Creep fracture modeling by use of continuum damage variable based on Voronoi simulation of grain boundary cavity

A new approach to creep cavitation damage is developed by combining the basic features of continuum damage mechanics and mechanism-based cavitation models. Based on a polycrystal microstructures simulated by Voronoi tessellation, an anisotropic continuum damage variable is defined, and its evolution is given by applying the mechanism-based equations of cavity nucleation and growth to each grain boundary. Macroscopic creep deformation coupled with the damage variable is calculated by damage mechanics equations. The proposed method has been applied to investigate the damage evolution under uniaxial tension and reversed shear loading conditions.     

基于改进GTN损伤模型的镁合金镦粗成形损伤及裂纹预测研究

镁合金在成形过程中极易产生开裂，精准的损伤预测可以为塑性成形工艺提供理论支撑。为此，基于含连续介质剪切损伤因子的Gurson-Tvergarrd-Needleman(GTN)损伤模型被应用于预测镁合金成形时的损伤演化，通过压缩试样的力-位移曲线标定了AZ31B镁合金的流动应力和剪切损伤参数，预测并验证了AZ31B镁合金在镦粗工艺下的表面损伤及开裂，扩展了模型对低应力三轴度下的成形工艺损伤预测的适用性。在此基础上，对AZ31B镁合金在受压条件下损伤成因、裂纹扩展进行了分析。结果表明，随着压缩位移的增加，镁合金侧面中心区域的切应力不断增加，在此作用下基体内部孔洞沿非垂直压缩方向伸长、聚合，最终形成宏观裂纹；镦粗后的试样侧面裂纹走向与垂直压缩方向所成角度范围为34°～46°，改进的GTN模型模拟结果为44°～54°，原始GTN模型模拟结果均呈90°；改进后的GTN模型可应用于预测镁合金在轧制、热冲压等工艺下的损伤演化行为，为后续工艺优化奠定基础。     

A variationally based nonlocal damage model to predict diffuse microcracking evolution

We explore a variationally based nonlocal damage model, based on a combination of a nonlocal variable and a local damage variable. The model is physically motivated by the concept of “nonlocal” effective stress. The energy functional which depends on the displacement and the damage fields is given for a one-dimensional bar problem. The higher-order boundary conditions at the boundary of the elasto-damaged zone are rigorously derived. We show that the gradient damage models can be obtained as particular cases of such a formulation (as an asymptotic case). Some new analytical solutions will be presented for a simplified formulation where the stress–strain damage law is only expressed in a local way. These Continuum Damage Mechanics models are well suited for the tension behaviour of quasi-brittle materials, such as rock or concrete materials. It is theoretically shown that the damage zone evolves with the load level. This dependence of the localization zone to the loading parameter is a basic feature, which is generally well accepted, from an experimental point of view. The computation of the nonlocal inelastic problem is based on a numerical solution obtained from a nonlinear boundary value problem. The numerical treatment of the nonlinear nonlocal damage problem is investigated, with some specific attention devoted to the damageable interface tracking. A bending cantilever beam is also studied from the new variationally based nonlocal damage model. Wood’s paradox is solved with such a nonlocal damage formulation. Finally, an anisotropic nonlocal tensorial damage model with unilateral effect is also introduced from variational arguments, and numerically characterized in simple loading situations.     

Elastoplastic buckling of rectangular plates in biaxial compression/tension

This paper examines the elastoplastic buckling of a rectangular plate, with various boundary conditions, under uniform compression combined with uniform tension (or compression) in the perpendicular direction. The analysis is based on the standard linear buckling equations and material behaviour is modelled by the small strain J₂ flow and deformation theories of plasticity. A detailed parametric study has been made for Al 7075 T6 over a range of plate geometries (a/b=0.25–4,a/h≈20–100) and with three sets of boundary conditions (four simply supported boundaries and the symmetric combinations of clamped/simply supported sides). For sufficiently thin plates we recover with both theories the classical elastic results. However, for thicker plates there is a remarkable difference in the buckling loads predicted by these two theories. Apart from the expected observation that deformation theory gives lower critical stresses than those obtained from the flow theory, we report on the existence of an optimal loading path for the deformation theory model. Buckling loads attained along the optimal path—specified by particular compression/tension ratios—are the highest possible over the entire space of loading histories. By contrast, no similar optimum has been found with the flow theory. This discrepancy in the buckling behaviour, obtained from the two competing plastic theories, provides a possibly new illustration of the plastic buckling paradox.     

The collapse of steel model columns with unequal flanges. I. Perfect

The paper is concerned with the collapse behaviour of initially straight pin-ended steel columns having unequal flanges. A modified Shanley model column with unequal flanges is presented and analysed, together with the corresponding modified Calladine construction. Each column flange is assumed to have a uniform state of stress and strain, and to behave elastically until fully yielding in compression or tension—thus local buckling is not included. However, column buckling is fully allowed for, and the complete collapse behaviour of various model column designs is investigated, the parameters varied being the normalised column slenderness, and the flange area ratio. The behaviour of the model columns is shown to agree well with that of corresponding real columns, i.e., columns of uniform cross-section that deform at all points within the volume. Compressive yield of the smaller flange is an expected source of failure, but the results show that tensile yield of the smaller flange can be equally important. Violent collapse behaviour is shown to be possible whether the smaller flange yields in compression or tension. This is particularly so at intermediate slenderness. The results apply most directly to unsymmetrical I-sections, but are also relevant to T-sections, and to wide stiffened compression panels. The Calladine construction greatly elucidates behaviour.     

Numerical modelling of ductile plastic damage in bulk metal forming

This work addresses the computational aspects of a model for rigid–plastic damage. The model is a modification of a previous established model formulated by Perzyna (Recent Advances in Applied Mechanics, Academic Press: New York, 1966, p. 243–377 (Chapter 9)) which is here extended to include isotropic damage. Such an extension is obtained by incorporating the constitutive equations introduced by Lemaitre (J. Eng. Mater. Technol. 107 (1985) 83; Comput. Meth. Appl. Mech. Eng. 51 (1985) 31; A Course on Damage Mechanics, Springer, Berlin, Heidelberg, New York, 1996) for ductile plastic damage into the original model. In its original version (J. Eng. Mater. Technol. 107 (1985) 83; Comput. Meth. Appl. Mech. Eng. 51 (1985) 31) this model does not distinguish tension and compression in the damage evolution law, so it was necessary to introduce a refinement proposed by Ladevèze (in: J.P. Boehler, (Ed.), Proceedings of CNRS International Colloquium 351 Villars-de-Lans, France (Failure Criteria of Structured Media, 1983, p. 355) and Lemaitre (A Course on Damage Mechanics, Springer, Berlin, Heidelberg, New York, 1996) which takes into account the partial crack closure effect with isotropic damage. The accuracy of the computational model, developed for the analysis of the material degradation in bulk metal forming processes, is shown through the discussion of the results of two examples, allowing to compare the simulation results with experimental and numerical results obtained by other authors.     

复合材料机械联接接头的寿命估算

以机械联接接头应力分布的解析解为基础，以单向板纵向拉拉ＳＮ曲线为依据，按照孔边一定范围内逐层逐单元损伤直至破坏的物理本质，从宏观唯象观点出发，提出了一种寿命估算方法。同时，文中还给出了孔的永久变形与循环次数之间的拟合关系式。     

珠光体球墨铸铁损伤力学性能的研究

利用损伤力学原理，研究了球光体球墨铸铁在疲劳和拉伸载荷作用下的损伤演变规律。结果表明：珠光体球墨铸铁在循环应力作用下，损伤变量呈指数规律变化；当拉伸应力大于损伤阈值后，损伤变量随应力的提高而增加，且球化率愈低，增加愈快；损伤阈值低于屈服强度，随球化率呈直线增加。     

A continuum plasticity model for the constitutive and indentation behaviour of foamed metals

A yield surface is proposed that can be fitted to the plastic flow properties of a broad class of solids exhibiting plastic compressibility and different yield points in tension and compression. The yield surface is proposed to describe cellular solids, including foamed metals, and designed to be fitted to three experimental results: (1) the compressive stress–strain response (including densification), (2) the difference between the tensile and compressive yield points and (3) the degree of compressibility of the foam, as measured by the lateral expansion during a uniaxial stress compression test. The model is implemented using finite elements and used to study the effects of plastic compressibility on two problems: the compression of a doubly notched specimen and indentation by a spherical indenter. The model is then fitted to the properties of a typical closed cell aluminum foam and used to study indentation into a dense aluminum face sheet on a foam foundation. The dependence of the indentation load–displacement curve on the relevant material and geometric parameters is determined, and a single load–displacement relation is presented which approximates the behaviour of a wide range of practical designs. These results can be used to design against indentation failure of sandwich panels.     

Bending creep of beams in aggressive media

The effect of an aggressive medium on high-temperature creep and creep-rupture characteristics of beams in pure bending is considered. Creep modeling is based on the Rabotnov kinetic theory that involves two structural parameters, i.e., damage and the concentration of the environmental chemical elements in a beam. The problem of beam bending allows for the difference in the material creep processes in tension and compression. The novelty of the problem under consideration is the use of the governing and kinetic equations in the form of singular fractional power dependencies of the creep rate and damage accumulation rate on the stress; instantaneous elastic deformations are neglected because they are low compared to creep deformations. The singularity makes it possible to allow for nonlinear viscosity together with instantaneous fracture characteristics.     

Non-linear one-dimensional continuum damage theory

The background of Non-Linear Continuum Damage Mechanics is presented for the case of one-dimensional tensile stresses. A brief critical analysis of the existing methods of non-linear damage models construction is given. A new approach to the damage theory development based on the “separability” principle is suggested. The condition of non-linearity and the criterion of long-term failure are formulated. The non-linear damage constitutive equations for static and cyclic loading, allowing one to take into account the loading history, are proposed on this basis. Within the framework of the approach suggested the problems of total and residual lifetime calculation under additional loads and partial unloads are solved. The predictions are compared with experimental data obtained using some particular heat-resistant materials.     

基于应变损伤模型的复合材料层合板低速冲击数值模拟

提出了一种基于应变的复合材料损伤模型,考虑了复合材料冲击过程中出现的面内纤维断裂与压缩,基体开裂与挤裂。在使用Abaqus软件进行数值模拟计算时,自编的用户子程序VUMAT和Cohe-sive模型分别实现了复合材料面板的损伤和层间分层。通过对层合板在不同能量下的低速冲击的有限元模拟发现,模拟得到的分层损伤形状和面积、冲头最大挠度、接触力和凹坑深度都与试验结果吻合较好。     

Ductile damage micromodeling by particles’ debonding in metal matrix composites

The elastic–plastic behaviour of particle-reinforced metal matrix composites undergoing ductile damage is modelled using a two-level micro-structural approach. The considered heterogeneous material is a polycrystal containing intra-crystalline elastic particles. Ductile damage is initiated by the matrix/particle interface debonding and the subsequent voids growth with plastic straining of the crystalline matrix. Homogenization techniques are used twice: first at mesoscale to derive the equivalent grain behaviour and then to obtain the macroscopic behaviour of the material. Plastic deformation of the crystalline matrix is due to crystallographic gliding on geometrically well-defined slip systems. The associative plastic flow rule and the hardening law are described on the slip system level. The evolution of micro-voids volume fraction is related to the plastic strain. The elastic–plastic stress–strain response of particle composite is investigated. Predictions of the proposed model are compared to experimental data to illustrate the capability of the suggested method to represent material behaviour. Furthermore, specific aspects such as the stress triaxiality and yield surfaces are discussed.     

螺纹紧固件耐久性分析方法的实际研究

在实验的基础上,提出了应用于螺栓螺纹表面裂纹上一种抗疲劳分裂研究方法-耐久性损伤分析方法,考虑了一个新的耐久性损伤模型,螺纹圆角处开裂,把适用于紧固孔上小裂纹模型上的理论方法发展延伸至螺 纺圆角模型大裂纹上,并通过实验得到了验证。同时给出一个例子,预测结果与实验结果拟合得很好,为带螺纹紧固件的耐久性分析方法的研究提供了一种可行的方法。     

Generation of double-frequency shear waves in materials with different resistances to tension and compression

Equations describing the dynamic processes in materials with different resistances to tension and compression have been derived. It is shown that, when a shear wave propagates in such a material, a quadratic nonlinearity arises that leads to the possibility of generating a shear wave at the double frequency, which is “prohibited” by the equation of the classical elasticity theory. Dependences relating the amplitudes of the waves propagating at the fundamental and double frequencies to the damage parameters are found. A characteristic length is determined at which a considerable transfer of the energy contained in the fundamental wave to the energy of the second harmonic can be expected, thereby allowing assessment of the integral parameter of the material damage. A dependence between the damage parameter and plastic strain has been established on the basis of a constructed mathematical model and experiments with specimens.     

基于连续介质损伤力学的7075铝合金高温成形极限理论预测与数值仿真

开展7075铝合金高温单向拉伸试验和成形极限试验,获得了不同温度和应变率的应力-应变曲线和成形极限曲线。结果表明,在较高的温度和应变率时7075铝合金的强度减小、成形性提高。为描述7075铝合金高温损伤演化过程,提出一种改进的连续介质损伤模型,并建立了耦合损伤的多轴统一黏塑性本构模型。基于试验结果,运用NSGAII遗传算法标定了模型中的参数,标定后的本构模型可以很好地预测7075铝合金的高温热力行为和极限应变。通过有限元软件Abaqus的用户材料子程序VUMAT,该本构模型被编入到Abaqus软件中进行数值仿真计算。结果表明,仿真获得的成形极限曲线和应变场分布与试验和理论结果吻合度好,进一步证明了所建立的耦合损伤的多轴本构模型的正确性及其在高温成形极限有限元仿真中的适用性。     

大滑动速度下弹流线接触的摩擦力问题

本文给出了一个滚动伴随滑动的滚子在弹流润滑工况下的非等温效值解。该解对能量方程进行了更全面、仔细的分析,既考虑了第二粘度系数的影响,又考虑了润滑油压缩生热的影响。在描述润滑油的粘压－粘温关系时,既采用了巴鲁士公式,又采用了茹兰兹公式,并作了对比。并在双盘试验机上测定摩擦系数。同时,还对时间相关粘度假说和艾林流体模型的影响进行了研究。理论计算结果表明,第二粘度系数和压缩生热对摩擦系数的影响很小,可以忽略不计。茹兰兹公式的应用可以使理论摩擦系数比用巴鲁士公式时小得多,更接近于实验数值,但是仍存在很大差异。结果还表明,牛顿流体模型和时间相关粘度假说都不能很了地解释弹流接触区的摩擦力特性。唯一能够解释这一特性的是艾林模型,其与实验数值之偏差只有10%左右。