Application of artificial neural network for predicting plain strain fracture toughness using tensile test results

A back‐propagation neural network was applied to predicting the K_IC values using tensile material data and investigating the effects of crack plane orientation and temperature. The 595 K_IC data of structural steels were used for training and testing the neural network model. In the trained neural network model, yield stress has relatively the most effect on K_IC value among tensile material properties and K_IC value was more sensitive to K_IC test temperature than to crack plane orientation valid in the range of material data covered in this study. The performance of the trained artificial neural network (ANN) was evaluated by comparing output of the ANN with results of a conventional least squares fit to an assumed shape. The conventional linear or nonlinear least squares fitting methods gave very poor fitting results but the results predicted by the trained neural network were considerably satisfactory. This study shows that the neural network can be a good tool to predict K_IC values according to the variation of the temperature and the crack plane orientation using tensile test results.     

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.     

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.     

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.     

Fracture initiation under impact

In the first part of this paper the influence of temperature T and loading rate K_I upon the fracture toughness K_IC of structural steels is considered. A review of experimental results is presented over a wide range of loading rate and temperature in the form of the cross-sections of the constitutive surface K_INC = f(K_I,T). The hypothesis is proposed that both yield stress σ_y in uniaxial tension and fracture toughness K_IC are controlled by the same process of thermally activated movements of dislocations. Consequently, an introduction of the characteristic time t_c leads to the master plot K_IC (σ_y) in double logarithmic coordinates which is temperature and rate-independent. Such an approach provides a simple method for estimating the value of K_IC under a given set of imposed conditions (T,K?_I)₁ provided it is known for another set of imposed conditions (T,K?_I)₂.In the next part of this paper an attempt is presented to model the effect of T and K?_I on fracture toughness K_IC [15]. A model is discussed which combines correlations between critical cleavage stress σ_F, yield stress σ_y and the concept of thermally activated plastic flow from side and the local fracture criteria from the other [15]. It has been demonstrated that this approach can be useful in the proper predictions of changes of K_IC as a function of loading rate and temperature. For some steels, however, a minimum of fracture toughness is observed and typically occurs for $\text{K}{}_{\mathrm{I}}\text{? 1×10}{}^4$ MPa/pv/m/s at room temperature. The last part of this study deals with this important phenomenon [34]. It is concluded that the behavior of the constitutive surface K_IC = f(K_I,T) is highly nonlinear for steels.     

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.     

An alternate measure of fracture toughness

Linear elastic fracture mechanics has been primarily used for very high strength materials. For such applications it is adequate to measure K_Ic, the plane-strain fracture toughness. It is the objective of this paper to discuss a method for making dynamic fracture toughness measurements, K_Id, which are appropriate for structural grade steels. A simplified scheme for measuring K_Id is also proposed.     

Evaluation by indentation of fracture toughness of ceramic materials

A transition fracture mode from Palmqvist to median has been observed in a number of ceramic materials. A new expression to determine the fracture toughness (K _IC) by indentation is presented. The K _IC values calculated by this formula are independent of the crack profile (median or Palmqvist) and of the applied load. This formula has been obtained by modifying the universal curve of Evans and Charles to incorporate Palmqvist and median cracks over a wide range of loads in the case of brittle materials with different mechanical properties (elastic properties: E, v, K _IC).     

Material scale length as a measure of fracture toughness in fracture mechanics of plastic materials

An approach is suggested for describing the fracture toughness of relatively tough materials, in particular, low-strength steels. It is shown that the fracture toughness of such materials is characterized by a material scale length {ie185-1} or {ie185-2} (K-cohesion modulus, K _IC-critical stress intensity factor) not only within the framework of LEFM, but also in the case of large-scale yielding of materials.The critical conditions for crack propagation are formulated in terms of L(L _IC) and are considered for materials of similar plastic properties, e.g. for a wide class of low-strength steels. For such materials the conditions of similarity of fracture are established. Some methods of determination of the L _IC temperature dependence in small specimens are considered. The results of such L _IC (T) determination for a number of steels (A533 B1, A302, A517, etc.) are in good agreement with that calculated using direct K _IC measurements and can be used for predicting the fracture toughness values in those ranges where direct measurement of K _IC is practically impossible. The applicability and convenience of the proposed concepts for the estimation of reliability of structures have been illustrated for an example of pressure vessels.

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Résumé On suggère une approche pour décrire la ténacité à la rupture de matériaux relativement ductiles, en particulier les aciers à faible résistance. On montre que la ténacité à la rupture de tels matériaux est caractérisée par une valeur propre aux matériaux ayant l'échelle d'une longueur {ie201-1} ou {ie201-2} (où K est le module de cohésion et K _IC le facteur critique d'intensité de contrainte) et ce non seulement dans le cadre de la mécanique de rupture linéaire élastique mais également dans le cas de l'écoulement plastique à grande échelle dans les matériaux. Les conditions critiques pour la propagation des fissures sont formulées en termes de L(L) _IC et sont considérées pour des matériaux possédant des propriétés plastiques similaires, notamment dans le cas d'une classe relativement large d'aciers à basse résistance. Pour ces matériaux, les conditions de similitude de ruptures ont été établies. Quelques méthodes de détermination de la manière dont L _IC dépend de la température dans des éprouvettes de petites dimensions sont considérées. Les résultats d'une telle détermination obtenue pour un certain nombre d'aciers (A533 B1, A302, A517, etc.) paraissent en bon agrément avec les valeurs calculées qui utilisent des mesures directes de K _IC et peuvent étre utilisées pour prédire les valeurs de ténacité à la rupture dans les conditions où des mesures directes de K _IC sont pratiquement impossibles. Les possibilités d'application et l'opportunité d'appliquer ces concepts à l'estimation de la fiabilité des structures ont été illustrées par un exemple dans le cas des récipients sous pression.

     

Forecasting the cracking resistance for low-strength and medium-strength steels

A method is given for selecting the value of the work-hardening parameter n in calculating the cracking resistance K _Icfor steels in a formula of the type K_Ic = const(_y)^–(t-n)/2n. One incorporates the planar deformation and the severity of the state of stress (three-dimensional) at the crack vertex. The value of n defined by this method describes satisfactorily the experimental K_ICfor steels of low and medium strength with the above formula.Translated from Problemy Prochnosti, No. 2, pp. 63–67, February, 1996.     

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 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.     

Fracture parameters for sintered steels

Measurements of the plane strain fracture toughness K _Ic of sintered steels have frequently been invalid because the requirement that P _max/P _Q<1.1 (where P _max = maximum load and P _Q=load used to calculate K _Ic) has not been met. We show that the reason for the criterion not being met is that sintered steels have a considerable crack growth resistance K _R. Values obtained in the past for K _Ic probably have been over-estimates of the initiation value of the crack growth resistance K _i and under-estimates of the maximum crack growth resistance K . The important point is that the assessment of the toughness of sintered steels by a single parameter is not appropriate. Test methods to determine the crack growth resistance of sintered steels are discussed. Crack growth, which is difficult to detect by visual observation, can be determined by compliance techniques. Because of the porous nature of sintered steel, fatigue cracks are unnecessary at the tip of the notch and indeed are undesirable as they can easily cause errors in toughness measurements through inadvertent overloading. The thickness requirement for plane strain measurements can also be relaxed.     

Morphology control of ductile second phase and improved mechanical properties in high-strength low-alloy steels with mixed structure

Mixed structures of martensite and non-martensitic decomposition product (ductile second phase) can often be produced in commercial heat treatments of low-alloy steels. Such mixed structures can sometimes produce a detrimental effect on the mechanical properties of steels, but they can significantly improve strength, ductility and notch toughness if the ductile second phase appears in a suitable morphology (size, shape and distribution) in association with tempered martensite. Therefore, microstructures have recently been produced in a deliberate attempt to improve the mechanical properties of ultrahigh-strength low-alloy steels. In this review, an attempt has been made to present the effect of the morphology (shape, size and distribution) of the ductile second phase on improved mechanical properties of ultrahighstrength low-alloy steels having mixed structures, This review first discusses the effect of the morphology of the second-phase bainite on mechanical properties of high-strength low-alloy steels with mixed structures of martensite and bainite, in which great improvement in the mechanical properties of the steel has been associated with the morphology of the bainite. Then, knowledge of the recent development of a steel having the mixed structures for low-temperature ultrahigh-strength applications is also reported.     

Crack-size dependence of fracture toughness in transformation-toughened ceramics

Fracture toughness (K _IC) has been determined for Y₂O₃-partially stabilized zirconia, Y₂O₃-partially stabilized hafnia, CaO-partially stabilized zirconia and Al₂O₃+ZrO₂ composites. It is shown thatK _IC determined using the identation technique may not yield a unique number but may depend upon the crack size (C) (on the indent load). The slope ofK _IC againstC ^1/2 yields the magnitude of the surface stress created by the tetragonal monoclinic transition on the surface induced by grinding.K _IC determined using the double cantilever beam (DCB) technique, on the other hand, is shown to be independent of crack length.     

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 fractographic criterion for subcritical crack-growth boundaries in hot-pressed alumina

The percent intergranular fracture (PIF) was measured along radii extending from fracture origins in hot-pressed alumina specimens, fractured at various loading rates and temperatures, and plotted versus estimates of stress intensity factors (K _I) at the various crack lengths. Minima in PIF occur at values ofK _I that are close to the critical stress intensity factors (K _IC) for cleavage on various crystal lattice planes in sapphire. The subcritical crack-growth boundary (K _I=K _IC of the polycrystalline material) occurs near the primary minimum in PIF suggesting that this minimum can be used as a criterion for locating this boundary. In addition, it was noted that the polycrystallineK _IC (4.2 MPa m^1/2) is very close to theK _IC for fracture on {¯1 ¯1 2 6} planes which is 4.3 MPa m^1/2. These observations suggest that critical crack growth begins when increased fracture energy can no longer be absorbed by cleavage on these planes. There is a secondary minimum atK _I>K _IC that appears to be associated with theK _IC necessary for fracture on combinations of planes selected by the fracture as alternatives to the high fracture-toughness basal plane.     

Development of fracture toughness of ultrahigh strength low alloy steels for aircraft and aerospace applications

Abstract

Recently, ultrahigh strength low alloy steels, e.g. AISI 4340 and 300M, have been used increasingly for critical structural aircraft and aerospace applications. These steels can be employed successfully at yield strengths of ≥1400 MN m^?2 but their use has often been limited in commercial practice because of low fracture toughness compared with other types of ultrahigh strength steel. The results of studies carried out over the past two decades to improve the fracture toughness are presented. Particular emphasis is placed on improvements obtained by microstructural control via thermal and thermomechanical treatments, sulphide inclusions, and new alloying design. The major metallurgical factors controlling fracture toughness are discussed for each of these techniques.

MST/1413     

Effect of long-term thermo-oxidative aging on weight and fracture toughness of polycyanate neat resin

This study focuses on the effect of long-term thermo-oxidative aging on weight and fracture toughness (K_IC) of polycyanate ester (PCy) neat resin (FSD-M-08178). Thermo-oxidative aging was conducted at 180 °C up to 8000 h under atmospheric pressure in order to investigate susceptibility to thermo-oxidative environment in the PCy. Weight and K_IC changes were investigated with chemical structure changes due to thermo-oxidative degradation. The chemical structure changes were analyzed by means of Fourier transformed infrared spectroscopy with attenuated total reflection system. To investigate degree of degradation, carbonyl index (CI) was analyzed with triazine ring peak which is characteristic peak of the cured polycyanate resin. Single-edge-notch bending test was conducted for each aged (non-aged, 100, 197, 500, 1000, 2000, 4000, and 8000 h) condition to investigate K_IC change and evaluated with CI. The result indicated that the weight increased first 500 h. Then, the weight decreased. The result also indicated that the K_IC sharply dropped first 100 h. After 100 h, the K_IC was almost same up to 8000 h. The result suggested the K_IC depend on the CI which was chemical structure changes of the specimen surface due to thermo-oxidation degradation.     

On effect of hydrogen on very high cycle fatigue behaviours of high strength steels

Abstract

In order to analyse the effect of hydrogen on very high cycle fatigue properties, hydrogen was precharged into two high strength steels. The applied stress intensity factor range at the periphery of inclusions before and after being precharged is approximately proportional to the cubic root of inclusion size. In addition, the applied stress intensity factor range at the periphery of inclusions after being precharged was lower compared with uncharged specimens. The additional stress intensity factor range generated by hydrogen ΔK_H is raised after the hydrogen was precharged. A simple prediction equation of S–N curve was proposed by introducing the hydrogen influence factor. The proposed prediction equation can reasonably describe the S–N curves for precharged specimens.