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.     

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.     

A model for the static fracture toughness of ductile structural steel

Fracture of ductile structural steels generally occurs after void initiation, void growth and void coalescence. In order for ductile fracture of structural steels to occur, energy must be spent to induce void initiation and void growth. Therefore, fracture toughness for ductile fracture should be contributed from void initiation and void growth. On the basis of this suggestion static fracture toughness (K_IC) of ductile structural steels is decomposed into two parts: void nucleation-induced fracture toughness (denoted as K_IC.n) and void growth-induced fracture toughness (K_IC.g). K_IC.n, defined as the stress intensity factor at which voids ahead of a crack begins to form, is calculated from crack tip strain distribution and void nucleation strain distribution. In contrast, K_IC.g is determined by the void growth from the beginning of void nucleation to void coalescence. Therefore, K_IC.g relates to the void sizes and void distribution. In this paper, the expression for K_IC.g is given from the void sizes directly from fracture surfaces. The relationship between K_IC.n, K_IC.g and K_IC is expressed in the form (K_IC)²=(K_IC.n)²+(K_IC.g)². The newly developed model was applied to the fracture toughness evaluation of three structural steels (SN490, X65 and SA440), and the theoretical calculation agrees with the experimental results.     

Effects of thickness and environmental temperature on fracture behaviour of polyetherimide (PEI)

The fracture behaviour of a polyetherimide (PEI) thermoplastic polymer was studied using compact tension (CT) specimens with a special emphasis on effects of specimen thickness and testing temperatures on the plane strain fracture toughness. The results show that the valid fracture toughness of the critical stress intensity factor, K _IC, and strain energy release rate, G _IC, is independent of the specimen thickness when it is larger than 5 mm at ambient temperature. On the other hand, the fracture toughness is relatively sensitive to testing temperatures. The K _IC value remains almost constant, 3.5 MPa in a temperature range from 25 to 130°C, but the G _IC value slightly increases due to the decrease in Young's modulus and yield stress with increasing temperature. The temperature dependence of the fracture toughness, G _IC, was explained in terms of a plastic deformation zone around the crack tip and fracture surface morphology. It was identified that the larger plastic zone and extensive plastic deformation in the crack initiation region were associated with the enhanced G _IC at elevated temperatures.     

A study on the ASTM E1921 standard in determining the fracture toughness of ferritic steels

One of the most important aims of the fracture mechanics is to determine the fracture toughness of a material. Various methods were developed for this purpose and have been still used nowadays. In the J‐integral method that is one of them, providing of a dominant linear elastic condition on the specimen is not required. However, in ferritic steels, the fracture toughness values (K_JC) obtained by the J‐integral method show some inconsistencies. Therefore, the ASTM E1921 standard was developed on ferritic steels, which are instabilities in the values of elastic or elastoplastic fracture toughness. In this study, a new method was used to determine the fracture toughness (K_IC) of ferritic steels, and it was compared with the standard. Three steels with different mechanical properties and average grain size were investigated in this study.     

A simplified prediction of Kic from tensile data

A previously developed theory of fracture toughness is extended so that the plane strain fracture toughness K_IC may be calculated by a simple integration of uniaxial tensile data. K_IC values calculated by this procedure are within 3 per cent of the values obtained by the previous theory for the materials considered.     

Thickness effect on the mode III fracture resistance and fracture path of rock using ENDB specimens

Study of the thickness effect in predicting the crack growth behavior and load bearing capacity of rock‐type structures is an important issue for obtaining a relation between the experimental fracture toughness of laboratory subsized samples and the real rock structures with large thickness. The fracture of rock masses or underground rock structures at deep strata may be dominantly governed by the tensile or tear crack growth mechanism. Therefore, in this research, a number of mode I and mode III fracture toughness experiments are conducted on edge notch disc bend (ENDB) specimen made of a kind of marble rock to investigate the effect of specimen thickness on the corresponding K_Ic and K_IIIc values. It is observed that the fracture toughness of both modes I and III are increased by increasing the height of the ENDB specimen. Also, the ratio of K_IIIc/K_Ic obtained from each thickness of the ENDB specimens is compared with those predicted by some fracture criteria, and it was shown that the minimum plastic radius (MPR) criterion is the main suitable criterion for investigating the fracture toughness ratio K_IIIc/K_Ic . Also, the effect of ENDB height on fracture trajectory of tested samples is assessed. It is shown that the crack grows curvilinearly in thicker ENDB samples and cannot extend along the crack front in small specimens.     

Fracture toughness of maraging steel from Charpy “V” notch specimens

Compact tension (CT) and Charpy V notch (CVN) (impact and three-point bend) specimens of 18 Ni 1800 MPa maraging steel (parent metal and weldment) were used to determine plane strain fracture toughness (K _IC) and CVN impact energy (CVNIE), respectively. Using an empirical equation,K _IC-CVNIE correlation is attempted which could be advantageously utilized for routine quality control of inward material to effect savings in cost and time. Investigations reveal betterK _IC-CVNIE correlation for tests using the precracked CVN specimens. Scanning electron microscopic (SEM) observations reveal good correlation between fractographic features and fracture toughness.     

Acoustic emission imaging of shear failure in large reinforced concrete structures

The averaged value of the strain energy density over a well-defined volume is used to predict the static strength of U-notched specimens under mixed-mode conditions due to combined bending and shear loads. The volume is centered in relation to the maximum principal stress present on the notch edge, by rigidly rotating the crescent-shaped volume already used in the literature to analyse U- and V-shaped notches subject to mode I loading. The volume size depends on the ultimate tensile strength σ _u and the fracture toughness K _IC of the material. In parallel, an experimental programme was performed. All specimens are made of polymethyl-metacrylate (PMMA), a material which exhibits quasi-brittle behaviour at -60°C. Good agreement is found between experimental data for the critical loads to failure and theoretical predictions based on the constancy of the mean strain energy density over the control volume.     

A new push‐pull sample design for microscale mode 1 fracture toughness measurements under uniaxial tension

A sample geometry is proposed for performing microscale tensile experiments based on a push‐pull design. It allows measuring mode 1 fracture toughness under uniform far‐field loading. Finite element simulations were performed to determine the geometry factor, which was nearly constant for Young's moduli spanning 2 orders of magnitude. It was further verified that mode 1 stress intensity factor K_I is nearly constant over the width of the tension rods and an order of magnitude higher than K_II and K_III. Notched samples with different a/w ratios were prepared in (100)‐oriented Si by a combination of reactive ion etching and focused ion beam milling. The mode 1 fracture toughness K_I,q was constant with a/w and in average 1.02 ± 0.06 MPa√m in good agreement with existing literature. The geometry was characterized and experimentally validated and may be used for fracture toughness measurements of all material classes. It is especially interesting when a uniaxial, homogeneous stress field is desired, if crack tip plasticity is important, or when positioning of the indenter is difficult.     

A new method for determining the fracture toughness of main pipeline steels

One of the fundamental aims of fracture mechanics is to define fracture toughness K_IC of a material. Hence, the ASTM E399 standard was developed. However according to the standard, large‐sized specimens are required to determine the fracture toughness of low alloy carbon steels. ASTM E1921 standard was developed on the fracture toughness of ferritic steels. In this study, a new method was proposed to determine the fracture toughness of ferritic steels. The purpose of the present paper is to compare the results of the method with the experimental results. Two steels that are used in gas and oil main pipelines were investigated in this study.     

Comparison of shear and tensile fracture in high strength aluminum alloys

A comparison was made between tensile (mode I) and shear (mode II) fracture characteristics in high strength aluminium alloys (7075-T6 and 6061-T651) using a relatively new mode II fracture specimen to evaluate the critical stress intensity factor. The enlarged plastic zone during mode II fracture required that an increased specimen thickness be used for determining K _Hc under a purely plane strain condition. Plane stress conditions prevailed in the mode II fracture of 7075-T6 with a specimen thickness less than 10 mm, while plane strain controlled mode II fracture at a thickness of 10 mm or greater. Fractographic analysis revealed a distinctive difference in the micromechanisms responsible for crack extension. Small dimples were observed only on the mode II fracture surfaces, resulting from a microvoid nucleation fracture mechanism. The mode I fracture surfaces showed a mixed distribution of dimple sizes resulting from a void growth fracture mechanism. Comparing the critical stress intensity factors, the shear mode of failure exhibited a substantially higher value than the tensile mode, resulting from the effect of the sign and magnitude of the hydrostatic stress state on the microvoid nucleation event. Zero hydrostatic tension in the mode II loading configuration helps delay microvoid nucleation, increasing the apparent toughness. The high hydrostatic tension resulting from a mode I loading configuration enhances microvoid nucleation which promotes crack propagation at relatively lower stress intensity factors.     

The grain size dependence of fracture toughness in an Al-6.0% Zn-2.5% Mg alloy

The grain size dependence of the fracture toughness (K _IC) of an aged Al-6.0% Zn-2.5% Mg alloy was studied experimentally. K _IC depended strongly upon grain size (L _G) in two ways. In the small grain size region K _IC decreased with increasing average grain size. In contrast, K _IC increased with increasing average grain size for large grain sizes. The increase in K _IC with increasing grain size arose as a result of the presence of abnormally large grains compared to the average grain size in the large-grained specimens.     

A model for the dynamic fracture toughness of ductile structural steel

We assume in this paper that the dynamic fracture toughness K_Id of ductile structural steels is dependent on void nucleation and void growth. The void nucleation-induced dynamic fracture toughness K_Id·n and the void growth-induced dynamic fracture toughness K_Id·g were obtained by modifying the void nucleation-induced and void growth-induced static fracture toughness models, respectively, considering the effect of strain rate and local temperature. By the relationship between the void nucleation-induced dynamic fracture toughness K_Id·n and the void growth-induced dynamic fracture toughness K_Id·g((K_Id)²=(K_Id·n)²+(K_Id·g)²) dynamic fracture toughness K_Id could be quantitatively evaluated. With this model the dynamic fracture toughness of two structural steels (X65 and SA440) was assessed, and the causes for the differences between the static and dynamic fracture toughness were also discussed.     

Softening and snap-back instability in cohesive solids

The nature of the crack and the structure behaviour can range from ductile to brittle, depending on material properties, structure geometry, loading condition and external constraints. The influence of variation in fracture toughness, tensile strength and geometrical size scale is investigated on the basis of the π-theorem of dimensional analysis. Strength and toughness present in fact different physical dimensions and any consistent fracture criterion must describe energy dissipation per unit of volume and per unit of crack area respectively. A cohesive crack model is proposed aiming at describing the size effects of fracture mechanics, i.e. the transition from ductile to brittle structure behaviour by increasing the size scale and keeping the geometrical shape unchanged. For extremely brittle cases (e.g. initially uncracked specimens, large and/or slender structures, low fracture toughness, high tensile strength, etc.) a snap-back instability in the equilibrium path occurs and the load–deflection softening branch assumes a positive slope. Both load and deflection must decrease to obtain a slow and controlled crack propagation (whereas in normal softening only the load must decrease). If the loading process is deflection-controlled, the loading capacity presents a discontinuity with a negative jump. It is proved that such a catastrophic event tends to reproduce the classical LEFM-instability (K_I = K_IC) for small fracture toughnesses and/or for large structure sizes. In these cases, neither the plastic zone develops nor slow crack growth occurs before unstable crack propagation.     

Fracture toughness of sea ice

Linear elastic fracture mechanics, which has been applied to fragile substances and successfully used for studying the brittle fracture of metallic materials, was utilized to gain an understanding of the fracture phenomena of sea ice.The present paper reports the first results of investigations into the fracture-toughness value of sea ice, which was analyzed experimentally as a function of strain rate on the basis of the stress-intensity-factor concept.The fracture toughness, K_IC, of sea ice, which was measured by an in-situ three-point bending test on notched specimens, shows almost constant value if the strain rate is less then 10^?3 s^?1 and decreases with increasing strain rate if the strain rate exceeds 10^?3 s^?1. K_IC data show considerably less scatter than existing data such as the compressive, tensile and flexural strengths.It was confirmed in the present study that the linear elastic-fracture-mechanics concept is effective for analyzing the fracture phenomena of sea ice. Moreover, the K_IC value was shown to be closely related to sea-ice structures (e.g. the size of crack-like flaws such as brine cells).It is also suggested that the fracture-toughness test might prove to be a standard testing method to obtain the sea-ice strength, since once K_1C and crack-like flaw sizes are determined, the less-scattered critical-fracture stress can be calculated.     

Interlaminar fracture toughness and associated fracture behaviour of bead-filled epoxy/glass fibre hybrid composites

To investigate enhancement of matrix-dominated properties (such as interlaminar fracture toughness) of a composite laminate, two different bead-filled epoxies were used as matrices for the bead-filled epoxy/glass fibre hybrid composites. The plane strain fracture toughness of two different bead-filled epoxies have been measured using compact tension specimens. Significant increases in toughness were observed. Based on these results the interlaminar fracture toughness and fracture behaviour of hybrid composites, fabricated using bead-filled epoxy matrices, have been investigated using double cantilever beam and end notch flexure specimens for Mode I and Mode II tests, respectively. The hybrid composites based on carbon bead-filled matrix shows an increase in both G _IC initiation and G _IIC values as compared to a glass fibre reinforced plastic laminate with unmodified epoxy matrix. The optimum bead volume fraction for the hybrid composite is between 15% and 20%. However, the unmodified epoxy glass-fibre composite shows a higher G _IC propagation value than that of hybrid composites, due to fibre bridging, which is less pronounced in the hybrids as the presence of the beads results in a matrix-rich interply region.     

Fatigue and fracture of a Ni–P amorphous alloy thin film on the micrometer scale

Fracture and fatigue tests have been performed on micro‐sized specimens for microelectromechanical systems (MEMS) or micro system technology (MST) applications. Cantilever beam type specimens with dimensions of 10 × 12 × 50 μm³, approximately 1/1000th the size of ordinary‐sized specimens, were prepared from a Ni–P amorphous thin film by focused ion beam machining. Fatigue crack growth and fracture toughness tests were carried out in air at room temperature, using a mechanical testing machine developed for micro‐sized specimens. In fracture toughness tests, fatigue pre‐cracks were introduced ahead of the notches. Fatigue crack growth resistance curves were obtained from the measurement of striation spacing on the fatigue surface, with closure effects on the fatigue crack growth also being observed for micro‐sized specimens. Once fatigue crack growth occurs, the specimens fail within one thousand cycles. This indicates that the fatigue life of micro‐sized specimens is mainly dominated by a crack initiation process, also suggesting that even a micro‐sized surface flaw may be an initiation site for fatigue cracks which will shorten the fatigue life of micro‐sized specimens. As a result of fracture toughness tests, the values of plane strain fracture toughness, K_IC, were not obtained because the criteria of plane strain were not satisfied by this specimen size. As the plane strain requirements are determined by the stress intensity, K, and by the yield stress of the material, it is difficult for micro‐sized specimens to satisfy these requirements. Plane‐stress‐ and plane‐strain‐dominated regions were clearly observed on the fracture surfaces and their sizes were consistent with those estimated by fracture mechanics calculations. This indicates that fracture mechanics is still valid for such micro‐sized specimens. The results obtained in this investigation should be considered when designing actual MEMS/MST devices.     

Effects of test procedures and lithology on estimating the mode I fracture toughness of rocks using empirical relations

Empirical estimation is a common method for getting mode I fracture toughness K_IC of rock. By collecting data from tests in this study and literature, 204 sets of K_IC and tensile strength σ_t test data are obtained for new empirical K_IC‐σ_t relations regression. The empirical relations make the estimation of K_IC values from σ_t conveniently, but test procedures and lithology will influence its reasonability and reliability. Results indicate that the empirical K_IC‐σ_t relations obtained from the four different suggested K_IC test methods are all in good but obviously different linear relationship. The analyses show that cracked chevron notch Brazilian disc specimen (CCNBD) test‐based empirical relation is more accurate for estimating K_IC than the other three test‐based empirical relations. As to different lithology, isotropic rocks such as sandstone and carbonatite may be more appropriate for the application of empirical estimation method. However, for coarse grained or anisotropic rocks such as granite and marble, estimation method should be applied carefully because of possibly weak K_IC‐σ_t relations.     

A model for the static fracture toughness of ductile structural steel

Fracture of ductile structural steels generally occurs after void initiation, void growth and void coalescence. In order for ductile fracture of structural steels to occur, energy must be spent to induce void initiation and void growth. Therefore, fracture toughness for ductile fracture should be contributed from void initiation and void growth. On the basis of this suggestion static fracture toughness (K_IC) of ductile structural steels is decomposed into two parts: void nucleation-induced fracture toughness (denoted as K_IC.n) and void growth-induced fracture toughness (K_IC.g). K_IC.n, defined as the stress intensity factor at which voids ahead of a crack begins to form, is calculated from crack tip strain distribution and void nucleation strain distribution. In contrast, K_IC.g is determined by the void growth from the beginning of void nucleation to void coalescence. Therefore, K_IC.g relates to the void sizes and void distribution. In this paper, the expression for K_IC.g is given from the void sizes directly from fracture surfaces. The relationship between K_IC.n, K_IC.g and K_IC is expressed in the form (K_IC)²=(K_IC.n)²+(K_IC.g)². The newly developed model was applied to the fracture toughness evaluation of three structural steels (SN490, X65 and SA440), and the theoretical calculation agrees with the experimental results.