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 _f and the macroscopic cleavage fracture stress _F is accurately measured. The _f and _F measured by 2D FEM are higher than that by 3D FEM. _f values are lower than the _F, and the _f values could be predicted by _f=(0.8––1.0)_F. With increasing specimen sizes (W,B and a) and specimen widths (B) and changing loading methods (4PB and 3PB), the fracture load P _f changes considerably, but the _F and _f remain nearly constant. The stable lower boundary _F and _f values could be obtained by using notched specimens with sizes larger than the Griffiths–Owen specimen. The local cleavage fracture stress _f could be accurately used in the analysis of fracture micromechanism, and to characterize intrinsic toughness of steel. The macroscopic cleavage fracture stress _F is suggested to be a potential engineering parameter which can be used to assess fracture toughness of steel and to design engineering structure.     

On locations initiating cleavage fracture in precracked specimens of low alloy steel and weld metal

On the basis of a model of an `active zone' for initiating cleavage fracture proposed by authors, the distributions of cleavage initiation location in precracked specimens are explained, and the factors affecting cleavage initiation locations are analyzed. The change of the length of the active zone with applied load determines the distributions of cleavage initiation locations. With increasing temperatures, the distance X_f from precrack tip to locations initiating cleavage fracture and its scatter increase, and the lower boundary of X_f increases slowly, and the scatter is mainly caused by the rapid increase of the upper boundary. With decreasing the strength of the weakest constituent in steels and increasing their number, the minimum distance X_min and the average distance for initiating cleavage fracture will decrease and the maximum distance X_max will increase, and the corresponding toughness values will be decreased.     

On the fracture toughness anisotropy of mechanically poled ferroelectric ceramics

In this paper an incremental constitutive theory for the deformation due to switching in ferroelectrics is applied to predict the fracture toughness anisotropy in these materials after mechanical poling. Mechanical poling of an initially unpoled specimen differs from electrical poling in that only mechanical stresses are applied to the material. Therefore, no electrical polarization can develop. After mechanical poling, for example by a uniaxial applied stress, the fracture toughness of a ferroelectric ceramic for cracks running parallel or orthogonal to the poling direction will differ. Finite element computations of the steady crack growth process have been carried out to quantify these differences. Results are generated for a range of constitutive properties for three crack growth directions with respect to the initial mechanical poling direction. The results are discussed in relation to available experimental data and to the toughness anisotropy due to electrical poling.     

A model to predict the fracture distance of cleavage fracture as a function of temperature

We propose a model which computes the fracture distance of materials (reactor pressure vessel steel, C–Mn steel, and four heat-treated HSLA steels) as a function of temperature. The fracture distance, an important length scale for predicting cleavage fracture, is determined using the parameters such as mean grain size, fracture toughness and yield stress of the material in the range of −250 to 0 °C. The fracture distances computed from the proposed model agreed with measurements for the materials. Some differences between the predictions and the measurements were observed for HSLA steel with fine grain size (30 μm) and coarse grain size (55 μm).     

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.     

A probabilistic model for cleavage fracture with a length scale-influence of material parameters and constraint

A probabilistic model for the cumulative probability of failure by cleavage fracture with a material related length scale is developed in this study. The model aims at describing the random nature of fracture in ferritic steels in the brittle-to-ductile transition temperature region. The model derives from use of an exponential function to describe the distribution of microstructural entities eligible to take part in the fracture initiation process, where also a dependence on effective plastic strain is incorporated. A nonlocal stress measure, calculated as the average stress in a spherical volume, drives the contribution to failure probability of an infinitesimal material volume. The radius of the spherical volume enters as the material length in this model. This length has a significant influence on failure probability predictions in geometries exposed to strong stress gradients as found ahead of cracks. The material length is associated with a fracture toughness threshold value. In a fracture application three model parameters need to be estimated based on testing; a parameter directly related to the mean fracture toughness, a parameter that primarily is related to crack-tip constraint effects and the material length parameter. The model is explored in a parametric study showing model features in concord with typical features found in toughness distributions from fracture mechanics testing in the transition region.     

Experimental and numerical investigation of thickness effect on ductile fracture toughness of steel alloy sheets

Effect of thickness on ductile fracture toughness of plates made of steel alloy GOST 08Ch22N6T is investigated experimentally. Multiple specimen tests for determining fracture toughness have been conducted using compact tension (CT) specimens with thicknesses of 1.25, 1.64 and 4.06 mm according to standard test method ASTM E813. The results show the significant effect of thickness on fracture toughness. It is observed that in low thickness, J_c increases with the thickness increase until it reaches a maximum; however, further increase in the thickness causes the J_c-value to decrease. Two-dimensional finite element analysis is also performed to reproduce the experimental results. The comparison shows a very good agreement.     

An FEM study on crack tip blunting in ductile fracture initiation

Ductile fracture is initiated by void nucleation at a characteristic distance (I_c) from the crack tip and propagated by void growth followed by coalescence with the tip. The earlier concepts expressed I_c in terms of grain size or inter-particle distance because grain and particle boundaries form potential sites for void nucleation. However, Srinivas et al. (1994) observed nucleation of such voids even inside the crack tip grains in a nominally particle free Armco iron. In an attempt to achieve a unified understanding of these observations, typical crack-tip blunting prior to ductile fracture in a standard C(T) specimen (Mode I) was studied using a finite element method (FEM) supporting large elasto-plastic deformation and material rotation. Using a set of experimental data on Armco iron specimens of different grain sizes, it is shown that none of the locations of the maxima of the parameters stress, strain and strain energy density correspond to I_c. Nevertheless, the size of the zone of intense plastic deformation, as calculated from the strain energy density distribution ahead of the crack tip in the crack plane, compares well with the experimentally measured I_c. The integral of the strain energy density variation from the crack tip to the location of void nucleation is found to be linearly proportional to J_IC. Using this result, an expression is arrived at relating I_c to J_IC and further extended to CTOD_c.     

平面应变断裂韧度评定中临界载荷研究

针对新版断裂韧性测试规范扩大的裂纹长度适用范围,利用有限元精细分析用于平面应变断裂韧度KIC评定中割线法确定临界载荷PQ的相对割线斜率ΔS的合理性,提出0.45≤a/W≤0.7范围内的相对割线斜率ΔS的表达式。结果表明:现行规范推荐的相对割线斜率ΔS不再适合于确定0.55a/W≤0.7范围内的临界载荷PQ,其最大相对误差已近8%。     

A statistical model for cleavage fracture in notched specimens of C–Mn steel

A statistical model for cleavage fracture in notched specimens of C-Mn steel has been proposed. This model is based on a recently suggested physical model. This statistical model satisfactorily describes the distributions of the cumulative failure probability and failure probability density of 36 notched specimens fractured at various loads at test temperature of −196 °C. The minimum notch toughness has also been discussed.     

A probabilistic model for the pearlite-induced cleavage of a plain carbon structural steel

The cleavage fracture of a carbon structural steel is shown to deviate from what is typical of a ferritic matrix. This occurs at temperatures ranging from −150 to 20 °C and affects the scatter of fracture toughness, and fractographic features. To explain the observed discrepancies a probabilistic model is developed by linking physical mechanisms of cleavage with continuum mechanics analysis applied to fracture. The model assumes that cleavage is nucleated and triggered in pearlite within the blunting zone of the crack tip by the mechanism of Miller and Smith. Once the model is calibrated for the steel, its predictions are shown to agree with the experimental results.     

Experimental and numerical assessment of fracture toughness of dual-phase austempered ductile iron

The effects of the microstructure topology on the fracture toughness of dual-phase austempered ductile iron are studied in this paper by means of finite element modelling and experimental testing. To this end, specimens with matrix microstructures ranging from fully ferrite to fully ausferrite were studied and the preferential zones and phases for crack propagation were identified in every case. The effectiveness of the ausferrite phase as a reinforcement of the ferritic matrix via the encapsulation of the brittle and weak last-to-freeze (LTF) zones was confirmed. The toughening mechanism is consequence of the increment in the crack path longitude as it avoids the encapsulated LTF zones. Besides, the presence of small pools of allotriomorphic ferrite increase the crack propagation resistance of the ausferrite-ferrite matrices.     

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.     

Statistical scatter in the fracture toughness and Charpy impact energy of pearlitic steel

The effect of microstructure on the fracture characteristics of high carbon hypo eutectoid steel was studied under conditions of quasistatic and dynamic loading. Experimentally determined sets of fracture toughness and Charpy impact energy values were statistically treated. A relationship was found between fracture toughness and Charpy impact energy. In the very brittle domain, the fracture toughness increases slightly with increasing Charpy impact energy. In the domain where the fracture toughness is higher, the rise in fracture toughness with increasing Charpy impact energy is more pronounced. Detailed SEM examination of fractured compact tension (CT) and Charpy V-notch (CVN) specimens showed that the fracture at ambient temperature occurred almost exclusively by cleavage. There were no visible differences in the morphology of cleavage facets on the fracture surfaces of Charpy and CT specimens. Mechanisms of cleavage initiation were revealed by the fractographical investigation of fracture surfaces. Whereas the fracture surfaces of broken CT specimens exhibit a number of cleavage origins, the fracture surfaces of CVN specimens usually show only one.     

A new statistical local criterion for cleavage fracture in steel. Part II: application to an offshore structural steel

In the first part of this paper, a new model for cleavage fracture in steel was presented, based on a new statistical local criterion, which expresses the necessity of simultaneously fulfilling the conditions for both cleavage microcrack nucleation and propagation. In this second part, the assumptions and predictive capabilities of the new model are assessed using a modern offshore structural steel plate (Grade 450EMZ). It is shown that the model assumptions are consistent with the cleavage fracture behaviour of the steel and that the new model has the potential of correctly quantifying the effects of size, constraint, temperature and strain rate on cleavage fracture risk.     

Evaluation of interfacial fracture toughness of a flip-chip package and a bimaterial system by a combined experimental and numerical method

In this paper, the interfacial fracture toughness of a flip-chip package subjected to a constant concentrated line load and a bimaterial system under thermal loading condition were evaluated using a unique six-axis submicron tester, a thermal vacuum chamber and FEM modeling coupled with a high density laser moiré interferometry. The six-axis submicron tester was used to provide a constant concentrated line load, whereas the moiré interferometry technique was used to monitor the crack length during the test. In addition, a finite element technique was simultaneously used to determine the near crack tip displacement fields of the specimens. The interfacial fracture toughness and phase angle were computed by using these near tip displacement variables through the analytical energy release rate and phase angle expressions derived by authors. The interfacial fracture toughness and the phase angle of the flip-chip package considered at the interface where the passivated silicon chip meets the underfill are 35 J/m² and −65°, respectively, while the interfacial fracture toughness and the phase angle of the tested bimaterial specimen at the interface of the molding compound/silicon with the crack length of 3.3 mm under the temperature rise thermal load from room temperature (20°C) to 138°C are 20.02 J/m² and −54.8°, respectively.     

On mixed-mode fracture of PVC foam

This paper reports on mixed-mode fracture in rigid cellular PVC foam based on experimental and numerical analyses. Experiments were performed on sharp-cracked specimens using the compact-tension-shear (CTS) test loading device. Foams of three different densities were tested. The CTS specimen was, in association with a special loading device, an appropriate apparatus for experimental mixed-mode fracture analysis. Experimentally-obtained fracture toughness results show good consistency. K_IC fracture toughness was marginally different in different directions. The ratio K_{II C}/K_{I C} was found to be between 0.4 and 0.65 depending on the foam density. For mixed-mode loading, Richard's criterion – using experimentally obtained K_{I C} and K_{II C} – was the best in predicting accurately fracture locus and fracture angle. When no experimental data were used, the maximum hoop stress criterion predicted best kinking angle. The principal strain criterion predicted the best fracture locus. Fracture boundary curve and kinking angle were best predicted for low mode II contribution. This revised version was published online in August 2006 with corrections to the Cover Date.     

Statistical scatter of fracture toughness in the ductile-brittle transition of a structural steel

The statistical scatter of fracture toughness in the ductile-brittle transition temperature range was experimentally examined on a 500 MPa class low carbon steel. Fracture toughness tests were replicatedly performed at −60 °C, −20 °C and −10 °C. The tests at −60 °C resulted in a single modal Weibull distribution with a shape parameter of 4 for the critical stress intensity factor converted from J-integral, whereas the Weibull distributions of the critical stress intensity factor at −20 °C and −10 °C showed a bilinear pattern with an elbow point, which caused a wider scatter than that at −60 °C. Such scatter transition behavior was discussed with reference to stable crack initiation. A model of the statistical scatter transition has been proposed in this work and the model reasonably explains the experimental results.