ELASTIC PERFECTLY-PLASTIC FIELDS AT A RAPIDLY PROPAGATING CRACK-TIP

All the stress components at a rapidly propagating crack-tipin an elastic perfectly-plastic material are the functions of θ only.Making use of this condition and theequations of steady-state motion.stress-strain relations and yield conditions,we obtain thegeneral solutions in both the cases of anti-plane and in-plane strain.Applying these twogeneral solutions to propagating Mode III and Mode I cracks.respectively,the elasticperfectly-plastic and the perfectly-plastic fields at the rapidly propagating tips of Mode IIIand Mode I crocks are derived.     

Asymptotic fields in steady crack growth with linear strain-hardening

The asymptotic stress and velocity fields of a crack propagating steadily and quasi-statically into an elastic-plastic material are presented. The material is characterized by J₂-flow theory with linear strain- hardening. The possibility of reloading on the crack flanks is taken into account. The cases of anti-plane strain (mode III), plane strain (modes I and II), and plane stress (modes I and II) are considered. Numerical results are given for the strength of the singularity and for the distribution of the stress and velocity fields in the plastic loading, elastic unloading and plastic reloading regions, as functions of the strain-hardening parameter. An attempt is made to make a connection with the perfectly-plastic solutions in the limit of vanishing strain-hardening.     

Some possible alternative solutions of near-tip fields for steady crack growth in elastic perfectly-plastic media

Some possible alternative solutions of near-tip fields are studied for plane-strain Mode—I quasi-static steady crack growth in incompressible (ν=1/2) elastic perfectly-plastic media. A group of four-sector solutions and a three-sector solution in which the elastic-unloading region vanishes are given. Stress functions, plastic flow factors and plastic strains in each region are also given. Project supported by the State Education Commission under a funding program for Excellent University Young Faculties and National Natural Science Foundation of China.     

Fields near a rapidly propagating crack-tip in an elastic perfectly-plastic material

Dynamic effects are investigated for the steady-state fields of stress and deformation in the immediate vicinity of a rapidly propagating crack-tip in an elastic perfectly-plastic material. Both the cases of antiplane strain and in-plane strain have been considered. The governing equations in the plastic regions are hyperbolic in nature. Simple wave solutions together with uniform fields provide explicit asymptotic expressions for the stresses and the strains in the near-tip regions. The dynamic solutions describe a region of plastic loading which completely surrounds the propagating crack-tip.     

Strain-hardening extrusion—I. Construction of slip-line fields from experimental flow patterns

A possible method of solving problems in strain-hardening flows is by perturbation of known perfectly-plastic solutions. It is shown that vertex singularities, which are possessed by most such solutions, are not admissible in steady hardening flows. The structure of regular local solutions, both perfectly-plastic and strain-hardening, is investigated, and it is shown how vertex singularities can be replaced by regular local corner solutions.A scheme for constructing strain-hardening slip-line fields based on experimental flow patterns is described, which uses the maximum shear strain-rate directions calculated from the digitized and smoothed flow pattern to perturb local Hencky-Prandtl nets, which are then patched together in conformity with the topology of the solution to form a complete slip-line field. This method has been implemented in a computer program to construct slip-line fields from flow patterns for extrusion through wedge-shaped dies, and some fields computed by the program are presented.     

Anisotropic plastic stress fields at a rapidly propagating crack-tip

All the stress components at a rapidly propagating crack-tip in an elastic perfectly-plastic material are the functions of only. Making use of this condition and the equations of steady-state motion, stress-strain relations and Hill anisotropic yield condition, we obtain the general solutions in both the cases of anti-plane and in-plane strain. Applying these two general solutions to propagating Mode III and Mode I cracks, respectively, the anisotropic plastic stress fields at the rapidly propagating tips of Mode III and Mode I cracks are derived.     

Elastic perfectly-plastic asymptotic mixed mode crack tip fields in plane stress

Elastic perfectly-plastic asymptotic plane stress crack tip fields have been constructed by assembling elastic, constant stress and fan sectors under a complete range of mixed mode I/II states of loading. The angular stress distributions are fully continuous, and do not contain the stress discontinuities which have been a feature of many previously proposed solutions. The analytic solutions are verified by finite element solutions under contained yielding conditions. The structure of the elastic perfectly-plastic fields is compared to the structure of the asymptotic strain hardening fields.     

A displacement bounding principle in shakedown of structures subjected to cyclic loads

Continua or structures composed of elastic perfectly-plastic material subjected to cyclic loads which vary within the shakedown limits are considered. A theorem bounding the residual deflection at any point is presented.Some numerical examples are discussed.     

Extended displacement bound theorems for continua subjected to dynamic loading

Continua or structures made of elastic perfectly-plastic material subjected to variable loads which vary within the shakedown limits are considered, allowing for dynamic effects, such as inertia forces due to the loading conditions. A theorem bounding the residual deflection at any point is presented. Some interesting specializations to certain classes of dynamic loading are discussed.     

Simple examples of non linear truss behavior

Nonlinear material models are defined to represent elastic/perfectly-plastic and elastic/buckling behavior. A simple three-bar truss is used to demonstrate that under a monotonically increasing prescribed displacement the truss may exhibit reverse stressing or non-uniqueness, and that when two different control displacements are applied the principal of superposition does not hold.     

Plane-strain crack-tip stress field for anisotropic perfectly-plastic materials

Plane-strain crack-tip stress solutions for anisotropic perfectly-plastic materials are presented. These solutions are obtained using the plane-strain slip-line theory developed by Rice (1973). The plastic anisosotropy is described by the Hill quadratic yield condition. The crack-tip stress solutions under symmetric (Mode I) and anti-symmetric (Mode II) conditions agree well with the low-hardening solutions for the corresponding power-law hardening materials. The crack-tip stress solutions under mixed Mode I and II conditions are also presented. All the solutions indicate that the general features of the slip-line field near a crack tip in orthotropic plastic materials with the elliptical yield contours in the Mohr plane are the same as those associated with isotropic plastic materials. However, the angular variations of the crack-tip stress fields for the materials with large plastic orthotropy differ substantially from those for isotropic plastic materials. Modifications due to polygonal yield contours are outlined and implications of solutions to the fracture analysis of ductile composite materials containing macroscopic flaws are discussed.     

Dynamic non-shakedown theorem for elastic perfectly-plastic continua

Sufficient and necessary conditions of a kinematic nature are established for alternating plasticity or incremental collapse (i.e. inadaptation or non-shakedown) of elastic perfectly-plastic media subjected to given histories of loads and thermal strains, in the presence of significant inertia and viscous damping forces. The classical second shakedown theorem, due to W.T. Koiter, is thus extended to the dynamic range.     

General displacement and work bounds for dynamically loaded bodies

In recent years a number of writers have developed theorems which allow the evaluation of bounds on deformation properties of bodies subject to both static and dynamic loading. Some of these results have proved useful to structural designers in assessing structural performance, thereby obviating the need for a complete analysis. In this paper a general theory is described for small strains which brings together results for both quasi-static and dynamic loading, and also provides a theoretical framework within which a wide range of constitutive relationships may be discussed. The material behaviour is included through a functional property of the constitutive relationship which gives a generalization of the concept of maximum complementary work. A new result for impulsively loaded bodies is illustrated by examples involving elastic and elastic perfectly-plastic materials.     

直角刚架在撞击作用下的塑性大挠度响应

本文研究了悬臂直角刚架在其自由端受到自身平面内的横向撞击时的塑性动力响应在本文报告的实验中,利用空气炮射出的子弹加载使软钢材料制成的直角刚架产生大挠度塑性变形;同时,依据理想刚塑性材料模型,给出了一个大挠度瞬时模态解。理论分析得到的挠度-载荷曲线与实验结果符合得很好。     

Dual extremum principles in the dynamics of rigid perfectly-plastic bodies undergoing finite deformations

A pair of dual extremum principles is derived for a rigid perfectly-plastic body subjected to dynamic loading. No restrictions are placed on the magnitude of the deformation. A Lagrangian formulation is used, and the dual principles are obtained in a systematic manner by using a saddle-shaped functional and a pair of operators adjoint to each other, to generate the governing equations and inequalities. This procedure was developed by B. Noble and M. J. Sewell (1972) in their study of dual extremum principles in applied mathematics. It is shown that the principles derived here are closely connected to those given by M. Capurso (1972c) for the case of small strains and large displacements.     

Plane-stress crack-tip stress fields for orthotropic perfectly-plastic materials

Under the hypothesis that the stress components of crack-tip fields are only thefunctions ofθ,the differential equations of plane-stress crack-tip stress fields fororthotropic perfectly-plastic materials are obtained by using Hill’s yield condition andequilibrium equations.By combining the general analytical expression with the numericalmethod the crack-tip stress fields for orthotropic perfectly-plastic materials for plane stressare presented.     

Hydrostatic stress-dependent perfectly-plastic stress fields at a stationary plane-stress crack-tip

Under the condition that all the stress components at a crack-tip are the functions of θ only, making use of equilibrium equations and hydrostatic stress-dependent yield condition, in this paper, we derive the generally analytical expressions of the hydrostatic stress-dependent perfectly-plastic stress fields at a stationary plane-stress crack-tip. Applying these generally analytical expressions to the concrete cracks, the analytical expressions of hydrostatic stress-dependent perfectly-plastic stress fields at the tips of mode Ⅰ and mode Ⅱ cracks are obtained.     

Logarithm strain singularity at tip of mode I growing crack in elasticand perfectly-plastic material

Reanalyzed in detail is the stress and strain distribution near the tip of a Mode I steadily growing crack in an elastic and perfectly-plastic material. The crack tip region is divided into five angular sectors, one of which is singular in character and represents a rapid transition zone that becomes a line of strain discontinuity in the limit as crack tip is approached. It is shown for an incompressible material (ν=0.5) under plane strain that the local strain in all the angular sectors possesses the same logarithm singularity, i.e., In r where r is the radial distance measured from the crack tip. This result also prevails for the compressible material ( v < 0.5) and resolves a long standing controversy concerning the strain singularity in the sector just ahead of the crack tip.     

夹杂对两相材料界面裂纹的影响

根据界面上应力和位移的连续条件,得到了单向拉伸状态下,含有椭圆夹杂的无限大双材料组合板的复势解。进一步通过求解Hilbert问题,得到了含有夹杂和半无限界面裂纹的无限大板的应力场,并由此给出了裂尖的应力强度因子K。计算了夹杂的形状、夹杂的位置、夹杂的材料选取以及上、下半平面材料与夹杂材料的不同组合对裂尖应力强度的影响。计算结果表明夹杂到裂尖的距离和夹杂材料的性质对K影响较大,对于不同材料组合,该影响有较大差异。夹杂距裂尖较近时,会对K产生明显屏蔽作用,随着夹杂远离裂尖,对K的影响也逐渐减小。另外,软夹杂对K有屏蔽作用,硬夹杂对K有反屏蔽作用,而夹杂形状对K几乎没有影响。