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The aim of this study is to represent the combined effect of mode mixity, specimen geometry and relative crack length on the T -stress, elastic–plastic stress fields, integration constant I n , angle of initial crack extension, and the plastic stress intensity factor. The analytical and numerical results are obtained for the complete range of mixed modes of loading between mode I and mode II. For comparison purposes, the reference fields for plane mixed-mode problems governing the asymptotic behavior of the stresses and strains at the crack tip are developed in a power law elastic–plastic material. For the common experimental fracture mechanics specimen geometries considered, the numerical constant of the plastic stress field I n and the T -stress distributions are obtained as a function of the dimensionless crack length and mode mixity. A method is also suggested for calculating the plastic stress intensity factor for any mixed-mode I/II loading based on the T -stress and power law solutions. It is further demonstrated that in both plane stress and the plane strain, the plastic stress intensity factor can be used to characterize the crack tip stress fields for a variety of specimen geometries and different mixed-mode loading. The applicability of the plastic stress intensity factor to analysis of the in-plane and out-of-plane constraint effect is also discussed.

This research work aims to compare the strength and fracture mechanics properties of plain concretes, obtained from different coarse aggregates. During the study, mechanical parameters including compressive strength (fcm) and splitting tensile strength (fctm), as well as fracture parameters involving critical stress intensity factor (KIcS) and critical crack tip opening displacement (CTODc) were evaluated. The effect of the aggregates used on the brittleness of the concretes was also analyzed. For better understanding of the crack initiation and propagation in concretes with different coarse aggregates, a macroscopic failure surfaces examination of the tested beams is also presented. Crushed aggregates covered were basalt (BA), granite (GT), and limestone (LM), and natural peeble gravel aggregate (GL) were used in the concrete mixtures. Fracture toughness tests were performed on an MTS 810 testing machine. Due to the high strength of the rock material, the rough surface of the aggregate grains, and good bonding in the ITZ area between the aggregate and the paste, the concretes with crushed aggregates exhibited high fracture toughness. Both of the analyzed fracture mechanics parameters, i.e.,  KIcS and CTODc, increased significantly in the case of concretes which were manufactured with crushed aggregates. They amounted, in comparison to concrete based on gravel aggregate, to levels ranging from 20% for concrete with limestone aggregate to over 30% for concrete with a granite aggregate, and to as much as over 70% for concrete with basalt aggregate. On the other hand, the concrete with gravel aggregate showed the lowest fracture toughness because of the smooth surface of the aggregate grains and poor bonding between the aggregate and the cement paste. However, the fracture process in each series of concrete was quasi-plastic in the case of gravel concrete, semi-brittle in the case of limestone concrete, and clearly brittle in the case of the concretes based on granite and basalt aggregates. The results obtained help to explain how the coarse aggregate type affects the strength parameters and fracture toughness at bending.

Weld bead geometry cannot, by its nature, be precisely defined. Parameters such as bead shape and toe radius vary from joint to joint even in well-controlled manufacturing operations. In the present paper the weld toe region is modelled as a sharp, zero radius, V-shaped notch and the intensity of asymptotic stress distributions obeying Williams’ solution are quantified by means of the Notch Stress Intensity Factors (NSIFs). When the constancy of the angle included between weld flanks and main plates is assured and the angle is large enough to make mode II contribution non-singular, mode I NSIF can be directly used to summarise the fatigue strength of welded joints having very different geometry. By using a large amount of experimental data taken from the literature and related to a V-notch angle of 135°, two NSIF-based bands are reported for steel and aluminium welded joints under a nominal load ratio about equal to zero. A third band is reported for steel welded joints with failures originated from the weld roots, where the lack of penetration zone is treated as a crack-like notch and units for NSIFs are the same as conventional SIF used in LEFM. Afterwards, in order to overcome the problem related to the variability of the V-notch opening angle, the synthesis is made by simply using a scalar quantity, i.e. the mean value of the strain energy averaged in the structural volume surrounding the notch tips. This energy is given in closed form on the basis of the relevant NSIFs for modes I and II and the radius RC of the averaging zone is carefully identified with reference to conventional arc welding processes. RC for welded joints made of steel and aluminium considered here is 0.28 mm and 0.12 mm, respectively. Different values of RC might characterise welded joints obtained from high-power processes, in particular from automated laser beam welding. The local-energy based criterion is applied to steel welded joints under prevailing mode I (with failures both at the weld root and toe) and to aluminium welded joints under mode I and mixed load modes (with mode II contribution prevailing on that ascribable to mode I). Surprising, the mean value of ΔW related to the two groups of welded materials was found practically coincident at 2 million cycles. More than 750 fatigue data have been considered in the analyses reported herein.

In this study a three-dimensional finite element method analysis of repairing plate with bonded composite patch subjected to tensile load was presented. The effect of the corrosion on the damage of the adhesive (FM73) in the length of inclined crack is presented. The obtained results show that the increase of (DR) is due to the increase of the inclination of the crack against it leads to the decrease of the values of the stress intensity factor in mode I (KI).

Weld defects such as porosity, inclusion, burn-through, and lack of penetration are difficult to detect and control effectively in an orthotropic steel deck (OSD), which will be a fatigue crack initiation site and lead to several fatigue cracking. The crack growth behavior in defective welded joints is different from that of defect-free joints. This study investigates crack–inclusion interaction for rib-to-deck welded joints in OSDs based on numerical simulation and linear elastic fracture mechanics (LEFM). A refined finite element model of a half U-rib with cracks and inclusions was established by using the FRANC3D-ABAQUS interactive technology. The full processes of the crack–inclusion interaction from approaching and penetrating were accurately simulated. Critical parameters, including the stress intensity factor (SIF), the shape factor, the growth rate, and the growth direction were analyzed. The stiff and soft inclusions amplify and shield the SIF of cracks when the crack grows to the local area of inclusions. During the entire process of crack growth, the soft and stiff inclusion accelerate and inhibit the crack growth, respectively. The stiff inclusion will lead to asymmetric growth of the crack shape, where the portion of the crack away from the inclusions has a higher growth rate. The soft and stiff inclusions will attract and repel the direction of crack growth at the proximal point, respectively.

This study presents test results and deep discussion regarding measurements of the fracture toughness of new concrete composites based on ternary blended cements (TCs). A composition of the most commonly used mineral additive (i.e., fly ash (FA)) in combination with nano-silica (NS) has been proposed as a partial replacement of the ordinary Portland cement (OPC) binder. The novelty of this article is related to the fact that ordinary concretes with FA + NS additives are most often used in construction practice, and there is a decided lack of fracture toughness test results concerning these materials. Therefore, in order to fill this gap in the literature, an extensive evaluation of the fracture mechanic parameters of TC was carried out. Four series of concretes were created, one of which was the reference concrete (REF), and the remaining three were TCs. The effect of a constant content of 5% NS and various FA contents, such as 0, 15%, and 25% wt., as a partial replacement of cement was studied. The parameters of the linear and nonlinear fracture mechanics were analyzed in this study (i.e., the critical stress intensity factor (KIcS), critical crack tip opening displacement (CTODc), and critical unit work of failure (JIc)). In addition, the main mechanical parameters (i.e., the compressive strength (fcm) and splitting tensile strength (fctm)) were evaluated. Based on the studies, it was found that the addition of 5% NS without FA increased the strength and fracture parameters of the concrete by approximately 20%. On the other hand, supplementing the composition of the binder with 5% NS in combination with the 15% FA additive caused an increase in all mechanical parameters by approximately another 20%. However, an increase in the FA content in the concrete mix of another 10% caused a smaller increase in all analyzed factors (i.e., by approximately 10%) compared with a composite with the addition of the NS modifier only. In addition, from an ecological point of view, by utilizing fine waste FA particles combined with extremely fine particles of NS to produce ordinary concretes, the demand for OPC can be reduced, thereby lowering CO2 emissions. Hence, the findings of this research hold practical importance for the future application of such materials in the development of green concretes.

When evaluating the safety of steel structures, welding residual stress is used as the secondary load and if there is any restraint, the yield stress of the base material is used for secondary load, regardless of the size of the restraint. Of late, as the yield stress of members is increasing with the increase in the use of high-strength steels, the proportion of the residual welding stress in the total load during the evaluation of the safety of structures is increasing. Therefore, it is necessary to investigate the effect of the size of the restraint on the residual welding stress, determine reasonable residual stress according to the size of the restraint, and apply the residual stress as a secondary load. To investigate the effect of constraint conditions on residual welding stress, thermoelastic–plastic analysis was performed for different member thicknesses, yield stresses, and constraint sizes. The restraint did not affect the residual stress in the direction of the weld line but did affect the residual stress in the direction perpendicular to the weld line. The restraint moved the tensile stress to the compression stress in the direction perpendicular to the weld line at the first layer of the weld and moved the compression stress to the tensile stress at the middle and final layers of the weld. The change in residual stress was the largest in the middle of the weld.

A correction is provided to the formula for the stress intensity factor for the double cleavage drilled compression (DCDC) specimen derived by Plaisted et al. in Int J Fract 141: 447–457, 2006 .

This paper presents the experimental results and deep discussion on the simultaneous effect of fly ash (FA) and synthetic nano-SiO2 on the main strength parameters and fracture toughness expressed by critical stress intensity factor, KIcS of a new concrete based on ternary blended cements (TC). Four series of concretes were made, one of which was the control concrete and the remaining three were TC. The effect of constant content of 5% nano-SiO2 and various FA contents such, i.e.: 0, 15 and 25% wt. as partial replacement of cement were studied. During the studies the DIC technique was applied to determine the deformation of the concrete beams in the propagation area of the modelled initial crack. Based on the studies it was found that the addition of 5% nano-SiO2 without FA increases the strength and fracture toughness of concrete by approx. 20%. On the other hand supplementing the composition of the binder with 5% nano-SiO2 in combination with the 15% FA additive causes an increase in all mechanical parameters by another approx. 20%. However, an increase in the FA content in the concrete mix by another 10% causes a smaller increase in the all analysed factors, i.e. by approx. 10% compared to composite with the addition of nano-SiO2 modifier only. In addition, based on the studies using DIC technique it was observed that in concrete including only nano-SiO2 the crack paths were almost perfectly rectilinear in shape, with a significant width of opening. However, in concrete containing 5% nano-SiO2 + 15% FA the crack paths were curvilinear with characteristic additional microcracks in the vicinity of the main crack, whereas in concrete with the addition of 5% nano-SiO2 + 25% FA the crack paths were very strongly curved and had pronounced branching and numerous additional microcracks in the vicinity of the main crack. From an application point of view, concretes involving FA and nano-SiO2 can be used in the execution of specific types of concrete and reinforced concrete structures that require a material with reduced brittleness and at the same time increased fracture toughness.

We review, unify and extend work pertaining to evaluating mode mixity of interfacial fracture utilizing the virtual crack closure technique (VCCT). From the VCCT, components of the strain energy release rate (SERR) are obtained using the forces and displacements near the crack tip corresponding to the opening and sliding contributions. Unfortunately, these components depend on the crack extension size, Δ, used in the VCCT. It follows that a mode mixity based upon these components also will depend on the crack extension size. However, the components of the strain energy release rate can be used for determining the complex stress intensity factors (SIFs) and the associated mode mixity. In this study, we show that several—seemingly different—suggested methods presented in the literature used to obtain mode mixity based on the stress intensity factors are indeed identical. We also present an alternative, simpler quadratic equation to this end. Moreover, a Δ-independent strain energy release based mode mixity can be defined by introducing a “normalizing length parameter.” We show that when the reference length (used for the SIF-based mode mixity) and the normalizing length (used for Δ-independent SERR-based mode mixity) are equal, the two mode mixities are only shifted by a phase angle, depending on the bimaterial parameter ε.