed between two rectangular epoxy plates to apply a load using a universal testing machine. Acoustic energy signals were monitored using two sensors attached to the epoxy plates during tensile loading. The difference between the material properties of specimens from the inlet and vent regions of the CFRP plate were statistically compared using one-way analysis of variance (ANOVA); we show that the specimens showed no statistically significant differences in the interlaminar fracture characteristics depending on the part of the mold from which they were taken.
International Journal of Fracture 05/2014; 187(1).
• ##### Article: Cohesive model approach to the nucleation and propagation of cracks due to a thermal shock
[Hide abstract]
ABSTRACT: This paper studies the initiation of cohesive cracks in the thermal shock problem through a variational analysis. A two-dimensional semi-infinite slab with an imposed temperature drop on its free surface is considered. Assuming that cracks are periodically distributed and orthogonal to the surface, at short times we show that the optimum is a distribution of infinitely close cohesive cracks. This leads us to introduce a homogenized effective behavior which reveals to be stable for small times, thanks to the irreversibility. At a given loading cracks with a non-cohesive part nucleate. We characterize the periodic array of these macro-cracks between which the micro-cracks remain. Finally, for longer times, the cohesive behavior converges towards that from Griffith’s evolution law. Numerical investigations complete and quantify the analytical results.
International Journal of Fracture 05/2014; 187(1).
• ##### Article: Cohesive crack, size effect, crack band and work-of-fracture models compared to comprehensive concrete fracture tests
[Hide abstract]
ABSTRACT: The simplest form of a sufficiently realistic description of the fracture of concrete as well as some other quasibrittle materials is a bilinear softening stress-separation law (or an analogous bilinear law for a crack band). This law is characterized by four independent material parameters: the tensile strength, $f'_t$ , the stress $\sigma _k$ at the change of slope, and two independent fracture energies—the initial one, $G_f$ and the total one, $G_F$ . Recently it was shown that all of these four parameters can be unambiguously identified neither from the standard size effects tests, nor from the tests of complete load-deflection curve of specimens of one size. A combination of both types of test is required, and is here shown to be sufficient to identify all the four parameters. This is made possible by the recent data from a comprehensive test program including tests of both types made with one and the same concrete. These data include Types 1 and 2 size effects of a rather broad size range (1:12.5), with notch depths varying from 0 to 30 % of cross section depth. Thanks to using identically cured specimens cast from one batch of one concrete, these tests have minimum scatter. While the size effect and notch length effect were examined in a separate study, this paper deals with inverse finite element analysis of these comprehensive test data. Using the crack band approach, it is demonstrated: (1) that the bilinear cohesive crack model can provide an excellent fit of these comprehensive data through their entire range, (2) that the $G_f$ value obtained agrees with that obtained by fitting the size effect law to the data for any relative notch depth deeper than 15 % of the cross section (as required by RILEM 1990 Recommendation), (3) that the $G_F$ value agrees with that obtained by the work-of-fracture method (based on RILEM 1985 Recommendation), and (4) that the data through their entire range cannot be fitted with linear or exponential softening laws.
International Journal of Fracture 05/2014; 187(1).
• ##### Article: Obtaining S–N curves from crack growth curves: an alternative to self-similarity
[Hide abstract]
ABSTRACT: A crack growth model that allows us to obtain the S–N curves from the crack growth rate curves is presented in an attempt to harmonize the stress based and fracture mechanics approaches in lifetime prediction of long cracks propagation. First, using the Buckingham theorem, the crack growth rate curve $\frac{da}{dN}-\varDelta K$ is defined over all its range as a cumulative distribution function based on a normalized dimensionless stress intensity factor range $\varDelta K^+$ . Then, a relevant theorem is derived that provides an alternative to self-similarity allowing significant reduction of experimental planning. In this way, different $a-N$ crack growth curves for different stress ranges $\varDelta \sigma$ and initial crack lengths $a_0$ can be obtained from a particular crack growth curve under some conditions. The S–N field is obtained from the crack growth curves, showing the close relation between the fracture mechanics and stress approaches. Finally, the model is applied to a particular set of experimental data to obtain the crack growth rate curve and the S–N curves of a certain material for a subsequent fatigue lifetime assessment
International Journal of Fracture 05/2014; 187(1).
• ##### Article: A new view on J-integrals in elastic–plastic materials
[Hide abstract]
ABSTRACT: It is well known that the application of the conventional $J$ -integral is connected with severe restrictions when it is applied for elastic–plastic materials. The first restriction is that the $J$ -integral can be used only, if the conditions of proportional loading are fulfilled, e.g. no unloading processes should occur in the material. The second restriction is that, even if this condition is fulfilled, the $J$ -integral does not describe the crack driving force, but only the intensity of the crack tip field. Using the configurational force concept, Simha et al. (J Mech Phys Solids 56:2876–2895, 2008), have derived a $J$ -integral, $J^{\mathrm{ep}}$ , which overcomes these restrictions: $J^{\mathrm{ep}}$ is able to quantify the crack driving force in elastic–plastic materials in accordance with incremental theory of plasticity and it can be applied also in cases of non-proportionality, e.g. for a growing crack. The current paper deals with the characteristic properties of this new $J$ -integral, $J^{\mathrm{ep}}$ , and works out the main differences to the conventional $J$ -integral. In order to do this, numerical studies are performed to calculate the distribution of the configurational forces in a cyclically loaded tensile specimen and in fracture mechanics specimens. For the latter case contained, uncontained, and general yielding conditions are considered. The path dependence of $J^{\mathrm{ep}}$ is determined for both a stationary and a growing crack. Much effort is spent in the investigation of the path dependence of $J^{\mathrm{ep}}$ very close to the crack tip. Several numerical parameters are varied in order to separate numerical and physical effects and to deduce the magnitudes of the crack driving force for stationary and growing cracks. Interpretation of the numerical results leads to a new, completed picture of the $J$ -integral in elastic–plastic materials where $J^{\mathrm{ep}}$ and the conventional $J$ -integral complement each other. This new view allows us also to shed new light on a long-term problem, which has been called the “paradox of elastic–plastic fracture mechanics”.
International Journal of Fracture 05/2014; 187(1).
• ##### Article: Three-dimensional mixed mode I+II+III singular stress field at the front of a {\varvec{(}}\mathbf{111 }{\varvec{)}[}\bar{\mathbf{1 }}\bar{\mathbf{1 }}\mathbf 2 {\varvec{]}\times [}\mathbf 1 \bar{\mathbf{1 }}\mathbf 0 {\varvec{]}} crack weakening a diamond cubic mono-crystalline plate with crack turning and step/ridge formation
[Hide abstract]
ABSTRACT: A heretofore-unavailable mixed Frobenius type series, in terms of affine-transformed x-y coordinate variables of the Eshelby–Stroh type, is introduced to develop a new eigenfunction expansion technique. This is used, in conjunction with separation of the z-variable, to derive three-dimensional mixed-mode I+II+III asymptotic displacement and stress fields in the vicinity of the front of a semi-infinite through-thickness $(111)[\bar{{1}}\bar{{1}}2]\times [1\bar{{1}}0]$ crack weakening an infinite diamond cubic mono-crystalline plate. Crack-face boundary conditions and those that are prescribed on the top and bottom (free, fixed or lubricated) surfaces of the diamond cubic mono-crystalline plate are exactly satisfied. Explicit expressions for the mixed mode I+II+III singular stresses in the vicinity of the front of the through-thickness crack, are presented. Most important mixed modes I+II+III response is elicited even though the far-field loading is only mode I or II or III or any combination thereof. Finally, atomistic modeling of cracks requires consideration of both the long range elastic interactions and the short range physico-chemical reactions, such as bond breaking. The Griffith-Irwin approach does not take the latter into account, and nano-structural details such as bond orientation must be accounted for. A new mixed-mode I+II+III crack deflection criterion elucidates the formation of steps and/or triangular ridges on the crack path. The planes of a multiply deflected crack are normal to the directions of broken bonds. Additionally, the mixed-mode (I+II+III) crack deflection and ridge formation are found to be strongly correlated with the elastic stiffness constants, ${c}^{\prime }_{14}$ and ${c}^{\prime }_{56}$ , of the diamond cubic single crystal concerned.
International Journal of Fracture 05/2014; 187(1).

#### Related Journals

• ##### European Journal of Environmental and Civil Engineering

ISSN: 1964-8189, Impact factor: 0.44

• ##### Procedia Engineering

ISSN: 1877-7058

• ##### IOP Conference Series Materials Science and Engineering

Institute of Physics (Grande-Bretagne)

ISSN: 1757-899X

• ##### Journal of the Mechanical Behavior of Biomedical Materials

Elsevier

ISSN: 1751-6161, Impact factor: 2.37

• ##### Bioinspiration &amp Biomimetics

ISSN: 1748-3190, Impact factor: 2.41

• ##### Soft Matter

Royal Society of Chemistry (Great...

ISSN: 1744-6848, Impact factor: 4.15

• ##### PAMM

Gesellschaft für Angewandte...

ISSN: 1617-7061

• ##### Landslides

International Consortium on...

ISSN: 1612-510X, Impact factor: 2.09