Towards a uniform precracking procedure for fracture toughness testing

The precracking requirements for fracture toughness testing of metallic materials are investigated in this study. In addition, some experiments were performed in the transition region to quantify the consequences of violating these requirements. It is found that the different standards are not consistent. For most of the requirements some rationale can be found. Some theoretical developments were performed to justify the use of a fixed maximum stress intensity factor. This limit is tightly related to the fracture mechanism and to the fracture process zone. From an experimental point of view, a relatively limited effect of precracking on the fracture toughness is found.     

Modelling of fracture toughness data in the ductile to brittle transition temperature region by statistical analysis

A fracture toughness database for a ferritic 22NiMoCr37 steel forging for 12.5, 25, 50 and 100 mm thick specimens tested at nine different temperatures has been analysed statistically. The method employed uses a statistical procedure based on competing risks to evaluate the fracture toughness and quantify the probability of cleavage fracture as a function of temperature, specimen thickness and ductile crack growth. This paper describes the application of the competing risks statistical methods to the fracture toughness database obtained from the joint European Project.     

Influence of statistical and constraint loss size effects on cleavage fracture toughness in the transition - A model based analysis

A database derived from tests on specimens with a large range of ligament (b) and thickness (B) dimensions was systematically analyzed to evaluate constraint loss and statistical size effects on cleavage fracture toughness. The objectives were to: (1) decouple size effects related to constraint loss, mediated by b and B, from those arising from statistical effects, primarily associated with B; and, (2) develop procedures to transfer toughness data to different conditions of constraint and B. The toughness database for a Shoreham pressure vessel steel plate, tested at a common set of conditions, was described in a companion paper. Quantification of constraint loss was based on an independently calibrated 3D finite-element critical stress-area, σ^∗-[K_Jm/K_Jc], model. The measured toughness data, K_Jm, were first adjusted using computed [K_Jm/K_Jc] constraint loss factors to the corresponding values for small scale yielding conditions, K_Jc=K_Jm/[K_Jm/K_Jc]. The K_Jc were then statistically adjusted to a K_Jr for a reference B_r = 25.4 mm. The B adjustment was based on a critically stressed volume criterion, modified to account for a minimum toughness, K_min, consistent with modest modifications of the ASTM E 1921 Standard procedure. The combined σ^∗-[K_Jm/K_Jc]-K_min adjustment procedure was applied to the Shoreham b − B database, producing a homogeneous population of K_Jr data, generally within the expected scatter. The analysis suggests that: (1) there may be a maximum B beyond which statistical size effects diminish, and (2) constraint loss in the three-point bend specimens begins at a relatively low deformation level. A corresponding analysis, based on a Weibull stress, σ_w-[K_Jm/K_Jc]-K_min, adjustment procedure, yielded similar, but somewhat less satisfactory, results. The optimized adjustment procedure was also applied to other K_Jm data for the Shoreham plate from this study, as well as a large database taken from the literature. The population of 489K_Jr data points, covering an enormous range of specimen sizes, geometries and test temperatures, was found to be consistent with the same master curve T₀ = −84 °C derived from the b − B database. Thus, calibrated micromechanical models can be used to treat size and geometry effects on K_Jm, facilitating using small specimens and data transfer to predict the fracture limits of structures.     

Development of the Euro fracture toughness dataset

Ten European laboratories have generated the Euro fracture toughness dataset in order to provide an experimental data base sufficiently large to study specimen size and temperature effects on cleavage fracture toughness in the ductile-to-brittle fracture transition regime. The Euro fracture toughness dataset quantifies the fracture behaviour of the quenched and tempered pressure vessel steel DIN 22NiMoCr37. This material is frequently used in nuclear power plants. About 800 fracture toughness tests were performed using compact tension specimens with a size range from 1/2T to 4T.In the lower shelf temperature regime, no significant specimen size effects on cleavage fracture toughness scatter was observed. At higher temperatures, the lower tails of the toughness scatter bands are not significantly effected by the specimen size but with decreasing specimen size the toughness scatter increases due to the fact that the upper part of the scatter band is extended. The presence of a specimen size effect on fracture toughness scatter coincides with the appearance of single cleavage initiation sites at the fracture surface. At the lower shelf temperature both, cleavage initiation sites and size effects are not observed whereas at higher test temperatures both phenomena are present. The specimen size effect trends and the corresponding fracture surface morphology support a weakest-link type cleavage fracture mechanism in the ductile-to-brittle transition regime. A unique correlation between the amount of ductile tearing and cleavage fracture toughness was observed for the steel investigated. This result offers the possibility to determine cleavage fracture toughness from post-test fracture surface examinations.Due to the large number of tests and the wide range of testing conditions, the Euro fracture toughness dataset gives a comprehensive insight into specimen size effects and temperature effects on ductile-to-brittle transition fracture. The Euro fracture toughness dataset includes a large set of raw test data such as load versus load line displacement curves and raw tensile test data for deriving stress-strain curves. The Dataset can be downloaded from the internet via the address ftp://ftp.gkss.de/pub/eurodataset.     

Mixed mode fracture toughness as a separation parameter when cutting polymers

Material separation at the tool edge during the cutting of polymers has been interpreted using fracture mechanics. The different types of chip that can be produced in the same material under different conditions reflect the cube–square scaling inherent in elastoplastic fracture mechanics. In the case of PMMA, it is shown that both globally-elastic brittle spalls and continuous ribbons formed by plastic shear may be produced merely by altering the depth of cut. In the case of LLDPE and Nylon 66, only continuous chips are formed as it was not possible to take the large depths of cut required in the sledge microtome used for experiments. The shape of the discrete brittle spalls arises because the loading of the tool edge on the workpiece is asymmetrical, resulting in both Mode I and Mode II displacements. The same loading applies when ductile chips are formed. Results seem to show that measured fracture toughnesses when chips form in shear can vary with tool rake angle (or equivalently with primary shear plane angle) and a model (based on a rule of mixtures of critical crack tip opening displacements) is presented that may explain the variation.     

The lower bound toughness procedure applied to the Euro fracture toughness dataset

The validity of a statistical method for estimating an engineering lower bound fracture toughness in the ductile-to-brittle transition region is investigated using the Euro fracture toughness dataset generated in the European SM&T Project “Fracture Toughness of Steel in the Ductile-to-Brittle Transition Regime”. The lower bound method is based on the empirical evidence that, in the low probability regime, the cumulative failure probability function tends to be a straight line rather than a curve as is the case for Weibull distributions. The investigation demonstrates that the engineering lower bound toughness values as predicted by the method are related to a cumulative cleavage failure probability lower than 2.5%. Such bound predictions can be achieved on the basis of a small number of cleavage toughness values measured at the temperature of interest. The results confirm the validity of the method.     

Large scale testing and statistical analysis of dynamic fracture toughness of ductile cast iron

The present paper deals with the experimental determination and statistical analysis of dynamic fracture toughness values of ductile cast iron. K_Id data from 140 mm thick single edge bend specimens of two dynamic fracture toughness test series on ductile cast iron from heavy-walled castings were analysed.At first, the statistical analysis of data at −40 °C was done based on ASME Code Case N-670 using a two-parameter Weibull distribution function. Weibull analyses of three samples covering different pearlite contents (?4%, ?9%, ?20%) were performed and characteristics of the distribution functions as well as two-sided confidence intervals were calculated. The calculated characteristics show that K_Id of ductile cast iron decreases with increasing pearlite content.In a second step, the applicability of the Master curve procedure according to ASTM E 1921 to ductile cast iron materials was investigated and it was formally used for statistical analysis of ductile cast iron dynamic fracture toughness data. Although the Master curve method was originally introduced for static fracture toughness data of ferritic steels, the successful individual analyses performed here support the engineering way taken to apply the method to ductile cast iron materials too. The results of both methods, the Master curve procedure and the ASME Code Case N-670, show acceptable congruity. At the same time, it is concluded from the present study that further investigations and experiments are required to improve precision and for verification before the results could be applied within component safety analyses.     

Experimental research on the compressive fracture toughness of wing fracture of frozen soil

It is commonly found that not only bending fracture but also compressive fracture occur frequently in compression, furthermore, in some specific conditions, compressive fracture sometimes has dominant effect on frozen soil. Therefore, it is extremely necessary to study the mechanical characteristics of the compressive fracture of frozen soil and to investigate the damage and fracture mechanism of frozen soil based on the previous research on frozen soil damage in compression. This study draws on the ideas and methods used in compression fracture research on ice that is very similar to frozen soil, and specific clay in Shenyang region was adopted as the experimental material, to make compressive specimens containing tilted wing crack of different angles, and uniaxial unconfined compression fracture experiments were conducted at different temperatures and loading rates. The fracture toughness K_IC and K_IIC of the main crack tip of the specimens are calculated with obtained experimental results and the law of K_IC and K_IIC changing with tilted angles, temperatures and loading rate is obtained to gain an insight to damage mechanism of frozen soil in compression. This paper presents a meaningful attempt for the research on compressive fracture of frozen soil, so as to better solve practical engineering problems.     

A statistical model of cleavage fracture

The aim of the paper is to provide a sound theoretical basis to the statistics of cleavage fracture in three-dimensional cracked structures. The probability of critically sized carbide being present in a Fracture Initiation Zone ahead of the crack tip has been derived, and shown to have a two-parameter Weibull distribution, with a shape parameter that is proportional to the strain-hardening exponent of the material. In a three-dimensional structure the cracking of such critically sized, intergranular carbide is necessary, but may not be sufficient to precipitate brittle fracture; this is because intergranular carbide is randomly orientated within the crack-opening stress field, so its orientation must also be unfavourable. It has been hypothesised that in three-dimensional structures the actual probability of fracture will be an extreme from the necessary distribution, in which case a sample of fracture toughness observations will be described by a Gumbel distribution, called here the LED model. After discussing the minimum number of fracture toughness observations needed to fit the model, its strength of evidence is compared with those of other candidate models, including the Master Curve model, and the LED model is shown to be the best.     

Master Curve implementation of the warm pre-stress effect

The Master Curve (MC) methodology has evolved from only being a brittle fracture testing and analysis procedure to a technological tool capable of addressing many more structural integrity issues like constraint and parameter transferability. One issue that not yet has been covered by the MC is the warm pre-stress (WPS) effect. This effect, which is known to produce an effective increase in fracture toughness, may be of great importance for some structural safety assessment situations where thermal transients are involved. Here, the WPS effect is re-examined and implemented into the MC methodology, by introducing a new simple WPS equation.     

Rethinking the role that the “step” in the load-displacement curves can play in measurement of fracture toughness for hard coatings

The “step” in the load-displacement curves during nanoindentation of hard coatings has been regarded as a representation of the energy dissipated during fracture of the coating thus is used in measuring the fracture toughness of this coating. This paper scrutinizes the “step” and finds that the “step” is a gap artificially bridged up with a straight line and that the “step” size corresponds with the thickness of the coating in testing. It is realized that the gap is formed due to loss of contact of the indenter with the sample. Upon catastrophic fracture of the coating, the indenter undergoes a freefall of a distance about the thickness of the coating. The size of such a “step” has no logic relationship with the energy dissipation that fractures the coating before the freefall of the indenter takes place.     

Warm pre-stress based pre-cracking criteria for fracture toughness testing

There are presently a magnitude of different fracture toughness testing standards that have different criteria for fatigue pre-cracking specimens prior to testing. The reason for the criteria is that too high pre-fatigue load may influence the subsequently measured fracture toughness value. The criteria have to a large extent been developed specifically for each standard in question and this has lead to the considerable variability in the criteria. The basic reason for the pre-fatigue having an effect on the fracture toughness is the warm pre-stress (WPS) effect. Here, existing data relating to pre-fatigue load levels are examined with the help of a newly developed simple WPS correction and a criteria and correction procedure for too high pre-fatigue loads are proposed. The new criteria focuses on brittle fracture, but is equally applicable for ductile fracture, thus enabling a unification of pre-fatigue criteria in different fracture toughness testing standards.     

Mixed mode fracture toughness of GFRP composites

Glass fibre reinforced polymer (GFRP) composites are used in a wide range of applications as a structural material. They have high specific mechanical properties but are prone to delamination as a result of manufacturing defects and impact/shock loading. The ability of the structure to continue to carry load after damage and the subsequent propensity of the damage to propagate are important considerations for the design of damage tolerant composite structures. In order to accurately predict the stability of damage under load, relevant mechanical properties of the material must be accurately determined. In particular, mixed mode fracture toughness data is required in order to study the damage criticality in such structures. This paper describes an experimental study to determine Mixed Mode fracture toughness for thick glass/vinylester specimens. The test methodology used for the experiments and its difficulties will be discussed. Mixed mode fracture toughness results are presented, as are Mode I and Mode II fracture toughness results obtained via Double Cantilever Beam (DCB) and End Notch Flexure (ENF) tests, respectively.     

Method of constraint loss correction of CTOD fracture toughness for fracture assessment of steel components

This paper presents a procedure for transferring the CTOD fracture toughness obtained from laboratory specimens to an equivalent CTOD for structural components, taking constraint loss into account. The Weibull stress criterion is applied to correct the CTOD for constraint loss, which leads to an equivalent CTOD ratio, β, defined as β = δ/δ_WP, where δ and δ_WP are CTODs of the standard fracture toughness specimen and the structural component, respectively, at the same level of the Weibull stress. The CTOD ratio β is intended to apply to the fracture assessment of ferritic steel components to stress levels beyond small-scale yielding. Nomographs are given to determine the β-value as a function of the crack type and size in the component, the yield-to-tensile ratio of the material and the Weibull shape parameter m. Examples of the fracture assessment using β are shown within the context of a failure assessment diagram (FAD). An excessive conservatism observed in the conventional procedure is reduced reasonably by applying the equivalent CTOD ratio, β.     

An assessment of fracture toughness in the ductile to brittle transition regime using the Euro fracture toughness dataset

The effect of specimen size on the fracture toughness of a ferritic steel in the transition regime has been investigated in a joint European Project. The project involved the testing of 25, 50, 100 and 200 mm wide compact specimens over the temperature range −154°C to 20°C with the aim of evaluating techniques for assessing the fracture toughness data.This paper evaluates the data at, or close to, the onset of stable tearing instead of at cleavage. The approach, which is applicable to structural assessment procedures, results in a temperature shift of less than 12°C between the specimen widths. The approach also enables simplified recommendations to be made for fracture toughness testing in the transition regime and the onset of upper shelf behaviour to be quantified.     

舰船结构钢的夏比冲击韧性与断口形貌

论述了从夏比冲击韧性分解出来的断裂扩展功与断口形貌的关系，指出冶金因素对夏比冲击韧性α＿ｋ值和扩展功的影响不完全是一致的，提出采用α＿ｋ，值和断口纤维率作为韧性指标的互补性，建议在我国的舰船结构钢韧性指标中增加断口纤维率的要求。     

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.     

Prometey local approach to brittle fracture: Development and application

Approach for prediction of brittle fracture proposed by the authors over recent years and known now as Prometey approach is briefly reviewed and new results for its development and application are represented. The physical and mechanical aspects of cleavage microcrack nucleation and propagation are considered. Application of the Prometey local approach is considered for prediction of the effect of irradiation and the shallow crack effect on the fracture toughness transition curve of RPV steels. The effect of the radiation damages on the cleavage microcrack nucleation is discussed.     

Fatigue fracture toughness of metals

The paper considers the peculiarities of fatigue crack propagation and final fracture of metals under cyclic loading. It is shown that the value of the fatigue fracture toughness of steels in an embrittled state is appreciably lower than that of the fracture toughness under static loading. A model of the transition from stable to unstable fatigue crack propagation is justified.