Center-cracked Tension Research Articles

OS03W0395 The effect of heat conduction on stress concentration factors and stress intensity factors determined by thermoelastic stress analyses

The stress concentration factors and stress intensity factors evaluated by thermoelastic stress analysis method were lower than the comparable values calculated by the finite element method (FEM), and the error increased in proportion to those values regardless of the stress ratio. In this study, the sources of the error between experimental results and numerical values were investigated in order to improve the accuracy of thermoelastic stress analyses. Since the major source was supposed to be the effect of heat conduction in specimens, the unsteady heat conduction analyses were conducted for three types of center holed specimens and center crack tension (CCT) specimens. According to the comparison between experimental results and numerical values, it was found that stress concentration factors were affected by heat conduction especially under 10Hz, but the errors of stress intensity factor were caused not by heat conduction but by the plastic zone size of a crack tip.

Fatigue behaviour and life prediction of fibre reinforced metal laminates under constant and variable amplitude loading

Fatigue crack growth of fibre reinforced metal laminates (FRMLs) under constant and variable amplitude loading was studied through analysis and experiments. The distribution of the bridging stress along the crackline in centre-cracked tension (CCT) specimen of FRMLs was modelled numerically, and the main factors affecting the bridging stress were identified. A test method for determining the delamination growth rates in a modified double cracked lap shear (DCLS) specimen was presented. Two models, one being fatigue-mechanism-based and the other phenomenological, were developed for predicting the fatigue life under constant amplitude loading. The fatigue behaviour, including crack growth and delamination growth, of glass fibre reinforced aluminium laminates (GLARE) under constant amplitude loading following a single overload was investigated experimentally, and the mechanisms for the effect of a single overload on the crack growth rates and the delamination growth rates were identified. An equivalent closure model for predicting crack-growth in FRMLs under variable amplitude loading and spectrum loading was presented. All the models presented in this paper were verified by applying to GLARE under constant amplitude loading and Mini-transport aircraft wing structures (TWIST) load sequence. The predicted crack growth rates are in good agreement with test results.

219 中央き裂を有する引張試験片の強磁場応力拡大係数評価

219 中央き裂を有する引張試験片の強磁場応力拡大係数評価

Plastic J-integral calculations using the load separation method for the center cracked tension specimen

The load separation method was used to determine the plastic work factor ( η pl) for the center crack tension geometry for power law hardening materials with Ramberg–Osgood hardening exponents n ranging from 2 to 20 and crack sizes a/ W ranging from 0.4 to 0.8. The resulting expression for η pl compares favorably to the analytical work of Rice, Paris, and Merkle and to Sharobeam and Landes. The results were also compared to η pl calculated from the plastic J results in EPRI Handbook NP-1931. Unlike the EPRI results, η pl from the load separation method are not a function of crack size.

Finite element analysis to assess the effect of initial plasticity on transient creep for defects under mechanical loading

Finite element (FE) transient creep analyses have been performed for geometries of differing constraint levels, namely compact and centre-cracked tension specimens and circumferentially-cracked cylinders. Elastic-creep and elastic–plastic-creep behaviour with the same stress exponents in power-law creep and plasticity were considered. The complete time history between initial transient creep response and steady state conditions has been analysed for a range of load levels. Estimates of J( t) and C( t) have been compared with computed values. The known asymptotic behaviour in the limits as time, t→0 and t→∞ has been confirmed. At intermediate times, estimation formulae are suggested which compare well with the FE results. The suggested expressions modify existing formulae in the literature and provide improved agreement with the FE results.

Behavior of plasticity-induced crack closure and roughness-induced crack closure in aluminum alloy

For center-cracked tension specimens subjected to constant amplitude loading, fatigue crack closure and crack growth behavior in an aluminum alloy 7050-T7451 were investigated. The specimens were tested with stress ratios of −1.0, 0.0, 0.1 and 0.3 under constant amplitude loading. Plasticity-induced crack closure and roughness-induced crack closure were found to be the main tools for explaining the crack growth behavior under plane strain and plane stress conditions. From a measurement of roughness height distribution of fractured surfaces using a surface profiler, the roughness-induced crack closure was evaluated as the main factor at low stress intensity factor range Δ K. This closure phenomenon was qualitatively predicted using a single asperity model. On the other hand, the plasticity-induced crack closure was the decisive factor at high Δ K and could be predicted by the modified strip-yield model based on a Dugdale model. In the case of concurrence of two crack closures, therefore, the total crack closure behavior with Δ K level for four stress ratios could be described effectively by two closure models, a single asperity model and a strip-yield model.

Fatigue crack opening stress based on the strip-yield model

The modified strip-yield model based on the Dugdale model and two-dimensional approximate weight function method were utilized to evaluate the effect of in-plane constraint, transverse stress, on the fatigue crack closure. The plastic zone sizes and the crack opening stresses considering transverse stress were calculated for four specimens: single edge-notched tension (SENT) specimen, single edge-notched bend (SENB) specimen, center-cracked tension (CCT) specimen, double edge-notched tension (DENT) specimen under uniaxial loading. And the crack opening behavior of the center-cracked specimen under biaxial loading was also evaluated. Normalized crack opening stresses σ op/ σ max for four specimens were successfully described by the normalized plastic zone parameter Δω ′ rev/ ω ′ considering transverse stress, where Δω ′ rev and ω ′ are the size of the reversed plastic zone at the moment of first crack tip closure and the size of the forward plastic zone for maximum stress, respectively. The normalized plastic zone parameter with transverse stress also was satisfactorily correlated with the behavior of crack closure for CCT specimen under biaxial loading.

Fatigue crack growth measurements under spectrum loading

Fatigue crack growth rates under variable amplitude stress cycles were measured on two center-cracked tension specimens made of SM520B steel. Four loading spectra, right-skewed and left-skewed β distributions with the minimum or maximum stress constant, were applied to the specimens. Based on the root-mean-cube stress range, the test results are compared with the fatigue crack growth behavior under constant amplitude loading with the same stress ratio. They are generally in good agreement, indicating that effect of stress ratio is generally dominant. However, when large number of stress cycles are in the low stress range region, the effect of threshold stress intensity factor range is found to be large.

Probabilistic analysis of weld cracks in center-cracked tension specimens

This paper describes the development of a probabilistic methodology for fracture-mechanics analysis of weld cracks in a center-cracked tension (CCT) specimen. It involves elastic–plastic analyses to predict J-integral, statistical models of uncertainties in loads and material properties, and standard computational methods of structural reliability theory for probabilistic analysis. Eighty-one deterministic finite element analyses were performed for a wide variety of crack size, material mismatch factors, and weld geometric parameters to develop approximate equations for the J-integral of a CCT specimen and were subsequently applied for probabilistic fracture evaluations. Both fast probability integrators, such as first- and second-order reliability methods, and Monte Carlo simulation were used to determine the probabilistic characteristics of the J-integral. The same methods were used later to predict the failure probability based on initiation of crack growth. Numerical results are presented to illustrate the proposed methodology. The effects of mismatch factors on both deterministic and probabilistic response characteristics were examined. The results indicate that the tensile properties of both base and weld materials should be accounted for when calculating J. These mismatch factors have a significant effect on the probabilistic characteristics of J and failure probability.

Effect of Residual Stress in Al5083 TIG Weld Region on Fatigue Crack Propagation Behavior

The welded structure unnecessarily remains residual stress due to the very high heating of local region and lastly cooling. The residual stress sometimes causes fracture initiation of welded structures. In this paper, distribution and magnitude of tensile and compressive residual stresses in the TIG(Tungsten Inert Gas) welded aluminum alloy such as Al5083-H112 are measured by using the hole-drilling method. Furthermore, the effects of residual stresses in the TIG welded aluminum CCT(Center Crack Tension) and SEN(Single Edge Notched) Specimens on the fatigue crack propagation behavior are analyzed. The fatigue cracks initiated at residual stresses region are influnced by tensile and compressive residual stresses. However, the effects are found to be released fast for both cases according to the cyclic loads and extension of crack length.

The effects of loading variables on overload induced fatigue crack growth retardation parameters

A growing fatigue crack is known to be retarded on application of an overload cycle. The retardation may be characterized by the total number of cycles involved during retardation, ND and the retarded crack length, aD. The loading variables play an important role to influence the retardation behaviour and thereby the retardation parameters ND and aD. The important loading variables are considered to be the stress intensity range, ΔK during constant amplitude loading, stress ratio, R and the ratio of the overload stress to the maximum stress in constant amplitude loading, OLR etc. The objective of the present investigation is to study the effect of different loading variables on the retardation parameters. The investigation has been conducted in a 2024-T3 Al-alloy with centre crack tension panels loaded using an Electromagnetic Resonance Machine. The crack extension and crack closure have been measured during cyclic loading under constant amplitude and under overloading situations. The results do indicate dependence of crack opening stress intensity factor, KOP on loading variables such as ΔK, R and OLR. The delay cycle ND is found to increase with loading variables ΔK, OLR and R. The functional dependence of retardation zone aD on loading variables has also been identified.

FATIGUE CRACK GROWTH BEHAVIOR OF VARIOUS STRUCTURAL STEEL AFTER SINGLE AND PERIODIC OVERLOADS

In order to evaluate accurately fatigue life of weldments under variable amplitude loading, load interaction effect due to load sequence has to be clarified. A simple case is the fatigue crack growth retardation effect resulting from single or periodic overloads. In the present study, fatigue crack growth rates were measured under single and periodic overload conditions on center-cracked tension specimens of structural steel SS400, SM520B and HT780. Effects of several parameters including overload ratio, stress ratio, yield strength of material and interval between overloads on fatigue crack growth retardation were investigated.

Influence of residual stresses and loading frequencies on corrosion fatigue crack growth behavior of weldments

The effect of residual stresses and loading frequencies on corrosion fatigue crack growth behavior under synthetic seawater with a free corrosion potential was examined using center-cracked tension (CCT) and single edge-cracked tension (SECT) specimens machined from mild steel butt-welded joints and the parent material. A series of fatigue crack growth tests were carried out with a sinusoidal loading wave form at a stress ratio of 0.05 with a loading frequency of 0.017 to 6.7 Hz. The results show that the crack growth resistance of a weld metal in the SECT specimen is higher than that in the CCT specimen regardless of testing conditions. The discrepancy is attributed to the differences in residual stress distribution at the crack tip in the two specimen geometries. The crack growth rate of the weld metal in the CCT specimen in seawater increased with decreasing loading frequency. The acceleration of the crack growth rate may be related to the occurrence of brittle striation or cleavage due to hydrogen embrittlement. It was found that the corrosion fatigue crack growth rate of a welded joint with tensile residual stress can be predicted using the effective stress intensity factor range, which takes into account both the residual stress and the loading frequency effects.

A photoelastic study of crack repair

Birefringent coatings have been employed to study the effectiveness of an adhesively bonded repair of a center-cracked tension panel. The repair was one sided, with photoelastic coatings applied to the opposite side. Photoelastic coatings were also applied over the patch. Analysis methods are presented to permit the stress intensity factor to be determined from the isochromatic fringe patterns recorded from both continuous andX- andY-edged coatings. The results showed that the one-sided adhesively bonded patch reduced the stress intensity factor; however, the repair did not markedly change the character of stress distributions. Fringe loops formed near the crack tips for both the cracked and repaired tension panels. The primary difference was in the size of the loops. The reduction inK I due to repair was smaller than anticipated, but even small improvements in ΔK I markedly enhance the life of a repaired panel. The Paris power law is used to show the relation between the reduction in ΔK I and the improvement in the crack growth rateda/dN. Fringe patterns from the birefringent coatings applied to the patch provided a means not only to investigate the stresses in the patch but also to detect the initiation of the local debonding of the adhesive in the neighborhood of the crack. The birefringent coating on the patch is an approach for producing an optically “smart” repair.

Study on the effect of the crack length on the JIC value

The ductile fracture tests are carried out using compact type (CT) specimen, three point bend specimen and center cracked tension (CCT) specimens made of A533B steel and aluminum alloy with different crack lengths. The effect of the crack tip constraint on the microscopic fracture behavior is studied by the scanning electron microscope (SEM). It is shown that the apparent J IC value increases due to the decrease of the crack tip constraint. It is pointed out that the increase of the apparent J IC value is partly due to the error of the conventional equation to estimate the J value. Based on the FEM analyses, these apparent J IC values are corrected and are compared with the valid J IC values. The good co-relation between apparent J IC value and the Q factor, proposed by O'Dowd and Shih, is shown for all the specimens. The FEM analyses based on the Gurson's constitutive equation is also carried out. The effect of the constraint on the crack tip field is discussed.

Stress Intensity Factor Equation for Center Cracked Tension (CCT) Specimens of Fiber Reinforced Metal Laminates under Cyclic Loading

Based on the experimental observations that crack growth in fiber reinforced metal laminates (FRMLs) under fatigue loading tends to reach a steady state, stress intensity factor equation of FRMLs was derived in this paper. A material constant, the equivalent crack length (l{sub 0}) of FRMLs, was first found. The analytical equation for the stress intensity factors of the CCT specimens of FRMLs was verified by experimental data, which were calculated from the testing results of crack growth rates in GLARE based upon the crack growth rate equation of the constituent metal sheet. The stress intensity factor equation agreed very well with the experimental data. (orig.) 9 refs.

Effect of constraint on ductile crack growth and ductile-brittle fracture transition of a carbon steel

Ductile-brittle fracture transition was investigated using compact tension (CT) specimens from −70 to 40°C for a carbon steel. Large deformation finite element analysis was carried out to simulate the stable crack growth in the compact tension (CT, aW = 0.6), three point-point bend [SE(B), aW = 0.1] and centre-cracked tension [M(T), aW = 0.5] specimens. An experimental crack tip opening displacement (CTOD) resistance curve was employed as the crack growth criterion. Ductile tearing is sensitive to constraint and tearing modulus increases with reduced constraint level. The finite element analysis shows that path-dependence of the J-integral occurs from the very beginning of crack growth and ductile crack growth elevates the opening stress on the remaining ligament. Cleavage may occur after some ductile crack growth due to the increase of opening stress. For both stationary and growing cracks, the magnitude of opening stress increases with increasing in-plane constraint. The ductile-brittle transition takes place when the opening stress ahead of the crack tip reaches the local cleavage stress as the in-plane constraint of the specimen increases.

Physical meaning of ΔKRP and fatigue crack propagation in the residual stress distribution field

Previous papers have shown ΔKRP to be a useful parameter describing fatigue crack propagation behavior, where ΔKRP is an effective stress intensity factor range corresponding to the excess RPG load (re-tensile plastic zone's generated load) in which the retensile plastic zone appears under the loading process. In this paper, the relationship between ΔKRP and the zone size (ω̃) (which is smaller between the tensile plastic zone at maximum load and the compressive plastic zone at minimum load) was investigated using a crack opening/closing simulation model so as to consider a physical meaning of ΔKRP. As a result, it becomes clear that ΔKRP dominates the zone size ω̃ where fatigue damage mostly occurs. This result supports the following crack propagation equationdadN=C(ω̃)mwhere C and m are material constants.Simulation and fatigue crack propagation tests were then carried out for compact tension (CT), center cracked tension (CCT) and four points bend (4PB) specimens under constant amplitude loading to obtain C and m values for HT-50 steel. Fatigue crack propagation tests were also carried out under constant amplitude loading using CCT specimens with residual stress distribution due to flame gas heating at the center line or edge lines. The T specimen introduced tensile residual stress at the tip of a notch, and the C specimen introduced compressive residual stress. It therefore becomes clear that tensile residual stress leads to a decrease in RPG load, while compressive residual stress leads to increase in RPG load, and that the simulation results are in good agreement with the experimental RPG load. It also becomes clear that simulated crack growth curve using the simulated ω̃ and the above equation is in good agreement with the experimental curve. It is understood that tensile residual stress creates only a slight increase in crack propagation rate and compressive residual stress create a big decrease a crack propagation rate.

The Measurement of the Crack in CCT Specimen Using the Image Processing Techniques

In the analysis of fatigue crack propagation behavior, the crack length is one of the most important factors. In the test of crack propagation, compliance method is widely used to detect crack length. The measurement of surface crack length is not so easy with compliance method. In this study, the image processing technique was applied to measure the surface crack length. CCD(Charge-coupled device) camera was used to observe the crack image and the computer program to detect crack length from stored crack image was developed. CCT(Center Cracked Tension) specimen was used to compare the compliance method with the image processing technique. The crack length which detected by the image processing techniques was found to be well consistent with that from the optical measurement.

Fatigue crack propagation in residual stress fields of welded plates

This paper presents some recent results of a research programme on the evaluation of the fracture mechanics properties, principally the crack propagation rate, of plasma welded aluminium joints, 2219-T851. Crack propagation tests were carried out on large centre cracked tension (CCT) specimens and on small compact tension (CT) specimens. The main difference between the two typs of specimens concerned the residual stresses, which were not present in the CT specimens, due to their reduced dimensions. The residual stresses were measured in cracked and uncracked plates, by means of strain gauges. The results of the crack propagation tests carried out on the two types of specimens were fully comparable in the case of a crack which propagates along the weld bead, in the heat-affected zone, as the residual stress effect was quite low, while the crack propagation rate measured in the CT specimens was lower than that in the CCT specimens in the case of a crack which propagates perpendicularly to the weld bead. Residual stress measurements allowed the evaluation of the residual stress effects on the crack propagation rate and close agreement was found between the results of the two set of tests.