Calculation of Stress Intensity Factors – An Interface Crack

A numerical study of the parameters influencing the accuracy of computed stress intensity factor (SIF) values is presented in this article. Mode I SIFs of a through-thickness center crack are calculated by employing the displacement extrapolation method (DEM) of near-tip field extrapolation and the energy-based interaction integral method (IIM). The results are compared with an analytical solution, and some recommendations are provided to increase the accuracy of the calculated mode I SIFs. Optimized influencing parameters can minimize the errors obtained with DEM, whereas the errors obtained with IIM are negligible for a variety of crack lengths. Based on the recommendations made for the mode I SIF calculation, assessment of the mode I and mode II SIFs is performed at the weld root crack tip of a load-carrying cruciform fillet welded joint loaded under a three-point bending condition. The accuracy of the mode I SIF calculated with DEM is independent of the crack length, whereas that of mode II is highly dependent. The IIM provides accurate SIFs for both modes for various crack lengths.

Fracture toughness resistance curves for a delamination in CFRP MD laminate composites, Part II: Mixed-mode deformation

Higher reliability and miniaturization for automotive sensor applications are more and more demanded. These sensors are exposed to harsh environments like extreme temperatures, fast temperature change and humidity. Flip chip interconnections using the Stud Bump Bonding (SBB) Technology provide a solution to fulfill these demands and requirements. For SBB interconnections, the failure modes during reliability testing are shifted from bump fatigue to crack initiation and propagation in the fillet, the die as well as cracks within the underfill. The present work focuses on chip side fillet cracking. The crack initiation and propagation and therefore the reliability of a flip chip interconnection depends strongly on the geometry of the components, the used assembly technology and the materials. Therefore, different chip sizes were used. Moreover, the SBB technology using underfill as well as Non Conductive Adhesive (NCA) were utilized. In order to identify the influence of board technology, different materials properties for the board were studied. In the FE analysis, a fracture mechanics approach was used to quantify the impact of these parameters. The locations of crack initiation in the underfill fillet were determined by conventional stress analysis. A bulk crack in the upper part of the fillet was modeled and the impact of the described parameters on the stress intensity factor was obtained. Once crack propagation occurred, the bulk cracks turns into a delamination of the vertical chip edge and the underfill. Therefore, interfacial fracture mechanics approach was utilized. The energy release rate and the bimaterial phase angle were used to characterize interfacial cracking. The Virtual Crack Closure Technique (VCCT) was used to obtain stress intensity factors for the bulk material as well as the energy release rate and phase angle for the delamination.

The collapse of overhanging rock is a common geological hazard in mountainous areas. The stability of overhanging rock is usually determined by the growth of a crack along a main structural plane. On the basis of linear fracture mechanics combined with the stress concentration coefficient, an analytical method to determine the stress intensity factor (SIF) of overhanging rock is developed to evaluate its stability. Experiments on pre-cracked sandstone were carried out to simulate failure of overhanging rock and verify the analytical solution to fracturing and failure of overhanging rocks. Additionally, numerical solutions using the finite element method are derived to compare with the experimental results. The J-integral and displacement extrapolation methods are used to determine stress changes at the crack tip in the overhanging rocks, and the results confirm that the analytical solutions are consistent with the results of the numerical solutions, including the displacement extrapolation used to analyze the SIF of the overhanging rock. The ratio of fracture toughness to effective SIF at the crack tip can be considered useful when examining the stability of overhanging rock.

The stress-intensity factors of a mixed-mode interface crack were measured by a speckle photography. A compact normal and shear specimen with an interface crack was employed. This specimen enables us to carry out the experiment under various kinds of mixed-mode loading. A steel and an epoxy resin were used as the dissimilar materials. The displacement along the crack lines at the free surface was measured by the speckle photography. The K1 and K11 values were determined by a least squares method using displacement data along the crack lines. The three-dimensional finite element analysis was carried out on the same specimen. The complex stress-intensity factor K associated with an elastic interface crack was discussed from three different approaches : virtual crack extension method, modified crack closure integral and displacement extrapolation. An accuracy of stress intensity factors obtained by the speckle photography was discussed by comparison of results obtained by the finite element analysis.

In this study, the first term of the asymptotic displacement and stress fields is determined analytically for a straight through crack along the interface between a ±45° transversely isotropic pair of materials. Since with this configuration, there is full coupling between the modes, this problem requires a three-dimensional treatment. To calculate stress intensity factors, a three-dimensional M-integral is derived using the asymptotic fields as auxiliary solutions. The displacement extrapolation method is derived as well, and used to check the results obtained by the M-integral. Two numerical test cases are employed to examine the accuracy of both methods. Results obtained for other mechanical problems are presented as well.

The use of quarter point element in dynamic crack analysis

Computation of the energy release rate, based on the FEA software ANSYS, with the virtual crack close technique, is studied. To reduce post-processing workload, the spring element is imposed at the cracktip. In practical applications, COMBIN14 spring elements are adopted to set up the finite element model. Then, the numerical analysis method is applied in interface crack. But the calculaed strain energy release rates are pseudo values, and only the total strain energy release rate convergences. At last, two numerical experiments are presented to validate this method. The results show that the calculated values of the total strain energy release rate are well with the theoretical values. This numerical analysis method is an efficient and accurate numerical analysis method.

Resin pocket area is a common defect in manufactruring of sandwich composite using vacuum infusion process (VIP). In this paper, a numerical study is performed on crack growth behavior and failure modes of a sandwich composite wind turbine blade by means of extended finite element method (XFEM) and considering virtual crack closure technique (VCCT). The effect of resin pocket area on crack growth is investigated by considering different sizes for this area. Results of numerical analysis have shown that crack growth in the specimen initiates in foam core under loading nose and propagates through the middle of foam core and decreases its angle and grows towards the tapered area until it reaches to the core-face interface. Calculation of stress intensity factors (SIFs) has shown that first and second fracture modes are dominant modes in crack initiation and propagation steps, respectively. It is also observed that small and average sizes of resin pocket area in sandwich composite specimens delays the damage propagation and large resin pocket area accelerates damage progress. Finally, numerical and experimental results of crack growth path and load-displacement behavior of four-point bending test have shown a good accordance.

Experiment has been conducted to measure the solubility Csat of mold compound and to obtain the moisture weight loss curves at various temperature. Moisture desorption modeling has been conducted to calculate the moisture diffusivity for desorption D(T) by matching with the experimental results. Finite Element Analysis (FEA) has also been conducted to calculate the transient development of strain energy release rate (ERR) at the interfacial crack tip due to thermal stress only (Gt), hygrostress only (Gh), and the combined effect (Gtotal) during solder reflow. ERR is computed based on the Virtual Crack Closure Technique (VCCT). It is found that Gh is significantly smaller than Gt, however the effect of hygrostress significantly increases the total strain energy release rate when combined with the thermal effect. The maximum Gtotal occurs at the peak of the solder reflow profile. The effects of crack size and geometrical parameters have been studied. The result imply that the interfacial crack is unstable and has a high tendency of growing to a significant extent. ERR is strongly influenced by the thickness of the package while length between the edge of die and pad has a moderate affect on the ERR.

전단응력에 의한 전단강도 및 모드 II 파괴인성은 이산화탄소 지중저장에서의 덮개암 및 주입층의 안정성 평가에 활용되는 중요한 인자들이다. 본 연구에서는 짧은 보 압축시험을 이용하여 코코니노 사암의 전단강도 및 모드 II 파괴인성을 측정하였다. 측정된 평균 전단강도는 23.53 MPa이며, 모드 II 파괴인성은 1.58 MPa<TEX>${\surd}$</TEX>m이다. 응력확대계수(stress intensity factor)는 변위외삽법(displacement extrapolation method)을 이용한 유한요소법으로 결정하였다. 또한 이축응력(biaxial stress)과 수분포화(water saturation)가 모드 II 파괴인성에 미치는 영향을 분석하였다. 그 결과 이축응력이 증가할수록 파괴인성도 증가하였고, 완전포화된 시험편의 파괴인성은 건조상태의 파괴인성보다 대략 11.4% 감소하였다. The mode II fracture toughness and strength due to shear stress are important parameters in the stability of caprock and injection zone with application to geological sequestration of carbon dioxide. In this research, a short beam compression test has been used to determine the shear strength and the mode II fracture toughness for Coconino sandstone. The average value of the shear strength and mode II fracture toughness are estimated to be 23.53 MPa and 1.58 MPa<TEX>${\surd}$</TEX>m respectively. The stress intensity factor is suggested by finite element analysis using the displacement extrapolation method. The effect of biaxial stress and water saturation on the fracture toughness has also been investigated. The fracture toughness increases with confining stresses, but decreases by 11.4% in fully saturated condition.

Influence of geometry and material on the stress intensity of an interfacial crack propagating from a bi-material notch

Thermoelastic and infrared-thermography methods for surface strains in cracked orthotropic composite materials

Introduction/purpose: The structural integrity of pressurized pipelines is often threatened by surface cracks, especially in welded regions. This study evaluates the effectiveness of composite wrap reinforcement in repairing longitudinal semi-elliptical cracks in welded steel pipelines subjected to internal pressure. Although environmental effects such as temperature, moisture, and chemical exposure were not modeled, they are acknowledged as key factors influencing the long-term durability of composite repairs. Methods: A three-dimensional finite element model was developed for a welded pipeline (outer diameter = 1016 mm, thickness = 12.8 mm) containing an external semi-elliptical crack (2c = 10.24 mm, a = 2.56 mm). The Virtual Crack Closure Technique (VCCT) was applied to compute Mode I Stress Intensity Factors (SIFs) under internal pressures of 2-12 MPa. A parametric study assessed the influence of patch length (100-400 mm), thickness (6-12 mm), and circumferential coverage angle (30°-360°), as well as adhesive shear modulus, thickness, and debonding effects. Results: Increasing patch length, thickness, and coverage angle reduced SIFs, improving crack-tip stress attenuation. A higher adhesive shear modulus enhanced interfacial load transfer, while excessive adhesive thickness impaired efficiency. Localized adhesive debonding significantly increased SIFs under pressure, highlighting the sensitivity of repair performance to bonding quality. Conclusions: This study provides design insights for optimizing composite reinforcement in welded pipeline repairs. Although a rectangular patch was analyzed, future work should investigate alternative geometries to mitigate edge stress concentrations and incorporate fatigue and environmental effects to better predict long-term service performance.

The effect of the mesh geometry on the accuracy of solutions obtained by the finite-element method for problems of linear fracture mechanics is investigated. The guidelines have been formulated for constructing an optimum mesh for several routine problems involving elements with linear and quadratic approximation of displacements. The accuracy of finite-element solutions is estimated based on the degree of the difference between the calculated stress-intensity factor (SIF) and its value obtained analytically. In problems of hydrofracturing of oil-bearing formation, the pump-in pressure of injected water produces a distributed load on crack flanks as opposed to standard fracture mechanics problems that have analytical solutions, where a load is applied to the external boundaries of the computational region and the cracks themselves are kept free from stresses. Some model pressure profiles, as well as pressure profiles taken from real hydrodynamic computations, have been considered. Computer models of cracks with allowance for the pre-stressed state, fracture toughness, and elastic properties of materials are developed in the MSC.Marc 2012 finite-element analysis software. The Irwin force criterion is used as a criterion of brittle fracture and the SIFs are computed using the Cherepanov–Rice invariant J-integral. The process of crack propagation in a linearly elastic isotropic body is described in terms of the elastic energy release rate G and modeled using the VCCT (Virtual Crack Closure Technique) approach. It has been found that the solution accuracy is sensitive to the mesh configuration. Several parameters that are decisive in constructing effective finite-element meshes, namely, the minimum element size, the distance between mesh nodes in the vicinity of a crack tip, and the ratio of the height of an element to its length, have been established. It has been shown that a mesh that consists of only small elements does not improve the accuracy of the solution.