A test specimen with constant stress intensity factor for prescribed displacement

A test specimen has been developed that gives a constant value of the stress intensity factor in mode I under fixed displacement loading conditions. The test specimen is a double contoured cantilever beam specimen whose shape is derived from engineering beam theory. A final shape for a range of crack extensions where stress intensity is constant was established using a finite element analysis. It is believed that this specimen could be useful for many applications where a constant stress intensity factor is needed over a range of crack extension for constant displacement loading e.g. viscoelastic crack growth in an adhesive layer or stress corrosion cracking.     

The evolution of the stress–strain fields near a fatigue crack tip and plasticity-induced crack closure revisited

The evolution of the stress–strain fields near a stationary crack tip under cyclic loading at selected R‐ratios has been studied in a detailed elastic–plastic finite element analysis. The material behaviour was described by a full constitutive model of cyclic plasticity with both kinematic and isotropic hardening variables. Whilst the stress/strain range remains mostly constant during the cyclic loading and scales with the external load range, progressive accumulation of tensile strain occurs, particularly at high R‐ratios. These results may be of significance for the characterization of crack growth, particularly near the fatigue threshold. Elastic–plastic finite element simulations of advancing fatigue cracks were carried out under plane‐stress, plane‐strain and generalized plane‐strain conditions in a compact tension specimen. Physical contact of the crack flanks was observed in plane stress but not in the plane‐strain and generalized plane‐strain conditions. The lack of crack closure in plane strain was found to be independent of the material studied. Significant crack closure was observed under plane‐stress conditions, where a displacement method was used to obtain the actual stress intensity variation during a loading cycle in the presence of crack closure. The results reveal no direct correlation between the attenuation in the stress intensity factor range estimated by the conventional compliance method and that determined by the displacement method. This finding seems to cast some doubts on the validity of the current practice in crack‐closure measurement, and indeed on the role of plasticity‐induced crack closure in the reduction of the applied stress intensity factor range.     

Weld residual stress effects on fatigue crack growth behaviour of aluminium alloy 2024-T351

The interaction between residual stress and fatigue crack growth rate has been investigated in middle tension and compact tension specimens machined from a variable polarity plasma arc welded aluminium alloy 2024-T351 plate. The specimens were tested at three levels of applied constant stress intensity factor range. Crack closure was continuously monitored using an eddy current transducer and the residual stresses were measured with neutron diffraction. The effect of the residual stresses on the fatigue crack behaviour was modelled for both specimen geometries using two approaches: a crack closure approach where the effective stress intensity factor was computed; and a residual stress approach where the effect of the residual stresses on the stress ratio was considered. Good correlation between the experimental results and the predictions were found for the effective stress intensity factor approach at a high stress intensity factor range whereas the residual stress approach yielded good predictions at low and moderate stress intensity factor ranges. In particular, the residual stresses accelerated the fatigue crack growth rate in the middle tension specimen whereas they decelerated the growth rate in the compact tension sample, demonstrating the importance of accurately evaluating the residual stresses in welded specimens which will be used to produce damage tolerance design data.     

Effect of loadline shift on applied crack tip stress intensity in WOL specimens

A change in applied stress intensity due to shifting of load line from the pin hole to a wedge located on the outside edge of the notch has been investigated by: (1) finite element analysis, (2) measurements of front face crack opening displacement and (3) strain relaxation near the crack tip.

Results show that this wedge loading procedure will result in a significant drop, up to a factor of two, in applied stress intensity. The drop in stress intensity is inversely related to the crack length (expressed by a/W). This drop in stress intensity is due to overall specimen distortion because of load line shift and local deformation of the wedge and notch surfaces. Implications of this drop on Stress Corrosion Cracking results are discussed. For reliable stress corrosion testing, modifications in specimen geometries and loading procedures are suggested.     

数字图像相关法测量聚碳酸酯板应力强度因子

本文以数字图像相关方法测量了聚碳酸酯板的张开型应力强度因子（SIF）。实验过程中以聚碳酸酯标准紧凑拉伸式样为样本,由数字图像相关（DIC）方法提取不同载荷下裂纹附近的全场位移。在已计算得到全场位移的情况下,由线弹性断裂理论可知,弹性区域内每一点位移可表示为SIF的函数。在计算SIF时考虑了实验中不可避免存在的刚体平移与转动的影响,应力强度因子、刚体平移与转动可由最小二乘法计算得到;还讨论了位移场的选择及位移展开项项数对SIF的影响。实验结果与理论值进行了比较,结果显示DIC方法准确地测量了聚碳酸酯板的应力强度因子,因此DIC为测量SIF提供了一种有效的试验方法。     

Prediction of fatigue crack growth in notched members under variable amplitude loading histories

A technique for estimating fatigue crack propagation in notched plates subjected to variable amplitude loading is outlined in this paper. An elastic-plastic finite element model is used to determine the effect of notch geometry and the residual plastic deformations. The analytic model for crack growth is based on an effective stress intensity concept. All of the calculations are based on constant amplitude materials data. Results of this procedure are compared to tests on a modified compact tension specimen. The program consisted of predicted propagation lives for forty-five (45) tests on two structural steels, three load histories and, at least, three maximum load levels.     

Improved test method for very low fatigue‐crack‐growth‐rate data

Currently, in North America, the threshold crack‐growth regime is experimentally defined by using ASTM Standard E647, which has been shown in many cases to exhibit anomalies due to the load‐reduction (LR) test method. The test method has been shown to induce remote closure, which prematurely slows down crack growth and produces an abnormally high threshold. In this paper, the fatigue‐crack growth rate properties in the threshold and near‐threshold regimes for a titanium alloy, Ti‐6Al‐4V (STOA), are determined by using the LR test method and an improved test method. The improved method uses ‘compression–compression’ precracking, as developed by Pippan, Topper and others, to provide fatigue‐crack‐growth rate data under constant‐amplitude loading in the near‐threshold regime, without load‐history effects. Tests were conducted over a wide range in stress ratios (R = 0.1–0.7) on compact C(T) specimens for three different widths (25, 51 and 76 mm). The slitting method was used on 51 mm C(T) specimens to confirm that the material did not contain significant levels of residual stresses from forming and/or machining. A crack‐mouth‐opening‐displacement gage was used to monitor crack growth. Data from the ASTM LR method gave near‐threshold values that were found to be dependent upon the specimen width. However, data from the compression precracking constant amplitude (CPCA) loading method gave near‐threshold data independent of specimen width. A crack‐closure analysis was performed for both the LR and CPCA data, to correlate data at the various stress ratios. The CPCA data correlated well with the effective stress‐intensity factor range against rate relation, whereas the LR data exhibited significant threshold fanning with both stress ratio and specimen width.     

Intralaminar toughness characterisation of unbalanced hybrid plain weave laminates

A numerical and experimental investigation on the mode-I intralaminar toughness of a hybrid plain weave composite laminate manufactured using resin infusion under flexible tooling (RIFT) process is presented in this paper. The pre-cracked geometries consisted of overheight compact tension (OCT), double edge notch (DEN) and centrally cracked four-point-bending (4PBT) test specimens. The position as well as the strain field ahead of the crack tip during the loading stage was determined using a digital speckle photogrammetry system. The limitation on the applicability of the standard data reduction schemes for the determination of intralaminar toughness of composite materials is presented and discussed. A methodology based on the numerical evaluation of the strain energy release rate using the J-integral method is proposed to derive new geometric correction functions for the determination of the stress intensity factor for composites. The method accounts for material anisotropy and finite specimen dimension effects regardless of the geometry. The approach has been validated for alternative non-standard specimen geometries. A comparison between different methods currently available for computing the intralaminar fracture toughness in composite laminates is presented and a good agreement between numerical and experimental results using the proposed methodology was obtained.     

EFFECT OF DISPLACEMENT RATES ON EAC OF AISI 4340 STEEL

The environmentally assisted cracking (EAC) of AISI 4340 steel in synthetic ocean water was investigated using the rising displacement test method. The stress intensity factor for crack initiation, K_init , in precracked compact tension specimens, was observed to increase with the displacement rates. However, a critical displacement rate existed which was associated with the K_IEAC of the steel in the environment. Here, K_IEAC is the threshold value of the stress intensity factor below which no EAC is expected. Constant load and constant deflection tests resulted in similar K_IEAC values. The method pursued in this investigation for the determination of the initial displacement rate needed to obtain a valid K_IEAC was found to be quite effective for the rapid and satisfactory evaluation of K_IEAC , requiring a minimum number of tests.     

Finite element modeling of plasticity-induced crack closure with emphasis on geometry and mesh refinement effects

Two-dimensional, elastic-perfectly plastic finite element analyses of middle-crack tension (MT) and compact tension (CT) geometries were conducted to study fatigue crack closure and to calculate the crack-opening values under plane-strain and plane-stress conditions. The behaviors of the CT and MT geometries were compared. The loading was selected to give the same maximum stress intensity factor in both geometries, and thus approximately similar initial forward plastic zone sizes. Mesh refinement studies were performed on both geometries with various element types. For the CT geometry, negligible crack-opening loads under plane-strain conditions were observed. In contrast, for the MT specimen, the plane-strain crack-opening stresses were found to be significantly larger. This difference was shown to be a consequence of in-plane constraint. Under plane-stress conditions, it was found that the in-plane constraint has negligible effect, such that the opening values are approximately the same for both the CT and MT specimens.     

Fracture mode identification of low alloy steels and cast irons by electron back-scattered diffraction misorientation analysis

The fracture modes of low alloy steels and cast irons under tensile and fatigue conditions were identified by electron back-scattered diffraction(EBSD) misorientation analysis in this research. The curves of grain reference orientation deviation(GROD) distribution perpendicular to the fracture surface were obtained by EBSD observation, and the characteristics of each fracture mode were identified. The GROD value of the specimen fractured in tension decreases to a constant related to the elongation of corresponding specimen in the far field(farther than 5 mm away from the fracture surface). The peak exhibits in GROD curves of two smooth specimens and a notched specimen near the fracture surface(within 5 mm away from the fracture surface), and the formation mechanisms were discussed in detail based on the influences of specimen geometries(smooth or notched) and material toughness. The GROD value of fatigue fractured specimen is close to that at undeformed condition in the whole field, except the small area near the crack path. The loading conditions(constant stress amplitude loading or constant stress intensity factor range K loading) and the EBSD striation formation during fatigue crack propagation were also studied by EBSD observation parallel to the crack path.     

Transferability of Charpy Absorbed Energy to Fracture Toughness Based on Weibull Stress Criterion

The relationship between Charpy absorbed energy and the fracture toughness by means of the (crack tip opening displacement (CTOD)) method was analyzed based on the Weibull stress criterion. The Charpy absorbed energy and the fracture toughness were measured for the SN490B steel under the ductile-brittle transition temperature region. For the instrumented Charpy impact test, the curves between the loading point displacement and the load against time were recorded. The critical Weibull stress was taken as a fracture controlled parameter, and it could not be affected by the specimen configuration and the loading pattern based on the local approach. The parameters controlled brittle fracture are obtained from the Charpy absorbed energy results, then the fracture toughness for the compact tension (CT) specimen is predicted. It is found that the results predicted are in good agreement with the experimental. The fracture toughness could be evaluated by the Charpy absorbed energy, because the local approach give     

RATE-DEPENDENT DEFORMATION AND FRACTURE OF α-TITANIUM

Aspects of combined rate-dependent deformation and crack growth in α-titanium at room temperature are examined. Results are presented for tests carried out on pre-cracked three point loaded single edge notch bend and compact tension specimens subjected to constant crack opening displacement rates and constant load. Curves of the ratio of the reference stress to the yield stress as a function of the ratio of the plastic displacement to specimen width are found to be different for different rates. The stress difference between continuously loaded curves and curves obtained from load relaxation tests (“relaxed” curves) is found to be similar to uniaxial results. Earlier uniaxial tests show that the “relaxed” curve represents a boundary below which no further creep takes place. The pre-cracked specimen constant load curves cross the “relaxed” curve, even though the contribution from crack growth to the overall deformation is found to be small. Sustained load crack growth is observed to take place under contained yielding conditions and the sustained load resistance curves are found to be different for different reference stresses.     

Fatigue crack retardation and closure in polymethylmethacrylate

The presented results are from an investigation of crack surface profiles and the influence of intermittent overloads on fatigue crack growth in polymethylmethacrylate, a transparent polymer. Fatigue cracks were grown in compact tension specimens under conditions of constant range in stress intensity factor. Tensile overloads were found to perturb subsequent crack growth in polymethylmethacrylate under certain conditions.

Examination of monochromatic light interference fringe patterns emanating from the fatigue cracks indicates that the crack perimeter was closed at zero load. The crack surfaces were displaced, however, in the interior of the specimen at zero load. Measurements of the crack opening displacements during loading revealed that a significant tensile load was required to displace the portions of the crack surfaces which Were initially closed. These observations are discussed in light of the Elber concept of crack closure.     

Energy release rate calculations for the compact tension specimen using brittle orthotropic materials

An energy release rate calculation is performed using the modified crack closure integral (MCCI) method applied to the compact tension (CT) specimen. Mechanical properties used are typical of short-fiber sheet molding compound (SMC) materials. Using orthotropic linear constant strain finite elements, the classical solution is closely approximated with a relatively coarse grid. The wedge opening of the CT specimen is shown to lower the expected energy release rate by 6·1%, introducing a systematic error. Orientation of the SMC material near the load application point perpendicular to the applied load will raise the energy release rate by 12·0%. The CT specimen results are shown to be insensitive to the distribution of the applied load around the hole periphery. A probabilistic method is developed for converting the distribution of applied failure load to the distribution of critical energy release rate. This method is applied to predict the distribution of failure load for other geometries.     

FE analysis of stresses and stress intensity factors of interfacial cracks in a CTS specimen

A plane stress finite element analysis was implemented to understand the stress fields for a crack lying at an aluminium/epoxy interface of a compact tension and shear specimen. The interaction integral method was used to separate the mixed-mode stress intensity factors at the interfacial crack-tip under different loading modes, which can have important implications for characterisation of interfacial crack growth.     

Numerical simulation of stress-strain state near crack tip in a compact tensile specimen

A computational scheme has been developed and a numerical simulation of the stress-strain state near the crack tip is performed at different levels of the stress intensity factor using a compact tensile specimen as an example. The authors analyze the influence of the finite element size near the crack tip and compare the results obtained in different codes (software packages) for different crack geometries. __________ Translated from Problemy Prochnosti, No. 1, pp. 134–140, January–February, 2009.     

Measuring residual stress and the resulting stress intensity factor in compact tension specimens

The measurement of residual stress through the remaining ligament of a compact tension specimen was studied. In the crack compliance method, a slot or notch is successively extended through the part, and the resulting strain is measured at an appropriate location. By using a finite element simulation of a specimen preloaded beyond yield, three techniques for determining the original residual stress from the measured strains were compared for accuracy and sensitivity to measurement errors. A common beam-bending approximation was substantially inaccurate. The series expansion method proved to be very versatile and accurate. The fracture mechanics approach could determine the stress intensity factor caused by the residual stresses with a very simple calculation. This approach offers the exciting possibility of determining the stress intensity factor prior to a fatigue or fracture test by measuring strains during the specimen preparation.     

Complex fracture parameters for an interface crack between twohardening materials: a photoelastic study

In this paper, complex stress intensity factors (SIFs) at an interface crack are determined for a range of applied loads, crack lengths and remote mode mixes using automated photoelasticity. The specimen geometries comprise epoxy resin and aluminium alloy halves bonded together, and are loaded in either compact tension in mixed‐mode conditions or in three‐point bend under mode I conditions. In the experiments, full‐field isochromatic data were obtained from the epoxy half using an established phase‐stepping technique. A reworked approach to the determination of the SIFs was developed by combining a least‐squares over‐deterministic method for fitting crack‐tip stress equations to the data and a weighting factor that ensures that only data in the singularity zone are used. For comparison, some of the specimens were tested using a linear‐elastic finite element (FE) analysis and/or by experiment using homogeneous test specimens. Excellent agreement between the experimental and numerical SIF moduli was achieved for remote mode I loadings. However, for good agreement to be made between the phase angle results requires an additional phase term to be added to the FE solution at each load to account for the development of a crack‐tip plastic zone. Further, results for the SIFs from remote mixed‐mode loadings of the compact tension specimen only have a meaningful interpretation in light of small‐scale yielding conditions. It is shown, qualitatively, that the experiments verify some of the predictions made in the literature of asymptotic behaviour at interface crack tips from results of elasto‐plastic FE analyses.     

Correlation of fatigue crack propagation in polyethylene pipe specimens of different geometries

Correlation in mechanisms and kinetics of step-wise fatigue crack propagation in polyethylene pipe specimens of different geometries is studied experimentally. It is shown that crack propagation in a non-standard specimen cut from a real pipe and conserving the pipe geometry can be effectively simulated using a standard compact tension specimen. Good correlation in both kinetics of step-wise crack propagation and fractography between the specimens is achieved if experimental conditions are chosen to assure equal values of (a) stress intensity factor and (b) stress intensity factor gradient at the initial notch tips. These results extend previous technique of fatigue accelerating slow crack growth used to predict lifetime of polyethylene pipes. This revised version was published online in August 2006 with corrections to the Cover Date.