Fourth-order phase-field modeling for brittle fracture in piezoelectric materials

Failure analyses of piezoelectric structures and devices are of engineering and scientific significance.In this paper,a fourth-order phase-field fracture model for piezoelectric solids is developed based on the Hamilton principle.Three typical electric boundary conditions are involved in the present model to characterize the fracture behaviors in various physical situations.A staggered algorithm is used to simulate the crack propagation.The polynomial splines over hierarchical T-meshes(PHT-splines)are adopted as the basis function,which owns the C1continuity.Systematic numerical simulations are performed to study the influence of the electric boundary conditions and the applied electric field on the fracture behaviors of piezoelectric materials.The electric boundary conditions may influence crack paths and fracture loads significantly.The present research may be helpful for the reliability evaluation of the piezoelectric structure in the future applications.

Improved Staggered Algorithm for Phase-Field Brittle Fracture with the Local Arc-Length Method

The local arc-length method is employed to control the incremental loading procedure for phase-field brittle fracture modeling.An improved staggered algorithm with energy and damage iterative tolerance convergence criteria is developed based on the residuals of displacement and phase-field.The improved staggered solution scheme is implemented in the commercial software ABAQUS with user-defined element subroutines.The layered system of finite elements is utilized to solve the coupled elastic displacement and phase-field fracture problem.A one-element benchmark test compared with the analytical solution was conducted to validate the feasibility and accuracy of the developed method.Our study shows that the result calculated with the developed method does not depend on the selected size of loading increments.The results of several numerical experiments show that the improved staggered algorithm is efficient for solving the more complex brittle fracture problems.

Characterizing the influence of stress-induced microcracks on the laboratory strength and fracture development in brittle rocks using a finite-discrete element method-micro discrete fracture network FDEM-μDFN approach

Heterogeneity is an inherent component of rock and may be present in different forms including mineralheterogeneity, geometrical heterogeneity, weak grain boundaries and micro-defects. Microcracks areusually observed in crystalline rocks in two forms： natural and stress-induced; the amount of stressinducedmicrocracking increases with depth and in-situ stress. Laboratory results indicate that thephysical properties of rocks such as strength, deformability, P-wave velocity and permeability areinfluenced by increase in microcrack intensity. In this study, the finite-discrete element method （FDEM）is used to model microcrack heterogeneity by introducing into a model sample sets of microcracks usingthe proposed micro discrete fracture network （mDFN） approach. The characteristics of the microcracksrequired to create mDFN models are obtained through image analyses of thin sections of Lac du Bonnetgranite adopted from published literature. A suite of two-dimensional laboratory tests including uniaxial,triaxial compression and Brazilian tests is simulated and the results are compared with laboratory data.The FDEM-mDFN models indicate that micro-heterogeneity has a profound influence on both the mechanicalbehavior and resultant fracture pattern. An increase in the microcrack intensity leads to areduction in the strength of the sample and changes the character of the rock strength envelope. Spallingand axial splitting dominate the failure mode at low confinement while shear failure is the dominantfailure mode at high confinement. Numerical results from simulated compression tests show thatmicrocracking reduces the cohesive component of strength alone, and the frictional strength componentremains unaffected. Results from simulated Brazilian tests show that the tensile strength is influenced bythe presence of microcracks, with a reduction in tensile strength as microcrack intensity increases. Theimportance of microcrack heterogeneity in reproducing a bi-linear or S-shape failure envelope and itseffects on the mechanisms leading to spalling damage near an underground opening are also discussed.

ANALYSIS OF BRITTLE FRACTURE DUE TO COMPRESSIVE LOADING USING CENTER-CRACKED BRAZILIAN DISK

The center cracked Brazilian disk subjected to diametral compressive stress uniformly distributed along parts of its cylindrical surface is used to investigate combined mode fracture of brittle material. A fracture analysis is made of this specimen configuration. Explicit formulae for mode Ⅰ and mode Ⅱ stress intensity factor calculation are derived based on boundary integral equation method and related numerical solution given by Atkinson. The proposed formulae are valid in wide range of crack length a/R . This configuration can avoid splitting along load line usually occuring in Brazilian test and permit one to achieve easily pure mode Ⅱ crack growth (crack coplanar extension) and any combination of K Ⅰ and K Ⅱ by a simple alignment of crack orientation with respect to load line. SIF values from the present calculation and finite element solution are also given for comparison.

INFLUENCE OF LOCAL BRITTLE ZONE ON THE FRACTURETOUGHNESS OF HIGH-STRENGTH LOW-ALLOYEDMULTIPASS WELD METALS

In this paper, toughness properties and microstructurc of low-alloyed multipass welds with yield strength above 700MPa have 6een studied using the weld thermal simulation and throughout thickness CTOD fracture mechanics tests. Impact testing of thermal simulated specimens showed that the primary weld metal and the fine gmmed weld metal had good toughness, while the coarse grained weld metal had the lowest toughness value as the local brittle zone (LBZ) in multipass weld metals. Cleavage fracture in CTOD testing of thick multipass weld metals was initiated from martensite-austenite (MA) phases in the LBZ. MA phases were distributed at the prior austenite grain boundaries and around ferrite grains. As the size of the local brittle zone along the fatigue crack front increases, CTOD frncture toughness of multipass weld metals decreases. The weakest link theory was used to evaluate effect of the local brittle zone on fracture toughness of thick multipass weld metals. The estimated curves agree well with the eaperimental data.

Thermo-hydro-mechanical-chemical(THMC)coupling fracture criterion of brittle rock

Based on analysis of thermo-hydro-mechanical-chemical(THMC)coupling mechanism for brittle rock,THMC coupling indicator in terms of rock porosity was introduced to represent the influencing degree of THMC coupling field on stress field in order to establish THMC coupling fracture criterion.A novel real-time measurement method of permeability(related to porosity)was proposed to determine the THMC coupling indicator,and self-designed THMC coupling tests and scanning electron microscope tests were conducted on pre-cracked red sandstone specimens to study the macroscopic and microscopic fracture mechanism.Research results show that the higher the hydraulic pressure is,the smaller the crack initiation load is and the easier the Mode I fracture occurs.Test results are in good agreement with prediction results(crack initiation load and angle,and fracture mode),which can verify the effectiveness of the newly established THMC coupling fracture criterion.This new fracture criterion can be also further extended to predict THMC coupling fracture of multi-crack problem.

Analysis of fracture process zone in brittle rock subjected to shear-compressive loading

An analytical expression for the prediction of shear-compressive fracture process zone(SCFPZ) is derived by using a proposed local strain energy density criterion, in which the strain energy density is separated into the dilatational and distortional strain energy density, only the former is considered to contribute to the brittle fracture of rock in different loading cases. The theoretical prediction by this criterion shows that the SCFPZ is of asymmetric mulberry leaf in shape, which forms a shear-compression fracture kern. Dilatational strain energy density along the boundary of SCFPZ reaches its maximum value. The dimension of SCFPZ is governed by the ratio of K_Ⅱ to (K_Ⅰ.) The analytical results are then compared with those from literatures and the tests conducted on double edge cracked Brazilian disk subjected to diametrical compression. The obtained results are useful to the prediction of crack extension and to nonlinear analysis of shear-compressive fracture of brittle rock.

Peridynamic Modeling of Brittle Fracture in Mindlin-Reissner Shell Theory

In this work,wemodeled the brittle fracture of shell structure in the framework of Peridynamics Mindlin-Reissener shell theory,in which the shell is described by material points in themean-plane with its drilling rotation neglected in kinematic assumption.To improve the numerical accuracy,the stress-point method is utilized to eliminate the numerical instability induced by the zero-energy mode and rank-deficiency.The crack surface is represented explicitly by stress points,and a novel general crack criterion is proposed based on that.Instead of the critical stretch used in common peridynamic solid,it is convenient to describe thematerial failure by using the classic constitutive model in continuum mechanics.In this work,a concise crack simulation algorithm is also provided to describe the crack path and its development,in order to simulate the brittle fracture of the shell structure.Numerical examples are presented to validate and demonstrate our proposed model.Results reveal that our model has good accuracy and capability to represent crack propagation and branch spontaneously.

Prediction of Quasi-Brittle Fracture of Concrete and Rock Structures Using Laboratory-Sized Specimens

A simple method is developed for predicting the fracture behaviour of structures made of quasi-brittle materials such as concrete and rock using the data from laboratory-sized specimens. The method is based on the recently-developed boundary effect concept and associated asymptotic model. It is demonstrated that the “apparent” size dependence of fracture behaviour of concrete and rock is in fact due to the influence of specimen boundaries. Various size effect phenomena that are often observed in fracture mechanics tests of concrete and rock are related to each other, and the asymptotic boundary effect model can explain all the observed “size” effect phenomena. Four types of experimental results available in the literature (including the data measured on (1) the specimens of identical size with different crack-to-size (%α%) ratios, (2) specimens of different sizes with different %α%-ratios, (3) different types of specimens and (4) geometrically similar specimens) are used to verify the asymptotic boundary effect model, and it is found that the predictions of the model agree very well with the experimental results. Furthermore, the important fracture properties, fracture toughness %K_{IC}% and strength %f_t% of quasi-brittle materials such as concrete and rock can also be calculated using the formulae provided in the model.

Experimental study on 3D internal penny-shaped crack propagation in brittle materials under uniaxial compression

Fractures are widely present in geomaterials of civil engineering and deep underground engineering.Given that geomaterials are usually brittle,the fractures can significantly affect the evaluation of underground engineering construction safety and the early warning of rock failure.However,the crack initiation and propagation in brittle materials under composite loading remain unknown so far.In this study,a three-dimensional internal laser-engraved cracking technique was applied to produce internal cracks without causing damage to the surfaces.The uniaxial compression tests were performed on a brittle material with internal cracks to investigate the propagation of these internal cracks at different dip angles under compression and shear.The test results show that the wing crack propagation mainly occurs in the specimen with an inclined internal crack,which is a mixed-ModeⅠ–Ⅱ–Ⅲfracture;in contrast,ModeⅠfracture is present in the specimen with a vertical internal crack.The fractography characteristics of ModeⅢfracture display a lance-like pattern.The fracture mechanism in the brittle material under compression is that the internal wing cracks propagate to the ends of the whole sample and cause the final failure.The initial deflection angle of the wing crack is determined by the participation ratio of stress intensity factors KII to KI at the tip of the internal crack.

PROBABILISTIC MODELING OF BRITTLE FRACTURE WITH PRIOR DUCTILE CRACK EXTENSION

A computation framework for brittle fracture which incorporates weakest link statistics and a microme- chanics model reflecting reflecting local damage of the material is described.The Weibull stress W emerges as a probabilistic fracture parameter to define the condition leading material failure. Unstable crack propa- gation occurs at a critical value of W which may be attained paior to or following some amount of duc- tile crack extension. A realistic model of ductile crack growth using the computation cell methodology is used to define the evolution of near tip stress fields during crack extension. An application of proposed framework to predict the measured geometry and ductile tearing effects on the statistical distributio of fracture toughness for the pipe line steel welded joint is described.

Effect of weld microstructure on brittle fracture initiation in the thermallyaged boiling water reactor pressure vessel head weld metal

Effects of the weld microstructure and inclusions on brittle fracture initiation are investigated in a thermally aged ferritic high-nickel weld of a reactor pressure vessel head from a decommissioned nuclear power plant.As-welded and reheated regions mainly consist of acicular and polygonal ferrite,respectively.Fractographic examination of Charpy V-notch impact toughness specimens reveals large inclusions(0.5-2.5μm)at the brittle fracture primary initiation sites.High impact energies were measured for the specimens in which brittle fracture was initiated from a small inclusion or an inclusion away from the V-notch.The density,geometry,and chemical composition of the primary initiation inclusions were investigated.A brittle fracture crack initiates as a microcrack either within the multiphase oxide inclusions or from the debonded interfaces between the uncracked inclusions and weld metal matrix.Primary fracture sites can be determined in all the specimens tested in the lower part of the transition curve at and below the 41-J reference impact toughness energy but not above the mentioned value because of the changes in the fracture mechanism and resulting changes in the fracture appearance.

The Influence of Welding Parameters on Brittle Fracture of Liquefied Natural Gas Storage Tank Welded Joint

Many applications operate at sufficiently low temperature conditions where most structural steels become very brittle and, therefore, unsuitable for use in safety-critical structures. So the materials used in the vessels or storage tanks which keep the natural gas at liquefaction temperatures need to remain ductile and crack resistant with a high level of safety. The material also needs to have high strength in order to reduce the wall thickness of the container and it must permit welding without any risk of brittle fracture. 9% Ni steel plates are one of most common used materials in the LNG storage tank application. However, the welding procedure for 9% Ni steel plates requires high level of skills of welding that is strictly controlled welding parameter for balancing avoidance of cold and hot cracking and maintenance of high strength. Mechanical properties are important characteristics of the weldment that must confirm to the application feasibility as well as functional requirements of the welded joint. The only way to enhanced the mechanical properties of welded joint by controlling the parameters of using welding process. From the main variables of the arc welding process are the heat input and interpass temperature where the two variables control the thermal cycle of welding process. The experiment show that for thin test specimen with thickness ≤ 14 mm, the heat input range from 1.4 to 2 KJ/mm and controlling interpass temperature within 80°C give high tensile strength with improving the toughness properties of welded joint and reduce the probability of brittle fracture happened by increase the ductility and reduce the yield strength and increased the transition temperature.

Nanoscale Morphology in Tensile Fracture of a Brittle Amorphous Ribbon

The paper reports on the observation of nanoscale morphology on the tensile fracture surface of a brittle amorphous Fe-based ribbon. The formation of nanoscale damage cavity structure is a main characteristic morphology on the fracture surfaces. Approaching the ribbon boundary, these damage cavities assemble and form the nanoscale periodic corrugations, which are neither Wallner lines nor crack front waves. The periodic corrugations result from the interactions between the reflected elastic waves by the boundaries of amorphous ribbon and the stress fields of the crack tip.

Two Modes and Criterion of Brittle Fracture

The plastic zone at the tip of the flaw (including acute cark and common notch) was investigated. Forthe notch specimen, a formula of toughness K was proposed, and its physical meaning was emphasized.Twomodes of brittle fracture was identified and the evaluating criterion was established.

MAGNETIC STRIPS TO SIMULATE LAYERED BRITTLE SOLIDS IN CLEAVAGE AND FRACTURE EXPERIMENTS

A characteristic of the fracture and cleavage experiments is that they are usually intrinsically destructive. Cracks do not completely heal in an unstressed system, even in crystals such as mica. Here, we used magnetic solids composed of magnetic strips for the non-destructive cleavage and brittle fracture experiments. Between the magnetic strips materials with different mechanical characteristics can be inserted, such as Teflon or foam strips, to change the mechanical properties of the solid. For the cleavage experiments, we developed an apparatus where parameters such as the main involved force can be measured easily. By inserting flaws, the magnetic solid can be used in dynamic fracture experiments, with the advantages of simulating macroscopically a non-destructive experiment in an easier way, that happen in real materials with much higher velocities. The apparatus and the used magnetic solid may be useful for demonstrations of fractures in classes.

A NONLOCAL THEORY FOR BRITTLE FRACTURE

In this paper,a nonlocal theory of fracture for brittle materials has been systematically devel- oped,which is composed of the nonlocal elastic stress fields of Griffith cracks of mode-Ⅰ,Ⅱ and Ⅲ,the asymptotic forms of the stress fields at the neighborhood of the crack tips,and the maximum tensile stress criterion for brittle fracture.As an application of the theory,the fracture criteria of cracks of mode-Ⅰ,Ⅱ, Ⅲ and mixed mode Ⅰ-Ⅱ,Ⅰ-Ⅲ are given in detail and compared with some experimental data and the theoretical results of minimum strain energy density factor.

Thermal-hydro-mechanical coupling stress intensity factor of brittle rock

A new calculation formula of THM coupling stress intensity factor was derived by the boundary collocation method, in which an additional constant stress function was successfully introduced for the cracked specimen with hydraulic pressure applied on its crack surface. Based on the newly derived formula, THM coupling fracture modes （including tensile, shear and mixed fracture mode） can be predicted by a new fracture criterion of stress intensity factor ratio, where the maximum axial load was measured by self-designed THM coupling fracture test. SEM analyses of THM coupling fractured surface indicate that the higher the temperature and hydraulic pressure are and the lower the confining pressure is, the more easily the intergranular （tension） fracture occurs. The transgranular （shear） fracture occurs in the opposite case while the mixed-mode fracture occurs in the middle case. The tested THM coupling fracture mechanisms are in good agreement with the predicted THM coupling fracture modes, which can verify correction of the newly-derived THM coupling stress intensity factor formula.

91W-Ni-Fe-Co合金的常温、低温力学性能及微观组织

通过粉末冶金方法制备91W-5.5Ni-3.3Fe-0.2Co和91W-5.5Ni-2.5Fe-1Co合金。采用硬度测试、室温低温拉伸试验、扫描电镜(SEM)和能谱(EDS)等方法,研究合金的微观组织演变和室温、低温力学行为。研究结果表明:在室温条件下,Co质量分数为1%的合金的力学性能更优异,抗拉强度和伸长率分别为1 400 MPa和11.7%,拉伸断裂行为以钨解理断裂和黏结相撕裂为主。微观组织上,相比于低Co合金,高Co合金的晶粒更加细小,钨-钨连续度降低,黏结相体积分数提高,黏结相中钨溶解度增大,合金性能得到优化;随着温度降低,2种合金的强度提高,伸长率下降;在-60℃时,高Co合金的伸长率相比于低Co合金的伸长率提高了20%,同时,合金的断裂模式仍以韧性相撕裂为主,而低Co合金在低于-20℃时,断裂由钨解理断裂主导。在一定范围内,Co质量分数增加能抑制杂质元素在晶界处偏聚,提高钨晶粒塑性变形程度,降低低温脆性。

宝坻-苗庄凸起新生断裂脆韧性转换深度研究

现今地震是最新构造活动的最直接表现,是认识大陆内部非刚性变形特征的最有力工具。尤其是对晚更新世以来开始活动的新生断裂来说,由于发育成熟度低,几何构造上贯通性差且不同区段走向/不同深度倾向差异明显,地震能够揭示其三维空间的变化,尤其是脆韧性转换深度特征,促进对新生活动断裂孕育、发震过程的认识。渤海湾盆地新生走滑活动断裂曾多次发生强震,如唐山M_(S)7.8、三次宁河M_(S)≥6.2地震,这些地震揭示的地壳脆-韧性转换深度对认识该地区地震发震机理和活动性具有重要的现实意义。本文以渤海湾盆地内宝坻-苗庄凸起新生断裂为目标断裂,以发生于宝坻凸起的2012年宝坻M_(S)4.0、M_(S)3.5地震以及发生于苗庄凸起的1976年宁河M_(S)6.2、M_(S)6.9、1977年宁河M_(S)6.2地震为研究对象,基于首都圈数字地震台网的波形资料,采用CAP方法研究宝坻M_(S)4.0、M_(S)3.5地震震源机制解和震源深度,利用近震转换波Sp精确确定震源深度,采用双差方法定位两个地震序列的震源位置,并结合其他资料探讨该地区地震的发震机理以及新生断裂脆韧性转换深度。结果显示:(1)宝坻M_(S)4.0、M_(S)3.5地震震源性质与宝坻-苗庄凸起出露地表的已知断裂不尽相符,结合宁河三次MS≥6.2地震震源参数的有关研究成果,推测它们均发震于宝坻-宁河深大断裂;(2)结合震源区电性结构以及流变结构等模型,宝坻-苗庄凸起这五次显著地震揭示出宝坻-宁河深大断裂的脆韧性转换深度为15km左右;(3)结合渤海湾盆地动力演化过程以及深部地球物理探测等相关资料,推测该地区地震活动主要是宝坻-宁河深大断裂与深部流体作用的结果。