Brittle Fracture Criterion Research Articles

A fractal criterion for ductile and brittle fracture

A universal relationship between roughness and toughness of fractures is proposed and a new criterion to define brittle and ductile fracture is derived from the Griffith energy balance concept and fractal geometry.

Brittle fracture criterion for structures with sharp notches

A brittle fracture criterion for structures with sharp notches is proposed. It is based on Irwin's and Novozhilov's criteria and states that a crack will propagate from a tip of a notch when the actual value of the stress intensity factor K I, II, III reaches a critical value. The considerations were carried out within the limits of linear elastic analysis and based on the general expressions for the stress distribution in the vicinity of the notch-tip. The parameters required to estimate the brittle fracture hazard can be easily obtained from experiments.

On the griffith criteria for brittle fracture in compression

Pre-existing flaws in materials are the potential source for brittle fracture in compression just as in tension. As in tension, both the stress and energy criteria should be taken into account for brittle fracture in compression. In the model presented, flaws are represented by three-dimensional ellipsoids, thus removing certain limitations of previous two-dimensional models. The formulation of the changes in the potential energy of the applied load and the strain energy of the infinite medium due to the introduction of an ellipsoidal void is presented and the implementation of the numerical calculation of the stress concentration and the energy release rate is developed. The required three-dimensional theory for a better understanding of brittle fracture in compression is provided.

A model emitting dislocation group from crack tip with stress singularity and its application to brittle—ductile transition

Taking into account the stress singularity near the crack tip, computer simulation of dislocation emission and motion has been carried out. A model is proposed in which the source emitting the dislocation group is located near by the crack tip. The numerical method has been used by programming to adjust time increment automatically. By this model and the analytical method, the converged solution has been obtained. The main results are as follows: The region where any dislocation does not exist along the slip plane near the stressed source, namely, dislocation free zone (DFZ) is found to appear. Also it has been found that inverse pile-up of dislocations against the tip of DFZ will appear. The formula is obtained correlating the maximum dislocation density with DFZ length. With increase of stress rate and decrease of the value of μ/τ 0 ∗ , the inverse pile-up at the tip of DFZ becomes more significant. Based on these results, a new fracture criterion for brittle fracture is proposed assuming critical local stress requisites within DFZ, where high stress concentration is induced by dynamic inverse pile-up of dislocations.

Discussion of the Compressive Testing Method of Ceramics.

In the previous paper, we reported several results of the compressive test for ceramics, and also proposed a dumbbell-type specimen and suitable equipment for measuring actual compressive strength. This paper discusses the fracture mechanism of ceramics under a compressive load and the edge effects in the specimen, using additional results for an acoustic emission (AE) test and the brittle fracture criterion under multiaxial stress. The results are as follows. (1) The compressive strength of ceramics is about 11 times as much as the tensile strength for Si3N4. (2) AE sounds are detected at the early stage of the compressive load, whose value coincides with the value estimated by means of the fracture criterion ; namely, about 22% of the fracture load. (3) The dumbbell-type specimen is highly recommended for ceramics as an edge effect-free specimen.

Crack-tip dislocation emission arrangements for equilibrium—II. Comparisons to analytical and computer simulation models

Theoretical analyses of thin film effects on an apparent dislocation free zone (DFZ), grain boundary effects on the number of dislocations required for equilibrium and a tip-emission condition to avoid the Rice paradox are compared to the in situ TEM study of Part I. It is first shown that the apparent DFZ is a thin film artifact and, second, that a grain boundary blocked slip band may require half as many dislocations for equilibrium compared to no blockage. It is further shown that the “DFZ” becomes diminishingly small for even relatively low applied stress intensities. Based on a disappearing “DFZ”, an asymptotical solution of Li's grain size analysis leads to the number of dislocations in equilibrium for a given applied stress intensity, friction stress and grain size. With an ad hoc failure criterion, this gives a first order prediction of fracture toughness for a large number of ferritic and ferrite-pearlites steels. Finally, based on local stress distributions obtained from a solution containing tip-emission conditions, it is suggested that a local stress intensity presents a more easily defined brittle fracture criterion. This is applied to observations of dislocation arrangements at large applied stress intensity in Part III.

Brittle fracture criterion: Structural mechanics approach

The authors proposed a criterion for the initiation of brittle fracture which takes into account the role of normal and effective stresses during microcrack initiation. A calculation and experimental method of determining the parameters included in the condition of initiation of brittle fracture is developed. The method is used to select these parameters for 15Kh2MFA steel'in the initial and deformed condition. The dependence of the critical stress of brittle fracture on plastic strain for different loading histories is analyzed. The use of the proposed criterion of brittle fracture makes it possible to predict satisfactorily the temperature dependence of the cracking resistance parameter KIc(T) and effect of prior strain on this parameter. The modified formulation of the criterion of brittle fracture makes it possible to describe the fracture process for different stress-strain states of the materials.

A nonlocal theory for brittle fracture

In this paper, a nonlocal theory of fracture for brittle materials has been systematically developed, which is composed of the nonlocal elastic stress fields of Griffith cracks of mode-I, II and III, the asymptotic forms of the stress fields at the neighborhood of the crack tips, and the maximum tensile stress criterion for brittle fracture. As an application of the theory, the fracture criteria of cracks of mode-I, II, III and mixed mode I–II, I–III are given in detail and compared with some experimental data and the theoretical results of minimum strain energy density factor.

Brittle fracture criterion and experimental research in rock under mixed-mode loads : Li Zhenzi; Li Zhenzi; Li Liyun; Sun Zongqi Proc International Symposium on Modern Mining Technology, Taian, October 1988 P395–402. Publ Taian: Shandong Institute of Mining and Technology, 1988

Brittle fracture criterion and experimental research in rock under mixed-mode loads : Li Zhenzi; Li Zhenzi; Li Liyun; Sun Zongqi Proc International Symposium on Modern Mining Technology, Taian, October 1988 P395–402. Publ Taian: Shandong Institute of Mining and Technology, 1988

An analysis of the conditions of brittle fracture origin

A modified criterion of brittle fracture, a necessary condition of which, the condition of origin of microcracks, is plastic deformation until some value of ɛ0 dependent upon temperature, is experimentally substantiated. An experimental-calculation method is developed for determination of the relationship of ɛ0 to temperature T, on the basis of which the ɛ0(T) relationship is obtained for type 15Kh2MFA steel. It is shown that the proposed formulation of the criterion of brittle fracture makes it possible to consistently describe the fracture processes with different stressed and strained states of the material.

Ductile and brittle fracture analysis of surface flaws using CTOD

A reference stress method is used to analyze both brittle and ductile fracture in structures containing surface flaws. Crack-tip opening displacement (CTOD) is used as the fracture-toughness input, althoughJ-based reference stress analyses are also possible. Both detailed and simplified analyses for brittle and ductile fracture are described. A brittle fracture analysis which takes account of stress concentrations, secondary stresses and stress gradients is presented, together with a complete ductile tearing analysis which utilizes a single CTOD value measured at maximum load. In addition, two simplified approaches are proposed: a yield-before-break criterion for brittle fracture and a critical learing modulus for ductile fracture.

A compressive strength criterion for anisotropic rock materials

This paper proposes a general compressive strength criterion for anisotropic rock materials under multiaxial states of stress. The proposed criterion is a generalization of the Von Mises' criterion for yielding of ductile metals, which has also been used previously as a strength criterion for brittle fracture in the spirit of both being limits of linear elastic behavior. The presently proposed criterion takes into consideration the effects of the confining pressure, the various stress components, and the material anisotropy on rock material failure in a multiaxial stress state. To verify the applicability of the proposed criterion, it has been used to construct the failure envelopes for several types of rock materials. Consequently, the constructed failure envelopes and the corresponding experimental results have been compared. In all cases, a close agreement with the experimental results has been achieved. This result demonstrates the versatility and applicability of the proposed strength criterion in representing the compressive strength behavior of anisotropic rock materials under complex multiaxial states of stress. Key words: strength, rock materials, anisotropy.

Closure on the discussion by G. C. Sih and D. Y. Tzou on “criteria for brittle fracture in biaxial tension”

Closure on the discussion by G. C. Sih and D. Y. Tzou on “criteria for brittle fracture in biaxial tension”

切削温度上昇を伴う断続切削時の切れ刃欠損発生の解析的予測 ＩＩ 断続切削回数による切れ刃欠損確率の推移

Transient variation of impact and thermal stress fields, and temperature distribution as well, within cutting edge during the edge engagement in interrupted turning were first obtained through FEM calculation using measured variation of impact cutting force and temperature on rake face. The probabilistic stress criterion of brittle fracture and its variation due to repetition of impact stress for each location within the tool edge using the deterioration rule reported in previous paper were next obtained. In collation of the most dangerous state of the transient stress with the fracture criterion at each element, variation of fracture probability distribution within the cutting edge with number of the interruption was predicted. Thermal stress had the effect to decrease the failure probability, while temperature rise did promote the probability. The predicted relation for edge failure occurrence shows good agreement with experimental results. It is also possible in practical manner to predict the edge failure for the tool with rounded or chamfered edge by applying a suitable flank force to the edge.

Fracture criteria of reactor graphite under multiaxial stesses

Abstract New fracture criteria for graphite under multiaxial stresses are presented for designing core and support materials of a high temperature gas cooled reactor. Different kinds of fracture strength tests are carried out for a near isotropic graphite IG-11. Results show that, under the stress state in which tensile stresses are predominant, the maximum principal stress theory is seen as applicable for brittle fracture. Under the stress state in which compressive stresses are predominant, there may be two fracture modes for brittle fracture, namely, slipping fracture and mode II fracture. For the former fracture mode the maximum shear stress criterion is suitable, but for the latter fracture mode the following mode II fracture criterion including a restraint effect for cracks is verified to be applicable, σ 3 ;= σ c σ t K Ic K IIc −1 σ 1 −σ c where δ1 and δ3 are the maximum and minimum principal stresses, δt and δc are the tensile and compressive strengths and KIc and KIIc are the mode I and II fracture toughness values, respectively. The above equation is similar in form to the Coulomb-Mohr criterion. Also a statistical correction for brittle fracture criteria under multiaxial stresses is discussed. By considering the allowable stress values for safe design, the specified minimum ultimate strengths corresponding to a survival probability of 99% at the 950 confidence level are presented.

The influence of tin inclusions on the brittle fracture of steel

1. With an increase in their volume content from ∼0.01 to ∼0.11% in type 06-14G2AF fine grained low-alloy steel with carbonitride hardening titanium nitride inclusions with an average size of 0.8–1.4 μm have little influence on the yield and flow stress, do not reduce the characteristics of brittle fracture resistance (ψ, eK, SK), but do significantly increase (by an average of 49–63°C) the ductile-to-brittle transition temperature in dynamic bend testing. 2. The reduction in cold resistance may be explained by participation of fractured TiN particles in initiation of formation of cleavage microcracks, elementary acts of discrete brittle fracture. This participation bears a statistical character and (at the maximum investigated inclusion content) to it is related the formation of 30–50% of the cleavage microsources. 3. With the use of the force criterion of brittle fracture it was shown that to the increase in the ductile-to-brittle transition temperature caused by TiN particles corresponds a mean-statistical reduction in microcleavage resistance to 0.73 of the original value. In the microvolumes weakened by particles the microcleavage resistance drops to an average of 0. 32 of the original value, which quantitatively agrees well with the Griffiths crack length, exceeding the average inclusion size. 4. The negative influence of TiN inclusions on cold resistance must be taken into consideration in the use of titanium for alloying and deoxidation and also in the case of its presence as an impurity.

The mixed mode brittle fracture criteria in siliding mode fracture

It is well-known that the present mixed mode brittle fracture criteria are all the opening mode fracture criterion. We consider that mixed mode brittle fracture of sliding mode fracture exists too. Hence we propose three criteria of mixed mode brittle fracture of sliding mode fracture;: the radial shearing stress criterion, the maximum shearing stress criterion and the distortional strain-energy-density criterion. Thus, we can overall explain the phenomena of brittle fracture in the structural elements with cracks.

Discussion on “criteria for brittle fracture in biaxial tension” by S. K. Maiti and R. A. Smith

Discussion on “criteria for brittle fracture in biaxial tension” by S. K. Maiti and R. A. Smith

Discussion: “Comparison of the criteria for mixed mode brittle fracture based on the preinstability stress-strain field. Part I: Slit and elliptical cracks under uniaxial tensile loading. Part II: Pure shear and uniaxial compressive loading”

Discussion: “Comparison of the criteria for mixed mode brittle fracture based on the preinstability stress-strain field. Part I: Slit and elliptical cracks under uniaxial tensile loading. Part II: Pure shear and uniaxial compressive loading”

Response: Discussion of “Comparison of the criteria for mixed mode brittle fracture based on the preinstability stress-strain field. Part I: Slit and elliptical cracks under uniaxial tensile loading. Part II: Pure shear and uniaxial compressive loading”

Response: Discussion of “Comparison of the criteria for mixed mode brittle fracture based on the preinstability stress-strain field. Part I: Slit and elliptical cracks under uniaxial tensile loading. Part II: Pure shear and uniaxial compressive loading”