Crack Tip Constraint Research Articles

Effect of Residual Stresses on Ductile Crack Growth in Pipeline Steel

In this study, the effects of residual stresses on the ductile crack growth resistance was investigated using single-edge-notched bending (SENB) and single-edge-notched tension (SENT) specimens as well as axisymmetric model. Weld residual stresses were introduced by the so-called eigenstrain method. The crack tip opening displacement (CTOD) and constraint parameter R were calculated for different specimens and residual stresses. Results show that the residual stresses slightly reduced the ductile crack growth resistance. However, crack tip constraint R elevated with the increase of residual stress.

Unified correlation of in-plane and out-of-plane creep constraints with creep crack growth rate

In this paper, the equivalent creep strain distributions ahead of crack tips in SEN(B), SEN(T) and M(T) specimens with different in-plane and out-of-plane constraints were calculated by extensive finite element analyses, and the creep crack growth (CCG) rates of these specimens were simulated over a wide range of C* by using stress dependent creep ductility and strain rate model in a ductility exhaustion based damage model. The capability and applicability of the constraint parameter Ac based on crack-tip equivalent creep strain for characterizing both in-plane and out-of-plane creep crack-tip constraints and establishing a unified correlation with CCG rate of a steel were investigated. The results show that with increasing constraints, the CCG rate increases, and the effect of out-of-plane constraint on CCG rate is more obvious than that of in-plane constraint. The CCG rate of high constraint specimen geometry (such as SEN(B)) is more sensitive to the out-of-plane and in-plane constraints than that of low constraint specimen geometry (such as M(T)). The parameter Ac is a unified characterization parameter of in-plane and out-of-plane creep constraints for the different specimen geometries. Base on the parameter Ac, the unified correlation formulas of in-plane and out-of-plane constraints with CCG rate of the steel have been obtained, and they are independent on the choices of the standard specimen. The unified correlation formulas may be used in constraint-dependent CCG life assessments of high-temperature components (such as pressure vessels and pipes) with any in-plane and out-of-plane constraint levels.

Review of fracture toughness test methods for ductile materials in low-constraint conditions

Fracture toughness is an important material property to describe the ability of a material containing a crack to resist fracture, and often characterized by the fracture parameters of J-integral or crack-tip opening displacement (CTOD) for ductile cracks. ASTM, BSI and ISO have developed their own standard test methods for measurement of initiation toughness and resistance curves in terms of J and CTOD using bending dominant specimens. Such bending specimens are typically designed with deep cracks to maintain high constraint conditions at the crack tip so as to determine conservative fracture toughness or resistance curve for the test material.Actual cracks in pressure vessels and welds are often shallow ones and dominated by tensile forces, leading to low crack-tip constraint conditions and rising resistance curves. As a result, the standard resistance curves could be overly conservative for a shallow crack in real structures. To determine more realistic fracture toughness for ductile cracks in low-constraint conditions, many experimental and analytical methods have been developed in the recent decades. This paper presents a critical review on fracture toughness test methods for standard and non-standard specimens, including (1) ASTM, BSI and ISO standard test methods for high-constraint specimens, (2) constraint correction methods using high and low-constraint specimens for developing a family of constraint-dependent resistance curves, and (3) direct test methods for low-constraint specimens of single edge-notched tension (SENT) or shallow-cracked bending specimens. Basic concepts, test methods, estimation equations, test procedures, limitations, historical effects and recent progresses are reviewed.

Mixed mode fracture toughness testing of PMMA with different three-point bend type specimens

Abstract Mixed mode fracture behavior of PMMA, was studied experimentally and theoretically using four different test configurations and with different crack types. Although all the test samples were subjected to three-point bend loading but completely different mixed mode fracture behaviors were observed for the tested samples. For each test configuration, especial mixed mode fracture toughness curves were obtained for fracture initiation direction and fracture toughness in the whole ranges of mixed mode I/II loading conditions. The level of crack tip constraint in the tested samples (which is related to the stress intensity factors ( K ) and the T -stress) was used as the main affecting parameter for predicting the mixed mode fracture results based on a two parameter ( K-T ) fracture theory. It was observed that the loss of crack tip constraint in the tested samples increases the mixed mode fracture resistance and decreases the fracture initiation direction and vice versa.

Examination of methods for the treatment of constraint effects within the FAD approach

This paper presents results of a study focusing on the effect of crack-tip constraint on the fracture behaviour of metallic materials. The principal goal is to validate two analytical methods for the consideration of constraint effects in engineering failure assessment – the R6/FITNET approach and the IST methodology. Those methods are briefly reviewed and applied to analyse available experimental data obtained in fracture tests on various cracked geometries and for two materials. Comparing to the conventional route which incorporates fracture toughness values derived in tests on highly constrained standard specimens, both methods provide an improved (less conservative) failure assessment. However, the assessment results from both methods are shown to be strongly dependent on the Weibull exponent which determination requires a certain level of expertise in the field of fracture mechanics. Since non-conservative results are possible when assuming high values, care should be taken to ensure a proper application of the respective assessment methodology.

The effect of subcritical ductile crack growth on cleavage fracture probability in the transition regime using continuum damage mechanics simulation

There are compelling experimental evidences that demonstrate a significant effect of specimen size, a/W ratio and ductile tearing on cleavage fracture toughness values (KJc) measured in the ductile-to-brittle transition region of materials such as ferritic steels. In this work, the influence of ductile tearing and constraint loss on Weibull stress and failure probability in ductile to brittle transition (DBT) region is investigated. The study was carried out using a modeling approach that combines the modified Beremin model (MBM) for cleavage fracture and the Bonora damage model (BDM) for ductile tearing. Here, CT and SEB, with deep and shallow crack, specimen geometries, which are characterized by different crack tip constraint, have been analyzed. Results show that the occurrence of ductile crack growth in the mid-to-upper transition region affects the nature of the stress field in the region surrounding the crack tip in terms of maximum principal stress peak, its spatial gradient – which has a direct consequence on the calculated Weibull stress – and stress triaxiality, which affects the constraint loss. This combination of effects leads to much lower fracture toughness values that those predicted by not considering ductile crack growth.

Application of R6 failure assessment method to obtain fracture toughness

Determination of fracture toughness, J–R curve from experimental test results requires certain geometry factors. These expressions of geometry factors are available for standard geometries and loading configurations. However, these expressions are not available in open literature for complex geometries and loading configurations. R6 Failure Assessment Diagram (FAD) methodology is used for assessment of failure in the failure regime of cleavage fracture, ductile crack initiation and plastic collapse. In this paper, the use of this method is extended to estimate the entire J–R curve from the fracture test results. Under comprehensive test programme initiated at RSD (Reactor Safety Division), BARC (Bhabha Atomic Research Centre), large numbers of straight pipes with circumferential cracks have been tested. These experimental results have been used to calculate material J–R curves using R6 FAD, which are subsequently compared with conventionally calculated J–R curves using η factor approach. It can be observed that the J–R curves calculated using both approaches are in good agreements for three out of total six pipes studied. Further, the segregation of J–R curves based on the size of pipes has been studied in the light of prevalent crack tip constraints. Here, crack tip constraints are calculated in terms of stress triaxiality parameters ‘Q’ for all pipes. It can be noted that the J–R curves for 8in. pipes are ‘toughened’ because they have lower constraints than 16in. pipes. This establishes the theory that high/low crack tip constraint causes low/high material fracture toughness.

Creep constraint analysis and constraint parameter solutions for circumferential surface cracks in pressurized pipes

Creep crack-tip constraints for inner circumferential surface cracks in pressurized pipes have been analyzed by three-dimensional finite element method and the constraint parameter R∗ solutions have been obtained for different pipe geometries and crack sizes. It has been shown that the constraint level of circumferential cracks is lower than that of axial cracks, and the constraint effects need to be considered in creep life assessments of pressurized pipes. The benefits from incorporating constraint effects are greater for the circumferential cracks than for the axial cracks and for the shallower and shorter cracks than for the deeper and longer cracks.

Numerical Prediction of Creep Crack Growth Rate in Cr-Mo-V Steel for Specimens with Different Constraints

The creep crack growth rate in Cr-Mo-V steel has been numerically predicted for specimens with different constraints for a wide range ofC*by using stress dependent creep model and ductility, and the simulatedda/dt-C*curves were compared and analyzed with experimental data. The results show that the simulatedda/dt-C*curves agree well with experimental data. At low and transitionC*regions, the crack-tip constraint has obvious effect on CCG rates, while at highC*region it almost has no effect. With increasing constraint, the CCG rates and transition region size onda/dt-C*curves increase due to higher stress traxiality ahead of crack tip and stress-regime dependent creep ductility. If the extrapolation CCG rate data of standard high constraint CT specimen from highC*region (above the turning point 2) or from transitionC*region are used in life assessments of the components with various constraints at lowC*region (below the turning point 1), the non-conservative or excessive conservative results may be produced. Therefore, the CCG rate data for considering constraint effect should be obtained for a wide range ofC*by long-term laboratory tests or numerical predictions using the stress dependent creep model and ductility.

Elastic-Plastic Constraints Analysis for Hole-Edge Crack

This paper mainly conducts an elastic-plastic constraint analysis on rectangular plate specimens with hole-edge crack under remote uniaxial uniformly distributed load by using J-A2 elastic-plastic fracture theory. In order to analyze the effect of orifice on elastoplastic stress field of hole-edge crack tip, this paper calculates a series of round hole-edge crack, diamond hole-edge crack and corresponding pure crack models. The interference effects of the orifice shape on elastic-plastic J integral and crack constraint parameter A2 are discussed. The results show that: the orifice has an amplification effect on the fracture driving force (J-integral), and this amplification effect in elastic-plastic is smaller than that in elastic; the orifice has a shielding effect on the crack tip constraint (A2 parameter), and this shielding effect gradually weaken with the crack increasing.

Understanding and accounting for the effects of residual stresses on cleavage fracture toughness measurements in the transition temperature regime

Secondary self-balancing stresses exist in structural components due to manufacturing processes, e.g. welding. When a defect is present, such secondary stresses will influence both the local crack driving force and the level of crack-tip constraint. Fracture mechanics specimens machined from welded components can also retain significant residual stresses, and these can influence the measurement of fracture toughness. This paper describes the results of an experimental and numerical programme aimed as quantifying the effect of residual stresses on cleavage fracture toughness measured in deeply-cracked and shallow-cracked fracture mechanics specimens and with a view to correcting the resultant data. The results indicate that the influence of retained residual stresses on cleavage fracture toughness in such specimens can be characterised using two-parameter fracture mechanics.

Characterization and correlation of 3-D creep constraint between axially cracked pipelines and test specimens

Three-dimensional creep crack-tip constraints of axially cracked pipes and conventional test specimens have been characterized and analyzed by a load-independent creep constraint parameter R∗ proposed by authors. An average measure of constraint over the crack front is utilized to correlate the creep constraint between the 3-D axially cracked pipelines and test specimens. It was found that single-edge notched tension specimens provide a closely matched creep crack-tip constraint with axially cracked pipes. The investigation results provide a strong support for use of constraint-designed specimens in creep life assessment of pressurized pipes.

Crack-tip constraint analysis of SENB specimen under creep condition

A higher-order asymptotic C(t)-A2(t)-M approach was used to investigate the crack-tip stress of single edge notched bend (SENB) specimen in a power-law creeping material under plane strain conditions. Comprehensive calculations were made of SENB specimen with a/W = 0.59 by using higher-order asymptotic C(t)-A2(t)-M approach, higher-order asymptotic C(t)-A2(t) approach and finite element analysis; the latter two methods were used to check the constraint significance and the calculation accuracy of C(t)-A2(t)-M approach, respectively. The results show that the stress components σθθ obtained from the higher-order asymptotic C(t)-A2(t)-M solution agreed well with that of finite element analysis, however, which gradually deviated from the results of C(t)-A2(t) approach as the distance far away from the crack tip for small-scale creep stage.

Crack-tip constraint analyses and constraint-dependent LBB curves for circumferential through-wall cracked pipes

The leak-before-break (LBB) concept has been widely applied in the structural integrity assessments of pressured pipes in nuclear power plants. However, the crack-tip constraint effects in LBB analyses and designs cannot be incorporated. In this paper, by using three-dimensional finite element calculations, the modified load-independent T-stress constraint parameter τ* for circumferential through-wall cracked pipes with different geometries and crack sizes has been analyzed under different loading conditions, and the solutions of the crack-tip constraint parameter τ* have been obtained. Based on the τ* solutions and constraint-dependent J–R curves of a steel, the constraint-dependent LBB (leak-before-break) curves have been constructed. The results show that the constraint τ* increases with increasing crack length θ, mean radius Rm and radius–thickness ratio Rm/t of the pipes. In LBB analyses, the critical crack length calculated by the J–R curve of the standard high constraint specimen for pipes with shorter cracks is over-conservative, and the degree of conservatism increases with decreasing crack length θ, Rm and Rm/t. Therefore, the constraint-dependent LBB curves should be constructed to modify the over-conservatism and increase accuracy of LBB assessments.

Delamination effects on fracture behavior of a pipeline steel: A numerical investigation of 3-D crack front fields and constraint

This work addresses a numerical investigation of the crack front fields and effects of crack-tip constraint in conventional fracture specimens with prescribed transverse delamination cracks. One purpose of this study is to conduct a systematic evaluation of delamination effects in side-grooved and plane-sided C(T) and clamped SE(T) fracture specimens, which are commonly utilized in fracture toughness testing of pipeline steels. Another is to quantify the potential coupling influence of specimen geometry and delamination size on crack-tip constraint by means of the J−Q theory thereby providing valuable insight into the effect of delamination cracks on macroscopic fracture behavior in conventional fracture specimens. Laboratory testing of an API 5L X70 steel at room temperature provides the mechanical properties used in the numerical analysis incorporating delamination cracks with varying sizes. Nonlinear finite element analyses of very detailed 3-D finite element models of C(T) and clamped SE(T) fracture specimens for the API X70 pipeline steel enable assessing the effects of prescribed delamination cracks on the crack front fields and constraint with increased deformation levels as characterized by the J-integral. Overall, the present analyses reveal important features of 3-D crack front fields in fracture specimens with a crack-divider delamination that have a direct bearing on the often observed toughness increase in fracture testing of materials with through-thickness anisotropy in mechanical properties.

Structural Integrity Analysis of Cracked Pressure Vessel Welds Using Conventional and Constraint-modified Failure Assessment Diagrams

In this study, four assessment procedures were used for the integrity analysis of the cracked Al alloy pressure vessel welds (PVWs), and the four methods are (1) to use BS 7910 Option 1 that is a conventional procedure, (2) to involve a modification to the FAD but retain the definition of Kr, (3) to retain the FAD but modifie the definition of Kr (4) to use constraint-based FAD and true Kmat values for SENB specimens with different a/W values. The fracture toughness tests were performed for single-edge notched bending (SENB) specimens with different a/W values to obtain the corresponding Kmat values and to determine the relationship between crack tip constraint (via a/W) and fracture toughness. To determine the constraint-based FAD curves, finite element analyses were performed to derive the functional relationships between normalized load and Q-constraint for SENB specimens. The results showed that the predictions using the second and third procedures was in good agreement with the experimental results of residual strength, and that BS 7910 Option 1 procedure was proved to be conservative for the shallow-cracked vessel specimens, and that the fourth method overestimated the residual strength.

Advances in Fracture Toughness Test Methods for Ductile Materials in Low-Constraint Conditions

Fracture toughness is an important material property in the fracture mechanics methods, and often described with the fracture parameters of J-integral and crack-tip opening displacement (CTOD) for ductile cracks. ASTM, BSI and ISO have developed their own standard test methods for measuring initial toughness and resistance curves in terms of J and CTOD using deeply cracked bending specimens. Such specimens are of high crack-tip constraints and give conservative toughness or resistance curves.Actual cracks in pressure vessels and welds are often shallow and dominated by tensile forces, resulting in low crack-tip constraint conditions and rising resistance curves. Thus the standard resistance curves could be overly conservative for a shallow crack in real structures. To obtain more reasonable fracture toughness for ductile cracks in low-constraint conditions, many experimental and analytical methods have been developed in the recent decades. This paper presents a critical technical review of fracture toughness test methods for standard and non-standard specimens, including (1) ASTM, BSI and ISO standard test methods for high-constraint specimens, (2) constraint correction methods for determining a family of constraint-dependent resistance curves, and (3) direct test methods for a low-constraint specimen: single edge-notched tension (SENT) specimen. This includes the basic concepts, basic methods, estimation equations, test procedures, limitations, historical effects, and recent progresses.

Crack-Tip Stress Field of Cracked Pipe under Combined Tension and Thermal Load

In the presence of excessive plasticity, the fracture toughness depends on the size and geometry. For material under fully yielded conditions, the stresses near the crack tip are not unique, but depend on geometry. So Single-parameter; J-approach is limited to high-constraint crack geometry. J-Q theory has been proposed in order to decide crack geometry constraint. This approach assumes that the crack-tip fields have two degrees of freedom. In this paper, based on J-Q theory, crack-tip stress field of fully circumferential cracked pipe under combined load is investigated using FE analysis. Combined loads are tensile axial force and thermal gradient of radial direction. Q-stresses of a crack geometry and it‘s loading state are used to determine constraint effect, and give a characteristic order for crack-tip constraint.

Unified Correlation of In-Plane and Out-of-Plane Creep Constraints with Creep Crack Growth Rate

In this paper, the equivalent creep strain distributions ahead of crack tips in different specimens were calculated by extensive finite element analyses, and the creep crack growth (CCG) rates of these specimens were simulated over a wide range of C*. The capability and applicability of the constraint parameter Ac for characterizing both in-plane and out-of-plane creep crack-tip constraints and establishing a unified correlation with CCG rate of a steel were investigated. Base on the parameter Ac, the unified correlation formulas of in-plane and out-of-plane constraints with CCG rate of a steel have been obtained.

Three-dimensional finite element analyses of in-plane and out-of-plane creep crack-tip constraints for different specimen geometries

Based on extensive three-dimensional finite element analyses, the creep crack-tip constraints for three specimen geometries (C(T), SEN(T) and M(T)) were quantified by using three constraint parameters (namely R*, h and Tz) for 316H steel at 550°C and steady-state power law creep. The three parameters were comparatively analyzed with respect to their capabilities for characterizing in-plane and out-of-plane creep constraints as well as the interaction between them. The results show that the specimen geometries with higher constraint strengthen the out-of-plane creep constraint effect. The parameters R* and h can quantify in-plane creep constraint, but they are inadequate to characterize higher out-of-plane creep constraint. The Tz can adequately incorporate out-of-plane creep constraint effect.