Deep Notch Bend Research Articles

Constraint effects on the ductile-to-brittle transition temperature of ferritic steels: a Weibull stress model

This study examines crack front length and constraint loss effects on cleavage fracture toughness in ferritic steels at temperatures in the ductile-to-brittle transition region. A local approach for fracture at the micro-scale of the material based on the Weibull stress is coupled with very detailed three-dimensional models of deep-notch bend specimens. A new non-dimensional function g(M) derived from the Weibull stress density describes the overall constraint level in a specimen. This function remains identical for all geometrically similar specimens regardless of their absolute sizes, and thus provides a computationally simple approach to construct (three-dimensional) fracture driving force curves σw vs. J, for each absolute size of interest. Proposed modifications of the conventional, two-parameter Weibull stress expression for cumulative failure probability introduce a new threshold parameter σw−min. This parameter has a simple calibration procedure requiring no additional experimental data. The use of a toughness scaling model including σw−min>0 increases the deformation level at which the CVN size specimen loses constraint compared to a 1T SE(B) specimen, which improves the agreement of computational predictions and experimental estimations. Finally the effects of specimen size and constraint loss on the cleavage fracture reference temperature T 0 as determined using the new standard ASTM E1921 are investigated using Monte Carlo simulation together with the new toughness scaling model.

Ductile tearing in part-through cracks: experiments and cell-model predictions

This study describes an application of the computational cell model to predict ductile crack growth measured in experiments performed on surface-cracked, thick plates fabricated from a ferritic pressure vessel steel. The cell model limits void growth and coalescence to within a thin layer of material over the crack plane. Outside this layer, the material deforms plastically but remains void free. The Gurson–Tvergaard dilatant plasticity model describes the evolution of void growth and the associated macroscopic softening within the cells. Material-specific, cell parameters readily separate into two categories: those describing the micromechanics of void growth rate and those describing the local fracture process of the cell. Calibration of these parameters utilizes both discrete (3-D) cell models and R-curves measured using standard deep-notch bend or compact tension specimens. The cell model is applied here to surface-cracked plates subjected to different loading histories of tension and bending. The calibrated cell model reproduces accurately full details of the load-deformation records and the crack growth profiles for all the cases. These numerical studies suggest that the computational approach based on the cell model provides an engineering tool to predict ductile crack growth behavior in flawed structural components.

Calibration of Weibull Stress Parameters Using Fracture Toughness Data

The Weibull stress model for cleavage fracture of ferritic steels requires calibration of two micromechanics parameters $$(m,\sigma _u ) $$ . Notched tensile bars, often used for such calibrations at lower-shelf temperatures, do not fracture in the transition region without extensive plasticity and prior ductile tearing. However, deep-notch bend and compact tension specimens tested in the transition region can provide toughness values under essentially small-scale yielding (SSY) conditions to support Weibull stress calibrations. We show analytically, and demonstrate numerically, that a nonuniqueness arises in the calibrated values, i.e., many pairs of $$(m,\sigma _u ) $$ provide equally good correlation of critical Weibull stress values with the distribution of measured (SSY) fracture toughness values. This work proposes a new calibration scheme to find $$(m,\sigma _u ) $$ which uses toughness values measured under both low and high constraint conditions at the crack front. The new procedure reveals a strong sensitivity to m and provides the necessary micromechanical values to conduct defect assessments of flawed structural components operating at or near the calibration temperature in the transition region. Results of a parameter study illustrate the expected values of m for a typical range of material flow properties and toughness levels. A specific calibration is carried out for a mild structural steel (ASTM A36).

A SIMPLE TEST METHOD FOR ENERGY DISSIPATION RATE, CTOA AND THE STUDY OF SIZE AND TRANSFERABILITY EFFECTS FOR LARGE AMOUNTS OF DUCTILE CRACK GROWTH

Abstract— Simple extensions to the standard deep notch bend test procedure are suggested to allow the collection of data relevant to the energy dissipation rate, D, crack opening angle, COA, and J, all for arbitrarily large amounts of growth in extensive plasticity. The methods of analysis are detailed for real elastic‐plastic behaviour of a high strength low‐hardening type metal with a view to encouraging use on a wider range of materials. A proposal is made, and equations given, that the particular version of J used for an R‐curve derived from the area under the loading diagram, should correspond to the value of the far‐field integral, Jff.The relationship between the global measure of COA that emerges from D and the local crack tip opening angle, CTOA, as used in computational studies, is established. Transferability of CTOA data is examined in the light of effects of size and configuration. An explicit rule of the form CTOA √G =f (material and configuration) is proposed for the modelling of ductile growth in finite element studies. It is applied to a set of data in the literature, for the variation of CTOA with size in the deep notch bend test and for the configurations, bending, double edge and centre cracked tension.

ローカルアプローチの適用によるぜい性破壊発生限界に及ぼす試験片形状・寸法の影響の評価

The effects of specimen geometry and loading mode on the resistance to brittle fracture initiation were analyzed by the local approach. The fracture resistance of materials under a large scale yielding condition evaluated by the conventional fracture mechanics parameters, such as crack tip opening displacement (CTOD), depends to a large extent on the specimen geometry and loading mode. This is due to the geometrical constraint effect on the crack tip stress field. The three-dimensional FE analysis figured out that, as plasticity developed, a shallow notch bend specimen and tension specimens (CCP and DECP) showed significant loss of constraint compared to a deep notch bend specimen. This led to a lower stress near the crack tip for the shallow notch bend specimen and tension specimens than the deep notch bend specimen. By contrast, the critical Weibull stress at brittle fracture according to the local approach did not depend on the geometry of specimens used. This paper demonstrates the independence of the critical Weibull stress on the crack depth of 3-point bend specimen. As an advantage, the local approach enabled us to predict the specimen geometry effect on the critical CTOD at fracture.The effects of specimen geometry and loading mode on the critical CTOD at fracture depend on the hardenability of materials. In the case of high hardening materials, the critical CTOD is not very sensitive to the specimen geometry and loading mode excepting the thickness effect on the critical CTOD for materials with a large scatter in toughness. On the other hand, for low hardening materials, the critical CTOD is affected to a large extent by the crack depth and loading mode of specimens.

Fully plastic ductile tearing of HY130 steel—an analysis by J, COD, energy rate and crack opening angle

The dependence of J-R curves on size of test piece is examined for fully plastic deep notch bend (DNB) tests on HY130 steel, taken to large amounts of ductile crack growth (60 per cent of the ligament) for a range of initial widths at 20 mm thick and one geometrically similar size, 50 mm thick. The object is to understand the cause of the widely different patterns of behaviour that have been reported in the literature, even within the DNB type of configuration. In the present tests, the proportion of shear lip is the same for the geometrically similar pair but the J-R curve for the 50 mm thick piece is much lower than for the similar piece, 20 mm thick. The rate of change of displacement, dq/da, is analysed using the factor. r∗, that defines the instantaneous centre of rotation at each step of growth, to give a measure of crack tip opening angle (CTOA), xg. After an initial transient regime of small growth, xg and r∗ remain constant. The normalized load. L, rises due to work hardening during crack growth by amounts that depend on size while xg and r∗ vary mildly with initial width to give an appreciable variation of the combined term Lxg/r∗, which is the factor that controls the behaviour of the JR curves. It is speculated that CTOA and its variation with configuration (as seen in the literature) may, for large growth, assume the role of the two parameters suggested in recent literature as controlling the variation of toughness with constraint.

Effect of Strength Mis-Match on Fracture Mechanical Behavior of HAZ-Notched Weld Joint.

Strength mis-matching between the base and weld metals exerts a marked influence on the deformation behavior as well as on the fracture resistance of the weld HAZ. HAZ-notched CTOD test results for high strength steel welds were discussed with attention to mis-matching effect. Stress fields in the HAZ were addressed by 3D FEM with a model having a notch at the HAZ/weld metal boundary. Strength overmatching of the weld metal brings about different effects depending on the toughness level of the HAZ. In the case of the HAZ with moderate toughness, strength overmatching results in crack path deviation toward a softer material due to asymmetrical plastic deformation. On the other hand, for the embrittled HAZ, the overmatch condition lowers the critical CTOD value of the HAZ. This is attributed to elevation of the local stress in the HAZ by constraint effect of the overmatched weld metal. The geometry of the test specimen also affects the degree of crack tip constraint. The deep notch bend specimen produces the largest geometrical constraint. The fracture resistance of the weld HAZ is controlled by the combined effects of strength mis-matching and the specimen geometry. The geometrical constraint in the deep notch bend specimen was more significant than the constraint by 25% strength overmatching in the tension specimen.

APPLICATION OF ENERGY DISSIPATION RATE ARGUMENTS TO STABLE CRACK GROWTH

Abstract— Energy dissipation rate, D, and crack tip opening angle (CTOA) have been related for large amounts of ductile crack growth in a fully plastic two‐dimensional model of real elastic plastic material. Several J‐type rising R‐curves have been constructed and related, some based on the cumulative energy dissipated and some as a characterising term that relates closely to the far‐field J contour value. These two meanings co‐exist but the relationship is geometry dependent. For deep notch bend (DNB) cases the non‐dimensional group Lα/r* (where L is normalised load, α is CTOA and r* defines the position of the instantaneous centre of rotation) governs the value of dJ. Certain DNB cases where R‐curves vary with size are resolved by this group rather than by CTOA itself whereas for centre‐cracked tension there is a higher value of CTOA than for DNB.

Ｓｈａｌｌｏｗ Ｎｏｔｃｈ ＣＴＯＤ試験の意義 溶接継手の破壊性能評価のための靭性評価手法に関する考察

The use of CTOD bend specimen with a deep notch whose length is equal to the plate thickness is not always appropriate to obtain the toughness data applicable to fracture performance evaluation of weld joints. In this paper, HAZ-notched bend test and tension test have been conducted using specimens with different notch depth, which were extracted from a multipass weld joint of 30 mm thick high strength steel (TMCP type) with 460 MPa class yield point. The critical CTOD value at unstable fracture initiation obtained by the deep notch bend test was apparently smaller than that for the tension specimen. Fracture mode was also affected by the specimen type : Perfect cleavage fracture was dominant in the deep notch bend specimen, whereas unstable fracture preceded by a large amount of stable crack growth was observed in the tension specimen. Difference between CTOD results for the deep notch bend specimen and the tension specimen can be attributed to the crack tip constraint effect. The deep notch bend specimen exhibits significantly elevated crack tip stress and higher stress triaxiality compared to the tension specimen. By contrast, a shallow notch bend specimen showed a similar fracture behavior and critical CTOD value as the tension specimen. For the assessment of fracture resistance of welds by the CTOD bend test, the notch depth should be designed to simulate the plastic constraint expected in weldments.

Effect of Strength Mismatch on Crack Tip Stress Fields of HAZ-notched Joints Subjected to Bending and Tension

A numerical investigation for a crack located in the boundary between the weld metal and the heat affected zone (HAZ) of a welded joint is presented. Three-dimensional finite element analyses are performed on a center cracked panel (CCP) subjected to tension and single edge notch bend (SENB) specimens. The numerical results show that the stresses that develop in the HAZ region of the overmatched welded joint are more intense than those in the undermatch and evenmatch cases. It is noted that highly stressed near-tip zones are detrimental to fracture resistance of HAZ regions containing local brittle zones. A discussion also follows on the significance of weld strength overmatch on fracture behavior of HAZ-notched welded joints, which is based on the local approach. The analyses indicate that the relative load-carrying capacity of a overmatched joint may be reduced, especially in the case of the high constrained deep notch bend specimen. Such features may be particularly deleterious to cleavage fracture resistance of welded joints containing cracks close to the HAZ region.