A model for the dynamic fracture toughness of ductile structural steel

We assume in this paper that the dynamic fracture toughness K_Id of ductile structural steels is dependent on void nucleation and void growth. The void nucleation-induced dynamic fracture toughness K_Id·n and the void growth-induced dynamic fracture toughness K_Id·g were obtained by modifying the void nucleation-induced and void growth-induced static fracture toughness models, respectively, considering the effect of strain rate and local temperature. By the relationship between the void nucleation-induced dynamic fracture toughness K_Id·n and the void growth-induced dynamic fracture toughness K_Id·g((K_Id)²=(K_Id·n)²+(K_Id·g)²) dynamic fracture toughness K_Id could be quantitatively evaluated. With this model the dynamic fracture toughness of two structural steels (X65 and SA440) was assessed, and the causes for the differences between the static and dynamic fracture toughness were also discussed.     

A model for the static fracture toughness of ductile structural steel

Fracture of ductile structural steels generally occurs after void initiation, void growth and void coalescence. In order for ductile fracture of structural steels to occur, energy must be spent to induce void initiation and void growth. Therefore, fracture toughness for ductile fracture should be contributed from void initiation and void growth. On the basis of this suggestion static fracture toughness (K_IC) of ductile structural steels is decomposed into two parts: void nucleation-induced fracture toughness (denoted as K_IC.n) and void growth-induced fracture toughness (K_IC.g). K_IC.n, defined as the stress intensity factor at which voids ahead of a crack begins to form, is calculated from crack tip strain distribution and void nucleation strain distribution. In contrast, K_IC.g is determined by the void growth from the beginning of void nucleation to void coalescence. Therefore, K_IC.g relates to the void sizes and void distribution. In this paper, the expression for K_IC.g is given from the void sizes directly from fracture surfaces. The relationship between K_IC.n, K_IC.g and K_IC is expressed in the form (K_IC)²=(K_IC.n)²+(K_IC.g)². The newly developed model was applied to the fracture toughness evaluation of three structural steels (SN490, X65 and SA440), and the theoretical calculation agrees with the experimental results.     

A model for the static fracture toughness of ductile structural steel

Fracture of ductile structural steels generally occurs after void initiation, void growth and void coalescence. In order for ductile fracture of structural steels to occur, energy must be spent to induce void initiation and void growth. Therefore, fracture toughness for ductile fracture should be contributed from void initiation and void growth. On the basis of this suggestion static fracture toughness (K_IC) of ductile structural steels is decomposed into two parts: void nucleation-induced fracture toughness (denoted as K_IC.n) and void growth-induced fracture toughness (K_IC.g). K_IC.n, defined as the stress intensity factor at which voids ahead of a crack begins to form, is calculated from crack tip strain distribution and void nucleation strain distribution. In contrast, K_IC.g is determined by the void growth from the beginning of void nucleation to void coalescence. Therefore, K_IC.g relates to the void sizes and void distribution. In this paper, the expression for K_IC.g is given from the void sizes directly from fracture surfaces. The relationship between K_IC.n, K_IC.g and K_IC is expressed in the form (K_IC)²=(K_IC.n)²+(K_IC.g)². The newly developed model was applied to the fracture toughness evaluation of three structural steels (SN490, X65 and SA440), and the theoretical calculation agrees with the experimental results.     

An alternate measure of fracture toughness

Linear elastic fracture mechanics has been primarily used for very high strength materials. For such applications it is adequate to measure K_Ic, the plane-strain fracture toughness. It is the objective of this paper to discuss a method for making dynamic fracture toughness measurements, K_Id, which are appropriate for structural grade steels. A simplified scheme for measuring K_Id is also proposed.     

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.     

Evaluation of dynamic fracture toughness KId by Hopkinson pressure bar loaded instrumented Charpy impact test

A novel method for measuring the dynamic fracture toughness, K_Id, using a Hopkinson pressure bar loaded instrumented Charpy impact test is presented in this paper. The stress intensity factor dynamic response curve (K_I(t)−t) for a fatigue-precracked Charpy specimen is evaluated by means of an approximate formula. The onset time of crack initiation is experimentally detected using the strain gauge method. The value of K_Id is determined from the critical dynamic stress intensity factor at crack initiation. A K_Id value for a high-strength steel is obtained using this method at a stress-intensity-factor rate () greater than 10⁶ MPa .     

Measurement of mode I and mode II rock dynamic fracture toughness with cracked straight through flattened Brazilian disc impacted by split Hopkinson pressure bar

In order to find an effective and convincing method to measure rock dynamic fracture toughness for mode I and mode II, cracked straight through flattened Brazilian disc specimens of marble, which were geometrically similar for three size, were diametrically impacted by split Hopkinson pressure bar on the flat end of the specimen with three load angle respectively. History of stress intensity factors (K_I(t) for opening mode I, and K_II(t) for sliding mode II), mode mixture ratio (K_I(t)/K_II(t)), as well as mode I and mode II dynamic fracture toughness at crack initiation (K_Id and K_IId) were determined with the experimental–numerical method. It is found that there is a unique size effect for dynamic fracture test with the specimens, the mode mixture ratio is not solely determined by load angle (the angle between load direction and crack line) as in the static loading; the pure mode II load angle is 19° for the ?50 mm specimen, however it is 10° for the ?130 mm and ?200 mm specimens; the mode II load angle decreases with increment of specimen size. Realization of pure mode II is justified by the mode mixture ratio approaching zero, it can be realized under certain load angle and loading rate for the specimen of specified size. K_IId is generally greater than K_Id. Both K_Id and K_IId increase with increment of specimen size, and this trend for K_IId is more remarkable than that for K_Id.     

Effect of welding thermal cycles and cold working on fracture toughness of SN490 steel under static and dynamic loading

Abstract

The static fracture toughness K _IC and dynamic fracture toughness K _Id of SN490, its pre-strained steel, and its welding heat affected zone were measured. K _IC tests were conducted according to the ASTM standard, and K _Id tests were carried out on an instrumented Charpy impacting machine. The experimental results were used to determine the effects of welding thermal cycle and cold working. It was found that both welding heat input and cold working are harmful to the fracture toughness of SN490 steel under both static and dynamic loading. The deleterious effects are serious under static loading. The detrimental effect of welding heat input during submerged arc welding was found to be more significant than that of the 10% plastic prestrain.     

Effect of pre-strain on fracture toughness of ductile structural steels under static and dynamic loading

The ductile fracture process consists of void nucleation, growth and coalescence. The whole ductile process can be divided into two successive steps: (I) the initial state to void nucleation, followed by (II) void growth up to void coalescence. Based on this suggestion, resistance to ductile fracture could be divided into the resistance to stage I and stage II, and accordingly the whole fracture toughness could be regarded to be due to contributions from stages I and II. The fracture toughness contributed from the two steps is, respectively, denoted as void nucleation-contributed fracture toughness and void growth-contributed fracture toughness. The effect of plastic pre-strain on the fracture toughness of ductile structural steels under static and dynamic loading (4.9 m/s) within the ductile fracture range was evaluated by summing contributions due to void nucleation-contributed and void growth-contributed fracture toughness. The effect of strain rate on fracture toughness was also investigated by the same means. The results show that both plastic pre-strain and high-speed loading decrease the void nucleation-contributed fracture toughness while their effects on the void growth-contributed fracture toughness depend on the variations in strength and ductility. Moreover, fracture toughness of structural steels generally decreases with increasing strain rate.     

Fracture behavior of ultra-fine grained steel bar under dynamic loading

Ultra-fine grained steel bars were recently developed by thermo-mechanical controlled rolling with rapid cooling for increasing the strength of low carbon and low alloy steels. The developed steels are characterized by fine ferrite grains of less than 1 m and high strength as a result of grain refinement. However, their correlations between tensile properties and impact behavior are not well understood. In this paper, impact absorbed energy (E _p) and dynamic fracture toughness (J _Id) were used to evaluate the dynamic fracture behavior of the ultra-fine grained steels, and the fracture mechanisms were also investigated. For the ultra-fine grained steels, tensile stress-strain curve was shown to be correlated with the impact curve of load vs. time, and to be related to the dynamic fracture toughness. The steel with large ferrite grains, small ferrite grain colony and martensite was found to have a good combination of strength and toughness.     

High strain rate behavior, transformation-induced plasticity and fracture toughness characterization of cast and additionally tempered Fe85Cr4Mo8V2C1 alloy manufactured using a rapid solidification technique

This study focuses on the characterization of the microstructures of an FeCrMoVC alloy in two states (an as-cast and a heat-treated state) as well as the compressive strain rate-dependent material and fracture toughness behavior. Both microstructures consist of martensite, retained austenite and complex carbides. Tempering results in a transformation of retained austenite into martensite, the precipitation of fine alloy carbides, and diffusion processes. High yield stresses, flow and ultimate compressive strength values at a relatively good deformability were measured. The yield and flow stresses at the onset of deformation are higher for the heat-treated state due to higher martensitic phase fractions and fine precipitations of alloy carbides respectively. Compressive deformation causes a strain-induced transformation of retained austenite to α′-martensite. Hence, both high-strength alloys are TRIP-assisted steels (TRansformation-Induced Plasticity). However, the martensitic transformation is more pronounced in the as-cast state due to higher phase fractions of retained austenite already in the initial state. Examinations of strained microstructures showed decreased crystallite sizes with increasing deformation. It is assumed that, during plastic deformation, the amount of low angle grain boundaries increases while the incremental formation of α′-martensite leads to decreased crystallite size. In general, lower microstrains were determined in the heat-treated state as a consequence of stress relaxation during tempering. In comparison to commercially available tool steels, the determined fracture toughness K _Ic of both variants revealed relatively high fracture toughness values. It was found that the lower shelf of K _Ic is already reached at room temperature. Higher loading rates $ \dot{K} $ resulted in lower dynamic fracture toughness K _Id values. Notch fracture toughness K _A measurements indicate that the critical notch tip radii of the examined materials are slightly smaller than 0.09?mm.     

Crack arrest in steels

This paper examines 3 theories that have been used to characterize the arrest capabilities of steels and structures: (1) The static analysis, arrest toughness ($\text{K}{}_{\mathrm{Ia}}$) theory; (2) The dynamically loaded/stationary crack toughness ($\text{K}{}_{\mathrm{Id}}$) theory, and (3) The dynamic analysis, propagating crack energy or toughness ($\text{R}{}_{\mathrm{ID}}$ or $\text{K}{}_{\mathrm{ID}}$) theory. These three concepts are examined in the light of measurements of unstable fracture and crack arrest in wedge-loaded DCB test pieces together with a fully dynamic analysis of the experiments.     

A new method to estimate the plane strain fracture toughness of materials

Although the testing method for fracture toughness K_IC has been implemented for decades, the strict specimen size requirements make it difficult to get the accurate K_IC for the high‐toughness materials. In this study, different specimen sizes of high‐strength steels were adopted in fracture toughness testing. Through the observations on the fracture surfaces of the K_IC specimen, it is shown that the fracture energy can be divided into 2 distinct parts: (1) the energy for flat fracture and (2) the energy for shear fracture. According to the energy criterion, the K_IC values can be acquired by small‐size specimens through derivation. The results reveal that the estimated toughness value is consistent with the experimental data. The new method would be widely applied to predict the fracture toughness of metallic materials with small‐size specimens.     

On Improvement of Methods for Experimental Determination of Strength Characteristics of NPP Component Materials

The methods for experimental determination of strength characteristics as per applicable standards have been reviewed. For some structural steels used in NPP facilities, the influence of loading parameters and specimen geometry are allowed for during the assessment of static fracture toughness (K_Ic, J_Ic). Recommendations are given on the setting of cycling conditions for fracture toughness testing of standard specimens with and without crack-guiding lateral grooves. The authors substantiate the applicability of the Master Curve method to determination of fatigue strength of small specimens with subsequent use of the results for calculating brittle fracture resistance of reactor pressure vessel materials in the welded joint.     

A study on the ASTM E1921 standard in determining the fracture toughness of ferritic steels

One of the most important aims of the fracture mechanics is to determine the fracture toughness of a material. Various methods were developed for this purpose and have been still used nowadays. In the J‐integral method that is one of them, providing of a dominant linear elastic condition on the specimen is not required. However, in ferritic steels, the fracture toughness values (K_JC) obtained by the J‐integral method show some inconsistencies. Therefore, the ASTM E1921 standard was developed on ferritic steels, which are instabilities in the values of elastic or elastoplastic fracture toughness. In this study, a new method was used to determine the fracture toughness (K_IC) of ferritic steels, and it was compared with the standard. Three steels with different mechanical properties and average grain size were investigated in this study.     

Dynamic fracture toughness of a high strength armor steel

This paper summarizes the results of a research being carried out to determine fracture behavior both in static and dynamic conditions of high strength armor steel Armox500T. In this research, notched specimens were cut to be tested in three-point bending test. Specimens were pre-cracked by flexural fatigue. Thereafter, some specimens were tested in bending up to rupture to determine the static fracture toughness K_IC. To obtain fracture toughness in dynamic conditions, a split Hopkinson bar modified to perform three-point bending tests was used. In this device, displacements and velocities of the specimen were measured, as well as the rupture time by means of fracture detection sensors, glued to the specimens. After that, a numerical simulation of the test was performed by using LS DYNA hydrocode, obtaining stresses and strain histories around the crack tip. From these results, the stress intensity factor history was derived. By using the rupture time, measured by the sensors, the value of the fracture toughness computed was unrealistic. Therefore, the use of a numerical procedure to obtain the rupture time was decided, by comparing experimental results of velocities at the transmission bar with numerical results obtained with several rupture times. With this procedure, the computation of dynamic fracture toughness was possible. The method shows that the measurement of the dynamic fracture toughness is possible without the needs of using crack sensors or strain gauges. It can be observed that fracture toughness of this steel under static and dynamic conditions is quite similar.     

A new method for determining the fracture toughness of main pipeline steels

One of the fundamental aims of fracture mechanics is to define fracture toughness K_IC of a material. Hence, the ASTM E399 standard was developed. However according to the standard, large‐sized specimens are required to determine the fracture toughness of low alloy carbon steels. ASTM E1921 standard was developed on the fracture toughness of ferritic steels. In this study, a new method was proposed to determine the fracture toughness of ferritic steels. The purpose of the present paper is to compare the results of the method with the experimental results. Two steels that are used in gas and oil main pipelines were investigated in this study.     

Correlation of fracture toughness with microstructural features for ultrafine‐grained 6082 Al alloy

In the present work, cryorolling (CR) and room temperature rolling (RTR) followed by annealing (AN) at 200°C were carried out to investigate the effects of grain size, precipitates (Mg‐Si‐phases), and AlFeMnSi‐phases on the fracture toughness of 6082 Al alloy. Using the values of the conditional fracture toughness, (K_Q), in the critical fracture toughness (K_IC) validation criteria, it was found that the sample size is inappropriate, which implies that the conditional fracture toughness obtained cannot be considered as the critical fracture toughness. Therefore, to establish the relative improvement in fracture toughness, the equivalent energy fracture toughness (K_ee) and J‐integral were calculated and used. The results show that the values of K_ee (89.91 MPa √m) and J (89.86 kJ/m²) obtained for the sample processed via CR followed by AN (CR + AN) are the highest when compared with the other samples processed through CR, RTR, and RTR followed by AN, RTR + AN. Microstructural features such as high fraction of low Taylor factor, high fraction of kernel average misorientation, Si‐rich particles, small size AlFeMnSi‐phases, and mixed mode of failure (transgranular shear and micro‐void coalescence) also support the high fracture toughness in the CR + AN sample. It was also observed that the effect of residual stresses on the fracture toughness of CR and RTR samples is minimal. Therefore, the correlation between microstructure and residual stresses is not considered in the present work due to very small values of the residual stresses for CR and RTR samples and the absence of residual stress from the heat‐treated samples.     

Fracture initiation under impact

In the first part of this paper the influence of temperature T and loading rate K_I upon the fracture toughness K_IC of structural steels is considered. A review of experimental results is presented over a wide range of loading rate and temperature in the form of the cross-sections of the constitutive surface K_INC = f(K_I,T). The hypothesis is proposed that both yield stress σ_y in uniaxial tension and fracture toughness K_IC are controlled by the same process of thermally activated movements of dislocations. Consequently, an introduction of the characteristic time t_c leads to the master plot K_IC (σ_y) in double logarithmic coordinates which is temperature and rate-independent. Such an approach provides a simple method for estimating the value of K_IC under a given set of imposed conditions (T,K?_I)₁ provided it is known for another set of imposed conditions (T,K?_I)₂.In the next part of this paper an attempt is presented to model the effect of T and K?_I on fracture toughness K_IC [15]. A model is discussed which combines correlations between critical cleavage stress σ_F, yield stress σ_y and the concept of thermally activated plastic flow from side and the local fracture criteria from the other [15]. It has been demonstrated that this approach can be useful in the proper predictions of changes of K_IC as a function of loading rate and temperature. For some steels, however, a minimum of fracture toughness is observed and typically occurs for $\text{K}{}_{\mathrm{I}}\text{? 1×10}{}^4$ MPa/pv/m/s at room temperature. The last part of this study deals with this important phenomenon [34]. It is concluded that the behavior of the constitutive surface K_IC = f(K_I,T) is highly nonlinear for steels.     

Loading rate effects on parameters of the Weibull stress model for ferritic steels

This study investigates the effects of loading rate on parameters of the Weibull stress model for prediction of cleavage fracture in a low strength, strongly rate-sensitive A515-70 pressure vessel steel. Based on measured, dynamic fracture toughness data from deep- and shallow-cracked SE(B) specimens, the calibrated Weibull modulus (m) at shows little difference from the value calibrated previously using static toughness data. This newly obtained result supports the hypothesis in an earlier study [Gao X, Dodds RH, Tregoning RL, Joyce JA. Weibull stress model for cleavage fracture under high-rate loading. Fatigue Fract Engng Mater Struct 2001;24:551-64] that the Weibull modulus likely remains rate independent for this material over the range of low-to-moderate loading rates. Additional experimental and computational results for higher rates show that a constant m-value remains applicable up to the maximum loading rate imposed in the testing program . Rate dependencies of the scale parameter (σ_u) and the threshold parameter (σ_w-min) are computed using the calibrated m, and the results indicate that σ_u decreases and σ_w-min increases with higher loading rates. The predicted cumulative probability for cleavage fracture exhibits a strong sensitivity to small changes in σ_u. Consequently, σ_u must be calibrated using dynamic fracture toughness data at each loading rate of interest in an application or selected to make the Weibull stress model predict a dynamic master curve of macroscopic toughness for the material.