A comparison of critical stress intensity parameter with other nonlinear toughness parameters

In structural steels, the two nonlinear toughness parameters, i.e. Rice's J-integral and Liebowitz's G have been evaluated over a wide range of yield strength varying from 235 to 1035 MPa. The K toughness parameter has also been obtained by applying an iterative plasticity correction. The three toughness parameters have been compared and the thickness regime, over which a valid K_Ic can be obtained, has been identified.     

On fracture toughness in the nonlinear range

A general definition of fracture toughness, designated by $\text{G}\text{?}{}_{\mathrm{c}}$, is developed which is appropriate to situations of subcritical crack growth and/or large-scale crack border plastic yield. The theoretical basis as well as comparisons with other proposed measures of fracture toughness are also discussed. A simple method is given for evaluating $\text{G}\text{?}{}_{\mathrm{c}}$ which is based on use of the load-displacement test record.     

Analysis of the geometry dependence of fracture toughness at cracking initiation by comparison of circumferentially cracked round bars and SENB tests on Copper

In the first part of the paper, the use of circumferentially cracked round bars (CRB geometry) for characterizing fracture toughness of a ductile material, namely copper, is assessed experimentally through a comparison with the single edge notched bend (SENB) geometry. The J_R curve method with multiple-specimens was applied, but, as unstable cracking appeared very early in the CRB specimen, an engineering definition of fracture toughness was not pertinent. Unloaded specimens were analyzed metallographically to determine the CTOD at physical cracking initiation. The fracture toughness measured using the CRB geometry was 50% larger than using the SENB geometry. The second part of the paper aims at justifying this difference of fracture toughness at cracking initiation. Finite element simulations revealed a slightly higher constraint in the SENB specimens. The main difference between the two specimen geometries lies in a 50% larger extension of the finite strain zone with respect to the CTOD in the case of the SENB specimens. Based on the observation that, in the studied material, the critical CTOD is one order of magnitude larger than the void spacing, we conclude that the geometry dependence of the fracture toughness is caused by the difference in the finite strain zone extension rather than by a stress triaxiality effect.     

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.     

Structural parameters controlling the fracture toughness of structural materials

This article examines two basic concepts associated with brittle fracture: so- called sequential fracture and counter fracture. Quantitative estimates are made of the threshold and minimum fracture toughnesses of materials exhibiting these phenomena. Methods of quickly determining fracture toughness are explored and along with the physical significance of the two main structural parameters that indicate the fracture toughness of a material: the characteristic distance and the cleavage stress. Methods are presented for rapid a prioridetermination of the fracture toughness of materials from standard mechanical characteristics.Translated from Problemy Prochnosti, No. 1, pp. 18–30, January, 1994.This study was completed as part of a program of basic research financed by the State Committee of the Ukraine for Science and Technology.     

Correlation of geometry effects with fracture toughness by damage equivalence

The near crack tip porosity fields in different fracture specimens, single edge notched, single edge notched loaded in centre of ligament, three point bending specimens, and small scale yielding (SSY) mode have been studied by the finite deformation finite element method. The presence and subsequent growth of smaller-scale voids were taken into account by using Gurson's model to describe the constitutive behaviour of the material. Based on damage equivalence at a characteristic position in the SSY mode and actual fracture specimens, the ratio of scaling parameters,J values, in both modes was obtained, and was used to eliminate the geometry dependence of fracture toughness through correlations to the small scale yielding mode.On leave, Department of Mechanical and Intelligent Systems Engineering, Tokyo Institute of Technology, Tokyo, Japan.     

Structure parameters governing fracture toughness of engineering materials

Conclusions 1. Of the two concepts of brittle fracture of engineering materials based on the decohesion and coalescence fracture mechanisms, respectively, the first reflects the threshold fracture toughness for materials of perfect structure, the second — the minimal fracture toughness of the material of a real structure. Since the coalescence fracture mechanism is observed with most engineering materials and requires higher fracture energy and the decohesion mechanism is a part of the coalescence mechanism, it is necessary to investigate both of them in order to study the nature of the fracture process and to optimize the material structure. 2. The model parameters on which the coalescence fracture mechanism is based, namely, characteristic distance X_c and microcleavage stress _f ^* , are directly related to the material minimal fracture toughness and are defined by the weakest elements of its microstructure. 3. Rigorous physical interpretation of the characteristic distance and microcleavage stress requires statistical (dimensional and orientation) consideration, yet modeling of the fracture process in mean values of the above parameters seems to be useful. 4. Fracture toughness dependences on the temperature and loading rate both for a number of ceramic materials and for steels in the brittle-to-ductile transition region have much in common. For this reason, it is possible to use some fracture models, and, in particular, the K_µ-model, to analyze fracture of ceramic materials and to optimize their structure. 5. The main ways of enhancing fracture toughness of engineering materials are associated not only with the plasticization of the latter but also with the creation of such structures that would contribute to an increase of their minimal fracture toughness values. This can be achieved by increasing each of the two fundamental parameters of the material fracture micromechanism: characteristic distance and cleavage stress.Institute of Strength Problems, Ukraine Academy of Sciences, Kiev. Université de Metz. Published in Fiziko-Khimicheskaya Mekhanika Materialov, Vol. 29, No. 3, pp. 113–123, May–June, 1993.     

An empirical model for estimating fracture toughness using the DCDC geometry

The double cleavage drilled compression (DCDC) geometry is useful for creating large cracks in a material in a controlled manner. Several models for estimating fracture toughness from DCDC measurements have been proposed, but each is suitable for a subset of geometries and material properties. In this work, a series of finite element fracture simulations are performed over a range of sample widths, hole sizes, heights, Young’s moduli, Poisson’s ratios, critical stress intensity factors, and boundary conditions. Analyzing the simulation results, fracture toughness is found to be a simple function of sample width, hole size, and an extrapolated stress at zero crack length obtained from a linear fit of the data. Experimental results in the literature are found to agree with this simple relationship.     

Fracture toughness characterization of several aluminum alloys in semi-brittle fracture

A method has recently been developed for determining a nonlinear fracture toughness parameter defined by the relation $\text{G}\text{?}{}_{\mathrm{c}}\text{=}\text{C}\text{?}\text{G}{}_{\mathrm{c}}$ where G_c is the critical elastic strain energy rate as defined by Irwin. The $\text{C}\text{?}$ term is a function of the nonlinearity of the load-displacement test record and has been evaluated using the three parameter Ramberg-Osgood approach, although other curve fitting techniques could be applied as well. The method is quite straightforward and is applicable to plane stress, plane strain and mixed mode testing although only plane stress conditions are considered in this paper. For the case of a linear load-displacement record $\text{C}\text{?}\text{→ 1}$ and $\text{G}\text{?}{}_{\mathrm{c}}$ reduces to the linear elastic result.The toughness parameter $\text{G}\text{?}{}_{\mathrm{c}}$ has been evaluated for a number of high strength aluminum alloys and compared with published G_c values for these materials. The tests were conducted on center-cracked sheets of 2014-T6, 2024-T81, 7075-T6 and 7475-T61 aluminum alloys under conditions of varying specimen geometry and displacement gage length. It was found that the values of $\text{G}\text{?}{}_{\mathrm{c}}$ obtained from displacement readings with a gage length of 2 in. generally agreed with published values of $\text{G}{}_{\mathrm{c}}\text{=}\text{K}{}_{\mathrm{c}}{}^2\text{E}$. The $\text{G}\text{?}{}_{\mathrm{c}}$ values were found to vary inversely with gage length and a/w ratios. The variation in values for $\text{G}\text{?}{}_{\mathrm{c}}$ is of the same order of magnitude as the scatter in published values for G_c. However, $\text{G}\text{?}{}_{\mathrm{c}}$ appears to be less sensitive than G_c to changes in a/w.     

On scattering of measured values of fracture toughness parameters

The values of fracture toughness K _1C of C-Mn steels and weld metal were calculated from values of COD measured in standard specimens tested at low temperatures. The analysis of scattering of 42 values of K _1C measured in normalized C-Mn steel showed that the highest value of K _1C could be as large as 360 percent of the lowest. The factors affecting the scattering were investigated in detail and it was found that the scattering was mainly caused by the variation of locations of cleavage initiation. The local fracture stress σ was found to be the most stable parameter and combined with the minimum cleavage distance min which is determined by the triaxiality of stress reaching a critical value, it could be used to characterize the lower boundary of fracture toughness of steels. This revised version was published online in July 2006 with corrections to the Cover Date.     

Calibration of Weibull stress parameters using fracture toughness data

The Weibull stress model for cleavage fracture of ferritic steels requires calibration of two micromechanics parameters . Notched tensile bars, often used for such calibrations at lower-shelf temperatures, do not fracture in the transition region without extensive plasticity and prior ductile tearing. However, deep-notch bend and compact tension specimens tested in the transition region can provide toughness values under essentially small-scale yielding (SSY) conditions to support Weibull stress calibrations. We show analytically, and demonstrate numerically, that a nonuniqueness arises in the calibrated values, i.e., many pairs of provide equally good correlation of critical Weibull stress values with the distribution of measured (SSY) fracture toughness values. This work proposes a new calibration scheme to find which uses toughness values measured under both low and high constraint conditions at the crack front. The new procedure reveals a strong sensitivity to m and provides the necessary micromechanical values to conduct defect assessments of flawed structural components operating at or near the calibration temperature in the transition region. Results of a parameter study illustrate the expected values of m for a typical range of material flow properties and toughness levels. A specific calibration is carried out for a mild structural steel (ASTM A36). This revised version was published online in August 2006 with corrections to the Cover Date.     

Microstructural dependence of fracture toughness in high-strength 7000 forging alloys

The effects of microstructural parameters associated with the coarse intermetallic phases particles and precipitates on the fracture toughness of the overaged 7000 alloy forgings are investigated. Detailed microstructural and fractographic analysis together with fracture toughness tests are carried out using three alloys with different (Fe + Si) contents. The fracture mechanisms are identified and area fractions of different fracture modes are assessed. The data are then quantitatively correlated to plane-strain fracture toughness, K_Ic, and the bulk microstructural attributes estimated via image analysis. A multiple micromechanism-based model is developed, which accurately describes the dependence of K_Ic on individual microstructural parameters.     

Temperature dependence of fracture toughness of epoxy resins cured with diamines

The fracture toughness (critical stress intensity factor, K _Ic) of epoxy resins cured with four diamines has been measured as a function of temperature over the range from –35° C to above T _g. It was found that K _Ic for each epoxy-diamine system did not vary below room temperature, and in the higher temperature range K _Ic increased with increasing temperature to a maximum and then decreased. The temperature which maximized K _Ic, agreed with the temperature at which the flexural modulus of the epoxy resins abruptly dropped. This temperature was therefore considered as T _g. This temperature was found to be about 20° C lower than the heat deflection temperature under load (1.82 M Pa) of the resins.