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• This paper presents the fracture model calibration of SS275 hot-rolled thin plates, which involved quasi-static tests and finite element analysis. • The hardening model parameters were determined using the Swift law, while the ductile fracture model parameters were calibrated using the Hosford-Coulomb model within the linear damage framework. • The accuracy of the model was validated by comparing the results with the test data, and it was found that the highest fracture strain occurred in the uniaxial tension state. • The calibrated model was then used to predict the cycle life to failure in an extreme low cycle fatigue test, which was found to be 70 cycles. • The results indicate that the ductile fracture model performed well in predicting extremely low-cycle fatigue. • The paper's findings can be useful in predicting the fracture initniaon of engineering structures and components under multiaxial stress states, which can ultimately lead to improved designs and increased safety. The complexity of the loading conditions makes it challenging to accurately predict the damage evolution and resulting ductile fracture in materials and structures. This paper presents an application method to predict fracture initiation for low cycle fatigue of 4-point bending in structural steel SS275. The swift isotropic hardening law was used in the numerical simulation to account for large strain deformation. The damage indicator framework with the Hosford-Coulomb (HC) model was adopted to characterize the damage accumulation and fracture behavior. Uniaxial tension tests on specimens with various fracture modes were conducted to determine the material properties required for calibration of the plasticity model and fracture model param1eters. Non-linear finite element analyses were performed to identify fracture model parameters based on the loading path of fracture initiation. The presented HC model was applied to an extremely low fatigue test (less than 100 cycles) and demonstrated good accuracy in predicting fracture initiation for complex loading scenarios. [ABSTRACT FROM AUTHOR]

[Display omitted] • Adhesion strength of dental ceramic to milled and SLM Ti6Al4V alloy is studied. • The novelty is that experimental load–strain graphs are used in FEM simulations. • Normal, tangential and equivalent von Mises stresses are determined. • Greatest values of normal stresses perpendicular to porcelain/bond/metal interface. • They are primary reason for adhesive delamination of porcelain coating. The aim of the present paper is to investigate the adhesion strength of dental ceramic to milled and selective laser melted (SLM) Ti6Al4V alloy by experiment and finite element method (FEM). The experimental study was done by three-point bending test. Before applying the porcelain, the metal surface was treated by sandblasting, application of bonding agent and a combination of sandblasting and bonding layer. The novelty is that FEM simulations of individual samples from each group were conducted using the experimental load–strain graphs. The normal, tangential and equivalent von Mises stresses at endpoint of the edge of porcelain coating and bonding agent sublayer were determined. It was found that the distribution of the equivalent stresses along the porcelain edge on the porcelain/metal interface is uneven: low stresses at both ends and maximum value in the central part. The Y-axis normal stresses, acting perpendicular to the porcelain/metal, bond/metal, or porcelain/bond interface, have greatest values which is primary reason the coating to be adhesively delaminated by peeling the porcelain off the metal or bonding agent. For the milled specimens, the stress trend follows the adhesion strength trend. In the combined treatment, the highest equivalent and normal stresses are generated in the bond sublayer. If they are higher than the cohesive strength of the ceramic, the porcelain coating is destroyed cohesively by cracking. For the SLM fabricated specimens, the bond treatment increased the stresses at the bond/metal interface, and the stresses at the bond/porcelain interface were commensurate with the experimental adhesion strength. This causes the destruction of the coating to occur by peeling the porcelain off the bonding agent. [ABSTRACT FROM AUTHOR]

Material properties are of great significance for structural safety. In this paper, the mechanical property tests are described and fatigue crack propagation (FCP) behavior for material that had experienced a certain number (10e7) of pre-cyclic stress (PCS) cycles are analyzed. The results illustrate that the material properties increase with the increase of PCS level for relatively lower PCS, and decrease with further increase of PCS. The FCP experiment shows that the FCP rates of the specimens subjected to PCS become lower than that of the specimen without PCS. ‘Turning’ points are clearly shown in the FCP rate curves, indicating that the FCP rate in the range of small Δ K is more sensitive to PCS. This paper presents a bi-linear approximation to describe the FCP behavior and predict the FCP life. It is found that the PCS has ‘coaxing’ effect on material FCP behavior. The fracture morphologies of the material with and without PCS are analyzed to discuss the ‘coaxing’ effect on microstructures. The PCS decreases the void number and void size in fatigue crack initiation zone, decreases the striation width in FCP zone, and increases the dimple size in final rupture zone. [ABSTRACT FROM AUTHOR]

• This paper investigated the effects of large plastic deformation and residual stress on the Rice's J-integral and its path independence for a crack in ductile materials. • Considered the effect of plasticity theory, finite strain, and residual stresses on the J-integral and provided a mathematical equation of the modified J-integral. • Calculated and compared the Rice's J-integral and the residual stress modified J-integral based on the FEA calculations of J-integral for a notched beam. Large plastic deformation and residual stress exist in the oil and gas transmission pipelines with mechanical damages that often contain a gouge or crack. Residual stresses can alter the mechanics behavior of the crack, and cause the standard J-integral to become path-dependent and unable to describe the crack driving force. This paper investigated the effects of large plastic deformation and residual stress on the path independence of the J-integral for a crack in ductile materials. The basic conditions required for the path independence of the standard J-integral were first reviewed, and the major factors that affect the path independence were then analyzed. This includes the theory of plasticity, finite strain formulation, and residual stresses. Then, a residual stress modified J-integral was introduced for ensuring the path independence. After that, the elastic–plastic finite element analyses were performed for a notched beam in terms of the incremental plasticity to create residual stresses and to simulate a crack at the notch root subject to three-point bending. The path independence of the standard and modified J-integrals was numerically evaluated for each of the major factors. Results showed that the modified J-integral is path-independent and able to describe the crack driving force for a crack in a residual stress field, but the standard J-integral cannot do so because of its nature of path dependence when residual stresses are present. Thus, the modified J-integral can be used as an appropriate fracture parameter to assess the pipeline integrity for line pipes containing cracks and residual stresses. [ABSTRACT FROM AUTHOR]

Due to the stress concentration and large strain gradient around the crack tip, strong flexoelectric effect would be produced there. Meanwhile, the flexoelectric effect could conversely affect the mechanical fields in materials, thus influence the fracture property of materials. To model the impact of flexoelectricity on crack tip fields and the electromechanical behaviors of materials, intensive mesh refinement is needed around the crack tip. Thus, an efficient numerical method is desired. In this paper, the flexoelectric effect around the tip of nano-cracks is simulated by using a collocation mixed finite element method (MFEM). Our collocation MFEM is based on C 0 continuous approximation and does not involve additional degrees of freedom (DOFs), so that it is quite efficient, which has been verified in our previous study (Tian et al., 2021). Using the collocation MFEM, we simulate the electric potential and field distributions around the crack tip in flexoelectric materials, and the influences of the direct flexoelectric effect on the crack tip opening displacement and J -integral are also studied. Numerical results indicate that the flexoelectric effect around the crack tip would be enhanced by increasing the tensile loading and crack length. Besides, the direct flexoelectric effect around the crack tip enhances the local strength of materials, and plays an important role in fracture mechanics of materials. [Display omitted] • The flexoelectric effect around the crack tip enhances the local strength. • Our collocation MFEM is based on C0 continuous approximation and efficient. • The existence of the direct flexoelectric effect decreases the J -integral. [ABSTRACT FROM AUTHOR]

This paper investigates the accuracy and robustness of three Stress Intensity Factor (SIF) extraction methods for the Generalized/eXtended Finite Element Method (G/XFEM): the Cutoff Function Method (CFM), the Contour Integral Method (CIM), and the Displacement Correlation Method (DCM). Challenges in SIF extraction from G/XFEM solutions using energy-based methods such as the CFM and the Interaction Integral Method are discussed. Numerical studies on problems with stress-free crack surfaces show that the CFM is path independent while the CIM is not. They also show that unless a proper enrichment scheme is adopted, SIFs extracted with the DCM are of low accuracy and sensitive to extraction parameters. Strategies to address both issues with the DCM are presented. This paper demonstrates that the DCM, with proper enrichment of the G/XFEM approximation, has an accuracy and robustness comparable to the CFM at a fraction of the computational cost. It is also shown that the DCM can be applied to problems where SIF extraction using domain integrals is not possible. Several problems aimed at investigating the applicability and accuracy of the various extraction methods are solved. [ABSTRACT FROM AUTHOR]

• A PF model is developed for electromechanical fracture in flexoelectric solids. • The PF model is validated through benchmark numerical examples. • The flexoelectric effect can have great influences on the fracture behavior. • The PF model can simulate complex fracture behaviors of flexoelectric solids. Flexoelectricity describes the electromechanical coupling between the stain gradient and the electric polarization, which can play an important role in the fracture behavior of piezoelectrics since large strain gradients exist near the crack tip. In this paper, in order to investigate this effect, a phase field (PF) model is developed for electromechanical fracture in brittle flexoelectric solids, where the crack surfaces are assumed to be either electrically impermeable or electrically permeable. The damage driving force of the PF model is derived from the non-negative energy dissipation rate for both kinds of crack surface conditions, where the mechanical part is regarded as the driving force for the crack evolution. A decomposition method of the mechanical driving force is proposed to characterize the asymmetric fracture behavior under tension and compression. The governing equations are solved numerically with finite element method. The finite element formulation is implemented in Abaqus through the user defined subroutine UEL. The PF model and its numerical implementation are validated by studying benchmark problems. The simulation results indicate that the proposed PF model can well characterize the flexoelectric effect and predict complex crack propagation paths in flexoelectric solids. In addition, the numerical results show that whether a negative applied electric field promotes the crack propagation or retard the crack propagation is closely related to the electric field strength and the flexoelectric coefficients, which can reconcile the contradictory phenomena observed in previous experimental studies. The influences of the applied electric field and the length scale parameters on the electromechanical fracture behavior of flexoelectric solids as well as the size effect are discussed in detail in the paper. [ABSTRACT FROM AUTHOR]

Graphical abstract Highlights • Improved analytical solutions of plastic zone size are obtained in cracked plates. • Correction factor can reflect the effects of materials on plastic zone size. • The effects of biaxial stress ratio on T -stresses and plastic zone size are studied. • The effects of specimen geometry can be ignored if SIF and T -stresses are constant. Abstract Crack tip plastic zone size is affected by biaxial loading and materials, and these effects are studied in the unstiffened and stiffened plates in this paper. By means of three-dimensional finite element method, the characteristics of crack tip stress field and plastic zone are investigated for various biaxial stress ratios. Under small scale yielding conditions, the analytical characterizations of plastic zone size (i.e. improved analytical solutions) are determined in the elastic perfectly-plastic material and strain-hardening materials, respectively. The results show that the biaxial stress ratio has slight influences on stress intensity factor (SIF) and out-of-plane T -stress, but it has significant effects on in-plane T -stress and plastic zone size. The correction factor can reflect the effects of materials on plastic zone size, and the improved analytical solutions are in excellent agreement with numerical solutions under the application ranges. Additionally, the plastic zone size is greatly affected by the hardening performances of materials, but it is slightly influenced by specimen geometry and Young's modulus when SIF and T -stresses are constant. [ABSTRACT FROM AUTHOR]

Highlights • A more appropriate FE model was proposed to predict the CCI and CCG behavior. • The effects of simulation method on CCI and CCG of brazed joint are investigated. • The brazed RS can promote CCI and enhance CCG rate, thus reducing creep life. • The predicted results by single-material method agree well with the experiment. • Bigger uniaxial creep strain can prolong the CCI time and reduce the CCG rate. Abstract In this paper, a more appropriate finite element (FE) model was proposed to predict the creep crack initiation (CCI) and growth (CCG) behavior of HastelloyC276-BNi2 brazed joint at high temperature. The effects of single-material, bi-material and three-material method on CCI and CCG behavior have been discussed fully. The relationships between CCG rate and parameter C ∗ for different simulation methods were obtained. The results show that the simulation method has a great influence on CCI and CCG behavior of brazed joint. The brazed residual stress (RS) can accelerate CCI and enhance CCG rate, leading to the reduction of creep life. The CCI time and creep life predicted by single-material method is smaller than those by bi-material and three-material method. The creep life and crack growth morphology predicted by single-material method have a good consistent with the experimental results. The single-material method can accurately predict the CCG behavior of brazed joints. Bigger uniaxial creep strain can prolong the CCI time and reduce the CCG rate. The creep life of brazed joint can be enhanced by increasing uniaxial creep strain. [ABSTRACT FROM AUTHOR]

This paper presents a model for the simulation of cracks in thin-walled structures using Trefftz-elements (T-elements) for crack tip regions. These elements are based on exact solutions to the governing differential equations and inner boundary conditions, resulting in high resolutions of the stress/strain fields. The T-elements are combined with standard elements using an extended variational principle. Beside this formalism the paper presents the derivation of particular solutions for a straight 2d-crack including a Dugdale strip-yield zone. The results are validated against high-resolution standard finite element simulations. Finally a crack propagation algorithm and some future enhancements are discussed. [ABSTRACT FROM AUTHOR]

The relation between the fatigue crack growth rate and stress state is significant for fatigue life estimation, especially for thick-welded structures with complex stress states. This paper proposes a hybrid Experimental-Finite Element Method aimed to obtain the fatigue crack growth rate corresponding to plane stress and plane strain states. A static load marking method is proposed to mark a series of crack fronts in a single edge notched bending specimen at known numbers of cycles, which is analysed by nonlinear finite element method to evaluate the stress state by a local constraint factor. Stress intensity factor at the center of the thickness and the surface position where plane strain and plane stress states approximately exist and remain unchanged with crack propagation, is calculated by the 1/4-node displacement method with consideration of non-orthogonal mesh influence. The J -integral method and the virtual crack closure technique are also applied to check the performance of the methods in dealing with the actual cracked body problem. Crack length increments are determined based on the crack front profiles. The da/dN-ΔK curves of plane strain and plane stress states are determined and compared with the results from normal fatigue crack growth rate tests according to Chinese standard: GB/T 6398-2000. The fatigue crack growth behavior of a semi-elliptical surface crack located at the weld toe of a T-plate welded joint subjected to cyclic tension loading is assessed based on the curves and the analytical results are compared with the experimental results. The asymptotic crack shape observed in experiments is successfully predicted by using the curves determined by the hybrid method. [ABSTRACT FROM AUTHOR]

A multiscale modelling framework is developed in this paper for analysing the degradation of mechanical behaviour of Engineered Cementitious Composites (ECCs) under fatigue tensile loading. Degradation models for calibrating fatigue-induced deterioration of the fibre-matrix interface and fibre fatigue rupture are proposed at the microscale. Based on these, the cycle-dependent crack bridging relation is derived at the mesoscale. At the macroscale, the degradation behaviour of the bridging stress in ECC with presence of multiple cracks is modelled using extended finite element method. This multiscale characterisation method is validated by comparing the computed degradation relation of the bridging stress to that obtained from the experiment. Good agreement is obtained, which demonstrates the effectiveness of the developed multiscale modelling framework for the analysis of fatigue behaviour of ECCs. In addition, the deterioration of the fibre-matrix interface is found to be responsible for a steady decreasing bridging stress, while the fibre fatigue rupture is found to contribute to an accelerated loss of bridging stress. [ABSTRACT FROM AUTHOR]

A software system to perform SCC crack propagation analyses for complex and realistically shaped structures consisting of dissimilar materials, such as weld metal, base metal, etc., under weld residual stresses is presented in this paper. The system consists of programs to perform automatic generation of the finite element mesh, weld residual stress mapping to the finite element model with weld residual stresses to carry out fracture analysis and finite element analysis, and evaluating the stress intensity factors and updating crack geometries for crack propagation analysis. The results of stationary crack and crack propagation analyses elucidate the influences of both the residual stress distribution and the crack geometry on the distribution of the stress intensity factors. Their influences on the crack propagation behavior are also clarified. [ABSTRACT FROM AUTHOR]

• Semi-empirical formula on notch stress field and SIF of orthotropic V-shaped thin plate with initial crack is presented. • The semi-empirical equation is verified with finite element method, traditional formula and various composite materials. • The proposed formula is extended to the solution of SIF for V-notch-cracked plate under tension-bending loads. For orthotropic materials, the solution of notch stress field and stress intensity factor (SIF) is not only related to crack opening angle, crack depth, notch length, geometric parameters, but also obviously influenced by material characteristics and constitutive relation. On the basis of isotropic notch stress field and SIF theoretical formula, a series of multi-parameter models of orthotropic materials were constructed and fitted. The effects of notch depth, crack length, the ratio of notch depth to plate width, opening angle and mechanical properties of composite materials on geometric correction coefficient Y I are systematically analyzed. On this basis, a semi-empirical formula of Y I is put forward by combining stress field analysis and multi-parameter fitting. The semi-empirical formula is further verified with finite element method, traditional formula and various composite materials. The numerical results show that the simple formula proposed in this paper has higher prediction accuracy. Finally, the proposed formula is extended to the solution of notch stress field and geometric correction coefficient for V-notch-cracked plate under bending load, tension-bending complex loads. [ABSTRACT FROM AUTHOR]

• A PF fracture model is developed based on the strain gradient elasticity theory. • An energy decomposition method is proposed for the new PF fracture model. • The PF model is numerically implemented through Abaqus subroutine UEL. • The proposed PF model can characterize the toughening effect of gradient elasticity. • The proposed PF model can well predict the curvilinear crack propagation path. In this paper, a novel phase field (PF) model for fracture is developed in the framework of strain gradient elasticity. The strain energy decomposition methods initially proposed for linear elastic fracture problems are extended to the gradient elasticity situation. The PF model is numerically implemented through Abaqus subroutine UEL (user defined element) with nine-node quatrilateral C1-continous element. The finite element implementation is validated by studying the stress field near the static crack tip. When the length-scale parameter of the gradient elasticity is zero, the stress field is consistent with the analytical solution predicted by linear elastic fracture mechanics (LEFM). For non-zero length-scale parameters, the Cauchy stress at the crack tip is found to be non-singular and the numerical results exhibit less mesh sensitivity in the crack tip region compared with the linear elastic case. After that, four different strain energy decomposition methods (Method I-IV) are compared and discussed by studying Mode I fracture behavior under tensile load. It is found that Method I can properly characterize the toughening effect of gradient elasticity. Based on Method I, the influences of the fracture length-scale parameter l c and the strain gradient length-scale parameter l on the characteristics of the smeared crack model and the load–displacement curves are systematically discussed. The specimen size effect of Mode I crack propagation is also investigated. It is found that the length-scale parameter l has a larger influence on the load–displacement curve as the specimen size decreases. Finally, crack propagation behavior in pure shear test, three point bending test and tensile test of a notched plate with hole is investigated. It is demonstrated that the proposed PF model can well predict the curvilinear crack propagation path and properly characterize the effect of gradient elasticity. Thus, the PF model developed in this paper can be applied to study complex fracture behaviors in the framework of gradient elasticity, where the effect of internal structure on the mechanical responses become significant. [ABSTRACT FROM AUTHOR]

• The paper focuses on FE modelling of the fracture process of porous 316L steel. • Modelling considers the 3D shape of the mesostructure using micro-CT. • Compensating method of the micro-CT inaccuracy was used. • The calculation models considers the effect of local fracture. • Influence of local fracture process on the macro behaviour was determined. This paper concerns numerical modelling of the deformation process, taking into account the local fracture of porous 316L sinters at the mesoscopic scale using the finite element method. Calculations are performed with the use of geometrical models, to map the realistic shape of the porous mesostructure of the material, obtained by means of computed microtomography. The microtomographic device has limited and insufficient measurement accuracy for materials such as the porous sinters studied. For this reason, a method to compensate the inaccuracy of mesostructure shape-mapping is used in the numerical modelling of the deformation and fracture process of the material. The normalised Cockroft-Latham ductile fracture criterion is used to model the local fracture process (at the mesostructure level) of porous metal sinters under tension. The paper describes the numerical modelling procedure and the results of the calculations. The influence of the material structure on the meso -scale fracture process is also discussed. The numerical nominal stress–strain curves are compared with the results of experimental testing. The analysis of stress and strain fields and their variability caused by local fracture in the investigated heterogeneous material is also carried out. [ABSTRACT FROM AUTHOR]

This paper presents a robust technique for experimental determination of mode I stress intensity factor in orthotropic materials using only a single strain gage. Theoretical foundation and finite element based analysis leading to the selection of the angular orientation and position of the strain gage for accurate estimation of K I in orthotropic materials is presented here. Applicability of the proposed method has been established through experiments conducted on edge-cracked carbon-epoxy laminates. Results show that the present single strain gage experiments yield accurate values of K I when strain gage locations are selected as per the criteria set by the proposed approach. [ABSTRACT FROM AUTHOR]

In this paper, the strain intensity factor at the tip of a rigid line inclusion, embedded in an isotropic matrix, is studied using analytical and numerical techniques. We first revisit the elasticity solution of a rigid inclusion embedded in an infinite elastic matrix using Stroh formulation as a basic framework. This study reveals that the strain intensity factor is appropriate for quantifying the magnitude of singularities at the inclusion tip. Next, we propose a numerical methodology, based on the reciprocal theorem, to calculate the strain intensity factor of the inclusion problem embedded in a matrix of finite geometry. The input to this method is the actual elasticity solution, which is obtained using finite element analysis (FEA). The FEA model is qualitatively validated by comparing FEA results with that of photoelasticity experiments. Finally, strain intensity factor in the case of finite geometry specimen is also estimated. [ABSTRACT FROM AUTHOR]

In this paper, the constraint effect caused by a side-groove on creep crack growth behavior in P92 steel was studied using finite element analysis. Creep crack growth simulations were conducted on compact tension specimens for side-grooves with different depths and angles. The simulated outcome indicated that the creep crack growth rate increased as the depth and the angles of the side-grooves in the specimen increased. Next, the profile of the crack front for the different specimens was discussed. The distribution of the average stress triaxiality and the average equivalent stress on the crack front were studied to investigate the mechanical mechanism describing the constraint effect on creep crack growth behavior. Finally, the creep crack growth rate determined from numerical simulation results was determined to be consistent with existing experimental data. [ABSTRACT FROM AUTHOR]

This paper investigates the crack tip plastic zone in a thin ductile layer sandwiched between two identical perfectly elastic adherents subjected to normal loading. The well-known Varias et al. model for calculation of the plastic zone length in a thin constrained elastic-plastic layer was extended by the second nonsingular term of the Williams expansion. A useful engineering formula for the length of the plastic zone has been deduced, where the mechanical properties of the substrates and the layer material as well as T -stress value are included. The proposed theoretical model was verified on the basis of numerical FEM calculations. The results obtained by the model are in good agreement with numerical data. [ABSTRACT FROM AUTHOR]

In this paper, a meso-scale analysis is performed (1) to study the size effect on the nominal stress at failure and, (2) to quantify the evolution of the fracture process zone (FPZ) in the context of the tensile splitting test. The meso-structure is based on a two-phase 3D representation of heterogeneous materials, such as concrete, where stiff aggregates are embedded into a mortar matrix. In order to take into account these heterogeneities without any mesh adaptation, a weak discontinuity is introduced into the strain field. In addition, a strong discontinuity is also added to take into account micro-cracking. This model is cast into the framework of the Enhanced Finite Element Method (E-FEM). Based on the Finite Element simulations, size effect on the nominal stress at failure is numerically investigated and then compared to the so-called Bažant size effect law. In addition, an analysis based on the spatial distribution of the fracture energy is also regarded, leading to the 3D representation of the FPZ and to its volume value estimation. [ABSTRACT FROM AUTHOR]

• The ASME formula used for calculating stress intensity factor for nozzles were verified by linear elastic fracture mechanics finite element analysis. • Five Taiwan domestic RPV nozzles were considered for finite element stress and fracture mechanics analysis. • ASME formula provides conservative results for circular-shape nozzle corner crack but underestimates for elliptical-shaped crack. • The adjusted magnification factors were proposed for the elliptical-shaped nozzle corner crack. Due to the structural discontinuity of geometry having higher stress concentration, the nozzles may dominate the structural integrity of reactor pressure vessel (RPV) system, even the material radiation embrittlement is insignificant. The nonmandatory Appendix G in Section XI of the ASME Boiler and Pressure Vessel code provides a fracture mechanics-based methodology using magnification factors to calculate the stress intensity factor of reference crack tips as long as the stress distribution through the nozzle section is available. This paper establishes various three-dimensional finite element models of Taiwan domestic RPV nozzles to conduct a series of stress and linear elastic fracture mechanics analyses to estimate the stress intensity factors. The circular and elliptical reference corner cracks with depths of one-fourth and one-tenth thickness of the vessel wall along the 45° path are considered. Two evaluation results using the ASME method and the finite element linear elastic fracture mechanics analysis are compared. It is found that the ASME method produces conservative values of stress intensity factor at crack tips of circular corner cracks but underestimates the elliptical corner cracks. Finally, an adjusted magnification factor formula is proposed to obtain more accurate stress intensity factors for elliptical-shaped nozzle corner cracks. [ABSTRACT FROM AUTHOR]

• A thermodynamically consistent PF-CZM with strain gradient elasticity and surface stresses is developed. • The proposed model can characterize the size effect of fracture behavior induced by strain gradient elasticity and surface stresses. • Strain gradient elasticity increases the fracture toughness. • Surface stresses improve the local-fracture strength at the crack tip. • Strain gradient elasticity further enhances the effect of surface stresses by changing the damage distribution at the crack tip. Microstructure and surface stresses play a vital role in the micro- and nano-scale. In this paper, a thermodynamically consistent phase-field regularized cohesive fracture model (PF-CZM) is initially proposed to analyze crack propagation in the micro- and nano-scale, where strain gradient elasticity is introduced by higher-order elastic energy, and surface stresses are obtained using geometrical nonlinearity. After that, the higher-order theory is implemented through a mixed-type formulation finite element method. The specimen size effect of Mode I crack propagation is investigated. It is found that both strain gradient elasticity and surface stresses increase the critical load of crack nucleation, which becomes more pronounced as the size of the specimen decreases. The strain gradient elasticity increases the fracture toughness due to the reduction in stress singularity, while the maximum value of stress is still equal to the fracture strength during crack propagation. The surface stresses improve the local-fracture strength at the crack tip. Finally, the strain gradient elasticity further enhances the effect of surface stresses by changing the damage distribution at the crack tip when surface stresses are taken into account along with strain gradient elasticity. The presented framework has shown great potential for modeling crack propagation in the micro- and nano-scale. [ABSTRACT FROM AUTHOR]

Abstract: This paper reports experimental results of the debonding propagation of bundled-fibers specimens subjected to a tensile stress wave. In addition, the paper also presents a dynamic debonding model for the problem on the basis of the cohesive zone model, and verifies the model by comparing the predicted debonding to the experimental data. The established numerical model is used to study the propagation mode of the debonding, and the result suggests that in this particular specimen design and loading condition, the debonding initiated in a mixed mode condition. However, the mode II quickly increased and dominated the mode I during an early debonding propagation up to certain extend where the mode mixity became constant. [Copyright &y& Elsevier]

Abstract: The simple circular notched specimen was originally proposed by Arcan to characterize the elastic properties of fibre-reinforced composites. Unfortunately, its optimized geometry does not allow to measure with reasonable accuracy both the material shear strength and the conditions of failure under a generic biaxial stress state, since the effects of stress concentration on the fillets of the two V-grooves and on the inner circular edges are responsible of premature fractures due to the uniaxial stress states of the notch edges. In a previous numerical study carried out by a parametric two-dimensional finite element model, some of the Authors of this paper found a new optimal geometry of the Arcan specimen able to minimize the notch effect and achieve a uniform pure shear stress field in the gauge cross-section. In the present paper, starting from such a geometry, a new type of Arcan specimen is proposed, having not uniform thickness. An extensive three-dimensional parametric finite element analysis has been done to define its optimal shape. The numerical results show that the new specimen is able to achieve, with a higher probability, material fracture in the minimum cross-section under a pure shear stress distribution which is more uniform than those acting in the Arcan specimen typologies until now proposed. [Copyright &y& Elsevier]

Abstract: This paper presents a study on the application of the weight function and finite element methods to evaluate residual stress intensity factors in welded test samples. Three specimen geometries and various residual stress profiles were studied. Comparisons of the two different methods were made in terms of the accuracy, easiness to use, conditions and limitations. Calculated residual stress intensity factors by the two different methods are in general in good agreement for all the configurations studied. Computational issues involved in executing these methods are discussed. Some practical issues are also addressed, e.g. treatment of incomplete or limited residual stress measurements, influence of transverse residual stresses, and modelling residual stress in short-length specimens. The finite element method is validated by well-established weight functions and thus can be applied to complex geometries following the procedures recommended in this paper. [Copyright &y& Elsevier]

Abstract: This paper describes a 2D FE modelling technique for predicting fatigue crack growth life of integral structures reinforced by bonded straps. This kind of design offers a solution to the intrinsic lack of damage tolerance of integral structures. Due to the multiple and complex failure mechanisms of bonded structures, a comprehensive modelling technique is needed to evaluate important design parameters. In this Part I of a two-part paper, the actions and mechanisms involved in a bonded structure are discussed first, followed by presenting the modelling approaches to simulate each mechanism. Delamination or disbond of the strap from the substrate is modelled by computing the strain energy release rate on the disbond front and applying a fracture mechanics criterion. Thermal residual stresses arising from the adhesive curing process and their redistribution with the substrate crack growth are calculated and taken into account in the crack growth analysis. Secondary bending effect caused by the un-symmetric geometry of one-sided strap is also modelled. In the classic linear elastic fracture mechanics, a non-dimensional stress intensity factor, i.e. the geometry factor , depends only on the sample’s geometry. This factor cannot be found for this kind of bonded structures, since the magnitude of disbond is related to the applied stress and the disbond size modifies the geometry of the structure. Moreover, secondary bending effect is geometric nonlinear thus the stress intensity factor cannot be normalised by the applied stress. For these reasons an alternative technique has been developed, which requires calculating the stress intensity factors at both the maximum and minimum applied stresses for each crack length. This analysis technique is implemented in a computer program that interfaces with the NASTRAN commercial code to compute the fatigue crack growth life of strap reinforced structures. [Copyright &y& Elsevier]

Abstract: In Part I of this paper a new metric, titled the “blade sharpness index” or “BSI”, for quantifying the sharpness of a straight edge blade when cutting soft solids was derived from first principles and verified experimentally by carrying out indentation type cutting tests with different blade types cutting different target or substrate materials. In this Part II companion paper, a finite element model is constructed to examine the effect of different blade variables including tip radius, wedge angle and blade profile on the BSI developed in Part I. The finite element model is constructed using ABAQUS implicit and experiments are performed to characterise the non-linear material behaviour observed in the elastomeric substrate. The model is validated against the experiments performed in Part I and a suitable failure criterion is determined by carrying out experiments on blades with different tip radii. The paper finds that a simple maximum stress criterion is a good indicator for predicting the onset of cutting. The validated model is then used to examine blade geometry. It is shown that finite element analysis is an important tool in helping to understand the mechanics of indentation. Furthermore, the study finds that all the blade geometric variables have an influence on the sharpness of a blade, with the BSI being most sensitive to tip radius. Increasing the tip radius and wedge angle decreases the sharpness of the blade. [Copyright &y& Elsevier]

Abstract: This paper addresses finite element evaluation of the non-singular T-stress and mixed-mode stress intensity factors in functionally graded materials (FGMs) under steady-state thermal loads by means of interaction integral. Interaction integral provides an accurate and efficient numerical framework in evaluating these fracture parameters in FGMs under thermal as well as mechanical loads. We use a non-equilibrium formulation and the corresponding auxiliary (secondary) fields tailored for FGMs. Graded finite elements have been developed to account for the spatial gradation of thermomechanical properties. This paper presents various numerical examples in which the accuracy of the present method is verified. [Copyright &y& Elsevier]

Abstract: The extended finite element method (X-FEM) has recently emerged as an alternative to meshing/remeshing crack surfaces in computational fracture mechanics thanks to the concept of discontinuous and asymptotic partition of unity enrichment (PUM) of the standard finite element approximation spaces. Level set methods have been recently coupled with X-FEM to help track the crack geometry as it grows. However, little attention has been devoted to employing the X-FEM in real-world cases. This paper describes how X-FEM coupled with level set methods can be used to solve complex three-dimensional industrial fracture mechanics problems through combination of an object-oriented (C++) research code and a commercial solid modeling/finite element package (EDS-PLM/I-DEAS®). The paper briefly describes how object-oriented programming shows its advantages to efficiently implement the proposed methodology. Due to enrichment, the latter method allows for multiple crack growth scenarios to be analyzed with a minimal amount of remeshing. Additionally, the whole component contributes to the stiffness during the whole crack growth simulation. The use of level set methods permits the seamless merging of cracks with boundaries. To show the flexibility of the method, the latter is applied to damage tolerance analysis of a complex aircraft component. [Copyright &y& Elsevier]

Abstract: Stress (SD) and displacement (DD) discontinuity methods have been developed for problems where seepage and deformation are not coupled. This is an important limitation in geomechanics where the ground is usually saturated. Of particular importance are problems that fall within the “short term analysis” concept, where a phenomenon occurs over a period of time that is very short compared to the permeability of the medium. In this paper we present an analytical formulation to solve undrained conditions and deformation problems in a poroelastic saturated medium in plane strain conditions, with the assumption of short term analysis (i.e. no change in volume of the medium). Explicit functions for SD and DD elements are obtained and are incorporated into the code FROCK. The new code is verified by a number of comparisons with theoretical solutions, also presented in the paper, and with solutions from the Finite Element Method. In undrained compression, the compression field around the tip of an open flaw decreases and the tension field increases compared to drained compression loading, while the shear stresses remain unchanged. For a closed frictional flaw undrained compression decreases the compression and tension fields around the tip. The shear stresses however have the same distribution as in drained loading but are larger. This is caused by the decrease of the effective normal stresses due to the excess pore pressures which in turn decrease the shear resistance of the flaw. [Copyright &y& Elsevier]

This work proposes that the Weibull stress scale parameter, σu, increases with temperature to reflect the increasing microscale toughness of ferritic steels caused by local events that include plastic shielding of microcracks, microcrack blunting, and microcrack arrest. The Weibull modulus, m, then characterizes the temperature invariant, random distribution of microcrack sizes in the material. Direct calibration of σu values at temperatures over the DBT region requires extensive sets of fracture toughness values. A more practical approach developed here utilizes the so-called Master Curve standardized in ASTM Test Method E1921-02 to provide the needed temperature vs. toughness dependence for a material using a minimum number of fracture tests conducted at one temperature. The calibration procedure then selects σu values that force the Weibull stress model to predict the Master Curve temperature dependence of KJc values for the material. At temperatures in mid-to-upper transition, the process becomes more complex as fracture test specimens undergo gradual constraint loss and the idealized conditions of high-constraint, small-scale yielding assumed in E1921-02 gradually degenerate. The paper develops the σu calibration process to incorporate these effects in addition to consideration of threshold toughness effects and the testing of fracture specimens with varying crack-front lengths. Initial illustrations of the calibration process for simpler conditions, i.e. 1T crack-front lengths, use the temperature dependent flow properties and a range of toughness levels for an A533B pressure vessel steel. Then using the extensive fracture toughness data sets for an A508 pressure vessel steel generated recently by Faleskog et al. [Engng. Fract. Mech., in press], the paper concludes with calibrations of both m and σu over the DBT region and assessments of the Master Curve calibration approach developed here. [Copyright &y& Elsevier]

In the accompanying paper [C.S. Chang, T.K. Wang, L.J. Sluys, J.G.M. van Mier, J. Eng. Fract. Mech. (this volume)], the theoretical aspects of a stress–strain model are described based on a microstructural approach. A finite element formulation was presented that incorporates the developed stress–strain relationship. In this paper the results of finite element analyses are described. The paper is focused on two main issues: the difference between the micropolar and the non-polar microstructural model, and the performance of the model respect to mesh size dependence. Specimens in uniaxial tension test and in biaxial tension–shear tests have been analyzed. To evaluate the applicability of this method, the finite element results are also compared with measured experimental results. [Copyright &y& Elsevier]

In this work, a new finite element framework is developed and applied to the study and modeling of ductile fracture mechanisms at the microscale. More particularly, a body-fitted meshing and remeshing methodology is introduced and applications to void coalescence are investigated. Though most studies focus on periodic arrangements of voids, it was proven in experiments as in simulations that random void clusters have a major influence on void growth and coalescence. With the method proposed in this paper, various void arrangements can be addressed and their effect on void growth and coalescence can be studied at large plastic strain and various stress states. [ABSTRACT FROM AUTHOR]

The scaled boundary finite element method is employed to obtain highly accurate solutions of the stress intensity factors (SIFs) and T-stress for standard homogeneous and bimaterial fracture specimens. The solutions are assembled into a practical database (up to 6 significant figures) corresponding to various crack lengths. Using a curve fitting technique, precise Padé approximants of the SIFs and T-stress are also developed, which retain a maximum error of <0.28% for any specimen. The findings of this paper are useful for engineering analysis and design, as well as verification of current and future numerical schemes for computing SIFs and T-stress. [ABSTRACT FROM AUTHOR]

This paper discusses the reproduction of the square root singularity in quarter-point tetrahedral (QPT) finite elements. Numerical results confirm that the stress singularity is modeled accurately in a fully unstructured mesh by using QPTs. A displacement correlation (DC) scheme is proposed in combination with QPTs to compute stress intensity factors (SIF) from arbitrary meshes, yielding an average error of 2–3%. This straightforward method is computationally cheap and easy to implement. The results of an extensive parametric study also suggest the existence of an optimum mesh-dependent distance from the crack front at which the DC method computes the most accurate SIFs. [ABSTRACT FROM AUTHOR]

It has recently been shown that a strong spatial variation of the Young’s modulus can improve greatly the fracture resistance and the fracture strength of an inherently brittle material. In this paper, using numerical modeling and application of the concept of the configurational forces, it is shown that spatial variations of the yield stress can also improve the fracture resistance. The reason is that, when the crack has crossed a soft interlayer, the crack driving force strongly decreases and the crack is arrested by the interlayer; this effect appears without previous delamination of the interlayer. From the numerical results, “optimum interlayer configurations” are derived, i.e. for a given matrix material and load, the magnitudes of thickness and yield stress of the soft interlayer are determined so that the crack driving force exhibits a minimum. Such optimum configurations can be used for the design especially fracture resistant materials and components. [ABSTRACT FROM AUTHOR]

Highlights: [•] This paper provides validation of R6 J-estimation methods for combined mechanical and thermal loads. [•] In FE analysis, relevant parameters are systematically varied. [•] Loading sequence effects for the mechanical and thermal loads are also considered. [•] Significant load order effects for large secondary stress cases are successfully treated by methods in R6. [Copyright &y& Elsevier]

• Modified Mazars damage model, for concrete with fracture energy regularization. • Regularization of both tensile and compressive behaviour during the softening branch. • Used classical benchmarks for studying new concrete damage models. • Validation with previous experimental campaigns. • Both constitutive relations for tensile and compressive behaviour, are based on new MC2010 from FIB. This paper presents a modified Mazars damage model, based on a strain formulation, for the physically nonlinear analysis of concrete structures. The main objective is to propose a modified damage model, in which both tension and compression damage evolution laws are regularized using a classical fracture energy methodology. The original loading functions are maintained, including their thermodynamic consistencies. The most relevant modification of the model is introduced in the damage evolutions laws, which are updated in order to produce similar stress–strain relations to those presented in fib Model Code 2010. The softening branch under both compressive and tensile strains is regularized with fracture energy. The damage model is then benchmarked with classical experimental and numerical tests considering monotonic loadings. The new constitutive relation was implemented in the commercial software ABAQUS via user subroutine UMAT. Research needs towards a definition of a generalized damage model with energy regularization are discussed and presented. [ABSTRACT FROM AUTHOR]

• The I-integral is developed for magneto-electro-elastic media with residual strain. • The intensity factors can be solved separately by the I-integral method. • The I-integral is domain-independent for arbitrary material properties. • The interface with jump residual strain affects the I-integral calculations. Magneto-electro-elastic (MEE) materials generally consist of piezoelectric and piezomagnetic constituent phases so that the residual strain often occurs during the manufacturing process. The distributed residual strain and complex interfaces between constituents cause a great challenge to the fracture analysis of MEE materials. Considering the effect of the residual strain, this paper develops an interaction integral (I-integral) method for the extraction of the fracture parameters of an impermeable crack in nonhomogeneous MEE materials. The I-integral method has several merits: 1) it can decouple stress intensity factors (SIFs), electric displacement intensity factor (EDIF) and magnetic induction intensity factor (MIIF); 2) the I-integral is independent of the size of the integration domain, even when the integration domain contains nonhomogeneous and discontinuous material properties. Combined with the extended finite element method (XFEM), the I-integral is adopted to investigate several crack problems subjected to homogeneous, nonhomogeneous and discontinuous residual strains. The I-integral values calculated by different integration domains agree well with each other (relative deviation < 1%) for nonhomogeneous and discontinuous MEE properties. Then, single-crack and multi-crack problems are studied to show the influences of residual strain distributions on the intensity factors. Homogeneous residual strain affects the SIFs dramatically but has a slight influence on the EDIF and MIIF. By comparison, nonhomogeneous residual strains affect the SIFs, EDIF and MIIF significantly. In addition, the residual strain gradients affect the variations of intensity factors with crack location extremely. [ABSTRACT FROM AUTHOR]

Abstract: This work presents an experimental and numerical investigation to characterise the fracture properties of pure bitumen (the binder in asphalt paving materials). The paper is divided into two parts. The first part describes an experimental study of fracture characterisation parameters of pure bitumen as determined by three-point bend tests. The second part deals with modelling of fracture and failure of bitumen by Finite Element analysis. Fracture mechanics parameters, stress intensity factor, KIC , fracture energy, GIC , and J-integral, JIC , are used for evaluation of bitumen’s fracture properties. The material constitutive model developed by Ossa et al. [40,41] which was implemented into a FE code by Costanzi [18] is combined with cohesive zone models (CZM) to simulate the fracture behaviour of pure bitumen. Experimental and numerical results are presented in the form of failure mechanism maps where ductile, brittle and brittle-ductile transition regimes of fracture behaviour are classified. The FE predictions of fracture behaviour match well with experimental results. [Copyright &y& Elsevier]

Abstract: This paper presents a technique to analyze two-dimensional fracture problems of piezoelectric materials. The proposed technique is based on the so-called scaled boundary finite element method, which only requires discretization on the boundary of the problem domain. The results of displacement and electric potential, stress and electric displacement at any point in the domain are analytically obtained. The stress and electric displacement intensity factors K I , K II and K IV are evaluated directly from the scaled boundary finite element solutions of the singular stress and electric displacement fields. No asymptotic solution, local mesh refinement or other special treatments around a crack tip are required. Numerical examples are presented to verify the proposed technique with the analytical solutions and the results from the literature. The present results highlight the accuracy, simplicity and efficiency of the proposed technique. [Copyright &y& Elsevier]

Abstract: In this paper, the results of three-dimensional finite element analyses for a rigid inclusion in a square plate under opening and bending loading conditions are presented. Based on the computational results, closed-form structural stress solutions with equivalent and numerical coefficients for a rigid inclusion in a square plate are introduced. Next, the results of three-dimensional finite element analyses for spot welds between square plates of similar material with equal thickness are presented. The results indicate that the computational mode I stress intensity factor solutions agree well with those based on the structural stress solutions. Finally, accurate closed-form stress intensity factor solutions with fitting coefficients for spot welds in the square overlap parts of cross-tension specimens are presented. [Copyright &y& Elsevier]

Abstract: In this paper the J–Q two-parameter characterization of elastic–plastic crack front fields is examined for surface cracked plates under static uniaxial and biaxial bending. Extensive three-dimensional elastic–plastic finite element analyses are performed for semi-elliptical surface cracks in a finite thickness plate, under remote uniaxial and biaxial bending conditions, covering from small-scale to large-scale yielding. Surface cracks with aspect ratios a/c =0.2, 1.0 and relative depths a/t =0.2, 0.6, corresponding to four specimen configurations, are investigated. The full stress field solutions are obtained in topological planes perpendicular to the crack fronts. The question of J–Q characterization is addressed by comparing these elastic–plastic crack-front stress fields with J–Q family of stress fields. It is found that the J–Q characterization provides good estimate for the constraint loss for crack front stress fields. It is also shown that for medium load levels, reasonable agreements are achieved between the T-stress based Q-factors and the Q-factors obtained from the finite element analyses. Complete distributions of the J-integral and Q-factors for the wide range of geometry and loading conditions are obtained. Size requirements in terms of crack depth (for shallow cracks) or ligament size (for deep cracks) that are necessary to ensure J–Q characterization of crack front fields in surface cracked plates are also discussed. [Copyright &y& Elsevier]

Abstract: In this paper, the stress intensity factors (SIFs) around a 3D semi-elliptical squat on a rail surface are investigated. Elastic foundation and water trapped inside the crack are considered as key factors in crack propagation. It is found that the opening mode and shear modes show different behavior compared with former models. Also the lateral load can change the SIF pattern significantly. The superposition traction ratio and lateral load can increase the equivalent SIF up to 200%. This study confirms the pressurized water in a crack changes crack propagation direction making a squat. [Copyright &y& Elsevier]

Abstract: This paper deals with the fracture analysis on the honeycomb sandwich composite double cantilever beam (DCB) specimens. Analytical expression for the strain energy release rate (GI ) of the specimen is derived from modified elastic foundation model utilising the compliance derivative method. The results obtained from 3D finite element analysis for various delamination lengths compare well with the analytical results. A simple and improved procedure is suggested for evaluation of the interface fracture toughness (GIC ), which takes into account the scatter in fracture data, and demonstrates its validity through comparison of existing test results with estimated failure loads. [Copyright &y& Elsevier]

Abstract: The tension softening curve (TSC), showing the relationship between the cohesive tensile stress and crack opening displacement, is the constitutive law of the cohesive crack model. Due to the difficulties in measuring local deformations around the crack tip, the TSC is usually determined inversely from the global responses such as load–deflection curve or load–crack mouth opening displacement curve of pre-notched specimens. However, the use of global responses alone in the inverse analysis usually causes problems that may affect the reliability and accuracy of the TSC which is basically a local material property. To overcome these limitations, an incremental displacement collocation method (IDCM) that is able to evaluate the TSC in a step-by-step manner is proposed in this paper. Both global and local responses of a pre-notched mortar beam, which are measured using an electronic speckle pattern interferometry technique, are used in the displacement collocation process. Furthermore, the finite element model (FEM) is utilized to simulate the response of the beam. The TSCs evaluated in this study are verified through the comparisons of the global and local displacements as well as the fracture energy. A tri-linear curve was found to be the best approximation of the TSC of mortar. [Copyright &y& Elsevier]

Abstract: The objective of this paper is to develop a probabilistic model for a stiffened panel subjected to correlated growth of cracks in the stiffener and plate elements. The geometry functions of the correlated cracks in the plate and in the stiffener are defined based on the stress intensity factors calculated by finite element analysis. A validation of the stress intensity factor and the geometry function calculation has been performed for an isolated crack in a plate with a central/edge through thickness crack. The Paris–Erdogan law is used to predict the crack propagation. Monte Carlo simulation is employed to define the statistical descriptors of the crack growth in the stiffened panel under different correlation functions and a probabilistic model of crack size as a function of time are presented adopting a truncated normal distribution to describe the probability density function of the crack size in the plate and in the stiffener. A procedure for the development of a probabilistic crack growth model for a stiffened panel has been proposed, allowing for the existence of multiple cracks both in the stiffeners and in the plate and accounting for the correlation between them. The developed probabilistic model may be used for fatigue crack growth analysis and is suitable for reliability assessment of a stiffened panel subjected to correlated crack growth. [Copyright &y& Elsevier]

Abstract: In this paper, an Extended Finite Element Method (X-FEM) axisymmetric model is developed and employed to compute stress intensity factors for cracked industrial specimens and components. The X-FEM model implementation is first validated by the analytical and computational stress intensity factors for penny-shaped and circumferential cracks in cylindrical bars. The validated X-FEM model is then employed to obtain the stress intensity factors for spot welds and associated kinked cracks in circular cup specimens with complex geometries. Finally, the X-FEM model is used to assess the integrity and durability of a cracked rotor coil retaining ring during the power plant operation. [Copyright &y& Elsevier]

Abstract: In this paper, by starting from the Inglis solution, the stress along the free border of an ellipse in a finite plate is investigated. The stress, divided into symmetric and skew-symmetric terms, is approximated by means of a linear combination of three independent stress equations. The coefficients of the combination are calculated by FE analysis and the proposed equations appear to be suitable for different elliptical notches in a plate under general loading conditions. Then, the J-integral (namely JVρ ) of an ellipse under general load conditions is evaluated analytically. Finally, in order to estimate the Stress Intensity Factors of cracks under mixed mode loading, FE analysis of equivalent ellipses is performed. This is possible because the terms of JVρ with null contribution when the ellipse becomes a crack are neglected. The errors in SIF predictions are approximately a few per cent, which is also the case for an ellipse close to a circle. [Copyright &y& Elsevier]