Elastic-plastic Fracture Mechanics Parameters Research Articles

A Simplified Method to Estimate Elastic-Plastic Fracture Mechanics Parameters under Combined Primary and Secondary Stresses

Detailed two- and three-dimensional finite element analyses are performed to develop an engineering method to estimate elastic-plastic J for cracked structures under combined primary and secondary stresses, based on the V-factor. Extensive analyses with a wide range of geometry and load combination are considered. The results suggest important factors affecting the value of the V-factor. The most important one is the load magnitude, parameterized by the proximity of plastic yielding. The second one is the relative magnitude of the secondary stress to the primary stress. Although the effect of material, in particular materials with Lüders strain seems to be present, such an effect could be neglected, compared to those of the above two parameters. Based on the present results, an engineering method to estimate J for combined primary and secondary stress can be proposed using bilinear equations in terms of the above two parameters.

Study on Fracture Properties of High-Density Polyethylene (HDPE) Pipe

Butt-fusion welding is the main technology to join high-density polyethylene (HDPE) plastic pipes, which are widely used in transport the water, gas and corrosive liquid. Investigation shows that one of the failure modes of HDPE pipe is the crack slowly grows across the thick direction and leads to failure at last, so that it is very important to study the resistance to crack initiation of HDPE pipe and its butt-fusion welded joint. In this study, the elastic-plastic fracture mechanics parameter, crack opening displacement (COD) is used to describe the fracture initiation behaviors for the HDPE materials and its butt-fusion welded joints. The resistance to initiation fracture of HDPE pipe materials and butt-fusion welded joints were investigated at different temperature by using multiple specimen resistance curve method and silicon-rubber replica method. The results show that saturation initial crack COD- δis of HDPE pipe materials and butt-fusion welded joints decreases with the decreasing temperature. The δis of butt-fusion welded joints is lower than that of HDPE pipe materials. Investigation also proved that the silicon-rubber replica method is more suitable for HDPE engineering material than the multiple specimen method. At the same time the statistic distribution of the δis of HDPE butt-fusion welded joint was conducted. The results show that the value of the δis has the statistic variance inherently. The optimum fitting distribution of COD is Weibull distribution with three parameters.

Empirical corrosion fatigue life prediction models of a high strength steel

Crack initiation and growth behaviour in plain hour-glass shaped fatigue specimens of quenched and tempered silico-manganese spring steel (BS250 A53) having a mirror image was studied under fully reversed torsional loading conditions in both the laboratory air and the aggressive (0.6 M, aerated NaCl solution) environments. A surface plastic replication technique was used alongwith optical microscopy to monitor the early stages of environment-assisted fatigue. Non-metallic inclusions were observed to play a major role in crack initiation in both the environments. De-bonding at matrix/inclusion interfaces and chemical pitting at inclusion sites were major processes in the early developmental stages of air and corrosion fatigue, respectively. A significant influence of microstructure, i.e. prior austenite grain boundaries, on defect development was also noted during air and corrosion fatigue cracking. Corrosion fatigue failure appears to be a multiple stage process namely; pit development, short crack growth, and long crack growth. Corrosion fatigue crack growth rates are predicted by employing models, which incorporate elastic plastic fracture mechanics parameters to characterise the influence of microstructure. Two empirical corrosion fatigue crack growth models, including a superposition model discussing the inert air and environmental terms involved in the corrosion fatigue process, are presented. A reasonable agreement was found between experimental and calculated lifetimes.

Assessment of temperature-dependent fracture behavior with different fracture mechanics concepts on examples of unoriented and cold-rolled polypropylene

Applicability of different fracture mechanics concepts, including linear elastic fracture mechanics (LEFM), equivalent energy concept, and elastic-plastic fracture mechanics (EPFM), to assessing the temperature-dependent fracture behavior was compared using examples of an unoriented and a cold-rolled polypropylene under quasistatic and under dynamic loading. Under quasistatic loading, the fracture toughness values were determined from the recorded load versus load-line displacement curves on compact tension (CT) specimens. Fracture toughness values under dynamic loading were determined from the recorded load versus deflection curves on single edge-notched bend (SENB) specimens. In spite of its simplicity as an engineering design parameter, on the basis of the LEFM concept, the stress intensity factor K can only be validly used in a limited temperature range. Instead, the EPFM parameters (i.e., the J integral and the crack opening displacement (COD) concepts) can be applied over a wider temperature range. © 1997 John Wiley & Sons, Inc. J Appl Polym Sci 66: 1237–1249, 1997

Application of fracture mechanics to the surface crack propagation in stainless steel at elevated temperatures

The propagation of small surface cracks in SUS 304 stainless steel is examined at elevated temperatures. In the temperature region studied, the crack growth is mainly cycle-dependent. When temperature is higher than 500°C, creep-dependent crack growth becomes dominant which results in a larger crack growth rate. By confirming that the surface crack maintains a semi-elliptic shape during its growth and by investigating the cyclic deformation behavior of the material, elastic-plastic fracture mechanics parameters are evaluated and used to correlate the crack growth rate. Both the J integral range ΔJ, and the effective J integral range ΔJ eff, which accounts for the crack closure effect, are found to be excellent to consolidate crack growth rates for the high temperature fatigue conditions.

Modelling short fatigue crack growth in a heat-treated low-alloy steel

Abstract Fatigue tests have been conducted both in laboratory air and using an intermittent air/corrosion fatigue sequential cycling technique. All tests were performed on smooth specimens made from a quenched and tempered steel and subjected to fully reversed torsional loading. Crack initiation and growth behaviour was recorded using a surface replication technique. Debonding at the metal matrix/ inclusion interface appears to be the main cause of the formation of short cracks. The growth of these short cracks dominates the fatigue lifetime, being significantly influenced by the material microstructure. Empirical models for short and long crack growth were developed by employing elastic plastic fracture mechanics parameters to predict the total fatigue life of a specimen. Later, these crack growth equations derived from air fatigue tests conducted at stresses above the fatigue limit were applied to the crack growth results obtained from intermittent air fatigue/corrosion fatigue tests carried out at sub-fatigue limit stress levels. A reasonable agreement was observed between predicted and experimental crack growth rates

Low cycle fatigue and ductile fracture for Japanese carbon steel piping under dynamic loadings

Dynamic fracture behavior of circumferentially cracked pipe is important to evaluate the structural integrity of nuclear piping from the viewpoint of the LBB concept under seismic conditions. Fracture tests have been conducted for Japanese carbon steel (STS410) circumferentially through-wall cracked pipes that are subjected to monotonic or cyclic bending loads at room temperature. In the monotonic-loading tests, the maximum load to failure increases slightly with increasing loading rate. The failure cycles can be expressed simply by ratio of the load amplitude to the plastic collapse load. Fracture analysis has been also conducted to model the pipe tests. A new equation for calculating ΔJ for a circumferentially through-wall cracked pipe subjected to bending has been proposed. The failure cycles under cyclic loads are satisfactorily evaluated using an elastic-plastic fracture mechanics parameter ΔJ.

Analysis of fracture mechanics parameters for a surface cracked plate using a nonlinear line-spring boundary element method

In this paper a nonlinear line-spring boundary element method (LSBEM) is proposed and the associated theoretical analysis is described. Numerical estimates of elastic-plastic fracture mechanics parameters for a surface cracked plate are carried out to verify the proposed method. The solutions obtained by nonlinear LSBEM indicate that the proposed method is economic and suitable for implementation on a personal computer.

Finite element study on size requirement for stress intensity factor characterization under biaxial loading

The size requirement for applying the stress intensity factor K I under biaxial loading in plane strain and plane stress conditions is studied by performing a two-dimensional elastic-plastic finite element analysis. The extent to which K I is validly used is determined by comparing the energy release rate G, a linear elastic fracture mechanics parameter, with the J-integral, an elastic-plastic fracture mechanics parameter. The result shows that the minimum value of the remaining uncracked ligament and the crack length for ensuring K-controlled crack tip characteristics is (0.5∼1.0)(K I/σ ys )2, where σ ys is yield stress depending on the load biaxiality, while ASME suggests 2.5(K I/σ ys )2 for uniaxial loading.

Low-cycle fatigue life prediction of circumferentially notched component in terms of elastic-plastic fracture mechanics.

The elastic-plastic stress analysis was made by the finite element method. The surface crack growth rate, da/dN, was analyzed in terms of the elastic-plastic fracture mechanics parameters of the J-integral range, ΔJ and the strain intensity factor range, ΔKε, which were estimated in association with the stress and strain gradients produced in the cross section of the notched specimen. The low-cycle fatigue life for the crack propagation, Nc, was calculated by combining the cyclic stress-strain curve and the crack growth law expressed by the da/dN vs. ΔJ and da/dN vs. ΔKε relations. The calculation based on the fracture mechanics parameters determined from the stress-strain response at the notch root leads to a shorter life in the more sharply notched specimen under the lower stress condition. Meanwhile, the fracture mechanics parameters associated with the stress and strain gradients in the cross section of the notched specimen give a good estimation of the life prediction.

Elastic-plastic models of surface cracks in tensile panels

The surface crack is a common flaw in structures and vessels, and its elastic characterization has been studied extensively as reviewed in Ref. 1 and its references. Elastic-plastic fracture-mechanics (EPFM) technology can be used to characterize surface cracks in tough materials. Two EPFM aprameters are commonly used: the crack-tip-opening displacement (CTOD) and the three-dimensionalJ integral. This paper draws on a series of studies2–11 at the National Bureau of Standards related to the development and verification of analyticalmodels for the calculation of EPFM parameters in surface-cracked tensile panels. The models previously verified for pipeline steel plates4–7 are used to calculate the crack-mouth-opening displacement (CMOD) andJ for surface cracks in welded-steel specimens.

き裂近傍の応力・ひずみ場を用いたＪ積分の測定 画像処理の応用

Currently, J-integral proposed by Rice is one of the most effective elastic-plastic fracture mechanics parameters. However, only a few experimental method, which restrict specimen's shape, have been developed for the evaluation of the J-integral. Some of them are Rice's formula for three point bend specimens, Merkle-Corten's formula for CT specimens and so on, which utilize a load vs. Load-point-displacement curve. The others are strain gauge methods, in which elastic strains around a crack are measured by many strain guages, and the J-integral is calculated by a contour integration technique.In this study, we propose a new measuring method of the J-integral for arbitrarily shaped specimens. In this method, the displacement field in an elastic-plastic region near a crack tip is measured by a computer picture processing technique. Then the strain field is calculated by differentiating the displacement field, and the corresponding stress field is calculated using the multi-axial stress-strain relation of the deformation theory of plasticity. Finally the J-integral is evaluated through a contour integration technique. Since the present method directly measures the displacement field near the crack tip and evaluates the J-integral in the similar fashion to the numerical analyses, it can be applied to arbitrarily shaped specimens.In this paper, after summarizing the displacement measurent process by the computer picture processing, the calculation method of the J-integral is described. Then the accuracy and applicability of the present method is discussed in detail by comparing it with the conventional procedure based on Merkle-Corten's formula in a tensile experiment of CT specimen.

Characterization of the sub-critical crack growth of low alloy steels in a hydrogen environment by means of a acoustic-emission.

Slow strain rate tests (SSRT) have been carried out using precracked compact tension specimens of low alloy steels in purified hydrogen gas at ambient temperature. By the use of elastic-plastic fracture mechanics parameters, the influence of hydrogen gas on sub-critical crack growth has been investigated in terms of the J-value at the onset of crack extension and also from a view point of fracture modes. Acoustic-Emission (AE) during the SSRT tests has been monitored to clarify the cracking behavior in hydrogen gas and by mechanical tearing. In a hydrogen gas environment, it is clearly shown that a crack initiates and propagates in a quasi-cleavage manner until applied the J value reaches J1c and after that the fracture mode changes to mixture of ductile dimple and quasi-cleavage. This result suggests that mechanical tearing occurs at J-values greater than J1c even in a hydrogen environment. In SA 533 B steels, the AE activity showed two energy peaks with respect to loading levels, whose origins are attributable to the onset of quasi-cleavage fracturing caused by the environment and to the onset of mechanical tearing.

An evaluation of crack growth in low cycle fatigue accompanied by ratchet deformation in terms of elastic-plastic fracture mechanics.

Center-cracked specimens of JIS S35C and SUS 304 steels were low-cycle fatigued under test conditions accompanies by ratchet deformation, and crack opening displacement, crack closure and crack growth were examined. Then, crack growth rates were analyzed in terms of elastic-plastic fracture mechanics parameters. The effect of ratchet deformation on crack growth rate appeared in the log da/dN vs. log ΔJ plot in the way of accelerating crack growth rate, where da/dN is crack growth rate and ΔJ is cyclic J-integral range. Such an acceleration of crack growth rate occurred under test conditions satisfying both of σmaxnet>σy and U = 1.0, where σmaxnet, σy and U are maximum net cross-section stress, static yield stress and crack opening load range ratio, respectively. The parameter of ΔJ(1-Φmint/Φmaxt)0.3 was proposed for evaluating the crack growth rate on a ΔJ basis, where the minimum and maximum values of crack tip opening displacement were denoted by Φmint and Φmaxt. The da/dN plotted against this parameter forms a straight line independent of ratchet deformation on double logarithmic controlling the croak growth rate under test condition including ratchet deformation.

A procedure for the experimental assessment of the [formula omitted] by means of specimens of different geometries

It is necessary to determine the elastic-plastic fracture mechanics parameter J on specimens of different loading mode and size in order to further clarify the dependence of the J- integral on these parameters. Using the fundamental equations of linear-elastic fracture mechanics and fully plastic material behaviour, the factors η el and η pl for the experimental evaluation of the J- integral for different specimen geometries are determined. The basic equations used are summarised, the relations obtained for η el and η pl are plotted. The application of these relations in the testing of large scale specimens of different specimen type and size shows the variation of the J- integral over the stable crack growth.

Crack Initiation and Growth Analysis by Direct Optical Observation during SSRT in High Temperature Water

Abstract The stress corrosion cracking behavior during the slow strain rate test (SSRT) has been investigated in high temperature water. SSRTs were performed on center-notched thin plate specimens of sensitized Type 304 stainless steel. A direct optical observation system consisting of single crystal sapphire windows was employed to separate the SCC into an initiation and a growth stage, and to measure the crack growth rate. Effects of the extension rate, test temperature, and dissolved oxygen concentration on the crack initiation and growth were examined. The crack growth data were analyzed with different variables, including the elastic plastic fracture mechanics parameters. The best interpretation of the crack growth rates is obtained by plotting them vs the time differential of J-integral, which is an estimate of the crack tip deformation rate during SSRT.

The Inelastic Line-Spring: Estimates of Elastic-Plastic Fracture Mechanics Parameters for Surface-Cracked Plates and Shells

Recent studies of the mechanics of elastic-plastic and fully plastic crack growth suggest that such parameters as the J-integral and the crack tip opening displacement can, under certain conditions, be used to correlate the initiation and early increments of the ductile tearing mode of crack growth. To date, elastic-plastic fracture mechanics has been applied mainly to test specimen geometries, but there is a clear need for developing practical analysis capabilities in structures. In principle, three-dimensional elastic-plastic finite element analysis could be performed, but, in fact, such analyses would be prohibitively expensive for routine application. In the present work, the line-spring model of Rice and Levy [1-3] is extended to estimate the J-integral and crack tip opening displacement for some surface crack geometries in plates and shells. Good agreement with related solutions is obtained while using orders of magnitude less computing time.