CCT Specimens Research Articles

A Study to Improve the Measurement Accuracy of .DELTA.K by the Infrared Method

Stress intensity factor ranges for CT and CCT specimens evaluated by infrared method in the previous studies were almost lower than analytical values. In addition, the difference between measurement results and numerical values increased in proportion to those values not to concern with the stress ratio. In this study, the effect of heat conduction in a body of CCT specimens under cyclic loading was conducted by a finite differential analysis in order to examine the source of the discrepancy between measurements and numerical values. As a result, the error was caused that locations of crack tips were misread due to heat conduction and plastic deformation near crack tips. Thus the method specifying a crack tip from a measurement result has been developed. The stress intensity factors evaluated by using accurate locations of crack tips coincided with numerical values within 7%.

変位制御弾塑性疲労条件下のき裂構造の破壊力学パラメータの推定

Quantitative prediction of crack growth under displacement-controlled conditions such as thermal fatigue is a key to the residual life prediction of plant components. In a previous paper, the authors proposed a simplified prediction method of fracture mechanics parameters such as J and C* of a perforated plate under thermal fatigue, on the basis of the reference stress approach under displacement-controlled conditions. In this paper, the fracture mechanics parameters of a CCT specimen and structural models of CrMoV cast steel under displacement-controlled conditions were experimentally and numerically examined on the basis of the proposed method. The ratio of the inelastic and the elastic crack opening displacement, as well as the ratio of the inelastic and the elastic load point displacement, was used to correlate the fracture mechanics parameters in the inelastic and elastic regions. The proposed method based on displacements was found to be insensitive to a small variation in the predicted macroscopic load in comparison with the original reference stress method, and is considered to be applicable to displacement-controlled conditions such as thermal fatigue.

Separable functions in load separation for the ηpland ηplCMODplastic factors estimation

The objective of this paper is to develop the load separation method for evaluating the ηpl and ηplCMOD plastic factors used in the J estimation approach based on load versus displacement records. Appropriate forms for the geometry and deformation functions have been suggested from the EPRI Handbook solutions to produce the separable form for the load. The obtained functions are applied to evaluate the ηpl and ηplCMOD plastic factors for center cracked tension specimen. The present load separation method gave results which are somewhat different from the estimated values of ηpl given in the literature. For shallow cracks, the ηpl and ηCMODpl plastic factors show considerable variation with crack size and the strain hardening exponent. For a deeply cracked CCT specimen, the ηCMODpl factor tends to the ηpl factor and equals approximately unity.

126 特異な異方性を有する純アルミニウム圧延板における疲労き裂進展経路に及ぼす応力集中の影響

Fatigue crack of pure aluminum plates with unique anisotropy propagated to rolling direction the made 30°to loading direction. The crack propagated as a mixed mode I + II crack. The effect of stress concentrations to fatigue crack were observed by conducting fatigue test on CCT specimens. The stress intensity factor (SIF) of the crack was analyzed by Finite Element Method (FEM) using the displacement extrapolation method. It is confirmed that even the stress concentrations exist and increase the SIF on the crack tip, if the SIF is still in the range of the SIF range of the crack that propagates to rolling direction (RD), the fatigue crack maintains to propagate to rolling direction. In case of specimen with rapid change of stress distributions, the SIF range of the crack that propagates to RD on specimens with stress concentrations is the same as that of specimens with no holes.

709 特異な異方性を有する純アルミニウム板における疲労き裂進展経路に及ぼす板厚の影響

Fatigue crack of pure aluminum plates with unique anisotropy propagated to rolling direction that made 30° to loading direction. The crack propagated as a mixed mode I+II crack. Effects of plate thickness to fatigue crack were observed by conducting fatigue test on CCT specimens with thickness of 0.8mm, 1.5mm and 2.5mm. The stress intensity factor of the crack was analyzed with Finite Element Method (FEM) using the displacement extrapolation method. As the result, the crack starts to grow to rolling direction as △K_<*>=5&acd;8MPa・m^<1/2>. It is also confirmed that the thicker plates cause the smaller monotonic plastic zone size r_p on the crack tip. It leads to near plane-strain condition on the crack tip and the crack grows easier to rolling direction.

205 純アルミニウム幅広板における疲労き裂進展経路に及ぼす特異な異方性挙動の FEM シミュレーション

In this study, the phenomenon of anisotropy affected fatigue crack growth path which propagated to rolling direction as mixed mode I+II crack was simulated with Finite Element Method (FEM) using displacement extrapolation method. Based on this FEM simulation, the crack propagates to rolling direction when total stress intensity factor ΔK_<total>&ge;3.9 and stress ratio between yield stress and the load stress R' is between 2.0 and 3.0. When mode II stress intensity factor ΔK_<II> of the crack that propagates to rolling direction has ΔK_<II>&ge;8.4,the crack does not continue to propagate to rolling direction but to the mode I direction. This simulation can also predict the fatigue crack propagation path near stress concentrators on wide CCT specimens.

Finite element simulation of metal forming and in-plane crack propagation using ductile continuum damage model

The continuum damage model for ductile damage and ductile fracture is applied to metal forming and crack propagation by finite element method. The highly nonlinear equilibrium equation is formulated in order to include geometric, material nonlinearities and frictional contact condition. The effect of friction on the damage concentration is shown in the upsetting process. Then it is verified that the ductile fracture using this damage model is reasonable by the comparison with the experimental result in CCT specimen. The influence of the hole at the crack tip is shown through the numerical simulations of edge-cracked plates with different hole size. Finally, the strain energy release rate in this damage model is compared with J-integral using ABAQUS to relate the result of damage analysis to the concept of fracture mechanics.

Endofem Integrated Methodology for Fatigue Crack Growth

AbstractIn this paper, the FEM with the incremental endochronic cyclic plasticity (EndoFEM) and the rccontrolled node-released strategy are employed to study the fatigue crack opened/closed load (Pop) of Al 2024-T3 CCT specimens provided by Mageed and Pandey under several crack lengths and the constant amplitude with various load ratio (R). After statisfactory results are achieved by comparisons of computed Popvalues and cited experimental data, the simulations will be extended to the crack lengths with significant bending effect due to short ligaments or high peak (Pmax) or high positive or very low negative R cyclic loads. Through these simulations, the complete map of Pop/Pmaxvs. Kmaxand R can be constructed and thereafter its correspondant empirical formulae can be proposed. Using these formulae and selecting the traditional fatigue crack growth parameter ΔKeff, the Al 2024-T3 fatigue crack growth rate da/dN vs. ΔK and R data, provided by Hiroshi and Schijve, can be employed to proposed empirical formulae of da/dN vs. ΔKeffand R. After integration, fatigue-crack-growth length a vs. N curves computed by EndoFEM can be obtained. The results are agreed very well with the existing experimental curves.According to the above procedures of simulation and steps of comparions with experiment, this paper may provides an integrate methodology of numerical simulation in the studies of fatigue crack growth for academic and industrial researches and design analysis.

A phenomenological model of the elastic–plastic CCT specimen containing a growing crack

A simple phenomenological model of the central crack tension elastic–plastic specimen containing a growing crack is presented. The aim of the paper is to provide a tool to visualize the influence of the basic geometrical and material parameters on the shape of the force–displacement curves observed during standard experiments performed in order to measure fracture parameters and fracture resistance curves (e.g. J R curves). In the model the classical as well as modified Dugdale models have been utilized. The analysis, although qualitative, provides information on the fracture processes themselves and may be a helpful tool in designing an experimental program.

Fracture behavior of stitched warp-knit fabric composites

Pilot studies are conducted to characterize the macroscopic fracture resistance behavior using linear elastic fracture mechanics and attempt to quantify the fracture parameters in which may govern the fracture and failure patterns of stitched warp-knit fabric composites. Methods based on the J-integral method and Betti's reciprocal theorem in extracting the fracture parameters, critical stress intensity factors, T-stress, and the second term of σy(r,0) near the crack tip prior to fracture initiation are formulated. Two fracture criteria, [σc,rc] and [ec,rc] are attempted to characterize the failure initiation for the fiber-dominated failure mode and self-similar crack extension in a given thickness of the laminate. Based on linear elastic fracture mechanics principle, these criteria are transformed into crack-driving forces [KQ,T] and [KQ,g32]. The two-parameter fracture criteria, [KQ,T] and [KQ,g32] provide a good correlation for the CCT and SENT specimens, but not for the high constraint CT specimens. With the limited experimental data, the results tend to show that the large tensile T-stress and large magnitude of negative g32 may inhibit the crack extension in the same crack plane and promote crack kinking.

EndoFEM Crack Closure Analysis of AL2024-T3 CCT Specimen Under All Tension Fatigue Loading

ABSTRACTThe endochronic cyclic plasticity with finite element analysis (EndoFEM) is employed to simulate plasticity-induced crack closure phenomenon of Al 2024-T3 CCT specimens under maximum cyclic stress of 80MPa and 0.1 stress ratio (R). Various fatigue crack lengths are generated by a rc dominated-node-released strategy. The suitability of element-mesh planning around crack tip is supported by the real simulations in the decreasing tendencies of crack opening load (Pop) with increased distance behind the crack tip, and the enough elements to reflect the reversed plastic responses at minimum load.EndoFEM results of vertical stress ahead of the crack tip show a typical distribution of small scale yield (SSY) in the realm of fracture mechanics; and Pop/Pmax ratio determined at 1mm behind crack tip is kept constant i.e. Kmax-independent. In these cases, fatigue parameters based on either the far field loading parameter ΔK, the effective ΔK (ΔKeff) with crack closure effect, or the mechanical responses ahead of crack tip (e.g. stress parameter, reversed (plastic) strain at 1mm) are all equivalent and are linearly correlated with the stage II fatigue crack growth (FCP) rate. However, for longer crack length with the ligament bending effect or shorter crack length with the starter notch effect, the Pop/Pmax ratio decreases and changes the SSY stress distribution. This result reduces the usefulness of the above fatigue parameters. As a consequence, a nonlinear correlation of FCP rates with ΔK or ΔKeff are purely empirical. The Kmax-dependent ΔKeff must be considered in the correlation as suggested by the present study of EndoFEM.

Evaluation of Creep-Fatigue Crack Propagation of Sn-37 Pb Solder.

The fatigue life estimation of micro solder joints is one of the most critical technologies for the reliable IC packages. In recent years, it is considered that the development of estimation methods for the crack propagation based on the fracture mechanics approach is important to the life prediction. In this study, the crack propagation behavior of Sn-37 Pb solder was investigated. Fatigue tests using CT specimens were carried out under 0.1 Hz, 0.01 Hz and 0.001 Hz. As a result, the crack propagation rate was correlated well with the fatigue J-integral range independently of the frequency. On the other hand, the fracture surfaces for all conditions were intergranular creep types. The creep-fatigue tests under stress waveforms with tensile hold (cp-type) and with tensile and compressive hold (cc-type) were carried out at room temperature using CCT specimens. The relationship between the crack propagation rate and the creep J-integral range was obtained. The crack propagation rate under the cc-type condition was lower than the one under the cp-type condition for the same value of creep J-integral range.

The fracture behaviour of mismatched centre-cracked welded specimens in tension

The unloading compliance technique has been developed to measure the crack growth fracture resistance (J-Δa) of a material using the centre-cracked tensile specimen. This paper describes experiments performed to measure the J-Δa behaviour of mismatched weld specimens in tension. The mismatched specimens were manufactured from two steel plates by electron beam welding one plate between the other and vice-versa. The mismatched J-Δa data are compared with the results obtained from the individual plates. It is shown that the use of the Hornet et al. [7, P. Hornet, C. Eripret and S. Hao, Experimental J estimation from a load-cmod curve for mismatched SENB and CCT specimens, Second International Symposium on Mismatching of Welds, GKSS Research Centre, Geesthacht, Germany, 1996, 24–26 April] η-factors for the mismatched J-Δa data give excellent agreement with the J-Δa data for the individual plates.

Approximate Solutions for KI and COD in CCT and CT Specimens Subjected to Closure Obstruction on the Crack Surface

Approximate analytical solutions for stress intensity factors (SIF) and crack surface opening displacements (COD) for a crack in CT and CCT specimens subjected to crack face forces have been obtained. These solutions account for the finite dimension of the specimens. The analytical geometric constant, which was derived by using existing analytical expressions, is checked by the finite element method. Both results appeared to be in good agreement within 5%. The results for geometric constant including a crack length and locations of internal stresses show that there are severe differences in solutions between for an infinite medium and for a finite size of specimens. Therefore, it is concluded that the effect of finite dimension on solutions such as SIF or COD must be considered in problems having internal stresses on the crack surfaces.

Bridging stress distribution in center-cracked fiber reinforced metal laminates: modeling and experiment

A theoretical model for the distribution of the bridging stress in center-cracked fiber reinforced metal laminates (FRMLs) was developed based upon fracture mechanics analysis, and a test method presented. The model includes the effect of the delamination shape and size, the saw-cut size and the shear deformation of the adhesive. Moiré technique was employed for measuring the crack opening profiles in the test method. The bridging stresses in CCT specimens of 2/1 GLARE were tested. The results of the bridging stress calculated by the present model were compared with test results, and good agreement was achieved. Based on the present model, the factors affecting the distribution of the bridging stress in FRMLs were analyzed. Delamination shape and size, and the saw-cut size were identified as the main factors.

疲労 回転曲げ疲労破面のＸ線フラクトグラフィ （第２報） 疲労破面の残留主応力とき裂進展方向

X-ray fractography is a technique for analyzing the cause of fractures through the information obtained by irradiating X-ray on the fractured surface. The residual stresses or full widths at half maximums are usually used as the information. This technique is a useful tool for fractrure analysis, since the quantitative loading condition etc. can be estimated. X-ray fractography is used in various countries alongside the electron-microscope fractography. In the previous paper, X-ray fractography has been applied to actual size four “Shinkansen (bullet train)” axles tested at the railway Technology Research Institute. The axles are about 200mm in diameters, induction hardened 0.38% carbon steel with semi-elliptical artificial flaw. X-ray stress measurements were carried out on the fractured surface along the line from the bottom of the artificial flaws to the axle center at intervals of 5mm. All the results showed that the residual stress on the fractured surface were tensile at the initial crack propagation region, increased to tensile maximums, decreased into compression reaching at the compressive maximums then went up toward zero stress near the final fractured surface.This paper describes the procedure estimating the crack propagation direction through rosette analyses of residual stresses. A CCT specimen, which was tested under similar stress condition as test axles, was analyzed and found out that crack propagation directions are coincide with the directions of residual principal stresses. This relationship was utilized in rosette analyses on fractured surface of a test axle, and crack propagation lines were estimated and also the crack closure behavior was discussed.

MODELLING THE INFLUENCE OF STRAIN HARDENING AND PLASTIC CONSTRAINT ON CRACK CLOSURE OF ARBITRARILY THICK CCT‐SPECIMENS

The triaxial stress constraint and the effective yield stress distribution in the plastic zone for strain hardening materials are studied, and then a modified strip‐yield model is proposed to investigate the thickness effect of CCT specimens. Consequently, a plastic constraint factor α is defined and analysed in detail. The results show that the factor α can comprehensively account for the influence of thickness, crack length, loading level and hardening exponent. A simple expression for the plastic zone length and a fitting expression involving α are obtained. Application of the modified strip model to Newman’s crack closure model, and comparison with FEM results, show that the model can account for the influence of thickness on crack closure.

A THEORETICAL MODEL FOR PREDICTING FATIGUE CRACK GROWTH RATES IN FIBRE‐REINFORCED METAL LAMINATES

This paper is concerned with the development and application of an analytical model for predicting fatigue crack growth in fibre‐reinforced metal laminates (FRMLs). An analytical model for the distribution of bridging traction is first introduced. Based upon observations of the delamination shapes in FRMLs under fatigue loading and a model for characterizing delamination growth in FRMLs, a model for predicting crack growth rates in CCT specimens of FRMLs is developed. The model is applied to two GLARE laminates (2/1, 3/2 lay‐ups) under various cyclic stress levels and stress ratios. The predicted crack growth rates are compared with experimental data. The predicted crack growth rates agree well with the experimental results.

EndoFEM Node-Released Strategy in the Simulations of Fatigue Crack Closure Phenomena

AbstractApplications of the EndoFEM with node-released methods had been used successfully to simulate the plastic wakes left behind the advancing fatigue crack. In this paper, employing the plastic zone size estimated by LEFM as a guideline, four strategies with various plans of node-released rates and two plans of finite element discretization near crack tip, are proposed to generate various fatigue cracked lengths of A12024-T3 CCT specimen under all tensile-cyclic loading. Evaluations based on the mechanical responses near crack tip and the crack opened/closure behaviors, it can be concluded that the EndoFEM with the rc dominant node-released strategy can lead to not only economical but also reliable results.

Constraint Effect at the Crack Tip. 2nd Report, Constraint Effect of High Toughness Material.

The effect of the specimen thickness and the crack length on the fracture toughness are investigated for three point bend (3PB) specimen and CCT specimen. In 3PB specimen the JICap value increases with decreasing the crack length and the clear thickness effect dose not exist for fracture toughness value. The three dimensional finite element analysis are conducted for these specimens. The Q factor decreases with decreasing the crack length or the specimen thickness in 3PB specimen. The Q factor of CCT specimen is lower than that of 3PB specimen. The relation between the Q factor and JICap value is examined. The JICap value increases with decreasing the Q factor when the crack length decreases in 3PB specimen. The dimple fracture surfaces of 3PB, CCT and CCB (center cracked bend) specimens are observed by SEM. The dimple diameter of CCB specimen is the smallest and the diameter of CCT specimen is smaller than that of 3PB specimen.