Mode Stress Intensity Factors Research Articles

Three-dimensional mode-I/III fatigue crack propagation: Computational modeling and experiments

Three dimensional mixed mode-I/III fatigue crack growth simulations and experiments are performed on Al 7075-T651 aluminum under different mode mixity ratios. The crack growth surfaces obtained from numerical models are compared to experimental results. Good agreement is achieved with experimental results on prediction of crack growth surfaces for up to upper intermediate levels of mixed mode loadings. Based on the computed mixed mode stress intensity factors from the numerical analyses, fatigue crack propagation lives are also predicted using different criteria. The results show that all of the mixed mode criteria evaluated in this study underestimate fatigue crack growth lives.

Mixed-mode fracture parameters estimation by genetic programming

The linear elastic fracture phenomenon has been characterized with stress intensity factors (SIFs). In this study a general function is obtained in order to predict the fracture parameters. Numerical calculation of the SIFs in a mixed-mode condition is a cumbersome task. In this research, more than 6800 numerical analyses using extended finite element method are conducted to simulate the fracture problem. States are considered for a plate with an arbitrary edge or center crack. Mixed mode SIFs were calculated using of interaction integral. Then, Gene Expression Programming (GEP) method is utilized to extraction of a function. Results show acceptable correlations between numerical calculations and genetic programming functions. R-square (R2) values are in a range of 0.91 to 0.96 that guarantees the accuracy of the inferred functions.

The determination of the stress intensity factor solutions for the new pipe-ring specimen using FEA

For safe transport and reliable supply of petrochemical substances, it is crucial to ensure the structural integrity of the equipment, pipelines in particular. Regarding the large diameters and high mass per distance, pipelines for natural gas are designed as thin-walled cylindrical structures. To ensure the structural integrity of the unknown material means to measure and therefore empirically test the material fracture properties of the laboratory specimen for giving an assessment of the accepted defect size. Compared to standards and regulations, such as the ASTM E-1820, BS 7448 standards and the GKSS procedure, the production of standard specimens for measuring the fracture toughness is commonly very difficult or even impossible for applications. On the basis of the Slovenian–Russian bilateral project, we investigate and propose a solution for this issue with a new kind of specimen, called the pipe-ring specimen. The specimens were made from a segment of the observed thin-walled pipeline from the construction filed or stored in a warehouse. The measurement procedure is similar as for the standard SENB specimens and extensometer because of the geometry of the specimen, which is cut from the pipe and contains only a machine-made notch. The next step is to test specimens axially on the three-point bending load test on the hydraulic machine. Because the ring as the specimen is not standardized, it is necessary to show and prove how, and if it is possible to use ring specimens as an alternative option to the standard specimens for testing and determining fracture properties of testing material for thin-walled pipelines. In the frame of the three main experimental, analytical and numerical approaches, this publication shows the numerical approach of defining the stress intensity factor (SIF) for crack opening mode I with and without prior fatigue pre-cracking. Besides the limit load, the SIF presents one of two main parameters for developing the failure assessment diagram and estimating the possible accepted defects in a material relating to its’ structural integrity.

Inclined surface cracks in a graded half-plane subjected to frictional sliding contact

Fracture parameters of an inclined surface crack in a graded half-plane subjected to sli- ding frictional contact are investigated in this study. The problem is modelled via the finite element method (FEM) under the plane strain assumption employing a newly developed di- splacement boundary condition. The shear modulus of the half-plane is graded exponentially through the thickness direction by means of the homogeneous finite element approach. The augmented Lagrange algorithm is selected as an iterative contact solver. The mixed mode stress intensity factors (SIFs) which are induced by the contact stresses are evaluated utili- zing the Displacement Correlation Technique (DCT). The accuracy of the present procedure is ensured comparing the SIF results to those calculated by an analytical method for verti- cal surface cracks. Additional SIF curves are generated as functions of the crack inclination in order to reveal the effects of non-homogeneity, punch location, crack length and friction coefficient. The prominent conclusion of this study indicates that the crack orientation has profound effects on the behavior of SIF curves, which has not been presented in any study published so far. Hence, consideration of crack inclination is proved essential to successfully predict fracture behavior of a graded medium under frictional contact.

Stochastic critical stress intensity factor response of single edge notched laminated composite plate using displacement correlation method

The second-order statistics of critical stress intensity factor (SIF) of single edge notched fiber reinforced composite plates with random system properties and subjected to uniaxial tensile loadings is investigated. This paper is an extension of reference (Lal and Kapania, 2013) by the present authors by considering more number of input random system parameters for higher accuracy. A C0 finite element method based on a higher-order shear deformation plate theory using displacement correlation method via isoparametric quarter point element is proposed for basic formulation. A stochastic finite element method using first-order perturbation technique and Monte Carlo simulation (MCS) is employed to examine the mean, coefficient of variance, and probability density faction of critical first mode SIF. The effect of different fiber orientations, crack length, plate thickness, a number of layers, and the lamination schemes with random system properties on the statistics of SIF of single edge crack laminated composite plate is evaluated. The tensile failure load is predicted using Hashin’s failure criteria. The present approach is validated with results available in literature and by employing independent MCS.

Relationship between crack propagation and the stress intensity factor in cutting parallel to the grain of hinoki (Chamaecyparis obtusa)

The method of digital image correlation (DIC) was applied to the digital image of orthogonal cutting parallel to the grain of hinoki, and the strain distribution near the cutting edge was evaluated. The wood fracture associated with chip generation was considered as mode I fracture, and the stress intensity factor KI for fracture mode I was calculated from the strain distribution according to the theory of linear elastic fracture mechanics for the anisotropic material. The calculated KI increased prior to crack propagation and decreased just after the crack propagation. The change in KI before and after crack propagation, ΔKI, decreased in accordance with the crack propagation length, although the variance in ΔKI should depend on the relationships between the resolution of DIC method and the dimensions of cellular structure. The calculated KI in this study was almost on the same order as reported in the literatures. It was also revealed, for the case of chip generation Type 0 or I, the stress intensity factor for fracture mode II could be negligible due to the higher longitudinal elastic properties of wood in the tool feed direction than the one radial ones, and the mode I fracture was dominant.

Effect of the angles of the cracks of corroded plate in bonded composite repair

In this study a three-dimensional finite element method analysis of repairing plate with bonded composite patch subjected to tensile load was presented. The effect of the corrosion on the damage of the adhesive (FM73) in the length of inclined crack is presented. The obtained results show that the increase of (DR) is due to the increase of the inclination of the crack against it leads to the decrease of the values of the stress intensity factor in mode I (KI).

Computation of mixed mode stress intensity factors for multiple axisymmetric cracks in an FGM medium under transient loading

In the present study, mixed-mode dynamic stress intensity factors (DSIFs) for the multiple axisymmetric cracks in an FGM medium under transient in-plane loading are formulated. It is assumed that the mass density and the shear modulus of the medium vary exponentially along the z-axis. The solution to the problem weakened by prismatic and radial dynamic dislocations is first obtained with the aid of the Laplace and Hankel transforms. This solution is used to construct integral equations in the Laplace domain for a system of coaxial axisymmetric cracks, including annular and penny-shaped cracks. The integral equations are of Cauchy singular type, which are solved numerically to obtain the dislocation density on the faces of the cracks and the results are used to determine DSIFs for cracks. Numerical examples are provided to study the effects of nonhomogeneity parameter and axisymmetric crack type as well as the interaction of multiple cracks on the DSIFs.

Crack Growth Direction in Mixed Mode Loading: A Strain Energy Density Approach

The crack growth in metallic materials using fast and reliable simulations of 2-D and linear elastic finite element models is investigated. The effect of the stress intensity factor in mode I and II (KI, KII) on the fracture behavior of stainless steel and the associated strain energy density factor in mixed mode crack propagation were studied numerically to determine crack propagation angle θ in linear elastic fracture investigation. In order to implement the determination of the crack propagation direction using the strain energy density criterion S, the numerical finite element program ANSYS was used. ANSYS APDL macros were developed to generate the geometry, material properties, boundary conditions and mesh size of the model for the conducted analyses. To demonstrate the capability of crack propagation trajectories using the proposed method under mixed mode situation, an edge crack specimen was considered with initial crack having the same length but at different inclination angles under a uniaxial tension load. Results obtained from the developed models had a good agreement (average deviation of 4.63%) with the results available in the literatures.

Experimental and numerical studies to estimate fatigue crack growth behavior of Ni-based super alloy

In this work, the fatigue crack growth behavior of the Nickel based super alloy is investigated at room (26 °C) and elevated temperature (650 °C). The fatigue crack growth experiments are performed to understand the effect of temperature and loading rate. The elasto plastic fracture toughness tests are performed to evaluate JIC. Paris law is used in conjunction with extended finite element method (XFEM) to numerically predict the fatigue life. The stress intensity factors of individual mode (KI and KII) are computed from J-integral by decomposing the stress, strain and strain derivatives into symmetric and antisymmetric parts. Few parametric studies are performed to show the mesh convergence and path independency of J-integral. Fatigue crack growth in an aero-engine turbine disc is predicted. The numerically predicted fatigue life is found in good match with the experimental results.

Fatigue life estimation and crack propagation analysis of orthotropic lamina using XIGA methodology

ABSTRACTIn the present work, a NURBS-based Extended Isogeometric Analysis (XIGA) code has been developed for fracture analysis of orthotropic lamina. The XIGA code is capable of an efficient analysis of crack problems using non-uniform rational B-spline basis functions for both the solution field and geometric description of model. The level set approach is used to track the crack geometry. Crack faces are enriched by Heaviside enrichment function and crack tip singularity is captured by asymptotic crack tip enrichment functions. The interaction integral (M-Integral) method is used to calculate mixed mode stress intensity factor for further stable crack growth. The Paris crack growth law is used to simulate the crack propagation and fatigue life estimation in orthotropic media using life cycle increment approach. The developed code has been validated for static and fatigue analysis. The effect of varying angle of orthotropy on fatigue life of 2D plate is investigated using XIGA methodology leading to an optimized ply orientation of orthotropic plate.

Mixed mode crack growth in elasto-plastic-creeping solids using XFEM

In this work, an extended finite element based fully implicit algorithm is proposed to predict the creep deformation and creep crack growth in elasto-plastic-creeping solids. The effect of stress relaxation and redistribution due to creep strain is captured through elasto-plastic-creep analysis. In creep crack growth analysis, mostly C∗ is used to compute the creep crack growth which includes only extensive creep whereas C(t)-integral includes small-scale creep, transition creep and extensive creep. Thus, in the present study, creep crack characterization parameter C(t)-integral is evaluated using XFEM to compute creep crack growth rate. The mixed mode stress intensity factors are evaluated using domain based interaction integral approach to estimate the crack growth direction. Various numerical issues related to history dependency of plasticity and creep are properly addressed. To validate the present approach, various numerical problems are solved and the predicted creep deformation and creep crack growth results are compared with the experimental observations.

A simple technique for estimation of mixed mode (I/II) stress intensity factors

A simple technique for estimation of mixed mode (I/II) stress intensity factors

The linear steady state analysis of multiple moving cracks in a piezoelectric half-plane under in-plane electro-elastic loading

In this work, the steady state problem of multiple Yoffe-type cracks propagating in a piezoelectric half-plane within the framework of linear electroelasticity under in-plane electro-elastic loading is studied. At first, the closed-form solution of the moving electric and Volterra type climb and glide edge dislocations are derived using the complex Fourier transforms to achieve the integral equations of a piezoelectric half-plane with several moving cracks. Then, the integral equations with Cauchy-kind singularity are solved numerically to determine the mixed mode stress intensity factors and the electric displacement intensity factors in a piezoelectric medium. Finally, the effects of the loading conditions, crack moving speed, cracks lengths, cracks interactions and geometrical parameters on the field intensity factors are considered.

Evaluation of mixed mode-I/II criteria for fatigue crack propagation using experiments and modeling

In this study, in-plane mixed mode-I/II fatigue crack growth simulations and experiments are performed for the Al 7075-T651 aluminum alloy which is widely used in the aerospace industry. Tests are carried out under different mode mixity ratios to evaluate the applicability of a fracture criterion developed in a previous study to mixed mode-I/II fatigue crack growth tests. Results obtained from the analyses and experiments are compared with existing and developed criteria in terms of crack growth lives. Compact Tension Shear (CTS) specimens, which enable mixed mode loading with loading devices under different loading angles, are used in the simulations and experiments. In an effort to model and simulate the actual conditions in the experiments, crack surfaces of fractured specimens are scanned, crack paths are modeled exactly, and contacts are defined between the contact surfaces of a specimen and the loading device for each crack propagation step in the analyses. Having computed the mixed mode stress intensity factors from the numerical analyses, propagation life cycles are predicted by existing and the developed mixed mode-I/II criteria and then compared with experimental results.

Atomic-scale mode separation for mixed-mode intergranular fracture in polycrystalline metals

In intergranular fractures, cracks tend to propagate along grain boundaries (GBs) even under mixed-mode loadings. To quantitatively characterize the mixed-mode intergranular fractures, the stress intensity factors (SIFs) of modes I and II at the crack tip need to be found individually. In this study, an atomic-scale mode separation method is developed to determine individual SIFs from the molecular dynamics (MD) simulation of the mixed-mode intergranular fracture in crystalline metals, for which the atomic-scale J-based mutual integral and asymptotic singular field (i.e., K-field) near a semi-infinite interfacial crack in an anisotropic bimaterial as an auxiliary field are used. Additionally, atomic-level J and M integrals are also performed to determine the energy release rate and the position of a crack tip under the applied mixed-mode loadings, respectively. As a model problem, the mixed-mode fracture along GBs of nickel is investigated to demonstrate that the present atomic-scale mode separation method is useful to examine mixed-mode intergranular fracture behaviors of polycrystalline metals at the atomic scale.

Stochastic XFEM based fracture behavior and crack growth analysis of a plate with a hole emanating cracks under biaxial loading

In the paper, the stochastic fracture response of an isotropic finite plate with a circular hole emanating radial cracks, having different angles, under biaxial loading with different biaxiality ratio (β=0,1 and −1) is examined. In this direction, the mean values and corresponding coefficient of variations (COVs) of mixed mode stress intensity factor (MMSIFs) using the second order perturbation technique (SOPT) combined with a finite difference method through extended finite element method (XFEM) are evaluated in MATLAB environment. The random system parameters, e.g., normalized crack length, crack angle, the normalized radius of the hole, are assumed as uncorrelated input random variables. The effects, of these input parameters and biaxial load factors, on the statistics of MMSIFs with input individual and combined random system parameters, are analyzed. Also, the stochastic fracture behavior is predicted with the increment in the radius of the hole and with the change in the position of the discontinuities (a hole emanating cracks) in the plate using uncorrelated combined randomness with different input variables. Further, the static crack propagation behavior of the plate with hole emanating cracks under biaxial loading with different biaxiality ratio is analyzed.

Improvement of the mode I interlaminar fracture toughness of glass fiber/epoxy composites using polystyrene electrospun nanofibres

In this paper, the polystyrene nanofiber (PSnF) with diameter in range 40–80 nm were fabricated using electrospinning technique from solution of polystyrene in toluene and used as an effective filler for glass fiber reinforced epoxy composite materials (GF/EP) with contents in range from 0 to 0.1 wt%. GF/EP composites with absence and presence of PSnF were characterized by different techniques, namely; mode I interlaminar fracture toughness, tensile testing and scanning electron microscope. The bonding between GF and EP were also accessed by interfacial shear strength test (IFSS). The obtained results indicated that at 0.07 wt% of PSnF incorporation in epoxy matrix the stress intensity factor (KIC), initiation and propagation interlaminar fracture toughness in mode I were improved by 42.2% from 0.631 to 0.839 MPa m1/2, and 43% from 389.82 to 512.09 J/m2 and 47% from 401.38 to 545.34 J/m2, respectively, when compared to pristine epoxy resin as well as pristine composite material. The scanning electron microscopy (SEM) observation pointed out that fibers pull out during initiation delamination accounting for fracture toughness improvement the fracture surface of GF/EP.

Experimental evaluation of effective surface energy for cleavage microcrack propagation across grain boundary in steels

Fracture tests and finite element analysis were conducted to evaluate the temperature dependence of the effective surface energy γmm corresponding to microcrack propagation across the grain boundary of steels. Steels containing coarse cementite particles were prepared to enable γmm evaluation. The critical fracture stress of microcrack propagation across the grain boundary is considered larger than the critical fracture stress of microcrack propagation across the interface between a cementite particle and a ferrite grain in these steels because of the large cementite particles; therefore, local fracture stress estimated by finite element analysis and fracture initiation site obtained by fractography reflect the critical fracture stress of microcrack propagation across the grain boundary. Thus, the accuracy of γmm calculated from local fracture stress is observed to be enhanced by employing the steels prepared for the present study. In addition, the effect of nickel on γmm was studied using steels containing different concentrations of nickel. Values of γmm were evaluated considering both the direction of a neighboring facet relative to the crack initiation facet and the mixed mode stress intensity factors. The authors proposed a new temperature dependence ofγmm. Additionally, the negligible effect of nickel addition on γmm was observed. The results of the present study can be used effectively to develop a probabilistic cleavage fracture model based on microstructural information.

Numerical studies on mixed mode fracture behavior of dissimilar (AISI 304 and AA1050) welded joints with multiple cracks

Effect of residual stresses on mixed mode stress intensity factor (SIF) of dissimilar welds (steel AISI 304 and aluminum AA1050) has been investigated numerically. Opposite surface cracks of various crack depth ratio [(a/t); “a” crack depth, “t” plate thickness] and crack aspect ratio [(a/c); “c” semi-major axis of the ellipse] were considered for different heat flux values. The geometry correction factor (Y) was determined with consideration of mode II and mode III fracture. It is noted that, at short crack depths, as the residual stress increases, SIF of steel region decreases and increases for aluminum region. When the crack depth ratio increases, SIF of both materials decreases due to relieving of residual stress at higher crack depths. Non-uniform crack opening was observed along the crack border, front, and rear side of the plate. A three-parameter relationship has been arrived to determine the structural integrity of dissimilar welded joint.