Effects of the strain-hardening exponent on two-parameter characterizations of surface-cracks under large-scale yielding

The influence of strain hardening exponent on two-parameter J-Q near tip opening stress field characterization with modified boundary layer formulation and the corresponding validity limits are explored in detail. Finite element simulations of surface cracked plates under uniaxial tension are implemented for loads exceeding net-section yield. The results from this study provide numerical methodology for limit analysis and demonstrate the strong material dependencies of fracture parameterization under large scale yielding. Sufficient strain hardening is shown to be necessary to maintain J-Q predicted fields when plastic flow progresses through the remaining ligament. Lower strain hardening amplifies constraint loss due to stress redistribution in the plastic zone and increases the ratio of tip deformation to J. The onset of plastic collapse is marked by shape change and/or rapid relaxation of tip fields compared to those predicted by MBL solutions and thus defining the limits of J-Q dominance. A radially independent Q-parameter cannot be evaluated for the low strain hardening material at larger deformations within a range where both cleavage and ductile fracture mechanisms are present. The geometric deformation limit of near tip stress field characterization is shown to be directly proportional to the level of stress the material is capable of carrying within the plastic zone. Accounting for the strain hardening of a material provides a more adjusted and less conservative limit methodology compared to those generalized by the yield strength alone. Results from this study are of relevance to establishing testing standards for surface cracked tensile geometries.     

Application of digital image correlation to the study of planar anisotropy of sheet metals at large strains

The aim of this work is to measure and model the planar anisotropy of thin steel sheets. The experimental data have been collected using the digital image correlation technique. This is a powerful tool to measure the strain field on differently shaped specimens subjected to large plastic deformations. In this manner, it is possible to observe the material behaviour under different stress-strain states, from small to large deformation conditions, on the entire specimen surface. The experimental results on smooth and notched samples have been used to characterize the flow stress curve after necking and a nonassociated plastic flow rule is proposed to describe the anisotropic behaviour of the material. To compare the experimental data with the predictions of the adopted constitutive model, a novel method, based on the image correlation results, has been implemented.     

Irreversible deformation with subsequent unloading of a spherical viscoelastoplastic layer

Analytic solutions are obtained for a sequence of one-dimensional quasistatic problems describing viscoelastic deformation processes in the material of a hollow ball and the plastic flow nucleation and evolution processes occurring in the ball as the pressure on the outer boundary increases. The unloading process under slow removal of the loading pressure is considered as well. The stress fields and the elastic and plastic strain fields in the spherical layer material, the law of motion of the elastoplastic boundary, and the residual stress level and distribution are computed. It is assumed that at the stage preceding the plastic flow the material obeys the viscoelastic Voigt model and the loading surface is determined by the von Mises plastic flow condition.     

Suppressed plastic deformation at blunt crack-tips due to strain gradient effects

Large deformation gradients occur near a crack-tip and strain gradient dependent crack-tip deformation and stress fields are expected. Nevertheless, for material length scales much smaller than the scale of the deformation gradients, a conventional elastic–plastic solution is obtained. On the other hand, for significant large material length scales, a conventional elastic solution is obtained. This transition in behaviour is investigated based on a finite strain version of the Fleck–Hutchinson strain gradient plasticity model from 2001. The predictions show that for a wide range of material parameters, the transition from the conventional elastic–plastic to the elastic solution occurs for length scales ranging from 0.001 times the size of the plastic zone to a length scale of the same order of magnitude as the plastic zone.     

Size-dependent yield strength of thin films

Biaxial strain and pure shear of a thin film are analysed using a strain gradient plasticity theory presented by Gudmundson [Gudmundson, P., 2004. A unified treatment of strain gradient plasticity. Journal of the Mechanics and Physics of Solids 52, 1379–1406]. Constitutive equations are formulated based on the assumption that the free energy only depends on the elastic strain and that the dissipation is influenced by the plastic strain gradients. The three material length scale parameters controlling the gradient effects in a general case are here represented by a single one. Boundary conditions for plastic strains are formulated in terms of a surface energy that represents dislocation buildup at an elastic/plastic interface. This implies constrained plastic flow at the interface and it enables the simulation of interfaces with different constitutive properties. The surface energy is also controlled by a single length scale parameter, which together with the material length scale defines a particular material.Numerical results reveal that a boundary layer is developed in the film for both biaxial and shear loading, giving rise to size effects. The size effects are strongly connected to the buildup of surface energy at the interface. If the interface length scale is small, the size effect vanishes. For a stiffer interface, corresponding to a non-vanishing surface energy at the interface, the yield strength is found to scale with the inverse of film thickness.Numerical predictions by the theory are compared to different experimental data and to dislocation dynamics simulations. Estimates of material length scale parameters are presented.     

Thermal softening induced plastic instability in rate-dependent materials

A linear perturbation analysis is performed for a class of rate-dependent materials, such as the Johnson-Cook model, in which the rate contribution to the stress can be separated from that of the plastic strain and temperature and in which the temperature rises adiabatically. The analysis is facilitated by perturbing both the rate of momentum equation and the momentum equation. An identical material stability/instability criterion is deduced from the characteristic spectral equations for one-dimensional deformation, one-dimensional shearing, and general three-dimensional field equations, and thus shows that the instability derived here is a material constitutive instability.The criteria indicate that the materials become unstable once the thermal softening overcomes the strain hardening, regardless of the strain rate. The strain rate enters the criteria through its effects on the accumulated temperature and the current stress. Based on the criterion, the three-dimensional instability surface is established in the space of plastic strain, plastic strain rate, and temperature. Instability surface is shown as a material property and independent of deformation histories or modes. Both necking and shear banding are simulated to validate the excellent predictive capability of the criterion.     

A plane stress anisotropic plastic flow theory for orthotropic sheet metals

A phenomenological theory is presented for describing the anisotropic plastic flow of orthotropic polycrystalline aluminum sheet metals under plane stress. The theory uses a stress exponent, a rate-dependent effective flow strength function, and five anisotropic material functions to specify a flow potential, an associated flow rule of plastic strain rates, a flow rule of plastic spin, and an evolution law of isotropic hardening of a sheet metal. Each of the five anisotropic material functions may be represented by a truncated Fourier series based on the orthotropic symmetry of the sheet metal and their Fourier coefficients can be determined using experimental data obtained from uniaxial tension and equal biaxial tension tests. Depending on the number of uniaxial tension tests conducted, three models with various degrees of planar anisotropy are constructed based on the proposed plasticity theory for power-law strain hardening sheet metals. These models are applied successfully to describe the anisotropic plastic flow behavior of 10 commercial aluminum alloy sheet metals reported in the literature.     

Plane stress state problems for notched bodies whose plastic properties depend on the form of the stress state

We consider one possible approach to the problem of describing the dependence of material plastic strain characteristics on the stress hydrostatic component arising in many porous, fractured, and other inhomogeneous materials. The plastic strain of the media under study is investigated under the plasticity assumption in the corresponding generalized form with the use of the form parameter of the stress state. The plasticity constitutive relations are stated on the basis of the plastic flow law associated with the accepted plasticity condition. For the conditions of plane stress state in the framework of the material rigid-plastic model, a system of partial differential equations is obtained and conditions for its hyperbolicity are determined. The relations for determining the stress fields and velocity fields in plastic domains are obtained, and their properties are investigated. The problem of tension of a strip with symmetric angular notches is solved, where the stress fields are determined and the continuous displacement rate field is constructed. The problem of uniform symmetric tension of a plane with a circular hole is considered. The stress fields in a strip with symmetric circular notches are examined. A comparison with solutions for plastically incompressible media whose properties are invariant with respect to the form of the stress state is performed.     

Determination of effective thermomechanical parameters of a mixture of two elastothermoviscoplastic constituents

We analyze plane strain deformations of a representative volume element (RVE) to evaluate effective thermophysical parameters of a particulate composite comprised of two perfectly bonded heat conducting elasto-thermo-visco-plastic constituents. It is assumed that the composite is also isotropic and its response elasto-thermo-visco-plastic. Effective values of material parameters so computed are compared with those obtained from either existing micromechanics models or the rule of mixtures or both. It is found that values computed from the rule of mixtures differ at most by 10% from those obtained by using the RVE. Effective stress versus effective strain curves obtained by analyzing simple shearing and axisymmetric deformations of the RVE and of the homogenized material, and also those obtained in plane strain deformations involving loading/unloading/reloading are found to be very close to each other. Time histories of the effective plastic strain at two neighboring points, one in each constituent, are quite different. The effective stress computed by the rule of mixtures from the average effective stress in each constituent and its volume fraction is very close to that obtained from surface tractions acting on the specimen boundaries. The average effective stress in a constituent is computed from the effective plastic strain averaged over that constituent. This also holds for a composite comprised of three constituents.     

Strain gradient crystal plasticity analysis of a single crystal containing a cylindrical void

The effects of void size and hardening in a hexagonal close-packed single crystal containing a cylindrical void loaded by a far-field equibiaxial tensile stress under plane strain conditions are studied. The crystal has three in-plane slip systems oriented at the angle 60° with respect to one another. Finite element simulations are performed using a strain gradient crystal plasticity formulation with an intrinsic length scale parameter in a non-local strain gradient constitutive framework. For a vanishing length scale parameter the non-local formulation reduces to a local crystal plasticity formulation. The stress and deformation fields obtained with a local non-hardening constitutive formulation are compared to those obtained from a local hardening formulation and to those from a non-local formulation. Compared to the case of the non-hardening local constitutive formulation, it is shown that a local theory with hardening has only minor effects on the deformation field around the void, whereas a significant difference is obtained with the non-local constitutive relation. Finally, it is shown that the applied stress state required to activate plastic deformation at the void is up to three times higher for smaller void sizes than for larger void sizes in the non-local material.     

Analysis of relationships between residual magnetic field and residual stress

The impact of stress on changes in magnetisation is one of the most complex issues of magnetism. Magnetic methods make use of the impact of stress on permeability, hysteresis and magnetic Barkhausen noise, which are examined with fields with a high strength and a small frequency. The paper presents an analysis of the impact of residual stress resulting from inhomogeneous plastic deformations in the notch area of the examined samples on the changes in the strength of the residual magnetic field (RMF). The RMF on the surface of the component is the superposition of the simultaneous effect of the shape, the anisotropic magnetic properties of the material, as well as of the values of the components of a weak external magnetic field (most commonly—the magnetic field of the Earth). Distributions of the RMF components were measured on the surface of samples with a various degree of plastic strain. The finite element method was used to model residual stress in the samples. The impact of residual stress on changes in the residual magnetic field was shown. A qualitative correlation was found between places with residual stress and areas with increased values of the gradients of the RMF components. Further research is now in progress in order to develop the quantitative relationships.     

Experimental evidence of macroscopic plastic flow nonhomogeneity development in uniaxial tensile test samples

An experimental study of the macroscopic plastic flow nonhomogeneity in the course of a uniaxial tensile test is conducted on several aluminum alloys, nickel and 4340 steel. It was observed that the plastic flow initiates throughout the entire gage length in a nonuniform fashion, so that the growth of the deformation in the middle of the gage is faster than it is at the edges. That initial strain rate gradient almost disappeared shortly after its evolution, and the strain rate through the entire gage length became about uniform. The plastic flow nonuniformity emerged again upon further stretching, producing a gradual acceleration in the middle of the gage with corresponding slowdown toward the edges. That final development of the strain rate gradient commenced well in advance of the load maxima and was the cause of the consequent neck formation in the middle portion of the gage. It is demonstrated that the origin of plastic flow nonhomogeneity stemmed from the second elastic strain component in the transverse direction and its gradient evolution along the reduced section upon loading. It is found empirically that acceleration in the strain rate in the middle part of the reduced section was accompanied by a reduction in the apparent strainhardening exponent,n, calculated from the stress/strain chart. The maxima in the apparent strain-hardening exponent,n, obtained from the common stress/strain charts can be used to indicate the strain rate gradient onset.     

Granular plasticity,a contribution from discrete mechanics

Failures by divergence instabilities in rate-independent non-associated material, such as granular matter, can occur from mechanical states described by the plastic stress limit surface, but also from stress states strictly included within this surface. Besides, the failure mode may be localized, with for instance the formation of shear bands, or diffuse with a strain field remaining homogeneous. All these failures can be described in a unique framework where plastic limit stress states appear as particular cases of generalized limit states; and where the effective development of failure is characterized by the unbounded increase of response parameters linked by a failure rule (i.e. a generalized plastic flow rule), together with a bifurcation of the mechanical response from a quasi-static pre-failure response to a dynamic post-failure one. All these features are discussed and highlighted from direct numerical simulations performed with a discrete element model. Moreover, the second order work criterion directly related at the macroscopic scale to divergence instabilities, is shown to be also relevant at the scale of inter-particle contacts.     

A two-phase elastoplastic model for unidirectionally-reinforced materials

A complete analytical formulation for the elastoplastic behaviour of a composite material comprising one single array of reinforcing inclusions perfectly bonded to the matrix is developed in this paper. Fundamental relationships establish the link between the total stress and strain variables, and those pertaining to the individual constituents (matrix and reinforcement) regarded as superposed continuous phases. Assuming that each constituent behaves as an elastic perfectly plastic material, the constitutive equations governing the evolution of the reinforced material as a whole are derived. They reveal a hardening phenomenon arising from the non-compatibility between matrix and reinforcement plastic strains. It is shown in particular that the obtained constitutive law falls within the formalism of generalized standard plasticity: the reinforcement residual stress plays the role of a hardening parameter which controls the evolution of the yield surface, while the associated kinematic variable is the plastic strain discrepancy between matrix and reinforcement phases.Owing to its inherent simplicity, the model is easily amenable to a numerical treatment for structural analysis. It is shown in particular how the classical iterative algorithm can be modified accordingly, and an illustrative application is finally presented in the field of civil engineering.     

Crack tip asymptotic character of anti-plane stress and strain rate for linear fractional constitutive relations

Linear-fractional strain rate and stress relations are used to simulate materials undergoing steady state creep. The crack tip asymptotic character of the stress and strain rate field is obtained in exact and approximate form. In the limit as the radial distance emanating from the crack tip approaches zero, the stress field corresponds to that for an ideal plastic material while the exact and approximate solutions tend to coincide. Discussed is the nonhomogeneous singular character of the strain rate field that possess different orders of singularities in a circular region around the crack tip.     

6061-T6铝合金动态拉伸本构关系及失效行为

采用HMH-206高速材料试验机开展了6061-T6铝合金在0.001～100 s?1应变率范围内的静、动态拉伸力学性能实验,分析了其应力-应变响应特征和应变率敏感性,讨论了应变率对6061-T6铝合金流动应力和应变率敏感性指数的影响,并基于实验结果对Johnson-Cook本构模型进行了修正。结合缺口试件的实验结果和模拟数据,得到了材料的Johnson-Cook失效模型参数,并对模型的准确性和适用性进行了验证。结果表明,在拉伸载荷作用下,6061-T6铝合金表现出明显的应变硬化特征和应变率敏感性,其流动应力随应变率的升高而提高,修正的Johnson-Cook本构模型可以描述材料的动态塑性流动行为,建立的Johnson-Cook失效模型能够表征材料的断裂失效行为。     

软化Mohr-Coulomb材料强度参数的测定方法

为了得到试件的粘聚力和内摩擦角随轴向塑性压应变变化的曲线提出本方法。试件的弹塑性本构关系遵循相关联的Mohr-Coulomb强度准则;对常规三轴试验,试件受力进入塑性状态后,处在棱椎状屈服面的棱上,加载过程遵循Koiter流动法则。按经典塑性力学理论,推导得到轴向塑性压应变与轴向应力与轴向应变的关系;在常规三轴试验机上获得不同围压下试件的全程应力-应变曲线,进而可得到各自围压下轴向塑性压应变随加载过程的变化曲线;把来自不同围压下对应同一轴向塑性压应变的应力分别代入屈服面方程,即可求得对应的粘聚力和内摩擦角。结果表明,Mohr-Coulomb材料的两个强度参数的变化由轴向塑性压应变确定。轴向塑性压应变可以作为塑性变形的状态参数,它和试件的受力过程可以唯一确定试件的变形过程。     

A simple plasticity model for prediction of non-coaxial flow of sand

A bounding surface plasticity model for non-coaxiality, another aspect of anisotropic behavior of sands under rotation of principal stress axes; is developed in the critical state framework. Numerous experimental evidences exist that corroborate dependence of plastic shear strain rate direction on inherent fabric anisotropy. At first, general expressions for plastic strain rate with respect to possible emerge of non-coaxial flow are obtained. Consequently, using an anisotropy state parameter that is specially developed for this model and accounts for the interaction between imposed loading and soil fabric; effect of anisotropy on plastic flow direction is taken into account. Besides, novel circumstances are proposed for plastic modulus and dilatancy under rotation of principal stress axes. Finally, it is shown that the model is able to simulate successfully the non-coaxial behavior of sands subjected to principal stress axes rotation.     

Deformation trapping due to thermoplastic instability in one-dimensional wave propagation

One-dimensional shear wave propagation in a half-space of a nonlinear material is considered. The surface of the half-space is subjected to a time dependent but spatially uniform tangential velocity. The half-space material exhibits strain hardening, thermal softening and strain rate sensitivity of the flow stress. For this system, a well-defined band of intense shear deformation can develop adjacent to the loaded surface, even though the material has no imperfections or other natural length scale. Representative particle velocity and strain profiles, which have been obtained numerically, are described for several different models.     

基于能量等效原理的应变局部化分析:Ⅰ.一维解析解

基于热力学第一定律和非局部塑性理论,提出了一种求解应变局部化问题的非局部方法.对材料的每一点定义了局部和非局部两种状态空间,局部状态空间的内变量通过非局部权函数映射到非局部空间,成为非局部内变量.在应变软化过程中,局部状态空间中的塑性变形服从正交流动法则,材料的软化律在非局部状态空间中被引入.通过两个状态空间的塑性应变能耗散率的等效,得到了应变软化过程中明确定义的局部化区域以及其中的塑性应变分布.应用本方法导出了一维应变局部化问题的解析解.解析解表明,应变局部化区域的尺寸只与材料内尺度有关;对于高斯型非局部权函数,局部化区域的尺寸大约是材料内尺度的6倍.一维算例表明,局部化区域的塑性应变分布以及载荷-位移曲线仅与材料参数和结构几何尺寸有关,变形局部化区域的尺寸随着材料内尺度的减小而减小,同时塑性应变也随着材料内尺度的减小变得更加集中.当内尺度趋近于零时,应用本文方法得到的解与采用传统的局部塑性理论得到的解相同.