A comparison on the effect of the ratio a/w on the fracture behaviour between ductile and brittle materials

The effect of the ratio a/W on the fracture behaviour of ductile and brittle materials has been studied by measuring the crack-opening displacement and J-integral for ductile material and the stress intensity factor for brittle material in three-point bend specimens with shallow and deep notches. It is shown that, for ductile material, the values of δ_i and J_i, for specimens with shallow notches are larger than those of deep notches. On the contrary, for brittle material, the values of K_IC for specimens with shallow notches are smaller than those of deep notches. The reason for this is explained.     

On the effect of plastic constraint on ductile tearing in a structural steel

The effect of plastic constraint on the initiation of ductile tears in a structural steel has been studied by measuring the crack opening displacement at initiation in 3-point bend specimens with deep and shallow notches. It is shown that δ_i for shallow notches where plastic flow reaches the surface is about twice that for deep notches. The crack opening displacement at maximum load is shown to be proportional to the specimen size. It is also shown that sidegrooves reduce this crack opening displacement.     

A study about Ji,and δi,in three-point bend specimens with deep and shallow notches

An experimental study for determining δ_i, and J_i, in three-point bend specimens with both shallow and deep notches has been described. A new method for obtaining δ_i is simply introduced. Two clip gauges were used, P-V and P-Δ plots were simultaneously obtained on the same specimen. COD values were obtained from both P-V and P-Δ plots. Experimental results of three different heat-treated alloy steels show that the crack opening displacement and J-integral values of shallow cracks at initiation are much larger than those of deep cracks. The relationship of COD and J-integral is also studied.     

A framework to correlate a/W ratio effects on elastic-plastic fracture toughness (J c )

Single edge-notched bend (SENB) specimens containing shallow cracks (a/W < 0.2) are commonly employed for fracture testing of ferritic materials in the lower-transition region where extensive plasticity (but no significant ductile crack growth) precedes unstable fracture. Critical J-values J _c ) for shallow crack specimens are significantly larger (factor of 2–3) than the J _c )-values for corresponding deep crack specimens at identical temperatures. The increase of fracture toughness arises from the loss of constraint that occurs when the gross plastic zones of bending impinge on the otherwise autonomous crack-tip plastic zones. Consequently, SENB specimens with small and large a/W ratios loaded to the same J-value have markedly different crack-tip stresses under large-scale plasticity. Detailed, plane-strain finite-element analyses and a local stress-based criterion for cleavage fracture are combined to establish specimen size requirements (deformation limits) for testing in the transition region which assure a single parameter characterization of the crack-tip stress field. Moreover, these analyses provide a framework to correlate J _c )-values with a/W ratio once the deformation limits are exceeded. The correlation procedure is shown to remove the geometry dependence of fracture toughness values for an A36 steel in the transition region across a/W ratios and to reduce the scatter of toughness values for nominally identical specimens.     

Evaluation of the cracking resistance of 15Kh2MFA steel in large sections on the basis of the results of tests on small specimens

On the basis of the results of tests on small compact specimens with top notches 12 and 24 ram thick and large compact specimens 150 mm thick made of 15Kh2MFA steel it is shown that the cracking resistance of this steel in large sections (J_Ic) can be estimated with the acceptable accuracy on the basis of the typical values of the J₁ integral determined on small specimens both at the moment of initiation of ductile separation and at the moment of the start of unstable cleavage failure. The data obtained in the latter case are used to predict the value of J_Ic on the basis of the statistical model of the weak member. Both approaches provide a conservative estimate of J_Ic, but the starting values of J_I integral are preferred because of the smaller scatter of the data and problems in inducing cleavage failure on small specimens.Translated from Problemy Prochnosti, No. 5, pp. 23–28, May, 1991.     

Effects of crack depth on elastic-plastic fracture toughness

Short crack test specimens (a/W 0.50) are frequently employed when conventional deep crack specimens are either inappropriate or impossible to obtain, for example, in testing of particular microstructures in weldments and in-service structures containing shallow surface flaws. Values of elastic-plastic fracture toughness, here characterized by the crack tip opening displacement (CTOD), are presented for square (cross-section) three-point bend specimens with a/W ratios of 0.15 and 0.50 throughout the lower-shelf and lower-transition regions. Three dimensional, finite-element analyses are employed to correlate the measured load and crack mouth opening displacement (CMOD) values to the corresponding CTOD values, thus eliminating a major source of experimental difficulty in previous studies of shallow crack specimens. In the lower-transition region, where extensive plasticity (but no ductile crack growth) precedes brittle fracture, critical CTOD values for short crack specimens are significantly larger (factor of 2–3) than the CTOD values for deep crack specimens at identical temperatures. Short crack specimens are shown to exhibit increased toughness at the initiation of ductile tearing and decreased brittle-to-ductile transition temperatures. Numerical analyses for the two a/W ratios reveal large differences in stress fields ahead of the crack tip at identical CTOD levels which verify the experimentally observed differences in critical CTOD values. Correlations of the predicted stresses with measured critical CTOD values demonstrate the limitations of single-parameter fracture mechanics (as currently developed) to characterize the response.     

On the relationship between crack tip opening displacement at the initiation of a ductile tear in low carbon steel,hydrostatic stress,and void growth

The effect of hydrostatic stress on the growth of voids from inclusions located near the tips of deep and shallow notches in three-point bend specimens is analysed using slip-line field theory and the Rice-Tracey void growth model. The analysis explains qualitatively the observed dependence of the crack tip opening displacement _i at the initiation of a ductile tear in low carbon steel on the hydrostatic stress. Although a plot of the experimental values of _i normalised by the inclusion spacing against the inclusion spacing/size ratio do not agree well with the theory, the plot is a promising means of determining experimentally the dependence of _i on hydrostatic stress for any particular steel.     

Accounting for porosity, time and temperature dependency in fracture mechanics concepts on polyvinylidene fluoride material

The polyvinylidene fluoride (PVDF) under study is a semi-crystalline polymer that exhibits sensitivity of mechanical properties to both strain rate and temperature. Furthermore, this material is subjected to a significant cavitation during deformation. A comprehensive experimental database was built in order to analyze the fracture behaviour in the ductile to brittle transition domain. Tensile tests were carried out on smooth and notched specimens at temperatures ranging from −50 °C to 20 °C. The results were used to determine temperature-dependent material parameters by using the mechanics of porous media. The obtained set of parameters was validated on two kinds of pre-cracked specimens, by using the local approach of fracture mechanics. With the help of a finite element code, both global and local approaches of fracture mechanics were shown to complement one another: whereas classical formulae of J-integral fail to characterize crack initiation for this PVDF, the present methodology allowed the plot of J_1C values with respect to temperature.     

Prediction of ductile fracture initiation using micromechanical analysis

In the paper ductile fracture initiation analysis of low-alloyed ferritic steel has been made by application of two micromechanical models: the Rice–Tracey void growth model and the Gurson–Tvergaard–Needleman (GTN) model. The aim of the study was to analyse transferability of micromechanical parameters determined on specimens without initial crack to pre-cracked specimens. A significant part of the research has been carried out through participation in the round robin project organised by the European Structural Integrity Society (ESIS). Tensile tests have been performed on cylindrical smooth specimens and CT specimens. Critical values of micromechanical parameters determined on smooth specimen for both applied models, have been used for prediction of the crack growth initiation in CT specimen. Modelling of the first phase of ductile fracture––void nucleation––has been carried out using quantitative metallographic analysis of non-metallic inclusion content in tested steel. For determination of critical values of model parameters corresponding to ductile fracture initiation a simple procedure has been applied based on a combination of experimental and numerical results. Evaluated J-integral values corresponding to onset of crack growth, J_i, are in good agreement with experimental result and both models have proved to be suitable for determination of the ductile fracture initiation in tested steel. The effect of FE size at a crack tip on J_i-value has been particularly analysed: it has been established that the calculation with FE size corresponding to the mean free path λ between inclusions in steel gives results that are in accordance with the experimental ones.     

Influence of notch root radius on ductile rupture fracture toughness evaluation with Charpy-V type specimens

The blunt notch fracture toughness of four types of carbon-manganese steel (ASTM A516 grade 70) has been determined by J-integral tests on Charpy-V type samples with different values of notch root radius, ρ. J-ρ plots, determined using specimens with a notch depth to width ratio, a/w, equal to 0.5, have shown the existence of a limiting ρ value (ρ_eff) below which applied J-intergral values at fracture initiation are constant. These ρ_eff values have been seen to depend only on second-phase particle distribution and not on their volume fraction or on the steel ferritic grain size. The procedure for deriving J-integral values at the onset of stable crack growth from J resistance curves in the case of notches has also been discussed. Experiments with Charpy specimens with a/w = 0.2 do not allow the derivation of meaningful J-ρ plots. In all cases, a ductile fracture criterion based on the constancy of the notch tip strain at rupture initiation has been proved when ρ >ρ_eff.     

State‐of‐the‐art review on the local strain energy density concept and its relation to the J‐integral and peak stress method

The local average strain energy density (SED) approach has been proposed and elaborated by Lazzarin for strength assessments in respect of brittle fracture and high‐cycle fatigue. Pointed and rounded (blunt) V‐notches subjected to tensile loading (mode 1) are primarily considered. The method is systematically extended to multiaxial conditions (mode 3, mixed modes 1 and 2). The application to brittle fracture is documented for PMMA flat bar specimens with pointed or rounded V‐notches inclusive of U‐notches. Results for other brittle materials (ceramics, PVC, duraluminum and graphite) are also recorded. The application to high‐cycle fatigue comprises fillet‐welded joints, weld‐like shaped and V‐notched base material specimens as well as round bar specimens with a V‐notch. The relation of the local SED concept to comparable other concepts is investigated, among them the Kitagawa, Taylor and Atzori–Lazzarin diagrams, the Neuber concept of fictitious notch rounding applied to welded joints and also the J‐integral approach. Alternative details of the local SED concept such as a semicircular control volume, microrounded notches and slit‐parallel loading are also mentioned. Coarse FE meshes at pointed or rounded notch tips are proven to be acceptable for accurate local SED evaluations. The peak stress method proposed by Meneghetti, which is based on a notch stress intensity factor consideration combined with a globally even coarse FE mesh and is used for the assessment of the fatigue strength of welded joints, is also presented.     

Effect of fracture path on the toughness of weld metal

The crack propagation direction may affect weld metal fracture behavior. This fracture behavior has been investigated using two sets of single edge notched bend (SENB) specimens; one with a crack propagating in the welding direction (B×2B) and the other with a crack propagating from the top in the root direction (B×B) of a welded joint. Two different weld metals were used, one with low and one with high toughness values. For Weld Metal A, two specimen types have been used (B×B and B×2B) both with deep cracks. The weld metal A (with high toughness values) has reasonably uniform properties between weld root and cap. The resulting J-R curves show little effect of the specimen type, are ductile to the extent that the toughness exceeds the maximum J_max, value allowed by validity limits and testing is in the large –scale yielding regime. In the case of weld metal B (with low toughness values) with two specimen types (B×B and B×2B) the B×B specimen has shallow cracks while the B×2B specimen has deep cracks. Both resulting J-R curves show unstable behavior despite the fact that the types of specimen and their constraints are different. The analysis has shown that crack propagation direction is most influential for a weldment with low toughness in the small scale yielding regime, whereas its influence diminishes due to ductile tearing during stable crack growth and large scale yielding. The results have shown that these effects are different in both the crack initiation phase and during stable crack growth, indicating a dependence on weld metal toughness and the microstructure of the weld metal. It can be concluded that, if resistance curves during stable crack growth do not show differences in both notch orientations, the fracture toughness values of the whole weld metal can be treated as uniform.     

Effect of small scale notches on the very high cycle fatigue of AISI 310 stainless steel

Fatigue behaviour of AISI 310 stainless steel has been investigated up to very high cycles. The fatigue crack initiation sites were found at the surface of the material. Persistent slip bands developed at the surface of the specimens led to the crack initiation. At lower stress levels, shallow persistent slip bands were found at the surface of the specimens, and the fatigue limit was obtained. Notched specimens showed lower fatigue lives. Notched specimens with higher stress concentration factor (K_t) showed higher fatigue strength reduction factor (K_f). It was found that shallow notches of depth ~100 µm may reduce the fatigue life substantially.     

Evaluation of critical fracture energy parameter Gfr and assessment of its transferrability

Prediction of maximum load bearing capacity and crack growth for ductile materials using existing models like J-R curve approach has the problem of transferability and the use of micro-mechanical model (e.g. Gurson Tvergaard, and Needleman [Tvergaard V, Needleman A. Analysis of cup cone fracture in a round tensile bar. Acta Metall 1984;32:157-169]) are limited by the requirements of the huge computation time and large numbers of critical metallurgical parameters as input to analysis. Marie and Chapuliot [Marie S, Chapuliot S. Ductile tearing simulation based on local energy criterion. Fatigue Fract Engng Mater Struct 1998;21:215-227] of CEA, France, proposed a simple but convenient ductile crack growth model using critical fracture energy (G_fr) for crack growth and J_i for initiation, both of which are material parameters. They also proposed several schemes, namely, graphical and slope of modified plastic J-integral vs crack growth, J_M-pl − Δa methods for the evaluation of the value of G_fr from specimens as well as from components. In all these methods the role of non-crack displacement in the crack growth process was not considered. The necessary modifications due to non-crack displacement in the above methods to evaluate the values of G_fr was studied and published [Acharyya S, Dhar S, Chattopadhyay J. (2003). The effect of non-crack component on Critical fracture energy on ductile material. Int J Pressure Vessels Piping 2004;81:345-353] by the authors earlier. In this paper, the modified methods and formulation have been applied to evaluate the values of G_fr from experimental and FE simulated results for compact tensile (CT), three point bend (TPB) specimens and also from components like pipes and elbows. Then statistical estimation is done from these G_fr values to assess whether G_fr can be accepted as constant value material parameter. Finally, the mean value of G_fr obtained from statistical computation is used as material constant along with crack initiation toughness parameter (J_i)_SZW to consider crack growth for FE simulation of load vs load-line-displacement (LLD) and load vs crack growth curves for different specimens and components. Finite element simulated results are compared with the experimental results and good matching between the two for several components are found and maximum error in prediction of maximum load is found to be within 12%.     

Evaluating the linear normalization technique for deriving J-resistance curves

In this paper, results from the linear normalization (LN) technique of Reese and Schwalbe for deriving J‐crack resistance (J–R) curves have been compared, related to J–Δa (J‐integral–ductile crack growth) data points, to those obtained from traditional elastic compliance technique. Research results regarding a nuclear grade steel exhibiting a wide range of elastic–plastic fracture resistance agree quite well for both techniques until a certain level of toughness of the material. Below this critical level, LN produces inconsistent results for the sub‐sized compact tension specimens (0.4T C[T]). The evidence suggests that the loss of applicability of the LN technique can be determined on the basis of the η plastic factor (η_pl) for the best linear correlation achieved for ΔP_N–Δa (normalised load gradient–ductile crack growth) data.     

Evaluation of the ISO <Emphasis Type="Italic">J</Emphasis> initiation procedure using the EURO fracture toughness data set

The multiple specimen J _0.2/BL initiation fracture toughness test procedure from the ISO standard, ISO 12135:2002, is evaluated using the EURO fracture toughness data set. This standard is also compared with the ASTM standard, ASTM E 1820, multiple specimen J _Ic procedure. The EURO round robin data set was generated to evaluate the transition fracture toughness methods for steels. However, many of the tests resulted in ductile fracture behavior giving final J versus ductile crack extension points. This is the information that is measured in a multiple specimen J initiation fracture toughness test. The data set has more than 300 individual points of J versus crack extension with four different specimen sizes. It may be the largest data set of that type produced for one material. Therefore, its use to determine J initiation values can provide an important evaluation of the standard procedures. The results showed that a J _0.2/BL value could be determined from the ISO standard for three of the four specimen sizes, the smallest size did not meet the specimen size requirement on J. The construction line slopes in this method are very steep compared with the ASTM construction line slopes. This resulted in low J initiation values, about a factor of two lower than the one from the ASTM method. Of the various criteria imposed to determine a valid J _0.2/BL value, the one limiting the maximum J value was the most questionable. It had an effect of eliminating small specimen data that was identical to acceptable large specimen data.     

Characterization of transition temperature behavior of HY130 steel by the JIc fracture toughness parameter

The objectives of this study were to determine whether the $\text{J-R}$ curve approach could be used to evaluate the ductile to brittle temperature performance of a high yield strength structural steel (HY130) and to demonstrate that the single specimen unloading compliance method is applicable to evaluate $\text{J}{}_{\mathrm{Ic}}$ values and $\text{J-R}$ curves for compact specimens tested at temperatures from ?192 to 150°C. The major conclusions of this work are that $\text{J}{}_{\mathrm{Ic}}$ and the complete $\text{J-R}$ curve can be obtained using the single specimen method over the above temperature range and that $\text{J}{}_{\mathrm{Ic}}$ does define a ductile to brittle transistion temperature for HY130 steel which should be more valuable for structural design than that found from Charpy $\text{V}$ or dynamic tear specimens because it is based on a fracture toughness parameter. The comparison of the ${}_{\mathrm{Ic}}$ transition temperature and that from Charpy $\text{V}$ specimens shows that the Charpy $\text{V}$ transition temperture is more conservative for the HY130 steel tested. In transitional $\text{J}{}_{\mathrm{I}}$ specimens which demonstrated a ductile crack tearing followed by a brittle failure, scanning microscope stereo pair fractography showed that the transition from ductile to brittle behavior was very gradual in comparison to the distinct crack tips obtained on ductile specimens broken in a brittle fashion at a cryogenic temperature.     

GEOMETRY INDEPENDENT R-CURVES IN A TITANIUM ALLOY USING A NORMALISED AXIS FOR CRACK GROWTH

Data from a study of the effect of geometric variation on J-R curves for a titanium alloy in three-point bending are presented up to large amounts of growth. Four series are reported, various widths, various a/W ratios, various thicknesses and various absolute sizes, all failing in the limit load regime by stable tearing. Analysis is made in terms of J_m-R curves, adjusted to a common initiation toughness, J₁, to clarify the effects of geometry. Strong trends are then found with absolute size over a four fold range and with width over a two fold range; a weaker trend with a/W over a four fold range but practically none with thickness over a nine fold range. Many of these trends are different from those reported for other more ductile materials but consistent in some cases with those reported for another high strength material, HY130. All the deep notch cases (14 tests) reduce to a single group when plotted as J_m against a normalised abscissa, Δa/b_o, with a very slight trend to a higher curve for the thinner pieces.     

Effect of crack depth on the shift of the ductile-brittle transition curve of steels

Nuclear reactor pressure vessel (RPV) steels degrade due to neutron irradiation during normal operation. As a result, the ductile-brittle transition curve of the steel shifts to higher temperature which decreases operation margins in both the temperature and pressure. The loss of these margins however can be offset somewhat by appealing to arguments based on constraint of potential/postulated shallow cracks. In this paper, it is demonstrated that the fracture toughness values for shallow flaws are higher than those determined from standard deep cracked test specimens based on constraint consideration. The J-A₂ three-term solution is used to characterize the crack-tip stress field where J represents the level of loading and A₂ quantifies the level of constraint. Based on the RKR cleavage model, procedures to quantify the temperature shift between specimens with different constraint levels are developed. The experimental data by Sherry et al. [Sherry AH, Lidbury DPG, Beardsmore DW. Validation of constraint based structural integrity assessment methods. Final report, Report No. AEAT/RJCB/RD01329400/R003, AEA Technology, UK, 2001] for the A533B RPV steel are used to demonstrate the procedure and it is shown that the ductile-brittle transition curve shifts to lower temperature from high constraint to low constraint specimens.     

The crack growth resistance of thin steel sheets under eccentric tension

The stable crack growth in thin steel sheets is the topic of this paper. The crack opening was observed using a videoextensometry system, allowing the crack extension determination. J_R-curve and δ_R-curve were established from obtained data. The ductile tearing properties of different thin sheets of steel were determined, including the impact of the specimen orientation, from test performed on compact tension specimens loaded under two conditions. The effect of the material, the rolling direction, and loading rate on the crack growth resistance of thin steel sheets was analyzed. In addition to the crack growth resistance, J-integral values for crack initiation were also estimated. The relation between J _i and J_0.2 was assessed using the basic mathematical and statistical methods. This relation was described by a linear regression model.