A theoretical approach for evaluating the plane strain fracture toughness of ductile metals

Fracture Mechanics of Ductile Metals (FMDM) theory is used to obtain the plane strain fracture toughness, K_lc, for different materials. The traditional approach for obtaining the K_lc value is to conduct several standard tests on cracked plates that are costly and time consuming. The fracture toughness value provided by the FMDM theory depends on the stress-strain curve for the material in question, and this is readily available in MIL-HDBK-5 and other reliable sources. The results of the plane strain fracture toughness (K_lc) values provided by the FMDM theory were compared with the experimental data and it was concluded that the two are in excellent agreement. It is proposed that, in the interest of economy and convenience, K_lc testing could be replaced by the FMDM theory.     

A direct complementarity approach for the elastoplastic analysis of plane stress and plane strain structures

This paper presents a direct complementarity approach for carrying out the elastoplastic analysis of plane stress and plane strain structures. Founded on a traditional finite‐step formulation, our approach, however, avoids the typically cumbersome implementation of iterative predictor–corrector procedures associated with the ubiquitous return mapping algorithm. Instead, at each predefined step, the governing formulation—cast in its most natural mathematical programming format known as a mixed complementarity problem—is directly solved by using a complementarity solver run from within a mathematical modeling system. We have chosen the industry‐standard General Algebraic Modeling System/PATH mixed complementarity problem solver that is called from within the General Algebraic Modeling System environment. We consider both von Mises and Tresca materials, with perfect or hardening (kinematic and isotropic) behaviors. Our numerical tests, five (benchmark) examples of which are presented in this paper, have been carried out using models constructed from the mixed finite element of Capsoni and Corradi (Comput. Methods Appl. Mech. Eng. 1997; 141 :67–93), which beneficially offers a locking‐free behavior and coarse‐mesh accuracy. The results indicate, in addition to an isochoric locking‐free behavior, good accuracy and the ability to circumvent the difficult singularity problem associated with the corners of Tresca yield surfaces. Copyright © 2012 John Wiley & Sons, Ltd.     

Kinetics of plastic strain zone formation near crack tip in fracture of construction materials under plane stress and plane strain

X-ray-diffraction analysis is used to determine the depth of the plastic deformation zones in steel. 15Kh2MFA and alloy D16 beneath the surface of fractures that are obtained under plane stress (PS) and plane deformation (PD) conditions. We propose a scheme illustrating the kinetics of the formation of two plastic deformation zones near the crack tip under one-time loading in conditions of the plane stress state: a strongly deformed microzone and a weakly deformed macrozone.Translated from Problemy Prochnosti, No. 4, pp. 57–63, April, 1993.     

Caustics in plane strain—evaluation of COD and the core region

The method of reflected caustics, which is believed up-to-now to apply only for plane-stress problems, was extended in this paper to elastic fields under conditions of plane-strain, containing any type of singularity due either to the mode of loading, or to the geometry of the stress field. The optical far-field theory valid in such types of fields was developed and experimental criteria were given for the first time, for deciding under what conditions the elastic field around a crack or any discontinuity is in a pure state of plane-stress or in a plane-strain, or in a mixed mode (triaxial) of deformation. Examples with transverse edge cracks of varying length in plates under uniaxial mode of loading corroborate the results of the theory.Finally, a technique was introduced for the accurate evaluation of the crack-opening displacement at the tip of the crack, as well as of the area covered by the core region for specimens under conditions of plane strain.     

一种平地楼梯两用助行机器人的建模与仿真分析

为解决老年人和残疾人出行不便的问题,提出了一种平地楼梯两用的助行机器人设计方案,采用轮足式结构实现爬楼梯功能.用R.Morales方法进行正、逆运动学分析,计算出机器人质心及各关节位移轨迹.用RobersonWittenburg方法推导出系统的动力学方程,将逆运动学解代入动力学模型中求得各关节所需的驱动力矩.同时在ADAMS中建立虚拟样机模型,进行运动学和动力学仿真,得到的机器人质心位移轨迹和各关节驱动力矩与MATLAB的计算结果一致,验证了设计方案的可行性和理论推导的正确性.     

An approximate solution for a plane strain hydraulic fracture that accounts for fracture toughness,fluid viscosity,and leak-off

The goal of this paper is to develop an approximate solution for a propagating plane strain hydraulic fracture, whose behavior is determined by a combined interplay of fluid viscosity, fracture toughness, and fluid leak-off. The approximation is constructed by assuming that the fracture behavior is primarily determined by the three-process (viscosity, toughness, and leak-off) multiscale tip asymptotics and the global fluid volume balance. First, the limiting regimes of propagation of the solution are considered, that can be reduced to an explicit form. Thereafter, applicability regions of the limiting solutions are investigated and transitions from one limiting solution to another are analyzed. To quantify the error of the constructed approximate solution, its predictions are compared to a reference numerical solution. Results indicate that the approximation is able to predict hydraulic fracture parameters for all limiting and transition regimes with an error of under one percent. Consequently, this development can be used to obtain a rapid solution for a plane strain hydraulic fracture with leak-off, which can be used for quick estimations of fracture geometry or as a reference solution to evaluate accuracy of more advanced hydraulic fracture simulators.     

An inverse problem approach to stiffness mapping for early detection of breast cancer: tissue phantom experiments

Early detection of breast cancer will continue to be crucial in improving patient survival rates. Our ultimate goal is to develop an electro-mechanical device to automate and refine the manual breast exam process, and use inverse techniques to generate a tissue stiffness map of the breast tissue. We have previously presented computational simulations of the stiffness mapping approach, which employs static indentations of the tissue and measurements of surface displacements. In this paper, we report on experimental validation of the technique with tissue phantom experiments. We tested 12 tissue phantom samples without simulated tumours and 14 tissue phantom samples with simulated tumours. Our stiffness mapping approach correctly identified all 26 samples.     

Modeling of localization and fracture phenomena in strain and stress space for sheet metal forming

In this study, a model based on a strain localization level to overcome the shortcomings of the well-established Forming Limit Diagram (FLD) in predicting the physical phenomenon of necking is introduced. An optical measurement system was used to capture the strain history of the Nakazima experiment until rupture occurred. In order to measure the fracture strain more accurately, a further method is introduced, which is based on the microscopic measurements of ruptured regions. This model is validated using a 3-point bending test. The results show the ability of the method to predict failure under bending conditions as well. Additionally, failure is investigated based on the pressure sensitivity and the Lode dependency. The results show that the triaxiality at the failure point is independent of the loading path.     

Modeling and simulation of crack propagation in mixed-modes interlaminar fracture specimens

A study of mixed-mode crack propagation in bending-based interlaminar fracture specimens is here presented. A numerical scheme to simulate full crack propagation is proposed which makes use of interface laws relating interlaminar stresses to displacement discontinuities along the plane of crack propagation. The relation between interface laws and mixed-mode failure loci in terms of critical energies is discussed and clarified. Numerical simulations are presented and compared with analytical and experimental results.     

On using linear elements in incompressible plane strain problems: a simple edge based approach for triangles

In this paper a simple iterative method is presented for finite element solution of incompressible plane strain problems using linear elements. Instead of using a mixed formulation approach, we use an equivalent displacement/velocity approach in an iterative manner. Control volumes are taken for regions which are to exhibit incompressible behaviour. For triangular elements the control volume is chosen as the area built on the parts of each pair of elements at the sides of an edge. In this case, elements are let to exchange volume. It is shown that the proposed edge based approach removes the deficiency of the linear triangular elements i.e. locking effect. Similar edge based approach is applied to the linear quadrilateral elements. However, if the control volume is chosen as the element volume the formulation gives similar results as the discontinuous mixed formulation using one pressure point without exhibiting instability behaviour. The formulation is based on decomposition of the displacement/velocity field into deviatoric and volumetric parts. The volumetric part is iteratively eliminated without confronting locking or instability phenomenon. The iterative procedure is very cheap and simple to be implemented in any FEM code. Several examples are given to demonstrate the performance of the procedure. Copyright © 2004 John Wiley & Sons, Ltd.     

Development of a reference strain approach for assessment of fracture response of reeled pipelines

As a result of recent increase in exploitation of hydrocarbon resources in harsher environments and also installation techniques which utilize the materials plastic deformation capacity, accurate assessment of fracture response of pipelines subject to large plastic strains (e.g., typical of reeled pipes) has attracted particular interest nowadays. In this paper, an approach, based on the evaluation of the J-integral, is developed for assessing the integrity of such pipelines, manifested in a model of a pipeline with a circumferential part-through crack subjected to plastic bending. The proposed approach is an extension of the reference strain method developed earlier by other researchers, and takes advantage of the displacement controlled loading nature in such pipes (thus being suitable for Strain Based Design methodologies), and the resulting high strain levels, which often cause fracture response of the material in the plastic regime. The developed formulation relates the fracture response of the pipe (in terms of the non-dimensionalized J-integral) as a linear function of the axial strain in the pipe at its uncracked state. A series of 300 3D nonlinear finite element models using the ABAQUS software were analyzed in preparation of the equation that could assess the fracture response of such pipes with great accuracy. The resulting equation, calibrated by the finite element results, can predict the fracture response of pipes with a maximum error of 2% for a practical uncracked material strain range of 1.5% ? ε_unc ? 4%.     

Modeling and simulation of osteoporosis and fracture of trabecular bone by meshless method

Osteoporosis is a skeletal disease characterized by a decrease in bone strength as a result of a decrease of bone mass and a deterioration of bone microstructure. In this work, the imaging data of a CT scanned human femoral neck trabecular bone is directly converted into a meshless model. A model is developed to analyze osteoporosis process. A fracture criterion and the corresponding post-failure are proposed for trabecular bone. The fracture process is modeled and simulated. The simulations show that the fracture stress is not a monotonically decreasing function in the process of fracture, and the microstructure of trabecular bone has a positive effect in preventing progressive failure. The approach in this work may be used to understand the osteoporosis-related fracture and the bone density–strength relationship, and to serve as a way for prognosis of osteoporosis.     

Transient responses of a special non-homogeneous magneto-electro-elastic hollow cylinder for a fully coupled axisymmetric plane strain problem

Summary By means of introducing a new dependent variable and the separation of variables technique as well as the superposition method, the axisymmetric plane strain dynamic problem of a special non-homogeneous magneto-electro-elastic hollow cylinder is finally transformed to two Volterra integral equations of the second kind with respect to two functions of time. At each time subinterval, a cubic Hermite polynomial is adopted to approximate the two undetermined functions, and the recursive formula is obtained.The integral equation is then solved successfully. The transient responses of displacements, stresses, electric and magnetic potentials are finally determined. Numerical results are presented at the end.     

Design of stationary plane strain drawing based on the ideal flow theory and a fracture criterion

Summary The ideal flow theory provides a tool for designing metal forming processes. However, quite often the design based on this theory is not unique. The purpose of the present work is to investigate a possibility of using an additional design criterion driven by fracture. The fracture criterion adopted is based on the concept of workability diagram for rate-independent materials and its generalization for rate-dependent materials. It is shown that for stationary forming processes of rate-independent materials this criterion does not lead to a design criterion, whereas for stationary forming processes of rate-dependent materials it does. In the latter case, a numerical example for plane-strain drawing is given.