Dynamic behaviors of mode III interfacial crack under a constant loading rate

In an earlier study on intersonic crack propagation, Gao et al. (J. Mech. Phys. Solids 49: 2113-2132, 2001) described molecular dynamics simulations and continuum analysis of the dynamic behaviors of a mode II dominated crack moving along a weak plane under a constant loading rate. The crack was observed to initiate its motion at a critical time after the onset of loading, at which it is rapidly accelerated to the Rayleigh wave speed and propagates at this speed for a finite time interval until an intersonic daughter crack is nucleated at a peak stress at a finite distance ahead of the original crack tip. The present article aims to analyze this behavior for a mode III crack moving along a bi-material interface subject to a constant loading rate. We begin with a crack in an initially stress-free bi-material subject to a steadily increasing stress. The crack initiates its motion at a critical time governed by the Griffith criterion. After crack initiation, two scenarios of crack propagation are investigated: the first one is that the crack moves at a constant subsonic velocity; the second one is that the crack moves at the lower shear wave speed of the two materials. In the first scenario, the shear stress ahead of the crack tip is singular with exponent -1/2, as expected; in the second scenario, the stress singularity vanishes but a peak stress is found to emerge at a distance ahead of the moving crack tip. In the latter case, a daughter crack supersonic with respect to the softer medium can be expected to emerge ahead of the initial crack once the peak stress reaches the cohesive strength of the interface.

Torsion fracture behavior of drawn pearlitic steel wires with different heat treatments

In this paper, torsion fracture behavior of drawn pearlitic steel wires with different heat treatments was investigated. Samples with different heat treatments was investigated. Samples with different heat treatment conditions were subjected to torsion and tensile tests. The shear strain along the torsion sample after fracture was measured. Fracture surface of wires was examined by Scanning Electron Microscopy. In addition, the method of Differential Scanning Calorimetry was used to characterize the thermodynamic process in the heat treatment. A numerical simulation via finite element method on temperature field evolution for the wire during heat treatment process was performed. The results show that both strain aging and recovery process occur in the material within the temperature range between room temperature and 435 degrees C. It was shown that the ductility measured by the number of twists drops at short heating times and recovers after further heating in the lead bath of 435 degrees C. On the other hand, the strenght of the wire increases at short heating times and decreases after further heating. The microstructure inhomogeneity due to short period of heat treatment, coupled with the gradient characteristics of shear deformation during torsion results in localized shear deformation of the wire. In this situation, shear cracks nucleate between lamella and the wire breaks with low number of twists.

Behavior of Multiple Shear Bands in Zr-Based Bulk Metallic Glass

The deformation behavior of Zr41.2Ti13.8Cu12.5Ni10Be22.5 bulk metallic glass was studied by in situ scanning electron microscopy (SEM) quasi-static uniaxial compression tests at room temperature. Multiple shear bands were observed with a large plasticity. Microscopic examination demonstrates that slipping, branching and intersecting of multiple shear bands are the main mechanisms for enhancing the plasticity of this metallic glass. Additionally, nano/micro-scale voids and cracks at the intersecting sites of shear bands and preferential etching of shear bands were observed as well. These observations demonstrated that the formation of shear bands in bulk metallic glasses is resulted mainly from local free volume coalescence.

Measurement Of Fracture Toughness And Interfacial Shear Strength Of Hard And Brittle Cr Coating On Ductile Steel Substrate

The fracture toughness and interfacial adhesion properties of a coating on its substrate are considered to be crucial intrinsic parameters determining performance and reliability of coating-substrate system. In this work, the fracture toughness and interfacial shear strength of a hard and brittle Cr coating on a normal medium carbon steel substrate were investigated by means of a tensile test. The normal medium carbon steel substrate electroplated with a hard and brittle Cr coating was quasi-statically stretched to induce an array of parallel cracks in the coating. An optical microscope was used to observe the cracking of the coating and the interfacial decohesion between the coating and the substrate during the loading. It was found that the cracking of the coating initiated at critical strain, and then the number of the cracks of the coating per unit axial distance increased with the increase in the tensile strain. At another critical strain, the number of the cracks of the coating became saturated, i.e. the number of cracks per unit axial distance became a constant after this critical strain. Based on the experiment result, the fracture toughness of the brittle coating can be determined using a mechanical model. Interestingly, even when the whole specimen fractured completely under an extreme strain of the substrate, the interfacial decohesion or buckling of the coating on its substrate was completely absent. The test result is different from that appeared in the literature though the identical test method and the brittle coating/ductile metal substrate system are taken. It was found that this difference can be attributed to an important mechanism that the Cr coating on the steel substrate has a good adhesion, and the ultimate interfacial shear strength between the Cr coating and the steel substrate has exceeded the maximum shear flow strength level of the steel substrate. This result also indicates that the maximum shear flow strength level of the ductile steel substrate can be only taken as a lower bound estimate on the ultimate shear strength of the interface. This estimation of the ultimate interfacial shear strength is consistent with the theoretical analysis and prediction presented in the literature.

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.

Deformation, Phase Transformation and Recrystallization in the Shear Bands Induced by High-Strain Rate Loading in Titanium and its Alloys

alpha-titanium and its alloys with a dual-phase structure (alpha+beta) were deformed dynamically under strain rate of about 10(4) s(-1). The formation and microstructural evolution of the localized shear bands were characterized by scanning electron microscopy (SEM) and transmission electron microscopy (TEM). The results reveal that both the strain and strain rate should be considered simultaneously as the mechanical conditions for shear band formation, and twinning is an important mode of deformation. Both experimental and calculation show that the materials within the bands underwent a superhigh strain rate (9 x 10(5) s(-1)) deformation, which is two magnitudes of that of average strain rate required for shear band formation; the dislocations in the bands can be constricted and developed into cell structures; the phase transformation from alpha to alpha(2) within the bands was observed, and the transformation products (alpha(2)) had a certain crystallographic orientation relationship with their parent; the equiaxed grains with an average size of 10 mu m in diameter observed within the bands are proposed to be the results of recrystallization.

Stress-strain fields and the effectiveness shear properties for three-phase composites with imperfect interface

Based on the 'average stress in the matrix' concept of Mori and Tanaka (:Mori, T., Tanaka, K., 1973. Average stress in matrix and average elastic energy of materials with misfitting inclusion. Acta Metall. 21, 571-580) a micromechanical model is presented for the prediction of the elastic fields in coated inclusion composites with imperfect interfaces. The solutions of the effective elastic moduli for this kind of composite are also obtained. In two kinds of composites with coated particulates and fibers, respectively, the interface imperfections are takes to the assumption that the interface displacement discontinues are linearly related to interface tractions like a spring layer of vanishing thickness. The resulting effective shear modulus for each material and the stress fields in the composite are presented under a transverse shear loading situation.

On the shear instability of saturated soil

In this paper. the dynamic instability of simple shear of saturated soil is discussed. The governing equations are obtained based on mixture theory in which the inertia effect and the compressibility of grains are considered. Perturbation method is used to analyze and it is shown that two types of instability may exist. One of them is dominated by pore-pressure-softening, while the other by strain-softening.

An exact solution for the three-phase piezoelectric cylinder model under antiplane shear and its applications to piezoelectric composites

A three-phase piezoelectric cylinder model is proposed and an exact solution is obtained for the model under a farfield antiplane mechanical load and a far-field inplane electrical load. The three-phase model can serve as a fiber/interphase layer/matrix model, in terms of which a lot of interesting mechanical and electrical coupling phenomena induced by the interphase layer are revealed. It is found that much more serious stress and electrical field concentrations occur in the model with the interphase layer than those without any interphase layer. The three-phase model can also serve as a fiber/matrix/composite model, in terms of which a generalized self-consistent approach is developed for predicting the effective electroelastic moduli of piezoelectric composites. Numerical examples are given and discussed in detail.

Material response and failure mechanism of unidirectional metal matrix composites under impulsive shear loading

The material response and failure mechanism of unidirectional metal matrix composite under impulsive shear loading are investigated in this paper. Both experimental and analytical studies were performed. The shear strength of unidirectional C-f/A356.0 composite and A356.0 aluminum alloy at high strain rate were measured with a modified split Hopkinson torsional bar technique. The results indicated that the carbon fibers did not improve the shear strength of aluminum matrix if the fiber orientation aligned with the shear loading axis. The microscopic inspection of the fractured surface showed a multi-scale zigzag feature which implied a complicated shear failure mechanism in the composite. In addition to testing, the micromechanical stress field in the composite was analyzed by the generalized Eshelby equivalent method (GEEM). The influence of cracking in matrix on the micromechanical stress field was investigated as well. The results showed that the stress distribution in the composite is quite nonhomogeneous and very high shear stress concentrations are found in some regions in the matrix. The high shear stress concentration in the matrix induces tensile cracking at 45 degrees to the shear direction. This in turn aggravates the stress concentration at the fiber/matrix interface and finally leads to a catastrophic failure in the composite. From the correlation between the analysis and experimental results, the shear failure mechanism of unidirectional C-f/A356.0 composite can be elucidated qualitatively.

Thermal-mechanical interface crack behaviour of a surface mount solder joint

The effect of thermal-mechanical loading on a surface mount assembly with interface cracks between the solder and the resistor and between the solder and the printed circuit board (PCB) was studied using a non-linear thermal finite element analysis. The thermal effect was taken as cooling from the solder eutectic temperature to room temperature. Mechanical loading at the ends of the PCB was also applied. The results showed that cooling had the effect of causing large residual shear displacement at the region near the interface cracks. The mechanical loading caused additional crack opening displacements. The analysis on the values of J-integral for the interface cracks showed that J-integral was approximately path independent, and that the effect of crack at the solder/PCB interface is much more serious than that between the component and solder.

An analysis on overall crack-number-density of short-fatigue-cracks

The evolution of dispersed short-fatigue-cracks is analysed based on the equilibrium of crack-number-density (CND). By separating the mean value and the stochastic fluctuation of local CND, the equilibrium equation of overall CND is derived. Comparing with the mean-field equilibrium equation, the equilibrium equation of overall CND has different forms in the expression of crack-nucleation-rate or crack-growth-rate. The simulation results are compared with experimental measurements showing the stochastic analyses provide consistent tendency with experiments. The discrepancy in simulation results between overall CND and mean-field CND is discussed.

Effect of Particle Size on the Formation of Adiabatic Shear Band In Particle Reinforced Metal Matrix Composites

In this paper, the effect of particle size on the formation of adiabatic shear band in 2024 All matrix composites reinforced with 15% volume fraction of 3.5, 10 and 20 mum SiC particles was investigated by making use of split Hopkinson pressure bar (SHPB). The results have demonstrated that the onset of adiabatic shear banding in the composites strongly depends on the particle size and adiabatic shear banding is more readily observed in the composite reinforced with small particles than that in the composite with large particles. This size dependency phenomenon can be characterized by the strain gradient effect. Instability analysis reveals that high strain gradient is a strong driving force for the formation of adiabatic shear banding in particle reinforced metal matrix composites (MMCp).

Investigation of Dynamic Fracture Toughness under Compressive-Shear Combinede Stress Wave Loading

提出亚微秒单脉冲应力波载荷作用下II型裂纹的平板冲击实验技术。加载率为dK/dt-10~8MPa·m~{”/d}·s~{-1}。实验中由锰铜应力片和弹性波理论分别测定和计算了压应力；通过微观分析确定了动态裂纹的平均扩展长度；引进等效应力强度因子,用动态断裂理论确定了60号钢的动态断裂韧性K_{Id}和K_{IId}；建立了亚微秒冲击载荷作用下确定材料动态断裂韧性的方法。

Experimental Study of the Earthquake Recurrence Period and the Trend of Post-Seismic Development

In order to study the earthquake recurrence and the characteristics of earthquake series, rupture tests of rock samples and plexiglass samples were made. On rock samples, a number of acoustic emission (AE) and strain measuring points were deployed; the load was one side direct shear. The variation characteristics of AE and strain at different detecting points around the extra large fracture were observed and studied. On plexiglass samples, a series of inclined cracks were prefabricated by a small-scale compressive testing machine. The samples were then loaded on a shockproof platen, when the samples were loaded, the stress intensity factor (SIF) was determined by the laser interferometric technique and shadow optical method of caustics. The fracture conditions such as material toughness around the extra large fracture were also studied. From those experimental results and the theory of fracture mechanics, the earthquake recurrence period and the trend of post-seismic development were studied.