Dynamic ductile crack growth and transition to cleavage – a cell model approach

The fracture behavior of ferritic steel in the transition regime is controlled by the competition between ductile tearing and cleavage. Many test specimens that failed by catastrophic cleavage showed significant amounts of ductile tearing prior to cleavage fracture. The transition from ductile tearing to cleavage has been attributed to the increase in constraint and sampling volume associated with ductile crack growth. This work examines the role of dynamic ductile crack growth on the fracture mode transition by way of a cell model of the material. The cell model incorporates the effects of stress triaxiality and strain rate on material failure characteristics of hole growth and coalescence. Loading rate and microstructure effects on the stress fields that evolve with rapid (ductile) crack growth are systematically studied. The stress fields are employed to compute the Weibull stress which provides probability estimates for the susceptibility to cleavage fracture. A center-cracked panel subjected to remote tension is the model problem under study. The computational model uses an elastic-viscoplastic constitutive relation which incorporates enhanced strain rate hardening at high strain rates. Adiabatic heating due to plastic dissipation and the resulting thermal softening are also accounted for. Under dynamically high loading rate, our model shows the crack speed achieves its peak value soon after crack initiation and quickly falls off to slower speeds with further crack growth. Remarkably, the Weibull stress follows a similar pattern which suggests that the transition to the cleavage fracture is most likely to occur, if at all, at the peak speed of ductile crack growth. Key words: Dynamic fracture, ductile tearing, crack growth, transition regime, cleavage fracture, cell model, finite element.     

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 . 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 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 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). This revised version was published online in August 2006 with corrections to the Cover Date.     

A transferability model for brittle fracture including constraint and ductile tearing effects: a probabilistic approach

This study describes a computational framework to quantify the influence of constraint loss and ductile tearing on the cleavage fracture process, as reflected by the pronounced effects on macroscopic toughness (J _c , _c). Our approach adopts the Weibull stress _w as a suitable near-tip parameter to describe the coupling of remote loading with a micromechanics model incorporating the statistics of microcracks (weakest link philosophy). Unstable crack propagation (cleavage) occurs at a critical value of _w which may be attained prior to, or following, some amount of stable, ductile crack extension. A central feature of our framework focuses on the realistic numerical modeling of ductile crack growth using the computational cell methodology to define the evolution of near-tip stress fields during crack extension. Under increased remote loading (J), development of the Weibull stress reflects the potentially strong variations of near-tip stress fields due to the interacting effects of constraint loss and ductile crack extension. Computational results are discussed for well-contained plasticity, where the near-tip fields for a stationary and a growing crack are generated with a modified boundary layer (MBL) formulation (in the form of different levels of applied T-stress). These analyses demonstrate clearly the dependence of _w on crack-tip stress triaxiality and crack growth. The paper concludes with an application of the micromechanics model to predict the measured geometry and ductile tearing effects on the cleavage fracture toughness J _c of an HSLA steel. Here, we employ the concept of the Dodds-Anderson scaling model, but replace their original local criterion based on the equivalence of near-tip stressed volumes by attainment of a critical value of the Weibull stress. For this application, the proposed approach successfully predicts the combined effects of loss of constraint and crack growth on measured J _c -values.     

Analysis of ductile to cleavage transition in part-through cracks using a cell model incorporating statistics

This paper describes an approach to study ductile/cleavage transition in ferritic steels using the methodology of a cell model for ductile tearing incorporating weakest link statistics. The model takes into account the constraint effects and puts no restriction on the extent of plastic deformation or amount of ductile tearing preceding cleavage failure. The parameters associated with the statistical model are calibrated using experimental cleavage fracture toughness data, and the effect of threshold stress on predicted cleavage fracture probability is investigated. The issue of two approaches to compute Weibull stress, the 'history approach' and the 'current approach', is also addressed. The numerical approach is finally applied to surface-cracked thick plates subject to different histories of bending and tension, and a new parameter, ψ, is introduced to predict the location of cleavage initiation.     

A probabilistic model for cleavage fracture with a length scale - Parameter estimation and predictions of growing crack experiments

A probabilistic model for the cumulative probability of failure by cleavage fracture was applied to experimental results where cleavage fracture was preceded by ductile crack growth. The model, introduced by Kroon and Faleskog [Kroon M, Faleskog J. A probabilistic model for cleavage fracture with a length scale - influence of material parameters and constraint. Int J Fract 2002;118:99-118], includes a non-local stress with an associated material related length scale, and it also includes a strain measure to account for the number of nucleated cleavage initiation sites. The experiments were performed on single edge cracked bend test specimens with three different crack lengths at the temperature 85 °C, which is in the upper transition region for the steel in question. The ductile rupture process is modelled using the cell model for nonlinear fracture mechanics. The original cleavage fracture model had to be modified in order to account for the substantial number of cleavage initiators being consumed by the ductile process. With this modification, the model was able to accurately capture the experimental failure probability distribution.     

Use of a Ring DWTT Specimen for Determination of Steel NDT from Pipe of Diameter Less than DN500

It has become recognized that the drop weight tearing test (DWTT) energy better represents the ductile fracture resistance of pipe steels since it utilizes a specimen that has the full thickness of the pipe and has a fracture path long enough to reach steady-state fracture resistance. However, the API 5L code does not require it for pipe sizes less than DN500. The aim of this paper is to propose a DWTT specific to small diameter pipes based on a new specimen, the ring drop weight tearing test (RDWTT) specimen; to evaluate the transition temperature T _{t, DWTT} and nil ductility temperature of the pipe steel API 5L X65; to introduce the transition temperature T _{t, DWTT} in the transition temperature material master curve of the API 5L X65 steel; and to compare the prediction of the crack ductile extension in a pipe based on the RDWTT’s energy and crack tip opening angle in the case of the steel API 5L X65.     

Probabilistic treatment of fracture using two failure models

A probabilistic methodology for brittle fracture based on two local failure models is presented. Probabilistic fracture parameters are obtained using a weakest link and a chain-of-bundles formulation. Both models define limiting distributions for the fracture stress described by a two-parameter Weibull distribution. Numerical procedures employing measured toughness data and finite element solutions are also described to calibrate the Weibull parameters. An application of the methodology then follows to predict geometry and stable crack growth effects on the distribution of macroscopic fracture toughness (J_c) for a high-strength steel. Measured fracture toughness values for a high-constraint geometry that exhibit no prior ductile tearing are effectively ‘transferred' to a different geometry having much lower constraint and in which tearing precedes cleavage. The inherent difficulty in predicting the scatter of experimental fracture toughness, as well as constraint and ductile tearing effects, within the scope of conventional procedures appears greatly reduced in the framework presented in this work.     

Application of local approach to inhomogeneous welds. Influence of crack position and strength mismatch

In steel welds there is often a large variation in fracture toughness and mechanical properties between the weld metal, base material and the various heat affected zone (HAZ) microstructures. The stress field in front of a crack in a weldment can be noticeably affected by the strength mismatch between the weld metal, HAZ and the base material. The crack position relative to the various microstructures will clearly influence the strength mismatch effect. In this paper the influence of crack tip positioning on the fracture performance of strength mismatched steel welds has been studied both experimentally and by FEM analysis. For a mismatched weld with local brittle zones small changes in crack tip location can give considerable changes in the fracture performance of a CTOD specimen. A high degree of strength mismatch increases the effect of crack positioning. Weld metal overmatch increases the stress level in the heat affected zone due to material constraint and thereby reduces the cleavage fracture resistance of the weldment when the coarse grained HAZ (CGHAZ) controls the fracture. The detrimental effect of high overmatch is most pronounced for specimens with notch position at fusion line and a short distance into the brittle CGHAZ. The Weibull stress has been shown to be a suitable fracture parameter in the case where one microstructure clearly controls the cleavage fracture and the calculation of the Weibull stress therefore can be limited to this zone.     

Fracture resistance testing of dissimilar nickel–chromium girth welds for clad line pipes

This work presents an experimental investigation of the ductile tearing properties for the girth weld of a typical C–Mn pipe internally clad with ASTM UNS N06625 Alloy 625 using measured crack growth resistance curves (\(J{-}\Delta a\) and \(\mathrm {CTOD}{-}\Delta a\) curves). Here, the material of the external pipe is a typical API 5L Grade X65 pipeline steel whereas the inner clad layer is made of a nickel–chromium corrosion resistant alloy steel. Testing of the girth weld employed side-grooved, clamped SE(T) specimens with a weld centerline notch to determine the crack growth resistance curves based upon the unloading compliance method using a single specimen technique. This experimental characterization provides additional toughness data which serve to evaluate the effectiveness of current procedures in determining accurate experimentally measured R-curves for this class of material, including the effects of weld strength mismatch.     

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 _w 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 _w–min. This parameter has a simple calibration procedure requiring no additional experimental data. The use of a toughness scaling model including _w–min>0 increases the deformation level at which the CVN size specimen loses constraint compared to a 1TSE(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.     

A probabilistic model for cleavage fracture with a length scale--parameter estimation and predictions of stationary crack experiments

This study presents a large experimental investigation in the transition temperature region on a modified A508 steel. Tests were carried out on single-edge-notch-bend specimens with three different crack depth over specimen width ratios to capture the strong constraint effect on fracture toughness. Three test temperatures were considered, covering a range of 85 °C. All specimens failed by cleavage fracture prior to ductile tearing. A recently proposed probabilistic model for the cumulative failure by cleavage was applied to the comprehensive sets of experimental data. This modified weakest link model incorporates a length scale, which together with a threshold stress reduce the scatter in predicted toughness distributions as well as introduces a fracture toughness threshold value. Model parameters were estimated by a robust procedure, which is crucial in applications of probabilistic models to real structures. The conformity between predicted and experimental toughness distributions, respectively, were notable at all the test temperatures.     

Impact and dynamic fracture of tough polymers by thermal decohesion in a Dugdale zone

At low temperatures and high loading rates, normally tough crystalline thermoplastics may undergo a transition from ductile tearing to brittle rapid crack propagation (RCP). It is proposed here that RCP — characterised by low toughness, high crack speed (>100 m/s) and a macroscopically smooth fracture surface — occurs by self-sustained melting of a layer, one chain length thick, at each cohesive surface of a crack-tip craze, due to adiabatic heating. Initiation of RCP from a rapidly loaded sharp notch, i.e. impact fracture, requires both the formation of this melt layer, and sufficient crack extension force to propagate it. A schematic linear-elastic analysis based on the Dugdale model accounts both for the measured dynamic fracture resistance, and for the variation of impact fracture resistance with impact speed, in two pipe-grade polyethylenes and in a neat and a rubber-toughened polyacetal. It is concluded that crack initiation resistance, unlike dynamic fracture resistance, cannot be defined as a geometry-dependent material property.     

Effect of residual stresses on ductile crack growth resistance

It is well known that residual stresses influence the ductile fracture behaviour. In this paper, a numerical study was performed to assess the effect of residual stresses on ductile crack growth resistance of a typical pipeline steel. A modified boundary layer model was employed for the analysis under plane strain, Mode I loading condition. The residual stress fields were introduced into the finite element model by the eigenstrain method. A sharp crack was embedded in the center of the weld region. The complete Gurson model has been applied to simulate the ductile fracture by microvoid nucleation, growth and coalescence. Results show that tensile residual stresses can significantly reduce the crack growth resistance when the crack growth is small compared with the length scale of the tensile residual stress field. With the crack growth, the effect of residual stresses on the crack growth resistance tends to diminish. The effect of residual stress on ductile crack growth resistance seems independent of the size of geometrically similar welds. When normalized by the weld zone size, the ductile crack growth resistance collapses into one curve, which can be used to assess the structural integrity and evaluate the effect of residual stresses. It has also been found that the effect of residual stresses on crack growth resistance depends on the initial void volume fraction f₀, hardening exponent n and T-stress.     

Finite element analysis and experimental evaluation of ductile-brittle transition in compact tension specimen

Using finite element analysis, metallographic observations and statistical analysis, the stress field ahead of stationary and growing cracks and the ductile-brittle transition mechanism in compact tension (CT) specimens have been evaluated. Compared to a stationary crack, a growing crack elevates the opening stress on the remaining ligament and this may be partially attributed to the re-sharpening of the crack tip after ductile growth. The area of material covered by the high opening stress of the same magnitude also increases with ductile crack growth. In this study, no significant difference for measured cleavage stress can be found for the specimens fractured with and without ductile crack growth. There is a large scatter for the distance between the cleavage initiation site and the stationary or growing crack tip. Cleavage fracture after some amount of ductile crack growth is attributed to the increase of both the opening stress and the area of material under high opening stresses. Finally, the lower bound toughness is predicted using a small data set statistical model in connection with constraint correction. The predicted values give the same trend as the lower bound of the experimental measurements from the lower-shelf to the temperature at which ductile crack growth occurs. This revised version was published online in August 2006 with corrections to the Cover Date.     

Statistical assessment of notch toughness against cleavage fracture of ferritic steels

The work is an initial effort on adopting a statistical approach to correlate the fracture behavior between a notched and a fracture mechanics specimen. The random nature of cleavage fracture process determines that both the microscopic fracture stress and the macroscopic properties including fracture load, fracture toughness, and the ductile to brittle transition temperature are all stochastic parameters. This understanding leads to the proposal of statistical assessment of cleavage induced notch brittleness of ferritic steels according to a recently proposed local approach model of cleavage fracture. The temperature independence of the 2 Weibull parameters in the new model induces a master curve to correlate the fracture load at different temperatures. A normalized stress combining the 2 Weibull parameters and the yield stress is proposed as the deterministic index to measure notch toughness. This proposed index is applied to compare the notch toughness of a ferritic steel with 2 different microstructures.     

Damage mechanics models of ductile crack growth in welded specimens

Two-dimensional, plane strain, finite element analyses of strength-mismatched welded joints have been performed using the modified boundary layer formulation. The welds were idealized as two-material joints with the material interface running parallel to the crack, which was embedded in the weld material. The Rousselier ductile damage model was employed within the weld material to simulate crack extension due to the growth and coalescence of microvoids. By analysing models with different levels of material mismatching, weld dimensions and applied T -stress levels, it was possible to analyse the effects of crack tip constraint due to both material mismatching and specimen geometry on the fracture resistance of the weld material.
The results show that material strength overmatching (where the weld material is stronger than the base material) reduces the level of constraint ahead of the crack, which can increase the resistance to fracture of the weld material. Conversely, material strength undermatching increases crack tip constraint, reducing the fracture resistance of the joint. By employing estimates for the crack tip constraint levels, Q _M , based on the applied load, level of material mismatching and weld region thickness, it has been possible to 'order' the J– resistance curves of overmatched joints by generating a family of J–Q _M loci which describe the effects of constraint on the fracture resistance of the weld material. However, it is shown that the Q _M-stress parameter is not capable of describing the effect of material strength undermatching on the fracture resistance of a joint, which can be much lower than that obtained from a high-constraint homogeneous specimen of weld material.     

Fracture toughness of grade D ship steel

Results from fracture mechanics tests on 15 mm thick grade D ship steel and weld are organised into a toughness distribution indexed to the Charpy 27 joule temperature, T_27J. The tests are carried out at 300 MPa√m/s to simulate the strain rate appropriate to a long (≈1 m) through thickness crack in the deck of a ship under storm conditions. Most of the data are in the brittle to ductile transition region and end in cleavage fracture. A best fit to the data is found using the exponential curve fit (ECF) method. Lack of censoring of invalid results means that the trend line is not a true ‘plane strain’ fit. It is argued that inclusion of ‘plane stress’ data makes the resultant toughness distribution more relevant to ship fracture predictions. Equations are presented which allow the toughness to be plotted at any chosen probability level as a function of temperature relative to T_27J. A safe lower bound to the data is given by the 0.1% probability trend assuming that T_27J for grade D plate and weld is no higher than −20 °C. The data are also used to propose that it is impossible to generate an elastic ductile tearing instability in ship steel with Charpy upper shelf values of 100 J or more.     

Influence of threshold parameters on cleavage fracture predictions using the Weibull stress model

This study explores applications of three-parameter Weibull stress models to predict cleavage fracture behavior in ferritic structural steels tested in the transition region. The work emphasizes the role of the threshold parameters (_th and _{w – min}) in cleavage fracture predictions of a surface crack specimen loaded predominantly in tension for an A515-70 pressure vessel steel. A recently proposed procedure based upon a toughness scaling methodology using a modified Weibull stress (^* _w) extends the calibration scheme for the Weibull modulus, m, to include the threshold parameters. The methodology is applied to calibrate the Weibull stress parameter for the tested material and then to predict the toughness distribution for the surface crack specimen. While the functional relationship between ^* _w and m suggests a strong effect of the threshold stress, _th, on the calibrated m-parameter, the results show a remarkably weak dependence of fracture predictions on _th as does the dependence of fracture predictions on _w–min for this specimen.