An experimental investigation of the effect of biaxial loading on the master curve transition temperature in RPV steels

During the 1990s considerable work was conducted to characterize the effect of biaxial loading on the ductile to brittle transition temperature. The work centered on a series of tests using large cruciform bend specimens from an experimental A533B test plate denoted as HSST Plate 14 (Heavy Section Steel Technology Plate 14). Recently a series of similar biaxial cruciform tests has been conducted on the steel used for an extensive European Round Robin that investigated the ductile-to-brittle transition master curve and associated T₀ reference temperature. The results of these tests have been used to promote the concept of a “Biaxial Effect” which corresponds to a shift in the shallow crack transition master curve of +20 °C or more when biaxial stresses are present, in comparison with the master curve for uniaxially loaded shallow crack specimens. A comprehensive analysis of the all of the available HSST Plate 14 data and data from two other structural steels was performed to investigate the extent of a biaxial effect on the reference temperature, T₀. The analysis included many additional biaxial cruciform test results on three different materials. The results of all three materials discussed in this paper fail to clearly demonstrate that biaxial loading, imposed through the use of a cruciform specimen geometry, has an effect on the fracture toughness, characterized using a master curve approach and reference temperature T₀. The analysis utilized in this paper assumes that the toughness distribution and temperature dependence of shallow cracked specimens can be modeled by using the master curve approach. This assumption has not been rigorously validated and would benefit from further study. Additional detailed stress analysis of the constraint evolution in the cruciform specimens may better define the precise conditions under which a biaxial effect on the fracture toughness could be realized.     

Probabilistic failure assessment of ferritic steels using the master curve approach including constraint effects

The present study is concerned with an enhancement of the master curve approach for the probabilistic failure assessment of ferritic steel structures considering constraint effects. In an experimental program based on a variety of different specimens, distinct effects of the specimen geometry on the reference temperature T₀ are observed. The experimental data base is examined in terms of the K-T_stress-, J-A₂-, J-Q- and J-h-concepts. Based on the results, a constraint enhancement for the master curve concept is suggested consisting of a constraint dependent temperature shift or an alternative constraint dependent scaling of the stress intensity factor.     

The jump-like crack growth model, the estimation of fracture energy and JR curve

In this paper the jump-like crack growth model for monotonic loading is applied to re-examine both the onset of crack growth and process of stable crack growth. In the former case the fracture energy associated with a new surface creation is estimated and the in-plane constraint influence on this quantity is examined using the J-A₂ approach. In the later case the formula to compute the J-resistance curve is re-examined and compared with the one known from the standards. In the analysis the plane strain model of a structural element made of elastic-plastic material is assumed.     

Constraint-modified J−R curves and its application to ductile crack growth

The concept of J-controlled crack growth is extended to J–A ₂ controlled crack growth using J as the loading level and A ₂ as the constraint parameter. It is shown that during crack extension, the parameter A ₂ is an appropriate constraint parameter due to its independence of applied loads under fully plastic conditions or large-scale yielding. A wide range of constraint level is considered using five different types of specimen geometry and loading configuration; namely, compact tension (CT), three-point bend (TPB), single edge-notched tension (SENT), double edge-notched tension (DENT) and centre-cracked panel (CCP). The upper shelf initiation toughness J _IC, tearing resistance T _R and J–R curves tested by Joyce and Link (1995) for A533B steels using the first four specimens are analysed. Through finite element analysis at the applied load of J _IC, the values of A ₂ for all specimens are determined. The framework and construction of constraint-modified J–R curves using A ₂ as the constraint parameter are developed and demonstrated. A procedure of transferring the J–R curves determined from standard ASTM procedure to non-standard specimens or practical cracked structures is outlined. Based on the test data, the constraint-modified J–R curves are presented for the test material of A533B steel. Comparison shows the experimental J–R curves can be reproduced or predicted accurately by the constraint-modified J–R curves for all specimens tested. Finally, the variation of J–R curves with the size of test specimens is produced. The results show that larger specimens tend to have lower crack growth resistance curves.     

Solutions of the second elastic-plastic fracture mechanics parameter in test specimens

Extensive finite element analyses have been conducted to obtain solutions of the A-term, which is the second parameter in three-term elastic-plastic asymptotic expansion, for test specimens. Three mode I crack plane-strain test specimens, i.e. single edge cracked plate (SECP), center cracked plate (CCP) and double edge cracked plate (DECP) were studied. The crack geometries analyzed included shallow to deep cracks. Solutions of A-term were obtained for material following the Ramberg-Osgood power law with hardening exponent of n = 3, 4, 5, 7 and 10. Remote tension loading was applied which covers from small-scale to large-scale yielding. Based on the finite element results, empirical equations to predict the A-terms under small-scale yielding (SSY) to large-scale yielding conditions were developed. In addition, by using the relationships between A and other commonly used second fracture parameters such as Q factor and A₂-term, the present solutions can be used to calculate parameters A₂ and Q as well. The results presented in the paper are suitable to calculate the second elastic-plastic fracture parameters for test specimens for a wide range of crack geometries, material strain hardening behaviors and loading conditions.     

Material constraint parameters for the assessment of shallow defects in structural components. Part II: Constraint-based assessment of shallow defects

This Part II paper describes a series of constraint-based R6 assessments of shallow-cracked specimens under equibiaxial loading using material constraint parameters obtained from lookup tables presented in the companion Part I paper. Parameters are derived for an A533B-1 steel forging from a knowledge of the yield and flow behaviour of the material and a calibration of the Beremin model parameter m. Resulting assessments, which use both T- and Q-stress to quantify constraint, are found to be conservative with respect to the available experimental data. The results are also used to predict the influence of T-stress on the Master Curve reference temperature. Available data are broadly in agreement with the predicted trend curve. Finally, the results demonstrate that out-of-plane biaxial loading increases constraint to the extent that the inherent conservatism of the elastic T-stress at high L_r is eroded. Out-of-plane constraint effects are only properly accounted for by the hydrostatic Q-stress and for this reason, the use of T to assess biaxial loading situations should be undertaken with a degree of caution.     

Establishing methodology to predict fracture behaviour of piping components by numerically predicting specimen fracture data using tensile specimen test

Using large deformation FEM analyses in SA333Gr.6 carbon steel material, the present study demonstrated the assessment of SZWc value that leads to J_SZWc and finally compares with the respective experimental results. It also includes numerical prediction of specimen J-R curve using Gurson-Tvergaard-Needleman parameters obtain from tensile specimen tests. Using numerically predicted results, the crack initiation and instability stages in circumferentially through-wall cracked elbows is finally predicted and compares with experimental results. The present study gives evidence that the non-linear FEM analysis supported with proper tensile test data can be helpful in assessing the safety of bend pipes with through-wall crack.     

J-Resistance curve testing of HY80 steel using SE(B) specimens and normalization method

The normalization method is adopted for standard and nonstandard specimens in this paper to develop J-R curves for HY80 steel directly from load versus load-line displacement records without use of automatic crack length measurement. The standard specimens usually contain high crack-tip constraints, while the nonstandard specimens involve low crack-tip constraints. To obtain J-R curves with different constraints, a series of single edge notched bend (SE(B)) specimens with different crack lengths for an HY80 steel are tested in accordance with ASTM standard E1820. The normalization method is then used for determining crack extension and J-R curves for these SE(B) specimens.To validate the normalization method, the J-R curves determined using the normalization method are compared with those obtained by the elastic unloading compliance method for the SE(B) specimens. The comparison shows that good agreements exist between the two methods, and the normalization method is a viable tool to be used to determine J-R curves of the HY80 steel for the standard as well as nonstandard SE(B) specimens. In the J-integral calculations, the resistance curve test method, the basic test method and the modified basic test method specified in ASTM E1820 are evaluated. The results indicate that the modified basic method can be equivalent to the resistance curve method.     

On the application of the damage work density as a new initiation criterion for ductile fracture

In this paper the ‘damage work’ proposed by Chaouadi et al. is used to formulate an energy crack initiation criterion to describe ductile crack initiation. The traditional assessment of structural integrity by the J-integral, a property of elastic-plastic fracture mechanics is compared. Two free-cutting and one structural steel are investigated. The measured values for the critical damage work density at initiation W_di are compared with values for copper and RPV steel. As the fracture mechanical approach is limited to sharp cracks in the material (high-constraint stress state) the present damage mechanics approach is regarded as important as a more general concept closer to reality. While old void growth models of damage mechanics cannot formulate a simple criterion for crack initiation the applied damage work reaches a constant value at initiation W_di which is independent of the stress state during the deformation process. We recommend W_di as a material property of toughness for testing and engineering purposes.     

The energy dissipation rate approach to tearing instability

Stable and unstable tearing in metals is currently analysed by J integral theory, or by the G_R curve approach. This paper explains an alternative analysis route based on energy dissipation rate, D. It is shown that the implication of increasing toughness with crack growth in G_R and J_R curves is misleading. Even in small scale yielding (SSY), it is possible to have stable tearing under increasing G or J whilst at the same time D is constant (or even reducing) with crack growth. New terms: C for crack driving force, D^* for geometry normalised D, D_ssy for D in SSY, and crack stability index are explained. A D based fracture analysis diagram is introduced. Comparisons are made between energy dissipation rate, J integral, and G_R curve instability prediction methods. It is shown that, in most instances, these different approaches are compatible; but that the use of J_R curves derived in fully yielded test pieces to predict failure in SSY has the potential to lead to an unconservative instability prediction. The practical advantage of the energy dissipation rate approach is that it can be applied to all product thicknesses at any extent of crack growth. The major advantage compared to the G_R approach is that toughness measurements can be made on much smaller specimens.     

Fracture toughness of unidirectional fiber-metal laminates: crack orientation effect

Fiber-metal laminates (FMLs) are structural composites developed for aeronautical applications. The application of FMLs to structures demands a deep knowledge of a wide set of properties, including fracture toughness. The objective of this work was to evaluate the effect of crack orientation on the fracture toughness (critical J-integral and CTOD δ₅) of unidirectional FMLs. Small C(T) and SE(B) specimens with notches parallel and perpendicular to the fibers direction were tested. A study of the relation and equivalence between J_C and δ_5C, which heavily depend on the yield strength and on the stress state, was performed motivated by apparently contradictory experimental results. These results can be explained by the direction-dependent yielding properties of unidirectional FMLs. The best overall equivalence between J_C and δ_5C was obtained considering plane stress state and using the effective yield strength, both for unidirectional FMLs notched parallel and perpendicular to the fibers direction.     

J–R curves corrected by load-independent constraint parameter in ductile crack growth

The constraint effect on J–resistance curves of ductile crack growth is considered under the condition of two-parameter J–Q^* controlled crack growth, where Q^* is a modified parameter of Q in the J–Q theory. Both J and Q^* are used to characterize the J–R curves with J as the loading level and Q^* as a constraint parameter. It is shown that Q^* is independent of applied loading under large-scale yielding or fully plastic deformation, and so Q^* is a proper constraint parameter during crack growth. An approach to correct constraint effects on the J–R curve is developed, and a procedure of transferring the J–R curves determined from standard ASTM procedure to nonstandard specimens or real cracked structures is outlined.The test data of fracture toughness, J_IC, and tearing modulus, T_R, by Joyce and Link (Engng. Fract. Mech. 57(4) (1997) 431) for a single-edge notched bend specimen with various depth cracks are employed to demonstrate the efficiency of the present approach. The variation of J_IC and T_R with the constraint parameter Q^* is obtained, and then a constraint-corrected J–R curve is constructed for the test material of HY80 steel. Comparisons show that the predicted J–R curves can match well with the experimental data for both deep and shallow cracked specimens over a reasonably large amount of crack extension.Finally, the present approach is applied to predict the J–R curves of ductile crack growth for five conventional fracture specimens. The results show that the effect of specimen geometry on the J–R curves is generally much larger than the effect of specimen sizes, and larger specimens tend to have lower crack growth resistance curves.     

Estimation procedure of J-resistance curves for SE(T) fracture specimens using unloading compliance

This work provides an estimation procedure to determine J-resistance curves for pin-loaded and clamped SE(T) fracture specimens using the unloading compliance technique and the η-method. A summary of the methodology upon which J and crack extension are derived sets the necessary framework to determine crack resistance data from the measured load vs. displacement curves. The extensive plane-strain analyses enable numerical estimates of the nondimensional compliance, μ, and parameters η and γ for a wide range of specimen geometries and material properties characteristic of structural and pipeline steels. Laboratory testing of an API 5L X60 steel at room temperature using pin-loaded SE(T) specimens with side-grooves provide the load-displacement data needed to validate the estimation procedure for measuring the crack growth resistance curve for the material. The results presented here produce a representative set of solutions which lend further support to develop standard test procedures for constraint-designed SE(T) specimens applicable in measurements of crack growth resistance for pipelines.     

Weibull应力方法预测低合金钢的韧脆转化曲线

采用三参数的Weibull分布描述断裂韧度的统计规律。结合ASTM E1921-05标准,详细讨论了标准断裂试样韧脆转化曲线的建立过程;为了将标准断裂试样的测试结果用于低约束断裂试样,采用两参数的Weibull分布描述裂纹尖端局部区域的应力状态与失效概率之间的关系,并用Weibull应力将各种不同约束水平的裂纹尖端应力场联系起来,得到了预测低约束断裂试样韧脆转化曲线的公式。然后对两种A533B钢三点弯曲断裂试样进行了实例计算,进一步分析了Weibull应力的有限元计算结果,根据这些结果预测的韧脆转化曲线与试验数据相比非常吻合,证明了该文提出的方法是有效的。     

Energy dissipation rate analysis of a low upper shelf data set

Stable and unstable tearing in metals is currently analysed by J integral theory. Test and analysis methods are fully standardised and the validity of the approach has been demonstrated by reference to laboratory and type testing. A central requirement of the J method is that the J_R curve remain invariant as size increases (specimen dimension to structure). A set of data from the literature which show the slope of the J_R curve decreasing with increasing specimen size are presented. This represents an unsafe trend in terms of predicting structural behaviour from small specimens tests. The observed behaviour is explained successfully with energy dissipation rate theory. At the same time energy dissipation rate theory can also explain the more normally observed behaviour of size invariant J_R curves. It is concluded that stable and unstable tearing in metals is best described by the energy dissipation rate approach.     

Experimental T33-stress formulation of test specimen thickness effect on fracture toughness in the transition temperature region

This paper describes a study of the test specimen thickness effect on fracture toughness of a material, in the transition temperature region, for CT specimens. In addition we studied the specimen thickness effect on the T₃₃-stress (the out-of-plane non-singular term in the series of elastic crack-tip stress fields), expecting that T₃₃-stress affected the crack-tip triaxiality and thus constraint in the out-of-plane direction. Finally, an experimental expression for the thickness effect on the fracture toughness using T₃₃-stress is proposed for 0.55% carbon steel S55C. In addition to the fact that T₃₃ (which was negative) seemed to show an upper bound for large B/W, these results indicate the possibility of improving the existing methods for correlating fracture toughness obtained by test specimen with the toughness of actual cracks found in the structure, using T₃₃-stress.     

Superconducting properties of internal-tin route Nb3Sn wires with radially arranged filaments : Development that realizes high Jc and low hysteresis loss

An internal-tin route Nb₃Sn superconducting wire that has both remarkably low hysteresis loss (Q_h) and high critical current density (J_c) was developed according to a new design idea. The wire was constructed by arranging the filaments in a radial layout, enlarging the outer filaments along the radial direction, narrowing the filament spacing in the radial direction intentionally and enlarging the filament spacing in tangential direction. Thus, the electromagnetic coupling among the filaments in tangential direction due to the bridging and/or proximity effect was suppressed without decreasing the volume fraction of Nb. As a result, excellent properties such as J_c(12 T) = 1.15 × 10³ A/mm² and Q_h = 301 mJ/cm³ (for 1 cycle of B = ±3 T) were obtained. We also evaluated the transition temperature (T_c) and upper critical field (B_c2) of the wire. The values for T_c and B_c2 were 17.3 K and 24.1 T, respectively, which were much better than those of usual internal-tin route wires. Moreover, electron probe micro-analyses confirmed that the good T_c and B_c2 were the result of the qualitative improvement of the Nb₃Sn compound based on the effects of arranging the Nb filaments radially, increasing the ratio of Sn-to-Nb and shortening the diffusion length for Sn. This wire is promising for use with conduction-cooled high-field magnets, in which there is a need to decrease the load of the cryocooler, and also for the strands of fusion coils.     

Experimental J estimation equations for single-edge-cracked bars in four-point bend: homogeneous and bi-material specimens

The present paper provides the plastic η factor solutions for J testing of single-edge-cracked specimens in four-point bend (SE(PB)), based on limit (slip line field) and detailed finite element limit analyses. Both homogeneous specimens and bi-material specimens with interface cracks are considered. Moreover, two different η factor solutions are developed, one for J (or C^* in creep crack growth testing) estimation based on the load-load line displacement (LLD) records, η_p^VLL, and the other J estimation based on the load-crack mouth opening displacement (CMOD) records, η_p^CMOD.It is found that the use of load-LLD records can be recommended only for testing deeply cracked SE(PB) specimens. Moreover, depending on how the LLD is measured, a different value of η_p^VLL should be used. On the other hand, the use of load-CMOD records is recommended for all possible crack lengths. Moreover, the proposed η_p^CMOD solution can be used not only for a homogeneous specimen but also for any bi-material specimen with an interface crack.     

Quantifying Tstress controlled constraint by the master curve transition temperature T0

Specimen size, crack depth and loading conditions may effect the materials fracture toughness. In order to safeguard against these geometry effects, fracture toughness testing standards prescribe the use of highly constrained deep cracked bend specimens having a sufficient size to guarantee conservative fracture toughness values. One of the more advanced testing standards, for brittle fracture, is the master curve standard ASTM E1921-97, which is based on technology developed at VTT Manufacturing Technology. When applied to a structure with low constraint geometry, the standard fracture toughness estimates may lead to strongly over-conservative estimate of structural performance. In some cases, this may lead to unnecessary repairs or even to an early “retirement” of the structure. In the case of brittle fracture, essentially three different methods to quantify constraint have been proposed, J small scale yielding correction, Q-parameter and the T_stress. Here, a relation between the T_stress and the master curve transition temperature T₀ is experimentally developed and verified. As a result, a new engineering tool to assess low constraint geometries with respect to brittle fracture has been obtained.