Fatigue cracking of laser hybrid welded eccentric fillet joints has been studied for stainless steel. Two-dimensional linear elastic fracture mechanics analysis was carried out for this joint geometry for four point bending load. The numerical simulations explain for the experimental observations why the crack propagates from the lower weld toe and why the crack gradually bends towards the root. Lack of fusion turned out to be uncritical for the initiation of cracks due to its compressive stress conditions. The linear elastic fracture mechanics analysis has demonstrated in good qualitative agreement with fatigue test results that lack of fusion slightly (<10%) reduces the fatigue life by accelerating the crack propagation. For the geometrical conditions studied here improved understanding of the crack propagation was obtained and in turn illustrated. The elaborated design curves turned out to be above the standard recommendations

Cross-ply laminate subjected to tensile loading provides a relatively well understood and widely used model system for studying progressive cracking of the transverse ply. This test allows to identify material strength and/or toughness characteristics as well as to establish relation between damage level and the composite stiffness reduction. The transverse ply cracking is an inherently stochastic process due to the random variability of local material properties of the plies. The variability affects both crack initiation (governed by the local strength) and propagation (governed by the local fracture toughness). The primary aim of the present study is elucidation of the relative importance of these phenomena in the fragmentation process at different transverse and longitudinal ply thickness ratios. The effect of the random crack distribution on the mechanical properties reduction of the laminate is also considered. Transverse ply cracking in glass fiber/epoxy cross-ply laminates of the lay-ups [02/902]s, [0/902]s, and [0/904]s is studied. Several specimens of each lay-up were subjected to uniaxial quasistatic tension to obtain crack density as a function of applied strain. Crack spacing distributions at the edge of the specimen also were determined at a predefined applied strain. Statistical model of the cracking process is derived, calibrated using crack density vs. strain data, and verified against the measured crack spacing distributions.

The failure and mechanical behavior of transversely isotropic rock are significantly affected by the original bedding planes. Until now, few studies have been performed to investigate the influence of the geometrical and mechanical parameters of the bedding planes on the fracture characteristics of transversely isotropic rocks under planar shear fracture loading conditions. For this purpose, experimental and numerical compression-shear tests on double-notched specimens are conducted to investigate the fracturing characteristics of transversely isotropic rock under planar shear fracture loading. The experimental study that focuses on the influence of bedding plane inclination on fracture load, fracture pattern and AE evolution, and six inclination angles is conducted in this study. Based on the flat joint contact model (for the rock matrix) and smooth joint contact model (for the original bedding plane) in PFC2D (particle flow code), the microscale fracturing process of transversely isotropic rock with different inclinations is simulated and analyzed. The results show that the inclination has an important influence on the fracture load and fracture pattern, and the maximum and minimum fracture loads are obtained for specimens with inclination angles of 30° and 60°, respectively. Moreover, the strength and spacing of the original bedding planes also play an important role in fracture loads. Higher bedding plane strength and wider bedding plane spacing result in higher fracture loads. In addition, with a moderate inclination angle, transversely isotropic rock with higher bedding plane strength tends to form cracks that cut through the rock matrix. However, with the decrease in the bedding plane strength, more fractures form along the bedding planes.

The finite deformation response of a planar block of polymer material subject to impact loading is analyzed using two constitutive models for glassy polymers, a reference Drucker-Prager type model and a physics-based macromolecular model, supplemented by a phenomenological model for craze initiation and widening. Full transient finite element analyses are carried out using a Lagrangian formulation of the field equations. The analyses allow an assessment of possible failure mechanisms under dynamic loading and the ability of the different models to predict such behavior. The results highlight the effect of the stress-strain behavior of polymers, notably the post-yield softening and large strain hardening, on localization of plastic flow. This behavior is adequately captured only by the macromolecular model.

The stress intensity factor and the J-integral have been derived analytically and numerically for a modified three-point bend specimen with partly tapered sides, for various crack lengths, taper and specimen cross-section proportions, in order to allow full-thickness testing of tapered samples, common in older steel structures, to obtain a fair effective fracture toughness value for a through thickness crack in inhomogeneous materials. The stress intensity factor is obtained with the approximate analytical method of Kienzler and Herrmann, based on the concept of material forces. The J-integral is calculated numerically with a 3D finite element model for a linear elastic material and an elastic ideal-plastic material. A simple single specimen fracture toughness evaluation procedure is proposed. It is found that the effect of taper in the range encountered in practice is small, of the order of a few percent.

Reactive molecular dynamics was applied in this study to construct the sodium aluminosilicate hydrate (N-A-S-H) and tensile fracture models with various crack angles. The impact of crack angle on the behavior of N-A-S-H fractures was explored while considering structural mechanical properties and energy evolution. Furthermore, the fracture toughness and brittleness index for various crack angle models were calculated. The findings indicated that the ultimate strength and elastic modulus of the fracture models grew linearly with the increase in crack angle. The fracture toughness value progressively grew while the model’s elastic energy efficiency and new surface energy efficiency decreased simultaneously. The 45° crack model possessed the largest oblique crack development surface in the fracture process due to the coupling effect of tensile and shear stress. Its elastic energy efficiency decreased as well the most, while the new surface energy efficiency increased and the fracture toughness value dropped sharply. It is crucial to place a stronger emphasis on spotting cracks both in the in-service structures or structures being demolished. This ensures optimal performance and safety by enabling more effective adjustments to the direction of external forces and energy input.

Automotive industry players have devoted large efforts to identify the material parameters governing the crash resistance of Advanced High Strength Steels (AHSS). Such knowledge is essential to improve impact performance prediction and optimize new steel development. Nevertheless, there is still an open discussion about which are the most relevant properties on AHSS crashworthiness. In this work, the authors investigate the correlation between the fracture toughness of different AHSS and their crash failure behaviour. Fracture toughness is measured in the frame of fracture mechanics, through the essential work of fracture methodology. Two fracture resistance parameters are characterized: the fracture toughness at cracking initiation, wei, and the essential work of fracture, we. Toughness values are compared with the results of axial impact tests, which are evaluated according to the energy absorbed and the cracking behaviour observed in crash boxes. Results show that fracture toughness permits to describe different crash events in terms of crack initiation and crack propagation and allows ranking AHSS impact resistance; steels with higher we present better crash performance. Therefore, fracture toughness is proposed as a key material property to predict the crash resistance of AHSS and as a relevant design parameter for crash resistant parts.

The fracture toughness of four advanced high strength steel (AHSS) thin sheets is evaluated through different characterization methodologies, with the aim of identifying the most relevant toughness parameters to describe their fracture resistance. The investigated steels are: a Complex Phase steel, a Dual Phase steel, a Trip-Aided Bainitic Ferritic steel and a Quenching and Partitioning steel. Their crack initiation and propagation resistance is assessed by means of J-integral measurements, essential work of fracture tests and Kahn-type tear tests. The results obtained from the different methodologies are compared and discussed, and the influence of different parameters such as specimen geometry or notch radius is investigated. Crack initiation resistance parameters are shown to be independent of the specimen geometry and the testing method. However, significant differences are found in the crack propagation resistance values. The results show that, when there is a significant energetic contribution from necking during crack propagation, the specific essential work of fracture (we) better describes the overall fracture resistance of thin AHSS sheets than JC. In contrast, energy values obtained from tear tests overestimate the crack propagation resistance and provide a poor estimation of AHSS fracture performance. we is concluded to be the most suitable parameter to describe the global fracture behaviour of AHSS sheets and it is presented as a key property for new material design and optimization.

We have performed controlled triaxial experiments on Stripa granite in a 'nearly stiff' environment. This means that, before the commencement of loading, an initial confining pressure was 'locked' in the pressurizing chamber of the triaxial vessel. During the axial loading of the sample, the confining pressure was unavoidably increased, opposing largely the 'free' expansion of the sample due to overall microcracking. Further increase in confining pressure beyond the peak load resulted from the dilation of the formed shear fracture, during shear displacement. Under triaxial testing condition a reasonable assumption is that the shear fracture in the specimen is a consequence of pure shear (mode II) state of stress prevailing in the sample, in the vicinity of a 'bandlike' zone, from which the shear fracture propagated. Under this assumption and by the relevant fracture mechanics approach incorporating the 'slip weakening' model, shear fracture energy of Stripa granite was estimated. The results were compared with those estimated through controlled triaxial experiments at constant confining pressure, recently reported by other workers. Also, the influence of the testing method described here on the process of laboratory failure of rock in shear is discussed.

A mixed mode I/II fracture criterion applicable to cracks oriented both along and across the fibres in wood is derived within the framework of linear elastic fracture mechanics. The use of a common fracture criterion for both types of cracks is made possible by the fact that cracks in wood generally propagate along the fibres, irrespective of both the original crack orientation and the degree of mode mixity. The derived criterion is simple, and contains a single material dependent fracture parameter. The applicability of the fracture criterion to spruce (Picea abies) is experimentally validated in part two of the paper

An experimental investigation of mixed mode I/II fracture in Norway spruce (Picea abies) is presented. Mixed mode fracture is studied in two principal crack systems, RL and LR, in which the crack planes extend along and across the wood fibres, respectively. The investigation shows that onset of mixed mode cracking can be predicted with a very simple fracture criterion in both these crack systems. However, the applicability of the fracture criterion to cross-fibre cracks is limited to configurations, in which the crack tip T-stress, i.e. the non-singular stress acting parallel to the crack plane, is low.

A path independent integral expression for the crack extension force of a two-dimensional circular arc crack is presented. The integral expression, which consists of a contour and an area integral, is derived from the principle of virtual work. It is implemented into a FEM post-processing program and the crack extension force is calculated for a circular are crack in a linear elastic material. Comparison with exact solutions by Cotterell and Rice for the effective elastic stress intensity factor shows acceptable accuracy for the numerical procedure used

Tensile testing of CF/EP AS4/8552 cross-ply laminates at room (RT) and cryogenic (around -150 deg C) temperatures has been performed to study the effect of temperature on damage (intralaminar cracking) evolution. Microscopy studies of the specimen edges showed a significant difference in damage pattern for the two different temperatures. At the low temperature (LT), more complex crack types were obtained that could not be found in specimens tested at the RT. The effect of these crack types on the laminate tensile modulus was studied by FEM. In analytical stiffness modelling complex shape crack was replaced by an 'effective' normal (straight) crack with an 'effective' crack opening displacement (COD) that leads to the same reduction in laminate stiffness. A crack efficiency factor was introduced to characterize the significance of complex crack shapes for stiffness reduction. The reduction of tensile modulus for a laminate damaged at low temperature was measured and compared with model predictions.

Non-crimp fabric (NCF) cross-ply composites response to tensile loading is investigated showing large effect of the fabric layer stacking sequence: much larger elastic modulus reduction was observed in [0/90/0/90]S than in [90/0/90/0]S case. Since transverse cracks in 90°-bundles may give modulus decrease about 5%, the observed 40% stiffness reduction is attributed to failure and delamination of bundles oriented in the direction of the applied load. Analysis of micrographs shows extensive delaminations and 0°-bundle breaks. FE calculations showed that failure of 0°-bundles at the surface is energetically more favorable. However, the fracture resistance of surface bundles is higher due to smaller bundle waviness and the density of bundle cracks on the surface was not larger than inside. Two possible reasons for the higher stiffness reduction in the [0/90/0/90]S NCF composite were suggested: (a) If two imperfect 0°-bundle layers are separated by a 90°-bundle layer their resistance to failure is lower than when they are situated next to each other; (b) the effect of each surface 0°-bundle break on the composite stiffness is larger (due to less constraint from the surrounding material the opening of surface bundle breaks is much larger).

In this work, the finite element method is employed to gain an understanding of the behaviour of a cracked bridge roller bearing in service. The cracked roller is considered as an edge-cracked disk (two-dimensional plane strain system) subjected to a radial compressive line load. The crack parameters K_I and K_II are calculated for the relevant load configuration and angle of disk rotation. The calculated data are also used to check the accuracy of approximate SIF solutions reported earlier [1] and [2]. For plain Mode I loading very good agreement is found between the obtained results and data presented in Schindler and Morf (1994). 

With the innovation of elastomeric bearings in the mid-1950s steel bearings lost their interest and significance both in research and development and subsequently even in application. Steel bearings were gradually abandoned in bridges, followed by the technical literature and design standards. However, a great number of steel bearings remain today in service world-wide and will pose their particular challenges in the future. To the author’s knowledge, just in Sweden, high strength stainless steel bearings still exist in no less than some 650 bridges. In recent years, a large number of such bearings have failed with an alarmingly high frequency in Sweden during a period of six to twenty years after installation making them a serious maintenance cost issue.

After a brief summary of the history of high strength stainless steel bearings, the paper reviews service experience of such bearings in Sweden and elsewhere. Accompanying finite element analyses were performed in order to gain insight into the likely failure mechanism. Finally, this comprehensive review leads to a conclusion that identifies the causes of the failures occurred and makes some recommendations.

Although previous investigations of the stainless steel bearings have not been able to clearly identify the cause(s) of the failures occurred, it is found that the failures primarily occurred due to initiation of cracks through stress corrosion cracking followed by fatigue crack growth requiring a certain stress range and a sufficiently large number of cycles until final failure ensued through sudden and instable fracture after fatigue growth to a critical crack size.

Results are presented from tests where the fracture energy and the fatigue strength have been determined for unreinforced concrete beams. The tests were performed at temperatures between +20 and −35°C with concrete with compressive strength varying between 25 and 100 MPa.

Model scale tests have been undertaken to find a model material which can give scaled fragmentation in sublevel caving blast models where the purpose is to study the swelling and fragmentation of the burden when blasted against waste rock and also to study the gravity flow of the blasted burden when being discharged into the drift. To achieve a wished Rosin Rammler distribution of the blasted material in the blasted model, it was shown necessary to introduce weakness plans of different size and stochastic orientation in the model material. Crushed microscopic glass plates or coarse magnetite grains were used for that purpose with success

A methodology for fracture characterisation at strain rates up to 1000 s⁻¹, temperatures up to 650 °C, and various stress triaxialities is presented. High-speed photography combined with digital image correlation is used to evaluate the strain at fracture. The methodology was successfully demonstrated on aged nickel based Alloy 718, commonly used in the containment structure of aircraft engines. Tensile specimens with four different geometries were loaded to get a wide range of positive stress triaxialities. All specimens originated from one single heat and batch to ensure consistent mechanical properties. The results showed evident stress state dependency on the failure strain, where lower failure strains were observed at higher stress triaxialities for all combinations of temperatures and strain rates. A coupled relationship between the temperature and the stress triaxiality controlling the fracture strain was found. However, any clear dependency on strain rate was hard to detect.

The influence of structural anisotropy on the fracture toughness of S1 type freshwater ice was investigated by fabricating and testing three different fracture geometries from a single ice core. The ice was tested at - 16°C using the Chevron Edge Notch Round Bar in Bending (CENRBB), a Chevron Notched Tension (CNT) specimen and the Semi-Circular Bend (SCB) specimen. By this procedure, a complete anisotropic apparent fracture toughness (KQ) characterization is possible from one core. The specimens can be prepared with very little machining. This approach is therefore suitable for both field and, as in this work, laboratory studies. Three models are presented for computation of the stress-intensity-factor expressions for these specimens. There is a wide scatter in the KQ results and the apparent fracture toughness was higher for cracks perpendicular, than for cracks parallel, to the c-axis and the columnar grains. Possible explanations for this ambiguous behavior are discussed in terms of the microstructural influences and specimen size effects.

method to determine the fatigue of structures subjected to multiple-amplitude loads is presented. Unlike the more common cumulative damage methods, which are usually based on fatigue life data, the proposed method is based on tensile strength data. Assuming the Weibull distribution for the initial tensile strength and the fatigue life, the probability distributions for the residual tensile strength in both the crack initiation and the crack propagation stages of fatigue are determined. The method is illustrated for two-amplitude loads by means of experimental results obtained by testing specimens of a structural steel and is shown to be more accurate than the Palmgren-Miner cumulative damage method

Load parameters for a stationary Gaussian random load are taken as the location, scale and shape parameters of its power spectrum. The centre frequency of a power spectrum is proposed as a measure of fatigue life. A fatigue life function, formulated in terms of the load parameters, is evaluated from the test results obtained by fatigue testing a structural steel under six different power spectral shapes. The concept of a shape operator is employed to correlate fatigue lives under different power spectral shapes.

We consider the problem of estimating the probability of survival (non-failure) and the probability of safe operation (strength greater than a limiting value) of structures subjected to random loads. These probabilities are formulated in terms of the probability distributions of the loads and the material strength. For the material strength, the Weibull distribution is assumed, the parameters of which are estimated by a statistical analysis of the experimental tensile strength of steel specimens subjected to different periods of random loads. The statistical analysis shows that, with the application of random loads, the initial homogeneous distribution of strength changes to a two-component distribution, reflecting the two-stage fatigue damage. In the crack initiation stage, the strength increases initially and then decreases, while an abrupt decrease of strength is seen in the crack propagation stage. The consequences of this behaviour on the fatigue reliability are discussed

Two modes of damage in composite laminates are considered: the intralaminar damage (matrix cracking) and the interlaminar damage (interior delamination). Using a vectorial representation of damage as internal variables in a phenomenological theory, relationships between the overall stiffness properties and the intensity of damage in the individual modes are determined. These relationships show that the intralaminar damage reduces all elastic moduli for a general orientation of the damage entities (cracks) and changes the initial orthotropic symmetry of a laminate. The interlaminar damage, however, does not change the symmetry but reduces the moduli. Predictions of the elastic moduli changes are compared with experimental results, showing excellent agreement

Two particular cases concerning crack propagation and coalescence in brittle materials have been modeled by using the rock failure process analysis code, RFPA2D, and the results have been validated by reported experimental observations. Firstly, axial compression of numerical samples containing a number of large, pre-existing flaws and a row of suitably oriented smaller flaws are simulated. It has been confirmed that under axial compression, wing-cracks nucleate at the tips of the pre-existing flaws, grow with increasing compression, and become parallel to the direction of the maximum far-field compression. However, coalescence of the wing-cracks may be in either tensile mode or shear mode, or a combination of both modes. The numerical results show qualitatively a reasonably good agreement with reported experimental observations for samples with similar flaw arrangements. The numerical results demonstrate that, with a confining pressure, the crack growth is stable and stops at some finite crack length; whereas a lateral tensile stress even with a small value will result in an unstable crack growth after a certain crack length is attained. Secondly, failure mode in a sample containing inhomogeneities on grain scale has also been simulated. The results show that the failure mode strongly depends on the mechanical and geometric properties of the grains and inclusions

The essential work of fracture methodology (EWF) has been successfully adopted to evaluate the fracture toughness of various metals and polymers. However, some aspects of the methodology are still far less understood, such as the influence of the experimental parameters on EWF measurement in thin metal sheets. In the present paper, the ligament range criterion of the EWF approach was revised for several advanced high-strength steels (AHSS). The validity of the upper and lower ligament length limits given by the ESIS protocol is redefined and rationalized according to the necking capability and the plasticity behaviour of the different AHSS grades. The work provides a new criterion to define the minimum ligament length to be tested, based on the minimum distance required by the crack to fully develop the necking capability of the material. The width constraint is too restrictive and has no effect on the deviation from linearity in the upper range. On the other hand, the maximum ligament length is proven to be controlled by the size of the plastic zone as proposed by the ESIS protocol.

The fracture of hydrides in zirconium alloys is under consideration. According to the present boundary value problem, a hydride platelet lies ahead of a semi-infinite crack, along the crack plane. The surrounding material is elastic-plastic zirconium alloy. The platelet is either continuous or split into two parts, connected by a ductile matrix ligament. At distances from the crack tip, which are large compared to the hydride and the plastic zone size, the K-T field is applied and mode I, plane strain and contained yielding conditions prevail. Hydride platelet failure initiation and growth is simulated by using a de-cohesion crack growth model and the stress intensity factor, which causes fracture, is estimated at various temperatures as well as under various constraint conditions. Comparison of the calculated temperature effect on toughness with the experimental one is satisfactory. Fracture toughness decreases with T-stress. This effect is attributed to the interaction of the K-T field with hydride expansion, during precipitation. The reduction becomes more important at elevated temperatures and moderates the benefits on fracture toughness, caused by temperature increase. In addition to the detailed finite element results, analytical estimates on fracture toughness are presented, based on a cohesive zone model

Using a dislocation simulation approach, the basic equation for a crack perpendicular to a bimaterial interface is formulated in this paper. A novel expansion method is proposed for solving the problem. The complete solution for the problem, including the T stress ahead of the crack tip and the stress intensity factors are presented. The stress field characteristics are analyzed in detail. It is found that ahead of the crack tip and near the interface the normal stress, perpendicular to the crack plane, σx, is characterized by the K fields and the normal stress σy is dominated by the K field plus T stress in the region of 0 < r/b < 0.4 for 6/ao≤0.1, where b is the distance from the crack tip to the interface

Steady-state energy release rate (ERR) for fiber/matrix interface debond growth originated from fiber break in unidirectional composite is calculated using 3-D FEM models with hexagonal fiber arrangement. In the model the debonded fiber is central in the hexagonal unit which is surrounded by effective composite. The effect of neighboring fibers focusing on local fiber clustering on the ERR is analyzed by varying the distance between fibers in the unit. The steady-state ERR is calculated from potential energy difference between a unit in the bonded region far away from the debond front and a unit in the debonded region far behind the debond front. The ERR for different modes of crack propagation is obtained from a FEM model containing a long debond by analyzing the stress at the debond front.Results show that in mechanical axial tensile loading fracture Mode II is dominating, it has strong angular dependence (effect of closest fibers) but the average ERR is not sensitive to the local fiber clustering. In thermal loading the Mode III is dominating and the average ERR is highly dependent on the distance to neighboring fibers. However, for realistic loads the thermal ERR is much smaller than the mechanical.