Local Fracture Stress Research Articles

Effects of loading rate on the local cleavage fracture stress σf in notched specimens

Four point bending (4PB) notched specimens with different notch sizes are tested at various loading rates at a temperature of −110 °C for a C–Mn steel. An elastic–plastic finite element method (FEM) is used to determine the stress and strain distributions ahead of notches. By accurately measuring the distances of the cleavage initiation sites from the notch roots, the local cleavage fracture stress σ f is measured. The results show that the local cleavage fracture stress σ f does not essentially change with loading rate V and notch size. The reason for this is that the cleavage micromechanism does not change in the different specimens at various loading rates. The cleavage micromechanism involves competition of two critical events of crack propagation and crack nucleation in the high stress and strain volume ahead of notch root. The large scatter of σ f and notch toughness are mainly caused by the different critical events in different specimens.

Effect of duplex ferrite grain size distribution on local fracture stresses of Nb-microalloyed steels

Abstract Two commercial thermomechanically controlled rolled (TMCR) microalloyed steel plates have been used to investigate the relationship between the duplex ferrite grain size distribution and local fracture stresses. Statistical analyses of the grain size distributions were performed for the fine and coarse ferrite grains in the two steel plates. Microhardness values were measured for each grain size region and it was found that the fine grain areas have significantly higher microhardness values than the coarse grain areas. Tensile and blunt-notch slow bend tests were carried out over a range of temperatures on samples from the two commercial TMCR steel plates. The local fracture stress (σF) values were calculated and the results show that the σF values are almost independent of temperature. The presence of a mixed grain size distribution results in significant scatter in the local fracture stresses of the steels. The distribution of fracture stress values can be correlated to the coarse grain size distribution in the steels examined.

Effects of sizes of ferrite grains and carbide particles on toughness of notched and precracked specimens of low-alloy steels

Four point bending (4PB) tests of notched specimens and COD tests of precracked specimens were carried out on two steels; one steel was treated into two groups with the same ferrite grain size but different carbide sizes, the other steel with different ferrite grain sizes but similar carbide sizes. The results of the tests show that the toughness measured in notched specimens is mainly determined by the grain sizes, which define the local fracture stress σf; the size of carbide particle plays a minor role. However, on the contrary, in precracked specimens the toughness is sensitive to the carbide sizes, which affect the critical plastic strain epc for initiating a crack nucleus; the effect of grain size is indistinct. By these inferences the behavioral discrepancy of large grain steel in improvement of crack fracture toughness while reducing the notch toughness is explained.

セラミックスの破壊じん性とき裂前方損傷域寸法

Our previous technique for estimating critical sizes of the frontal process zone (FPZ) in ceramics was improved using exact solutions of stress distributions around crack and elliptical hole tips in an infinite plate for calculating local fracture stresses. The local fracture stress was calculated at the characteristic distance from the notch tip on the basis of a local fracture criterion. A three-point flexure test for alumina was carried out using V-notched specimens, and a formula for the relation between the strength and the notch depth including the short notch depth region was successfully established. The critical FPZ size of alumina was estimated from the fracture toughness and strength of the material. The critical FPZ sizes for alumina-based nanocomposites were also estimated. A concept of material design for toughened ceramics was discussed on the basis of these data. It was proved that there was a linear relationship between the fracture toughness and the product of strength and square-root of the FPZ size for these materials. This relation suggests that both the strength and the critical FPZ size must be increased to enhance the fracture toughness of ceramics.

04/00195 Application of the local fracture stress model on the cleavage fracture of the reactor pressure vessel steels in the transition temperature region: Yang, W.-J. et al. Journal of Nuclear Materials, 2003, 317, (2–3), 234–242

04/00195 Application of the local fracture stress model on the cleavage fracture of the reactor pressure vessel steels in the transition temperature region: Yang, W.-J. et al. Journal of Nuclear Materials, 2003, 317, (2–3), 234–242

On the statistical analysis of local fracture stresses in notched bars

Test results for critical local fracture stresses are analysed statistically for both “as-received” and “degraded” pressure-vessel weld metal. The values were determined from the fracture loads of blunt-notch four-point-bend specimens fractured over a range of low test temperatures, making use of results from a finite-element stress analysis of the stress–strain distributions ahead of the notch root. The “degraded” material tested in this work has been austenitized at a high temperature, followed by both prestraining and temper embrittlement. This has led to a situation in which the fracture stress for the “degraded” material is reduced significantly below that for the “as-received” material. The fracture mechanisms are different in that the “degraded” material shows evidence of intergranular fracture as well as cleavage fracture (in coarse grain size) whereas the “as-received” material shows only cleavage fracture (in fine grain size). The critical stress ( σ F) distributions plotted on normal probability paper show that the experimental cumulative distribution function (CDF) is linear for each condition with different mean values: 1560 MPa for “as-received” material and 1400 MPa for “degraded” material. The values of standard deviation are small and almost identical (33– 35 MPa ). The decrease of the local fracture stress after degradation is related to the local fracture micro-mechanisms. Statistical analysis of the results for the two conditions supports the hypothesis that the values of σ F are essentially single valued, within random experimental errors. A similar analysis of the data treating both conditions as a single population reveals some interesting points relating to statistical modelling and lower-bound estimation for mechanical properties. Comparisons are made with Weibull analysis of the data. A further conclusion is that it is extremely important to base any statistical model on inferences drawn from micro-mechanical modelling of processes, and that examination of “normal” CDFs can often provide good indications of when it is necessary to subject data to further statistical and physical analysis.

Statistical investigation of the fracture behaviour of inhomogeneous materials in tension and three-point bending

Development of damage in heterogeneous materials submitted to tensile tests and flexural tests is analysed using finite element analysis and considering statistical distribution of material strength. Materials are assumed to have a brittle local behaviour and fracture stresses are distributed randomly through test specimens. Also, the analysis considers that it exists a dimension which is characteristic of damage growing, depending on the fracture processes induced. A simulation procedure for evaluating damage development through test specimens is next implemented and the influence of the scattering width of the fracture stress distributions is analysed.

Analysis of Shape Variation of a Fatigue Surface Crack in a Pipeline

The authors have elaborated a model of nonthrough surface flaws in a pipeline under variable internal pressure. The model involves a proposed scheme allowing for variation of local fracture stresses along a curvilinear crack front. Verification of the theoretical model is carried out by comparing it with the available experimental data reported elsewhere. The authors have performed a comprehensive parametric study of the influence of initial flaw geometry, pipeline dimensions and variation of properties of steels due to heat treatment and test temperature on the surface crack behavior.

Effects of grain size on fracture toughness in transition temperature region of Mn–Mo–Ni low-alloy steels

An investigation was conducted into the effect of grain size on fracture toughness in the transition temperature region of Mn–Mo–Ni low-alloy steels used for nuclear pressure vessels. Three kinds of steels with different austenite grain sizes (AGS) were fabricated by varying the contents of Al and N, and their microstructures and mechanical properties were examined. Elastic–plastic cleavage fracture toughness, K Jc, was determined by three-point bend tests of precracked Charpy V-notch (PCVN) specimens according to ASTM E1921 standard test method. When the AGS decreased, the total number of carbides increased, while the size and the aspect ratio of carbides decreased. Local fracture stresses, estimated from a theoretical stress distribution in front of a crack tip, were found to be mainly determined by the 92nd% size of carbides. Cross-sectional areas beneath fracture surfaces were observed to understand microstructural features to affect the cleavage crack propagation behavior. The results showed that measured cleavage fracture units were smaller than AGSs, indicating that packet boundaries as well as austenite grain boundaries played an important role in the cleavage crack propagation. Based on the electron back-scatter diffraction (EBSD) results, the cleavage fracture units could also be matched with the effective grain sizes determined by the misorientation tolerance angle of 25°.

Analysis of fracture toughness in the transition-temperature region of an Mn-Mo-Ni low-alloy steel

This study is concerned with the analysis of fracture toughness in the transition region of an Mn-Mo-Ni low-alloy steel, in accordance with the ASTM E1921 standard test method. Elastic-plastic cleavage fracture toughness (K Jc ) was determined by three-point bend tests, using precracked Charpy V-notch (PCVN) specimens, and relationships between K Jc , the critical component of J (J c ), critical distance (X c ), stretch-zone width (SZW), local fracture stress, and plane-strain fracture toughness (K Ic were discussed on the basis of the cleavage fracture behavior in the transition region. The master curve and the 95 pct confidence curves well explained the variation in the measured K Jc , and the Weibull slope measured on the Weibull plots was consistent with the theoretical slope of 4. Fractographic observation indicated that X c linearly increased with increasing J c , and that the SZW had a good correlation with K Jc , irrespective of the test temperature. In addition, the local fracture stress was independent of the test temperature, because the tempered bainitic steel used in this study showed a propagation-controlled cleavage fracture behavior.

Application of the local fracture stress model on the cleavage fracture of the reactor pressure vessel steels in the transition temperature region

The fracture toughness in the ductile–brittle transition region of reactor pressure vessel steels was evaluated by means of an RKR-type model which describes the temperature dependence of the cleavage fracture toughness based on the constant fracture stress σ f. The fracture stress σ f and the characteristic distance are two main parameters in the RKR model. In order to apply the RKR model to the transition temperature region, these two parameters were investigated in different manners. In this study, the local fracture stress, σ f ∗ , was determined from the pre-cracked specimens. The results showed that the local fracture stress σ f ∗ determined from the pre-cracked specimens was higher than the fracture stress σ f from the notched specimens, while those values were practically independent of the temperatures. The CID (cleavage initiation distance), which represents the distance from the crack tip to the cleavage initiation site, was measured in every fractured specimen. The measured CID values were strongly dependent on the test temperatures. Besides, the fracture toughness K JC in the transition region was dependent on the measured CID. The RKR model, when the local fracture stress σ f ∗ and the measured CIDs were applied, could describe the temperature dependency of the median transition fracture toughness K JC(med).

Effects of geometry of notched specimens on the local cleavage fracture stress σf of C–Mn steel

An elastic–plastic three-dimensional finite element method analysis is used to determine the stress and strain distributions ahead of notches of four-point bending (4PB) specimens with various sizes ( W, B and a) and widths ( B). By measuring the location of the cleavage initiation sites for a C–Mn steel, the local cleavage fracture stress σ f is accurately determined. With increasing specimen sizes and widths the fracture load P f increases considerably, but σ f remains nearly constant. The reason that the σ f of the specimen with minimum size is slightly larger than that of the other specimens is analyzed by an active zone model of cleavage fracture for notched specimens. The critical event for cleavage fracture is the propagation of a ferrite grain-sized crack into the neighboring matrix, and is independent of specimen sizes and widths. σ f is mainly determined by the length of the critical microcrack, and the specimen sizes and widths have little effect on it.

ON THE MEASUREMENT AND PHYSICAL MEANING OF THE CLEAVAGE FRACTURE STRESS IN STEEL

Elastic-plastic two-dimensional (2D) and three-dimensional (3D) finite element models (FEM) are used to analyze the stress distributions ahead of notches of four-point bending (4PB) and three-point bending (3PB) specimens with various sizes of a C-Mn steel. By accurately measuring the location of the cleavage initiation sites, the local cleavage fracture stress σf and the macroscopic cleavage fracture stress σF is accurately measured. The σf and σF measured by 2D FEM are higher than that by 3D FEM. σf values are lower than the σF, and the σf values could be predicted by σf=(0.8−−1.0)σF. With increasing specimen sizes (W,B and a) and specimen widths (B) and changing loading methods (4PB and 3PB), the fracture load Pf changes considerably, but the σF and σf remain nearly constant. The stable lower boundary σF and σf values could be obtained by using notched specimens with sizes larger than the Griffiths–Owen specimen. The local cleavage fracture stress σf could be accurately used in the analysis of fracture micromechanism, and to characterize intrinsic toughness of steel. The macroscopic cleavage fracture stress σF is suggested to be a potential engineering parameter which can be used to assess fracture toughness of steel and to design engineering structure.

Mechanism of detrimental effects of carbon content on cleavage fracture toughness of low-alloy steel

The variation in fracture toughness of low-alloy base steels and weld steels with carbon contents of 0.08 and 0.21 wt pct was investigated using notched and precracked specimens tested at low temperatures. The attention is focused on the mechanism associated with detrimental effects on cleavage fracture toughness resulting from increasing carbon content. Analyses reveal that, in the case of constant ferrite grain sizes with increasing carbon content, the yield stress σy increases and the local fracture stress σf remains constant for notched specimens. For precracked specimens, the σy increases, whereas the σf decreases. In both cases, the ratio σf/σy decreases; this ratio is one of the principal factors inducing the deterioration in the cleavage fracture toughness of the higher carbon steels. Analyses also reveal that the critical strain for initiating a crack nucleus, which decreases with increasing carbon content and impurity elements, appears to be another principal factor that has a negative effect on the fracture toughness in both notched and precracked specimens. The results of the fracture toughness measured for weld metal with various grain sizes further support the predominant effect of grain size on the toughness of notched specimens.

Physical Fundamentals of a Local Approach to Analysis of Brittle Fracture of Metals and Alloys

We give a review of original investigations and the literature data on the local approach to the description of brittle (quasibrittle) fracture of metals with emphasis on the physical aspect of the problem. Two variants of the local approach are considered, namely: deterministic and probabilistic ones. We show that the local fracture stress σ F is not a constant but varies depending on the local plastic deformation and the degree of its inhomogeneity. We establish that a considerable excess of the local fracture stress over the brittle strength of a metal RMC under uniaxial tension is caused by a scale effect related to the localization of the induced fracture in an extremely small region. We consider a new variant of the local approach to brittle fracture without the Weibull distribution. In this case, the probability of fracture is found by computer simulation of the processes of formation of incipient cracks and loss of their stability. This approach enables us to separate the influence of the microstructure of a metal and its stress-strain state in the vicinity of a notch or a sharp crack on the local fracture stress. We established three main factors that control the regularities of micro- and macrofracture of a metal under conditions of stress concentration. These factors are the distribution of the lengths and orientations of incipient cracks and their density.

Effects of precracked specimen geometry on local cleavage fracture stress σf of low alloy steel

An elastic-plastic finite element method (FEM) is used to analyze the stress distributions ahead of crack tips for three types of COD specimens with different precracked depth a/W and height W of a low alloy steel, and the tensile and COD tests are carried out at various temperatures. By accurately measuring the distances of the cleavage initiation sites from the blunted crack tips, the local cleavage fracture stresses σf are measured. With increasing precrack depth a/W, specimen height W and test temperatures in a certain range, it was found that the σf essentially does not change. The σf is a steady inherent parameter of the material whose value is independent of the precracked specimen geometry.

Fracture Strength of Polysilicon thin Films at Stress Concentrations

AbstractThe fracture strengths of 3.5 microns thick and 20 or 50 microns wide polysilicon specimens were measured. One set of specimens was straight in the gage section, another set had a central hole 5.0 microns in diameter, and the third set had symmetric semicircular notches 2.5 microns in radius on each side. The local maximum fracture stresses of the non- uniform specimens, as calculated from the remote fracture stress with a stress concentration factor, were higher than measured in the straight specimens. This indicates a size effect, which is presumably due to the smaller highly stressed volume or area in the non-uniform specimens.

Study on cleavage fracture criteria of the quasi-brittle and micro-inhomogeneous materials

On the bases of recent achievements on the micro-mechanism of cleavage this paper analyses the inherent deficiencies of the stress intensity factor KI which is used to evaluate the fracture toughness of quasi-brittle and micro-inhomogeneous materials. The KI parameter can uniquely determine the field intensity ahead of a crack tip in the condition of elastic and small scale yielding (SSY). However, the KI cannot uniquely determine the critical condition triggering the cleavage fracture in a quasi-brittle and inhomogeneous steel where the cleavage fracture process is not a direct extension of the precrack but is initiated at a variable distance from the precrack tip. The variable distances of cleavage initiations invoke varied critical values of KI. On the bases of authors' experiments, this paper analyses the physical meaning of the local fracture stress σf, its stability and the feasibility to be used as an engineering parameter for assessing the fracture toughness.

Quantification of the warm prestressing effect in a shape welded 10 MnMoNi 5-5 material

This work describes investigations of the warm prestressing (WPS) effect in a 10 MnMoNi 5-5 shape welded material. Three point bend tests of precracked specimens were carried out for the following load cycles: cooling and loading to fracture without prestressing (CF), warm prestressing with loading, cooling, fracturing (LCF), and loading, unloading, cooling, fracturing (LUCF). The specimens were prestressed at room temperature (RT) and at a load level corresponding to K WPS of 70–80 MPa m 1/2, and fractured in the temperature range of −130°C to −158°C. Fracture surfaces of a number of specimens were observed in detail to measure the stretch zone width, the size and distance of cleavage origins from the blunted crack tip and to determine the character of the origins. For various loading cycles the stress distribution ahead of the crack tip and the crack tip opening displacement were numerically calculated. An increase in the apparent fracture toughness after WPS can be correlated with the geometry of the specimens, the loading cycle and, in particular, with the blunting of the original crack during prestressing. Based on the numerical results, the local fracture stress, σ f , was estimated. The local fracture stress turns out to be almost constant (2400–2500 MPa) for different specimens and load cycles. This suggests the use of σ f as a criterion to predict cleavage fracture after WPS. A statistical model is developed to predict failure loads from the calculated stress and strain fields. It is based on the Beremin concept and evaluates the incremental fracture probability, which depends not only on the maximum principal stress, but also on the equivalent plastic strain and its increment. This incremental probabilistic failure model predicts realistic fracture loads after WPS compared to the experiments, whereas the original Beremin model yields values which are too low.

Effects of notch geometry on the local cleavage fracture stress σf

An elastic–plastic finite element method (FEM) is used to analyse the stress and strain distributions ahead of notches with various depths and flank angles in four‐point bending (4PB) specimens of a C–Mn steel. By accurately measuring the distances of the cleavage initiation sites from the notch roots, the local cleavage fracture stress σf is measured. By increasing the notch depth and notch flank angle from 2.25 to 8.25 mm and 10 to 90°, respectively, the distributions of high stress and strain at the moment of fracture show considerable variations. However, the value of σf stays relatively constant. The critical fracture event is thus shown to be identical, i.e. the propagation of a ferrite grain‐sized crack into the neighbouring matrix. It is concluded that σf is mainly determined by the length of the critical microcrack, while the notch geometry and its associated stress volume have little effect on the value of σf . The cleavage site ahead of a notch is determined by the stress distributions and the positions of the weakest grains.