Influence of specimen size and microstructure on the fracture toughness of a martensitic stainless steel

The fracture toughness of alloy HT-9,² a martensitic stainless steel under consideration for fast reactor and fusion reactor applications, was determined from circular compact tension specimens using the multi-specimen R-curve method. Specimens with thicknesses of 11.94, 7.62 and 2.54mm and widths of 23.88 and 11.94 mm were tested to investigate the effects of specimen size on fracture toughness. The test results obtained from all specimens are in good agreement and thickness requirements for a valid J_1c test are satisfied. The experiment indicates that small specimens of HT-9 may be used for post-irradiation fracture toughness testing.Fractographic examination of the fracture surfaces reveals that fracture in HT-9 is significantly influenced by delta ferrite stringers present in the material. The fracture surface examination and crack opening displacement measurements for specimens tested at various temperatures are consistent with the temperature dependence of the J_1c results.     

Size effect on the fracture toughness of metallic foil

The size effects on fracture behavior of Cu foil are investigated by a new optical technique, the digital speckle correlation method (DSCM). Displacement and strain fields around a crack tip are analyzed for different thicknesses of Cu foil. Then, the J integral and fracture toughness J _C are evaluated directly from the strain fields around the crack tip. The fracture toughness J _C is obtained as a function of foil thickness. The results indicate that J _C indeed depends on foil thickness within a certain range of thickness (the thickness varies from 20 micron to 1 millimeter in this work).     

Essential work of fracture compared to fracture mechanics—towards a thickness independent plane stress toughness

The essential work of fracture (EWF) and the J-integral methods were applied in a study of the effect of the thickness on the cracking resistance of thin plates. The paper discusses two themes: (1) the relationships between the two methods or concepts is elucidated, and (2) a new, thickness independent plane stress toughness parameter is proposed. For that purpose, cracked aluminium 6082O thin plates of 1-6 mm thickness were tested in tension until final separation. The EWF, w_e, and the J-integral at cracking initiation, J_i, increase identically with thickness except at larger thickness for which the increase of J_i levels off. J_i reaches a maximum for 5-6 mm thickness whereas w_e keeps increasing linearly with thickness. This difference is related to the more progressive development of the necking zone in front of the crack tip when thickness increases: at large thickness, cracking initiates well before the neck has developed to its stationary value during propagation. A linear regression on the fracture toughness/thickness curve allows partitioning the two contributions of the work of fracture: the plastic work per unit area for crack tip necking and a plane stress work per unit area for material separation. The pertinence of this new measure of the pure plane stress cracking resistance is critically discussed based on a micromechanical model for ductile fracture. The micromechanical void growth model incorporates void shape effects, which is essential in the low stress triaxiality regime.     

Comparison of mode I and mode II elastic-plastic fracture toughness for two low alloyed high strength steels

In the present work, mode I and mode II tests were carried out on two low alloyed high strength steels. An asymmetrical four point bend specimen and J _II-integral vs. crack growth resistance curve technique were used for determining the mode II elastic-plastic fracture toughness, J _IIc · J _II-integral expression of the specimen was calibrated by finite element method. The results indicate that the present procedure for determining the J _IIc values is easy to use. Moreover, the mode I fracture toughness J _Ic is very sensitive to the rolling direction of the test steels, but the mode II fracture toughness J _IIc is completely insensitive to the rolling direction of the steels, and the J _IIc /J _Ic ratio is not a constant for the two steels, including the same steel with different orientations. Finally, the difference of the fracture toughness between the mode I and mode II is discussed with consideration of the different fracture mechanisms.     

An alternative formulation of the Ritchie-Knott-Rice local fracture criterion

In the paper an alternative formulation of the RKR local fracture criterion is proposed. It is based on the features of the stress distribution in front of a blunted crack in an elastic-plastic material. The stress distribution is computed using the finite strain option in the finite element method. It is postulated that the opening stress in front of the crack should be greater than the critical one, σ_c, over the distance l ? l_c, where l_c is considered as a material parameter. The hypothesis is applied to estimate the influence of the in-plane constraint on fracture toughness. New formulas to compute the critical value of the J-integral are derived both for the small scale yielding and large plastic deformations in front of the crack. The results obtained are compared with the Sumpter and Forbes experimental results and with the O’Dowd analytical formula concerning the J_c = J_c(J_IC,Q) relation.     

Fracture behaviour of chemical vapour deposited and hot isostatically pressed zinc sulphide ceramics

Fracture behaviour of zinc sulphide ceramics prepared by chemical vapour deposition (CVD) followed by hot isostatic pressing (CVD + HIP) was investigated in terms of flexural strength (σ_f), plane-strain fracture toughness (K_Ic), even conditional fracture toughness (K_IQ), R-curve behaviour (variation of total fracture energy release rate, J_c with crack extension, δ/δ_c) and fracture mode. The corresponding Knoop Hardness number (KHN) and its correlations to flexural strength (σ_f) are also evaluated and reported. The present study showed that the zinc sulphide (ZnS) ceramics processed by CVD exhibited higher fracture resistance compared to ZnS processed by CVD + HIP condition. This observation is principally attributed to higher grain size associated with post-CVD HIPing process. In both conditions, the ZnS materials exhibited conditional fracture toughness (K_IQ) that decreased moderately with increased crack length due to the change in fracture mode form grossly tensile to predominant shear. A constantly rising R-curve behaviour was indicated in both the materials with significant increase in total fracture energy release rate (J_c with the normalised displacement (δ/δ_c), a parameter representing crack extension.     

DAMAGE MECHANICS APPROACH TO REMOVE THE CONSTRAINT DEPENDENCE OF ELASTIC–PLASTIC FRACTURE TOUGHNESS

It is now generally agreed that the applicability of a one-parameter J-based ductile fracture approach is limited to so-called high constraint crack geometries, and that the elastic-plastic fracture toughness J_1c, is not a material constant but strongly specimen geometry constraint-dependent. In this paper, the constraint effect on elastic-plastic fracture toughness is investigated by use of a continuum damage mechanics approach. Based on a new local damage theory for ductile fracture(proposed by the author) which has a clear physical meaning and can describe both deformation and constraint effects on ductile fracture, a relationship is described between the conventional elastic-plastic fracture toughness, J_1c, and crack tip constraint, characterized by crack tip stress triaxiality T. Then, a new parameter J_dc (and associated criterion, J_d=J_dc) for ductile fracture is proposed. Experiments show that toughness variation with specimen geometry constraint changes can effectively be removed by use of the constraint correction procedure proposed in this paper, and that the new parameter J_dc is a material constant independent of specimen geometry (constraint). This parameter can serve as a new parameter to differentiate the elastic-plastic fracture toughness of engineering materials, which provides a new approach for fracture assessments of structures. It is not necessary to determine which laboratory specimen matches the structural constraint; rather, any specimen geometry can be tested to measure the size-independent fracture toughness J_dc. The potential advantage is clear and the results are very encouraging.     

Comparative studies of several methods to determine the dynamic fracture toughness of a nuclear pressure vessel steel A508 CL3 with Charpy-size specimen

In this investigation, five estimation methods have been adopted to estimate the dynamic fracture toughness of a nuclear pressure vessel steel A508 CL3 by using pre-cracked Charpy-size specimens on an instrumented impact test machine. Furthermore, the merits and the demerits of the five methods have also been compared. The experimental results indicate that the maximum load energy method based on the curve of load versus load-point displacement overestimates the dynamic fracture toughness J _Id , especially above room temperature. The method of compliance changing rate underestimates the dynamic fracture toughness. The method of measuring the critical stretch zone width (SZW _c ) at the crack tip by means of SEM fractography and then converting the SZW _c into J _Id has a relatively large error. In addition, it is expensive and difficult to measure the SZW _c . The method of energy revised at the maximum load may be considered a better single-specimen method for determining the dynamic fracture toughness. Furthermore, the results indicate that although the dynamic resistance curve method can exactly estimate the dynamic fracture toughness of the material, this method needs several specimens. Moreover, the test procedure is complicated. Thus, it is not suitable for nuclear reactor pressure vessel embrittlement surveillance.     

Comparison of methods for fracture toughness testing of thin low carbon steel plates

Abstract

The fracture toughness of double edge notched tension (DENT) specimens of a low carbon steel sheet was evaluated using experimental and numerical methods. The concepts of critical J integral J_c critical crack tip opening displacement δ_c, essential work of fracture We_e, and essential work of fracture and initiation we^init were compared. The numerical methods were based on finite strain, three-dimensional finite element simulations of the tensile straining of the DENT specimens. Good agreement was found between numerical and experimental J_c values. Fair agreement was also found between J_c and we^init. The essential work of fracture W_e was ～20% lower than J_c. This discrepancy is attributed to inaccuracy in the detection of cracking initiation. The Shih factor derived from the measured J_c and δ_c values closely corresponds with the plane stress prediction.     

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.     

Mixed-mode fracture toughness testing of concrete beams in three-point bending

Results obtained for mixed-mode fracture toughness parameters K _c , G _c , J _c , G _F (plane strain mixed-mode stress-intensity factor, energy release rate, J-integral and fracture energy, respectively) for small notched concrete beams in bending indicate that all these parameters decrease with x/S (x is the distance from support, S is the span) in general to values near midspan consistent with Mode I results. All the parameters except J _c vary with notch depth in a similar manner for each notch location.     

Mechanical and metallurgical aspects of fracture behaviour of an Al-alloy

Fracture toughness testing was carried out on an Al-⁴C% Cu alloy in the form of a fully heat treated 21/2-in thick plate. Three types of test, the three point slow bend, instrumented Charpy impact, and double cantilever beam tests, enabled values of plane strain fracture toughness (K _1c ) to be studied over a range of temperature, testing speed and specimen size. Dependence of K _1c upon temperature (?200°C to +160°C) was found to be relatively small except at very low temperatures. The alloy was found not to be appreciably strain rate sensitive over the range of testing speeds (0.002 in/min to 2000 in/min) used. Higher toughness values, obtained from plane strain fractures of the smaller size specimens, were compared with low results from large specimens. The results became variable when curved fracture surfaces developed in the smallest DCB specimens. There was an apparent increase in toughness towards the centre of the plate and the effects of specimen size were most marked in the lower yield strength metal of this layer. The results indicate a genuine increase in toughness K _1c with decreasing temperature, but also show that large specimens are required to approach the lowest and constant K _1c value in circumstances where the yield strength decreases. The DCB test is also shown to be still valid for the measurement of K _1c for this non-brittle alloy, where yield strength may be only about 40,000 lbf/in². Electron fractography showed a ductile intergranular fracture mode. The results are consistent with theories of solute precipitation in Al-alloys.     

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.     

Fracture toughness of grade D ship steel

Results from fracture mechanics tests on 15 mm thick grade D ship steel and weld are organised into a toughness distribution indexed to the Charpy 27 joule temperature, T_27J. The tests are carried out at 300 MPa√m/s to simulate the strain rate appropriate to a long (≈1 m) through thickness crack in the deck of a ship under storm conditions. Most of the data are in the brittle to ductile transition region and end in cleavage fracture. A best fit to the data is found using the exponential curve fit (ECF) method. Lack of censoring of invalid results means that the trend line is not a true ‘plane strain’ fit. It is argued that inclusion of ‘plane stress’ data makes the resultant toughness distribution more relevant to ship fracture predictions. Equations are presented which allow the toughness to be plotted at any chosen probability level as a function of temperature relative to T_27J. A safe lower bound to the data is given by the 0.1% probability trend assuming that T_27J for grade D plate and weld is no higher than −20 °C. The data are also used to propose that it is impossible to generate an elastic ductile tearing instability in ship steel with Charpy upper shelf values of 100 J or more.     

Combination of Ag Substrate Decoration with Introduction of?BaZrO3 Nano-Inclusions for?Enhancing Critical Current Density of?YBa2Cu3O7 Films

The combination of two methods: Ag substrate decoration and introduction of BZO nano-inclusions has been used in a pulsed laser deposition (PLD) method to increase the critical density (J _c ) of YBCO films. The films were deposited on single crystal SrTiO₃ (STO) substrates decorated with various architecture of Ag nano-dots. We have studied the diameter and density of Ag nano-dots and their influence on J _c of BZO-added YBCO films. We found that 15 laser pulses on the Ag target gives an optimum result in increasing J _c in comparison with BZO-doped YBCO films of the same thickness in self-field and low applied magnetic fields. A higher number of laser pulses on the Ag target led to increasing critical current density in high applied magnetic fields only (above 2 T). We have studied films of the thickness from 0.4 ??m to 3.8 ??m and found that the highest J _c at all applied fields investigated is achieved for a 1.2 ??m thick film. The transmission electron microscopy clearly shows BZO nano-rods that provide strong c-axis pinning centres in the films.     

A mechanical model to predict elastic-plastic fracture toughness in high strength materials

A mechanical model of crack initiation and propagation, which is based on the actual mechanism of ductile fracture in high strength materials, is proposed. Assuming that a crack initiates when the equivalent stress at a distance ρ from the crack tip reaches a critical value $\text{}\text{?}$gsf, an equation for predicting fracture toughness J_IC is obtained. From comparison between the predicted values and the experimental results, it is found that the distance ρ corresponds to the spacing of micro-inclusions. The temperature dependence of fracture toughness J_IC estimated according to the derived equation is given in an Arrhenius form of equation and is nearly consistent with the experimental results.     

Temperature dependence of fracture toughness J IC and ductility for BCC materials in the transition region

The temperature dependence of ductility, strength and fracture toughness for a BCC material undergoing predominantly linear elastic behavior at low temperatures and elastic-plastic behavior at higher temperatures is examined. A model, based on ductile fracture mechanisms involving void nucleation followed by cavity growth and void coalescence, is developed to relate the fracture toughness parameter J _IC with temperature. Two general equations for linear elastic and elastic plastic regimes of J _IC versus temperature T, are obtained. Applications of this model to experimental data obtained on a carbon steel show that J IC varies with T ² at low temperatures and with T at higher temperatures, thus defining a transition temperature.     

Effect of microstructure on the relationship between fracture toughness and ductility

The relationship between fracture toughness, expressed as J_IC, and ductility, given by measurements of the bulge ductility, was studied experimentally for two microstructures of 1045 steel. These microstructures consist of annealed pearlitic structure with hardness R_c = 15 and a tempered matensitic structure with R_c = 23. J_IC and bulge ductility measurements were performed in the temperature range of −100-25°C. The tensile properties at these temperatures were also obtained. The results show that the variation in flow stress with temperature is similar for both microstructures. However, the flow stress is higher, and the bulge ductility is lower, at a given temperature, for the martensitic structure. Also shifts in the transition temperature from linear elastic to elastic-plastic behavior are observed. Previously developed models by the authors describing the variation of J^IC with temperature and ductility are used to account for the behavior of the different microstructures examined.