Impact fracture of a ferritic steel in the lower shelf regime

This paper reports the results of a systematic investigation on the fracture of Charpy-V notch A508 steel specimens, tested in the lower shelf regime. The fracture energy has been determined for quasi-static, standard Charpy and one-point-bend impact. The results show a general trend for the fracture energy to increase with the loading rate, at the lower temperature (–160 °C). At this temperature, the roughness of the fracture surface increases markedly with the loading rate. The fractographic analysis shows the presence of 3–4 cleavage initiation sites situated at 100–800 m from the crack front, irrespective of the loading rate. Numerous cleavage microcracks are observed underneath the main fracture plane. The statistical analysis shows that the length distribution of the microcracks is adequately described by Weibull statistics. It is also found that the number of microcracks increases with the loading rate. It is suggested that the larger number of microcracks is responsible for the observed increased roughness and energy dissipation.     

The fracture stress of float glass

A fracture test [1] which uses concentrically loaded square plates supported near their corners has been used to measure the fracture stress of float glass. The plates were 102mm square and 5.98mm thick. The maximum displacement at fracture was less than 0.4mm. Under these circumstances it has been shown that use of a linear finite element solution for the stress distribution and the plate deflections is justified. The glass plates had greater edge damage than had the alumina plates tested in an earlier investigation. In order to secure an adequate proportion of failures in the central plate region, it was necessary to move the supports inwards towards the centre of the plate. This reduced the ratio of the maximum edge stress to the maximum stress in the plate. Batches of plates were tested with loading circle diameters of 7.5 and 25mm, to measure volume effects, with the side of the plate that had been in contact with the liquid tin in tension. Median ranking was used in the statistical analysis and edge failures were treated as suspensions, it being assumed that the minimum fracture stress of the central region of the edge-fractured plates was the plate centre stress at the fracture load. The Weibull modulus was determined by a linear regression in which extreme members of the population were given reduced weighting using the relationship of Faucher and Tyson [3]. The average fracture stresses were 147.2 and 107.3 N mm^–2 for the 7.5 and 25 mm loading circles, respectively, and the Weibull moduli were 4.49 and 5.44. These data are shown to agree well with Weibull statistics. Tests using a 7.5 mm diameter loading circle on plates with the non-tin side in tension gave a significantly higher average fracture stress of 242.1 N mm^–2, confirming the fact that the non-tin side has a higher strength.     

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.     

A statistical approach for transferring fracture events across different sample shapes

The paper investigates the capability of a novel calibration method to predict accurately fracture events across different sample shapes at low temperatures. It is shown that the emergence of a threshold Weibull stress in the Weibull stress distribution is inherent in the fundamental assumptions of the Beremin model. The mathematical concept underlying the suggested calibration method is the correlation between the probability distributions of the fracture loads and the associated Weibull stresses. The calibration procedure is demonstrated using fracture data obtained in tests conducted at a test temperature of −150 °C on specimens fabricated of A533B ferritic steel. In contrast to the values found in the literature, the calibrated Weibull modulus is small and ranges from 2 to 4. The proposed methodology is straightforward to apply and yields reliable predictions of the failure probabilities of samples of different shapes.     

Monte-Carlo simulation of multiple fracture in the transverse ply of cross-ply graphite-epoxy laminates

Graphite-epoxy cross-ply laminates generally show multiple fracture of the transverse ply at higher applied stress. This phenomenon is described by means of a Monte Carlo simulation method based on the assumption that the strength of the transverse ply obeys a two-parameter Weibull distribution function. The main results show that the smaller the scatter of strength of the 90°-ply (i.e. the larger the shape parameter at a constant mean strength of the Weibull distribution), the higher becomes the threshold for the multiple fracture to occur, and the more rapidly the length of 90°-ply segments decreases with increasing applied stress once multiple fracture takes place. The methods to determine the shape and scale parameters of the Weibull distribution for the strength of the 90°-ply proposed by Manderset al. and Peters are proved to be useful even for a small number of test specimens. When the interfacial bond strength between 0°- and 90°-plies is low, saturation of 90°-ply cracking occurs at higher applied stress. The stress-carrying capacity and stiffness of the composites as a whole are reduced by multiple fracture of the 90°-ply. This reduction is more pronounced at increasing applied stress or at a larger number of transverse cracks, especially when the interfacial bond strength is low.     

The sensitivity of fracture location distribution in brittle materials

The Weibull weak-link theory allows for the computation of distribution functions for both the fracture location and the applied far-field stress. Several authors have suggested using the fracture location information from tests to infer Weibull parameters, and others have used the predictive capabilities of the theory to calculate average fracture locations for brittle bodies. By a simple set of example calculations, it is shown that the fracture location distribution function is distinctly more sensitive to perturbations in the stress state than the fracture stress distribution function is. In general, the average fracture location is more subject to stress perturbations than the average fracture stress. The results indicate that care must be exercised in applying fracture location theory.     

The role of constraint on the calibration functions for the prediction of ductile fracture behavior in structural components

The role of constraint in ductile fracture has been studied for its effect on fracture toughness. When toughness is characterized by the J–R curve, a lowering of constraint will usually increase the level of the J–R curve. In a ductile fracture methodology both the J–R curve and the calibration functions which relate the applied load to the plastic deflection of a structure, are required to predict structural behavior. Constraint also influences the calibration functions. In many cases the calibration functions play a more important role in the prediction of maximum load than does the J–R curve. Therefore in predicting the behavior of a structural component the effect of the constraint must be accounted for in determining the calibration functions to be used as input in the ductile fracture methodology.The calibration functions have been traditionally taken from the EPRI-GE Handbook [6]. Using the format of the Handbook calibration functions, a constraint factor is derived which can be used to evaluate the relative constraint in the calibration function. For prediction of the behavior of a structural component from a laboratory test specimen the constraint factor must be known for each component. This constraint factor for the test specimen can then be used to predict the calibration function that is appropriate for the geometry and constraint of the structural component.A number of examples taken from test specimens of various thicknesses are presented to show that the constraint factor for the calibration function can be reasonably predicted based on information given in the Handbook. This method of prediction is applied to develop calibration functions that can be used in a ductile fracture methodology for a new structural constraint. The methodology is then used to predict load versus displacement behavior for cases of different constraints. Results from a test with essentially plane strain constraint are used to predict behavior of a plane stress structure. Finally a list of general rules is developed to account for the constraint of an arbitrary structural component. Along with this, some indication is given of where additional information is needed to make the prediction of constraint more complete.     

Precise evaluation of fast fracture velocities in acrylic polymers at the slow-to-fast transition

Transient fast fracture velocities at the onset of the slow-to-fast transition in polymethylmethacrylate (PMMA) have been measured precisely in single-edge-notched specimens of various geometries by using ultrasonic fractography. Little sign of the fracture velocity of the order of 10° m sec^–1 have been detected on the instability onset. The fast fracture starts from a point source almost instantaneously. The initial velocity has been shown to fall in a small range, 90 to 150 m sec^–1, almost independent of the loading speeds from 0.1 to 100 mm min^–1 and specimen temperature from –50 to 40° C, with exceptional cases for specimens loaded slowly (0.1 mm min^–1) at a low temperature (–50° C). As the final minimum velocity of an arresting crack, a value of 42 m sec^–1 has been obtained under room temperature. Crack propagation in low molecular weight PMMA has been shown to be more temperature, as well as loading rate, dependent than in higher molecular weight PMMA.     

Comparison of the wet and dry fatigue properties of all ceramic crowns

The purpose of this paper was to investigate the influence of fatigue on the fracture strength of In ceram, optimal pressable ceramic (OPCTM) and IPS Empress in both wet and dry environments. Twenty-six crown shapes 8 mm in diameter and 8.5 mm in height were fabricated for each ceramic system. For each ceramic system, ten specimens were tested for fracture strength without fatiguing. The second group was submitted to a fatigue and fracture test in a dry (eight specimens) and a third group in a wet (eight specimens) environment using an Instron testing machine. The results were statistically analysed using a Mann–Whitney test. The results indicated that: (i) the fracture strength for In ceram was significantly stronger than OPCTM and IPS Empress (p<0.05) – no difference was found between OPCTM and IPS Empress; (ii) fatiguing and fracture testing showed a significant decrease in the fracture strength for In ceram and IPS Empress in the wet environment and no difference was found in the dry environment – no difference was found for OPCTM; and (iii) when fatigued in a dry environment, In ceram crown shapes were significantly stronger than OPCTM and IPS Empress (p<0.05) – the same statistical differences were found when fatigued in a wet environment.     

Influence of temperature on the fracture of a W-Ni-Fe alloy

A 95wt%W 3.5wt%Ni 1.5wt%Fe alloy is strained to failure in uniaxial tension at temperatures in the range –100°C to 300°C. The fracture surfaces of the tensile specimens are examined and the contributions from the fracture mechanisms: tungsten-tungsten intergranular decohesion, tungsten-binder interface decohesion, binder rupture and tungsten cleavage, are identified as a function of temperature. The observed variations are explained in terms of the flow stress temperature dependence of the two phases within the alloy. The results are consistent with a changing mode of specimen rupture from one of a localized cascade of nucleation events at low temperatures to one of crack propagation through linking of cracks within the necked region of the specimens deformed at higher temperatures.     

Fracture toughness of sub-zero-chilled cast iron

A series of fracture toughness experiments were carried out involving sub-zero-chilled (using liquid nitrogen) cast iron containing 1.5% Cu, and chromium contents ranging from 0.0%–0.2%. By using copper chills of different thicknesses, the effect on fracture toughness of varying the chill rate was also examined. The fracture toughness tests were carried out using three-point bend specimens, each with a chevron notch, as per ASTM E 399-1974 standards. It was found that fracture toughness is highly dependent on the location on the casting from where the test specimens are taken and also on the chromium content of the material. Chill thickness, however, does not significantly affect the fracture toughness of the material. There was found to be an approximately linear relationship between fracture toughness and pearlite content, in which fracture toughness increases as pearlite content decreases and vice versa.     

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

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

Analysis of the curve of cyclic elastoplastic fracture of a specimen with a crack. Report no. 1

Fatigue curves and curves describing the cyclic elastoplastic fracture of specimens of carbon steels 30 and 45 with cracks are constructed experimentally. Characteristics of the cyclic fracture toughness of these steels are obtained in tests of compact specimens 10, 20, and 40 mm thick. An analysis is made of the cyclic elastoplastic fracture curves of specimens of different thicknesses.Translated from Problemy Prochnosti, Nos. 5–6, pp. 39–51, May–June, 1995.     

Statistical analysis of the Hertzian fracture of pyrex glass using the Weibull distribution function

Hertzian fracture tests were carried out on specimens of ground-and-polished Pyrex glass using polished Pyrex glass balls of 6 and 8 mm diameter. The results were analysed according to the theory of flaw statistics originally proposed by Weibull. The Weibull parameters m and ₀ were found to be independent of ball size; _u however decreased with increase in ball size. The parameters _u,₀ and m obtained from the Hertzian tests differed from those obtained from a four-point bend test. The predicted mean fracture stress and the mean fracture location for Hertzian fracture using the derived Weibull parameters agreed reasonably well with the experimental values.     

Criteria of nonlinear fracture mechanics

Conclusions Difficulties are experienced in using some of the examined fracture criteria in the elastoplastic region. The apparent fracture toughness varies in a wide range. The effect of the thickness of the specimen on cracking resistance is relatively small.In a partial case examined in this work, i.e., in fracture of the low-strength aluminum alloy with slight hardening in the conditions of the plane stress state at the crack tip, the range of applicability of certain critria is very small so that it is necessary to use the fracture criterion which does not take into account the crack length. Consequently, in this case, the two-parametric fracture criterion is more suitable for the apparent fracture toughness K^*–a/W ratio curve. This is illustrated clearly by Fig. 9 where the fracture load, i.e., the fracture criterion belonging in the group of the fracture criteria of the intermediate state, was predicted by the Newman method.In fact, the criteria of nonlinear fracture mechanics can be used in the conditions restricted by two limiting states: fracture at linear elastic strains, and fracture as a result of the formation of a plastic hinge.The interpolated curve used in such a method is usually known as the two-parametric Newman method or the CEGB method which is the same in the present case. This is possible owing to the fact that the extent of hardening of the aluminum alloy examined in this work is only very small.Further investigations are required for predicting the critical crack growth with satisfactory accuracy.Metz Institute, France. Translated from Problemy Prochnosti, No. 11, pp. 14–23, November, 1988.     

Size effect on fracture strength in the probabilistic strength of materials

For two bodies manufactured in respective sizes V₁, V₂ with the same material, subjected to a fracture stress σ and whose cumulative probabilities of fracture are F₁(σ), F₂(σ), respectively, the Probabilistic Strength of Materials supplies a formula in order to deduce F₂(σ) from F₁(σ) when the stress field is constant. This formula is applied in particular to the cases were the two bodies are subjected to bending and where they are affine for any kind of stress field. It is shown that the relationship linking stresses σ₁ and σ₂ of the same probability of fracture, in bodies of whatever shape and material and following the Kies-Kittl function of the specific risk of fracture, is a bilinear function. The general case of affine bodies, for which the correlation of isoprobable stresses σ₁ and σ₂ are known and allows oneto establish the Weibull function of the specific risk of fracture, has been studied.     

On the dependence of the Weibull exponent on geometry and loading conditions and its implications on the fracture toughness probability curve using a local approach criterion

In a previous paper the authors assessed the probability of failure of a three point bend specimen, SE(B), using a local approach criterion. In that paper the Weibull exponent, m, was derived from tests performed on round notch bars in traction, RNB(T), following the procedure suggested by Mudry. In the present study, it is addressed the issue of the dependence of the Weibull exponent m on geometry and loading conditions. It is shown that the amplitude and shape of the notch tip stress field and, in particular, the triaxiality characterising the stress state determines the value of the exponent m. Tests performed on RNB(T) specimens of carbon steel 22NiMoCr37, type A 508 Cl 3, at temperatures ranging from –18 °C to –196 °C actually indicate that m varies from 6 to 40, depending on the notch depth and root radius while for specimens carrying sharp cracks its value drops down to 4. This last result seems to be consistent with the Wallin hypothesis of a theoretical value equal to 4 for fracture mechanics specimens with high constraint, such as C(T) or SE(B), with positive values of the Q-stress or T-stress and triaxiality factor, TF, approaching 2.5. Temperature, in as long as it does not modify the stress state from plane strain to plane stress and the TF, has no effect on the value of m which is independent of the material as well.     

Fabrication and probabilistic fracture strength prediction of high-aspect-ratio single crystal silicon carbide microspecimens with stress concentration

Single crystal silicon carbide micro-sized tensile specimens were fabricated with deep reactive ion etching (DRIE) in order to investigate the effect of stress concentration on the room-temperature fracture strength. The fracture strength was defined as the level of stress at the highest stressed location in the structure at the instant of specimen rupture. Specimens with an elliptical hole, a circular hole, and without a hole (and hence with no stress concentration) were made. The average fracture strength of specimens with a higher stress concentration was larger than the average fracture strength of specimens with a lower stress concentration. Average strength of elliptical-hole, circular-hole, and without-hole specimens was 1.53, 1.26, and 0.66 GPa, respectively. Significant scatter in strength was observed with the Weibull modulus ranging between 2 and 6. No fractographic examination was performed but it was assumed that the strength controlling flaws originated from etching grooves along the specimen side-walls. The increase of observed fracture strength with increasing stress concentration was compared to predictions made with the Weibull stress-integral formulation by using the NASA CARES/Life code. In the analysis isotropic material and fracture behavior was assumed — hence it was not a completely rigorous analysis. However, even with these assumptions good correlation was achieved for the circular-hole specimen data when using the specimen data without stress concentration as a baseline. Strength was over predicted for the elliptical-hole specimen data. Significant specimen-to-specimen dimensional variation existed in the elliptical-hole specimens due to variations in the nickel mask used in the etching. To simulate the additional effect of the dimensional variability on the probabilistic strength response for the single crystal specimens the ANSYS Probabilistic Design System (PDS) was used with CARES/Life. The ANSYS-PDS & CARES/Life simulation correlated better to the elliptical-hole specimen data than CARES/Life predictions based on average specimen dimensions.     

Probabilistic aspects of fracture energy of concrete

A test method to determine fracture energy and strain-softening in direct tension is described. Experimental results on cylinders of equal diameter and varying length are reported. It is found that the tensile strength decreases with increasing volume while the fracture energy remains constant within the observed volume range. By means of numerical simulation, it is shown that in a direct tension test several fracture process zones appear in the initial states of cracking and that final rupture is induced by the development of only one of these fracture zones. This phenomenon has been observed experimentally by other authors. A comparatively large number (44) of identical samples were tested by using the wedge-splitting test. Half the specimens were grooved. The fracture energy of the grooved and ungrooved specimens turned out to be the same within the given range of accuracy. It was observed experimentally and simulated numerically that in grooved specimens the crack is forced to follow a ragged fracture surface which is statistically not the weakest one. In an ungrooved specimen the crack path generally diverts from the centre line and advances through weaker zones. For the formation of these skew cracks, however, more energy is consumed due to aggregate interlock. In addition, the fracture process zone observed in ungrooved specimens is generally wider.     

Diffuse damage accumulation in the fracture process zone of human cortical bone specimens and its influence on fracture toughness

This study was concerned with the mechanics and micromechanisms of diffuse (ultrastructural) damage occurrence in human tibial cortical bone specimens subjected to tension–tension fatigue. A nondestructive technique was developed for damage assessment on the surfaces of intact compact tension specimens using laser scanning confocal microscopy. Results indicated that diffuse damage initiates as a result of fractures in the inter-canalicular regions. Subsequent growth of those microscopic flaws demonstrated multiple deflections from their paths due to 3D spatial distribution of microscopic porosities (lacunae–canalicular porosities) and the stress-concentrating effects of lacunae. Damage dominating effects in the early stages of fatigue had been verified by the observed variations of the fracture toughness due to artificially induced amounts of damage. Toughening behavior was observed as a function of diffuse damage. © 2001 Kluwer Academic Publishers