Gradient-dependent plasticity where a characteristic length is involved to consider the microstructural effect (interactions and interplaying among microstructures due to the heterogeneous texture) is introduced into Zerilli-Armstrong model based on the framework of thermally activated dislocation motion. Effect of initial temperature on the distributions of plastic shear strain and deformation in adiabatic shear band (ASB), the axial compressive stress-axial compressive strain curve, the shear stress-average plastic shear strain in ASB curve and the plastic shear strain corresponding to the occurrence of shear strain localization is investigated. The axial deformation within aluminum-lithium alloy specimen in uniaxial compression in strain-hardening stage is considered to be uniform. Beyond the peak compressive stress, a single ASB with a certain thickness determined by internal length is formed and intersects the specimen. The axial plastic deformation is decomposed into uniform deformation and localized deformation due to the shear slip along ASB. Lower temperature leads to earlier occurrence of shear strain localization, i.e., lower critical plastic compressive strain, steeper post-peak shear stress-average plastic shear strain in ASB curve, higher peak shear stress and more apparent shear strain localization. The calculated distributions of plastic shear strain and deformation in ASB are highly nonuniform due to the microstructural effect, as cannot be predicted by classical elastoplastic theory applicable to completely homogenous material. The predicted average plastic shear strains in ASB for different widths of ASB agree with the measured values for under-aged Al-Li alloy at 298K and at strain rate of approximately 103s-1.

The coexistent phenomenon of deformed and transformed adiabatic shear bands (ASBs) is analyzed using Johnson-Cook model and gradient-dependent plasticity for heterogeneous ductile metal material. The size of deformed ASB is described by the internal length reflecting the heterogeneity of material. Microstructural effect leads to a nonuniform distribution of temperature rise in deformed ASB. When the peak temperature in deformed ASB exceeds the transformation temperature, a transformed ASB appears at the center of deformed ASB. With a decrease of flow shear stress, the width of transformed ASB increases until its upper bound, i.e., the size of deformed ASB, is reached. The effects of initial temperature and strain rate on the occurrence of transformation, evolution of the thickness of transformed ASB, distributions of local temperature and plastic shear deformation in ASB are investigated. Lower initial temperature results in higher peak shear stress, later occurrence of shear strain localization, lower shear stress when transformation occurs, later occurrence of transformation, thinner transformed ASB, lower peak temperature in ASB, and lower value of local plastic shear deformation in the boundaries of transformed ASB. At higher strain rates, the transformed ASB is wider; the peak temperature in ASB is higher; the value of local plastic shear deformation in the boundaries of transformed ASB is higher; the flow shear stress that corresponds to transformation is higher; earlier occurrence of transformation and higher peak shear stress will be expected.

Peak strength, mechanical behavior, and shear band (SB) of anisotropic jointed rock (JR) were modeled by Fast Lagrangian Analysis of Continua (FLAC). The failure criterion of rock was a composite Mohr-Coulomb criterion with tension cut-off and the post-peak constitutive relation was linear strain-softening. An inclined joint was treated as square elements of ideal plastic material beyond the peak strength. A FISH function was written to find automatically elements in the joint. For the lower or higher joint inclination (JI), the higher peak strength and more apparent strain-softening behavior are observed; the failure of JR is due to the slip along the joint and the new generated SBs initiated at joint’s two ends. For the lower JI, the slope of softening branch of stress-strain curve is not concerned with JI since the new and longer SBs’s inclination is not dependent on JI, as can be qualitatively explained by previous analytical solution of post-peak slope of stress-strain curve for rock specimen subjected to shear failure in uniaxial compression based on gradient-dependent plasticity. For the higher JI, the post-peak stress-strain curve becomes steeper as JI increases since the contribution of the new SBs undergoing strain-softening behavior to axial strain of JR increases with JI. For the moderate JI, the lower strength and ideal plastic behavior beyond the elastic stage are found, reflecting that the inclined joint governs the deformation of JR. The present numerical prediction on anisotropic peak strength in plane strain compression qualitatively agrees with triaxial experimental tests of many kinds of rocks. Comparison of the present numerical prediction on JI corresponding to the minimum peak strength of JR and the oversimplified theoretical result by Jaeger shows that Jaeger’s formula has overestimated the value of JI.

The failure process of heterogeneous rock specimen with initially random material imperfections in uniaxial plane strain compression and the macroscopically mechanical response are numerically modeled by using FLAC (Fast Lagrangian Analysis of Continua). A FISH function is generated to prescribe the initial imperfections within the heterogeneous specimen by using Matlab. The imperfection is weaker than the intact rock. Beyond the failure of the imperfection, it undergoes ideal plastic behavior, while intact rock exhibits linear strain-softening behavior and then ideal plastic behavior once failure occurs. The specimen with smooth ends is loaded at a constant strain rate and is divided into 3200 elements. The maximum numbers of the initial imperfections in five schemes are 100, 300, 500, 700 and 900. The effects of the number of the imperfections on the fracture process, the final fracture pattern and the complete stress-strain curve are investigated. Prior to the peak stress, some imperfections extend in the axial direction and then a part of them coalesce to form inclined shear bands. Beyond the peak stress, shear bands progressively intersect the specimen; in the process the number of the yielded elements approximately remains a constant. With an increase of the number of the initial imperfections, the spacing of shear fractures decreases, the peak stress and corresponding axial strain decrease; the post-peak branch of stress-strain curve becomes steeper; much more elements fail in tension; the number of the yielded elements in tension in the vicinity of the two lateral edges of the specimen remarkably increases.

Grinder is one of key equipments in machining of crank shaft of automobile motor. So its vibration monitoring and fault diagnosis plays an important role in guaranteeing product quality and productivity. This paper builds an on-line vibration monitoring system for spindle bearings in which the complex shifted Morlet wavelet is adopted to realize the envelop demodulation and feature extraction so as to identify the type of fault. The main advantage of this method is that the center frequency and bandwidth are obtained not by user according to experience value manually, but by calculating for vibration signal. Therefore, it is very suitable for on-line monitoring and automatic fault diagnosis. The analysis of typical fault signal of rolling elements bearing shows that it can diagnose the fault accurately.