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The purpose of this paper is to introduce a numerical investigation used to calculate the J-integral of the main crack behavior emanating from a semicircular notch and double semicircular notch and its interaction with another crack which may occur in various positions in (TiB/Ti) functionally graded material (FGM) plate subjected to tensile mechanical load.

For this purpose the variations of the material properties are applied at the integration points and at the nodes by implementing a subroutine USDFLD in the ABAQUS software. The variation of the J-integral according to the position, the length and the angle of rotation of cracks is demonstrated. The variation of the J-integral according to the position, the length and the angle of rotation of cracks is examined; also the effect of different parameters for double notch FGM plate is investigated as well as the effect of band of FGM within the ceramic plate to reduce J-integral.

According to the numerical analysis, all parameters above played an important role in determining the J-integral.

The present study consists in investigating the simulation used to calculate the J-integral of the main crack behavior emanating from a semicircular notch and double semicircular notch and its interaction with another crack which may occur in various positions in (TiB/Ti) FGM plate under Mode I. The J-integral is determined for various load applied. The cracked plate is joined by bonding an FGM layer to TiB plate on its double side. The determination of the gain on J-integral by using FGM layer is highlighted. The calculation of J-integral of FGM’s involves the direction of the radius of the notch in order to reduce the J-integral.

The purpose of this paper is to perform a theoretical analysis of non-linear delamination fracture in cantilever beam opened notch (CBON) configuration. It is assumed that the non-linear mechanical behavior of the CBON can be described by using a stress-strain curve with power-law hardening.

The fracture analysis is carried-out by applying the integration contour independent J-integral. For this purpose, a model based on the technical beam theory is used. Equation is derived for determination of the CBON specimen curvature in elastic-plastic stage of deformation. The equation is solved by using the MatLab program system. Solutions of the J-integral are obtained at linear-elastic as well as elastic-plastic behavior of the CBON. The influence of the power-law exponent on the non-linear fracture is evaluated.

The analysis reveals that the J-integral value increases when the exponent of the power-law increases. The solution obtained here is very useful for parametric analyses of the non-linear fracture behavior, since the simple formulas derived capture the essentials of the fracture response.

Beside for parametric investigations, the solution obtained here can also be applied for calculating the critical J-integral value at non-linear behavior using experimentally determined critical fracture load at the onset of crack growth from the initial crack tip position in the CBON configuration.

An analysis is performed of the non-linear fracture in the CBON configuration by applying the J-integral approach, assuming that the mechanical response can be modeled using a stress-strain curve with power-law hardening.

The purpose of this paper is to perform a theoretical analysis of delamination fracture behaviour of the Crack Lap Shear layered beam configuration taking into account the material non-linearity. A delamination crack located arbitrarily along the beam height was considered in this study.

The beam mechanical behaviour was described by using the Ramberg-Osgood stress-strain relation. Fracture was analysed by applying the J-integral approach. Besides by using symmetric Ramberg-Osgood stress-strain curve, fracture was investigated also by Ramberg-Osgood stress-strain curve that is not symmetric with respect to tension and compression. The J-integral solutions were verified by performing elastic-plastic analyses of the strain energy release rate.

The effects of crack location and material properties on the non-linear fracture behaviour were evaluated. It was found that the material non-linearity leads to increase of the J-integral values. Therefore, the material non-linearity has to be taken into account in fracture mechanics based safety design of structural members composed by layered materials. The analytical solutions derived are very useful for parametric investigations of delamination fracture with considering the material non-linearity. The results obtained can be applied for optimisation of the beam structure with respect to fracture performance.

The present study contributes for the understanding of delamination fracture in layered beams that exhibit non-linear material behaviour.

The purpose of this paper is to deal with an analytical investigation of delamination fracture in the mixed-mode bending (MMB) multilayer beam configurations taking into account the material non-linearity.

The J-integral approach was applied in fracture analysis. The beam layers non-linear mechanical response was described by using a power-law stress-strain relation with four material constants. Analytical solutions of the J-integral were derived by using the technical beam theory. The fracture analysis developed is valid for MMB beams whose layers may have different thicknesses. Also, the values of material constants in the non-linear stress-strain equation may be different for each layer.

The effect of material constants, crack location and layer thicknesses on the non-linear fracture was evaluated. The analytical solutions obtained are very suitable for parametric studies of non-linear fracture behaviour. The approach developed here can be used for optimization of multilayered beam structures with respect to the delamination fracture performance. The present study can also be useful for the understanding of fracture in multilayered beams exhibiting material non-linearity.

For the first time, an analytical study was performed of the delamination fracture behaviour of the MMB multilayered beam configuration taking into account the material non-linearity.

This study aims to investigate the reliability issues of microvoid cracks in solder joint packages exposed to thermal cycling fatigue.

The specimens are subjected to JEDEC preconditioning level 1 (85 °C/85%RH/168 h) with five times reflow at 270°C. This is followed by thermal cycling from 0°C to 100°C, per IPC-7351B standards. The specimens' cross-sections are inspected for crack growth and propagation under backscattered scanning electronic microscopy. The decoupled thermomechanical simulation technique is applied to investigate the thermal fatigue behavior. The impacts of crack length on the stress and fatigue behavior of the package are investigated.

Cracks are initiated from the ball grid array corner of the solder joint, propagating through the transverse section of the solder ball. The crack growth increases continuously up to 0.25-mm crack length, then slows down afterward. The J-integral and stress intensity factor (SIF) values at the crack tip decrease with increased crack length. Before 0.15-mm crack length, J-integral and SIF reduce slightly with crack length and are comparatively higher, resulting in a rapid increase in crack mouth opening displacement (CMOD). Beyond 0.25-mm crack length, the values significantly decline, that there is not much possibility of crack growth, resulting in a negligible change in CMOD value. This explains the crack growth arrest obtained after 0.25-mm crack length.

This work's contribution is expected to reduce the additional manufacturing cost and lead time incurred in investigating reliability issues in solder joints.

The work investigates crack propagation mechanisms of microvoid cracks in solder joints exposed to moisture and thermal fatigue, which is still limited in the literature. The parametric variation of the crack length on stress and fatigue characteristics of solder joints, which has never been conducted, is also studied.

This study aims to contribute to the numerical modelling of drop impact on a flip-chip component assembled on printed circuit boards using solder micro-bumps. This contribution is based on the introduction of non-linear fracture mechanics in the numerical approach.

The integration of non-linear fracture mechanics into the numerical approach requires the proposal and validation of several simplifying assumptions. Initially, a dynamic 3D model was simplified to a dynamic 2D model. Subsequently, the dynamic 2D model is replaced with an equivalent static 2D model. The equivalent static 2D model was used to perform calculations considering the non-linear fracture mechanics. A crack was modelled in the critical bump. The J-integral was used as a comparative parameter to study the effects of crack length, crack position and chip thickness on the fracture toughness of the solder bump.

The different simplifying assumptions were validated by comparing the results obtained by the various models. Numerical results showed a high risk of failure at the critical solder bump in a zone close to the intermetallic layer. The obtained results were in agreement with the post-test observations using the “Dye and Pry” methods.

The originality of this study lies in the introduction of non-linear fracture mechanics to model the mechanical response of solder bumps during drop impact. This study led to some interesting conclusions, highlighting the advantage of introducing non-linear fracture mechanics into the numerical simulations of microelectronic components during a drop impact.

It has been usual to prefer an enrichment pattern independent of the mesh when applying singular functions in the Generalized/eXtended finite element method (G/XFEM). This choice, when modeling crack tip singularities through extrinsic enrichment, has been understood as the only way to surpass the typical poor convergence rate obtained with the finite element method (FEM), on uniform or quasi-uniform meshes conforming to the crack. Then, the purpose of this study is to revisit the topological enrichment strategy in the light of a higher-order continuity obtained with a smooth partition of unity (PoU). Aiming to verify the smoothness' impacts on the blending phenomenon, a series of numerical experiments is conceived to compare the two GFEM versions: the conventional one, based on piecewise continuous PoU's, and another which considers PoU's with high-regularity.

The stress approximations right at the crack tip vicinity are qualified by focusing on crack severity parameters. For this purpose, the material forces method originated from the configurational mechanics is employed. Some attempts to improve solution using different polynomial enrichment schemes, besides the singular one, are discussed aiming to verify the transition/blending effects. A classical two-dimensional problem of the linear elastic fracture mechanics (LEFM) is solved, considering the pure mode I and the mixed-mode loadings.

The results reveal that, in the presence of smooth PoU's, the topological enrichment can still be considered as a suitable strategy for extrinsic enrichment. First, because such an enrichment pattern still can treat the crack independently of the mesh and deliver some advantage in terms of convergence rates, under certain conditions, when compared to the conventional FEM. Second, because the topological pattern demands fewer degrees of freedom and impacts conditioning less than the geometrical strategy.

Several outputs are presented, considering estimations for the J–integral and the angle of probable crack advance, this last computed from two different strategies to monitoring blending/transition effects, besides some comments about conditioning. Both h- and p-behaviors are displayed to allow a discussion from different points of view concerning the topological enrichment in smooth GFEM.

The purpose of this paper is to present a methodology to assess material damage parameters for ductile crack initiation and growth ahead of a crack/notch tip in high hardening steel like AISI type 316L(N) stainless steel.

Ductile damage parameter and far field J-integral have been obtained from standard FEM analysis for a crack/notch tip undergoing large plastic deformation and resulting in crack initiation/growth. In conjunction with experimental results, the damage variable for low strength and high hardening material has been derived in terms of continuum parameters: equivalent plastic strain (ε_eq) and stress triaxiality (φ). The material parameters for damage initiation and growth in 316LN SS have been evaluated from tensile and fracture tests. With these material tensile/fracture parameters as input, elastic-plastic eXtended Finite Element Method (X-FEM) simulations were carried out on compact tension (CT) specimen geometry under varying initial stress triaxiality conditions.

The material parameters for damage initiation and growth have been assessed and calibrated by comparing the X-FEM predicted load-displacement responses with the experimental results. It is observed that the deviations in the predicted load values from the experimental data are within 6 percent for specimens with a/W=0.39, 0.55, 0.64, while for a/W=0.72, it is 17 percent.

The present study is a part of developing methods to obtain calibrated material damage parameters for crack growth simulation of components made of AISI 316L(N) stainless steel. This steel is used for fast breeder reactor-based power plant being built at Kalpakkam, India.

The purpose of this paper is to analyze the repair of a straight and angular crack in the structure using a piezoelectric material under thermo-mechanical loading by the extended finite element method (XFEM) approach. This provides a general and simple solution for the modeling of crack in the structure to analyze the repair.

The extended finite element method is used to model crack geometry. The crack surface is modeled by Heaviside enrichment function while the crack front is modeled by branch enrichment functions.

The effectiveness of the repair is measured in terms of stress intensity factor and J-integral. The critical voltage at which patch repair is most effective is evaluated and presented. Optimal patch shape, location of patch, adhesive thickness and adhesive modulus are obtained for effective repair under thermo-mechanical loading environment.

The presented numerical modeling and simulation by the XFEM approach are of great benefit to analyze crack repair in two-dimensional and three-dimensional structures using piezoelectric patch material under thermo-mechanical loading.

A delamination fracture analysis of two-dimensional functionally graded multilayered end-loaded split beam configuration with non-linear mechanical behaviour of material is conducted. The beam is made of an arbitrary number of longitudinal layers. Perfect adhesion between layers is assumed. The material is two-dimensional functionally graded in the cross-section of each layer. Also, each layer has individual thickness and material properties. A delamination crack is located arbitrary along the beam height. The paper aims to discuss these issues.

The delamination fracture behaviour is investigated analytically in terms of the strain energy release rate by analysing the balance of the energy. An additional analysis of the delamination fracture is performed by applying the J-integral approach for verification.

The solutions derived are used to evaluate the effects of crack location, material gradients and material non-linearity on the delamination fracture behaviour of end-loaded split beam. The effect of material gradient on the distribution of the J-integral value along the crack front is elucidated too.

Delamination in the multilayered functionally graded end-loaded split beam exhibiting non-linear mechanical behaviour of the material is analysed assuming that the material property is distributed non-linearly in both thickness and width directions in each layer.