Crack Initiation Load Research Articles

A coupled stress and energy failure model for crack initiation in arbitrarily shaped adhesive lap joints

AbstractIn this work, crack initiation in adhesive lap joints of arbitrary joint configuration is studied by means of a finite fracture mechanics approach. The analysis is based on a general stress solution for adhesive joints combined with a coupled stress and energy criterion. The instantaneous formation of a crack of finite size is predicted if a stress and energy criterion are satisfied simultaneously. The closed‐form analytical solution of the stress field allows for an efficient evaluation of the crack initiation load and corresponding finite crack length. A comparison to experimental results from literature and to numerical results obtained with a cohesive zone model approach shows a good agreement. (© 2016 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Effect of size and cohesive assumptions on the double-K fracture parameters of concrete

This paper studies the effect of size and cohesive assumptions on the double-K parameters in concrete fracture. These two parameters are the fracture toughnesses KIcini and KIcun, related with the crack initiation and the limit of the stable crack propagation, respectively, which are calculated using data from a load-crack mouth opening curve, P-wM (Xu and Reinhardt, 2000). The study starts from three-point bending tests with three different beam sizes, whose results calibrate a numerical model, used to produce additional P-wM curves from a wider beam-size range, with beam depths from 13 to 1300mm. The paper presents a simplification to obtain KIcini experimentally based on the loss of linearity in the P-wM curve, which allows avoiding the use of strain gauges to measure the crack initiation load. The evolution of KIcun and KIcini shows size dependence. The calculated values of KIcun increase slightly with the beam size whereas those of KIcini remain constant but below the experimental range and, later, they diminish for large beam sizes. This points out that KIcini calculation procedure is not correct, especially for sizes out of the usual experimental range. These shortcomings can be overcome by an appropriate selection of the initial stretch of the cohesive law, which leads to a proposal for improving the procedure to calculate KIcini. The analysis includes the calculation of the complete toughness-crack length curves (KIc-a), which are also dependent on the specimen size.

Crack initiation in metallic glasses under nanoindentation

Simulated nanoindentation tests on a model metallic glass reveal that the crack initiates inside a shear band via cavitation. The load-displacement curve was shown to be insensitive to the crack initiation but sensitive to subsequent crack propagation. The critical conditions for crack initiation were identified at both the macroscopic and microscopic levels. At the macroscopic level, the indenter geometry affects the overall critical load for crack initiation. Interestingly, the indentation volume at crack initiation appears to be a constant for different indenter geometries, based on which an analytical formula of the critical load as a function of the indenter geometry was derived. At the microscopic level, cavitation occurs once the normal stress perpendicular to the shear band exceeds a temperature-dependent critical cavitation stress. This critical cavitation stress was shown to reduce significantly upon shear deformation.

Evaluation of Fracture Toughness of Tantalum Carbide Ceramic Layer: A Vickers Indentation Method

A tantalum carbide (TaC) ceramic layer was produced on gray cast iron matrix by in situ technique comprising a casting process and a subsequent heat treatment at 1135 °C for 45 min. Indentation fracture toughness in TaC ceramic layer was determined by the Vickers indentation test for various loads. A Niihara approach was chosen to assess the fracture toughness of TaC ceramic layer under condition of the Palmqvist mode in the experiment. The results reveal that K IC evaluation of TaC ceramic layer by the Vickers indentation method strongly depends on the selection of crack system and K IC equations. The critical indentation load for Vickers crack initiation in TaC ceramic layer lies between 1 and 2 N and the cracks show typical intergranular fracture characteristics. Indentation fracture toughness calculated by the indentation method is independent of the indentation load on the specimen. The fracture toughness of TaC ceramic layer is 6.63 ± 0.34 MPa m1/2, and the toughening mechanism is mainly crack deflection.

Effect of adhesive fillet geometry on bond strength between microelectronic components and composite circuit boards

Printed circuit boards (PCBs) assembled with ball grid array (BGA) microelectronics packages were tested in a double cantilever beam (DCB) configuration. The results were compared for a filled and an unfilled underfill epoxy adhesive as well as a cyanoacrylate adhesive. The original fillet, formed in the underfilling process, was modified to create fillets of different sizes. Regardless of the underfill thermal and mechanical properties as well as its curing profile, the crack initiation load and the failure mode were solely a function of the size of the underfill fillet, and the failure always initiated within the PCB. Moreover, the strength of the underfilled solder joints was increased significantly (approximately 100%) by the presence of a relatively large fillet. This effect of the underfill fillet on the crack path and the fracture load was then examined in terms of differences in the stress states using a finite element model.

Analytical solution for crack growthing of semi-submersible platform’s horizontal brace

The article present an analytical solution to calculate the crack growth characteristics of semi-submersible platform’s horizontal brace with a circumferential through–crack lies at the boundary between the horizontal brace and column loaded by tension. The results of the proposed model may be applied in the full range of fracture from stationary crack to plastic collapse and the solution process is clear and the closed form solution is found which is especially suitable to solve problems in practical engineering application. The relationship between tension and crack growth and the influence of different initial angles and material parameters of the horizontal brace to the crack initiation load and ultimate load have been got as well as the variation tendencies of crack tip opening displacement on the cracked section and the relationship between plastic zone and elastic zone of the cracked section with different tension under stationary crack condition in this article with a practical engineering application example which could give good suggestion to semi-submersible platform designers and managers. The article present an analytical solution to calculate the crack growth characteristics of semi-submersible platform’s horizontal brace with a circumferential through–crack lies at the boundary between the horizontal brace and column loaded by tension. The results of the proposed model may be applied in the full range of fracture from stationary crack to plastic collapse and the solution process is clear and the closed form solution is found which is especially suitable to solve problems in practical engineering application. The relationship between tension and crack growth and the influence of different initial angles and material parameters of the horizontal brace to the crack initiation load and ultimate load have been got as well as the variation tendencies of crack tip opening displacement on the cracked section and the relationship between plastic zone and elastic zone of the cracked section with different tension under stationary crack condition in this article with a practical engineering application example which could give good suggestion to semi-submersible platform designers and managers. The article present an analytical solution to calculate the crack growth characteristics of semi-submersible platform’s horizontal brace with a circumferential through–crack lies at the boundary between the horizontal brace and column loaded by tension. The results of the proposed model may be applied in the full range of fracture from stationary crack to plastic collapse and the solution process is clear and the closed form solution is found which is especially suitable to solve problems in practical engineering application. The relationship between tension and crack growth and the influence of different initial angles and material parameters of the horizontal brace to the crack initiation load and ultimate load have been got as well as the variation tendencies of crack tip opening displacement on the cracked section and the relationship between plastic zone and elastic zone of the cracked section with different tension under stationary crack condition in this article with a practical engineering application example which could give good suggestion to semi-submersible platform designers and managers.

Elastic properties and indentation cracking behavior of Na2O-TiO2-SiO2 glasses

The effects of composition on indentation deformation and cracking behavior of Na2O-TiO2-SiO2 glasses were studied in the light of structural considerations and parameters such as the atomic packing density (Cg) and the network energy, using a combination of elastic measurements and micro-hardness indentation experiments. Na2O-TiO2-SiO2 glasses with titania contents of 4–10mol% and sodium oxide contents of 10–25mol% were prepared through a traditional melt-quench process. Indentation experiments were conducted using a Vickers indenter with loads ranging from 10 mN to 49N. Critical loads for crack initiation and cracking patterns were systematically investigated and correlated with the elastic properties of glass. In this ternary system concerning a relatively large range of Poisson's ratio (ν), a minimum in critical crack initiation load was observed at a ν of 0.21–0.22. This study brings to light the unusual role of titanium in the glass network, which gives birth to peculiar trends in the structural and mechanical properties.

Analytical study of composite beams with different arrangements of channel shear connectors

Channels are implemented in composite beams as shear connectors in two arrangements, face to face and back to back. No relevant explanation is found in the design codes to clarify the preference of the mentioned arrangements. Besides, the designers do not have a common opinion on this subject; i.e., some recommend the face to face and others, back to back status. In this research, channel shear connectors in composite beams are studied analytically for both arrangements using ABAQUS software. For this purpose, they have been modeled in simply supported beams in the arrangements of face to face and back to back; their effects on the crack initiation load of concrete slabs were monitored. The stiffness values of composite beams were also compared in the two arrangements using force-displacement curve; the results are relatively the same in both cases. Furthermore, the effects of compressive strength of concrete, channel size, length and spacing of channels as well as steel type of channels on the performance of composite beams have been investigated. According to the results obtained in this research, the face to face status shows better performance in comparison with that of back to back, considering the load of concrete fracturing.

Reference stress based J and COD estimation of circumferential through-wall cracked elbows under in-plane bending

This paper proposes J-integral and crack opening displacement (COD) estimation equations based on the reference stress method for circumferential through-wall cracked elbows under in-plane bending. For best estimates of J and COD, an optimized reference load, used to define the reference stress, is given. The proposed equations are compared with detailed finite element results. They are further validated against eight published full-scale pipe test data. Comparison of crack initiation and maximum loads shows good agreement.

Scratch Fracture of Polycrystalline Silicon Wafers

Fracture of silicon wafers is responsible for lower than desirable manufacturing yields in the photovoltaic industry. This study investigates the fracture response of polycrystalline silicon wafers under sliding contacts at different length scales, by means of macro and microscratch tests which simulate cutting processes. The dominant fracture modes were found to be partial cone cracking (macro) and radial cracking (micro). Statistical analysis of the critical loads for crack initiation showed that polycrystalline wafers are weaker than their single‐crystal counterparts, that is, they crack at lower applied loads under comparable conditions. Moreover, the Weibull modulus of polycrystalline silicon was found to be the average of the relevant single‐crystal directions. Subsequent microscopic observations and flexure tests reveal that the lower resistance of polycrystalline silicon to scratch fracture is due mainly to the presence of relatively large polishing defects, and not to the weakness of its grain boundaries. Alternatives are proposed to minimize damage during ingot cutting, with a view to minimizing wafer breakages during wafer handling and machining.

Crack influence on load-bearing capacity of glued laminated timber using extended finite element modelling

Most of the cracks are caused by changes in temperature and relative humidity which lead to shrinkage and swelling of the wood and thereby induce stresses in the structure. How these cracks influence the strength of the wooden structure, especially the shear strength, is not well understood. However, it is reasonable to expect that cracks have an impact on the shear strength as they preferably run along the beams in the direction of grain and bond lines. The purpose of this study was to investigate the load-bearing capacity of cracked glulam beams and to find a model that could predict the failure load of the beams due to the cracks. Three-point bending tests were used on glulam beams of different sizes with pre-manufactured cracks. An orthotropic elastic model and extended finite element method was used to model the behaviour of the cracked beams and to estimate the load-bearing capacity. The conclusions were validated by numerical simulations of the mechanical behaviour of three-point bending of glulam beams with different crack locations. The crack initiation load was recorded as the failure load and compared to the experimental failure load. The results of the compaction simulations agree well with the experimental results.

Prediction of Crack Initiation Load in Throughwall Circumferentially Cracked Pipes Using 3D Cohesive Zone Model

Prediction of Crack Initiation Load in Throughwall Circumferentially Cracked Pipes Using 3D Cohesive Zone Model

Mechanical properties, sliding wear and solid particle erosion behaviors of plasma enhanced magnetron sputtering CrSiCN coating systems

CrSiCN coating systems with different concentrations of Cr, Si, C, and N were investigated for their microstructure, mechanical properties (hardness H, elastic modulus E and indentation fracture toughness KIC) and tribological behaviors using SEM, nano-indentation, indentation, pin-on-disk wear test, and sand particle erosion test. The wear behaviors, such as specific wear rate and Archard wear coefficient, showed inverse relationships with H3/E2 ratio, confirming that the resistance to plastic deformation is the essential factor governing sliding wear behavior. High H3/E2 ratios also contributed to increased resistances to erosion at low impingement angles. However, at higher impingement angles (>60°), coatings with lower index of brittleness (B=2.656µm−1/2), higher critical load (P⁎=6.670N) for crack initiation and fracture surface energy (γf=0.123Jm−2) offered a higher erosion resistance. The indentation fracture toughness (KIC), hardness (H) and elastic modulus (E) are limited to interpret erosion behaviors in a comprehensive approach, suggesting that erosion is a complex process where multiple mechanical properties contribute to erosion performance.

A 2000-year perspective on indentation crack resistance and brittleness of glass

Data on micromechanical properties of ancient and medieval glass fragments and glasses of early modern and today's manufacturing were compiled to offer a tentative look on changes in the brittleness of glass over the past 2000years. Chronology of glass making was based on glass chemistry using rare earth element (REE) pattern, fluxing agents and provenance analysis while cracking and brittleness were evaluated from Vickers indentation in the course of the mean crack initiation load CR and the crack length-to-half diagonal ratio c/a. A structural analysis revealed that CR increases and c/a decreases with increasing molar volume i.e. decreasing atomic packing fraction, which allows us to classify periods of high and low crack-resistant and brittle glasses along the time line of historic glass technology.

In-situ SEM study of transverse cracking and delamination in laminated composite materials

Abstract Transverse microcrack growth and delamination are two key damage mechanisms in laminated composite materials, and while often treated separately in damage prediction studies, they are, in fact, highly coupled. Essentially, transverse cracks initiate around fibres, coalesce and grow until they extend to ply boundaries, at which point they initiate micro-delaminations. Under increasing load these micro-delaminations eventually coalesce to form macroscopic delaminations, which severely reduce material stiffness and lead to catastrophic failure of the composite structure. This paper presents an investigation into how altering transverse crack densities can influence the growth of delaminations. Novel in-situ SEM micromechanical testing and acoustic damage detection techniques were coupled and used to determine transverse crack initiation loads, transverse crack density, and local micro-delamination lengths for a number of cross-ply laminates. The laminates were loaded in a four-point bending mode to induce crack opening direct stresses on the tension side. To examine the effect of combined direct and shear stresses, the laminates were also loaded in a three-point bending mode, and suitable comparisons between both bending modes allowed for the influence of the shear stress to be isolated. The main variable under investigation is the thickness of the transverse ply block, and it is shown that increasing the number of transverse plies (i.e. thickness) can significantly increase the load carrying capacity of the laminate by reducing the transverse crack density. It was found that the lower transverse crack densities meant that the micro-delaminations which initiated at the ply boundary required significantly greater stress to fully coalesce as the distance between transverse cracks was greater. Once micro-delamination had initiated, its length was found to be linearly related to the load applied. For all layups investigated, the average micro-delamination length seen immediately prior to catastrophic failure was approximately 1.2 times the thickness of the tensile 90° ply portion of the laminate.

유리/다공성 알루미나의 접촉하중에 의한 기계적 거동

Porous alumina with different porosities, 5.2 - 47.5%, were coated with cover-glass having a thickness of 160 μm, using epoxy adhesive. We investigated the effect of the porosity of the substrate layer on the crack initiation load, and the size of cracks propagated in the coating layer. Hertzian indentations were used to evaluate the damage behavior under a constrained loading condition. Typically, two types of cracks, ring cracks and radial cracks, were observed on the surface of the glass/porous alumina structure. Indentation stress-strain curves, crack initiation loads, crack propagation sizes, and flexural strengths were investigated as a function of porosities. The results indicated that a porosity of less than 30% and a higher substrate elastic modulus were beneficial at suppressing cracks occurrence and propagation. We expect lightweight mechanical components with high strength can be successfully fabricated by coating and controlling porosities in the substrate layer.

Reprint of: Acoustic emission analysis for characterisation of damage mechanisms in fibre reinforced thermosetting polyurethane and epoxy

Acoustic emission analysis is used to investigate microscopic damage mechanisms and damage progress in unidirectional glass and carbon fibre reinforced composites. Under static loading the influence of fibre orientation on damage initiation and propagation is determined. A novel polyurethane matrix system significantly enhances material performance in terms of crack initiation load levels, crack growth, damage tolerance and off-axis tensile strength. Hysteresis measurements during stepwise increasing dynamic load tests highlight the effect of fibre–matrix-adhesion and resin fracture toughness in unidirectional 0° fibre reinforced composites. Acoustic detection of beginning fibre breakage correlates with a significant increase of loss work per cycle.

Analytical Solution for Stress Field and Intensity Factor in CSTBD under Mixed Mode Conditions

Considering the fact that rocks fail faster under tensile stress, rock tensile strength is of greatimportance in applications such as blasting, rock fragmentation, slope stability, hydraulic fracturing,caprock integrity, and geothermal energy extraction. There are two direct and indirect methods tomeasure tensile strength. Since direct methods always encompass difficulties in test setup, indirectmethods, specifically the Brazilian test, have often been employed for tensile strength measurement.Tensile failure is technically attributed to crack propagation in rock. Fracture mechanics hassignificant potential for the determination of crack behaviour as well as propagation pattern. To applyBrazilian tests, cracked disc geometry has been suggested by the International Society for RockMechanics ISRM. Accordingly, a comprehensive study is necessary to evaluate stress field and stressintensity factor (SIF) around the crack in the centre of the specimen. In this paper, superpositionprinciple is employed to solve the problem of cracked straight-through Brazilian disc (CSTBD), usingtwo methods of dislocation and complex stress function. Stress field and SIF in the vicinity of thecrack tip are then calculated. With the proposed method, the magnitude of critical load for crackinitiation in structures can be predicted. This method is valid for any crack of any arbitrary length andangle. In addition, numerical modelling has been carried out for the Brazilian disc. Finally, theanalytical solution has been compared with numerical modelling results showing the same outcomefor both methods.

A coupled stress and energy criterion for the assessment of crack initiation in single lap joints: A numerical approach

In this work, a new approach for the prediction of the crack initiation loads of single lap joints (SLJ) is presented. The failure model for crack initiation in brittle adhesive layers is based on Finite Fracture Mechanics and makes use of a coupled stress and energy criterion. It requires only two fundamental material parameters: the tensile strength and the fracture toughness. A Finite Element Model for the SLJ yields the required stress field and energy release rates. It is found that the SLJ contains a non-positive geometry at the expected crack initiation point leading to a non-monotonically increasing incremental energy release rate function. It follows a discussion of results of exemplary joint designs and a comparison with experimental results from literature. The failure load predictions of the present failure model show very good agreement with experimental results. It is emphasized that no parameter fitting was necessary to obtain these results. In contrast to the majority of the existing failure criteria, the adhesive layer thickness effect is described correctly.

Ductile Fracture Simulation of Full-scale Circumferential Cracked Pipes: (I) Carbon Steel

This paper reports ductile fracture simulation and comparison with carbon steel test data of full-scale cracked pipes via 3-D finite element damage analysis based on stress-modified fracture strain model. Although there are few test results and discussion of full-scale cracked pipes, it is not an easy task to properly evaluate fracture behaviour of large-scale components for various pipe sizes with different shape of a crack-like defect. In such a situation, finite element (FE) damage analysis can be a competitive alternative to characterize the fracture behaviour of cracked components such as crack initiation and maximum loads. In recent years, a simple FE method [1] to simulate ductile fracture has been developed based on the stress-modified fracture strain model [2,3]. The technique appropriately simulated ductile failure for miscellaneous cracked components [4,5]. However, for some cases, large-scale components using small element size, FE analysis couldn’t give reliable values because of numerical instability. Element-size-dependent critical damage model enhanced by taking the effect of element-size on the ductile fracture damage analysis is introduced to overcome this problem and to be applicable to the large-scale structures. In order to validate proposed method, two types of carbon steel (A106 Gr. B and SA333 Gr. 6) pipes with a circumferential crack taken from [6] are considered, subjected to four-point bending only and combined loading. It is shown that predicted crack initiation and maximum loads are compared with experimentally measured values, showing overall good agreements.