A least squares procedure for the evaluation of multiple generalized stress intensity factors at 2D multimaterial corners by BEM

Detailed characterization of linear elastic stress states at corners and crack tips requires knowledge of the stress singularity orders, the characteristic angular functions and the generalized stress intensity factors (GSIF). Typically a high accuracy is found in the literature for the evaluation of the stress singularity orders and characteristic angular functions (numerically computed from analytical expressions in most cases). Nevertheless, GSIF values, evaluated by means of a numerical model using FEM or BEM and usually by postprocessing the results, are often reported with a lower level of confidence. A robust procedure is presented in this work for the evaluation of the GSIF at multimaterial corners. The procedure is based on a simple least squares technique involving stresses and/or displacements, computed by BEM, at the neighborhood of the corner tip. A careful verification of the robustness and accuracy of the procedure using a few benchmark problems in the literature has been carried out. Applications of the procedure developed to the evaluation of GSIFs appearing at corners in metal-composite adhesive lap joints are presented.     

Analytical and numerical study of cohesive zones for a crack in an adhesive layer between identical isotropic materials

A crack in a thin adhesive elastic-perfectly plastic layer between two identical isotropic elastic half-spaces is considered. Uniformly distributed normal stress is applied to the substrates at infinity. First, stress distribution in the cohesive zones and the J-integral values are defined numerically by the finite element method (FEM). Further, a mathematical formulation of the problem is given and its analytical solution is proposed. It is assumed that, at the crack continuations, there exist cohesive zones. The interlayer thickness is neglected since it is much smaller than the crack length. The distribution of the normal stress, which was obtained by means of the FEM, is now approximated by a piecewise-constant function and assumed to be applied at the faces of the cohesive zones. The formulated problem is solved analytically and an equation for determination of the cohesive zone lengths is derived. Also, closed expressions for the crack tip opening displacement and for the J-integral are obtained in an analytical form. These parameters are found with respect to the values of the normal stress applied at infinity. Finally, a universal approximating function, which describes the stress distribution in the cohesive zones, is constructed. This function depends on the ratio between the interlayer thickness and the crack length and on the ratio between the normal stress applied at infinity and the yield limit of the interlayer’s material. Once again, the problem is solved analytically, but this time for the stress distribution prescribed by the universal approximating function. The cohesive zone lengths, the values of the crack tip opening displacement and of the J-integral are calculated. A comparative analysis of the obtained results is carried out. A good agreement of the J-integral values calculated by means of the developed analytical models and by the associated finite element analysis is demonstrated.     

Establishing methodology to predict fracture behaviour of piping components by numerically predicting specimen fracture data using tensile specimen test

Using large deformation FEM analyses in SA333Gr.6 carbon steel material, the present study demonstrated the assessment of SZWc value that leads to J_SZWc and finally compares with the respective experimental results. It also includes numerical prediction of specimen J-R curve using Gurson-Tvergaard-Needleman parameters obtain from tensile specimen tests. Using numerically predicted results, the crack initiation and instability stages in circumferentially through-wall cracked elbows is finally predicted and compares with experimental results. The present study gives evidence that the non-linear FEM analysis supported with proper tensile test data can be helpful in assessing the safety of bend pipes with through-wall crack.     

Effect of material gradation on K-dominance of fracture specimens

This work describes the effect of material gradation (parallel to the crack plane) on stress intensity factors and K-dominance, i.e. the dominance of the singular region, of fracture specimens; SE(T), SE(B) and C(T). The extent of K-dominance is investigated by comparing the actual stress field with the Williams’ asymptotic stress field. Linear-elastic finite element analyses are performed using graded elements which incorporate graded material properties at the element level. Material gradation and crack geometry are systematically varied to perform the parametric study. Results reveal that the effect of material gradation on K_I is most pronounced when a short crack is located on the stiffer side of the fracture specimen. For a given specimen and crack geometry, the extent of K-dominance yields a curve with a peak point at a certain material gradation. Results of the present study provide valuable insight into the K-dominance of FGMs.     

Evaluation of R-curve behavior of ceramic-metal functionally graded materials by stable crack growth

This paper deals with the fracture toughness and R-curve behavior of ceramic-metal functionally graded materials (FGMs). A possibility of stable crack growth in a three-point-bending specimen is examined based on the driving force and resistance for crack growth in FGMs, and the distribution of fracture toughness or R-curve behavior is evaluated on FGMs fabricated by powder metallurgy using partially stabilized zirconia (PSZ) and stainless steel (SUS 304). The materials have a functionally graded surface layer (FGM layer) with a thickness of 1 mm or 2 mm on a SUS 304 substrate. Three-point-bending tests are carried out on a rectangular specimen with a very short crack in the ceramics surface. On the three-point-bending test, a crack is initiated from a short pre-crack in unstable manner, and then it propagates in stable manner through the FGM layer with an increase in the applied load. From the relationship between applied load and crack length during the stable crack growth in the FGM layer, the fracture toughness is evaluated. The fracture toughness increases with an increase in a volume fraction of SUS 304 phase.     

Effects of component size, geometry, microstructure and aging on the embrittling behavior of creep crack growth correlated by the Q parameter

The driving force for creep crack growth is dominated by local elastic-plastic stress in the creep damage zone around a crack tip, temperature and microstructure. In previous work, C^∗, C_t, load line displacement rate dδ/dt and Q^∗ parameters have been proposed as formulations of creep crack growth rate (CCGR). Furthermore, using parameters mentioned above, the construction of the algorithm of predictive law for creep crack growth life is necessary for life assessment procedures. The aim of this paper is to identify the effects of component size, geometry, microstructure, aging and weldment on the embrittling behavior of creep crack growth and incorporate these effects in a predictive law, using the Q^∗ parameter. It was found that for specimen size (width and thickness) and of material softening due to aging the values of the activation energy were the same whereas for grain size change and structural brittleness, which affected crack tip multi-axial stress state the values for the activation energy for CCGR differ.     

A boundary layer framework considering material gradation effects

This paper describes the development and application of a novel modified boundary layer (MBL) model for graded nonhomogeneous materials, e.g. functionally graded materials (FGMs). The proposed model is based on a middle-crack tension, M(T), specimen with traction boundary conditions applied to the top and lateral edges of the model. Finite element analyses are performed using WARP3D, a fracture mechanics research finite element code, which incorporates elements with graded elastic and plastic properties. Elastic crack-tip fields obtained from the proposed MBL model show excellent agreement with those obtained from full models of the cracked component for homogeneous and graded nonhomogeneous materials. The K-T dominance of FGMs is investigated by comparing the actual stress fields with the asymptotic stress fields (the Williams’ solution). The examples investigated in the present study consider a crack parallel to the material gradient. Results of the present study provide insight into the K-T dominance of FGMs and also show the range of applicability of the proposed MBL model. The MBL model is applied to analyze the elastic-plastic crack-tip response of a Ti/TiB FGM SE(T) specimen. The numerical results demonstrate that the proposed MBL model captures the effect of T-stress on plastic zone size and shape, constraint effects, etc. for such configurations.     

Effect of stress relief groove on fretting fatigue strength and index for the selection of optimal groove shape

The applicability of small stress relief groove for the improvement of fretting fatigue strength was studied. Fretting fatigue tests were done using several kinds of grooved specimens. The shape of groove was systematically changed with parameters of groove radius R and tangential angle θ. The improvement of fatigue limit by a stress relief groove depended on both R and θ. The fretting fatigue limit with stress relief groove was increased with the increase of R and θ. The parameter θd (d: groove depth) was selected for the unified evaluation of the improvement. FEM stress analyses were done to investigate the stress condition. In a simple elastic FEM analysis assuming that the contact edge is ideally shaped, a highly compressive stress field was generated near the contact edge, where small cracks could never propagate. This suggested that such a simple analysis was not enough to solve this problem. Thus, an assumption to relieve the highly compressive contact pressure near the contact edge was introduced to explain the experimental fact that a crack could propagate. The profile change was simulated by the local plastic deformation at the contact edge calculated by elasto-plastic FEM deformation analysis. This deformation reduced the highly compressive contact pressure and enabled the crack propagation. As a result, it was found that fretting fatigue limit of grooved specimen could be evaluated on the basis of the maximum axial stress near the contact edge. The estimation of fretting fatigue limit using a relationship between K_t/K_t0 and θd provided a good estimation with the experimental results and it would be a useful method to select the optimal groove shape.     

Mechanics of tunnelling cracks in trilayer elastic materials in tension

In this work, the crack driving force for a tunnelling crack in a thin brittle layer confined by dissimilar thick, and more compliant, elastic layers is considered at tensile loading. The steady-state energy release rate is evaluated using distributed dislocation technique and series representation of the complex potentials for an isotropic trimaterial. Evolution of the energy release rate with the crack length is studied by means of FEM. The 3D FEM simulations for tunnel cracks suggest that the ERR can represented by a universal relation (mastercurve) in suitably normalised co-ordinates. An analytical approximation of the ERR mastercurve is obtained as a function of crack length, cracking layer thickness, and a non-dimensional steady-state ERR.     

Comparison of creep crack growth rate in heat affected zone of welded joint for 9%Cr ferritic heat resistant steel based on C, dδ/dt, K and Q parameters

Creep crack growth behavior is very sensitive to the materials’ micro-structures such as the heat affected zone of a weld joint. This is a main issue to be clarified for 9%Cr ferritic heat resistant steel for their application in structural components. In this paper, high temperature creep crack growth tests were conducted on CT specimens with cracks in the heat affected zone of weld joints of W added 9%Cr ferritic heat resistant steel, ASME grade P92. The creep crack growth behavior in the heat affected zone of welded joint was investigated using the Q^∗ concept following which the algorithm of predicting the life of creep crack growth has been proposed. Furthermore, three-dimensional elastic-plastic creep FEM analyses were conducted and the effect of stress multiaxiality of welded joint on creep crack growth rate was discussed as compared with that of base metal.     

XFEM simulation of stable crack growth using J–R curve under finite strain plasticity

In the present work, extended finite element method (XFEM) has been extended to simulate stable crack growth problems using J–R criterion under finite strain plasticity. In XFEM, a physical representation of crack is not required, and a crack is completely modeled by enrichment functions. The modeling of large deformation is performed using updated Lagrangian approach. The nonlinear equations obtained as a result of large deformation are solved by Newton–Raphson iterative method. Von-Mises yield criterion is used with isotropic hardening to model the finite strain plasticity. The elastic-predictor and plastic-corrector algorithm is employed for stress computation. Three problems i.e. crack growth in compact tension specimen; crack growth in triple point bend specimen and crack growth in bi-metallic triple point bend specimen are solved using J–R curve under plane stress condition to demonstrate the capability of XFEM in crack growth problems.     

Interlaminar fracture analysis in the GII-GIII plane using prestressed transparent composite beams

This work presents the mixed-mode II/III prestressed split-cantilever beam specimen for the fracture testing of composite materials. In accordance with the concept of prestressed composite beams one of the two fracture modes is provided by the prestressed state of the specimen, and the other one is increased up to fracture initiation by using a testing machine. The novel beam-like specimen is able to provide any combinations of the mode-II and mode-III ERRs. Data reduction is made by using the virtual crack-closure technique. The applicability and the limitations of the novel fracture mechanical test are demonstrated using unidirectional glass/polyester composite specimens. If only crack propagation onset is involved then the mixed-mode beam specimen can be used to obtain the fracture criterion of transparent composite materials in the G_II-G_III plane in a relatively simple way.     

Interfacial fatigue crack growth in foam core sandwich structures

This paper deals with the experimental measurement of face/core interfacial fatigue crack growth rates in foam core sandwich beams. The so-called ‘cracked sandwich beam’ specimen is used, slightly modified, which is a sandwich beam that has a simulated face/core interface crack. The specimen is precracked so that a more realistic crack front is created prior to fatigue growth measurements. The crack is then propagated along the interface, in the core material, during fatigue loading, as is assumed to occur in a real sandwich structure. The crack growth is stable even under constant amplitude testing. Stress intensity factors are obtained from the FEM which, combined with the experimental data, result in standard da/dN versus ΔK curves for which classical Paris’ law constants can be extracted. The experiments to determine stress intensity factor threshold values are performed using a manual load-shedding technique.     

Effect of geometry and electrical boundary conditions on R-curves for lead zirconate titanate ceramics

R-curve measurements on PZT poled in thickness direction were carried out on CT specimens under different electric boundary conditions. The effect of specimen geometry was evaluated by measuring R-curves in CT specimens of different thickness and comparing these with R-curves in bend bars. A low coercive stress is responsible for the development of a large switching zone. This switching zone is of high relevance for the computation of the actual stress intensity factor at the crack tip and for the R-curve calculation.     

Two-parameter characterization of elastic-plastic crack front fields: Surface cracked plates under tensile loading

In this paper the J-Q two-parameter characterization of elastic-plastic crack front fields is examined for surface cracked plates under uniaxial and biaxial tensile loadings. Extensive three-dimensional elastic-plastic finite element analyses were performed for semi-elliptical surface cracks in a finite thickness plate, under remote uniaxial and biaxial tension loading conditions. Surface cracks with aspect ratios a/c = 0.2, 1.0 and relative depths a/t = 0.2, 0.6 were investigated. The loading levels cover from small-scale to large-scale yielding. In topological planes perpendicular to the crack fronts, the crack stress fields were obtained. In order to facilitate the determination of Q-factors, modified boundary layer analyses were also conducted. The J-Q two-parameter approach was then used in characterizing the elastic-plastic crack front stress fields along these 3D crack fronts. Complete distributions of the J-integral and Q-factors for a wide range of loading conditions were obtained. 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 finite element analysis. These results are suitable for elastic-plastic fracture mechanics analysis of surface cracked plates.     

Methods for calculating stress intensity factors in anisotropic materials: Part II—Arbitrary geometry

The problem of a crack in a general anisotropic material under conditions of linear elastic fracture mechanics (LEFM) is examined. In Part I, three methods were presented for calculating stress intensity factors for various anisotropic materials in which z = 0 is a symmetry plane and the crack front is along the z-axis. These included displacement extrapolation, the M-integral and the separated J-integrals.In this study, general material anisotropy is considered in which the material and crack coordinates may be at arbitrary angles. A three-dimensional treatment is required for this situation in which there may be two or three modes present. A three-dimensional M-integral is extended to obtain stress intensity factors. It is applied to several test problems, in which excellent results are obtained. Results are obtained for a Brazilian disk specimen made of isotropic and cubic material. Two examples for the latter are examined with material coordinates rotated with respect to the crack axes.     

The effective T-stress estimation and crack paths emanating from U-notches

The concept of the T-stress as a local constraint factor has been extended to U-notch tip stress distribution as the effective T-stress. The effective T-stress has been estimated as the average value of the T-stress in the region corresponding to the effective (characteristic) distance ahead of the notch tip. The T-stress is evaluated by finite element method using the experimental load for crack initiation and computing the difference between principal stresses along ligament. A large range of critical effective T-stress values is investigated for different specimen configurations and notch aspect ratios. Crack stabilisation and crack bifurcation for fracture emanating from notches according to the critical effective T-stress is discussed. A model involving the influence of the critical effective T-stress on void growth for ductile failure in the vicinity of the notch tip has been proposed.     

Advantages of the J-integral approach for calculating stress intensity factors when using the commercial finite element software ABAQUS

A predictive method for remaining component lifetime evaluation consists in integrating the crack growth law of the material considered in a finite element step-by-step process. So, as part of a linear elastic fracture mechanics analysis, the determination of the stress intensity factor distribution is a crucial point. The aim of the present work is to test several existing numerical techniques reported in the literature. Both the crack opening displacement extrapolation method and the J-integral approach are applied in 2D and 3D ABAQUS finite element models. The results obtained by these various means on CT specimens and cracked round bars are in good agreement with those found in the literature. Nevertheless, since the knowledge of the field near the crack tip is not required in the energetic method, the J-integral calculations seem to be a good technique to deal with the fatigue growth of general cracks.