Asymptotic tensile crack-tip stress fields in elastic-perfectly plastic crystals

For a crack in an elastic-perfectly plastic crystal, there exist more than one asymptotic stress field around the crack tip. The condition governing which field occurs cannot be determined by the asymptotic fields, but depends on external loading conditions. For a plane-strain tensile crack in the (0 1 0) plane and growing in the [1 0 1] direction in a face-centered-cubic (fcc) crystal, there exist three asymptotic stress fields around the crack tip, including a previously established four-sector field and two new families of three-sector fields. The four-sector field gives a large mean stress ahead of the crack, 6.12, where is the critical resolved shear stress for slip systems {1 1 1}1 1 0. The first family of three-sector fields is parameterized by a single parameter p ranging from 0 to 1. In the limit p=0, the field degenerates to uniform tension in the direction parallel to the crack surface. In the other limit p=1, the corresponding field gives the maximum mean stress, 4.90 , in the family. The other family of three-sector fields also has two limits: one corresponds to uniform compression parallel to the crack, and the other provides the maximum mean stress in the family, 2.45 much less than the four-sector field. The stress distributions obtained by the finite element method confirm not only the four-sector field, but also two families of fields.     

Distributions of stress and plastic strain in notched tensile bars

The paper deals with a classical problem in fracture mechanics, namely the determination of stresses and plastic strains at the minimum cross-section of a notched tensile specimen. Ideas of Hill and Bridgman are combined to develop a new approximate method for solving this problem. The main aim of the paper is to introduce a damage variable in the analysis without any complicated numerical procedure. The material model proposed by Lemaitre is used to predict the evolution of the damage variable. However, any other model resulting in the incompressibility condition may be adopted with no difficulties. This revised version was published online in July 2006 with corrections to the Cover Date.     

Development of secondary plastic strips near tensile cracks in the plate

We suggest a method for the solution of the elastoplastic problem of biaxial tension-compression of a thin cracked plate under the assumption that plastic strains at each tip of the crack are localized along three slip lines. The plastic zone is simulated by three inclined slip strips at the tips of the crack. It is assumed that the material of the plate is absolutely elastoplastic and the yield criterion is satisfied along the slip lines. The strips lying on the continuation of the crack are simulated by segments of discontinuity of normal stresses, while the other strips are simulated by segments of discontinuity of tangential stresses Thus, the elastoplastic problem under consideration is reduced to the boundary-value problem of the linear theory of elasticity for a body weakened by branched cuts with unknown lengths and orientations of side branches. These parameters are determined in the process of numerical solution of the problem by the method of singular integral equations. Numerical results are presented for the semiinfinite plane with edge crack and under the conditions of uniform tension at infinity. We present numerical values of some parameters of nonlinear fracture mechanics, such as crack tip opening displacement and lengths and angles of inclination of plastic strips, for various combinations of the components of external load.Karpenko Physicomechanical Institute, Ukrainian Academy of Sciences, L'viv. Translated from Fiziko-Khimicheskaya Mekhanika Materialov, Vol. 31, No. 2, pp. 7–13, March – April, 1995.     

基于电磁超声的塑性损伤铝材抗拉强度预测

针对电磁超声信号信噪比低这一问题,在利用相对非线性系数预测抗拉强度的同时引入应力三轴度来提升塑性损伤试件抗拉强度预测的准确性.建立了电磁超声非线性检测塑性损伤试件的有限元三维仿真模型,计算两个特征参量:应力三轴度和相对非线性系数,研究试件的内部应力状态特征和电磁超声检测信号的频谱特征.仿真分析结果表明这两个特征参量敏感...     

The plastic deformation of oriented polypropylene: tensile and compressive yield criteria

Polypropylene, oriented by hot-drawing, has been deformed in tension and compression, at various angles to the initial draw direction. The behaviour in tension is described well by a three-part criterion of the type applied in previous work to fibre-composites [8, 9]. The Hill-von Mises treatment of the plasticity of an anisotropic metal, which has been previously extended successfully to polymers [1], can be applied to describe the tensile yield stresses but is unsatisfactory in its prediction of the form of the strain in polypropylene. In compression, the variation of the yield stress with the angle of the stress axis is much less than in tension, and the modes of deformation are different from those operating in tension at the same angle. In particular, compressing at right angles to the molecules produces shear in a direction normal to the molecules (transverse shear). The critical stress for transverse shear in compression is approximately the same as the critical stress for shear parallel to the molecules in tension.     

Dynamic subgrain coalescence during low-temperature large plastic strains

Large plastic strains of polycrystals, from a substructural point of view, are characterized by the development of subgrains. It is proposed that, once a subgrain structure with low content of redundant dislocations in the boundaries is formed, the election of active sets of slip systems among those minimizing the expended plastic work tends to minimize the increment of internal energy associated with the presence of low-angle boundaries in a grain; this selective choice could contribute to the observed dynamic subgrain annihilation and average misorientation stabilization at large strains. Some tests about the capability of this hypothetical contribution to substructural evolution have been made taking the simple case of axisymmetric elongation of close-packed arrays of up to 27 hexagonal 〈111〉 f c c fibres. For the particular ideal example chosen, the proposed contribution for dynamic subgrain coalescence is very strong. Even if only 1% of the total amount of crystallographic slip responds to the tendency of energy minimization, noticeable effects are registered.     

Evaluation of indentation tensile properties of Ti alloys by considering plastic constraint effect

The uniaxial tensile properties of metallic materials can be determined by representing the indentation stress and strain by the load/depth parameters from instrumented indentation tests using a spherical indenter. Here we propose a modified algorithm for evaluating the tensile properties of Ti alloys with low E/σ_y values by taking into account the plastic constraint effect in low-strain regions. The ratio of elastic modulus to yield strength, E/σ_y, can be interpreted as a measure of the amount of deformation plastically accommodated during indentation. For low E/σ_y materials, deformation is elastic-dominated, so less constraint occurs than in high E/σ_y materials. Finite element methods and spherical indentation tests were used to explore the constraint effect for a variety of materials characterized by different E/σ_y. The constraint factors were plotted as (E/σ_y)(a/R) based on expanding cavity model. The modified approach was experimentally verified by comparing tensile properties from uniaxial tensile test and instrumented indentation tests.     

Effects of tensile plastic deformation on the magnetic properties of AISI 4140 steel

The magnetic properties of a number of specimens of AISI 4140 alloy steel were measured after they had been subjected to different amounts of tensile plastic deformation. Results showed that while some magnetic parameters such as coercivity and initial permeability varied in a simple manner with plastic deformation, others such as anhysteretic permeability and maximum differential permeability were largely insensitive to the deformation. These conclusions have implications for the separation of elastic and plastic strain from magnetic nondestructive evaluation measurements.     

Families of asymptotic tensile crack tip stress fields in elastic-perfectly plastic single crystals

In this work, two families of asymptotic near-tip stress fields are constructed in an elastic-ideally plastic FCC single crystal under mode I plane strain conditions. A crack is taken to lie on the (010) plane and its front is aligned along the direction. Finite element analysis is first used to systematically examine the stress distributions corresponding to different constraint levels. The general framework developed by Rice (Mech Mater 6:317–335, 1987) and Drugan (J Mech Phys Solids 49:2155–2176, 2001) is then adopted to generate low triaxiality solutions by introducing an elastic sector near the crack tip. The two families of stress fields are parameterized by the normalized opening stress prevailing in the plastic sector in front of the tip and by the coordinates of a point where elastic unloading commences in stress space. It is found that the angular stress variations obtained from the analytical solutions show good agreement with finite element analysis.