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.     

A new method to estimate the plane strain fracture toughness of materials

Although the testing method for fracture toughness K_IC has been implemented for decades, the strict specimen size requirements make it difficult to get the accurate K_IC for the high‐toughness materials. In this study, different specimen sizes of high‐strength steels were adopted in fracture toughness testing. Through the observations on the fracture surfaces of the K_IC specimen, it is shown that the fracture energy can be divided into 2 distinct parts: (1) the energy for flat fracture and (2) the energy for shear fracture. According to the energy criterion, the K_IC values can be acquired by small‐size specimens through derivation. The results reveal that the estimated toughness value is consistent with the experimental data. The new method would be widely applied to predict the fracture toughness of metallic materials with small‐size specimens.     

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.     

Alternative test method for interlaminar fracture toughness of composites

Two methods of determining the mode I interlaminar fracture toughness for fiber-reinforced polymer matrix (FRPM) composites using a double cantilever beam (DCB) test are compared. The standard method of determining G _IC is based in linear-elastic fracture mechanics theory and requires a visual measurement of the crack length, presenting data acquisition and analysis difficulties. The proposed method makes use of elastic–plastic fracture mechanics theory and an analytical closed form solution to the J-integral to relate the fracture toughness J _IC , load, and angular displacement at the load application points. This method has the advantage of replacing visually acquired data with data easily obtained using inexpensive transducers as well as being applicable to a broader class of materials.     

Specimen Size Requirements for Two-parameter Fracture Toughness Testing

Using a single parameter fracture mechanics theory, a minimum specimen size requirement of min(a, b, B) >200J/σ₀ in tension and min(a, b, B) >25J/σ₀ in bending, where B is the thickness, b the remaining ligament and a is the crack length of the specimen, were derived [Shih and German (1981), International Journal of fracture 17, 27–43] which have provided the basis for modern fracture toughness testing procedures. Two-parameter fracture toughness testing including the constraint, on the other hand, is desirable since it offers a solution to the transferability issue. A size requirement for a valid two-parameter fracture toughness testing based on the J-A₂ three-term solution was determined as min(a, b, B) > 11J/σ₀ [Chao and Zhu (1998), International Journal of fracture 89, 285–307] in which the limiting case is bend specimens under large scale yielding (LSY). Recent work by Chao et al. (2004, International Journal of fracture, 27, 283–302) has shown that the J-A₂ dominance at a crack tip can be significantly enhanced for bending specimens under LSY if a modified J-A₂ solution is adopted. This current paper further studies the size of the J-A₂ dominant zone using the modified J-A₂ solution for deep bend specimens with hardening from low to high and loading from SSY to LSY using finite element analysis. Based on the results, a rather relaxed specimen size requirement min(a, b, B) >6J/σ₀ is developed and recommended for a valid two-parameter fracture toughness testing using the J-A₂ fracture criterion. Validity of the size requirement is demonstrated by using the experimental J-R curves from non-standard bending specimens for A285 steel.     

On the Applicability of the Schwalbe's Model to the Fracture Toughness Calculation in 7075 Aluminum Alloys

Four 7075-T651 aluminum alloys have been tested in tension in order to assess the applicability of the Schwalbe's model to the fracture toughness calculation. Standard K _IC tests were performed on compact tension samples at room temperature, and the results compared with those from the Schwalbe's model which takes into account several mechanical properties derived from a conventional tensile test applied on round unnotched tensile samples, and the average dimple size of the corresponding fracture surfaces. The values of K _IC calculated through the Schwalbe's model, correlate qualitatively well with those from the standard technique.Fracture toughness deterioration is accompanied by a loss of the true fracture strain, strain hardening capacity and average dimple size. On the other hand, the higher the Zn/Mg ratio, the volume fraction of precipitates and the yield strength, the lower the fracture toughness. All these effects are originated in the presence of matrix precipitates. Therefore, the reduction in K _IC can be explained in terms of the matrix response to the applied stress field as a function of the differences in volume fraction of the strengthening precipitates.The round tension samples corresponding to the four materials, failed in a predominantly ductile transgranular fashion, which facilitates the application of the Schwalbe's model based in the characteristic dimples, developed in this mode of fracture, as a microstructural element size.     

Predicting the J integral fracture toughness of Al 6061 using the small punch test

The 6000 series aluminium alloys (Al–Mg–Si systems) are commonly used as medium‐strength structural materials; in particular, the 6061 (Al–1Mg–0.6Si) alloy is widely utilized as a general‐purpose structural material due to its excellent formability and corrosion‐resisting capabilities. The objective of this study was to obtain a correlation between the small punch (SP) test estimated equivalent fracture strain (ɛ_qf) and fracture toughness (J_1C) property for 6061 aluminium, and determine its viability as a non‐destructive fracture toughness test technique for remaining life assessment of in‐service components. Samples of 6061‐T6 aluminium were cut from bulk plate, in both the longitudinal and transverse directions, for the as‐received condition as well as subjected to three different over‐ageing heat‐treatment schedules. A strong linear correlation between valid J_1C and SP estimated biaxial fracture strain ɛ_qf is presented for aluminium 6061 at room temperature.     

Vickers Indentation Fracture (VIF) modeling to analyze multi-cracking toughness of titania, alumina and zirconia plasma sprayed coatings

For massive brittle materials, the fracture toughness in mode I, K_IC, can be determined using various reliable techniques. Besides, Vickers Indentation Fracture (VIF) technique has been developed to locally determine fracture toughness. However, since the indentation test generates a complex three-dimensional crack system around the indent, fracture toughness, K_C, is calculated instead of K_IC. Consequently some authors rightly reject the VIF technique to determine standard fracture toughness by arguing that the literature counts numerous VIF crack equations thus revealing discrepancies of this technique. Nevertheless in some cases (e.g. brittle ceramic coatings) inclusive material techniques are not applicable since presence of the substrate and/or multi-crack network can modify the crack propagation into the coating.In this work, we employed VIF technique to study multi-cracking behavior of titania, alumina and zirconia ceramic oxide coatings obtained by plasma spraying. To calculate VIF toughness, we propose (i) to select two crack equations for radial-median and Palmqvist cracking modes respectively, (ii) to adjust the crack equation of Miranzo and Moya for intermediate cracking mode, (iii) to develop a mathematical approach to determine the cracking mode, (iv) to take into account the multi-crack network by defining an equivalent four-crack system and (v) to propose a universal crack equation applicable independently of the cracking mode.     

Correlation of fracture toughness with microstructural features for ultrafine‐grained 6082 Al alloy

In the present work, cryorolling (CR) and room temperature rolling (RTR) followed by annealing (AN) at 200°C were carried out to investigate the effects of grain size, precipitates (Mg‐Si‐phases), and AlFeMnSi‐phases on the fracture toughness of 6082 Al alloy. Using the values of the conditional fracture toughness, (K_Q), in the critical fracture toughness (K_IC) validation criteria, it was found that the sample size is inappropriate, which implies that the conditional fracture toughness obtained cannot be considered as the critical fracture toughness. Therefore, to establish the relative improvement in fracture toughness, the equivalent energy fracture toughness (K_ee) and J‐integral were calculated and used. The results show that the values of K_ee (89.91 MPa √m) and J (89.86 kJ/m²) obtained for the sample processed via CR followed by AN (CR + AN) are the highest when compared with the other samples processed through CR, RTR, and RTR followed by AN, RTR + AN. Microstructural features such as high fraction of low Taylor factor, high fraction of kernel average misorientation, Si‐rich particles, small size AlFeMnSi‐phases, and mixed mode of failure (transgranular shear and micro‐void coalescence) also support the high fracture toughness in the CR + AN sample. It was also observed that the effect of residual stresses on the fracture toughness of CR and RTR samples is minimal. Therefore, the correlation between microstructure and residual stresses is not considered in the present work due to very small values of the residual stresses for CR and RTR samples and the absence of residual stress from the heat‐treated samples.     

Limitations of elastic definitions in Al-Si-Mg cast alloys with enhanced plasticity: linear elastic fracture mechanics versus elastic-plastic fracture mechanics

Linear elastic fracture mechanics describes the fracture behavior of materials and components that respond elastically under loading. This approach is valuable and accurate for the continuum analysis of crack growth in brittle and high strength materials; however it introduces increasing inaccuracies for low-strength/high-ductility alloys (particularly low-carbon steels and light metal alloys). In the case of ductile alloys, different degrees of plastic deformation precede and accompany crack initiation and propagation, and a non-linear ductile fracture mechanics approach better characterizes the fatigue and fracture behavior under elastic-plastic conditions.To delineate plasticity effects in upper Region II and Region III of crack growth an analysis comparing linear elastic stress intensity factor ranges (ΔK_el) with crack tip plasticity adjusted linear elastic stress intensity factor ranges (ΔK_pl) is presented. To compute plasticity corrected stress intensity factor ranges (ΔK_pl), a new relationship for plastic zone size determination was developed taking into account effects of plane-strain and plane-stress conditions (“combo plastic zone”). In addition, for the upper part of the fatigue crack growth curve, elastic-plastic (cyclic J based) stress intensity factor ranges (ΔK_J) were computed from load-displacement records and compared to plasticity corrected stress intensity factor ranges (ΔK_pl). A new cyclic J analysis was designed to compute elastic-plastic stress intensity factor ranges (ΔK_J) by determining cumulative plastic damage from load-displacement records captured in load-control (K-control) fatigue crack growth tests. The cyclic J analysis provides the true fatigue crack growth behavior of the material. A methodology to evaluate the lower and upper bound fracture toughness of the material (J_IC and J_max) directly from fatigue crack growth test data (ΔK_FT(JIC) and ΔK_FT(Jmax)) was developed and validated using static fracture toughness test results. The value of ΔK_FT(JIC) (and implicitly J_IC) is determined by comparing the plasticity corrected elastic fatigue crack growth curve with the elastic-plastic fatigue crack growth curve. A most relevant finding is that plasticity adjusted linear elastic stress intensity factor ranges (ΔK_pl) are in remarkably good agreement with cyclic J analysis results (ΔK_J), and provide accurate plasticity corrections up to a ΔK corresponding to J_IC (i.e. ΔK_FT(JIC)). Towards the end of the fatigue crack growth test (above ΔK_FT(JIC)) when plasticity is accompanied by significant tearing, the cyclic J analysis provides a more accurate way to capture the true behavior of the material and determine ΔK_FT(Jmax). A procedure to decouple and partition plasticity and tearing effects on crack growth rates is given.Three cast Al-Si-Mg alloys with different levels of ductility, provided by different Si contents and heat treatments (T61 and T4) are evaluated, and the effects of crack tip plasticity on fatigue crack growth are assessed. Fatigue crack growth tests were conducted at a constant stress ratio, R = 0.1, using compact tension specimens.     

Synthesis,microstructure, and mechanical properties of boron suboxide materials doped with chromium boride

Improvement on the densification and fracture toughness of ceramic materials based on boron suboxide (B₆O) has been of great importance. The mechanical properties of B₆O with and without chromium boride addition, hot pressed at a temperature range of 1850–1900°C and pressures of 50–80?MPa for 20 minutes, were investigated. The relative density, phase relationship, microstructures and mechanical properties of the processed ceramics were examined. More than 96% of the theoretical density was obtained for both ceramic systems. A good combination of mechanical properties was obtained with the B₆O-CrB₂ material (H_V?=?32.1?GPa, K_IC?=?4.5?MPa?·?m^0.5) compared to the pure B₆O material (H_V?=?30.5?GPa, K_IC?=?brittle). The addition of 1.7?wt.% CrB₂ resulted in a pronounced improvement in both the hardness and fracture toughness values. Crack bridging and deflection are some of the toughening mechanisms liable for the enhanced fracture toughness of the sintered ceramic materials.     

Dynamic fracture of tungsten base heavy alloys

A recently developed short beam experimental technique has been applied to the characterization of the mode I dynamic fracture toughness (KId) of a commercial tungsten base heavy alloy (w/o-90W-7Ni-3Fe). The specimens were taken from a cylindrical swaged alloy bar and tested at a typical loading rate of the order of 10⁶ MPa\sqrtm/s. Three different crack orientations (one longitudinal and two radial) were investigated. The KIdvalues obtained for the three crack orientations are compared with the corresponding values obtained under quasi-static loading conditions (KIc). Our results show that the dynamic fracture of heavy alloys is both anisotropic and rate sensitive. For specimens containing radial cracks (LR, RR), the dynamic fracture toughness is higherthat its static counterpart. By contrast, for longitudinal cracks (RL), the dynamic fracture toughness is lowerthan the static one. Also, for radial cracks, both the (average) static and the dynamic fracture toughness are higher than in the longitudinal orientation. These new results about the anisotropy of the dynamic fracture toughness of the heavy alloys are reported and correlated with metallographic and fractographic examinations.     

Fatigue behavior and plane-strain fracture toughness of sand-cast Mg–10Gd–3Y–0.5Zr magnesium alloy

In this study, the tensile properties, high cycle fatigue behavior and plane-strain fracture toughness of the sand-cast Mg–10Gd–3Y–0.5Zr magnesium alloy were investigated, comparison to that of sand-cast plus T6 heat treated magnesium alloy which named after sand-cast-T6. The results showed that the tensile properties of the sand-cast alloy are greatly improved after T6 heat treatment, and the fatigue strength (at 10⁷ cycles) of the sand-cast Mg–10Gd–3Y–0.5Zr magnesium alloy increases from 95 to 120 MPa after T6 heat treatment, i.e. the improvement of 26% in fatigue strength has been achieved. The plane-strain fracture toughnesses K_IC of the sand-cast and sand-cast-T6 alloys are about 12.1 and 16.3 MPa m^1/2, respectively. In addition, crack initiation, crack propagation and fracture behavior of the studied alloys after tensile test, high cycle fatigue test and plane-strain fracture toughness test were also investigated systematically.     

Study of elastic-plastic fracture toughness determination

The elastic-plastic fracture toughness viaJ-integral and crack tip opening displacement (CTOD) has been obtained in two structural steels using several fitting equations representing the resistance curve of the material. The toughness is determined as the values corresponding to the critical stretched zone width (SZW) on theR-curves and with respect to 0.2 mm crack growth. The SZW measurements were performed by scanning electron microscopy. The various toughness values have been compared and the importance of using appropriateR-curves based on physical considerations has been pointed out. TheJ-CTOD relationship during the blunting process has been experimentally investigated from load-displacement records of the fracture test.     

Low-temperature fracture toughness study of Fe-7Al-27Mn-C alloys

This research studied the fracture toughness of the Fe-7Al-27Mn alloys with increasing carbon contents: 0.5% C, Fl alloy: 0.7% C, F2 alloy (with 4.0% Cr); and 1.0% C, F3 alloy. Fracture toughness experiments were conducted at temperatures of 25, – 50, – 100 and – 150 °C. It was found that plane-stress,K _C, values as measured by the R-curve method, decreased as the temperature dropped. F1 alloy possessed the highestK _C value at all temperatures among the three alloys. TheK _C values of the F2 and F3 alloys were similar at ambient temperatures, but F3 maintained the toughness property and ductility better at sub-zero temperatures. Quantitatively,K _IC values of the F2 alloy at – 150 °C were ca, 60% less than at 25 °C, but F1 and F3 alloys dropped by only ca. 30%. Using a compact-tension specimen, 20.0 mm thick, at –150°C only alloy F2 satisfied the requirement of plane-strain fracture toughness with aK _C value of 106 MPa m^1/2. The existence of Cr (4.0%) and the formation of a ferrite phase in an austenite matrix was responsible for the low toughness value observed.     

Unified correlation of in‐plane and out‐of‐plane constraints with fracture toughness

In this paper, the specimens with different geometries and loading configurations were used to study the unified correlation of in‐plane and out‐of‐plane constraints with fracture toughness by using numerical simulation method. The results show that the unified constraint parameter A_p which was defined on the basis of the areas surrounded by the equivalent plastic strain isolines ahead of crack tip can characterise both in‐plane and out‐of‐plane constraints induced by different specimen geometries and loading configurations. A sole linear relation between the normalised fracture toughness J_IC/J_ref and was obtained. The J_IC/J_ref ‐ line is a unified correlation line of in‐plane and out‐of‐plane constraints with fracture toughness of a material, and the constraint dependent fracture toughness of a material can be determined from the unified correlation line. The results also demonstrate that the out‐of‐plane constraint effect is related to the in‐plane constraint effect, and there exists interaction between them. The higher in‐plane constraint strengthens the out‐of‐plane constraint effect, whereas the lower in‐plane constraint is not sensitive to the out‐of‐plane constraint effect.     

Residual strength of unidirectional fibre-metal laminates based on JC toughness of C(T) and SE(B) specimens: comparison with M(T) test results

Fibre‐metal laminates (FMLs) are structural composites designed with the aim of producing very low fatigue crack‐propagation rate, damage‐tolerant and high‐strength materials, if compared to aeronautical Al alloys. Their application in aeronautical structures demands a deep knowledge of a wide set of mechanical properties and technological values, including both fracture toughness and residual strength. The residual strength of FMLs have been traditionally determined by using wide centre‐cracked tension panels M(T). The use of this geometry requires large quantities of material and heavy laboratory facilities. In this work, fracture toughness ( J_C) of some unidirectional FMLs laminates was measured using a recently proposed methodology for critical fracture toughness evaluation on compact tension C(T) and single‐edge bend SE(B) specimens. Additionally, residual strength values of wider M(T) specimens with different widths (W from 150 to 200 mm) and several crack to width ratios (2a/W) were experimentally obtained. Some experimental residual strength values of M(T) specimens (W from 150 to 400 mm and different 2a/W ratios) of Arall were also obtained from the bibliography. Based on J_C results from C(T) and SE(B) specimens, and either using or not using crack‐tip plasticity corrections, the residual strengths of the M(T) specimens were predicted and compared to the experimental ones. The results showed good agreement, especially when crack‐tip plasticity corrections were applied.     

Effect of Cux substituted for Gax on the thermodynamic and fracture behavior in magnetic shape memory Ni50Mn30Ga20 − xCux with high transformation temperature

The effect of Cu_x substituted for Ga_x on the thermodynamic characteristic, evolution of phases and fracture behavior in Ni₅₀Mn₃₀Ga_20???xCu_x alloys have been investigated. The results show that the martensitic transformation, reverse transformation temperatures and average interface temperature of Ni₅₀Mn₃₀Ga_20???xCu_x sample increase remarkably with increased content of Cu. The hysteresis temperature of the austenite to martensite transition firstly showed a steep rising trend, then almost reduced to a lower rate with the increased content of Cu up to 4 at.% (the maximum level of copper addition studied). The (202) diffraction peak position was observed to shifted towards high angles, when the Cu content was lower than 1 at.%. Further, the, M₂₀₂ diffraction peak was found to split into two diffraction peaks when the Cu content was more than 1 at.%. In addition, the compressive strength and fracture strain of alloys is clearly enhanced with increased content of Cu. Furthermore, the fracture type of Ni₅₀Mn₃₀Ga_20???xCu_x alloys was found to changes from intergranular fracture for the Ni–Mn–Ga alloys, to transgranular cleavage fracture with increase in Cu content.     

Microstructural and superconductive studies of Ag-YBa2Cu3O7?x composites

Composites of Ag-YBa₂Cu₃O_7–x were synthesized and carefully characterized for crystal structure and microstructure by X-ray diffraction, optical microscopy, SEM, TEM, and EDAX techniques in order to investigate the effect of Ag additions on the superconducting properties of 123 compounds. The a.c. susceptibility data show thatT _c (onset) of 123+Ag composites vary between 90.2 and 91.8 K. TheJ _c values we measured for 123 material without silver were in the range of earlier reported values for the pure 123 material. Whereas there is a relatively small increase in the critical current for the YBCO/Ag₂O ratio of 3, the variation of the grain size of the composites shows that theseJ _c changes are due to slight variations in the grain size rather than any dramatic effect of Ag inclusions as speculated earlier.