Cracks In Brittle Materials Research Articles

Finite element analysis of horizontal and branched subsurface cracks in brittle materials

Finite element analyses of a horizontal subsurface and branched crack in brittle materials, under repeated sliding contact, were performed. It was found that the horizontal crack experiences pure shear loading. Previous experimental investigation suggests that cracks in brittle materials such as monolithic ceramics propagate at angles close to 45° under pure shear loading. Thus, the horizontal subsurface crack is expected to branch at 45° to the horizontal. Finite element analysis of a branched subsurface crack at 45° to the horizontal, under sliding contact, suggests that such cracks typically experience both mode I and mode II type loading. A method has been proposed to predict the crack growth direction in brittle materials subject to mixed mode loading. The predicted direction of crack propagation agrees well with the values determined experimentally for low K I/ K II ratio. Based on the proposed method, the leading tip of the horizontal subsurface crack is expected to reach the surface before the trailing edge.

Cleavage Fracture Model for Granular Bainite in Simulated Coarse-Grained Heat-Affected Zones of High-Strength Low-Alloyed Steels

A model of cleavage fracture in granular bainite was developed. It involves two-dimensional elastic interaction between a main crack and multiple microcracks induced by the existence of martensite-austenite (M-A) particles in front of the main crack. A factor of fracture toughness reduction due to the presence of M-A particles (f(MA)) was introduced to describe the effect of M-A particles on the stress intensity factor at the tip of the main crack. The values of f(MA) can be expressed as the inverse of the amplification coefficient of the stress intensity factor as a result from the interference between microcracks and a main crack in brittle materials. An equation was derived which describes the relationship between fracture toughness and microstructural variables, including the influence of the effective grain size as well as the average width and interspacing of M-A particles. Moreover, simple linear regression equations were used to check the validation of the present model for predicting cleavage fracture toughness in simulated coarse-grained heat-affected zones of quenched and tempered high-strength low-alloyed steels.

Length distribution of secondary cracks in brittle materials

Abstract It is shown that the length distribution of secondary cracks in the ‘mist’ zone of brittle materials is a magnified picture of the flaw length distribution. The magnification factor increases exponentially with increasing distance between the initial flaw and the secondary crack. On the basis of this correlation we have developed a new simple technique by which the flaw size distribution of the total flaw population in the material can be established by a single fracture experiment. An indirect check of this result is given by an analysis of a previous ‘roughness’ experiment.

Studies of acoustic emission from point and extended sources: Materials Analysis by Ultrasonics - Metals, Ceramics, Composites. Edited by A. Vary. pp. 47–52 Noyes Data Corporation, New Jersey, United States (1987)

The use of simulated and controlled acoustic emission signals forms the basis of a powerful tool for the detailed study of various deformation and wave interaction processes in materials. The results of experiments and signal analyses of acoustic emission resulting from point sources such as various types of indentation-produced cracks in brittle materials and the growth of fatigue cracks in 7075-T6 aluminum panels are discussed. Recent work dealing with the modeling and subsequent signal processing of an extended source of emission in a material is reviewed. Results of the forward problem and the inverse problem are presented with the example of a source distributed through the interior of a specimen.

STM on cracks in brittle materials

For a better understanding of local materials faults such as dislocation, grain boundaries and cracks, the stress and strain fields must be known near the defect cores where continuum theories predict singular behavior. Scanning tunneling microscopy allows the examination of these defects in detail. Because of the limited positioning possibilities of conventional STM's these defects can only be examined when they are very numerous. Therefore, a STM was developed which allows the exact positioning of the measuring system and macroscopic as well as high-resolution surface scanning. Special problems like convolution effects (between STM tip and the surface) and preparation problems are discussed, and examples are given. First measurements on such rough surfaces as fracture surfaces, and on macroscopic defects, e.g. cracks, are presented.

Instability in dynamic fracture.

Cracks in brittle materials have terminal velocities far below theoretical predictions. To address this problem we have investigated the propagation of cracks in a brittle plastic (polymethylmethacrylate). Velocity measurements with resolution an order of magnitude better than past experiments reveal the existence of a critical velocity at which the velocity begins to oscillate, the mean acceleration drops sharply, and a pattern is formed on the fracture surface. Thus the dynamics of cracks may be governed by a dynamical instability.

Mixed mode interface fracture criteria

The shielding of the full effect of mode II and III for interface cracks in brittle materials is demonstrated to be very important such that proper interface fracture criteria need to be modelled. A method for comparison of different phenomenological fracture criteria is discussed and applied to an experiment for a polyimide/glass interface. Finally, micromechanical models describing shielding for interface geometries with kinks are set up, allowing the phenomenological criteria to be linked up with measurable quantities such as the interface roughness.

Crossover between different growth regimes in crack formation.

The formation of cracks in brittle materials is investigated for arbitrary dependence of the crack growth on the stresses at its boundary. It is shown that, despite the possible complexity of the growth law, the shape of the crack for large sizes and long times is determined by the high-stress limit of the growth law, provided only that the probability of cracking increases with stress. This result may help to explain the appearance of long and straight cracks in many fracture processes. Other pattern-formation models are expected to show the same features.

Studies of acoustic emission from point and extended sources : Sachse, W.; Kim, K.Y.; Chen, C.P. Materials analysis by ultrasonics - metals, ceramics, composites. Edited by A. Vary. pp. 47–52 Noyes data corporation, New Jersey, United States (1987)

The use of simulated and controlled acoustic emission signals forms the basis of a powerful tool for the detailed study of various deformation and wave interaction processes in materials. The results of experiments and signal analyses of acoustic emission resulting from point sources such as various types of indentation-produced cracks in brittle materials and the growth of fatigue cracks in 7075-T6 aluminum panels are discussed. Recent work dealing with the modeling and subsequent signal processing of an extended source of emission in a material is reviewed. Results of the forward problem and the inverse problem are presented with the example of a source distributed through the interior of a specimen.

Crack nucleation at the surface of stressed fibers

A model is proposed for crack initiation on a pristine surface. In this model failure starts from a flat surface and the crack develops during the strength or lifetime experiment. Both energy and kinetic arguments are used. The model is applied to lifetime calculations of pristine optical fibers. Surface energy and bulk elastic energy are calculated for a fiber with a flat and a slightly distorted surface. When a small amount of elastic energy is removed locally from the fiber, e.g., by dissolution, the distorted state is more stable. Like cracks in brittle materials, the stable distortions for pristine optical fibers have local radii of curvature at atomic dimensions. In this model the lifetime of a pristine fiber is mainly determined by the time needed to pass from a flat surface to a relatively small surface distortion. From the derived expression for the lifetime, the exponent n in the empirical power law expression for subcritical crack growth can be interpreted. It is shown that n is stress dependent. The discrepancy in n value observed for silica glass fibers (n≂20) and bulk fused silica (n≂40) is removed.

Evaluation of the performance of thick-walled cylindrical shells made of S�T-1 glass

1. The strength of TSM506, SET-1, and MKR-1 lighting engineering glass varies in range 1225–1410 MPa, i.e., 56–64% of the ultimate strength of 13v technical glass. 2. The aqueous and oil media reduce on the whole the short-term strength of lighting engineering glass. The strength of the effect of the median depends on the type of the stress state in such a manner than the largest (up to 30%) reduction of strength is detected under the effect of tensile stresses. It is evident that this is associated with the general relationships governing the growth of surface cracks in brittle material in compression and tension in surface-active media. 3. In the glass thick-walled cylindrical shells in the examined method of connection with the rigid plug in the conditions of longitudinal compression and external pressure, the lower level of the fracture stresses of compression in the contact zone decreases by a factor of three-four in comparison with the strength of the specimens σcc determined in the tests on the flat support. This is associated with the operation of the scale-technological effect and with the unfavorable variation of the contact conditions and requires the introduction of high (five–six) strength satisfy factors to ensure the reliability of components. 4. Taking into account the real technological initial deviations of the form and dimensions of the support sections of the thick-walled cylindrical glass elements, we designed and tested in short-term and long-term (up to 100 days) effects of the external pressure and experimental batch of transparent shells. The experiments confirm that the experimental-theoretical approach is suitable for designing these objects. The selection of the permissible stresses and working loads with special reference to the devices working in the conditions of long-term static loading was justified.

Moment modified compact tension specimen for measuring crack arrest toughness

Crack arrest toughness in reactor vessel steels in the transition and Charpy upper shelf energy temperature range are of particular interest to the nuclear industry to aid with the analysis of the phenomenon known as pressurized thermal shock (PTS). A test specimen and analysis technique have been developed to measure crack arrest toughness at temperatures from the transition region up to and beyond the Charpy upper shelf energy level. The moment modified compact tension (MMCT) specimen combines a thermal gradient with mechanical loadings to initiate a crack in brittle material below NDT and then have arrest take place in hot, ductile material. A finite element model was used to help design the specimen and fixturing geometry as well as calculate the arrest toughness. Tests have been conducted on ASME SA533 Grade B Class 1 steel plate with a variety of loadings confirming the veracity of the technique and developing valuable data. Crack arrest toughness has been measured from 0°F to 110°F (−18°C to 43°C). This work has been part of a research program performed by C-E, Windsor and funded by the Electric Power Research Institute.

The nature of machining damage in brittle materials

The micromechanics of failure emanating from machining-induced cracks in brittle materials is investigated. In situ monitoring of crack response during breaking tests (with use of acoustic wave scattering), strength measurements and post-failure fractography all indicate that the crack response is dominated by residual stresses. Two components of residual stress have been identified: a crack-wedging force due to the plastic zone beneath the strength-controlling machining groove, and a compressive surface layer due to adjacent grooves. The wedging force dominates and causes stable equilibrium crack extension during a breaking test. The implications of the results for non-destructive evaluation of surface damage by acoustic wave scattering is discussed.

Evaluation of effective sueface energy by a microindentation method

1. The Indentation made by a Vickers pyramid, like the elastic indentation of a spherical indenter, produces a tapered crack in brittle materials under indentation. The size of visible radial cracks surrounding the pyramid indentation is practically the same as that of a tapered crack. 2. A method is proposed for the evaluation of the effective surface energy from the results of microhardness tests. Some features connected with allowances for plastic strain under the indentation are noted.

Determination of the growth of branched cracks by numerical methods

In order to determine the growth of branched cracks in brittle materials, a static stress analysis for a branched crack model is performed by the finite element method. Assuming vanishing Mode II stress intensity factor as the governing criterion the growth is followed in several steps. Secondary branching is also analysed. In a quasi-dynamic analysis energy balance considerations are used to study growth of two branches of unequal lengths. It is shown that at low velocities the shorter branch will be rapidly arrested, while at very high velocities the two branches will continue to grow with nearly the same velocity.

The strain intensity criterion for crack branching in ceramics

Using a fracture mechanics method, crack branching data from three investigations were put on a comparable basis and used to demonstrate a strong correlation between the stress intensity at crack branching and Young's modulus. This strong correlation suggests a strain intensity criterion for crack branching at sharp cracks in brittle materials fractured at room temperature. Crack branching in 20 ceramics and glasses occurs at a strain intensity close to 3.3 × 10 −5 m 1 2 .

Surface energy and surface tension at holes and cracks

The concept of surface tension and surface energy of solids was used by Griffith to obtain a criterion for the extension of cracks in brittle materials. Griffith, however, neglected the stresses due to the normal traction at the crack implied by the surface tension. A complete solution to the problem of an elliptic hole in an infinite plate with surface tension loading at the hole is given. Complex potentials are given in closed form in terms of elliptic integrals of the first, second, and third kinds. Stress distributions are studied. For a flat crack, the nature of the singularity at the tip is shown to be radically different from that usually encountered in fracture mechanics. The implications of our analysis for theories of fracture in brittle materials are discussed.

The strength of brittle materials containing second phase dispersions

Abstract Cracks in brittle materials can be impeded by obstacles in the form of second phase dispersions. The crack tends to bow out between obstacles forming secondary semi-elliptical flaws. The strength is determined by the stress to propagate these secondary cracks. Stress calculations show that this depends on the ratios of the obstacle dimensions and the obstacle spacing and, except for large relative obstacle spacings, the stress is larger than the stress to extend the primary crack. Second phase dispersions will usually increase strength, therefore, through an effect equivalent to the ‘line tension effect’ observed for dislocation motion. A comparison of the calculated ‘line tension effect’ with observed increases in strength in brittle matrix composites shows that line tension is the major contribution to the strength increase for brittle obstacles, but only a minor contribution for fibre composites, and probably a minor contribution for ductile obstacles.

Complex stress-intensity factors at bifurcated cracks

Thin plates made of Perspex and containing a long transverse internal crack, side-branched at one of its ends, were subjected to tension at infinity. The thickness variation of the plates was depicted by the reflected shadow method. According to this method the absolute retardations of the light rays impinging normally on the plates were partly reflected on their front and rear faces, while they were refracted during their passage through the plate thickness. The emerging light was deviated because of the thickness variation and the refractive index variation of the plate when loaded. These rays, received on a screen placed at a distance from the plate, were concentrated along an envelope, which was strongly illuminated, and formed a caustic. The size of the caustic is directly related to the complex stress intensity factor K ∗ at the crack-tip. A series of cracked plates were studied, where the sidebranch subtended different angles to the main-branch, while the ratio of the lengths of the two branches varied between certain limits. The size and the angular displacement of the caustics formed at each tip of branches were compared with the size of the caustic formed at the single tip at the other extremity of the crack, which was used as a reference. In this way, the influence of the angle between branches, as well as of the relative velocities of the branches, which were represented by their different lengths, on the stress-intensity factors of the crack was studied, and important features related to the branching of running cracks in brittle materials were disclosed.

Diffraction of Antiplane Shear Waves by a Finite Crack

The scattering of polarized harmonic shear waves by a sharp crack of finite length under antiplane strain is considered. Use is made of integral transforms, which reduce the problem to the evaluation of a system of coupled integral equations. Special emphasis is placed on obtaining the detailed structure of the crack-front stress and displacement fields, which control the instability behavior of cracks in brittle materials. While the dynamic stresses around the singular crack point are found to be qualitatively the same as those encountered under statical loading, they differ quantitatively in that the intensity of the dynamical stress field, which may be regarded as a measure of the force tending to cause crack propagation, depends on the incident wavelength. At certain wavelengths, this intensification is shown to be larger than the static case. The method of solution in this paper applies equally well to boundary value problems in electromagnetic and acoustic theory.