Dynamic crack growth under stress wave loading

The crack growth process has been analysed on the basis of a fracture criterion of a dynamic stress intensity factor when a crack in an infinite plate was subjected to a pulse type of stress wave. The crack velocity and the amount of crack extension were related to the constant amplitude and the duration of the stress pulse. The calculated amount of crack extension was well in agreement with the experimental one for the polymer material Acrylite (which is similar to polymethylmethacrylate) found by the authors, thus indicating the validity of the present approach.     

An elastic wave scattering problem relating to the rapid movement of a fracture in a plate: Part II — Numerical results

In Part I of this two part paper, we developed analytical expressions for the crack face displacements due to an applied point traction as well as a moving point source of dilatation. In this sequel to Part I, we present numerical results for the crack face displacements in the form of displacement-time records at fixed locations on the crack face. For the stationary point traction problem, the results are more or less in keeping with the predictions made in Part I, with the Rayleigh pulse giving a large contribution for an applied step load.In the case of the moving point microfracture with a step time dependence, in addition to the diffracted compressional, shear and Rayleigh arrivals there is observed the evolution of a new pulse whose amplitude and position on the time record shifts changes if the calculations are done for a different crack speed. Results are also presented for a microfracture with an oscillatory time dependence. Once again, the first arrival of the surface pulse appears to be the most prominent arrival on the record. Further explorations of the parameters and source functions would be required before comparisons with experimental data can be made.     

Properties of dynamic rupture and energy partition in a solid with a frictional interface

We study properties of dynamic ruptures and the partition of energy between radiation and dissipative mechanisms using two-dimensional in-plane calculations with the finite element method. The model consists of two identical isotropic elastic media separated by an interface governed by rate- and state-dependent friction. Rupture is initiated by gradually overstressing a localized nucleation zone. Different values of parameters controlling the velocity dependence of friction, the strength excess parameter and the length of the nucleation zone, lead to the following four rupture modes: supershear crack-like rupture, subshear crack-like rupture, subshear single pulse and supershear train of pulses. High initial shear stress and weak velocity dependence of friction favor crack-like ruptures, while the opposite conditions favor the pulse mode. The rupture mode can switch from a subshear single pulse to a supershear train of pulses when the width of the nucleation zone increases. The elastic strain energy released over the same propagation distance by the different rupture modes has the following order: supershear crack, subshear crack, supershear train of pulses and subshear single pulse. The same order applies also to the ratio of kinetic energy (radiation) to total change of elastic energy for the different rupture modes. Decreasing the dynamic coefficient of friction increases the fraction of stored energy that is converted to kinetic energy. General considerations and observations suggest that the subshear pulse and supershear crack are, respectively, the most and least common modes of earthquake ruptures.     

Crack energy density of a piezoelectric material under general electromechanical loading

Crack energy density is considered and used as a possible fracture parameter in piezoelectricity under arbitrary electromechanical remote loads. The closed-form solution of a crack in a piezoelectric infinite plate subjected to general static electromechanical loading is obtained through a method alternative to the more common Stroh’s formalism. This analytical method, which is based on the spectral theorem of linear algebra, involves a transformation of similarity induced by the fundamental matrix in order to express the equations governing the problem in terms of complex potentials. The application of the mechanical boundary condition of stress-free crack and of one of the three considered electric boundary conditions (impermeable, permeable or semipermeable) leads then to the formulation of a Hilbert problem whose solution yields the stress and displacement fields. The crack energy density factors for mixed mode are then calculated under different mechanical and electrical loadings, as well as under different electric boundary conditions. The non-singular terms of the stress expressions are retained as well. The definition of the minimum energy density fracture criterion, as proposed by Sih, is given, and the influence of load biaxiality and positive or negative applied electric field on the criterion results is analyzed. The prediction of the incipient branching angle as from the energy density approach is also compared to that arising from the maximum circumferential stress theory for a mixed mode loading condition. Numerical results and graphs are presented and discussed for a PZT-4 piezoelectric ceramic.     

A theoretical investigation on the vibrational characteristics and torsional dynamic response of circumferentially cracked turbo-generator shafts

Turbo-generator shafts are often subjected to complex dynamic torsional loadings, resulting in generation and propagation of circumferential cracks. Mode III fatigue crack growth generally results in a fracture surface consisting of peaks and valleys, resembling a factory roof. The fracture surface roughness depends on the material microstructure, the material yield strength, and the applied cyclic torque amplitude. This crack pattern can severely affect the vibration characteristics of the shafts. The accurate evaluation of the torsional dynamic response of the turbo-generator shafts entails considering the local sources of energy loss in the crack vicinity. The two most common sources of the energy loss are the local energy loss due to the plasticity at the crack tip and frictional energy loss due to interaction of mutual crack surfaces. A theoretical procedure for evaluating the values of the system loss factors corresponding to these sources of energy loss is presented. Furthermore, the local flexibility is obtained by evaluating the resistance of the cracked section of the shaft to the rotational displacement. The shaft material is assumed to be elastic perfectly plastic. The effects of the applied Mode III stress intensity factor and the crack surface pattern parameters on the energy loss due to the friction and the energy loss due to the plasticity at the crack tip are investigated. The results show that depending on the amplitude of the applied Mode III stress intensity factor, one of these energy losses may dominate the total energy loss in the circumferentially cracked shaft. The results further indicate that the torsional dynamic response of the turbo-generator shaft is significantly affected by considering these two sources of the local energy loss.     

Shock wave method for monitoring crack repair processes in reinforced concrete structures

A nondestructive method for monitoring the crack state in reinforced concrete structures based on the recoding of wave processes in these structures under shock actions is proposed. The essence of the method and its possibilities are demonstrated by an example of the study of the behavior of a reinforced concrete beam with a crack at various stages of crack development and repair. Numerical simulation was used to study variations in the wave front characteristics in the crack area. A quantitative criterion was formulated, which permits estimating the concrete integrity or the existence of crack in it and monitoring the variations in the crack state in the process of loading the structure and the crack repair. The criterion is determined as the ratio of the amplitudes of the first half-waves of the acceleration wave front registered in regions on the opposite shores of the crack. The criterion value is independent of the amplitude of the shock action and the beam fixation conditions and is solely determined by the mechanical state of the material used to repair the crack. The criterion adequacy was demonstrated by comparing the results of numerical simulation with experimental data. A cycle of numerical experiments were carried out, which, for each duration of the shock action, permits determining the optimal values of the distance between the pulse application point and the acceleration recording points at which the criterion is most sensitive to the crack state.     

Mode-I crack projection procedure using the strain energy density criterion

A practice used in linear elastic fracture mechanics is the projection of a crack onto a plane normal to the principal tensile stress axes for computing the stress intensity factor K_I. The minimum strain-energy criterion is applied for different crack configurations with the introduction of a safety factor S_i which is the ratio of the strain energy density factor of the projected crack and that of the original crack. Numerous crack configurations are investigated to illustrate the degree of conservativeness of the crack projection procedure.     

两自由度可调非线性减振器

研究了可调非线性减振器的优化设计. 基于哈密尔顿最小势能原理建立非线性动力学模型,系统局域参数内,实现非线性系统幅值优化. 利用平均法求解可调非线性减振器频响方程. 分析系统解的稳定性,优化系统参数,降低系统幅值响应.     

Analysis of crack growth and crack-tip plasticity in ductile materials using cohesive zone models

Crack initiation and crack growth resistance in elastic plastic materials, dominated by crack-tip plasticity are analyzed with the crack modeled as a cohesive zone. Two different types (exponential and bilinear) of cohesive zone models (CZMs) have been used to represent the mechanical behavior of the cohesive zones. In this work, it is suggested that different forms of CZMs (e.g., exponential, bilinear) are the manifestations of different micromechanisms-based inelastic processes that participate in dissipating energy during the fracture process and each form is specific to each material system. It is postulated that the total energy release rate comprises the plastic dissipation rate in the bounding material and the separation energy rate within the fracture process zone, the latter is determined by CZMs. The total energy release rate then becomes a function of the material properties (e.g., yield strength, strain hardening exponent) and cohesive properties of the fracture process zone (e.g., cohesive strength and cohesive energy), and the form of cohesive zone model (CZM) that determines the rate of energy dissipation in the forward and wake regions of the crack. The effects of material parameters, cohesive zone parameters as well as the form/shape of CZMs in predicting the crack growth resistance and the size of plastic zone (SPZ) surrounding the crack tip are systematically examined. It is found that in addition to the cohesive strength and cohesive energy, the form (shape) of the traction–separation law of CZM plays a very critical role in determining the crack growth resistance (R-curve) of a given material. It is further observed that the shape of the CZM corresponds to inelastic processes active in the forward and wake regions of the crack, and has a profound influence on the R-curve and SPZ.     

Crack initiation behavior of functionally graded piezoelectric material: prediction by the strain energy density criterion

Transient response of a functionally graded piezoelectric medium is considered for a through crack under the mixed-mode in-plane mechanical and electric load. Integral transforms and dislocation density functions are employed to reduce the problem to singular integral equations. The energy density factor criterion is applied to obtain the maximum of the minimum energy density factor. This determines the direction of crack initiation. Numerical results display the effects of material constants, loading combination parameter, mechanical loading angle and material gradient parameter on the possible fracture behavior.     

Material plasticity dependence of mixed mode fatigue crack growth in commonly used engineering materials

In this paper, an investigation of fatigue crack propagation in rectangular plates containing an inclined surface crack is presented. A criterion for the three-dimensional stress state is proposed to predict fatigue crack initiation angles. It is assumed that the direction of crack initiation coincides with the direction of the minimum radius of the plastic zone defined by the von Mises yield criterion. The maximum energy release rate criterion, i.e., G_max criterion, is extended to study the fatigue crack growth characteristics of mixed mode cracks. A modification has been made to this criterion to implement the consideration of the plastic strain energy. Subsequently, this concept is applied to predict crack growth due to fatigue loads. Experiments for checking the theoretical predictions from the proposed criterion have been conducted. The results obtained are compared with those obtained using the commonly employed fracture criteria and the test data.     

激励脉冲信号对基于周向导波的圆环损伤检测的影响

针对含有径向裂纹的圆环,本文主要研究了不同激励脉冲信号对基于周向导波的圆环损伤检测结果的影响.对具有径向裂纹以及没有裂纹的圆环,分别用不同宽度的脉冲信号激励,然后用ABAQUS程序数值计算其应变信号.由Gabor连续小波转换(CWT)处理上述应变信号以确定径向裂纹的位置.结果显示,脉冲宽度对确定裂纹位置的精确性有很大影响.根据圆环的群速弥散曲线,讨论了圆环上裂纹的确定方法.最后,为验证检测圆环损伤所选择脉冲宽度的合理性,进行了两次实验.两次实验提供了相同的结论.     

The Pulsed Ultrasonic Backscatter Polar Scan and its Applications for NDT and Material Characterization

In a conventional ultrasonic polar scan (UPS) experiment, the amplitude or time-of-flight-diffraction (TOFD) values of the transmitted and/or reflected acoustic pulse are recorded for a wide range of incidence angles, in view of gaining knowledge about the elastic properties at the insonified material spot. Here we apply the pulsed UPS technique and investigate the backscattered signal, resulting in the ultrasonic backscatter polar scan (UBPS). It is shown that a UPBS contains a blueprint of geometrically related features of the insonified material spot which can be of particular interest for various industrial applications. We applied the UBPS for (i) the determination of the stacking sequence of a cross-ply composite laminate, (ii) the semi-quantification of a multidirectional microscopic surface corrugation, (iii) the detection of corrosion in an early stage as well as (iv) the detection and the localization of a closed surface breaking crack.     

Stability analysis of crack path using the strain energy density theory

Prediction of crack growth path is a pre-requisite for estimating the final shape of broken solids and structures. Crack path in broken specimens provides information for the loading conditions just before fracture. Experiments on brittle materials, pre-cracked specimens of the same geometry under similar loading conditions, however, may yield different crack trajectories at times. The existing theories for the prediction of the crack path are based on the perturbation method combining the analytical and finite elements methods. They require a knowledge of the toughness equations. Moreover, they can only be applied to specimens with simple geometry and loadings.A different approach is used in the present work. The finite element technique is used to calculate the strain energy density (SED) contours. The predicted trajectory of the crack during unstable propagation is assumed to coincide with the minimum of the strain energy density function according to the SED criterion.The degree of crack path stability depends on the sharpness of the SED oscillations. This simple method offers a reliable prediction of the crack path stability for two as well as three-dimensional problems with complex geometry structures and arbitrary loadings. To be specific, both the TPB and DCB specimens are analysed. The findings are in good agreement with the theoretical and experimental results in the literature.     

Mitigating impact/blast energy via a novel nanofluidic energy capture mechanism

To effectively mitigating intense impact and blast waves, a novel protection mechanism is proposed in this study where a significant amount of the incident energy can be temporarily captured as potential energy in a nonwetting liquid-nanoporous material system, thereby weakening the peak pressure and elongating the impact pulse. When the pressure of a compressive wave traveling in a liquid overcomes the capillary resistance, the liquid molecules quickly intrude into nanopores while retaining highly compressed form. The incident energy is thus captured (temporarily stored) in nanopores in the form of potential energy of intercalated water molecules, and then gradually released upon unloading (which makes the system reusable). Comparing with other energy absorption materials, the present system has the unique advantage of low activation pressure and high energy density. Using comprehensive molecular dynamics (MD) simulations, the effects of several key parameters (e.g., impact velocity, nanopore size, and pore composition) on energy capture are investigated, and the molecular mechanism is elucidated. The findings are qualitatively validated by a parallel blast experiment on a zeolite/water system.     

Frictional energy dissipation in materials containing cracks

Kachanov's simplified model of microcrack interaction is applied to an investigation of the behaviour of a cracked body under predominantly compressive periodic loading, so that the cracks experience periods of closure and slip, with frictional dissipation. The model is shown to be equivalent to a discrete elastic frictional system with each crack representing one node. Theorems and algorithms from such systems are applied to determine the conditions under which the system shakes down to a state with no slip and hence no energy dissipation in friction. For conditions not too far beyond the shakedown state, the dissipation is significantly affected by the initial conditions, but with larger oscillating loads, it becomes a unique and increasing function of load amplitude. The effect of crack interaction is assessed by comparison with an uncoupled model, for which the dissipation is obtained as a summation of closed form expressions over the crack population. For small numbers of cracks, the results are significantly dependent on the randomly chosen crack locations and sizes, but with larger populations, a statistically significant decrease in dissipation is observed with increasing interaction terms.     

Strain energy density prediction of fatigue crack growth from hole of aging aircraft structures

Fatigue crack growth rate depends not only on the load amplitude, but also on the morphology of crack path. The strain energy density theory has the ability to analyze crack growth rate. A strain energy density crack growth model is proposed. It can predict the lifetime of fatigue crack growth for mixed mode cracks while an equation for mode I crack is also obtained. The validity of the model is established with two cases: a center-crack panel and cracks emanating from the edge of a hole. The stress intensity factor expression for the former case is analytical while that of the latter is calculated numerically using finite elements. The results are compared with the testing data. Good agreement shows that the proposed model is useful.     

New model of propagation rates of long crack due to structure fatigue

By comparison of the characteristics of existing models for long fatigue crack propagation rates, a new model, called the generalized passivation-lancet model for long fatigue crack propagation rates （GPLFCPR）, and a general formula for characterizing the process of crack growth rates are proposed based on the passivation-lancet theory. The GPLFCPR model overcomes disadvantages of the existing models and can describe the rules of the entire fatigue crack growth process from the cracking threshold to the critical fracturing point effectively with explicit physical meaning. It also reflects the influence of material characteristics, such as strength parameters, fracture parameters and heat treatment. Experimental results obtained by testing LZ50 steel, AlZnMgCu0.5, 0.5Cr0.5Mo0.25V steel, etc., show good consistency with the new model. The GPLFCPR model is valuable in theoretical research and practical applications.     

Determination of crack spacing and penetration due to shrinkage of a solidifying layer

A method based on energy minimisation is used to determine the spacing and penetration of a regular array of cracks in a layer of material whose thickness is increasing as it solidifies from a liquid. After solidification, the slab shrinks and subsequently cracks due to internal stresses. A simple Stefan solidification model is used to determine the thickness of the slab as time progresses as well as the temperature profile in the slab. The key feature of the results is that a minimum crack spacing occurs early in the solidification process and this minimum defines a basic spacing for the crack array. The minimum spacing occurs for a range of constraints (boundary conditions) and thermal profiles in the material, indicating the robustness of the phenomenon. Cracks propagating with the unique minimum spacing are subject to a period doubling instability that acts to coarsen the crack pattern, which brings the crack spacing close to the minimum energy state for later time. Good numerical comparison between the crack spacings predicted by energy minimisation and those observed in basalt columns is demonstrated.     

The measurement and significance of energy in acoustic-emission testing

A technique for measuring the energy sensed at an acoustic-emission transducer is presented that utilizes a squaring circuit and digital integrator. Theoretical relationships between energy and other more conventional acoustic-emission parameters, such as counts and RMS voltage, are derived for certain idealized cases. Experimental results from the following types of tests are presented: (1) unflawed tensile (‘continuous’ emission); (2) precracked stress-corrosion cracking; (3) precracked fracture toughness; and (4) fatigue-crack growth. Energy, counts, RMS-voltage, energy/event and counts/event measurements are included. In the case of unflawed tensile specimens, energy techniques appeared somewhat superior to counts. In all other cases, a direct relationship between counts and energy was obtained. Energy measurements tended to give a larger weight to higher amplitude events. Other than this, energy measurements appeared to have no advantage over counts. The theoretical relationship predicted between energy/event and count/event agreed quite well with experimental observations. Overall, the test results presented indicate that energy techniques provide no significant advantage over counting threshold crossings in cases in which crack extension in metals is the primary source of acoustic emission.