The geometry effects for stress intensity factor of sandwich specimen for measuring interfacial fracture toughness

The interfacial stress intensity factors for three types of sandwich specimens: the single edge crack tensile specimen, the three point bend specimen and the four point shear specimen were obtained by the finite element analysis and compared with the asymptotic solutions. The results show that the geometric effect for mode II specimen is larger than mode I specimen. The limit curves for geometry factor equal to 1.05 were obtained to indicate the usable range of validity of the asymptotic solution.     

纯弯曲Sandwich 梁试样界面裂纹扩展的应变能释放率

纯弯曲的Sandwich 梁试样在评价界面断裂抗力方面有重要作用。利用能量的叠加原理和截面转换方法, 本文导出了纯弯曲Sandw ich 梁试样界面裂纹扩展应变能释放率的显式解, 并根据实验测得的界面裂纹扩展的临界载荷, 用其计算出了四点弯曲Si₃N₄/Al/Si₃N 4试样Si₃N₄/Al 扩散连接界面的断裂韧度。      

Mixed Mode Fracture of Concrete under Proportional and Nonproportional Loading

A novel testing procedure for mixed mode crack propagation in concrete is presented: four point bend of notched beams under the action of two independent force actuators. In contrast to classical procedures, this method allows nonproportional loading and crack trajectory modifications by changing the action of one actuator. Different experimental crack trajectories, under mixed mode and nonproportional loading, are presented together with the corresponding curves of load-CMOD and load-displacement. The tests were performed for three homotetic specimen sizes and two mixed mode loading conditions. The results are useful for checking the accuracy of mixed mode fracture analytical and numerical models. The models should predict the crack trajectory and a complete group of experimental records of load and displacements on several control points in the specimen. This revised version was published online in July 2006 with corrections to the Cover Date.     

Short-crack growth in corrosion fatigue for a high strength steel

Fatigue crack growth tests of HY130 steel were conducted under either constant-load-range or constant-stress-intensity-range conditions, by using four-point-bend and compact-tension specimens with a crack of length 0.4–41 mm. The tests were conducted in 3.5% NaCl solution under either the freely corroding condition or with the specimen coupled to a sacrificial zinc anode.Crack growth rates for the zinc-coupled case were higher than those for the freely corroding case, for either the long crack or short crack specimen. The growth rates of short cracks were faster than those of long cracks for the same environment. The maximum amount of crack growth acceleration due to crack size effect was about a factor of two for these alloy-environment combinations. With increasing crack length, the rate for short cracks converges to that for long cracks. Since there was no crack-size effect in air, the additional enhancement in the rate of crack growth for short cracks must be chemical in nature.The upper limit of chemically short cracks (as delineated by the point of convergence of rates) was shorter for the freely corroding case than for the zinc-coupled case, and was longer for the higher stress intensity range, for both the constant-load-range and the constant-stress-intensity-range tests. The observed effect of crack size on crack growth rates is discussed in terms of the hydrogen embrittlement mechanisms.     

Experimental fatigue crack growth analysis and modelling in part‐through circumferentially pre‐cracked pipes under pure bending load

In the present work, an attempt has been made to study the fatigue crack growth in a part‐through circumferentially notched pipe specimen. It has been observed that under four‐point bend cyclic load, the crack propagates in a transverse plane in the radial direction initially followed by propagation in the circumferential direction. The crack extension in the circumferential direction resulted crack growth retardation in the radial direction. This behaviour of the fatigue crack growth has been modelled, and a fatigue life prediction methodology based on an exponential model has been applied for prediction of fatigue crack growth.     

The effect of crack front curvature and side-grooving on three point bend specimen fracture toughness measurements

Finite element simulations of the three point bend fracture toughness specimen have been performed to investigate the effect of crack front curvature and side-grooving. Even modest crack front curvature moves the position of maximum energy release rate from the center towards the free surfaces of the specimen. A 30 percent difference between the maximum and minimum crack length can double the maximum energy release rate compared to that calculated for a straight crack of the same average length. A correction curve has been derived from which the curved crack energy release rate can be obtained using two dimensional solutions. Deep side-grooving substantially increases the energy release rate at the root of the groove, but for groove depths no more than 30 percent of the section, an energy release rate can be estimated from the two dimensional ungrooved solution scaled by the ratio of ungrooved to grooved thicknesses.     

Automatic 3-D crack propagation calculations: a pure hexahedral element approach versus a combined element approach

This article presents an evaluation of two different crack prediction approaches based on a comparison of the stress intensity factor distribution for three example problems. A single edge notch specimen and a quarter circular corner crack specimen subjected to shear displacements and a three point bend specimen with a crack inclined to the mid-plane are examined. The stress intensity factors are determined from the singular stress field close to the crack front. Two different fracture criteria are adopted for the calculation of an equivalent stress intensity factor and crack deflection angle. The stress intensity factor distributions for both numerical methods agree well to available reference solutions. Deviations are recorded at crack front locations near the free surface probably due to global contraction effects and the twisting behaviour of the crack front. Crack propagation calculations for the three point bending specimen give results that satisfy intuitive expectations. The outcome of the study encourages further pursuit of a crack propagation tool based on a combination of elements.     

Numerical analysis of dynamic T stress of moving interfacial crack

A method to extract dynamic T stress term of moving interfacial crack is proposed. Anisotropic bimaterial which has subsonic crack propagation is considered, and interaction energy method is applied. Stress fields by the constant T stress and stress fields by the point force moving with the crack are obtained by using the series expansion method and Stroh formalism. J based interaction energy (J^I) between the constant T stress and the point force is calculated by Yeh formulation and the relation between interaction energy and T stress is obtained. Energy release rate and T stress of a moving interfacial crack are calculated numerically. Elastodynamic finite element code is developed to investigate fracture parameters for the propagating crack. Four nodes linear elastodynamic element is used and Newmark formulae are applied to integrate displacement and velocity. Node release method is adapted to simulate crack propagation along the interface. The energy release rate is calculated in the area moving with crack. T stress term is calculated from the interaction energy with a stress field formed by the moving point force. Five examples are solved to show the validity and time history of energy release rate and T stress. The energy release rate calculated from numerical analysis agrees well with an analytic solution and experimental results. The T stress of homogeneous specimen under the steady state condition shows a slightly different value compared with the stationary result. It is observed that the T stress of polymethyl methacrylate–steel specimen shows continuous change and the T stress of aluminum-polymethyl methacrylate specimen shows discontinuous jump when the initial crack initiates. From the result of the variation of T stress, the effect of T stress on the stability of crack propagation is observed.     

Photoelastic investigation of the double-torsion specimen

The stress distribution of the double-torsion fracture mechanics specimen geometry is presented using a photoelastic “frozen stress” technique. Isochromatic fringes of a plastic double-torsion specimen under load were photographed and analyzed in the top, middle and bottom planes parallel to the top surface. Principal stress directions for these planes are also given. The relative magnitudes of the principal stresses perpendicular to the crack plane at the crack tip, crack origin and a point midway between the origin and crack tip are shown.     

On the use of an anti‐symmetric four‐point bend specimen for mode II fracture experiments

The edge‐cracked beam specimen subjected to anti‐symmetric four‐point bend (ASFPB) loading has been conventionally used in the past for investigating the pure mode II fracture experiments in many engineering materials. However, it is shown through finite element analysis that the ASFPB specimen sometimes fails to produce pure mode II conditions. For anti‐symmetric loads applied close to the crack line, there are considerable effects from K_I and T‐stress in the ASFPB specimen. Pure mode II is provided only when the applied loads are sufficiently far from the crack plane.     

Elastoplastic crack analysis by boundary integral method and surface spectrum measurement

The paper describes a hybrid experimental-numerical technique for elastoplastic crack analysis. It consists of the experimental surface spectrum measurement of plastic strains ahead the crack tip and the boundary element method (BEM). The light scattering method is used to measure the power density spectrum from which the values of plastic strains are obtained by comparison with a calibration experiment on the same material. Plastic strains obtained experimentally are conveniently used for the calculation of unknown boundary displacement or traction vectors by the boundary element method. Instead of an iterative solution of the boundary integral equations in pure numerical solution, the boundary unknowns are computed once for a required loading level. Also asymptotic distribution of strains or stresses is not needed in the evaluation of the domain integral for the BEM formulation in the vicinity of the crack tip. Significant CPU time saving is achieved in comparison with the pure BEM solution. The method presented is illustrated by the example for a three point bending specimen with an edge crack.     

The M-integral for calculating intensity factors of an impermeable crack in a piezoelectric material

In this study, a conservative integral is derived for calculating the intensity factors associated with piezoelectric material for an impermeable crack. This is an extension of the M-integral or interaction energy integral for mode separation in mechanical problems. In addition, the method of displacement extrapolation is extended for this application as a check on results obtained with the conservative integral. Poling is assumed parallel, perpendicular and at an arbitrary angle with respect to the crack plane, as well as parallel to the crack front. In the latter case, a three-dimensional treatment is required for the conservative integral which is beyond the scope of this investigation. The asymptotic fields are obtained; these include stress, electric, displacement and electric flux density fields which are used as auxiliary solutions for the M-integral.Several benchmark problems are examined to demonstrate the accuracy of the methods. Numerical difficulties encountered resulting from multiplication of large and small numbers were solved by normalizing the variables. Since an analytical solution exists, a finite length crack in an infinite body is also considered. Finally, a four point bend specimen subjected to both an applied load and an electric field is presented for a crack parallel, perpendicular and at an angle to the poling direction. It is seen that neglecting the piezoelectric effect in calculating stress intensity factors may lead to errors.     

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.     

AGEING EFFECTS ON FATIGUE CRACK CLOSURE OF AN Al–Li–Zr ALLOY IN Na2SO4, SOLUTION

Abstract— Fatigue of an Al–Li–Zr alloy has been studied as a function of ageing stage by measuring crack closure in Na₂SO₄ solution with an unloading elastic compliance technique and comparing results in dry air and oxygenated solution. Anodic behaviour of peak-aged and overaged alloy specimens in the Na₂SO₄ solution has been investigated by potentiodynamic polarisation and potentiostatic current transient experiments. The Na₂SO₄ solution increased the intrinsic fatigue crack propagation (FCP) rate for the overaged specimen in dry air compared to that for the peak-aged sample. The Na₂SO₄ solution inhibited the development of crack closure for the peak-aged specimen in dry air, but aided it in the overaged condition. The result of the environmental crack closure study is discussed in terms of the more enhanced through-thickness tortuosity of the overaged specimen in the Na₂SO₄ solution when compared to that of the peak-aged specimen. The oxygen dissolved in the Na₂SO₄ solution slightly increased the environmental intrinsic FCP rate, which seems to be due to the reduced repassivation rate as compared to that in the N₂-purged solution. The anodic dissolution rate from the bare surface of the overaged specimen in the Na₂SO₄ solution was higher than that from the peak-aged sample. The difference between environmental FCP rates and crack closures for the peak-aged and overaged specimens is discussed in terms of environment-assisted crack-tip damage processes involving anodic dissolution.     

Subcritical crack propagation under cyclic stress impulse

An equipment has been designed to observe subcritical crack propagation under cyclic impulse (impact) loads. The equipment design uses the concept of stress wave propagation in bars. A four point bend notched specimen is struck by an incident bar with a known stress wave. The test specimens were machined from PMMA sheet (Lucite^®). The crack, initiated from the notch, was detected by a step wise increase of a graphitic grid imprinted on one side of the specimen. The data was analyzed using fracture mechanics theory and compared with that of conventional fatigue.Although the applied strain rate was quite high (1s^–1), stable crack propagation was significant. It appears that the elastic energy stored in the specimen within the duration of each impulse is dissipated in craze formation at the tip of the advancing crack. Furthermore, the magnitude of stable crack propagation was larger under impulse loading than under sinusoidal fatigue. On the other hand, cracks were slower under impulse loading. Fractographic evidence attributes these phenomena to the nature of craze growth under each loading condition.     

A Fracture Probability Competition Mechanism of Stress Corrosion Cracking

The stress corrosion cracking (SCC) of austenitic stainless steel was studied via polarization, slow strain rate and scanning electron microscope (SEM) techniques. Many SCC mechanisms have been proposed in which hydrogen embrittlement and passive film rupture-repassivation theories are generally accepted, but they can hardly explain the SCC mechanism of austenitic stainless steel in acidic chloride solution adequately, because the steel is in active dissolution state and cathodic polarization can prevent it from occurring. Our experiment shows that the anodic current increases the creep rate and decreases the plastic strength of the material on single smooth specimen as well as at the SCC crack tip. The fractured surface was characterized as brittle cleavage, while the surface crack of smooth specimen was almost vertical to the tensile strength, which can confirm that the cracks were caused by tensile stresses. A fracture probability competition mechanism of SCC was proposed on the basis of the experimental results combined with the viewpoint of ductile-brittle fracture competition. When the anodic dissolution current is increased to a certain degree, the probability of fracture by tensile stress will exceed that by shear stress, and the brittle fracture will occur. The proposed SCC mechanism can riot only explain the-propagation of SCC cracks but can explain the crack initiation as well. The strain on the surface distributes unevenly when a smooth specimen is deformed, so does the anodic current distribution. The crack will initiate at a point where the anodic current density is large enough to cause the material at a specific point to fracture in brittle manner.     

SHORT CRACK PROPAGATION AND CLOSURE EFFECTS IN A508 STEEL

Abstract— Fatigue crack growth measurements are usually made on standard specimens containing long cracks (～10 mm) although in most practical situations, a large part of the fatigue life is spent with much shorter dimensions. The purpose of the present study is a comparison of crack growth behaviour for long cracks (～13–16 mm) in CT specimens and smaller ones (～0.3–0.5 mm) in four point bend specimens. Large effects are noticed indicating that, at a given stress intensity factor amplitude, the crack growth rate is significantly higher in specimens with short cracks. Mouth displacement measurements for both specimen configurations show that the crack closure phenomenon accounts for the observed effect. Crack closure is likely to be associated with fracture surface roughness as shown by partly machining the material left behind the crack tip in CT specimens.     

Statistical analysis and reliability prediction with short fatigue crack data

This paper proposes a probability model to describe the growth of short fatigue cracks. The model defines the length of each crack in a specimen as a random quantity, which is a function of randomly varying local properties of the material microstructure. Once the model has been described, the paper addresses two questions: first, statistical inference, i.e. the fitting of the model parameters to data on crack lengths; and secondly, predicting the future behaviour of observed cracks or cracks in a new specimen. By defining failure of a specimen to be the time at which the largest crack exceeds a certain length, the solution to the prediction problem can be used to calculate a probability that the specimen has failed at any future time. The probability model for crack lengths is called a population model, and the statistical inference uses the ideas of Bayesian statistics. Both these concepts are described. With a population model, the solution to statistical inference and prediction requires quite complicated Monte Carlo simulation techniques, which are also described.     

Investigation on the Static Fatigue Mechanism and Effect of Specimen Thickness on the Static Fatigue Lifetime in WC–Co Cemented Carbides

The static fatigue mechanism and effect of specimen thickness on static fatigue lifetime for four WC–Co cemented carbides were studied with different binder contents and carbide grain sizes. Static fatigue tests under three-point bend loading were conducted on different sized specimens. The fracture surfaces of rupture specimens were examined by scanning electron microscopy to investigate the static fatigue micromechanisms. Experimental results show that microcracks nucleate from defects or inhomogeneities and the connection of microcracks produces a main crack. The main crack propagates rapidly, resulting in the fracture of specimens. The extension of static fatigue lifetime with the increase of specimen thickness is due to the decrease of plastic zone size near the crack tip and relevant energy change during the crack growth. The effect of specimen thickness on static fatigue lifetime is much greater for cemented carbides with larger WC grain size or higher cobalt content, which is attributed to operative toughening mechanisms.     

13SiMnNiCrMoV钢切口疲劳裂纹萌生门槛值

本文研究在13SiMnNiCrMoV 结构钢中用尖裂纹的应力强度因子来反映三点弯曲缺口试样的疲劳裂纹萌生规律。当 R=0.1,f=100Hz,试样尺寸 B×W×L=12.5×25×117mm 时,缺口名义应力幅的门槛值为Δσ_(th)=3315ρ~(0.352) MPa,0.5mm≤ρ≤5mmΔK_(th)=250ρ~(0.352) MPam~(1/2)门槛值与ρ有关。同时得到缺口裂纹萌生的循环次数 N_i 与名义应力幅Δσ、缺口曲率半径ρ的定量关系是N_i=3.98×10~(22)ρ~(1.62)/Δσ~(4.85),N_i≤10~(5.5)并讨论了(ΔK_1/ρ~(1/2))_(th)与ρ无关的结论。