Fracture Toughness Distribution Research Articles

Composition-dependent brittleness and ductility of the multicomponent phase (Fe, Cr)23(C, B)6 in Fe–Cr–B–C alloys: First-principles calculations and modeling

(Fe, Cr)23(C, B)6, as a strengthening phase in Fe–Cr–B–C alloys, has not been reported on the relationship between its properties and composition over the entire composition range. (Fe, Cr)23(C, B)6 tends to exhibit brittleness, which is difficult to regulate through traditional experiments. The mechanical properties of (Fe, Cr)23(C, B)6 phase in Fe–Cr–B–C alloy have been studied by first principles calculation. With the help of CALPHAD method, the distribution of elastic constant, modulus, hardness and fracture toughness in the whole component space was obtained, so that the suitable component with good wear resistance and strong toughness was obtained. The mechanical properties of (Fe, Cr)23(C, B)6 phase is better in the range of ∼0.4–0.6 at. % B and ∼0.5–0.7 at. % Cr. The mechanism of these differences is explained in terms of state density, bond length, population analysis and differential charge density, as the addition of boron and the increase in chromium content led to a significant increase in the formation of covalent bonds between metals and non-metals, in which these bonds play a decisive role. The combination of the first principles calculation and the CALPHAD model provides a feasible model for constructing the composition-property relationship of medium entropy compounds.

A comparative study on characterizing the fracture toughness variations in thick-wall hydrogenation reactor welded joint by spherical indentation tests

This study provides an investigation on the existing models in predicting the fracture toughness distributions in thick-wall hydrogenation reactor welded joint from SITs. Three criterions, namely the critical stress, the critical strain, and the critical damage variable, were used in determining the critical indentation depth in the IEF model, together with the ERR model. Experimental results proved that none of the existing four criterions (or models) works for all zones in the welded joint. The critical stress criterion well reproduces the decrease of KIC in the weld (compared with that of the base metal) and the KIC distributions along the thickness, but may provide highly non-conservative predictions (more than 100% over-estimation). Highly stable KIC predictions were obtained from the critical strain criterion and the ERR model, but the critical strain criterion failed in characterizing weakest parts of the welded joint (i.e., the HAZ and weld) as assuming all zones with the same plasticity, and the ERR model failed in characterizing one of the weakest parts (i.e., weld) due to the existence of initial damage. Compared with the critical strain criterion and the ERR model, highly instable prediction results were observed in the CDV criterion, with the maximum error exceeds 50%. Source of errors in the existing fracture toughness prediction models were extensively explored through the physical basis of each criterion (or model) and from the solidarity of the phenomenologically summarized criterions.

An experimental investigation on predicting the fracture toughness distributions in ferritic-austenitic stainless steel dissimilar metal welds from spherical indentation tests

This study provides an experimental investigation on predicting the fracture toughness distributions in dissimilar metal welds (DMWs) connecting the nozzle of reactor pressure vessel (made of low-alloy steel) and the safety end of pipes (made of stainless steel). Indentation energy to fracture model with three criteria (namely the critical stress, critical strain, and critical damage variable, CDV) and the energy release rate (ERR) model were introduced into fracture toughness predictions from spherical indentation tests (SITs). It was found that consistency of the fracture toughness KIC calculated from the repeated tests using the critical strain criterion and ERR model is even higher than that from mini-CTs, while high dispersion predictions were observed in critical stress criterion. Compared with the CDV criterion, the ERR model focuses on the dissipation energy required to form unit area “equivalent-crack” (i.e., the rate) rather than the whole indentation energy till a critical depth, and thus it is less affected by the absolute value of damage variations in three repeated SITs. Source of errors were first investigated through the damage developments in uniaxial tensile specimens manufactured from different zones of the DMWs, which proves the CDV varies from 0.1 to 0.25 and thus shall not be regarded as a constant. Then, SEM observations were conducted on both the fracture surfaces from mini-CTs and the section surfaces from SITs, indicating both the changes in fracture mechanism (from ductile dominated to the joint effort of ductile void developments and cleavage micro-crack propagations) and the existence of small initial voids from welding lead to the errors in damage-mechanics-based predictions.

Determination on the fracture toughness of the welded joints of X80 pipeline steels based on small punch test

For the sake of design and integrity assessment of the fracture toughness of high-grade pipelines, it is necessary to carry out accurate fracture toughness assessment of the welded joints. The study of more concise and effective fracture toughness testing methods has important theoretical and engineering value. At present, the fracture control of girth welding joints is mainly based on J integral, CTOD and CTOA. However, it is hard to carry out standard fracture toughness tests at some local narrow areas of the welded joints such as the heat affected zone for the difficulty of sampling. On this basis, this paper aims to propose a method to determine the fracture initiation toughness JIC of the welded joints of high-grade pipeline steels based on the micro-sample test method - small punch test. Firstly, small punch specimen with through-thickness notch was designed. Secondly, the finite element model of the notched specimen was established, and verified by the notched specimen tests of X80 steel. Furthermore, the elastic–plastic material properties of different zones of the welded joint were obtained by the empirical correlation method of small punch test and further used for the determination of J contour integral. The GTN damage parameters were calibrated by the three-point bending tests and further used for the determination of the crack initiation displacement. Finally, the fracture initiation toughness JIC(SPT) of different zones of the welded joint were obtained by the SPT method and verified by the three-point bending test. The results show that the fracture initiation toughness JIC(SPT) of each region of the welded joint obtained by notched SPT specimen were all less than the SENB test results. But there is a good empirical correlation between the two results so that the SPT method can be further modified by establishing an empirical correlation model. The SPT method has good engineering application prospect for the accurately characterization of the different distribution of fracture toughness in different areas of the welded joints.

Determination of the temperature dependence of the fracture toughness of the metal of a thick-walled shell taking into account the inhomogeneity of the material

The estimates of the reference temperature T 0 , obtained for the base metal and the weld-seam metal of the Cr - Ni - Mo - V type (shell 200 mm thick) on the basis of statistical modeling by the Monte Carlo method are presented. T 0 was determined according to the ASTM E1921 standard taking into account the inhomogeneity of the material. The sample size of the fracture toughness values KJC for T 0 modeling was 12, 24 and 70. The Monte Carlo method was used for analysis of the correctness of metal identification (homogeneous/inhomogeneous). It is shown that sampling of 12 samples do not provide a reliable determination whether the metal is homogeneous or inhomogeneous (incorrect results were obtained in 50% of cases for the base metal and in 37% of cases for the weld-seam metal). When the sample size increased to 24 samples, the incorrect results were obtained in 5% of cases. The T 0 values with allowance for the material inhomogeneity were determined by two ways: using a screening procedure and proceeding from the actual bimodal representation of the fracture toughness distribution (parameters of the bimodal distribution were determined by the maximum likelihood method). It is shown that both methods give close results for the base and weld-seam metal, the magnitude of the shift towards positive values in the average T 0 values determined with allowance for the inhomogeneity being about 22°C. Using the obtained T 0 estimates, the lower envelopes of the temperature curves of the fracture toughness are constructed (master curves for 5 % failure probability).

CALPHAD aided mechanical properties screening in full composition space of NbC-TiC-VC-ZrC ultra-high temperature ceramics

High-entropy ceramics (HECs), especially ultrahigh-temperature ceramics, attract much attention from the refractory-materials community. However, current research about HECs focuses on the equimolar system, causing a gap between traditional and high-entropy ultrahigh-temperature ceramics. In this paper, we build the calculation of phase diagrams (CALPHAD) model of lattice parameters and elastic constants using the data from our first-principles calculation in the full composition space of NbC-TiC-VC-ZrC pseudo-quaternary NaCl-type monocarbides. With the aid of the CALPHAD model, we obtain the distribution of lattice parameters, elastic constants, hardness, fracture toughness, and wear resistance over the full composition space and give the maximum and minimum values for each property. Furthermore, the combination of first-principles calculations and CALPHAD modeling demonstrated in this paper provides a feasible paradigm for mapping the composition-property relationship, which can be applied in other HECs, such as high-entropy nitrides and high-entropy borides.

Microstructure, toughness, and tribological properties of laser cladded Mo2FeB2-based composite coating with in situ synthesized WC and La2O3 addition

Mo2FeB2-WC-La2O3 composite coatings were prepared using a preplaced method of laser cladding. The forming quality, microstructure, distribution of La, microhardness, fracture morphology, fracture toughness, and tribological properties were examined. The effect of La2O3 on the microstructure and properties of the coatings was analyzed. The results showed that the metallurgical bonding between the coating and substrate was significantly improved. La2O3 had no significant effect on the phases of the composite coatings. The microstructure growth of the La2O3 coating had no obvious direction and a block-like structure. The microstructure was initially refined and then coarsened with an increase in La2O3; La was found to exist at the Mo2FeB2 phase grain boundaries. The microhardness of the Mo2FeB2-WC coating was 1584.6 HV0.5. The microhardness of the composite coating that contained 0.3 wt% La2O3 reached 1494.7 HV0.5; its coefficient of friction (COF), wear rate, and fracture toughness were 0.31, 3.13 × 10−5 mm3/Nm, and 14.35 MPa·mm1/2, respectively. The crack resistance of the composite coating was the highest at 0.3 wt% La2O3 addition. The wear mechanisms of the coatings containing La2O3 were typical abrasive wear, and the coating without La2O3 was a combined mechanism of slight adhesive and abrasive wear. The coating exhibited an evident brittle fracture morphology.

A Three-Parameter Weibull Distribution Method to Determine the Fracture Property of PMMA Bone Cement.

Poly (methyl methacrylate) (PMMA) bone cement is an excellent biological material for anchoring joint replacements. Tensile strength and fracture toughness have a considerable impact on its application and service life. Considering the variability of PMMA bone cement, a three-parameter Weibull distribution method is suggested in the current study to evaluate its tensile strength and fracture toughness distribution. The coefficients of variation for tensile strength and fracture toughness were the minimum when the characteristic crack of PMMA bone cement was . Using the simple equation and fictitious crack length , the mean value (= 43.23 ), minimum value (= 26.29 ), standard deviation (= 6.42 ) of tensile strength, and these values of fracture toughness ( = 1.77 , = 1.02 , = 0.2644 ) were determined simultaneously through experimental data from a wedge splitting test. Based on the statistical analysis, the prediction line between peak load and equivalent area was obtained with 95% reliability. Nearly all experimental data are located within the scope of a 95% confidence interval. Furthermore, relationships were established between tensile strength, fracture toughness, and peak load . Consequently, it was revealed that peak load might be used to easily obtain PMMA bone cement fracture characteristics. Finally, the critical geometric dimension value of the PMMA bone cement sample with a linear elastic fracture was estimated.

A probabilistic approach for cleavage fracture including the statistics of microcracks: Application to a reactor pressure vessel steel

This work describes a probabilistic framework for cleavage fracture incorporating the measured statistics of microcracks to characterize the cleavage fracture toughness distribution in structural ferritic steels. Fracture toughness testing conducted on standard compact tension C(T) specimens for a 22NiMoCr37 pressure vessel steel, known as the EURO steel A, for varying test temperatures provides the cleavage fracture resistance data needed to determine the experimentally measured Jc-distribution. Metallographic examination of etched surfaces for the EURO steel also provides the distribution of carbides, which are assumed as the Griffith fracture-initiating particles, dispersed in the material from which the cleavage fracture toughness distribution is predicted. Overall, the analyses conducted in the present work show that the probabilistic model incorporating the statistics of microcracks holds significant promise as an engineering-level procedure to predict the fracture behavior in structural components with diverse range of temperature and possibly crack-tip constraint.

Analysis of thermal embrittlement of a low alloy steel weldment using fracture toughness and microstructural investigations

A thermally aged low alloy steel weld metal is investigated in terms of its fracture toughness and microstructural evolution and compared to a reference. The main purpose of the study is to investigate the effects of embrittlement due to thermal ageing on the brittle fracture toughness, and its effects on the influence of loss of crack tip constraint. The comparison of the investigated materials has been made at temperatures that give the same median fracture toughness of the high constraint specimens, ensuring comparability of the low constraint specimens. Ageing appears to enable brittle fracture initiation from grain boundaries besides initiation from second phase particles, making the fracture toughness distribution bimodal. Consequently, this appears to reduce the facture toughness of the low constraint specimens of the aged material as compared to the reference material. The microstructure is investigated at the nano scale using atom probe tomography where nanometer sized Ni-Mn-rich clusters, precipitated during ageing, are found primarily situated on dislocation lines.

A Comparative Study of Fracture Toughness Distribution of Reactor Pressure Vessel Material with Generalized Extreme Value Distribution and Weibull Distribution in the Lower Self of Ductile to Brittle Transition Region

A Comparative Study of Fracture Toughness Distribution of Reactor Pressure Vessel Material with Generalized Extreme Value Distribution and Weibull Distribution in the Lower Self of Ductile to Brittle Transition Region

Influence of Material Toughness on Fracture Reliability in Steel Bridges

The fracture limit state of the AASHTO LRFD Bridge Design Specifications is addressed by requiring minimum impact toughness values for base material and mitigating potential fracture initiators through proper structural detailing. This fracture control approach has been successful in minimizing the number of fractures in steel bridges designed since its inception; however, it is not a calibrated limit state and the structural reliability against sudden brittle fracture has not been previously established. Accordingly, the objective of this study was to quantify the relationship between material toughness and fracture reliability in steel bridge members, considering the probabilistic distribution of fracture toughness and applied stress for a variety of structural steels and assumed crack sizes. The master curve approach is used to account for the probabilistic distribution of fracture toughness, and reliabilities are determined using Monte Carlo simulation and the Hasofer-Lind approach. The results indicate that the fracture reliability for modern bridge steels is consistent with the reliability of AASHTO strength limit states, and that certain steels currently available on the market can provide enough reliability against fracture to essentially eliminate brittle fracture as a limit state of concern. This finding holds the potential for a new way of approaching the design of fracture-critical members.

The method for calculating the probability of brittle destruction of NPP equipment in different operating modes with postulated defectiveness

The destruction of equipment metal by a brittle fracture mechanism is a probabilistic event at nuclear power plants (NPP). The calculation for resistance to brittle destruction is performed for NPP equipment exposed to neutron irradiation; for example, for a reactor plant such as a water-water energetic reactor (WWER), this is a reactor pressure vessel. The destruction of the reactor pressure vessel leads to a beyond design-basis accident, therefore, the determination of the probability of brittle destruction is an important task. The research method is probabilistic analysis of brittle destruction, which takes into account statistical data on residual defectiveness of equipment, experimental results of equipment fracture toughness and load for the main operating modes of NPP equipment. Residual defectiveness (a set of remaining defects in the equipment material that were not detected by non-destructive testing methods after manufacturing (operation), control and repair of the detected defects) is the most important characteristic of the equipment material that affects its strength and service life. A missed defect of a considerable size admitted into operation can reduce the bearing capacity and reduce the time of safe operation from the nominal design value down to zero; therefore, any forecast of the structure reliability without taking into account residual defectiveness will be incorrect. The application of the developed method is demonstrated on the example of an NPP reactor pressure vessel with a WWER-1000 reactor unit when using the maximum allowable operating loads, in the absence of load dispersion in different operating modes, and taking into account the actual values of the distributions of fracture toughness and residual defectiveness. The practical significance of the developed method lies in the possibility of obtaining values of the actual probability of destruction of NPP equipment in order to determine the reliability of equipment operation, as well as possible reliability margins for their subsequent optimization.

Reliability prediction of a microwave sintered Si3N4-based composite ceramic tool

The wear life reliability prediction model of microwave sintered Si3N4/(W,Ti)C/Y2O3/MgO/Al2O3 composite ceramic tools based on the random distribution characteristics of hardness and fracture toughness of ceramic tool material was established. It showed that the Vickers hardness of ceramic tool materials followed a normal distribution and the fracture toughness followed a lognormal distribution. Distribution law of wear life can be determined by the joint distribution of hardness and fracture toughness. Experimental research on tool reliability of continuous dry cutting quenched high quality carbon steel T10A was carried out and the applicability of the tool reliability prediction model was verified. The results showed that the error between the theoretical reliable life and the actual life of the ceramic tool was less than 5% under the same reliability when the reliability was above 0.5.

A weakest link model for multiple mechanism brittle fracture — Model development and application

A multiple mechanism weakest link model for intergranular and transgranular brittle fracture is developed on the basis of experimental observations of a thermally aged low alloy steel. The model development is carried out in tandem with micro mechanical analysis of grain boundary cracking using crystal plasticity modeling of polycrystalline aggregates with the purpose to inform the weakest link model. The fracture modeling presented in this paper is carried out by using a non-local porous plastic Gurson model where the void volume fraction evolution is regularized over two separate length scales. The ductile crack growth preceding the final brittle fracture is well predicted using this type of modeling. When applied to the brittle fracture tests, the weakest link model predicts the fracture toughness distribution remarkably well, both in terms of the constraint and the size effect. Included in the study is also the analysis of a reference material.

The simplified approach for estimating probabilistic safety factors in fracture mechanics

Basic principles of the simplified probabilistic approach in structural integrity assessment are proposed to estimate probabilistic safety factors against fracture. The coefficients of variation for the material resistance are assumed to be the same independently on modes of failure and the resistance effects, namely, fracture or plastic collapse. The load for engineering components under consideration is assumed to be described by the stochastic distribution independently on modes of failure. In this case, probabilistic safety factor against collapse can be employed to estimate safety factors against fracture taking into account correlation of the safety factor against collapse in terms of the yield stress with safety factors against fracture in terms of the fracture toughness or the failure assessment diagram. Thus, safety factors against fracture calculated by this simplified method can be considered as probabilistic safety factors. The probability of failure as a function of the safety factor against collapse is estimated by means of the reliability index β calculated for representative combinations of the coefficients of variation (COV). The effect of the failure probability on the safety factor against fracture in terms of the fracture toughness and the failure assessment diagram for representative combinations of the values COV is analyzed. This approach will allow avoiding more complex and costly probabilistic analysis of failure for fracture based on the fracture toughness distribution.

Optimization of chevron-notched short bar specimen configuration for determination of the fracture toughness and crack growth rate of aluminum alloys

The goal of the study is optimization of the fracture toughness determination procedure on the samples with a chevron notch. Well-known principles of fracture mechanics are used to determine the geometry of a specimen with a chevron notch, which ensures the independence of the stress intensity factor from the crack length in the range sufficient for its practical application. A requirement to the shape of the dependence «compliance – crack length» is formulated for a chevron-notched specimen. The choice of the cross-sectional shape of the specimen with a chevron notch, the geometric dimensions of the specimen, and the drawing of the gripping device are justified. The formula for calculation of the fracture toughness from the maximum test load and thickness of the specimen is derived and experimentally validated. The results of the fracture toughness tests of the samples with a chevron notch and standard samples are compared for a number of aluminum alloys. The data on the scale factor in the range of a sample thicknesses of 12.5, 25, and 50 mm and variation coefficient obtained upon the fracture toughness determination revealed the absence of the significant effect of the scale factor, 6% variation under the normal law of the fracture toughness distribution in the tests of chevron-notched specimens. The results on the fracture toughness distribution in the height of the thick plates of alloys 1163T1 and V95pchT2 are presented. The temperature dependence of the fracture toughness of the plate (alloy 1201T1) are constructed for chevron-notched specimens within a temperature range of –196 – +200°C. The features of using chevron-notched specimens for determination of the crack growth rate attributed to independence of the stress intensity factor at the crack tip on crack length are considered in a rather wide range. The method of the crack growth rate determination is described and the results of assessing d a /d N – Δ K for an aluminum alloy plate 1163T are presented. The simplicity and reliability of the methods for determination of the fracture toughness and fracture growth rate (fatigue, creep, corrosion) on chevron-notched specimen of the proposed geometry allow us to recommend them for control tests and research in various test conditions.

Probability of brittle failure in different geometries using a simplified constraint based local criterion method

This paper introduces a novel calibration method for the original Beremin model to predict cleavage fracture in various fracture mechanics geometries with differing crack tip constraints. Calibration of Weibull parameters were conducted with respect to the goodness of fitness and the probability of the fracture toughness distributions for low and high constraint specimens. By introducing a reference diagram for a specific material based on the T-stress as a crack tip constraint parameter, the applicability of calibrated parameters was investigated for the experimental data of specimens with different geometry. The findings indicated that the ratio of Weibull stresses to associated calibrated scale parameters (here denoted as σw,R) at fracture loads for specimens with different shapes were in a same range. Therefore, by calculating T-stress as crack tip constraint for a typical geometry, a suitable prediction of probability of failure would be possible with respect to the reference diagram.

Determination of fracture toughness of nano-scale cement composites using simulated nanoindentation technique

With the advent of instrumented nanoindentation, mechanical properties of cement paste composites such as elastic modulus, hardness, creep have been explored at micro- and nano- level. However, fracture toughness studies on hydrating cementitious composites at these levels, though very crucial in characterizing the material at the macro scales, are rarely reported. First, simulated nanoindentation method is used to determine the fracture toughness of three different phases of cement paste, i.e., Tri-calcium Silicate (C3S), Di-calcium Silicate (C2S) and Calcium – Silicate – Hydrate (CSH) individually. Subsequently, a discretized multi-phase microstructural model of cement paste is used to represent the multi-phase characteristics of cement hydration. To evaluate the fracture toughness properties of hydrating cement paste, a novel grid indentation technique for simulated nanoindentation is established and the values obtained are presented. Experimental grid nanoindentation has been conducted on hydrated cement paste to obtain fracture toughness property and compared with those obtained through numerical studies. These obtained phase fracture toughness values will help in understanding the evolution and distribution of fracture toughness in cementitious composites. This study establishes a validated procedure to evaluate fracture toughness of the microstructural phases present in cement paste by simulated grid nanoindentation.

A Statistical Model of Cleavage Fracture Toughness of Ferritic Steel DIN 22NiMoCr37 at Different Temperatures

It is a conventional practice to adopt Weibull statistics with a modulus of 4 for characterizing the statistical distribution of cleavage fracture toughness of ferritic steels, albeit based on a rather weak physical justification. In this study, a statistical model for cleavage fracture toughness of ferritic steels is proposed according to a new local approach model. The model suggests that there exists a unique correlation of the cumulative failure probability, fracture toughness and yield strength. This correlation is validated by the Euro fracture toughness dataset for 1CT specimens at four different temperatures, which deviates from the Weibull statistical model with a modulus of four.