Fracture mechanics for a mode III crack in a magnetoelectroelastic solid

In this paper, we developed a Stroh-type formalism for anti-plane deformation and then investigated the fracture mechanics for an elliptical cavity in a magnetoelectroelastic solid under remotely uniform in-plane electromagnetic and/or anti-plane mechanical loading, which allowed us to take the electromagnetic field inside the cavity into account. Reducing the cavity into a crack, we had explicit solutions in closed forms for a mode III crack, which included the extreme cases for an impermeable crack and a permeable crack. The results were illustrated with plots, showing that in the absence of mechanical loads, an applied electric or magnetic field, positive or negative, always tended to close the crack. On the other hand, in the presence of a mechanical load, a negative electric or magnetic field retarded crack growth, while a positive field could either enhance or retard crack propagation, depending on the strengths of the applied electric/magnetic fields and the level of the mechanical load as well. In other words, the effect of electric/magnetic fields on the fracture behavior is mechanical load-dependent.     

地磁环境下结构变形引起的扰动磁场

基于磁弹性相互作用的线性化理论，针对地磁环境特点，忽略磁场对结构位移的影 响而仅考虑位移对磁场的耦合作用，通过将位移梯度引入变形后界面外法线矢量方 法，给出了变形引起的扰动磁场计算的定解场方程和界面衔接条件，并计算了符拉 芒问题的变形扰动磁场. 结果表明，变形扰动磁场完全取决于位移梯度在界面外法 向上的投影；扰动场强与外力成正比；空气中扰动磁场的法向强度和切向强度分布 特征明显不同，法向强度在力作用点对称分布，并且在 力作用点处存在奇点；切向强度则呈反对称分布，在力作用点处发生突变.     

粒状材料中水力劈裂的认识

水力劈裂在岩土工程、环境工程和石油工程中已得到很好地应用,但另一方面又会造成大坝渗漏破坏、浆液流失以及石油行业中经常遇到的浅水流动等严重后果。连续固体材料（如岩石）中的水力劈裂理论是建立在抗拉强度基础之上,对此,国内外的研究已经比较深入。而对于粒状材料中的研究尚处于起步阶段,仅有少数的试验和数值研究。本文综述了粒状材料中水力劈裂室内试验、现场试验、解析分析和数值模拟的研究成果,分析了当前研究中对这一现象认识的不足,并对今后可能的研究方向进行了预测。     

Initiation and propagation of localized deformation in elasto-plastic strips under uniaxial tension

This paper deals with the evolution of inhomogeneous deformation in shape memory alloy strips and mild steel strips under uniaxial tension. New experiments on NiTi strips, which initially are in an austenitic phase, show that at a critical stress level martensite nucleates in sharp bands inclined at 55° to the axis of loading. Under prescribed end displacement martensite subsequently spreads either by steady-state propagation of inclined transition fronts or via a criss-cross pattern of finger-like features. Similar events have been reported in the literature regarding the evolution of Lüders bands in fine grained steel strips and wires. The similarity of macroscopic events, despite the different mechanisms of instability at the micro-level, prompted us to approximate the material behavior as a finitely deforming elasto-plastic solid with a trilinear up-down-up nominal stress-strain response. Two such stress-strain responses were used in finite element simulations of strip tension tests. In the first the true stress-strain response maintains its stability and in the second the intermediate branch has a negative slope. While both material models produced inhomogeneous deformations with features similar to those of the experiments, the larger initiation peak associated with the second gave results which closely resembled specific experiments. The numerical simulations confirmed that the evolution of events seen in experiments on SMAs and mild steels is strongly influenced by overall geometric (structural) effects. Furthermore, the success of this simple continuum constitutive model strongly suggests that continuum level events remain dominant players in such fine grained materials.     

Ultrasonic testing of non-metallic materials: concrete and marble

Experimental investigation is made to examine the ability of non-destructive testing (NDT) methods for evaluating the integrity of non-metallic materials. Among the known methods, the ultrasonics seem to stand out because the method could be used to determine many properties of the material. Examined in the work are construction materials such as concrete and marble. In particular, the dynamic moduli of elasticity and damage states due to fracture are studied.     

Coupled continuum and discrete analysis of random heterogeneous materials: Elasticity and fracture

Recent work has suggested that the heterogeneous distribution of mechanical properties in natural and synthetic materials induces a toughening mechanism that leads to a more robust structural response in the presence of cracks, defects or other types of flaws. Motivated by this, we model an elastic solid with a Young′s modulus distribution described by a Gaussian process. We study the pristine system using both a continuum and a discrete model to establish a link between the microscale and the macroscale in the presence of disorder. Furthermore, we analyze a flawed discrete particle system and investigate the influence of heterogeneity on the fracture mechanical properties of the solid. We vary the variability and correlation length of the Gaussian process, thereby gaining fundamental insights into the effect of heterogeneity and the essential length scales of heterogeneity critical to enhanced fracture properties. As previously shown for composites with complex hierarchical architectures, we find that materials with disordered elastic fields toughen by a ‘distribution-of-weakness’ mechanism inducing crack arrest and stress delocalization. In our systems, the toughness modulus can increase by up to 30% due to an increase in variability in the elastic field. Our work presents a foundation for stochastic modeling in a particle-based micromechanical environment that can find broad applications within natural and synthetic materials.     

金属非晶的强度和变形特性

金属非晶发展至今已有多种体系并可实现厘米量级的块体制备,其各种性能也都有了广泛的研究。本文主要介绍金属非晶的单轴拉伸、单轴压缩、微柱压缩、薄板弯曲、拉伸-扭转等物理力学特性及关于其变形的理论分析。文章涵盖了金属非晶的以下一些力学特性：金属非晶的弹性模量和其溶剂金属的相近性―金属非晶通常具有2% 左右的弹性应变极限,对应着GPa量级的高失效强度;金属非晶单轴拉伸、压缩时的宏观塑性特征及塑性变形的典型机制;金属非晶微观上的短程与中程原子团簇结构特点及其与非晶塑性的关联;金属非晶塑性屈服与静水压力的相关性,拉扭组合时呈现的螺旋断口特征,以及Mohr-Coulomb本构模型对这些屈服特征的适用性。最后,作者也介绍了金属非晶塑性变形的微观物理模型及连续介质力学本构,以及金属非晶的断裂与疲劳特性。     

含瓦斯煤单轴压缩的尺度效应实验研究

含瓦斯煤与其它岩石类材料一样,在力学特性等方面具有尺度效应。利用特制的饱和加压装置和电子万能试验机,对不同尺度、不同饱和瓦斯压力下的煤样进行了单轴压缩试验,探讨了煤样变形破坏及强度特性的变化规律。分析表明,煤样抗压强度、弹性模量随瓦斯压力的增大而减小,抗压强度随高径比的增加明显减小,弹性模量随高径比的增加略有提高。利用Weibull模型和线弹性强化理论对含瓦斯煤产生尺度效应的原因进行了合理地解释,为含瓦斯煤样尺度效应在强度表征等方面的深入研究提供了新的实验和理论依据。     

轻质合金压印接头质量判断及其力学性能研究

在结构轻量化的进程中,新型薄板材料被大量使用,新兴的压印连接技术可以实现这些材料的连接．以钛合金为主要材料进行压印连接实验,结果显示材料的母材性能对连接性能、接头强度、失效形式均有一定的影响．压印接头的拉伸-剪切失效形式为颈部断裂时,拉伸-剪切实验过程中载荷位移曲线有两次明显的下降过程,分别是由于圆形压印点的上半部分颈部被拉断,圆压印点的下半部分颈部被拉断造成的．微观分析显示TA1-TA1压印接头断口呈现类解理穿晶断裂,5052-TA1压印接头断口出现拉长韧窝特征,属于塑性断裂,1420-TA1接头断口呈现大面积平面及少量冰糖状花样,属于沿晶脆性断裂．     

Critical defect size distributions in concrete structures detected by the acoustic emission technique

Extensive research and studies on concrete fracture and failure have shown that concrete should be viewed as a quasi-brittle material having a size-dependent behavior. Numerous experimental techniques have been employed to evaluate fracture processes, and a number of modeling approaches have been developed to predict fracture behavior. A non-destructive method based on the Acoustic Emission (AE) technique has proved to be highly effective, especially to assess and measure the damage phenomena taking place inside a structure subjected to mechanical loading. In this paper, comparing AE frequency-magnitude statistics in solids subjected to damage processes with defect size distributions for disordered materials, critical parameters defining instability conditions for monitored structures are found. In addition, an experimental investigation conducted on concrete and RC structures by means of the AE technique is described. Experimental results confirm the described theories.     

冲击载荷作用下黑砂岩动态断裂参数的分形修正

基于分形理论研究了偏折裂纹扩展路径对动载荷作用下黑砂岩的动态断裂力学参数的测试误差影响作用,采用传统的分离式霍普金森压杆（split Hopkinson pressure bar, SHPB）实验装置对修正侧开单裂纹半孔板（improved single cleavage semi-circle specimen, ISCSC）试样进行动态冲击实验,随后采用裂纹扩展计进行裂纹起裂时间与裂纹扩展速度等动态断裂力学参数测试,采用分形理论对测试的裂纹扩展速度与动态应力强度因子进行修正,利用实验-数值法对黑砂岩的动态断裂韧度进行计算。研究结果表明,ISCSC构型构件能够有效应用于岩石材料动态裂纹扩展行为的研究,并发生了止裂现象,经分形修正的裂纹扩展速度与动态断裂韧度更接近实际裂纹动态扩展情况,修正前后得到黑砂岩材料的裂纹扩展速度误差为33.51%,动态断裂韧度最大误差为7.68%,说明利用分形理论对动态断裂韧度等动态断裂参数计算更合理。     

Mechanics of nanocrack: Fracture, dislocation emission, and amorphization

Understanding the nanoscale fracture mechanisms is critical for tailoring the mechanical properties of materials at small length scales. We perform an atomistic study to characterize the formation and extension of nano-sized cracks. By using atomistic reaction pathway calculations, we determine the energetics governing the brittle and ductile responses of an atomically sharp crack in silicon, involving the competing processes of cleavage bond breaking, dislocation emission, and amorphization by the formation of five- and seven-membered rings. We show that the nanoscale fracture process depends sensitively on the system size and loading method. Our results offer new perspectives on the brittle-to-ductile transition of fracture at the nanoscale.     

A mathematical model of cortical bone remodeling at cellular level under mechanical stimulus

A bone cell population dynamics model for cortical bone remodeling under mechanical stimulus is developed in this paper. The external experiments extracted from the literature which have not been used in the creation of the model are used to test the validity of the model. Not only can the model compare reasonably well with these experimental results such as the increase percentage of final values of bone mineral content (BMC) and bone fracture energy (BFE) among different loading schemes (which proves the validity of the model), but also predict the realtime development pattern of BMC and BFE, as well as the dynamics of osteoblasts (OBA), osteoclasts (OCA), nitric oxide (NO) and prostaglandin E₂ (PGE₂) for each loading scheme, which can hardly be monitored through experiment. In conclusion, the model is the first of its kind that is able to provide an insight into the quantitative mechanism of bone remodeling at cellular level by which bone cells are activated by mechanical stimulus in order to start resorption/formation of bone mass. More importantly, this model has laid a solid foundation based on which future work such as systemic control theory analysis of bone remodeling under mechanical stimulus can be investigated. The to-be identified control mechanism will help to develop effective drugs and combined nonpharmacological therapies to combat bone loss pathologies. Also this deeper understanding of how mechanical forces quantitatively interact with skeletal tissue is essential for the generation of bone tissue for tissue replacement purposes in tissue engineering.     

Crack instability of ferroelectric solids under alternative electric loading

The low fracture toughness of the widely used piezoelectric and ferroelectric materials in technological applications raises a big concern about their durability and safety. Up to now, the mechanisms of electric-field induced fatigue crack growth in those materials are not fully understood. Here we report experimental observations that alternative electric loading at high frequency or large amplitude gives rise to dramatic temperature rise at the crack tip of a ferroelectric solid. The temperature rise subsequently lowers the energy barrier of materials for domain switch in the vicinity of the crack tip, increases the stress intensity factor and leads to unstable crack propagation finally. In contrast, at low frequency or small amplitude, crack tip temperature increases mildly and saturates quickly, no crack growth is observed. Together with our theoretical analysis on the non-linear heat transfer at the crack tip, we constructed a safe operating area curve with respect to the frequency and amplitude of the electric field, and validated the safety map by experiments. The revealed mechanisms about how electro-thermal-mechanical coupling influences fracture can be directly used to guide the design and safety assessment of piezoelectric and ferroelectric devices.     

Fracture of a body with a periodic set of coaxial cracks under forces directed along them: an axisymmetric problem

Linearized solid mechanics is used to solve an axisymmetric problem for an infinite body with a periodic set of coaxial cracks. Two nonclassical fracture mechanisms are considered: fracture of a body with initial stresses acting in parallel to crack planes and fracture of materials compressed along cracks. Numerical results are obtained for highly elastic materials described by the Bartenev–Khazanovich, Treloar, and harmonic elastic potentials. The dependence of the fracture parameters on the loading conditions, the physical and mechanical characteristics of the material, and the geometrical parameters is analyzed Translated from Prikladnaya Mekhanika, Vol. 45, No. 2, pp. 3–18, February 2009.     

Acoustic emission monitoring of crack propagation in additively manufactured and conventional titanium components

Additive manufacturing (AM) is a novel and innovative production technology that can produce complex and lightweight engineering products. In AM components, as in all engineering materials, fatigue is considered as one of the principle causes of unexpected failure. In order to detect, localise and characterise cracks in various material components and metals, acoustic emission (AE) is used as a non-destructive monitoring technique. One of the main advantages of AE is that it can be also used for dynamic damage characterisation and specifically for crack propagation monitoring. In this research, we use AE to monitor the fatigue crack growth behaviour of Ti6Al4V components under four-point bending. The samples were produced by means of AM as well as conventional material. Notched and unnotched specimens were investigated with respect to the crack severity and crack detection using AE. The main AE signal parameters –such as cumulative events, hits, duration, average frequency and rise time– were evaluated and indicate sensitivity to damage propagation in order to lead to a warning against the final fracture occurrence. This is the first time that AE is applied in AM components under fatigue.     

ANTI-PLANE ANALYSIS FOR ELLIPTICAL INCLUSION IN MAGNETOELECTROELASTIC MATERIALS

This paper considers the multi-field coupling in magneroelectroelastic composite materials consisting of the inclusion and the matrix are magnetoelectroelastic materials. The mechanical,electric and magnetic fields around an elliptical cylinder inclusion are formulated by complex potentials. Inside the inclusion,the strain,electric and magnetic fields are found to be uniform and vary with the shape of the ellipse. When the inclusion is reduced to a crack,along the interface,the strain,electric field strength and magnetic field strength equal the corresponding remote ones,which can be used as the boundary condition. Special cases,such as a rigid and permeable inclusion,a soft and impermeable inclusion,a line inclusion and a crack problem are discussed in detail.     

Combined analysis of fracture under stresses acting along cracks

A joint approach to the study of two non-classical fracture mechanisms, namely fracture of cracked materials with initial (residual) stresses acting along the crack planes and fracture under compression along parallel cracks, is considered in the framework of three-dimensional linearized solid mechanics. Mathematical statements of problems for pre-stressed solids that contain interacting circular cracks are given. Problems for an infinite solid containing two parallel co-axial cracks and for a space with the periodical set of co-axial parallel cracks as well as for a half-space with near-the-surface crack are solved. Several patterns of loading on the crack faces (normal loading, radial shear and torsion) are considered. The effects of initial stresses on stress intensity factors are analyzed for highly elastic materials with some types of elastic potentials. Formulation of fracture criteria accounting effect of initial (residual) stresses is given. Critical parameters of fracture of solids containing interacting cracks under compression along the cracks are calculated. The influence of geometrical parameters of the problems as well as physical and mechanical properties of materials on these critical parameters is analyzed.     

The behavior of two non-symmetrical permeable cracks emanating from an elliptical hole in a piezoelectric solid

Based on the Stroh-type formalism, we present a concise analytic method to solve the problem of complicated defects in piezoelectric materials. Using this method and the technique of conformal mapping, the problem of two non-symmetrical collinear cracks emanating from an elliptical hole in a piezoelectric solid is investigated under remotely uniform in-plane electric loading and anti-plane mechanical loading. The exact solutions of the field intensity factors and the energy release rate are presented in closed-form under the permeable electric boundary condition. With the variation of the geometrical parameters, the present results can be reduced to the well-known results of a mode-III crack in piezoelectric materials. Moreover, new special models used for simulating more practical defects in a piezoelectric solid are obtained, such as two symmetrical edge cracks and single edge crack emanating from an elliptical hole or circular hole, T-shaped crack, cross-shaped crack, and semi-infinite plane with an edge crack. Numerical results are then presented to reveal the effects of geometrical parameters and the applied mechanical loading on the field intensity factors and the energy release rate.     

材料的微结构损伤与韧性断裂

Ⅰ.前言50年代起至60年代,国际上开展了材料宏观力学性能的大量研究,提出了应力强度因子K和J积分,确定了断裂韧性参数的测定方法,创立了断裂力学学科并制定了规范,对材料的断裂、疲劳性能的预测和安全设计做出了很大贡献。进入70年代后开始注意到现有技术远远不能认识和控制各类裂纹的起因和发展。例如,K和J不能解决裂纹的稳态扩展、复