土木结构损伤多尺度并发计算方法及其应用

大型土木结构的损伤破坏是跨尺度演化的结果, 因此单一尺度下的结构分析难以正确地反映结构的非线性损伤失效过程。该文根据结构损伤在宏观、细观尺度下的不同特征建立结构一致多尺度模型, 并通过多点约束法进行跨尺度关联, 实现了结构整体线弹性响应分析和局部细节易损部位的细观层次上弹塑性损伤分析的并发进行。计算结果表明:该文提出的结构损伤多尺度并发计算方法能够兼顾结构整体上的线弹性响应和局部易损部位在细观层次上的塑性损伤特征, 在对结构多尺度响应与损伤特征进行准确描述的基础上, 能够获得结构易损局部的细观损伤状态、演化过程及其对结构宏观响应与失效的影响。     

Damage evolution and heterogeneity of materials: Model based on fuzzy set theory

A mathematical model of damage evolution in heterogeneous materials is developed using the methods of the theory of fuzzy sets. The fuzzy concept of damage is formulated and some applications of this concept are considered. The influence of the material heterogeneity on the damage as well as the heterogenization of the material due to the damage evolution are studied. On the basis of the fuzzy concept of damage, it is shown that the greater the heterogeneity of material, the closer is the material to failure under loading.     

Stochastic modeling of damage evolution in composites under environmental ageing

A mathematical model is proposed for predicting damage evolution and stiffness degradation in composite materials under environmental ageing. Environmental parameters such as moisture, temperature, and ultraviolet (UV) radiation cause hygrothermal loads on the structure, which leads to damage evolution. The present work establishes a constitutive model for treating the damage density as a random variable. A forward stochastic differential equation (FSDE) is proposed to predict the damage density evolution. Damage nucleation and annihilation rates are taken into consideration in terms of Brownian motions. A second-order damage tensor is developed using the solution of the FSDE. The damage tensor is incorporated into the constitutive model for predicting the elastic moduli. Finally, the proposed model is verified against experimental observations under certain hygrothermal conditions.     

Auto‐adaptive multiblock cycle jump algorithm for fatigue damage simulation of long‐span steel bridges

An algorithm is developed for fatigue damage evolution simulation of long‐span steel bridges based on continuum damage mechanics (CDM) in this study. The progressive fatigue damage from local component damage evolution to entire structural failure is simulated with nonstandard varying block cycle length, which is automatically obtained during computation to speed up fatigue evolution simulation without user intervention. In this paper, progressive fatigue damage evolution of the Stonecutters cable‐stayed bridge due to vehicle loading is simulated by using the proposed algorithm and the bridge model. It shows that the algorithm is effective, and it can improve the computational efficiency of fatigue damage simulation of a large‐scale steel bridge.     

Damage behaviour of laminated composites during fatigue loading

This study deals with the modelling of damage evolution in the carbon/epoxy laminated composites under static and fatigue loading. A cumulative damage model is developed on the basis of damage evolution due to static and fatigue during cyclic loading. A continuum damage mechanics (CDM)‐based damage model coupling with the micromechanics has been utilized to predict the fatigue behaviour of laminate composites. A multicriterion approach has been introduced to predict the damage behaviour in the longitudinal, transverse, and shear direction at the ply scale. Extensive experimental results on T300/EPL1012 carbon/epoxy laminates are prepared to characterize under static and fatigue loading and to evaluate the proposed model in different conditions. The obtained results show that at the beginning of the cyclic loading, the damage grows suddenly and increases until final failure, which justifies the proposed method is able to predict the evolution of the damage due to static and fatigue loading separately during cyclic loading. The obtained results show that considering damage due to static loading leads to more accurate results, particularly in low‐cycle fatigue.     

Impact damage patterns studied by a model simulation

A lattice model has been developed to explore impact damage patterns in brittle materials. The damage evolution was modelled as a process involving the change of strain-energy distribution by cracking. Using a cubic lattice system, a large strain energy was supplied to the system surface. Crack growth initiated by this local energy supply was followed by means of computer simulations. The damage patterns were compared for systems which have different distributions of strain energy stored prior to the local energy supply. The simulations reveal a characteristic difference in the damage pattern. Impact damage for a system with a spatially fluctuating distribution of strain energy is limited around an impact point. Impact damage for a systen with a relatively uniform distribution of strain energy penetrates deeply. The results of the simulations are discussed in connection with the material evaluation and the material resistance.     

拉伸载荷下贴补复合材料层合板的渐进损伤分析

基于连续介质损伤力学和粘聚区模型建立了贴补复合材料层合板的渐进损伤分析模型,计算了拉伸载荷下修补结构的极限强度。数值仿真结果和实验结果吻合较好,验证了该模型的有效性。基于建立的模型研究了贴补复合材料层合板的损伤演化过程,并讨论了补片参数对修补结构拉伸性能的影响。研究结果表明：补片参数对贴补复合材料层合板的破坏模式与损伤演化过程有显著影响;不同破坏模式下,补片参数的改变对修补结构极限强度的影响效果不同。研究结果可为复合材料层合板的贴补设计提供部分理论参考。     

A statistical model of fatigue damage evolution in particulate-reinforced metal-matrix-composites

A statistical model of fatigue damage evolution has been developed for particulate-reinforced metal-matrix-composites (MMCs) by taking into considerations both the initial damage distribution and the effect of particulate reinforcement on fatigue damage development. The growth of microscopically fatigue-damaged regions in particulate-reinforced MMCs is considered as a stochastic process, and both the non-equilibrium statistical method and minimum strength principle are used to establish the evolution equation of fatigue damage. The fatigue damage evolution equation developed in the present study characterizes not only the kinetic process of fatigue damage evolution but also sets up the relationship between the mechanism of fatigue damage growth of the microscopically damaged regions and the result of fatigue damage, i.e. degradation of mechanical properties of particulate-reinforced MMCs. A new expression for calculating the cumulative fatigue damage and a new formula for predicting the average fatigue strength of the particulate-reinforced MMCs are derived. Experimental data of 2080Al/SiC_p composites are analysed and compared with results obtained with the present model. It is shown that the experimental results can be described well by the calculations.     

Multi-axial thermo-mechanical analysis of power plant components from 9–12% Cr steels at high temperature

The aim of this paper is to analyze local changes of stress and strain states in a power plant component under a transient thermal environment. A robust constitutive model is developed to describe inelastic behavior of advanced 9–12% Cr heat-resistant steels at high temperature and in a multi-axial stress state. The model includes the constitutive equation for the inelastic strain rate tensor, the evolution equation for a tensor-valued state variable to reflect hardening/recovery processes and two evolution equations for two scalar-valued variables that characterize softening and damage states. The model is calibrated against experimental creep curves and verified for inelastic responses under different isothermal and non-isothermal loading paths. Steam temperature and loading profiles that correspond to an idealized start-up, holding and shut-down sequence of a power plant component are assumed. To estimate the thermal fields, transient heat transfer analysis is performed. The results are applied in the subsequent structural analysis using the developed inelastic constitutive model. The outcome is a multi-axial thermo-mechanical fatigue loop which can be used for damage assessment.     

Damage evaluation of concrete plates by high-velocity impact

This paper describes the evaluation of the local damage of concrete plates by the impact of high-velocity rigid projectiles. A new launching system of mushroom-shaped projectiles has been developed. Impact tests for concrete plates have been conducted by using the system to examine failure modes of the local damage of concrete plates. The damage or failure behavior has been discussed on the basis of the failure process captured by a high speed video camera and the strain histories obtained by strain gauges on the concrete plate. Numerical simulations have been also carried out in order to explain the mechanism of the local damage observed by the experiment. A reasonable numerical model has been discussed in terms of a constitutive model and strain rate effect of concrete material. Mechanism of the local damage of concrete plates has been illustrated schematically.     

Non-local modelling of cyclic thermal shock damage including parameter estimation

In this paper, rate dependent evolution laws are identified and characterized to model the mechanical (elasticity-based) and thermal damage occurring in coarse grain refractory material subject to cyclic thermal shock. The interacting mechanisms for elastic deformation driven damage induced by temperature gradients and thermal damage induced by isotropic thermal expansion are combined and represented by a single variable for the total damage. The constitutive model includes the shielding of micro-structural thermal damage by the non-local elasticity-based damage developed at the macroscopic and microscopic scale. Quasi-stationary thermal experiments are used to identify the parameters used in the evolution law for thermal damage. The remaining model parameters, including a micro-structural length scale, are quantified by inverse modelling of cyclic thermal shock experiments. Longitudinal wave propagation measurements through damaged material are simulated, enabling the identification on the basis of the first and second thermal shock cycle. A third thermal shock cycle enabled the evaluation of the quality of the obtained parameter set. The set-up of the thermal shock experiments has been optimized through a parameter identifiability analysis. The damage evolution in three consecutive thermal shock cycles is investigated numerically with the optimized model.     

THE INFLUENCE OF THE HARDENING STATE ON TIME DEPENDENT DAMAGE AND ITS CONSIDERATION IN A UNIFIED DAMAGE MODEL

Abstract— A model is presented for the prediction of the lifetime of metals in the high-temperature range under arbitrary variable multiaxial load. The definition of an internal variable for damage in continuum damage mechanics is adopted, which allows indirect measurement of damage via the deformation behaviour. To acquire some knowledge of damage evolution, damage is measured in two ways during uniaxial strain controlled cyclic tests: (a) a change of the modulus of elasticity and (b) a decrease of the peak stress. Surprisingly, both methods lead to results which are in good agreement. A new damage law is then developed (with reference to known models and lifetime rules) which is a modification of the creep damage law of Rabotnov that is extended by a dependence on the inelastic strain rate instead of the dependence on internal variables to take into account the hardening state. Uniaxial as well as multiaxial formulations of the new damage model (Inelastic Strain Rate Modified (ISRM) model) are presented.
The parameters of the ISRM model are determined with a view to applying them to AISI 316 L(N) austenitic steel. Some of the parameters are derived from standard creep experiments. To determine further parameters, the ISRM model is applied to uniaxial cyclic tests. Both failure behaviour and damage evolution are well described.     

A continuum damage mechanics method for fracture simulation of quasi‐brittle materials

This paper addresses a novel continuum damage‐based method for simulating failure process of quasi‐brittle materials starting from local damage initiation to final fracture. In the developed method, the preset characteristic length field is used to evaluate damage instead of element, which is used to reduce the spurious sensitivity. In addition, damage is only updated in the most dangerous location at a time for considering stress redistribution due to damage evolution, which is used to simulate competitive fracture process. As cases study, representative numerical simulations of two benchmark tests are given to verify the performance of the developed continuum damage‐based method together with a used damage model. The simulation results of the crack paths for two concrete specimens obtained from the developed method matched well with the corresponding experimental results. The results show that the developed continuum damage‐based method is effective and can be used to simulate damage and fracture process of brittle or quasi‐brittle materials. And the simulation results based on the developed method depend only the preset characteristic length field and not grid mesh.     

含脆性界面相的颗粒增强金属基复合材料的损伤

通过引入双夹杂模型,将传统增量损伤理论扩展应用到三相复合材料颗粒尺寸效应问题,同时提出一个可以研究颗粒增强金属基复合材料的弹塑性变形及渐进式脱黏损伤模型,该模型还可以研究含脆性界面相的颗粒增强金属基复合材料弹塑性损伤变形行为的颗粒尺寸效应。研究发现,包含各种不同颗粒尺寸的颗粒增强金属基复合材料的脱黏损伤按照颗粒尺寸从大到小的顺序先后发生,并且该模型与SiC/Al复合材料的试验结果比较一致。     

Kinematics of damage zone accompanying curved crack

This paper presents a methodology of a quantitative characterization of the kinematics of evolution of a damage zone surrounding the tip of a slowly propagating crack. On the basis of the Crack Layer Theory, the evolution of the damage zone is modelled as a combination of a few elementary motions: translation, rotation, isotropic expansion and distortion. A procedure for evaluating the rates of the elementary motions on the basis of direct measurements is developed. The procedure is illustrated for curved crack layer growth in the vicinity of a hole in commercial polystyrene. The important role of the damage zone in determining the main crack trajectory and speed is clearly demonstrated.     

单向复合材料横向裂纹黏弹性损伤演化模型

建立一个考虑基体黏弹性的纤维增强聚合物单向复合材料在产生横向裂纹时的损伤演化模型,有效地预测了单向复合材料横向拉伸行为。假设呈现威布尔分布的缺陷会在变形的驱动下演化为损伤,并以此为基础建立了单向复合材料横向损伤演化模型。通过此模型,时间-温度叠加原理（TTSP）得到了更具有物理基础的解释。最后,通过具体例子阐述了此模型的应用,并通过试验对模型预测结果进行了验证。本模型有效地预测了单向复合材料横向拉伸行为。由于单向复合材料横向性能存在脆性,此模型还无法准确预测失效和强度。      

Towards a micromechanics-based modelling of damage development during the forming of food-can lids

Building on the local approach to fracture, a framework for finite element simulations of damage development during metal forming is presented. Its application to the fabrication of a food-can lid demonstrates the capabilities, but also the limitations of the framework. One such limitation, the phenomenological basis on which the damage evolution laws are formulated, is subsequently addressed by studying the micromechanics of the underlying damage mechanism – micro-void-growth. Finite element studies illustrate the relevant phenomena and are subsequently used to calibrate evolution laws which are based on understanding of these phenomena. The paper closes with directions for future developments.     

简谐激励下复合材料加筋板的基体微裂纹损伤演化

研究了在简谐激励作用下复合材料加筋板基体微裂纹损伤的演化行为及其对加筋板动力特性的影响。基于平均微裂纹密度和断裂力学方法, 建立了复合材料加筋板基体微裂纹演化的刚度退化准则。由于该准则考虑了载荷作用周期数的影响, 从而能够更合理地分析周期性动载荷作用下基体微裂纹损伤演化规律。采用Mindlin一阶剪切理论和复合材料模态阻尼模型, 建立了复合材料加筋板动力分析的有限元方法, 研究了在简谐激励作用下, 含分层损伤复合材料加筋板振动过程中诱发的基体微裂纹损伤的演化、 刚度退化, 频率折减和动力响应。      

Finite element analysis of local damage and post-failure behavior for strain-softening solid

A finite element analysis of the viscoplastic-softening model with the evolution of local damage for strain softening material is presented. An effective damage matrix is introduced to consider the influence of isotropic damage on different types of micro-cracking by different states of stress. The localized strain mode with local damage occurs in the post-failure regime of deformation. The computational techniques for tracing the post-failure path of the softening response are discussed with several examples.     

Progressive damage and failure modeling in notched laminated fiber reinforced composites

A novel progressive damage and failure model for fiber reinforced laminated composites is presented in this work. The model uses the thermodynamically based Schapery Theory (ST) to model progressive microdamage in the matrix phase. Matrix failure is not governed with a matrix failure criterion, but rather matrix failure occurs naturally through the evolution of microdamage. A maximum strain criterion is used to dictate tensile failure in the fiber direction, while compressive failure is automatically accounted for by allowing local fiber rotations and tracking the evolution of rotation. The results of this model are compared to a previously developed model that used ST at the lamina level to calculate matrix microdamage, but used the Generalized Method of Cells to resolve the lamina level strains into constituent level stresses and strains and determines constituent failure by evaluating failure criteria at the micro, fiber/matrix level. Results for global load versus displacement and local strain from both models are compared to experimental data for notched laminates loaded in uniaxial tension. The results show remarkable agreement qualitatively, and in many cases the quantitative agreement is good. Accurate damage contours and failure paths are predicted.