CCT Specimens Research Articles

Relation of ηpl and γpl with separation parameter (S) and their usefulness for fracture toughness evaluation

Geometrical factor ηpl and γpl are required for fracture toughness evaluation in terms of JIC, JQ and J-R curve. Load separation method is said to be most accurate method to evaluate the ηpl. In this method, established relation between ηpl and separation parameter (S) as well as fitted function between S and b/W is used to obtain the relation between ηpl and b/W. In this paper, relations of ηpl and γpl with the S are derived. Based on the fact that the value of γpl cannot be negative, limit of exponent of power law function between S and b/W as well as second order derivative of polynomial functions between S and b/W are evaluated. Limitations of power law function and usefulness of polynomial functions are highlighted. Usefulness of the relationships are discussed for CCT and clamped SENT specimens. The problem with Ernst type equation to calculate Jpl for growing crack are also discussed for CCT.

Finite element analyses of crack extensions in curved compact tension specimens of irradiated Zr-2.5Nb pressure tube materials by nodal release method and cohesive zone modeling approach

Crack extensions in thin CCT specimens of irradiated and hydrided irradiated Zr-2.5Nb pressure tube materials are simulated using the nodal release method and cohesive zone modeling (CZM) approach. The load vs displacement curves from the 3-D FE analyses with consideration of plastic orthotropy using the nodal release method match with the experimental data. The changing separation work rates of the 3-D FE analyses using the nodal release method and the experimental J-R curves are adopted as references for the changing cohesive energies in 2-D plane strain and plane stress FE analyses with the CZM approach. The simulation results with the CZM approach match well with the experimental data.

Measuring crack growth and related opening and closing stresses using continuous potential drop recording

To improve resolution of in-situ measurement of crack closure and opening in fatigue, potential drop (PD) measurement technique has been further developed to measure thousands of times through each load cycle with high precision. The results are interpreted with physical phenomena like strain, Poisson’s effect, piezo-resistivity, plasticity, and crack growth. Application of the technique to fatigue crack growth tests on aluminum 2024-T3 CCT specimens at different maximum stresses and stress ratios, demonstrate that indeed variations in PD can be associated to development of plasticity and crack opening and closure. Hence, the technique allows to measure timing and magnitude of crack opening and closure stresses in-situ in fatigue crack growth experiments.

Effect of specimen thickness on fatigue crack growth behavior of A6063 thin plate CCT specimen by friction stir welding under constant amplitude loading

Effect of specimen thickness on fatigue crack growth behavior of A6063 thin plate CCT specimen by friction stir welding under constant amplitude loading

Experimental and FE Modeling of Mixed-Mode Crack Initiation Angle in High Density Polyethylene

In this paper, an experimental and a numerical analysis were carried out using High density polyethylene (HDPE). Sheets with an initial central crack (CCT specimens) inclined with a given angle are investigated and compared to the loading direction. The kinking angle is experimentally predicted and numerically evaluated under mixed mode (I+II), as a function of the strain energy density (SED) around the crack-tip, using the Ansys Parametric Design Language (APDL).According to the experimental observations and numerical analysis, the plan of crack propagation is perpendicular to the loading direction. Moreover, as suggested by Sih in the framework of linear elastic fracture mechanics (LEFM), the minimum values Sminof the factor S are reached at the points corresponding to the crack propagation direction. These results suggest that the concept of the strain energy- density factor can be used as an indicator of the crack propagation direction.

Epistemic uncertainty quantification in metal fatigue crack growth analysis using evidence theory

Uncertainties originate from physical variability, data uncertainty, and modeling errors in the fatigue crack growth prediction analysis. This study presents an evidential uncertainty quantification (UQ) approach for determining uncertainties involved in revealing the material constants of the metal fatigue crack growth model with imprecise uncertainty information (i.e., epistemic uncertainty). The parameters in fatigue crack growth model are obtained by fitting the available sparse experimental data, and then the uncertainties in these parameters are considered. To alleviate the computational difficulties in the UQ analysis based on evidence theory, an interval optimization method based on differential evolution is used in finding the propagated belief structure. The overall procedure is demonstrated using the results of several replicated experiments on aluminum alloy CCT specimens.

Quantifying the creep crack-tip constraint effects using a load-independent constraint parameter Q*

In this work, a load-independent creep constraint parameter Q* was introduced, and its load-independence was confirmed by 3D finite element analyses of six different cracked specimens. A fixed distance r=0.2mm ahead of crack tips was chosen to define the Q*. In addition, the parameter Q* was used to quantify the in-plane constraint induced by crack depths, specimen widths and loading configurations and the constraint effects induced by specimen thicknesses. The results revealed that the values of Q* increased with increasing the crack depths (a/W ≤0.5) and specimen thicknesses and decreased with increasing the width-thickness ratio W/B of specimens. Furthermore, the highest constraint level occurred in the CT specimen while the lowest occurred in the CCT specimen.

A systematic investigation of T-stresses for a variety of center-cracked tension specimens

In this work, a systematic investigation of three-dimensional (3D) T-stresses (T11 and T33) was conducted using detailed elastic finite element analysis (FEA). The interaction integral method was applied to extract the T-stress solutions. Standard CCT specimens with a thickness-to-width ratio of B/(2W)⩽0.0625 and a crack length-to-width ratio of a/W=0.25–0.7, as specified in ASTM E2472, were considered, and the cases of B/(2W)=0.1–1.0 and a/W=0.05–0.2 and 0.8 were also added. From the FEA results, it was found that both T11 and T33 at the specimen mid-plane showed significant changes with crack lengths and specimen thicknesses for those CCT configurations that satisfy ASTM E2472. Because both the in-plane and out-of-plane T-stresses were negative and showed large variations for all the considered CCT specimens which was true even for the CCT specimens complying with the ASTM E2472 standard, it was noted that these CCT specimens that complying with the standard might show the test specimen size effect (including the crack length and specimen thickness effect) on the fracture toughness if tested.

Derivation of constraint-dependent J–R curves based on modified $$T$$ T -stress parameter and GTN model for a low-alloy steel

In this paper, a modified load-independent \(T\)-stress constraint parameter \(\tau ^{*}\) was defined. The \(\tau ^{*}\) of specimens with different crack-tip constraint levels at different \(J\)-integrals was calculated, and its load-independence has been validated. Based on the modified constraint parameter \(\tau ^{*}\) and the numerically calculated J–R curves by using the Gurson–Tvergaard–Needleman (GTN) model for the SENB specimens with different \(a/W\), the equations of constraint-dependent J–R curves for the A508 steel were obtained. The predicted J–R curves using the equations essentially agree with the experimental and calculated J–R curves. The transferability of the constraint-dependent J–R curves to the CT, SENT and CCT specimens was validated. The results show that the modified constraint parameter \(\tau ^{*}\) and the GTN model can be effectively used to derive the constraint-dependent J–R curves for ductile materials.

점탄성을 고려한 고체추진제의 파괴인성 평가

A crack in a solid propellant increases the area of burning surface, which leads to excessive burning that causes motor failure. Therefore, it is necessary to evaluate fracture toughness of solid propellants. However, it is very difficult to measure fracture toughness of solid propellants because of the nonlinear mechanical behavior. In this study, evaluation of fracture toughness on a solid propellant was carried out under the assumption that the solid propellant is a linear viscoelastic material. Actual displacements from fracture toughness tests using CCT specimens were converted into pseudo-elastic displacements by using stress relaxation characteristics and fracture toughness was evaluated using ASTM E399 standard. Also, effects of test temperature and speed on the fracture toughness were considered.

OS0716 XFEMのHermite型要素への適用(OS7-3 解析・評価・き裂II,OS-7 多軸応力下における疲労損傷および疲労き裂進展2)

The extended finite element method (XFEM) has an advantage that an arbitrary shaped crack and its extension can be treated easily. But it is also pointed out that the results of the fracture parameter have significant errors that come from the existence of 'blending elements'. In the standard formulation of XFEM, the nodes in the element including the crack tip have enriched additional degrees of freedom. The nodes in the outer region have usual degrees of freedom, i.e. 2 in the two dimensional problem. The elements in the region surrounding the crack site have nodes with enriched freedom at the crack side and normal freedom at the outer region side. These elements are called 'blending elements'. In this paper, a new Hermite element with three nodes has been formulated and applied to a crack problem with XFEM. Errors of fracture parameters calculated by the M-integral method were discussed from the point of view of the effect of the blending elements. Stress intensity factor of CCT specimen has a 10% of error with a simple formulation. It decreases down to 0.5% by considering the improvement of XFEM proposed by Shibanuma et. al.

Application of digital image correlation to the investigation of crack closure following overloads

This paper describes a set of fatigue experiments carried out on 6082 Aluminium CCT specimens. Crack propagation rates and crack opening loads were measured before and after a single overload in an otherwise constant amplitude loading sequence. Crack retardation was observed after the overload, and this was more significant in thin (3 mm) specimens than in thick (25 mm) specimens of otherwise similar geometry. Digital image correlation and conventional strain gauges were used to monitor crack closure, and it was found that surface closure levels were similar in the two thicknesses of specimen. However, the thick specimens showed lower closure levels as detected by the strain gauges. This observation is consistent with the lower levels of crack retardation observed. A plane stress strip-yield model of crack closure was employed to simulate the experimental loading cycle and this showed qualitatively similar behaviour to that observed on the surface of the specimens.

Simulation of Fatigue Crack Growth in Integrally Stiffened Panels Under the Constant Amplitude and Spectrum Loadin

Simulation of Fatigue Crack Growth in Integrally Stiffened Panels Under the Constant Amplitude and Spectrum LoadinThe paper describes methodology of numerical simulation of fatigue crack growth and its application on integrally stiffened panels made of 2024-T351 aluminium alloy using high speed cutting technique. Presented approach for crack growth simulation starts by the calculation of stress intensity factor function from finite element results obtained using MSC. Patran/Nastran. Subsequent crack growth analysis is done in NASGRO and uses description of crack growth rates either by the Forman-Newman-de Koning relationship or by the table lookup form. Three crack growth models were applied for spectrum loading: non-interaction, Willenborg and Strip Yield model. Relatively large experimental program comprising both the constant amplitude and spectrum tests on integral panels and CCT specimens was undertaken at the Institute of Aerospace Engineering laboratory in order to acquire crack growth rate data and enable verification of simulations. First analyses and verification tests of panels were performed under the constant amplitude loading. For predictions of crack growth using the spectrum loading a load sequence representing service loading of the transport airplane wing was prepared. Applied load spectrum was measured on B737 airplane within the joint FAA/NASA collection program. The load sequence is composed of 10 flight types with different severity analogous to the standardized load sequence TWIST. Before application on the stiffened panels a calculation of crack growth under the spectrum loading was performed for simple CCT specimen geometry. The paper finally presents comparison of simulations of fatigue crack propagation in two-stringer stiffened panel under the spectrum loading with verification test carried out in the IAE lab. The work was performed within the scope of the 6th Framework Programme project DaToN - Innovative Fatigue and Damage Tolerance Methods for the Application of New Structural Concepts.

Deterministic Approach to Predicting the Fatigue Crack Growth in the 2024-T3 Aluminum Alloy Under Variable Amplitude Loading

Deterministic Approach to Predicting the Fatigue Crack Growth in the 2024-T3 Aluminum Alloy Under Variable Amplitude LoadingThe paper presents the attempt to predict fatigue crack growth rate in a component subjected to variable amplitude loading containing overload-underload cycles. For this goal in a deterministic approach the modified Willenborg retardation model was applied. To provide experimental data the research into fatigue crack growth for 2024-T3 aluminum alloy sheet CCT specimens under LHL type block program loading with multiple overload-underload cycles was developed. The microfractographic analysis of fatigue fractures with the use of the transmission electron microscope (TEM) made it possible to trace the effect of block program loading on the crack growth rate. The knowledge of the affection of a particular overload-underload cycle or a block of these cycles on crack rate on the basis of microfractographic analysis was utilized for assessing the equivalent loading for the LHL block program. The diagrams that presented the crack growth rate both on the surface and inside the aluminum alloy sheet was performed. The crack growth rate inside the sheet was estimated on the basis of the striation spacing analysis.

Optimization of contact conditions between iron base alloys and mercury at room temperature

The intimate contact or wetting of iron-base alloys by mercury is obtained at room temperature by varying the environmental conditions, quasi immediately for Armco iron and a high purity Fe–25Ni alloy, after ∼30 min of contact for the 316L/Hg couple, after one week of contact for the T91/Hg couple. Careful mechanical polishing allows for wetting the notches of CCT specimens made in T91 steel with Hg, whereas chemical etching in 4%HCl is required to wet 316L SS identical specimens. Using ICP-OES measurements, values of solubility limit are given for both Fe (45.5 ± 0.4 wt ppm) and Cr (0.56 ± 0.07 wt ppm) in mercury at room temperature, the one of nickel (2.6 ± 0.39 wt ppm) being in agreement with the literature data.

Evaluation of Corrosion Fatigue Crack Propagation Characteristics of TMCP Steel in Synthetic Seawater under Cathodic Protection

In this research, corrosion fatigue tests using tensile strength of 490MPa TMCP steel were performed in synthetic seawater condition to investigate the corrosion fatigue crack propagation characteristics. The influence of cathodic protection at -800mV vs. SCE on the corrosion fatigue crack propagation behavior was investigated. Relationships between da/dN versus ΔK for the material were obtained by two types of test specimens. In the present study, F(α,β) versus α(= 2a/W) relationship for the CCT specimen was calculated by J integral approach, while that for the CT specimen was determined from ASTM E647. It is found that the fatigue crack propagation rate of TMCP steel in synthetic seawater condition is faster than that in air condition at least twice. Also, it is observed that the fatigue crack propagation rate of steel with cathodic protection is in between those of seawater condition without cathodic protection and air condition.

Stochastic Characteristics of Fatigue Crack Propagation for 2024-T3 Aluminium Alloy in Corrosive Environments

Crack propagation tests were conducted with CCT specimens made by 2024-T3 Aluminum alloy in benign and corrosive environments to investigate the stochastic characteristics of crack growth. A random variable probability crack growth model, base on the modified form of Paris law, was used to characterize the stochastic performance. Distribution significance test has been done, which shows that the random variable X can be considered reasonably to follow log-normal distribution in all the 4 kind of environments. Variance analysis indicates that the scatter in wet air is greater than that in laboratory air significantly. Expressions for the probability distribution of crack size at any given loading cycle and the probability distribution of the random fatigue life at which a given crack size is reached were discussed. The corresponding calculations for the crack length distribution and P-a-N curves with certain reliability were carried out. The comparisons with experimental data indicate the validity of the proposed method.

Fracture of elastomers under static mixed mode: the strain-energy-density factor

This work deals with the fracture of rubbers under a mixed mode loading (I + II) and it is an extension of our previous papers on that subject [Aït Hocine N, Naït Abdelaziz M, Imad A (2002) Int J Fract 117:1–23; Aït Hocine N, Naït Abdelaziz M (2004) In: Sih GC, Kermanidis B, Pantelakis G (eds) 6th international conference for mesomechanics. Patras (Greece), May 31–June 4, pp 381–385]. An experimental and a numerical analysis were carried out using a Styrene Butadiene Rubber (SBR) filled with 20 and 30% of carbon black. Sheets with an initial central crack (CCT specimens) inclined with a given angle compared to the loading direction were used. The J-integral and its critical values J c (fracture surface energy) were determined by combining experimental data and finite element results. These critical values, determined at the onset of crack growth, were found to be quite constant for each elastomer tested, which suggests that J c represents a reasonable fracture criterion of such materials. Then, the strain–stress field and the strain-energy-density factor S, earlier introduced by Sih [Sih GC (1974) Int J Fract 10(3):305–321; Sih GC (1991) Mechanics of fracture initiation and propagation. Kluwer Academic Publishers, Dordrecht, 428 pp] were numerically calculated around the crack tip. According to the experimental observations, the plan of crack propagation is perpendicular to the direction of the maximum principal stretch. Moreover, as suggested by Sih in the framework of linear elastic fracture mechanics (LEFM), the minimum values S min of the factor S are reached at the points corresponding to the crack propagation direction. These results suggest that the concept of the maximum principal stretch and the one of the strain-energy-density factor can be used as indicators of the crack propagation direction.

異方性を有する純アルミニウム冷間圧延薄板の特異な疲労き裂進展経路に及ぼす圧下率並びに結晶組織と結晶方位の影響

Effects of rolling ratios, microstructures and crystal orientations on the fatigue cracks that grow on the rolling direction as mixed mode I + II cracks in pure aluminum sheets were investigated by conducting fatigue tests. The CCT specimens were used and made from cold-rolled pure aluminum sheets with rolling ratio of 50%, 75%, and 90%. It was found that the cracks grow to the rolling direction as mixed mode I + II cracks in the specimens with rolling ratio above 75%. It was also confirmed that microstructures in the high rolling ratio specimens are smaller and more elongated to the rolling direction than those with lower rolling ratio. However, there was no effect of microstructure size on the fatigue crack path. The crystal planes on the fracture surfaces and the slip plane of aluminum, (111) planes in the sheets were measured using X-ray diffraction. It was found that (111) planes mainly existed on the fracture surface of the crack that grew on the rolling direction. In addition, there were strong textures of (111) planes on the rolling direction of specimens with rolling ratio higher than 75%. It was clarified that the fatigue cracks, which grow to the rolling direction as mixed mode I + II cracks, are caused by strong textures of (111) planes on the rolling direction that exist in the maximum shear-stress region.

Behavior of Fatigue Crack Growth Paths in Peculiar Anisotropic Commercial Pure-Aluminum Sheets (A1100P)

Behavior of fatigue crack that grows to the rolling direction about 30 degrees to the loading direction as a mixed mode I + II crack in peculiar anisotropic commercial pure aluminum sheets (A 11110 p) was investigated using CCT specimens. From fatigue tests, it was found that the crack started to change the direction from mode I to the rolling direction when mode I stress intensity factor range was 4.2 MPa·mm1/2 and crack grew continuously to the rolling direction when mode II stress intensity factor range was 4.3 MPa·mm1/2 under small scale yielding state. However, in the case of specimen annealed in 563 k, 30 minutes, the crack did not grow to the rolling direction. The crack that grew on the rolling direction changed direction to mode I direction, due to the nominal stress which was about 80 percent of yield stress. According to the measurement on crystal planes using X ray diffraction, it was found that the slip plane of aluminum. (III) plane dominantly existed on the fracture surface of the crack that grew to the rolling direction. From pole figures, it was also verified that strong textures of (III) planes existed in rolling direction, so that the shear strength on the rolling direction was low as confirmed by shear test. Due to the strong textures of (III) planes that exist around the maximum shear stress region, the mode II crack component becomes easily to occur that makes the mixed mode I+II crack to grow to the rolling direction around 30 degrees towards loading direction.