Crack Tip Constraint Research Articles

Material constraint parameters for the assessment of shallow defects in structural components—Part I: Parameter solutions

This Part I paper describes the numerical derivation of a series of material constraint parameters appropriate for the prediction of constraint effects on cleavage fracture toughness in ferritic steels. A series of Lookup Tables and functions are derived which enable parameters to be readily established based on a knowledge of the yield and work hardening behaviour of the material at the temperature of interest and the Beremin cleavage fracture model parameter m. These are provided for use where crack-tip constraint is quantified either in terms of the elastic T-stress normalised by the yield stress or the elastic–plastic Q-stress. Methods for the derivation of these values are described and illustrated with respect to a mild steel plate tested at −50 °C. A comparison of the predicted variation of cleavage fracture toughness with decreasing constraint has been shown to provide a conservative description of the fracture toughness data. The companion Part II paper describes the use of the tables within the context of the R6 defect assessment procedure to assess the behaviour of a cruciform specimen containing a shallow crack under equibiaxial loading.

A review of the effect of a/W ratio on fracture toughness (II) —experimental investigation in LEFM

Many experimental investigations have previously been performed and recently done on different shipbuilding structural steels where the specimens size and crack depth/specimen width (a/W) were varied. A series of interesting results have been gained. It is worthwhile to have a review on the effect of a/W ratio on fracture toughness, and further theoretical analysis is necessary. In this paper, experimental work in elasticplastic fracture mechanics (EPFM) was discussed. Tests had been carried out on 10 kinds of strength steels. Results showed that Ji and δ1 values increased with decreasing a/W when a/W 0.3, the toughness was found to be independent of a/W. Slip line field analysis shows that for shallow cracks, the hydrostatic stress is lower than that from standard deeply cracked bend specimen which develops a high level of crack tip constraint, provides a lower bound estimate of toughness, and will ensure an unduly conservative approach when applied to structure defects especially if initiation values of COD/J-integral are used.

Crack growth in a new nickel-based superalloy at elevated temperature

Crack growth at elevated temperature has been examined in a new fine-grained nickel-based superalloy under triangular, fast-slow, slow-fast, dwell and sustained loading conditions at 650 and 725∘C. The effect of loading waveform seems to be minimal for base frequencies over 0.01 Hz with a mixture of time and cycle dependent crack growth observed for all but the fast-slow waveform, where the crack growth remained cycle-dependent and the crack growth rate mostly constant. For base frequencies less than 0.01 Hz, crack growth under dwell load clearly accelerated and the crack growth rates were comparable with those under sustained load. Creep contribution was found to be negligible while crack tip constraint may be relevant to the out-of-plane crack growth observed under predominantly sustained load conditions.

Fracture mechanics safety analysis of components based on fracture mechanics characteristics combined with multiaxiality of the stress state

Currently several parameters for quantifying the crack tip constraint in fracture mechanics specimens as well as in cracked components are under discussion. The parameters are briefly described and compared on the basis of analyses of fracture mechanics specimens. The parameters are able to show loss of constraint, but for high constraint situations the predictions are inconsistent. It is shown that one parameter is able to explain different fracture modes at the same load level for a small scale fracture mechanics specimen and a large scale component like specimen.

Correlation of fracture behavior in high pressure pipelines with axial flaws using constraint designed test specimens––Part I: Plane-strain analyses

This work presents a numerical investigation of crack-tip constraint for SE(T) specimens and axially surface cracked pipes using plane-strain, nonlinear computations. The primary objective is to gain some understanding of the potential applicability of constraint designed fracture specimens in defect assessments of pressurized pipelines and cylindrical vessels. The present study builds upon the J–Q approach using plane-strain solutions to characterize effects of constraint on cleavage fracture behavior for the analyzed fracture specimens and cracked pipes. Under increased loading, each cracked configuration follows a characteristic J–Q trajectory which enables comparison of the corresponding driving force curve in the present context. A key outcome of this investigation is that toughness data measured using SE(T) specimens appear more applicable for cleavage fracture predictions of pressurized pipelines and cylindrical vessels than standard, deep notch fracture specimens under bend loading. The results provide a strong support for use of constraint-designed SE(T) specimens in fracture assessments of pressurized pipes and cylindrical vessels.

Increased Temperature Margins Due to Constraint Loss

Enhanced levels of toughness due to loss of crack tip constraint have been related to temperature shifts in the ductile–brittle transition curve. An argument to quantify the temperature shift is developed using the self-similarity of near-tip stress fields under contained yielding combined with scaling techniques developed by Dodds and co-workers (12) for cleavage. This allows the temperature changes which give the same stress field at failure in constrained and unconstrained fields to be determined. The procedure is illustrated using the data of Sherry et al. (3) for an A533B pressure vessel steel. The results are consistent with empirical expressions proposed by Wallin (4), and enable a discussion of the micromechanics of cleavage.

Prediction of cleavage fracture in ferritic steels: a modified Weibull stress model

A modified three-parameter Weibull stress model is proposed in this paper, which considers the conjoint influences of plastic strain and stress triaxiality in the region of the crack tip. The model parameters are calibrated using two sets of fracture toughness data obtained from specimens exhibiting different constraint conditions at fracture, namely, deep-cracked compact tension specimens and shallow-cracked single-edge bending specimens. The master curve method is used to relate the fracture toughness data obtained at the different test temperatures. The calibrated Weibull stress model is then used to predict the cumulative failure probability of cleavage fracture for specimens containing surface cracks and loaded in varying combinations of tension and bending. The model predictions capture the measured toughness distributions for both bolt-loaded and pin-loaded specimens, while concurrently revealing a strong influence of the difference in crack tip constraint, due to different mode of loading, on probability of failure by cleavage. This effectively proves the applicability of the modified model for predicting cleavage-type fracture in ferritic steels.

Effect of biaxial loads on elastic-plastic J and crack tip constraint for cracked plates: finite element study

Based on detailed two-dimensional (2-D) and three-dimensional (3-D) finite element (FE) analyses, this paper attempts to quantify in-plane and out-of-plane constraint effects on elastic-plastic J and crack tip stresses for a plate with a through-thickness crack and semi-elliptical surface crack under positive biaxial loading. For the plate with a through-thickness crack, plate thickness and relative crack length are systematically varied, whereas for the plate with a semi-elliptical surface crack, the relative crack depth and aspect ratio of the semi-elliptical crack are systematically varied. It is found that the reference stress based approach for uniaxial loading can be applied to estimate J under biaxial loading, provided that the limit load specific to biaxial loading is used, implying that quantification of the biaxiality effect on the limit load is important. Investigation on the effect of biaxiality on the limit load suggests that for relatively thin plates with small cracks, in particular with semi-elliptical surface cracks, the effect of biaxiality on the limit load can be neglected for positive biaxial loading, and thus elastic-plastic J for a biaxially loaded plate could be estimated, assuming that such plate is subject to uniaxial load. Regarding the effect of biaxiality on crack tip stress triaxiality, it is found that such effect is more pronounced for a thicker plate. For plates with semi-elliptical surface cracks, the crack aspect ratio is found to be more important than the relative crack depth, and the effect of biaxiality on crack tip stress triaxiality is found to be more pronounced near the surface points along the crack front.

Prediction of stable crack growth in surface cracked plate of Aluminum 7050 alloy

To simulate stable crack growth, three-dimensional finite element analysis using the constant Crack Tip Opening Angle (CTOA) fracture criterion was performed for a thin plate made of Aluminum 7050 alloy. The critical CTOA value was experimentally obtained by the Rubber Impression Method, which directly measures the three-dimensional crack profiles by inserting the gel-state silicon rubber into the crack, and taking out the solid-state rubber later. From the microscopic observation from the broken specimen, it was found that, as the crack extends, the amount of crack growth near the free surface is more than that in the depth/thickness direction, which creates the special tunneling, e.g., canoe-shaped crack extension. For the numerical simulation, the surface-cracked plate was analyzed by quasi-static elastic-plastic finite strain analysis with the node release and the reloading technique. Consistent with experimental observations, numerical simulation with constant CTOA fracture criteria produced tunneling of a surface crack, but the shape of the crack front deviated from the experimental crack front as the free surface was approached. To address the local crack tip constraint effect on the stable crack growth, various fracture parameters - crack tip triaxiality, equivalent plastic strain, and void growth ratio as the crack extends – were also investigated.

Prediction of Failure Behavior for Nuclear Piping Using Curved Wide-Plate Test

One important element of the Leak-Before-Break analysis of nuclear piping is how to determine relevant fracture toughness (or the J-resistance curve) for nonlinear fracture mechanics analysis. The practice to use fracture toughness from a standard C(T) specimen is known to often give conservative estimates of toughness. To improve the accuracy of predicting piping failure, this paper proposes a new method to determine fracture toughness using a nonstandard testing specimen, curved wide-plate in tension. To show validity of the proposed curved wide-plate test, the J-resistance curve from the full-scale pipe test is compared with that from the curved wide-plate test and that from C(T) specimen. It is shown that the J-resistance curve from the curved wide-plate tension test is similar to, but that from the C(T) specimen is lower than, the J-resistance curve from the full-scale pipe test. Further validation is performed by investigating crack-tip constraint conditions via detailed three-dimensional finite element analyses, which shows that the crack-tip constraint condition in the curved wide-plate tension specimen is indeed similar to that in the full-scale pipe under bending.

A method for measuring mode I crack tip constraint under static and dynamic loading conditions

A novel experimental technique for measuring crack tipT-stress, and hence in-plane crack tip constraint, in elastic materials has been developed. The method exploits optimal positioning of stacked strain gage rosette near a mode I crack tip such that the influence of dominant singular strains is negated in order to determineT-stress accurately. The method is demonstrated for quasi-static and low-velocity impact loading conditions and two values of crack length to plate width ratios (a/W). By coupling this new method with the Dally-Sanford single strain gage method for measuring the mode I stress intensity factorK I , the crack tip biaxiality parameter\(\beta = T\sqrt {{{\pi a} \mathord{\left/ {\vphantom {{\pi a} K}} \right. \kern-\nulldelimiterspace} K}} \) is also measured experimentally. Complementary small strain, static and dynamic finite element simulations are carried out under plane stress conditions. Time histories ofK I andT-stress are computed by regression analysis of the displacement and stress fields, respectively. The experimental results are in good agreement with those obtained from numerical simulations. Preliminary data for critical values ofK I and β for dynamic experiments involving epoxy specimens are reported. Dynamic crack initiation toughness shows an increasing trend as β becomes more negative at higher impact velocities.

A Method for Measuring Mode I Crack Tip Constraint under Static and Dynamic Loading Conditions

A Method for Measuring Mode I Crack Tip Constraint under Static and Dynamic Loading Conditions

Characterization of crack-tip field and constraint for bending specimens under large-scale yielding

Elastic-plastic crack-tip fields and constraint levels in bending specimens under large-scale yielding (LSY) are examined. The J−A2 three-term solution is modified by introducing an additional term caused by the global bending. Three different methods, i.e. two-point matching, constant A2 and elastic stress estimation method, are proposed to determine the fourth term. It is shown that the elastic stress estimation method is the simplest, yet effective, in that the fourth term can be derived from the strength theory of materials and the concept of plastic hinge, and effectively quantifies the contribution of the global bending moment on the crack-tip field. Consequently, the modified J−A2 solution, with the inclusion of the correction for global bending, does not introduce any new parameter. The two parameters remain as the loading (J and M) and the constraint level (A2). To validate the present solution, detailed finite element analyses (FEA) were conducted for a Three Point Bend (TPB) specimen with a/W=0.59 in A285 steel, and Single Edge Notched Bend (SENB) specimen subjected to pure bending with a/W=0.5 in A533B steel at different deformation levels ranging from small-scale yielding (SSY) to LSY. Results show that the modified J−A2 solution matches fairly well with the FEA results for both TPB and SENB specimens at all deformation levels considered. In addition, the fourth stress term is (a) proportional to the global bending moment and inversely proportional to the ligament length; (b) negligibly small under SSY; and (c) significantly large under LSY or fully plastic deformation. Accordingly, the present model effectively characterizes the crack-tip constraint for bending dominated specimens with or without the large influence from the global bending stress on the crack-tip field.

Effect of Constraint on the Initiation of Ductile Fracture in Shear Loading

Research studies for mode I cracks have shown that fracture toughness or the critical value of J for fracture initiation, Jcrit is not merely a material property but depends also on the geometry and loading configurations. The geometry dependency of fracture toughness can be attributed to the effect of the crack tip constraint. In this paper, the constraint effect is studies for the initiation stage in mode II ductile crack growth. Two major mechanisms of ductile fracture: 'void growth and coalescence' and 'shear band localization and de-cohesion' are considered. A boundary layer model is simulated using the finite element method and the effect of far-filed T-stress on the relevant stress parameters near the crack tip is studied. It is shown that the initiation of the ductile crack growth in mode II is influenced significantly by T for the mechanism of void growth and coalescence and is insensitive to T for the mechanism of shear localisation and de-cohesion.

흰 광폭평판 시험을 이용한 원자력 배관의 파괴거동예측

One important element of the Leak-Before-Break analysis of nuclear piping is how to determine relevant fracture toughness (or the J-resistance curve) for nonlinear fracture mechanics analysis. The practice to use fracture toughness from a standard C(T) specimen is known to often give conservative estimates of toughness. To improve the accuracy, this paper proposes a new method to determine fracture toughness using a non-standard testing specimen, curved wide-plate in tension. To show validity of the proposed curved wide-plate test, the J-resistance curve from the full-scale pipe test is compared with that from the curved wide-plate test and that from the C(T) specimen. It is shown that the J-resistance curve form the curved wide-plate tension test is similar to, but that from the C(T) specimen is lower than, the J-resistance curve from the full-scale pipe test. Further validation is performed by investigating crack-tip constraint conditions via detailed 3-D FE analyses, which shows that the crack-tip constraint condition in the curved wide-plate tension specimen is indeed similar to that in the full-scale pipe under bending.

Plastic dissipation in fatigue crack growth under mixed-mode loading

A new theory of fatigue crack growth in ductile solids has recently been proposed based on the total plastic energy dissipation per cycle ahead of the crack. This and previous energy-based approaches in the literature suggest that the total plastic dissipation per cycle can be closely correlated with fatigue crack growth rates under mode I loading. The goal of the current study is to extend the dissipated energy approach to steady-state crack growth under mixed-mode I/II loading conditions, with ultimate application to cyclic delamination of ductile interfaces in layered materials. The total plastic dissipation per cycle is obtained herein by 2-D elastic–plastic finite element analysis of a stationary crack in a general mixed-mode specimen geometry under constant amplitude loading. Both elastic–perfectly plastic and bilinear kinematic hardening constitutive behaviors are considered, and numerical results for a dimensionless plastic dissipation per cycle are presented over the full range of relevant mechanical properties and mixed-mode loading conditions. Results provide substantial insight into the effects of crack-tip constraint, material hardening behavior and applied mode–mix ratio on the dissipated energy during fatigue crack growth.

Experimental and numerical modelling of ductile crack propagation in large-scale shell structures

This paper presents a combined experimental–numerical procedure for development and calibration of macroscopic crack propagation criteria in large-scale shell structures. A novel experimental set-up is described in which a mode-I crack can be driven 400 mm through a 20(+) mm thick plate under fully plastic and controlled conditions. The test specimen can be deformed either in combined in-plane bending and extension or in pure extension. Experimental results are described for 5 and 10 mm thick aluminium and steel plates. By performing an inverse finite-element analysis of the experimental results where the simulated crack growth is forced to correspond to the experimental observations, empirical criteria for ductile crack propagation emerge very clearly. Using the experiments with edge crack specimens (ECS) in combined in-plane bending and extension, crack propagation criteria are developed for steel and aluminium plates, mainly as curves showing the critical element deformation versus the shell element size. These derived crack propagation criteria are then validated against a separate set of experiments considering centre crack specimens (CCS) which have a different crack-tip constraint. The applicability of the often-used equivalent strain criterion is discussed versus a more rationally based criterion which takes into account the stress tri-axiality. A large-scale grounding experiment is also simulated showing very good agreement with measurements. The performance of the proposed model is in general good and it is believed that the presented results and experimental–numerical calibration procedure can be of use in practical finite-element simulations of collision and grounding events with the use of shell elements. As discussed, the paper provides a clean framework for further development of macroscopic crack propagation criteria in large-scale plate structures.

The effect of plastic constraint on the initiation of ductile tears in shipbuilding structural steels

In this paper, the effect of plastic constraint on the initiation of ductile tears in four different shipbuilding structural steels has been experimentally studied by measuring the J-integral and crack opening displacement COD at initiation in three-point bend specimens with deep and shallow notches. Experimental results of seven groups of different strength alloy steels show that both δi and Ji values of ductile tear from the shallow crack specimens which have less constraint flow field are significantly higher than those of deeply notched specimens. Slip-line-field analysis shows that, for shallow crack, the hydrostatic stress is lower than that from standard deeply cracked bend specimen, which develops a high level of crack tip constraint, provides a lower bound estimate of toughness, and will ensure an unduly conservative approach when applied to structural defects, especially if initiation values of COD and J-integral are used.

A two-parameter framework to describe effects of constraint loss on cleavage fracture and implications for failure assessments of cracked components

This study builds upon the J-Q approach to characterize constraint effects on cleavage fracture behavior of cracked structural components. Discussions emphasize features of current two-parameter fracture methodologies which extend the limits of applicability of single parameter fracture approaches when LSY effects prevail. Inclusion of the second parameter (Q) in failure assessment procedures leads to the construction of experimentally derived fracture toughness loci, rather than conventional, single-valued definitions of toughness. The plan of the article is as follows. First, the notion of crack tip constraint and its connection with SSY reference fields is introduced. This is followed by a brief description of the J-Q theory to define the hydrostatic parameter Q. The paper then addresses representative numerical solutions which provide J-Q trajectories for common fracture specimens under bend and tensile loading, including deep and shallow crack SE(B) and SE(T) specimens. These analyses, when taken together with previous works, provide a fairly extensive body of results against which the robustness of the J-Q methodology can be weighed.

Interaction of hydrogen with crack-tip plasticity: effects of constraint on void growth

This study describes the results of finite element simulations to explore the effects of crack-front constraint variations on the distributions of hydrogen, stress, and plastic strain fields ahead of a blunting crack tip under plane-strain, small-scale yielding (SSY) conditions. Application of the non-singular T-stress in the SSY model provides a wide variety in crack tip constraint. The calculated near-tip fields drive the classical Rice and Tracey model for void growth that here couples the microscale effects of hydrogen on the local strain–stress values with this key mechanism of ductile fracture. The numerical results for a high solubility niobium system indicate that in the absence of hydrogen-induced softening, hydrogen-induced dilatation increases (decreases) void growth in low (high) constraint configurations—a result opposite of that in the absence of hydrogen. In the presence of hydrogen-induced softening, the relative resistance to ductile fracture of low and high constraint configurations depends on the initial hydrogen concentration and on the associated amount of softening. In all cases, the present model of hydrogen degradation by void growth argues for the existence of a fracture process strongly influenced by the plastic strain.