Variable power singular interface elements for a crack normal to the bimaterial interface

Zero thickness crack tip interface elements for a crack normal to the interface between two materials are presented. The elements are shown to have the desired r(lambda-1) (0 < lambda < 1) singularity in the stress field at the crack tip and are compatible with other singular elements. The stiffness matrices of the quadratic and cubic interface element are derived. Numerical examples are given to demonstrate the applicability of the proposed interface elements for a crack perpendicular to the bimaterial interface.

Collapsed isoparametric element as a singular element for a crack normal to the bi-material interface

It is shown that the variable power singularity of the strain field at the crack tip can be obtained by the simple technique of collapsing quadrilateral isoparametric elements into triangular elements around the crack tip and adequately shifting the side-nodes adjacent to this crack tip. The collapsed isoparametric elements have the desired singularity at crack tip along any ray. The strain expressions for a single element have been derived and in addition to the desired power singularity, additional singularities are revealed. Numerical examples have shown that triangular elements formed by collapsing one side lead to excellent results.

Crack deflection at an interface between dissimilar elastic-materials

A crack intersecting an interface between two dissimilar materials may advance by either penetrating through the interface or deflecting into the interface. The competition between deflection and penetration can be assessed by comparison of two ratios: (i) the ratio of the energy release rates for interface cracking and crack penetration; and (ii) the ratio of interface to material fracture energies. Residual stresses caused by thermal expansion misfit can influence the energy release rates of both the deflected and penetrating crack. This paper analyses the role of residual stresses. The results reveal that expansion misfit can be profoundly important in systems with planar interfaces (such as layered materials, thin film structures, etc.), but generally can be expected to be of little significance in fiber composites. This paper corrects an earlier result for the ratio of the energy release rate for the doubly deflected crack to that for the penetrating crack in the absence of residual stress.

Effect of grain size on slow fatigue crack propagation and plastic deformation near crack tip

Fatigue crack growth and its threshold are investigated at a stress ratio of 0.5 for the three-point bend specimen made of Austenitic stainless steel. The effect of grain size on the crack tip plastic deformation is investigated. The results show that the threshold value Δkth increases linearly with the square root of grain size d and the growth rate is slower for materials with larger grain size. The plastic zone size and ratio for different grain sizes are different at the threshold. The maximum stress intensity factor is kmax and σys is the yield strength. At the same time, the characteristics of the plastic deformation development is discontinuous and anti-symmetric as the growth rate is increased from 2·10—8 to 10−7 mm/cycle.

Mixed-mode fracture mechanisms near the fatigue threshold of aisi-316 stainless-steel

Near threshold, mixed mode (I and II), fatigue crack growth occurs mainly by two mechanisms, coplanar (or shear) mode and branch (or tensile) mode. For a constant ratio of ΔK_I/ΔK_II the shear mode growth shows a self-arrest character and it would only start again when ΔK_I and ΔK_II are increased. Both shear crack growth and the early stages of tensile crack growth, are of a crystallographic nature; the fatigue crack proceeds along slip planes or grain boundaries. The appearance of the fracture surfaces suggest that the mechanism of crack extension is by developing slip band microcracks which join up to form a macrocrack. This process is thought to be assisted by the nature of the plastic deformation within the reversed plastic zone where high back stresses are set up by dislocation pile-ups against grain boundaries. The interaction of the crack tip stress field with that of the dislocation pile-ups leads to the formation of slip band microcracks and subsequent crack extension. The change from shear mode to tensile mode growth probably occurs when the maximum tensile stress and the microcrack density in the maximum tensile plane direction attain critical values.

Discontinuous growth mechanisms of mode II crack under high-speed impact conditions

A recoverable plate impact testing technology has been used for studying the growth mechanisms of mode II crack. The results show that interactions of microcracks ahead of a crack tip cause the crack growth unsteadily. Failure mode transitions of materials were observed. Based on the observations, a discontinuous crack growth model was established. Analysis shows that the shear crack grows unsteady as the growth speed is between the Rayleigh wave speed c(R) and the shear wave speed c(s); however, when the growth speed approaches root 2c(s), the crack grows steadily. The transient microcrack growth makes the main crack speed to jump from subsonic to intersonic and the steady growth of all the sub-cracks leads the main crack to grow stably at an intersonic speed.

Subsonic interface crack with crack face contact

A steady-state subsonic interface crack propagating between an elastic solid and a rigid substrate with crack face contact is studied. Two cases with respective to the contact length are considered, i.e., semi-infinite and finite crack face contact. Different from a stationary or an open subsonic interface crack, stress singularity at the crack tip in the present paper is found to be non-oscillatory. Furthermore, in the semi-infinite contact case, the singularity of the stress field near the crack tip is less than 1/2. In the finite contact case, no singularity exists near the crack tip, but less than 1/2 singularity does at the end of the contact zone. In both cases, the singularity depends on the linear contact coefficient and the crack speed. Asymptotic solutions near the crack tip are given and analyzed. In order to satisfy the contact conditions, reasonable region of the linear contact coefficient is found. In addition, the solution predicts a non-zero-energy dissipation rate due to crack face contact.

Asymmetry of the photoionization rate of H atoms by a sequence of one-cycle laser pulses

Using an unperturbed scattering theory, the characteristics of H atom photoionization are studied respectively by a linearly- and by a circularly- polarized one-cycle laser pulse sequence. The asymmetry for photoelectrons in two directions opposite to each other is investigated. It is found that the asymmetry degree varies with the carrier-envelope (CE) phase, laser intensity, as well as the kinetic energy of photoelectrons. For the linear polarization, the maximal ionization rate varies with the CE phase, and the asymmetry degree varies with the CE phase in a sine-like pattern. For the circular polarization, the maximal ionization rate keeps constant for various CE phases, but the variation of asymmetry degree is still in a sine-like pattern.

The precocious Chinese mitten crab: Changes of gonad, survival rate, and life span in a freshwater lake

Changes of the gonad. survival rate, and life span of the precocious (i.e., sexually mature in their first October-November, at the age of 5 or 6 months) Chinese mitten crab (Eriocheir sinensis) were studied in a small, shallow, macrophytic, freshwater lake along the middle reaches of the Changjiang River, China. The gonosomatic index (GSI) reached peak during the next March when the female GSI was 12.32 +/- 1.75 SD% and the male GSI A as 4.24 +/- 0.19%. The sexual glands degraded from then on. In the first ten-day period of the following July, there was no complete ovum in the ovary. and the sperm became thin and lost adhesion. The population declined sharply from November to July, and the last one (a female) died in the middle of July, which indicated that the life span of the precocious crab was about 12 months (from larval hatching in June to death in July of next year). The survival curve might be expressed as Y = 1.09exp(-0.018x) (Y survival rate; x: days) for the precocious crabs stocked in experimental cages.

Plastic zone in front of mode I crack in phenolphthalein polyether ketone

The plastic zone size and crack opening displacement of phenolphthalein polyether ketone (PEK-C) at various conditions were investigated. Both of them increase with increasing temperature (decreasing strain rate), i.e. yield stress steadily falls. Thus, the mechanism increasing the yield stress leads to increased constraint in the crack tip and a corresponding reduction in the crack opening displacement and the plastic deformation zone. The effect of the plastic deformation on the fracture toughness is also discussed.

TEMPERATURE AND STRAIN-RATE DEPENDENCE OF FRACTURE-TOUGHNESS OF PHENOLPHTHALEIN POLYETHER KETONE

A strong strain-rate and temperature dependence was observed for the fracture toughness of phenolphthalein polyether ketone (PEK-C). Two separate crack-blunting mechanisms have been proposed to account for the fracture-toughness data. The first mechanism involves thermal blunting due to adiabatic heating at the crack tip for the high temperatures studied. In the high-temperature range, thermal blunting increases the fracture toughness corresponding to an effectively higher test temperature. However, in the low-temperature range, the adiabatic temperature rise is insufficient to cause softening and Jic increases with increasing temperature owing to viscoelastic losses associated with the p-relaxation there. The second mechanism involves plastic blunting due to shear yield/flow processes at the crack tip and this takes place at slow strain testing of the single-edge notched bending (SENB) samples. The temperature and strain-rate dependence of the plastic zone size may also be responsible for the temperature and strain-rate dependence of fracture toughness.

Rifting process and formation mechanisms of syn-rift stage prolongation in the deepwater basin, northern South China Sea

Based on the latest seismic and geological data, tectonic subsidence of three seismic lines in the deepwater area of Pearl River Mouth Basin (PRMB), the northern South China Sea (SCS), is calculated. The result shows that the rifting process of study area is different from the typical passive continental margin basin. Although the seafloor spreading of SCS initiated at 32 Ma, the tectonic subsidence rate does not decrease but increases instead, and then decreases at about 23 Ma, which indicates that the rifting continued after the onset of seafloor spreading until about 23 Ma. The formation thickness exhibits the same phenomenon, that is the syn-rift stage prolonged and the post-rift thermal subsidence delayed. The formation mechanisms are supposed to be three: (1) the lithospheric rigidity of the northern SCS is weak and its ductility is relatively strong, which delayed the strain relaxation resulting from the seafloor spreading; (2) the differential layered independent extension of the lithosphere may be one reason for the delay of post-rift stage; and (3) the southward transition of SCS spreading ridge during 24 to 21 Ma and the corresponding acceleration of seafloor spreading rate then triggered the initiation of large-scale thermal subsidence in the study area at about 23 Ma.

Effect of ambient pressure and radiation reabsorption of atmosphere on the flame spreading over thermally thin combustibles in microgravity

For the flame spread over thermally thin combustibles in an atmosphere, if the atmosphere cannot emit and absorb the thermal radiation (e.g. for atmosphere Of O-2-N-2), the conductive heat transfer from the flame to the fuel surface dominates the flame spread at lower ambient atmosphere. As the ambient pressure increases, the flame spread rate increases, and the radiant heat transfer from the flame to the fuel surface gradually becomes the dominant driving force for the flame spread. In contrast, if the atmosphere is able to emit and absorb the thermal radiation (e.g. for atmosphere Of O-2-CO2), at lower pressure, the heat transfer from flame to the fuel surface is enhanced by the radiation reabsorption of the atmosphere at the leading edge of the flame, and both conduction and thermal radiation play important roles in the mechanism of flame spread. With the increase in ambient pressure, the oxygen diffuses more quickly from ambient atmosphere into the flame, the chemical reaction in the flame is enhanced, and the flame spread rate increases. When the ambient pressure is greater than a critical value, the thermal radiation from the flame to the solid surface is hampered by the radiation reabsorption of ambient atmosphere with the further increase in ambient pressure. As a result, with the increase in ambient pressure, the flame spread rate decreases and the heat conduction gradually dominates the flame spread over the fuel surface.

Molecular dynamics simulation of the role of dislocations in microcrack healing

The molecular dynamics method is used to simulate microcrack healing during heating or/and under compressive stress. A centre microcrack in Cu crystal would be sealed under compressive stress or by heating. The role of compressive stress and heating in crack healing was additive. During microcrack healing, dislocation generation and motion occurred. When there were pre-existing dislocations around the microcrack, the critical temperature or compressive stress necessary for microcrack healing would decrease, and, the higher the number of dislocations, the lower the critical temperature or compressive stress. The critical temperature necessary for microcrack healing depended upon the orientation of the crack plane. For example, the critical temperature for the crack along the (001) plane was the lowest, i.e. 770K.

Analysis of strip electric saturation model of crack problem in piezoelectric materials

This paper presents a fully anisotropic analysis of strip electric saturation model proposed by Gao et al. (1997) (Gao, H.J., Zhang, T.Y., Tong, P., 1997. Local and global energy release rates for an electrically yielded crack in a piezoelectric ceramic. J. Mech. Phys. Solids, 45, 491-510) for piezoelectric materials. The relationship between the size of the strip saturation zone ahead of a crack tip and the applied electric displacement field is established. It is revealed that the critical fracture stresses for a crack perpendicular to the poling axis is linearly decreased with the increase of the positive applied electric field and increases linearly with the increase of the negative applied electric field. For a crack parallel to the poring axis, the failure stress is not effected by the parallel applied electric field. In order to analyse the existed experimental results, the stress fields ahead of the tip of an elliptic notch in an infinite piezoelectric solid are calculated. The critical maximum stress criterion is adopted for determining the fracture stresses under different remote electric displacement fields. The present analysis indicates that the crack initiation and propagation from the tip of a sharp elliptic notch could be aided or impeded by an electric displacement field depending on the field direction. The fracture stress predicted by the present analysis is consistent with the experimental data given by Park and Sun (1995) (Park, S., Sun, C.T., 1995. Fracture criteria for piezoelectric materials. J. Am. Ceram. Soc 78, 1475-1480).