柱体扭转断裂问题的有限元对偶分析

St Venant扭转问题同样存在J积分对偶积分形式。采用基于最小势能原理的等参元可得J的下降；另一方面，采用基于最小作能原理的平衡元可得J的对偶积分的上限。本文构造了一个性能优越的罚平衡扭转杂交元，计算结果显示其可得到扭转问题应力强度因子的上限。     

狭长矩形截面杆自由扭转的材料力学解法

以往矩形截面杆自由扭转问题的解仅在弹性力学中查到,本文从材料力学的教学法和便于应用的观点重新分析了该问题,得到了其材力力学的解,当$h/b \ge 6$时,可以满足工程应用的精度要求.     

对矩形截面杆弹性自由扭转的探讨

利用柱体扭转问题的经典弹性力学解析解,结合自编电算程序绘制了沿截面控制线上剪应力的分布图,同时利用ANSYS有限元分析软件模拟了等直矩形截面杆的自由扭转问题. 将各种材料力学教材中的截面剪应力分布图与准确计算结果进行了比较,并对截面剪应力分布规律进行了总结.     

含中心裂纹任意截面柱体扭转时的应力强度因子计算

本文提出了一组应力函数,采用边界配置方法计算了含中心裂纹不同截面形状柱体扭转时的应力强度因子。有关椭圆截面柱体的算例表明,本文方法具有良好的精度。同时,文中给出了圆、椭圆和矩形等不同截面柱体的计算结果。     

周边切口短圆柱试件的杆杆型冲击拉伸试验系统的弹塑性有限元分析

基于一维试验原理提出了用带有周边切口的短金属圆柱试件进行平面应变型弹塑性动态断裂韧度的测试方法;对该复杂的动力学系统进行了轴对称的弹塑性有限元分析,并计算了动态围道积分;根据对试件功能转换关系的分析和Rice公式的物理意义,提出了用试件两端平均载荷-两端相对位移曲线(-Δ)推广Rice公式计算试件的远场J积分,由此得到的-Δ曲线基本上消除了与裂纹运动无关的质心运动动能的影响.论证了J积分作为裂端的表征参量,且当切口深度比大于70%时,Rice公式有较高的计算精度.为平面应变型弹塑性动态断裂韧度的表征与测试提供了依据.     

对“狭长矩形截面杆自由扭转的材料力学解法”的讨论

对文[1]“狭长矩形截面杆自由扭转的材料力学解法”从图形的代替上作以修 正,进一步分析了应力和变形,提高了精确度.     

弹塑性扭转问题具多项式基的径向点插值无网格法

对于弹塑性扭转问题描述的椭圆变分不等式,采用具多项式基的径向点插值法无网格方法与Uzawa方法耦舍,得到了带松弛因子的离散迭代算法,并给出了数值算例,分析了参数对结果的影响.通过与有限元法比较,表明该方法是求解弹塑性扭转问题的有效的方法之一.     

有限厚双边U型切口板的三维弹塑性有限元分析

针对单向拉伸载荷作用下的有限厚双边 U型切口板 ,本文对其切口根部的三维效应进行了详细的三维弹塑性大变形有限元分析 ,得到了不同于平面切口问题的新结果 :( 1 )在线弹性阶段 ,三维切口根部的应力集中因子 Kt高于二维情形 ,且 Kt在板厚 ( B)约为 8倍切口根部半径 (ρ)时达到峰值 ;进入塑性后 ,切口根部的 Kt随载荷水平的增加逐渐下降 ,并介于平面应力和平面应变情形之间 ;( 2 )切口前缘等效应变εe的最大值出现在约束最高的中面 ,且可比约束最低的自由表面处的应变值高一倍 ;( 3)薄板中 ,塑性区尺寸 xp 的最大值不是出现在约束较低的自由表面 ,而是出现在约束较高的中面 ,但随 B/ρ的增大逐渐向自由表面外推 ;( 4 )面内应力比 Tx在切口根部塑性区内的分布对板厚和载荷水平不敏感 ,可以用 Hill的滑移线解很好地近似。另外 ,对三维影响区内一些重要的三维约束参量进行了详细分析 ,总结了它们的三维分布规律。     

周边切口短圆柱试件裂纹稳态扩展过程的有限元分析

以实测的平均载荷P作为试件端面的力边界条件,以实测的起裂时间tid和a(t)作为运动边界条件,将周边切口短圆柱试件简化为左右对称且轴对称的精细有限元模型,模拟了冲击加载下裂纹稳态扩展的运动过程;论证了裂纹起裂时围道 J(t)积分和稳态扩展时修正的围道 J(t)积分在离裂尖稍远处是守恒的;还论证了依据P-δ曲线计算得到的JMR-△a阻力曲线与试件尺寸无关,论证了相应的表征和测试方法是合理有效的.     

Path-independentJ-integral and its dual form in elastic-plastic solids with finite displacements

In this paper, based on energy variational principles of elastic-plastic solids, the path-independentJ-integral and its dual form in elastic-plastic solids with finite displacements are presented. Whose testification is given there after.     

The stress concentration near a rigid line inclusion in a prestressed, elastic material. Part II.: Implications on shear band nucleation, growth and energy release rate

The full-field and asymptotic solutions derived in Part I of this article (for a lamellar rigid inclusion, embedded in a uniformly prestressed, incompressible and orthotropic elastic sheet, subject to a far-field deformation increment) are employed to analyse shear band formation, as promoted by the near-tip stress singularity. Since these solutions involve the prestress as a parameter, stress and deformation fields can be investigated near the boundary of ellipticity loss (but still within the elliptic range). In the vicinity of this boundary, the incremental stress and displacement fields evidence localized deformations with patterns organized into shear bands, evidencing inclinations corresponding to those predicted at ellipticity loss. These localized deformation patterns are shown to explain experimental results on highly deformed soft materials containing thin, stiff inclusions. Finally, the incremental energy release rate and incremental J-integral are derived, related to a reduction (or growth) of the stiffener. It is shown that this is always positive (or negative), but tends to zero approaching the Ellipticity boundary, which implies that reduction of the lamellar inclusion dies out and, simultaneously, shear bands develop.     

The sliding interface crack with friction between elastic and rigid bodies

The paper analyzes the frictional sliding crack at the interface between a semi-infinite elastic body and a rigid one. It gives solutions in complex form for non-homogeneous loading at infinity and explicit solutions for polynomial loading at the interface. It is found that the singularities at the crack tips are different and that they are related to distinct kinematics at the crack tips. Firstly, we postulate that the geometry of the equilibrium crack with crack-tip positions b and a is determined by the conditions of square integrable stresses and continuous displacement at both crack tips. The crack geometry solution is not unique and is defined by any compatible pair (b,a) belonging to a quasi-elliptical curve. Then we prove that, for an equilibrium crack under given applied load, the “energy release rate” G_tip, defined at each crack tip by the J_ε-integral along a semi-circular path, centered at the crack tip, with vanishing radius ε, vanishes. For arbitrarily shaped paths embracing the whole crack, with end points on the unbroken zone, the J-integral is path-independent and has the significance of the rate, with respect to the crack length, of energy dissipated by friction on the crack.     

OnJ-integrals in the plane fracture of composite materials

By using a complex function method in this paper, the complex form of J-integral of mixed mode crack tip for unidirectional plate of linear-elastic orthotropic composites is obtained first by substituting crack tip stresses and displacements into general formula of J-integral. And then, the path-independence of this J-integral is proved. Finally, the computing formula of this J-integral is derived. As special examples, the complex forms, path-independence and computing formulae of J-integrals of mode Ⅰ and mode Ⅱ crack tips for unidirectional plate of linear-elastic orthotropic composites are given.     

Experimental study and BEM analysis of fatigue crack growth in a cracked heterogeneous body

A model for analysing a soft-hard heterogeneous body with a crack in the hard region is presented in this paper. The result of fatigue experiments shows that mechanical heterogeneity affects the rate of propagation of fatigue crack. Meanwhile the results computed by BEM for cracked heterogeneous bodies under cycling loading indicate that the smaller the distance between the crack and the interface of hard and soft regions is, the smaller the amplitude of crack opening displacement, COD and ofJ-integral as well at the same step during the fatigue crack growth will be. The effect of heterogeneity on the rate of fatigue crack propagation is shown by the variation of J. The smaller the distance of the crack to the interface is, the smaller the rate of fatigue crack growth will be.     

子弹撞击作用下固支浅圆拱的弹塑性动力响应

基于大变形动力学微分方程并利用有限差分离散分析,研究了子弹撞击作用下固支浅圆拱的弹塑性动力响应。通过对响应不同时刻内力分布特征的分析,阐明了圆拱的响应模式和变形机制。研究表明,弹塑性响应过程可分为六个阶段。在响应早期,拱的变形以塑性弯曲挠动由撞击点向拱根部传播为主;在响应后期,则主要以轴力主导下的轴向拉伸变形为主。在高速撞击下,塑性弯曲挠动的不均匀性可以引起浅拱的反向弯曲变形。固支浅圆拱的动力响应对撞击速度的某个变化范围非常敏感,在此范围内,撞击速度的较小增加可以导致响应的很快增长,但动力响应随撞击速度连续变化,未发生突然的跳跃失稳。本文中计算结果同实验数据吻合较好。     

Sharp-crack limit of a phase-field model for brittle fracture

A matched asymptotic analysis is used to establish the correspondence between an appropriately scaled version of the governing equations of a phase-field model for fracture and the equations of the two-dimensional sharp-crack theory of Gurtin and Podio-Guidugli (1996) that arise on assuming that the bulk constitutive behavior is nonlinearly elastic, requiring that surface energy provides the only factor limiting crack propagation, and assuming that the fracture kinetics are isotropic. Consistent with the prominence of the configurational momentum balance at the crack tip in the latter theory, the approach capitalizes on the configurational momentum balance that arises naturally in the context of the phase-field model. The model developed and utilized here incorporates irreversibility of the phase-field evolution. This is achieved by introducing a suitable constraint and by carefully heeding the influence of that constraint on the kinetics underlying microstructural changes associated with fracture. The analysis is predicated on the assumption that the phase-field variable takes values in the closed interval between zero and unity.     

A material force method for inelastic fracture mechanics

A material force method is proposed for evaluating the energy release rate and work rate of dissipation for fracture in inelastic materials. The inelastic material response is characterized by an internal variable model with an explicitly defined free energy density and dissipation potential. Expressions for the global material and dissipation forces are obtained from a global balance of energy-momentum that incorporates dissipation from inelastic material behavior. It is shown that in the special case of steady-state growth, the global dissipation force equals the work rate of dissipation, and the global material force and J-integral methods are equivalent. For implementation in finite element computations, an equivalent domain expression of the global material force is developed from the weak form of the energy-momentum balance. The method is applied to model problems of cohesive fracture in a remote K-field for viscoelasticity and elastoplasticity. The viscoelastic problem is used to compare various element discretizations in combination with different schemes for computing strain gradients. For the elastoplastic problem, the effects of cohesive and bulk properties on the plastic dissipation are examined using calculations of the global dissipation force.     

Strip electric-magnetic breakdown model in a magnetoelectroelastic medium

Extending the polarization saturation model [Gao et al., 1997. Local and global energy release rates for an electrically yielded crack in a piezoelectric ceramic. J. Mech. Phys. Solids 45, 491-510] and the dielectric breakdown (DB) model [Zhang et al., 2005. The strip dielectric breakdown model. Int. J. Fract. 132, 311-327] in piezoelectric materials, the Strip Electric-Magnetic Breakdown (SEMB) model is proposed for electrically and magnetically impermeable crack in a magnetoelectroelastic medium to study the effect of the nonlinear character of electric field and magnetic field on fracture of magnetoelectroelastic materials. In the SEMB model, the electric field in the strip of the electric breakdown zone ahead of the crack tip is equal to the electric breakdown strength, while the magnetic filed in the strip of the magnetic breakdown zone is equal to the magnetic breakdown strength. By using the extended Stroh formalism and the extended dislocation modeling of a crack, the Griffith crack problem under the electrically and magnetically elastic-plastic condition in a magnetoelectroelastic medium is reduced to a set of dual integral equations. The sizes of the electric breakdown zone and the magnetic breakdown zone, the extended intensity factors and the local J-integral are obtained. The effect of the combined mechanical-electric-magnetic loadings on the local J-integral is studied.     

Calculation of the J-integral for limited permeable cracks in piezoelectrics

Summary This paper deals with the calculation of the J-integral for electrically limited permeable cracks in piezoelectrics. The electromechanical J-integral is extended to account for electrical crack surface charge densities representing electric fields inside the crack. To avoid the costly implementation of the line integral along the crack faces, an alternative is proposed replacing the line integral by a simple jump term across the crack faces. Previous work by other authors related to the same subject is critically illuminated. The derivation was inspired by the Dugdale- Barenblatt cohesive zone model and yields an expression containing solely the local jump of displacements and electric potentials across the crack faces. This approach is shown to be exact for the Griffth crack.Numerical examples give evidence that the simplified approach works well for arbitrary crack configurations too.