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• Extending the fracture criterion for orthotropic materials under mixed mode II/I loading. • A new fracture criterion based on the extension of the Tsai-Hill failure criterion is presented. • Extension of the presented criteria in the case where the crack is aligned or perpendicular to the fibers. • Examining the effects of the non-singular stress component on crack growth. • Extraction of Russian pine wood mechanical and fracture test data. An essential study in the discourse surrounding composite materials is the investigation of their fracture mechanics due to the intricate nature of composite structures, it is necessary to take into account the presence of cracks and faults throughout the design process. In this research, within the context of linear elastic fracture mechanics, the fracture criterion for orthotropic materials under mixed mode II/I loading is presented by expanding the Tsai-Hill failure criterion. According to the crack, it may be aligned or perpendicular to the fibers; the criterion is stated for both cases. Also, the effects of the non-singular stress component on crack growth have been investigated. The mechanical and fracture data of Russian pine wood was extracted through tensile testing and the finite element (FE) method. The validity of the proposed criterion, in comparison with the experimental findings extracted in this research, has been proved. The precision of the previous proposed fracture criteria has been reviewed in comparison with the proposed criterion. The appropriate behavior of the fracture limit curves compared to the experimental data shows the efficacy of the proposed criterion to predict the initiation and propagation of cracks in orthotropic materials. [ABSTRACT FROM AUTHOR]

This paper aims to propose a novel fracture criterion to predict complex propagation behaviors of a bimaterial interface crack, either delaminating along the interface or kinking out of the interface into one of the adjoining materials. A strength-based criterion is used to predict the crack deflection, and an energy-based criterion is adopted to assess delamination along the interface. To determine the competition between these two cracking modes, a competing strategy is developed by comparing the strength-based and energy-based criteria. This coupled strength-energy fracture criterion eliminates the disadvantages arising from a criterion based solely on strength or energy, and is convenient to be calculated and embedded into numerical models. As practice, we embed the criterion into a homemade extended finite element model to simulate bimaterial interface crack propagation. Several numerical examples are performed to verify the effectiveness and accuracy of the developed model. Finally, this model is applied to simulate an interface crack propagation in a sandwich structure that has a specially designed peel-stopper. Parametric studies reveal that the material and interface toughness as well as geometrical dimensions of the structure have significant effects on the propagation mode of the interface crack. The results provide practical suggestions on the optimal design of peel-stopper in sandwich structures. • A novel strength-energy fracture criterion is proposed for crack propagation. • The developed XFEM model embedded with fracture criterion is established. • The developed model correctly captures the crack propagation behavior. [ABSTRACT FROM AUTHOR]

It is known that a local deformation mode affects the fracture behavior. First, a parameter that represents the deformation mode is defined for a fracture criterion that can consider the deformation mode in ordinary state-based peridynamics. This parameter is analogous to stress triaxiality in conventional continuum mechanics. The calculated values of the parameter agree well with the theoretical values under uniaxial compression, pure shear, uniaxial tension, and equi-biaxial tension. Then, modified fracture strain by a function using the parameter is proposed as a fracture criterion. The intended fracture strains of uniaxial tensioned cubes and those of equi-biaxial tensioned cubes were well reproduced by calculations with the criterion. Further, the intended ratio of fracture strain of a uniaxial tensioned round bar to that of an equi-biaxial tensioned thin plate was reproduced by calculations with the criterion. In a pipe bending simulation, the crack propagation behavior was reproduced by the proposed criterion. [ABSTRACT FROM AUTHOR]

• A nano-notch based modulation method is proposed for the fracture of nano-multilayer. • Cohesive zone model is used to extract fracture criterions of corresponding materials. • Competitive fracture among Cu/Si and Cu/SiN interfaces and SiN monolayer is analyzed. • A fracture phase diagram is proposed to predict fracture behaviors in nano-multilayer. This study presents an efficient methodology to assess fracture behavior in nanoscale multilayers. After fabricating a nano-cantilever specimen of Cu/Si/SiN, a notch with the tip radius of 3 ∼ 15 nm was introduced into the SiN layer. By changing the position of notch tip, the delamination of Cu/SiN or Cu/Si interfaces, and the fracture of SiN layer were obtained by in situ TEM bending experiments, respectively. The fracture strength of interfaces and SiN layer was determined using an exponential cohesive zone model (CZM) and the crack propagation from the notch tip was analyzed by phase field simulation. Finally, a fracture phase diagram related to the typical position parameters of nano-notch is proposed to predicted the fracture behaviors including the delamination of different interfaces and the fracture of monolayer in nanoscale multilayers. This study provides significant insights into the fracture behavior occurred at nanoscale and a simple but efficient methodology to evaluate the fracture strength of any part in nanoscale multilayers. [ABSTRACT FROM AUTHOR]

This paper presents the results of ductile fracture tests conducted on axisymmetric specimens with notch made from EN AW 2024 T351 aluminum alloy. Tests were conducted for five notch radius and seven cases of biaxial, proportional loading with tensile force and torsional moment. A model of damage accumulation and fracture based on variables of stress strain state and damage on a physical plane is proposed. The fracture criterion assumes that crack initiation will occur when a certain combination of normal and shear stress on the physical plane (elliptical criterion in the tensile stress zone and Coulomb criterion in the shear stress zone) reaches a critical value dependent on the value of the damage state variable on this plane. The damage accumulation law was formulated incrementally, and the increment of the damage state variable was made dependent on the increment of plastic deformations and stress values on the physical plane. This model was successfully verified by experimental tests and numerical simulations, which are presented in papers by Derpenski and Seweryn (2016a,b) . [ABSTRACT FROM AUTHOR]

Perforation of circular 2024-T3(51) aluminum alloy plates of various normalized thicknesses by a rigid spherical projectile is considered as a benchmark problem to validate material plasticity and fracture models. A new set of experiments with circular 2024-T3(51) aluminum alloy plates and AISI 52100 alloy steel spheres was conducted in order to augment available in literature experimental data and to form more precise reference solution for the benchmark problem. Numerical simulations of a plate perforation using Johnson–Cook plasticity model with two sets of parameters, Johnson–Cook fracture criterion with one set of fitting parameters and pressure and Lode dependent ductile fracture criterion with three sets of material constants are performed. Problem formulation, types of plasticity and fracture models and their parameters are estimated independently in the context of their effect on the accuracy of numerical solution. Ballistic limit velocity and residual velocity tests are employed for validation procedure. With one of the considered formulation-models combination quantitative discrepancy of less than 10% and good and physically sound qualitative agreement with the experiment were obtained. [ABSTRACT FROM AUTHOR]

Abstract: An extension of the Gurson model that incorporates damage development in shear is used to simulate the tension–torsion test fracture data presented in Faleskog and Barsoum (2013) (Part I) for two steels, Weldox 420 and 960. Two parameters characterize damage in the constitutive model: the effective void volume fraction and a shear damage coefficient. For each of the steels, the initial effective void volume fraction is calibrated against data for fracture of notched round tensile bars and the shear damage coefficient is calibrated against fracture in shear. The calibrated constitutive model reproduces the full range of data in the tension–torsion tests thereby providing a convincing demonstration of the effectiveness of the extended Gurson model. The model reinforces the experiments by highlighting that for ductile alloys the effective plastic strain at fracture cannot be based solely on stress triaxiality. For nominally isotropic alloys, a ductile fracture criterion is proposed for engineering purposes that depends on stress triaxiality and a second stress invariant that discriminates between axisymmetric stressing and shear dominated stressing. [Copyright &y& Elsevier]

Abstract: We analyse a problem of anti-plane shear in a bi-material plane containing a semi-infinite crack situated on a soft imperfect interface. The plane also contains a small thin inclusion (for instance an ellipse with high eccentricity) whose influence on the propagation of the main crack we investigate. An important element of our approach is the derivation of a new weight function (a special solution to a homogeneous boundary value problem) in the imperfect interface setting. The weight function is derived using Fourier transform and Wiener–Hopf techniques and allows us to obtain an expression for an important constant (which may be used in a fracture criterion) that describes the leading order of tractions near the crack tip for the unperturbed problem. We present computations that demonstrate how varies depending on the extent of interface imperfection and contrast in material stiffness. We then perform perturbation analysis to derive an expression for the change in the leading order of tractions near the tip of the main crack induced by the presence of the small defect, whose sign can be interpreted as the inclusion’s presence having an amplifying or shielding effect on the propagation of the main crack. [Copyright &y& Elsevier]

Abstract: A new constitutive model describing the pressure dependence of plasticity and fracture in solder joints is proposed. The pressure dependence of the solders flow stress is obtained from the Peierls stress necessary to move mobile dislocations. Conservation of volume during plastic deformation is achieved through a deviatoric associated flow rule. Fracture is considered as a result of damage accumulation depending on the amount of plastic strain and triaxiality of stress the sample has experienced. The constitutive model was implemented in the FEM code Abaqus using the user subroutine UMAT. The model predictions were compared to experimental results of tensile tests performed with Sn-3.5Ag solder joints of various thicknesses. Ultimate tensile strength and ductility showed a strong dependency on the solder joints geometry. It is demonstrated that the model can nicely be fitted to experimental results. [Copyright &y& Elsevier]

Abstract: A novel method combining the experimental data at only two different mixed mode fractures and an empirical interface toughness function has been proposed to establish the interfacial toughness function of a bimaterial in submicron scale. The modified four-point bend specimen was used in experiment to evaluate the first type of mixed mode fracture, while the sandwiched cantilever specimen was employed to get the second one. An empirical interface toughness function reflecting quite accurately the delamination behavior was adopted as a typical one. The obtained results investigated that the proposed method could be used to calibrate not only the interfacial fracture criteria at pure modes but also at any mixed mode fracture of bimaterials in submicron scale. [Copyright &y& Elsevier]

Abstract: We extend Sih’s strain energy density criterion () for crack kinks and material failure by weighting differently the volumetric and distortional parts in the extended strain energy density factor. The work is inspired by the factor that failure by microscopic shearing governed by distortion and microscopic separation controlled by hydrostatic tension represent distinct deformation processes, and should be treated differently as we count their influences to material failure. With the weight parameter introduced to the extended strain energy density factor criterion, we explain satisfactorily several critical experiments which reported crack kink in samples subjected to mixed-mode loading. The extended strain energy density idea is also used to derive a generalized pressure-dependent yielding criterion, which supplies a theoretical basis for those novel strength criteria for materials like bulk metallic glasses. Corresponding methods to determine the two material parameters, the critical strain energy density factor and the weight parameter quantifying the relative contribution by distortion over volumetric deformation, are discussed. [Copyright &y& Elsevier]

The effect of the hole-edge condition on the hole-expansion ratio (HER) of ferrite-bainite (FB) dual-phase steel is analyzed by developing a dual-scale finite element (FE) approach. The proposed dual-scale approach consists of macroscale simulation of hole expansion test (HET) and microscale simulation for capturing localized inhomogeneous deformation at the microstructure level. The macroscale HET simulation considers the experimentally measured hole-edge geometry and hardness profile under different clearance conditions. The deformation history in the region of interest calculated from the macroscale simulation was transferred to the microscale simulation as boundary conditions. In the microscale simulation, the deformation inhomogeneity within the two-phase microstructure was calculated by considering the dislocation pile-up at the grain boundaries. In the experimental aspect, the geometry and surface roughness of the hole edge, which are factors for quantifying the damage from the punching process, were measured using a confocal microscope. The work hardening of the material was quantitatively analyzed by measuring the hardness profile in the radial direction from the hole edge. For the work hardening due to the punching process, the measured hardness is converted into an equivalent plastic strain, which is transferred to both macro-and microscale models in the form of pre-strain. The predicted HERs are compared with the experimentally measured HER values, and it is confirmed that the damage caused by punching is critical to the hole expansion formability of the dual-phase FB steel. [ABSTRACT FROM AUTHOR]

Abstract: This paper considers the explicit solutions of free-edge stresses near circumferential cracks in surface coatings of circular torsion bars and their application in determining the progressive cracking density in the coating layers. The problem was formulated within the framework of linear elastic fracture mechanics (LEFM). The free-edge stresses near crack tip and the shear stresses in the cross-section of the torsion bar were approached in explicit forms based on the variational principle of complementary strain energy. Criterion for progressive cracking in the coating layer was established in sense of strain energy conservation, and the crack density is thereby estimated. Effects of external torque, aspect ratio, and elastic properties on the density of progressive cracking were examined numerically. The present study shows that, in the sense of inducing a given crack density, compliant coating layer with lower modulus has much higher critical torque than that of a stiffer one with the same geometries and substrate material, i.e., compliant coating layer has greater cracking tolerance. Meanwhile, the study also indicates that thicker surface coating layer is more pliant to cracking than the thinner ones. The present model can be used for analyzing the damage mechanism and cracking tolerance of surface coatings of torsion shafts and for data reduction of torsional fracture test of brittle surface coatings, etc. [Copyright &y& Elsevier]

Abstract: The hybrid time-domain boundary element method, together with the multi-region technique, is applied to simulate the dynamic process of propagation and/or kinking of an interface crack in a two-dimensional bi-material. The whole bi-material is divided into two regions along the interface. The traditional displacement boundary integral equations are employed with respect to each region. However, when the crack kinks into the matrix material, the non-hypersingular traction boundary integral equations are used with respect to the part of the crack in the matrix. Crack propagation along the interface is numerically modelled by releasing the nodes in the front of the moving crack-tip controlled by the fracture criterion. Kinking of the interface crack is controlled by a criterion developed from the quasi-static one. Once the crack kinks into the matrix, its propagation is modeled by adding new elements of constant length to the moving crack-tip controlled by a criterion extended from the quasi-static maximum circumferential stress. The numerical results of the crack growth trajectory for different material combinations are computed and compared with the corresponding experimental results. Good agreement between numerical and experimental results implies that the present boundary element numerical method can provide an excellent simulation for the dynamic propagation and deflection of an interface crack. [Copyright &y& Elsevier]

A piezoelectric material with a Griffith crack perpendicular to the poling axis is analyzed within the framework of the theory of linear piezoelectricity. Using exact electric boundary conditions at the crack surfaces, the nonlinear behavior between the electric displacement at the crack faces and applied loading is given, and it can be approximated by a linear relation on applied electric field. The Fourier transform technique is employed to reduce the mixed boundary value problem to dual integral equations. Solving resulting equations, expressions for the electroelastic field in the entire plane are obtained explicitly for a cracked piezoelectric material subjected to uniform combined electromechanical loading. The distribution of asymptotic field and the intensity factors of electroelastic field as well as the elastic T-stress are determined. Particularly, the maximum hoop strain sθθ is suggested as a fracture criterion for piezoelectric materials. Based on this criterion, relevant experimental results can be explained successfully. As an illustrative example, theoretical predictions for PZT-4 ceramic with a crack are in excellent agreement with existing experimental data, not only in qualitative behavior but also in quantitative results. [Copyright &y& Elsevier]

• RIS-MSS for mixed mode I/II fracture investigation of cracked orthotropic materials. • Maximum shear stress criterion in combination with RIS concept. • Cracks are assumed to be oriented along and across the fibers. • The effect of T-stress term on crack propagation of off-axis cracks is investigated. • RIS-MSS criterion is applicable for both cracks oriented along and across the fibers. Due to the existence of cracks and defects in composite materials during the manufacturing process, damage and crack growth in these materials must be anticipated before application. In the present research, an efficient theoretical mixed mode I/II fracture criterion is proposed for fracture investigation of orthotropic materials considering the effects of non-singular stress term in William's series expansion. This criterion is developed combining the maximum shear stress (MSS) theory with reinforcement isotropic solid concept (RIS) as a superior material model. RIS is based on the fact that cracks in orthotropic materials generally propagate along the fibers in the isotropic matrix media regardless of initial crack-fiber orientation. According to this fact, RIS offers to employ an isotropic stress field around the crack tip with defined stress reduction coefficients as fiber effects. This criterion is applicable for two cases wherein crack is placed both along and across the fibers. A comparison between available experimental data for two wood species and the results of the proposed criterion shows that this criterion can accurately predict both crack initiation and crack propagation direction and is in full compliance with the fracture nature of composite materials. [ABSTRACT FROM AUTHOR]